Finite Group Databasebeta

← #17241679

Subgroups — #17241679

Order 4352.

2954 conjugacy classes of subgroups.

The subgroup lattice has 1924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763375C211yesmaximal, characteristic, complemented
2C2×#11763367C211yesmaximal, characteristic, complemented
3#14537065C211yesmaximal, characteristic, complemented
4#14537065C211yesmaximal, characteristic, complemented
5#14535618C211yesmaximal, characteristic, complemented
6#14535512C211yesmaximal, characteristic, complemented
7#14535507C211yesmaximal, characteristic, complemented
8#14535505C211yesmaximal, characteristic, complemented
9#14535218C211yesmaximal, characteristic, complemented
10#14535196C211yesmaximal, characteristic, complemented
11#14535190C211yesmaximal, characteristic, complemented
12#14535161C211yesmaximal, characteristic, complemented
13#14535054C211yesmaximal, characteristic, complemented
14#14535052C211yesmaximal, characteristic, complemented
15#14535016C211yesmaximal, characteristic, complemented
16#14535014C211yesmaximal, characteristic, complemented
17#14534995C211yesmaximal, characteristic, complemented
18#14534994C211yesmaximal, characteristic, complemented
19#14534989C211yesmaximal, characteristic, complemented
20#14534519C211yesmaximal, characteristic, complemented
21#14534517C211yesmaximal, characteristic, complemented
22#14533231C211yesmaximal, characteristic, complemented
23#14533223C211yesmaximal, characteristic, complemented
24#14532393C211yesmaximal, characteristic, complemented
25#14532391C211yesmaximal, characteristic, complemented
26#14532183C211yesmaximal, characteristic, complemented
27#14532182C211yesmaximal, characteristic, complemented
28#14532153C211yesmaximal, characteristic, complemented
29#14532151C211yesmaximal, characteristic, complemented
30D17×#386C211yesmaximal, characteristic, complemented
31C17×#2688C211yesmaximal, characteristic, complemented
32C22×#63252C2211yescharacteristic, complemented
33C22×D4×D17C2211yescharacteristic
34C22×D4×D17C2211yescharacteristic
35C23×C4×D17C2211yescharacteristic, complemented
36#11763375—28no—
37#11763367—28no—
38C2×#10587626C2211yescharacteristic
39C2×#10587626C2211yescharacteristic, complemented
40C2×#10587571C2211yescharacteristic
41C2×#10587571C2211yescharacteristic, complemented
42C2×#10587580C2211yescharacteristic
43C2×#10587580C2211yescharacteristic
44C2×#10587615C2211yescharacteristic, complemented
45C2×#10587569C2211yescharacteristic
46C2×#10587569C2211yescharacteristic
47C2×#10587621C2211yescharacteristic, complemented
48C2×#10587581C2211yescharacteristic
49C2×#10587581C2211yescharacteristic
50C2×#10587616C2211yescharacteristic
51C2×#10587616C2211yescharacteristic
52C2×#10587570C2211yescharacteristic
53C2×#10587570C2211yescharacteristic
54C2×#10587570C2211yescharacteristic, complemented
55C2×#10587570C2211yescharacteristic, complemented
56C2×#10587625C2211yescharacteristic
57C2×#10587625C2211yescharacteristic
58C2×#10587625C2211yescharacteristic, complemented
59C2×#10587625C2211yescharacteristic, complemented
60C2×#10587624C2211yescharacteristic
61C2×#10587624C2211yescharacteristic, complemented
62C2×#10587568C2211yescharacteristic
63C2×#10587568C2211yescharacteristic
64C2×#10587568C2211yescharacteristic
65C2×#10587568C2211yescharacteristic, complemented
66C2×#10587568C2211yescharacteristic, complemented
67C2×#10587623C2211yescharacteristic
68C2×#10587623C2211yescharacteristic
69C2×#10587623C2211yescharacteristic
70C2×#10587623C2211yescharacteristic, complemented
71C2×#10587623C2211yescharacteristic, complemented
72C2×#10587578C2211yescharacteristic, complemented
73C22×#63227C2211yescharacteristic
74C2×C22⋊C4×D17C2211yescharacteristic
75C2×C22⋊C4×D17C2211yescharacteristic
76C2×C22⋊C4×D17C2211yescharacteristic, complemented
77#11762749C2211yescharacteristic, complemented
78#11762745C2211yescharacteristic, complemented
79#11762744C2211yescharacteristic, complemented
80#11762740C2211yescharacteristic, complemented
81#11762739C2211yescharacteristic, complemented
82#11762738C2211yescharacteristic, complemented
83#11762738C2211yescharacteristic, complemented
84#11762738C2211yescharacteristic, complemented
85#11762738C2211yescharacteristic, complemented
86#11762736C2211yescharacteristic, complemented
87#11762736C2211yescharacteristic, complemented
88#11762735C2211yescharacteristic, complemented
89#11762734C2211yescharacteristic, complemented
90#11762730C2211yescharacteristic, complemented
91#11762729C2211yescharacteristic, complemented
92#11762727C2211yescharacteristic, complemented
93#11762727C2211yescharacteristic, complemented
94#11762727C2211yescharacteristic, complemented
95#11762727C2211yescharacteristic, complemented
96#11762725C2211yescharacteristic, complemented
97#11762725C2211yescharacteristic, complemented
98#11762724C2211yescharacteristic, complemented
99#11762724C2211yescharacteristic, complemented
100#11762724C2211yescharacteristic, complemented
101#11762724C2211yescharacteristic, complemented
102#11762724C2211yescharacteristic, complemented
103#11762724C2211yescharacteristic, complemented
104#11762724C2211yescharacteristic, complemented
105#11762724C2211yescharacteristic, complemented
106#11762723C2211yescharacteristic, complemented
107#11762723C2211yescharacteristic, complemented
108#11762723C2211yescharacteristic, complemented
109#11762722C2211yescharacteristic, complemented
110#11762721C2211yescharacteristic, complemented
111#11762719C2211yescharacteristic, complemented
112#11762718C2211yescharacteristic, complemented
113#11762718C2211yescharacteristic, complemented
114#11762718C2211yescharacteristic, complemented
115#11762717C2211yescharacteristic, complemented
116#11762717C2211yescharacteristic, complemented
117#11762717C2211yescharacteristic, complemented
118#11762717C2211yescharacteristic, complemented
119#11762703C2211yescharacteristic, complemented
120#11762703C2211yescharacteristic, complemented
121#11762698C2211yescharacteristic, complemented
122#11762698C2211yescharacteristic, complemented
123#11762696C2211yescharacteristic, complemented
124#11762696C2211yescharacteristic, complemented
125#11762691C2211yescharacteristic, complemented
