Finite Group Databasebeta

← #17241389

Subgroups — #17241389

Order 4352.

2644 conjugacy classes of subgroups.

The subgroup lattice has 1818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763392C211yesmaximal, characteristic, complemented
2C2×#11763318C211yesmaximal, characteristic, complemented
3#14537079C211yesmaximal, characteristic, complemented
4#14537065C211yesmaximal, characteristic, complemented
5#14535458C211yesmaximal, characteristic, complemented
6#14535413C211yesmaximal, characteristic, complemented
7#14535383C211yesmaximal, characteristic, complemented
8#14535372C211yesmaximal, characteristic, complemented
9#14535207C211yesmaximal, characteristic, complemented
10#14535150C211yesmaximal, characteristic, complemented
11#14535140C211yesmaximal, characteristic, complemented
12#14535137C211yesmaximal, characteristic, complemented
13#14535117C211yesmaximal, characteristic, complemented
14#14535115C211yesmaximal, characteristic, complemented
15#14535111C211yesmaximal, characteristic, complemented
16#14535108C211yesmaximal, characteristic, complemented
17#14535037C211yesmaximal, characteristic, complemented
18#14535008C211yesmaximal, characteristic, complemented
19#14535002C211yesmaximal, characteristic, complemented
20#14534995C211yesmaximal, characteristic, complemented
21#14534675C211yesmaximal, characteristic, complemented
22#14534633C211yesmaximal, characteristic, complemented
23#14534469C211yesmaximal, characteristic, complemented
24#14534410C211yesmaximal, characteristic, complemented
25#14534379C211yesmaximal, characteristic, complemented
26#14533753C211yesmaximal, characteristic, complemented
27#14533670C211yesmaximal, characteristic, complemented
28#14532129C211yesmaximal, characteristic, complemented
29#14532105C211yesmaximal, characteristic, complemented
30#14531424C211yesmaximal, characteristic, complemented
31C17×#2600C211yesmaximal, characteristic, complemented
32C22×#63252C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic, complemented
34#11763392—28no—
35C2×#10587626C2211yescharacteristic
36C2×#10587584C2211yescharacteristic, complemented
37C2×#10587562C2211yescharacteristic, complemented
38C2×#10587561C2211yescharacteristic
39C2×#10587571C2211yescharacteristic, complemented
40C2×#10587571C2211yescharacteristic, complemented
41#11763318—28no—
42C2×#10587580C2211yescharacteristic
43C2×#10587580C2211yescharacteristic
44C2×#10587580C2211yescharacteristic, complemented
45C2×#10587615C2211yescharacteristic, complemented
46C2×#10587569C2211yescharacteristic
47C2×#10587621C2211yescharacteristic
48C2×#10587610C2211yescharacteristic, complemented
49C2×#10587582C2211yescharacteristic, complemented
50C2×#10587564C2211yescharacteristic, complemented
51C2×#10587564C2211yescharacteristic, complemented
52C2×#10587616C2211yescharacteristic
53C2×#10587616C2211yescharacteristic, complemented
54C2×#10587570C2211yescharacteristic
55C2×#10587570C2211yescharacteristic
56C2×#10587570C2211yescharacteristic
57C2×#10587625C2211yescharacteristic
58C2×#10587625C2211yescharacteristic
59C2×#10587625C2211yescharacteristic
60C2×#10587568C2211yescharacteristic
61C2×#10587568C2211yescharacteristic
62C2×#10587568C2211yescharacteristic
63C2×#10587568C2211yescharacteristic
64C2×#10587568C2211yescharacteristic, complemented
65C2×#10587568C2211yescharacteristic, complemented
66C2×#10587623C2211yescharacteristic
67C2×#10587623C2211yescharacteristic
68C2×#10587623C2211yescharacteristic, complemented
69C2×#10587623C2211yescharacteristic, complemented
70C2×C4×D68C2211yescharacteristic, complemented
71C2×C4×C22⋊D17C2211yescharacteristic
72C2×C4×C22⋊D17C2211yescharacteristic, complemented
73C2×#10587558C2211yescharacteristic, complemented
74C22×#63227C2211yescharacteristic, complemented
75#11762751C2211yescharacteristic, complemented
76#11762744C2211yescharacteristic, complemented
77#11762743C2211yescharacteristic, complemented
78#11762742C2211yescharacteristic, complemented
79#11762740C2211yescharacteristic, complemented
80#11762738C2211yescharacteristic, complemented
81#11762738C2211yescharacteristic, complemented
82#11762733C2211yescharacteristic, complemented
83#11762733C2211yescharacteristic, complemented
84#11762733C2211yescharacteristic, complemented
85#11762731C2211yescharacteristic, complemented
86#11762731C2211yescharacteristic, complemented
87#11762731C2211yescharacteristic, complemented
88#11762729C2211yescharacteristic, complemented
89#11762727C2211yescharacteristic
90#11762727C2211yescharacteristic
91#11762727C2211yescharacteristic, complemented
92#11762727C2211yescharacteristic, complemented
93#11762726C2211yescharacteristic
94#11762726C2211yescharacteristic, complemented
95#11762725C2211yescharacteristic
96#11762725C2211yescharacteristic
97#11762725C2211yescharacteristic, complemented
98#11762725C2211yescharacteristic, complemented
99#11762724C2211yescharacteristic
100#11762724C2211yescharacteristic
101#11762724C2211yescharacteristic, complemented
102#11762724C2211yescharacteristic, complemented
103#11762724C2211yescharacteristic, complemented
104#11762724C2211yescharacteristic, complemented
105#11762723C2211yescharacteristic, complemented
106#11762722C2211yescharacteristic, complemented
107#11762722C2211yescharacteristic, complemented
108#11762722C2211yescharacteristic, complemented
109#11762719C2211yescharacteristic
110#11762719C2211yescharacteristic
111#11762719C2211yescharacteristic
112#11762719C2211yescharacteristic
113#11762718C2211yescharacteristic
114#11762718C2211yescharacteristic
115#11762718C2211yescharacteristic, complemented
116#11762718C2211yescharacteristic, complemented
117#11762717C2211yescharacteristic
118#11762717C2211yescharacteristic, complemented
119#11762715C2211yescharacteristic, complemented
120#11762713C2211yescharacteristic, complemented
121#11762711C2211yescharacteristic, complemented
122#11762710C2211yescharacteristic
123#11762710C2211yescharacteristic
124#11762710C2211yescharacteristic, complemented
125#11762709C2211yescharacteristic
126#11762709C2211yescharacteristic
127#11762709C2211yescharacteristic
128#11762709C2211yescharacteristic, complemented
129#11762709C2211yescharacteristic, complemented