126#11762691C2211yescharacteristic, complemented
127#11762689C2211yescharacteristic, complemented
128#11762688C2211yescharacteristic
129#11762688C2211yescharacteristic, complemented
130#11762688C2211yescharacteristic, complemented
131#11762688C2211yescharacteristic, complemented
132#11762687C2211yescharacteristic
133#11762687C2211yescharacteristic
134#11762687C2211yescharacteristic
135#11762687C2211yescharacteristic
136#11762687C2211yescharacteristic, complemented
137#11762687C2211yescharacteristic, complemented
138#11762687C2211yescharacteristic, complemented
139#11762687C2211yescharacteristic, complemented
140#11762687C2211yescharacteristic, complemented
141#11762687C2211yescharacteristic, complemented
142#11762686C2211yescharacteristic
143#11762686C2211yescharacteristic, complemented
144#11762685C2211yescharacteristic
145#11762685C2211yescharacteristic
146#11762685C2211yescharacteristic, complemented
147#11762685C2211yescharacteristic, complemented
148#11762685C2211yescharacteristic, complemented
149#11762685C2211yescharacteristic, complemented
150#11762685C2211yescharacteristic, complemented
151#11762685C2211yescharacteristic, complemented
152#11762685C2211yescharacteristic, complemented
153#11762685C2211yescharacteristic, complemented
154#11762683C2211yescharacteristic, complemented
155#11762683C2211yescharacteristic, complemented
156#11762682C2211yescharacteristic, complemented
157#11762682C2211yescharacteristic, complemented
158#11762681C2211yescharacteristic, complemented
159#11762680C2211yescharacteristic, complemented
160#11762680C2211yescharacteristic, complemented
161#11762670C2211yescharacteristic, complemented
162#11762668C2211yescharacteristic, complemented
163#11762668C2211yescharacteristic, complemented
164#11762668C2211yescharacteristic, complemented
165#11762668C2211yescharacteristic, complemented
166#11762668C2211yescharacteristic, complemented
167#11762668C2211yescharacteristic, complemented
168#11762667C2211yescharacteristic, complemented
169#11762667C2211yescharacteristic, complemented
170#11762664C2211yescharacteristic, complemented
171#11762664C2211yescharacteristic, complemented
172#95×D17C2211yescharacteristic, complemented
173#95×D17C2211yescharacteristic, complemented
174C2×C17×#121C2211yescharacteristic
175C2×C17×#121C2211yescharacteristic, complemented
176C17×#400C2211yescharacteristic, complemented
177C17×#397C2211yescharacteristic, complemented
178C17×#397C2211yescharacteristic, complemented
179C17×#394C2211yescharacteristic, complemented
180C17×#392C2211yescharacteristic, complemented
181C17×#392C2211yescharacteristic, complemented
182C17×#386C2211yescharacteristic, complemented
183C17×#386C2211yescharacteristic, complemented
184C17×#386C2211yescharacteristic, complemented
185C17×#386C2211yescharacteristic, complemented
186C17×#386C2211yescharacteristic, complemented
187C17×#385C2211yescharacteristic, complemented
188C17×#381C2211yescharacteristic, complemented
189C24×D17C2311yescharacteristic
190C24×D17C2311yescharacteristic
191C24×D17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C22×D4×C17C2311yescharacteristic
195C22×D4×C17C2311yescharacteristic
196C22×D4×C17C2311yescharacteristic
197C22×D4×C17C2311yescharacteristic
198C23×C4×C17C2311yescharacteristic
199C23×C4×C17C2311yescharacteristic
200C23×C4×C17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C22×C22⋊D17C2311yescharacteristic
205C22×C22⋊D17C2311yescharacteristic
206C22×C22⋊D17C2311yescharacteristic
207C22×C22⋊D17C2311yescharacteristic
208C22×C22⋊D17C2311yescharacteristic
209C22×C22⋊D17C2311yescharacteristic
210C22×C22⋊D17C2311yescharacteristic
211C22×C22⋊D17C2311yescharacteristic
212C22×C22⋊D17C2311yescharacteristic
213C22×C22⋊D17C2311yescharacteristic
214C22×C22⋊D17C2311yescharacteristic
215C23×Dic17C2311yescharacteristic
216C23×Dic17C2311yescharacteristic
217C2×D4×D17—24no—
218C2×D4×D17—42no—
219C2×D4×D17—42no—
220C2×D4×D17—42no—
221C2×D4×D17—42no—
222C2×D4×D17D418yescomplemented
223C2×#63252—24no—
224C2×#63252—42no—
225C2×#63252—42no—
226C22×D68C2311yescharacteristic
227C22×D68C2311yescharacteristic
228C22×D68C2311yescharacteristic
229C22×D68C2311yescharacteristic
230C22×D68C2311yescharacteristic
231C22×D68C2311yescharacteristic
232C22×D68C2311yescharacteristic
233C22×C4×D17—42no—
234C22×C4×D17—42no—
235C22×C4×D17—42no—
236C22×C4×D17C2311yescharacteristic
237C22×C4×D17C2311yescharacteristic
238C22×C4×D17C2311yescharacteristic
239C22×C4×D17C2311yescharacteristic
240C22×C4×D17C2311yescharacteristic
241C22×C4×D17C2311yescharacteristic
242C22×C4×D17C2311yescharacteristic
243C22×C4×D17C2311yescharacteristic
244C22×C4×D17C2311yescharacteristic
245C22×Dic34C2311yescharacteristic
246C17×#121—24no—
247C17×#121—24no—
248C2×C4⋊C4×C17C2311yescharacteristic
249C2×C4⋊C4×C17C2311yescharacteristic
250C2×C4⋊C4×C17C2311yescharacteristic
251C2×C22⋊C4×C17C2311yescharacteristic
252C2×C22⋊C4×C17C2311yescharacteristic
253C2×C22⋊C4×C17C2311yescharacteristic
254C2×C22⋊C4×C17C2311yescharacteristic
255C2×C22⋊C4×C17C2311yescharacteristic
256C2×C22⋊C4×C17C2311yescharacteristic
257C2×C22⋊C4×C17C2311yescharacteristic
258C2×C22⋊C4×C17C2311yescharacteristic
259C2×C22⋊C4×C17C2311yescharacteristic
260C2×C22⋊C4×C17C2311yescharacteristic
261C2×C22⋊C4×C17C2311yescharacteristic
262C2×C22⋊C4×C17C2311yescharacteristic
263C2×C22⋊C4×C17C2311yescharacteristic
264C2×C22⋊Dic17C2311yescharacteristic
265C2×C22⋊Dic17C2311yescharacteristic
266C2×C22⋊Dic17C2311yescharacteristic
267C2×C22⋊Dic17C2311yescharacteristic
268C2×C22⋊Dic17C2311yescharacteristic
269C2×C22⋊Dic17C2311yescharacteristic
270C2×C22⋊Dic17C2311yescharacteristic
271C2×C22⋊Dic17C2311yescharacteristic
272C2×C22⋊Dic17C2311yescharacteristic
273C2×C22⋊Dic17C2311yescharacteristic
274C2×C22⋊Dic17C2311yescharacteristic
275C2×C22⋊Dic17C2311yescharacteristic
276C2×C22⋊Dic17C2311yescharacteristic
277#10587626—24no—
278#10587626—24no—
279#10587625—24no—
280#10587625—24no—
281#10587625—42no—
282#10587625—42no—
283#10587624—24no—
284#10587624—42no—
285#10587623—24no—
286#10587623—24no—
287#10587623—24no—
288#10587623—24no—
289#10587623—42no—
290#10587621—42no—
291#10587616—24no—
292#10587616—24no—
293#10587615—42no—