130#11762706C2211yescharacteristic, complemented
131#11762706C2211yescharacteristic, complemented
132#11762706C2211yescharacteristic, complemented
133#11762703C2211yescharacteristic, complemented
134#11762703C2211yescharacteristic, complemented
135#11762701C2211yescharacteristic, complemented
136#11762701C2211yescharacteristic, complemented
137#11762701C2211yescharacteristic, complemented
138#11762700C2211yescharacteristic, complemented
139#11762700C2211yescharacteristic, complemented
140#11762698C2211yescharacteristic, complemented
141#11762698C2211yescharacteristic, complemented
142#11762698C2211yescharacteristic, complemented
143#11762697C2211yescharacteristic, complemented
144#11762697C2211yescharacteristic, complemented
145#11762688C2211yescharacteristic
146#11762688C2211yescharacteristic
147#11762687C2211yescharacteristic
148#11762687C2211yescharacteristic
149#11762687C2211yescharacteristic
150#11762687C2211yescharacteristic
151#11762687C2211yescharacteristic, complemented
152#11762687C2211yescharacteristic, complemented
153#11762686C2211yescharacteristic
154#11762686C2211yescharacteristic
155#11762686C2211yescharacteristic, complemented
156#11762685C2211yescharacteristic, complemented
157#11762685C2211yescharacteristic, complemented
158#11762685C2211yescharacteristic, complemented
159#11762681C2211yescharacteristic, complemented
160#11762680C2211yescharacteristic, complemented
161#11762680C2211yescharacteristic, complemented
162#11762680C2211yescharacteristic, complemented
163#11762671C2211yescharacteristic, complemented
164#11762671C2211yescharacteristic, complemented
165#11762670C2211yescharacteristic, complemented
166#11762669C2211yescharacteristic, complemented
167#11762668C2211yescharacteristic, complemented
168#11762668C2211yescharacteristic, complemented
169#11762667C2211yescharacteristic, complemented
170#11762664C2211yescharacteristic, complemented
171#11762664C2211yescharacteristic, complemented
172#11762660C2211yescharacteristic, complemented
173#11762654C2211yescharacteristic, complemented
174C2×C4×D4×C17C2211yescharacteristic
175C2×C4×D4×C17C2211yescharacteristic, complemented
176C17×#397C2211yescharacteristic, complemented
177C17×#394C2211yescharacteristic
178C17×#394C2211yescharacteristic, complemented
179C17×#392C2211yescharacteristic
180C17×#388C2211yescharacteristic, complemented
181C17×#388C2211yescharacteristic, complemented
182C17×#387C2211yescharacteristic, complemented
183C17×#387C2211yescharacteristic, complemented
184C17×#386C2211yescharacteristic, complemented
185C17×#386C2211yescharacteristic, complemented
186C17×#385C2211yescharacteristic, complemented
187C17×#385C2211yescharacteristic, complemented
188C17×#381C2211yescharacteristic, complemented
189C24×D17C2311yescharacteristic
190C24×D17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C23×C4×C17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C22×C22⋊D17C2311yescharacteristic
205C22×C22⋊D17C2311yescharacteristic
206C22×C22⋊D17C2311yescharacteristic
207C22×C22⋊D17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C23×Dic17C2311yescharacteristic
210C2×#63252—24no—
211C2×#63252—42no—
212C2×#63252—42no—
213C22×D68C2311yescharacteristic
214C22×D68C2311yescharacteristic
215C22×D68C2311yescharacteristic
216C22×D68C2311yescharacteristic
217C22×D68C2311yescharacteristic
218C22×D68C2311yescharacteristic
219C22×D68C2311yescharacteristic
220C22×D68C2311yescharacteristic
221C22×C4×D17—24no—
222C22×C4×D17—42no—
223C22×C4×D17—42no—
224C22×C4×D17C2311yescharacteristic
225C22×C4×D17C2311yescharacteristic
226C22×C4×D17C2311yescharacteristic
227C22×C4×D17C2311yescharacteristic
228C22×C4×D17C2311yescharacteristic
229C22×Dic34C2311yescharacteristic
230C22×Dic34C2311yescharacteristic
231C4×D4×C17—24no—
232C4×D4×C17—24no—
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C4⋊C4×C17C2311yescharacteristic
235C2×C4⋊C4×C17C2311yescharacteristic
236C2×C4⋊C4×C17C2311yescharacteristic
237C2×C4⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C22⋊C4×C17C2311yescharacteristic
247C2×C22⋊C4×C17C2311yescharacteristic
248C2×C22⋊C4×C17C2311yescharacteristic
249C2×C22⋊C4×C17C2311yescharacteristic
250C2×C42×C17C2311yescharacteristic
251C2×C42×C17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261#10587626—42no—
262#10587625—24no—
263#10587625—24no—
264#10587625—42no—
265#10587623—24no—
266#10587623—24no—
267#10587623—42no—
268#10587623—42no—
269#10587621—42no—
270#10587616—24no—
271#10587616—42no—
272#10587615—24no—
273C4×C22⋊D17—24no—
274C4×C22⋊D17D418yescomplemented
275C2×#63227—24no—
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×#63227C2311yescharacteristic
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×C4⋊Dic17C2311yescharacteristic
316C2×C4⋊Dic17C2311yescharacteristic
317C2×C4⋊Dic17C2311yescharacteristic
318C2×C4⋊Dic17C2311yescharacteristic
319#10587610—42no—
320C2×#63225C2311yescharacteristic
321C2×#63225C2311yescharacteristic
322C2×#63225C2311yescharacteristic
323C2×#63225C2311yescharacteristic
324C2×#63225C2311yescharacteristic
325C2×#63225C2311yescharacteristic
326C2×#63225C2311yescharacteristic
327C2×#63225C2311yescharacteristic
328C2×#63225C2311yescharacteristic
329C2×#63225C2311yescharacteristic
330C2×#63225C2311yescharacteristic
331C2×#63225C2311yescharacteristic
332C2×#63225C2311yescharacteristic
333C2×#63225C2311yescharacteristic
334C2×#63225C2311yescharacteristic
335C2×C4×Dic17C2311yescharacteristic
336C2×C4×Dic17C2311yescharacteristic
337C2×C4×Dic17C2311yescharacteristic
338C2×C4×Dic17C2311yescharacteristic
339C2×C4×Dic17C2311yescharacteristic
340#10587584—24no—
341#10587582—24no—
342#10587580—24no—
343#10587580—24no—
344#10587580—42no—
345#10587571—24no—
346#10587571—42no—
347#10587570—24no—
348#10587570—24no—
349#10587570—42no—
350#10587569—24no—
351#10587568—24no—
352#10587568—24no—
353#10587568—42no—
354#10587568—42no—
355#10587568—42no—
356#10587568—42no—
357#10587564—24no—
358#10587564—24no—
359#10587562—24no—
360#10587561—24no—
361C4×D68—24no—
362#10587558—24no—
363C17×#95C2311yescharacteristic
364C17×#95C2311yescharacteristic
365C17×#95C2311yescharacteristic
366C17×#95C2311yescharacteristic
367C17×#95C2311yescharacteristic