294C2×#63227—24no—
295C2×#63227C2311yescharacteristic
296C2×#63227C2311yescharacteristic
297C2×#63227C2311yescharacteristic
298C2×#63227C2311yescharacteristic
299C2×#63227C2311yescharacteristic
300C2×#63227C2311yescharacteristic
301C2×#63227C2311yescharacteristic
302C2×#63227C2311yescharacteristic
303C2×#63227C2311yescharacteristic
304C2×#63227C2311yescharacteristic
305C2×#63227C2311yescharacteristic
306C2×#63227C2311yescharacteristic
307C2×#63227C2311yescharacteristic
308C2×#63227C2311yescharacteristic
309C2×#63227C2311yescharacteristic
310C2×#63227C2311yescharacteristic
311C2×#63227C2311yescharacteristic
312C2×#63227C2311yescharacteristic
313C2×#63227C2311yescharacteristic
314C2×#63227C2311yescharacteristic
315C2×#63227C2311yescharacteristic
316C2×#63227C2311yescharacteristic
317C2×#63227C2311yescharacteristic
318C2×#63227C2311yescharacteristic
319C2×#63227C2311yescharacteristic
320C2×#63227C2311yescharacteristic
321C2×#63227C2311yescharacteristic
322C2×#63227C2311yescharacteristic
323C2×#63227C2311yescharacteristic
324C2×#63227C2311yescharacteristic
325C2×#63227C2311yescharacteristic
326C2×#63227C2311yescharacteristic
327C2×C4⋊Dic17C2311yescharacteristic
328C2×C4⋊Dic17C2311yescharacteristic
329C2×C4⋊Dic17C2311yescharacteristic
330C2×#63225C2311yescharacteristic
331C2×#63225C2311yescharacteristic
332C2×#63225C2311yescharacteristic
333C2×#63225C2311yescharacteristic
334C2×#63225C2311yescharacteristic
335C2×#63225C2311yescharacteristic
336C2×#63225C2311yescharacteristic
337C2×#63225C2311yescharacteristic
338C2×#63225C2311yescharacteristic
339C2×#63225C2311yescharacteristic
340C2×#63225C2311yescharacteristic
341C2×#63225C2311yescharacteristic
342C2×C4×Dic17C2311yescharacteristic
343C2×C4×Dic17C2311yescharacteristic
344#10587581—24no—
345#10587581—42no—
346#10587580—24no—
347#10587580—24no—
348#10587578—24no—
349#10587571—24no—
350#10587571—24no—
351#10587570—42no—
352#10587570—42no—
353#10587570—42no—
354#10587570—42no—
355#10587569—24no—
356#10587569—24no—
357#10587568—24no—
358#10587568—24no—
359#10587568—24no—
360#10587568—24no—
361#10587568—42no—
362C22⋊C4×D17—42no—
363C22⋊C4×D17—42no—
364C22⋊C4×D17—42no—
365C17×#95C2311yescharacteristic
366C17×#95C2311yescharacteristic
367C17×#95C2311yescharacteristic
368C17×#95C2311yescharacteristic
369C17×#95C2311yescharacteristic
370C17×#95C2311yescharacteristic
371C17×#95C2311yescharacteristic
372C17×#95C2311yescharacteristic
373C17×#95C2311yescharacteristic
374C17×#95C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379#10587502C2311yescharacteristic
380#10587502C2311yescharacteristic
381#10587502C2311yescharacteristic
382#10587502C2311yescharacteristic
383#10587502C2311yescharacteristic
384#10587502C2311yescharacteristic
385#10587502C2311yescharacteristic
386#10587502C2311yescharacteristic
387#10587502C2311yescharacteristic
388#10587502C2311yescharacteristic
389#10587502C2311yescharacteristic
390#10587502C2311yescharacteristic
391#10587502C2311yescharacteristic
392#10587502C2311yescharacteristic
393#10587502C2311yescharacteristic
394#10587502C2311yescharacteristic
395#10587502C2311yescharacteristic
396#10587502C2311yescharacteristic
397C24×C17C2411yescharacteristic
398C24×C17C2411yescharacteristic
399C24×C17C2411yescharacteristic
400C24×C17C2411yescharacteristic
401C23×D17—22no—
402C23×D17—22no—
403C23×D17—22no—
404C23×D17—22no—
405C23×D17—22no—
406C23×D17—41no—
407C23×D17—41no—
408C23×D17—41no—
409C23×D17—41no—
410C23×D17—41no—
411C23×D17—41no—
412C23×D17—41no—
413C23×D17—41no—
414C23×D17—41no—
415C23×D17—41no—
416C23×D17—41no—
417C23×D17—41no—
418C23×D17—41no—
419C23×D17—41no—
420C23×D17C2×D414yes—
421C23×D17C2×D414yes—
422C23×D17C2411yescharacteristic
423C23×D17C2411yescharacteristic
424C23×D17C2411yescharacteristic
425C23×D17C2411yescharacteristic
426C23×D17C2411yescharacteristic
427C2×D4×C17—22no—
428C2×D4×C17—22no—
429C2×D4×C17—22no—
430C2×D4×C17—22no—
431C2×D4×C17—41no—
432C2×D4×C17—41no—
433C2×D4×C17—41no—
434C2×D4×C17—41no—
435C2×D4×C17—41no—
436C2×D4×C17—41no—
437C2×D4×C17—41no—
438C2×D4×C17—41no—
439C2×D4×C17—41no—
440C2×D4×C17—41no—
441C2×D4×C17—41no—
442C2×D4×C17—41no—
443C2×D4×C17—41no—
444C2×D4×C17C2×D414yes—
445C22×C4×C17—22no—
446C22×C4×C17—22no—
447C22×C4×C17—41no—
448C22×C4×C17—41no—
449C22×C4×C17—41no—
450C22×C4×C17—41no—
451C22×C4×C17—41no—
452C22×C4×C17—41no—
453C22×C4×C17—41no—
454C22×C4×C17C2411yescharacteristic
455C22×C4×C17C2411yescharacteristic
456C22×C4×C17C2411yescharacteristic
457C22×C4×C17C2411yescharacteristic
458C22×C4×C17C2411yescharacteristic
459C22×C4×C17C2411yescharacteristic
460C22×C4×C17C2411yescharacteristic
461C22×C4×C17C2411yescharacteristic
462C22×C4×C17C2411yescharacteristic
463C22×C4×C17C2411yescharacteristic
464C22×C4×C17C2411yescharacteristic
465C2×C22⋊D17—22no—
466C2×C22⋊D17—22no—
467C2×C22⋊D17—22no—
468C2×C22⋊D17—22no—
469C2×C22⋊D17—22no—
470C2×C22⋊D17—22no—
471C2×C22⋊D17—22no—
472C2×C22⋊D17—22no—
473C2×C22⋊D17—22no—
474C2×C22⋊D17—22no—
475C2×C22⋊D17—22no—
476C2×C22⋊D17—22no—
477C2×C22⋊D17—22no—
478C2×C22⋊D17—22no—
479C2×C22⋊D17—22no—
480C2×C22⋊D17—22no—
481C2×C22⋊D17—41no—
482C2×C22⋊D17—41no—
483C2×C22⋊D17—41no—
484C2×C22⋊D17—41no—
485C2×C22⋊D17—41no—
486C2×C22⋊D17—41no—
487C2×C22⋊D17—41no—
488C2×C22⋊D17—41no—
489C2×C22⋊D17—41no—
490C2×C22⋊D17—41no—
491C2×C22⋊D17—41no—
492C2×C22⋊D17—41no—
493C2×C22⋊D17—41no—
494C2×C22⋊D17—41no—
495C2×C22⋊D17—41no—
496C2×C22⋊D17—41no—
497C2×C22⋊D17—41no—
498C2×C22⋊D17—41no—
499C2×C22⋊D17—41no—
500C2×C22⋊D17—41no—
501C2×C22⋊D17—41no—
502C2×C22⋊D17—41no—
503C2×C22⋊D17—41no—
504C2×C22⋊D17—41no—
505C2×C22⋊D17C2×D414yes—
506C2×C22⋊D17C2×D414yes—
507C22×Dic17—22no—
508C22×Dic17—22no—
509C22×Dic17—22no—
510C22×Dic17—41no—
511C22×Dic17—41no—
512C22×Dic17—41no—
513C22×Dic17C2411yescharacteristic
514C22×Dic17C2411yescharacteristic
515C22×Dic17C2411yescharacteristic
516C22×Dic17C2411yescharacteristic
517C22×Dic17C2411yescharacteristic
518C22×Dic17C2411yescharacteristic
519C22×Dic17C2411yescharacteristic
520C22×Dic17C2411yescharacteristic
521C22×Dic17C2411yescharacteristic
522C22×Dic17C2411yescharacteristic
523C22×Dic17C2411yescharacteristic
524D4×D17—416no—
525D4×D17—416no—
526#63252—416no—
527C2×D68—22no—
528C2×D68—22no—