368C17×#95C2311yescharacteristic
369C17×#95C2311yescharacteristic
370C17×#95C2311yescharacteristic
371C17×#95C2311yescharacteristic
372C17×#95C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
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
391C24×C17C2411yescharacteristic
392C24×C17C2411yescharacteristic
393C24×C17C2411yescharacteristic
394C23×D17—22no—
395C23×D17—22no—
396C23×D17—22no—
397C23×D17—22no—
398C23×D17—41no—
399C23×D17—41no—
400C23×D17—41no—
401C23×D17—41no—
402C23×D17—41no—
403C23×D17—41no—
404C23×D17—41no—
405C23×D17—41no—
406C23×D17—41no—
407C23×D17—41no—
408C23×D17C2411yescharacteristic
409C23×D17C2411yescharacteristic
410C23×D17C2411yescharacteristic
411C23×D17C2411yescharacteristic
412C23×D17C2411yescharacteristic
413C2×D4×C17—22no—
414C2×D4×C17—22no—
415C2×D4×C17—22no—
416C2×D4×C17—22no—
417C2×D4×C17—41no—
418C2×D4×C17—41no—
419C2×D4×C17—41no—
420C2×D4×C17—41no—
421C2×D4×C17—41no—
422C22×C4×C17—22no—
423C22×C4×C17—22no—
424C22×C4×C17—41no—
425C22×C4×C17—41no—
426C22×C4×C17—41no—
427C22×C4×C17—41no—
428C22×C4×C17—41no—
429C22×C4×C17—41no—
430C22×C4×C17C2×D414yes—
431C22×C4×C17C2411yescharacteristic
432C22×C4×C17C2411yescharacteristic
433C22×C4×C17C2411yescharacteristic
434C22×C4×C17C2411yescharacteristic
435C22×C4×C17C2411yescharacteristic
436C22×C4×C17C2411yescharacteristic
437C22×C4×C17C2411yescharacteristic
438C22×C4×C17C2411yescharacteristic
439C22×C4×C17C2411yescharacteristic
440C22×C4×C17C2411yescharacteristic
441C22×C4×C17C2411yescharacteristic
442C22×C4×C17C2411yescharacteristic
443C2×C22⋊D17—22no—
444C2×C22⋊D17—22no—
445C2×C22⋊D17—22no—
446C2×C22⋊D17—22no—
447C2×C22⋊D17—22no—
448C2×C22⋊D17—22no—
449C2×C22⋊D17—22no—
450C2×C22⋊D17—22no—
451C2×C22⋊D17—22no—
452C2×C22⋊D17—22no—
453C2×C22⋊D17—22no—
454C2×C22⋊D17—22no—
455C2×C22⋊D17—41no—
456C2×C22⋊D17—41no—
457C2×C22⋊D17—41no—
458C2×C22⋊D17—41no—
459C2×C22⋊D17—41no—
460C2×C22⋊D17—41no—
461C2×C22⋊D17—41no—
462C2×C22⋊D17—41no—
463C2×C22⋊D17—41no—
464C2×C22⋊D17—41no—
465C2×C22⋊D17—41no—
466C2×C22⋊D17—41no—
467C2×C22⋊D17—41no—
468C2×C22⋊D17—41no—
469C2×C22⋊D17—41no—
470C2×C22⋊D17—41no—
471C2×C22⋊D17—41no—
472C2×C22⋊D17—41no—
473C2×C22⋊D17—41no—
474C2×C22⋊D17—41no—
475C2×C22⋊D17C2×D414yes—
476C22×Dic17—22no—
477C22×Dic17—22no—
478C22×Dic17—22no—
479C22×Dic17—41no—
480C22×Dic17—41no—
481C22×Dic17—41no—
482C22×Dic17C2411yescharacteristic
483C22×Dic17C2411yescharacteristic
484C22×Dic17C2411yescharacteristic
485C22×Dic17C2411yescharacteristic
486C22×Dic17C2411yescharacteristic
487C22×Dic17C2411yescharacteristic
488C22×Dic17C2411yescharacteristic
489C22×Dic17C2411yescharacteristic
490C22×Dic17C2411yescharacteristic
491C22×Dic17C2411yescharacteristic
492C22×Dic17C2411yescharacteristic
493#63252—416no—
494C2×D68—22no—
495C2×D68—22no—
496C2×D68—22no—
497C2×D68—22no—
498C2×D68—22no—
499C2×D68—22no—
500C2×D68—22no—
501C2×D68—41no—
502C2×D68—41no—
503C2×D68—41no—
504C2×D68—41no—
505C2×D68—41no—
506C2×D68—41no—
507C2×D68—41no—
508C2×D68—41no—
509C2×D68—41no—
510C2×D68—41no—
511C2×D68—41no—
512C2×D68—41no—
513C2×D68—41no—
514C2×D68—41no—