529C2×D68—22no—
530C2×D68—22no—
531C2×D68—22no—
532C2×D68—22no—
533C2×D68—22no—
534C2×D68—22no—
535C2×D68—22no—
536C2×D68—41no—
537C2×D68—41no—
538C2×D68—41no—
539C2×D68—41no—
540C2×D68—41no—
541C2×D68—41no—
542C2×D68—41no—
543C2×D68—41no—
544C2×D68—41no—
545C2×D68—41no—
546C2×D68—41no—
547C2×D68C2×D414yes—
548C2×C4×D17—22no—
549C2×C4×D17—22no—
550C2×C4×D17—22no—
551C2×C4×D17—22no—
552C2×C4×D17—22no—
553C2×C4×D17—22no—
554C2×C4×D17—22no—
555C2×C4×D17—22no—
556C2×C4×D17—22no—
557C2×C4×D17—22no—
558C2×C4×D17—22no—
559C2×C4×D17—22no—
560C2×C4×D17—41no—
561C2×C4×D17—41no—
562C2×C4×D17—41no—
563C2×C4×D17—41no—
564C2×C4×D17—41no—
565C2×C4×D17—41no—
566C2×C4×D17—41no—
567C2×C4×D17—41no—
568C2×C4×D17—41no—
569C2×C4×D17—41no—
570C2×C4×D17—416no—
571C2×C4×D17—41no—
572C2×C4×D17—41no—
573C2×C4×D17—41no—
574C2×C4×D17—41no—
575C2×C4×D17C2×D414yes—
576C2×Dic34—22no—
577C2×Dic34—41no—
578C2×Dic34—41no—
579C4⋊C4×C17—22no—
580C4⋊C4×C17—22no—
581C4⋊C4×C17—41no—
582C22⋊C4×C17—22no—
583C22⋊C4×C17—22no—
584C22⋊C4×C17—22no—
585C22⋊C4×C17—22no—
586C22⋊C4×C17—41no—
587C22⋊C4×C17—41no—
588C22⋊C4×C17—41no—
589C22⋊C4×C17—41no—
590C22⋊C4×C17—41no—
591C22⋊C4×C17—41no—
592C22⋊C4×C17—41no—
593C22⋊C4×C17—41no—
594C22⋊C4×C17—41no—
595C22⋊Dic17—22no—
596C22⋊Dic17—22no—
597C22⋊Dic17—22no—
598C22⋊Dic17—22no—
599C22⋊Dic17—22no—
600C22⋊Dic17—22no—
601C22⋊Dic17—22no—
602C22⋊Dic17—22no—
603C22⋊Dic17—41no—
604C22⋊Dic17—41no—
605C22⋊Dic17—41no—
606C22⋊Dic17—41no—
607C22⋊Dic17—41no—
608#63227—22no—
609#63227—22no—
610#63227—22no—
611#63227—22no—
612#63227—22no—
613#63227—22no—
614#63227—22no—
615#63227—22no—
616#63227—22no—
617#63227—22no—
618#63227—22no—
619#63227—22no—
620#63227—22no—
621#63227—22no—
622#63227—22no—
623#63227—22no—
624#63227—22no—
625#63227—22no—
626#63227—41no—
627#63227—41no—
628#63227—41no—
629#63227—41no—
630#63227—41no—
631#63227—41no—
632#63227—41no—
633#63227—41no—
634#63227—41no—
635#63227—41no—
636#63227—41no—
637#63227—41no—
638#63227—41no—
639#63227—41no—
640C4⋊Dic17—22no—
641C4⋊Dic17—22no—
642C4⋊Dic17—41no—
643#63225—22no—
644#63225—22no—
645#63225—22no—
646#63225—22no—
647#63225—41no—
648#63225—41no—
649#63225—41no—
650#63225—41no—
651#63225—41no—
652#63225—41no—
653#63225—41no—
654#63225—41no—
655C4×Dic17—22no—
656C4×Dic17—22no—
657#36737—171nomaximal, Sylow
658C23×C17—21no—
659C23×C17—21no—
660C23×C17—21no—
661C23×C17—21no—
662C23×C17—21no—
663C23×C17—21no—
664C23×C17—21no—
665C23×C17—21no—
666C23×C17—21no—
667C23×C17—21no—
668C23×C17—21no—
669C23×C17—21no—
670C23×C17—21no—
671C23×C17—21no—
672C23×C17—21no—
673C23×C17—21no—
674C23×C17—21no—
675C23×C17—21no—
676C23×C17—21no—
677C23×C17—21no—
678C23×C17—21no—
679C23×C17—21no—
680C23×C17—21no—
681C23×C17—21no—
682C23×C17—21no—
683C23×C17—21no—
684C23×C17C22×D412yes—
685C23×C17C22×D412yes—
686C23×C17C2511yescharacteristic
687C22×D17—21no—
688C22×D17—21no—
689C22×D17—21no—
690C22×D17—21no—
691C22×D17—21no—
692C22×D17—21no—
693C22×D17—21no—
694C22×D17—21no—
695C22×D17—21no—
696C22×D17—21no—
697C22×D17—21no—
698C22×D17—21no—
699C22×D17—21no—
700C22×D17—21no—
701C22×D17—21no—
702C22×D17—21no—
703C22×D17—28no—
704C22×D17—28no—
705C22×D17—21no—
706C22×D17—21no—
707C22×D17—21no—
708C22×D17—21no—
709C22×D17—21no—
710C22×D17—21no—
711C22×D17—21no—
712C22×D17—21no—
713C22×D17—21no—
714C22×D17—21no—
715C22×D17—21no—
716C22×D17—21no—
717C22×D17—21no—
718C22×D17—21no—
719C22×D17—44no—
720C22×D17—44no—
721C22×D17—44no—
722C22×D17—44no—
723C22×D17—44no—
724C22×D17—44no—
725C22×D17—44no—
726C22×D17—44no—
727C22×D17—44no—
728C22×D17—82no—
729C22×D17—82no—
730C22×D17—82no—
731C22×D17—82no—
732C22×D17—82no—
733C22×D17—82no—
734C22×D17—82no—
735C22×D17—82no—
736C22×D17—82no—
737C22×D17—82no—
738C22×D17C22×D412yes—
739C22×D17C22×D412yes—
740C22×D17C22×D412yes—
741C22×D17H(5,𝔽2)12yes—
742C22×D17H(5,𝔽2)12yes—
743D4×C17—44no—
744D4×C17—44no—
745D4×C17—82no—
746D4×C17—82no—
747D4×C17—82no—
748D4×C17—82no—
749C2×C4×C17—21no—
750C2×C4×C17—21no—
751C2×C4×C17—21no—
752C2×C4×C17—21no—
753C2×C4×C17—21no—
754C2×C4×C17—21no—
755C2×C4×C17—21no—
756C2×C4×C17—21no—
757C2×C4×C17—21no—
758C2×C4×C17—21no—
759C2×C4×C17—21no—
760C2×C4×C17—21no—
761C2×C4×C17—21no—
762C2×C4×C17—21no—
763C2×C4×C17—21no—
764C2×C4×C17—21no—
765C2×C4×C17—21no—
766C2×C4×C17—21no—
767C2×C4×C17—21no—
768C2×C4×C17—21no—
769C2×C4×C17—21no—
770C2×C4×C17—21no—
771C2×C4×C17—21no—
772C2×C4×C17—21no—
773C2×C4×C17—21no—
774C2×C4×C17—21no—
775C2×C4×C17—21no—
776C2×C4×C17—21no—
777C2×C4×C17—21no—
778C2×C4×C17—21no—
779C2×C4×C17—21no—
780C2×C4×C17—21no—
781C2×C4×C17—44no—
782C2×C4×C17—44no—
783C2×C4×C17—82no—
784C2×C4×C17C22×D412yes—
785C22⋊D17—44no—
786C22⋊D17—44no—
787C22⋊D17—44no—
788C22⋊D17—44no—
789C22⋊D17—44no—
790C22⋊D17—44no—
791C22⋊D17—82no—
792C22⋊D17—82no—
793C22⋊D17—82no—
794C22⋊D17—82no—
795C22⋊D17—82no—
796C22⋊D17—82no—
797C22⋊D17—82no—
798C22⋊D17—82no—
799C2×Dic17—21no—
800C2×Dic17—21no—
801C2×Dic17—21no—
802C2×Dic17—21no—
803C2×Dic17—21no—
804C2×Dic17—21no—
805C2×Dic17—21no—
806C2×Dic17—21no—
807C2×Dic17—21no—
808C2×Dic17—21no—
809C2×Dic17—21no—
810C2×Dic17—21no—
811C2×Dic17—21no—
812C2×Dic17—21no—
813C2×Dic17—21no—
814C2×Dic17—21no—
815C2×Dic17—21no—
816C2×Dic17—21no—
817C2×Dic17—21no—
818C2×Dic17—21no—
819C2×Dic17—21no—
820C2×Dic17—21no—
821C2×Dic17—21no—
822C2×Dic17—21no—
823C2×Dic17—21no—
824C2×Dic17—21no—
825C2×Dic17—21no—
826C2×Dic17—21no—
827C2×Dic17—21no—
828C2×Dic17—21no—
829C2×Dic17—44no—
830C2×Dic17—82no—
831C2×Dic17C22×D412yes—
832C2×Dic17H(5,𝔽2)12yes—
833C2×Dic17H(5,𝔽2)12yes—
834D68—44no—
835D68—44no—
836D68—44no—
837D68—82no—
838D68—82no—
839D68—82no—
840D68—82no—
841C4×D17—28no—
842C4×D17—44no—
843C4×D17—44no—
844C4×D17—44no—
845C4×D17—44no—
846C4×D17—44no—
847C4×D17—44no—
848C4×D17—82no—
849C4×D17—82no—
850Dic34—44no—
851C2×#535—171no—
852C2×#534—171no—
853#2847—171no—
854#2847—171no—
855#2717—171no—
856#2709—171no—
857#2708—171no—
858#2708—171no—
859#2688—171no—
860#2688D1711yescharacteristic, complemented
861#2686—171no—
862#2686—171no—
863#2684—171no—
864#2673—171no—
865#2673—171no—
866#2671—171no—
867#2671—171no—
868#2669—171no—
869#2668—171no—
870#2668—171no—
871#2617—171no—
872#2617—171no—
873#2498—171no—
874#2498—171no—
875#2430—171no—
876#2430—171no—
877#2412—171no—
878#2412—171no—
879#2410—171no—
880#2410—171no—
881C2×#386—171no—
882C22×C17—22no—
883C22×C17—22no—
884C22×C17—22no—
885C22×C17—22no—
886C22×C17—22no—
887C22×C17—22no—
888C22×C17—41no—
889C22×C17—41no—
890C22×C17—41no—
891C22×C17—41no—
892C22×C17—41no—
893C22×C17—41no—
894C22×C17—41no—
895C22×C17—41no—
896C22×C17—41no—
897C22×C17—41no—
898C22×C17—41no—
899C22×C17—41no—
900C22×C17—41no—
901C22×C17—41no—
902C22×C17—41no—
903C22×C17—41no—
904C22×C17—41no—
905C22×C17—41no—
906C22×C17—41no—
907C22×C17—41no—
908C22×C17—41no—
909C22×C17—41no—
910C22×C17C23×D411yescharacteristic
911C22×C17C2×H(5,𝔽2)11yescharacteristic
912C22×C17C2×H(5,𝔽2)11yescharacteristic
913C22×C17C2×H(5,𝔽2)11yescharacteristic
914C22×C17C2×H(5,𝔽2)11yescharacteristic
915C22×C17#58511yescharacteristic
916C22×C17#58511yescharacteristic
917C2×D17—22no—
918C2×D17—22no—
919C2×D17—22no—
920C2×D17—22no—
921C2×D17—22no—
922C2×D17—22no—
923C2×D17—22no—
924C2×D17—22no—
925C2×D17—22no—
926C2×D17—22no—
927C2×D17—22no—
928C2×D17—22no—
929C2×D17—416no—
930C2×D17—41no—
931C2×D17—41no—
932C2×D17—41no—
933C2×D17—41no—
934C2×D17—41no—
935C2×D17—41no—
936C2×D17—41no—
937C2×D17—41no—
938C2×D17—41no—
939C2×D17—41no—
940C2×D17—41no—
941C2×D17—41no—
942C2×D17—41no—
943C2×D17—41no—
944C2×D17—41no—
945C2×D17—41no—
946C2×D17—41no—
947C2×D17—41no—
948C2×D17—41no—
949C2×D17—41no—
950C2×D17—41no—
951C2×D17—41no—
952C2×D17—88no—
953C2×D17—88no—
954C2×D17#53414yes—
955C4×C17—22no—
956C4×C17—41no—
957C4×C17—41no—
958C4×C17—41no—
959C4×C17—41no—
960C4×C17—41no—
961C4×C17—41no—
962C4×C17—41no—
963C4×C17—41no—
964C4×C17—41no—
965C4×C17—41no—
966Dic17—22no—
967Dic17—22no—
968Dic17—22no—
969Dic17—41no—
970Dic17—41no—
971Dic17—41no—
972Dic17—41no—
973Dic17—41no—
974Dic17—41no—
975Dic17—41no—
976Dic17—41no—
977C22×#41—171no—
978C23×D4—171no—
979C23×D4—171no—
980C24×C4—171no—
981#535—348no—
982#534—348no—
983C2×#127—171no—
984C2×#127—171no—
985C2×#124—171no—
986C2×#124—171no—
987C2×#123—171no—
988C2×#123—171no—
989C2×#123—171no—
990C2×#123—171no—
991C2×#123—171no—
992C2×#123—171no—
993C2×#121—171no—
994C2×#121—171no—
995C2×#121—171no—
996C2×#121—171no—
997C2×#121—171no—
998C2×#121—171no—
999C2×#121—171no—
1000C2×#121—171no—
1001C2×#121—171no—
1002C2×#121—171no—
1003C2×#121—171no—
1004C2×#121—171no—
1005C2×#121—171no—
1006C2×#121—171no—
1007C2×#121C2×D1711yescharacteristic
1008C2×#121C2×D1711yescharacteristic, complemented
1009C2×#120—171no—
1010C2×#120—171no—
1011C2×#120—171no—
1012C2×#120—171no—
1013C2×#120—171no—
1014C2×#120—171no—
1015C2×#120—171no—
1016C2×#120—171no—
1017C2×#120—171no—
1018C2×#120—171no—
1019C2×#117—171no—
1020C22×C22⋊C4—171no—
1021C22×C22⋊C4—171no—
1022C22×C22⋊C4—171no—
1023C22×C22⋊C4—171no—
1024#400—171no—
1025#400C2×D1711yescharacteristic, complemented
1026#399—171no—
1027#399—171no—
1028#398—171no—
1029#398—171no—
1030#397—171no—
1031#397—171no—
1032#397—171no—
1033#397—171no—
1034#397—171no—
1035#397—171no—
1036#397—171no—
1037#397—171no—
1038#397C2×D1711yescharacteristic, complemented
1039#397C2×D1711yescharacteristic, complemented
1040#395—171no—
1041#395—171no—
1042#394—171no—
1043#394—171no—
1044#394—171no—
1045#394—171no—
1046#394—171no—
1047#394—171no—
1048#394—171no—
1049#394—171no—
1050#394—171no—
1051#394—171no—
1052#394—171no—
1053#394—171no—
1054#394—171no—
1055#394—171no—
1056#394—171no—
1057#394—171no—
1058#394—171no—
1059#394C2×D1711yescharacteristic, complemented
1060#393—171no—
1061#393—171no—
1062#392—171no—
1063#392—171no—
1064#392—171no—
1065#392—171no—
1066#392—171no—
1067#392—171no—
1068#392—171no—
1069#392—171no—
1070#392C2×D1711yescharacteristic, complemented
1071#392C2×D1711yescharacteristic, complemented
1072#388—171no—
1073#388—171no—
1074#388—171no—
1075#388—171no—
1076#387—171no—
1077#387—171no—
1078#387—171no—
1079#387—171no—
1080#386—171no—
1081#386—171no—
1082#386—171no—
1083#386—171no—
1084#386—171no—
1085#386—171no—
1086#386—171no—
1087#386—171no—
1088#386—171no—
1089#386—171no—
1090#386—171no—
1091#386—171no—
1092#386—171no—
1093#386—171no—
1094#386—171no—
1095#386—171no—
1096#386—171no—
1097#386—171no—
1098#386—171no—
1099#386—171no—
1100#386—171no—
1101#386—171no—
1102#386—171no—
1103#386—171no—
1104#386—171no—
1105#386—171no—
1106#386—171no—
1107#386C2×D1711yescharacteristic, complemented
1108#386C2×D1711yescharacteristic, complemented
1109#386C2×D1711yescharacteristic, complemented
1110#386C2×D1711yescharacteristic, complemented
1111#386C2×D1711yescharacteristic, complemented
1112#385—171no—
1113#385—171no—
1114#385—171no—
1115#385—171no—
1116#385—171no—
1117#385—171no—
1118#385—171no—
1119#385C2×D1711yescharacteristic, complemented
1120#381—171no—
1121#381C2×D1711yescharacteristic, complemented
1122#380—171no—
1123#380—171no—
1124#380—171no—
1125#380—171no—
1126#380—171no—
1127#380—171no—
1128#380—171no—
1129#380—171no—
1130#379—171no—
1131#379—171no—
1132C2×#95—171no—
1133C2×#95—171no—
1134C2×C17—42no—
1135C2×C17—42no—
1136C2×C17—81no—
1137C2×C17—81no—
1138C2×C17C2×#53411yescharacteristic
1139C2×C17#349611yescharacteristic
1140C2×C17#349611yescharacteristic
1141C2×C17#353211yescharacteristic
1142C2×C17#353311yescharacteristic
1143C2×C17#354211yescharacteristic
1144C2×C17#354211yescharacteristic
1145D17—24no—
1146D17—42no—
1147D17—42no—
1148D17—81no—
1149D17—81no—
1150C25—171no—
1151C25—171no—
1152C25—171no—
1153C2×#41—344no—
1154C2×#41—682no—
1155C2×#41—682no—
1156C22×Q8—171no—
1157C22×D4—171no—
1158C22×D4—171no—
1159C22×D4—178no—
1160C22×D4—171no—
1161C22×D4—171no—
1162C22×D4—171no—
1163C22×D4—171no—
1164C22×D4—171no—
1165C22×D4—171no—
1166C22×D4—171no—
1167C22×D4—171no—
1168C22×D4—171no—
1169C22×D4—171no—
1170C22×D4—171no—
1171C22×D4—171no—
1172C22×D4—171no—
1173C22×D4—171no—
1174C22×D4—171no—
1175C22×D4—171no—
1176C22×D4—171no—
1177C22×D4—171no—
1178C22×D4—171no—
1179C22×D4—344no—
1180C22×D4—682no—
1181C22×D4—682no—
1182C22×D4—682no—
1183C22×D4—682no—
1184C22×D4C22×D1711yescharacteristic
1185C22×D4C22×D1711yescharacteristic
1186C22×D4C22×D1711yescharacteristic
1187C22×D4C22×D1711yescharacteristic
1188C22×D4C22×D1711yescharacteristic
1189C22×D4C22×D1711yescharacteristic
1190C23×C4—171no—
1191C23×C4—171no—
1192C23×C4—171no—
1193C23×C4—171no—
1194C23×C4—171no—
1195C23×C4—171no—
1196C23×C4—171no—
1197C23×C4—171no—
1198C23×C4—171no—
1199C23×C4—171no—
1200C23×C4—171no—
1201C23×C4—682no—
1202C23×C4—682no—
1203C23×C4—682no—
1204C23×C4C22×D1711yescharacteristic
1205C23×C4C22×D1711yescharacteristic
1206C23×C4C22×D1711yescharacteristic
1207#127—344no—
1208#127—344no—
1209#124—344no—
1210#124—344no—
1211#123—344no—
1212#123—344no—
1213#123—344no—
1214#123—344no—
1215#123—682no—
1216#123—682no—
1217#121—24no—
1218#121—24no—
1219#121—344no—
1220#121—344no—
1221#121—344no—
1222#121—344no—
1223#121—344no—
1224#121—344no—
1225#121—682no—
1226#121—682no—
1227#121—682no—
1228#121—682no—
1229#121—682no—
1230#121—682no—
1231#121—682no—
1232#121—682no—
1233#120—344no—
1234#120—344no—
1235#120—344no—
1236#120—344no—
1237#120—344no—
1238#120—344no—
1239#120—344no—
1240#120—344no—
1241#120—682no—
1242#120—682no—
1243#117—344no—
1244C2×C4⋊C4—171no—
1245C2×C4⋊C4—171no—
1246C2×C4⋊C4—171no—
1247C2×C4⋊C4—171no—
1248C2×C4⋊C4—171no—
1249C2×C4⋊C4—171no—
1250C2×C4⋊C4—171no—
1251C2×C4⋊C4—171no—
1252C2×C4⋊C4—171no—
1253C2×C4⋊C4—171no—
1254C2×C4⋊C4—171no—
1255C2×C4⋊C4—171no—
1256C2×C4⋊C4—171no—
1257C2×C4⋊C4—171no—
1258C2×C4⋊C4—171no—
1259C2×C4⋊C4C22×D1711yescharacteristic
1260C2×C4⋊C4C22×D1711yescharacteristic
1261C2×C4⋊C4C22×D1711yescharacteristic
1262C2×C22⋊C4—171no—
1263C2×C22⋊C4—171no—
1264C2×C22⋊C4—171no—
1265C2×C22⋊C4—171no—
1266C2×C22⋊C4—171no—
1267C2×C22⋊C4—171no—
1268C2×C22⋊C4—171no—
1269C2×C22⋊C4—171no—
1270C2×C22⋊C4—171no—
1271C2×C22⋊C4—171no—
1272C2×C22⋊C4—171no—
1273C2×C22⋊C4—171no—
1274C2×C22⋊C4—171no—
1275C2×C22⋊C4—171no—
1276C2×C22⋊C4—171no—
1277C2×C22⋊C4—171no—
1278C2×C22⋊C4—171no—
1279C2×C22⋊C4—171no—
1280C2×C22⋊C4—171no—
1281C2×C22⋊C4—171no—
1282C2×C22⋊C4—171no—
1283C2×C22⋊C4—171no—
1284C2×C22⋊C4—171no—
1285C2×C22⋊C4—171no—
1286C2×C22⋊C4—171no—
1287C2×C22⋊C4—171no—
1288C2×C22⋊C4—171no—
1289C2×C22⋊C4—171no—
1290C2×C22⋊C4—171no—
1291C2×C22⋊C4—171no—
1292C2×C22⋊C4—171no—
1293C2×C22⋊C4—171no—
1294C2×C22⋊C4—171no—
1295C2×C22⋊C4—171no—
1296C2×C22⋊C4—171no—
1297C2×C22⋊C4—171no—
1298C2×C22⋊C4—171no—
1299C2×C22⋊C4—171no—
1300C2×C22⋊C4—171no—
1301C2×C22⋊C4—171no—
1302C2×C22⋊C4—171no—
1303C2×C22⋊C4—171no—
1304C2×C22⋊C4—171no—
1305C2×C22⋊C4—171no—
1306C2×C22⋊C4—171no—
1307C2×C22⋊C4—344no—
1308C2×C22⋊C4—682no—
1309C2×C22⋊C4—682no—
1310C2×C22⋊C4—682no—
1311C2×C22⋊C4C22×D1711yescharacteristic
1312C2×C22⋊C4C22×D1711yescharacteristic
1313C2×C22⋊C4C22×D1711yescharacteristic
1314C2×C22⋊C4C22×D1711yescharacteristic
1315C2×C22⋊C4C22×D1711yescharacteristic
1316C2×C22⋊C4C22×D1711yescharacteristic
1317C2×C22⋊C4C22×D1711yescharacteristic
1318C2×C22⋊C4C22×D1711yescharacteristic
1319C2×C22⋊C4C22×D1711yescharacteristic
1320C2×C22⋊C4C22×D1711yescharacteristic
1321C2×C22⋊C4C22×D1711yescharacteristic
1322C2×C22⋊C4C22×D1711yescharacteristic
1323C2×C22⋊C4C22×D1711yescharacteristic
1324C2×C42—171no—
1325C2×C42—171no—
1326#95—171no—
1327#95—171no—
1328#95—171no—
1329#95—171no—
1330#95—171no—
1331#95—171no—
1332#95—171no—
1333#95—171no—
1334#95—171no—
1335#95—171no—
1336#95—171no—
1337#95—171no—
1338#95—171no—
1339#95—171no—
1340#95—171no—
1341#95—171no—
1342#95—171no—
1343#95—171no—
1344#95—171no—
1345#95—171no—
1346#95—171no—
1347#95—171no—
1348#95C22×D1711yescharacteristic
1349#95C22×D1711yescharacteristic
1350#95C22×D1711yescharacteristic
1351#95C22×D1711yescharacteristic
1352#95C22×D1711yescharacteristic
1353#95C22×D1711yescharacteristic
1354#95C22×D1711yescharacteristic
1355#95C22×D1711yescharacteristic
1356#95C22×D1711yescharacteristic
1357#95C22×D1711yescharacteristic
1358C17#3673711yescharacteristic, complemented, Sylow
1359C24—171no—
1360C24—171no—
1361C24—171no—
1362C24—174no—
1363C24—174no—
1364C24—171no—
1365C24—171no—
1366C24—342no—
1367C24—342no—
1368C24—342no—
1369C24—342no—
1370C24—342no—
1371C24—681no—
1372C24—681no—
1373C24—681no—
1374C24—681no—
1375C24—681no—
1376C24—681no—
1377C24—681no—
1378C24—681no—
1379C24—681no—
1380C24—681no—
1381C24—681no—
1382C24—681no—
1383C24—681no—
1384C24—681no—
1385C24C23×D1711yescharacteristic
1386C24C23×D1711yescharacteristic
1387C24C23×D1711yescharacteristic
1388C24C23×D1711yescharacteristic
1389#41—6816no—
1390C2×Q8—342no—
1391C2×Q8—681no—
1392C2×Q8—681no—
1393C2×D4—22no—
1394C2×D4—22no—
1395C2×D4—22no—
1396C2×D4—22no—
1397C2×D4—41no—
1398C2×D4—41no—
1399C2×D4—41no—
1400C2×D4—41no—
1401C2×D4—41no—
1402C2×D4—41no—
1403C2×D4—41no—
1404C2×D4—41no—
1405C2×D4—41no—
1406C2×D4—41no—
1407C2×D4—41no—
1408C2×D4—41no—
1409C2×D4—41no—
1410C2×D4—174no—
1411C2×D4—174no—
1412C2×D4—174no—
1413C2×D4—342no—
1414C2×D4—342no—
1415C2×D4—342no—
1416C2×D4—342no—
1417C2×D4—342no—
1418C2×D4—342no—
1419C2×D4—342no—
1420C2×D4—342no—
1421C2×D4—342no—
1422C2×D4—342no—
1423C2×D4—342no—
1424C2×D4—342no—
1425C2×D4—342no—
1426C2×D4—342no—
1427C2×D4—342no—
1428C2×D4—342no—
1429C2×D4—342no—
1430C2×D4—342no—
1431C2×D4—342no—
1432C2×D4—342no—
1433C2×D4—342no—
1434C2×D4—342no—
1435C2×D4—342no—
1436C2×D4—342no—
1437C2×D4—342no—
1438C2×D4—681no—
1439C2×D4—681no—
1440C2×D4—681no—
1441C2×D4—681no—
1442C2×D4—681no—
1443C2×D4—681no—
1444C2×D4—681no—
1445C2×D4—681no—
1446C2×D4—681no—
1447C2×D4—681no—
1448C2×D4—681no—
1449C2×D4—6816no—
1450C2×D4—681no—
1451C2×D4—681no—
1452C2×D4—681no—
1453C2×D4—681no—
1454C2×D4—681no—
1455C2×D4—681no—
1456C2×D4—681no—
1457C2×D4—681no—
1458C2×D4—681no—
1459C2×D4—681no—
1460C2×D4—681no—
1461C2×D4—681no—
1462C2×D4—681no—
1463C2×D4—681no—
1464C2×D4—681no—
1465C2×D4—681no—
1466C2×D4—681no—
1467C2×D4—681no—
1468C2×D4—681no—
1469C2×D4—681no—
1470C2×D4—681no—
1471C2×D4—681no—
1472C2×D4—681no—
1473C2×D4—681no—
1474C2×D4—6816no—
1475C2×D4D4×D1714yes—
1476C22×C4—22no—
1477C22×C4—22no—
1478C22×C4—41no—
1479C22×C4—41no—
1480C22×C4—41no—
1481C22×C4—41no—
1482C22×C4—41no—
1483C22×C4—41no—
1484C22×C4—41no—
1485C22×C4—171no—
1486C22×C4—171no—
1487C22×C4—171no—
1488C22×C4—174no—
1489C22×C4—171no—
1490C22×C4—171no—
1491C22×C4—171no—
1492C22×C4—171no—
1493C22×C4—171no—
1494C22×C4—171no—
1495C22×C4—171no—
1496C22×C4—171no—
1497C22×C4—342no—
1498C22×C4—342no—
1499C22×C4—342no—
1500C22×C4—342no—
1501C22×C4—342no—
1502C22×C4—342no—
1503C22×C4—342no—
1504C22×C4—342no—
1505C22×C4—342no—
1506C22×C4—342no—
1507C22×C4—342no—
1508C22×C4—342no—
1509C22×C4—342no—
1510C22×C4—342no—
1511C22×C4—342no—
1512C22×C4—681no—
1513C22×C4—681no—
1514C22×C4—681no—
1515C22×C4—681no—
1516C22×C4—681no—
1517C22×C4—681no—
1518C22×C4—681no—
1519C22×C4—681no—
1520C22×C4—681no—
1521C22×C4—681no—
1522C22×C4—681no—
1523C22×C4—681no—
1524C22×C4—681no—
1525C22×C4—681no—
1526C22×C4—6816no—
1527C22×C4—681no—
1528C22×C4—681no—
1529C22×C4—681no—
1530C22×C4C23×D1711yescharacteristic
1531C22×C4C23×D1711yescharacteristic
1532C22×C4C23×D1711yescharacteristic
1533C22×C4C23×D1711yescharacteristic
1534C22×C4C23×D1711yescharacteristic
1535C22×C4C23×D1711yescharacteristic
1536C22×C4C23×D1711yescharacteristic
1537C22×C4C23×D1711yescharacteristic
1538C22×C4C23×D1711yescharacteristic
1539C22×C4C23×D1711yescharacteristic
1540C22×C4C23×D1711yescharacteristic
1541C4⋊C4—22no—
1542C4⋊C4—22no—
1543C4⋊C4—41no—
1544C4⋊C4—342no—
1545C4⋊C4—342no—
1546C4⋊C4—342no—
1547C4⋊C4—342no—
1548C4⋊C4—342no—
1549C4⋊C4—342no—
1550C4⋊C4—681no—
1551C4⋊C4—681no—
1552C4⋊C4—681no—
1553C4⋊C4—681no—
1554C4⋊C4—681no—
1555C4⋊C4—681no—
1556C4⋊C4—681no—
1557C4⋊C4—681no—
1558C4⋊C4—681no—
1559C22⋊C4—22no—
1560C22⋊C4—22no—
1561C22⋊C4—22no—
1562C22⋊C4—22no—
1563C22⋊C4—41no—
1564C22⋊C4—41no—
1565C22⋊C4—41no—
1566C22⋊C4—41no—
1567C22⋊C4—41no—
1568C22⋊C4—41no—
1569C22⋊C4—41no—
1570C22⋊C4—41no—
1571C22⋊C4—41no—
1572C22⋊C4—342no—
1573C22⋊C4—342no—
1574C22⋊C4—342no—
1575C22⋊C4—342no—
1576C22⋊C4—342no—
1577C22⋊C4—342no—
1578C22⋊C4—342no—
1579C22⋊C4—342no—
1580C22⋊C4—342no—
1581C22⋊C4—342no—
1582C22⋊C4—342no—
1583C22⋊C4—342no—
1584C22⋊C4—342no—
1585C22⋊C4—342no—
1586C22⋊C4—342no—
1587C22⋊C4—342no—
1588C22⋊C4—342no—
1589C22⋊C4—342no—
1590C22⋊C4—342no—
1591C22⋊C4—342no—
1592C22⋊C4—342no—
1593C22⋊C4—342no—
1594C22⋊C4—342no—
1595C22⋊C4—342no—
1596C22⋊C4—342no—
1597C22⋊C4—342no—
1598C22⋊C4—681no—
1599C22⋊C4—681no—
1600C22⋊C4—681no—
1601C22⋊C4—681no—
1602C22⋊C4—681no—
1603C22⋊C4—681no—
1604C22⋊C4—681no—
1605C22⋊C4—681no—
1606C22⋊C4—681no—
1607C22⋊C4—681no—
1608C22⋊C4—681no—
1609C22⋊C4—681no—
1610C22⋊C4—681no—
1611C22⋊C4—681no—
1612C22⋊C4—681no—
1613C22⋊C4—681no—
1614C22⋊C4—681no—
1615C22⋊C4—681no—
1616C22⋊C4—681no—
1617C42—342no—
1618C42—342no—
1619C23—21no—
1620C23—21no—
1621C23—21no—
1622C23—21no—
1623C23—21no—
1624C23—21no—
1625C23—21no—
1626C23—21no—
1627C23—21no—
1628C23—21no—
1629C23—21no—
1630C23—21no—
1631C23—21no—
1632C23—21no—
1633C23—21no—
1634C23—21no—
1635C23—21no—
1636C23—21no—
1637C23—21no—
1638C23—21no—
1639C23—21no—
1640C23—21no—
1641C23—21no—
1642C23—21no—
1643C23—21no—
1644C23—21no—
1645C23—172no—
1646C23—172no—
1647C23—172no—
1648C23—172no—
1649C23—172no—
1650C23—348no—
1651C23—348no—
1652C23—341no—
1653C23—341no—
1654C23—341no—
1655C23—341no—
1656C23—341no—
1657C23—341no—
1658C23—341no—
1659C23—341no—
1660C23—341no—
1661C23—341no—
1662C23—341no—
1663C23—341no—
1664C23—341no—
1665C23—341no—
1666C23—341no—
1667C23—341no—
1668C23—341no—
1669C23—341no—
1670C23—341no—
1671C23—341no—
1672C23—341no—
1673C23—341no—
1674C23—341no—
1675C23—341no—
1676C23—341no—
1677C23—341no—
1678C23—341no—
1679C23—341no—
1680C23—341no—
1681C23—341no—
1682C23—684no—
1683C23—684no—
1684C23—684no—
1685C23—684no—
1686C23—684no—
1687C23—684no—
1688C23—684no—
1689C23—684no—
1690C23—684no—
1691C23—1362no—
1692C23—1362no—
1693C23—1362no—
1694C23—1362no—
1695C23—1362no—
1696C23—1362no—
1697C23—1362no—
1698C23—1362no—
1699C23—1362no—
1700C23—1362no—
1701C23C2×D4×D1712yes—
1702C23C2×D4×D1712yes—
1703C23C24×D1711yescharacteristic
1704Q8—684no—
1705D4—44no—
1706D4—44no—
1707D4—82no—
1708D4—82no—
1709D4—82no—
1710D4—82no—
1711D4—684no—
1712D4—684no—
1713D4—684no—
1714D4—684no—
1715D4—684no—
1716D4—684no—
1717D4—684no—
1718D4—684no—
1719D4—684no—
1720D4—1362no—
1721D4—1362no—
1722D4—1362no—
1723D4—1362no—
1724D4—1362no—
1725D4—1362no—
1726D4—1362no—
1727D4—1362no—
1728D4—1362no—
1729D4—1362no—
1730D4—1362no—
1731D4—1362no—
1732C2×C4—21no—
1733C2×C4—21no—
1734C2×C4—21no—
1735C2×C4—21no—
1736C2×C4—21no—
1737C2×C4—21no—
1738C2×C4—21no—
1739C2×C4—21no—
1740C2×C4—21no—
1741C2×C4—21no—
1742C2×C4—21no—
1743C2×C4—21no—
1744C2×C4—21no—
1745C2×C4—21no—
1746C2×C4—21no—
1747C2×C4—21no—
1748C2×C4—21no—
1749C2×C4—21no—
1750C2×C4—21no—
1751C2×C4—21no—
1752C2×C4—21no—
1753C2×C4—21no—
1754C2×C4—21no—
1755C2×C4—21no—
1756C2×C4—21no—
1757C2×C4—21no—
1758C2×C4—21no—
1759C2×C4—21no—
1760C2×C4—21no—
1761C2×C4—21no—
1762C2×C4—21no—
1763C2×C4—21no—
1764C2×C4—44no—
1765C2×C4—44no—
1766C2×C4—82no—
1767C2×C4—172no—
1768C2×C4—172no—
1769C2×C4—172no—
1770C2×C4—348no—
1771C2×C4—341no—
1772C2×C4—341no—
1773C2×C4—341no—
1774C2×C4—341no—
1775C2×C4—341no—
1776C2×C4—341no—
1777C2×C4—341no—
1778C2×C4—341no—
1779C2×C4—341no—
1780C2×C4—341no—
1781C2×C4—341no—
1782C2×C4—341no—
1783C2×C4—341no—
1784C2×C4—341no—
1785C2×C4—341no—
1786C2×C4—341no—
1787C2×C4—341no—
1788C2×C4—341no—
1789C2×C4—341no—
1790C2×C4—341no—
1791C2×C4—341no—
1792C2×C4—341no—
1793C2×C4—341no—
1794C2×C4—341no—
1795C2×C4—341no—
1796C2×C4—341no—
1797C2×C4—341no—
1798C2×C4—341no—
1799C2×C4—341no—
1800C2×C4—341no—
1801C2×C4—684no—
1802C2×C4—684no—
1803C2×C4—684no—
1804C2×C4—684no—
1805C2×C4—684no—
1806C2×C4—684no—
1807C2×C4—684no—
1808C2×C4—1362no—
1809C2×C4—1362no—
1810C2×C4—1362no—
1811C2×C4C2×D4×D1712yes—
1812C22—22no—
1813C22—22no—
1814C22—22no—
1815C22—22no—
1816C22—22no—
1817C22—22no—
1818C22—41no—
1819C22—41no—
1820C22—41no—
1821C22—41no—
1822C22—41no—
1823C22—41no—
1824C22—41no—
1825C22—41no—
1826C22—41no—
1827C22—41no—
1828C22—41no—
1829C22—41no—
1830C22—41no—
1831C22—41no—
1832C22—41no—
1833C22—41no—
1834C22—41no—
1835C22—41no—
1836C22—41no—
1837C22—41no—
1838C22—41no—
1839C22—41no—
1840C22—174no—
1841C22—342no—
1842C22—342no—
1843C22—342no—
1844C22—342no—
1845C22—342no—
1846C22—342no—
1847C22—342no—
1848C22—342no—
1849C22—342no—
1850C22—342no—
1851C22—342no—
1852C22—342no—
1853C22—6816no—
1854C22—681no—
1855C22—681no—
1856C22—681no—
1857C22—681no—
1858C22—681no—
1859C22—681no—
1860C22—681no—
1861C22—681no—
1862C22—681no—
1863C22—681no—
1864C22—681no—
1865C22—681no—
1866C22—681no—
1867C22—681no—
1868C22—681no—
1869C22—681no—
1870C22—681no—
1871C22—681no—
1872C22—681no—
1873C22—681no—
1874C22—681no—
1875C22—681no—
1876C22—1368no—
1877C22—1368no—
1878C22C22×D4×D1711yescharacteristic
1879C22H(5,𝔽2)×D1711yescharacteristic
1880C22H(5,𝔽2)×D1711yescharacteristic
1881C22H(5,𝔽2)×D1711yescharacteristic
1882C22H(5,𝔽2)×D1711yescharacteristic
1883C22#1176364511yescharacteristic
1884C22#1176364511yescharacteristic
1885C4—22no—
1886C4—41no—
1887C4—41no—
1888C4—41no—
1889C4—41no—
1890C4—41no—
1891C4—41no—
1892C4—41no—
1893C4—41no—
1894C4—41no—
1895C4—41no—
1896C4—342no—
1897C4—342no—
1898C4—342no—
1899C4—681no—
1900C4—681no—
1901C4—681no—
1902C4—681no—
1903C4—681no—
1904C4—681no—
1905C4—681no—
1906C4—681no—
1907C2—42no—
1908C2—42no—
1909C2—81no—
1910C2—81no—
1911C2—344no—
1912C2—682no—
1913C2—682no—
1914C2—1361no—
1915C2—1361no—
1916C2D17×#53411yescharacteristic
1917C2#1454254411yescharacteristic
1918C2#1454254411yescharacteristic
1919C2#1454293711yescharacteristic
1920C2#1454294211yescharacteristic
1921C2#1454309111yescharacteristic
1922C2#1454309911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2688C2
hypercenter#2688D17
hypocenterC17#36737
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2688

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11763375C2semidirect
2. C2×#11763367C2semidirect
3. #14537065C2semidirect
4. #14537065C2semidirect
5. #14535618C2semidirect
6. #14535512C2semidirect
7. #14535507C2semidirect
8. #14535505C2semidirect
9. #14535218C2semidirect
10. #14535196C2semidirect
11. #14535190C2semidirect
12. #14535161C2semidirect
13. #14535054C2semidirect
14. #14535052C2semidirect
15. #14535016C2semidirect
16. #14535014C2semidirect
17. #14534995C2semidirect
18. #14534994C2semidirect
19. #14534989C2semidirect
20. #14534519C2semidirect
21. #14534517C2semidirect
22. #14533231C2semidirect
23. #14533223C2semidirect
24. #14532393C2semidirect
25. #14532391C2semidirect
26. #14532183C2semidirect
27. #14532182C2semidirect
28. #14532153C2semidirect
29. #14532151C2semidirect
30. D17×#386C2semidirect
31. C17×#2688C2semidirect
32. C22×#63252C22semidirect
35. C23×C4×D17C22semidirect
39. C2×#10587626C22semidirect
41. C2×#10587571C22semidirect
44. C2×#10587615C22semidirect
47. C2×#10587621C22semidirect
54. C2×#10587570C22semidirect
55. C2×#10587570C22semidirect
58. C2×#10587625C22semidirect
59. C2×#10587625C22semidirect
61. C2×#10587624C22semidirect
65. C2×#10587568C22semidirect
66. C2×#10587568C22semidirect
70. C2×#10587623C22semidirect
71. C2×#10587623C22semidirect
72. C2×#10587578C22semidirect
76. C2×C22⋊C4×D17C22semidirect
77. #11762749C22semidirect
78. #11762745C22semidirect
79. #11762744C22semidirect
80. #11762740C22semidirect
81. #11762739C22semidirect
82. #11762738C22semidirect
83. #11762738C22semidirect
84. #11762738C22semidirect
85. #11762738C22semidirect
86. #11762736C22semidirect
87. #11762736C22semidirect
88. #11762735C22semidirect
89. #11762734C22semidirect
90. #11762730C22semidirect
91. #11762729C22semidirect
92. #11762727C22semidirect
93. #11762727C22semidirect
94. #11762727C22semidirect
95. #11762727C22semidirect
96. #11762725C22semidirect
97. #11762725C22semidirect
98. #11762724C22semidirect
99. #11762724C22semidirect
100. #11762724C22semidirect
101. #11762724C22semidirect
102. #11762724C22semidirect
103. #11762724C22semidirect
104. #11762724C22semidirect
105. #11762724C22semidirect
106. #11762723C22semidirect
107. #11762723C22semidirect
108. #11762723C22semidirect
109. #11762722C22semidirect
110. #11762721C22semidirect
111. #11762719C22semidirect
112. #11762718C22semidirect
113. #11762718C22semidirect
114. #11762718C22semidirect
115. #11762717C22semidirect
116. #11762717C22semidirect
117. #11762717C22semidirect
118. #11762717C22semidirect
119. #11762703C22semidirect
120. #11762703C22semidirect
121. #11762698C22semidirect
122. #11762698C22semidirect
123. #11762696C22semidirect
124. #11762696C22semidirect
125. #11762691C22semidirect
126. #11762691C22semidirect
127. #11762689C22semidirect
129. #11762688C22semidirect
130. #11762688C22semidirect
131. #11762688C22semidirect
136. #11762687C22semidirect
137. #11762687C22semidirect
138. #11762687C22semidirect
139. #11762687C22semidirect
140. #11762687C22semidirect
141. #11762687C22semidirect
143. #11762686C22semidirect
146. #11762685C22semidirect
147. #11762685C22semidirect
148. #11762685C22semidirect
149. #11762685C22semidirect
150. #11762685C22semidirect
151. #11762685C22semidirect
152. #11762685C22semidirect
153. #11762685C22semidirect
154. #11762683C22semidirect
155. #11762683C22semidirect
156. #11762682C22semidirect
157. #11762682C22semidirect
158. #11762681C22semidirect
159. #11762680C22semidirect
160. #11762680C22semidirect
161. #11762670C22semidirect
162. #11762668C22semidirect
163. #11762668C22semidirect
164. #11762668C22semidirect
165. #11762668C22semidirect
166. #11762668C22semidirect
167. #11762668C22semidirect
168. #11762667C22semidirect
169. #11762667C22semidirect
170. #11762664C22semidirect
171. #11762664C22semidirect
172. #95×D17C22semidirect
173. #95×D17C22semidirect
175. C2×C17×#121C22semidirect
176. C17×#400C22semidirect
177. C17×#397C22semidirect
178. C17×#397C22semidirect
179. C17×#394C22semidirect
180. C17×#392C22semidirect
181. C17×#392C22semidirect
182. C17×#386C22semidirect
183. C17×#386C22semidirect
184. C17×#386C22semidirect
185. C17×#386C22semidirect
186. C17×#386C22semidirect
187. C17×#385C22semidirect
188. C17×#381C22semidirect
222. C2×D4×D17D4semidirect
860. #2688D17semidirect
1008. C2×#121C2×D17semidirect
1025. #400C2×D17semidirect
1038. #397C2×D17semidirect
1039. #397C2×D17semidirect
1059. #394C2×D17semidirect
1070. #392C2×D17semidirect
1071. #392C2×D17semidirect
1107. #386C2×D17semidirect
1108. #386C2×D17semidirect
1109. #386C2×D17semidirect
1110. #386C2×D17semidirect
1111. #386C2×D17semidirect
1119. #385C2×D17semidirect
1121. #381C2×D17semidirect
1358. C17#36737semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117633752
C2×#117633672
#145370652
#145356182
#145355122
#145355072
#145355052
#145352182
#145351962
#145351902
#145351612
#145350542
#145350522
#145350162
#145350142
#145349952
#145349942
#145349892
#145345192
#145345172
#145332312
#145332232
#145323932
#145323912
#145321832
#145321822
#145321532
#145321512
D17×#3862
C17×#26882
#3673717