515C2×D68—41no—
516C2×D68—41no—
517C2×D68—41no—
518C2×C4×D17—22no—
519C2×C4×D17—22no—
520C2×C4×D17—22no—
521C2×C4×D17—22no—
522C2×C4×D17—22no—
523C2×C4×D17—22no—
524C2×C4×D17—22no—
525C2×C4×D17—22no—
526C2×C4×D17—416no—
527C2×C4×D17—41no—
528C2×C4×D17—41no—
529C2×C4×D17—41no—
530C2×C4×D17—41no—
531C2×C4×D17—41no—
532C2×C4×D17—41no—
533C2×C4×D17C2×D414yes—
534C2×Dic34—22no—
535C2×Dic34—22no—
536C2×Dic34—22no—
537C2×Dic34—41no—
538C2×Dic34—41no—
539C2×Dic34—41no—
540C4⋊C4×C17—22no—
541C4⋊C4×C17—22no—
542C4⋊C4×C17—41no—
543C4⋊C4×C17—41no—
544C4⋊C4×C17—41no—
545C22⋊C4×C17—22no—
546C22⋊C4×C17—22no—
547C22⋊C4×C17—22no—
548C22⋊C4×C17—22no—
549C22⋊C4×C17—22no—
550C22⋊C4×C17—41no—
551C22⋊C4×C17—41no—
552C22⋊C4×C17—41no—
553C22⋊C4×C17—41no—
554C22⋊C4×C17—41no—
555C22⋊C4×C17—41no—
556C22⋊C4×C17—41no—
557C42×C17—22no—
558C42×C17—22no—
559C22⋊Dic17—22no—
560C22⋊Dic17—22no—
561C22⋊Dic17—22no—
562C22⋊Dic17—22no—
563C22⋊Dic17—22no—
564C22⋊Dic17—41no—
565C22⋊Dic17—41no—
566C22⋊Dic17—41no—
567C22⋊Dic17C2×D414yes—
568#63227—22no—
569#63227—22no—
570#63227—22no—
571#63227—22no—
572#63227—22no—
573#63227—22no—
574#63227—22no—
575#63227—22no—
576#63227—22no—
577#63227—22no—
578#63227—22no—
579#63227—22no—
580#63227—22no—
581#63227—22no—
582#63227—22no—
583#63227—22no—
584#63227—22no—
585#63227—41no—
586#63227—41no—
587#63227—41no—
588#63227—41no—
589#63227—41no—
590#63227—41no—
591#63227—41no—
592#63227—41no—
593#63227—41no—
594#63227—41no—
595#63227—41no—
596#63227—41no—
597#63227—41no—
598#63227—41no—
599#63227—41no—
600#63227—41no—
601#63227—41no—
602#63227—41no—
603#63227—41no—
604#63227—41no—
605#63227—41no—
606#63227C2×D414yes—
607C4⋊Dic17—22no—
608C4⋊Dic17—22no—
609C4⋊Dic17—41no—
610C4⋊Dic17—41no—
611#63225—22no—
612#63225—22no—
613#63225—22no—
614#63225—22no—
615#63225—22no—
616#63225—22no—
617#63225—22no—
618#63225—41no—
619#63225—41no—
620#63225—41no—
621#63225—41no—
622#63225—41no—
623#63225—41no—
624#63225—41no—
625#63225C2×D414yes—
626C4×Dic17—41no—
627C4×Dic17—41no—
628C4×Dic17—41no—
629C4×Dic17—41no—
630C4×Dic17C2×D414yes—
631#36724—171nomaximal, Sylow
632C23×C17—21no—
633C23×C17—21no—
634C23×C17—21no—
635C23×C17—21no—
636C23×C17—21no—
637C23×C17—21no—
638C23×C17—21no—
639C23×C17—21no—
640C23×C17—21no—
641C23×C17—21no—
642C23×C17—21no—
643C23×C17—21no—
644C23×C17—21no—
645C23×C17—21no—
646C23×C17—21no—
647C23×C17—21no—
648C23×C17—21no—
649C23×C17—21no—
650C23×C17—21no—
651C23×C17C22×D412yes—
652C23×C17H(5,𝔽2)12yes—
653C23×C17C2511yescharacteristic
654C22×D17—21no—
655C22×D17—21no—
656C22×D17—21no—
657C22×D17—21no—
658C22×D17—21no—
659C22×D17—21no—
660C22×D17—21no—
661C22×D17—21no—
662C22×D17—21no—
663C22×D17—21no—
664C22×D17—21no—
665C22×D17—21no—
666C22×D17—21no—
667C22×D17—21no—
668C22×D17—21no—
669C22×D17—21no—
670C22×D17—21no—
671C22×D17—21no—
672C22×D17—21no—
673C22×D17—21no—
674C22×D17—21no—
675C22×D17—21no—
676C22×D17—21no—
677C22×D17—21no—
678C22×D17—21no—
679C22×D17—21no—
680C22×D17—21no—
681C22×D17—21no—
682C22×D17—21no—
683C22×D17—21no—
684C22×D17—21no—
685C22×D17—21no—
686C22×D17—21no—
687C22×D17—44no—
688C22×D17—44no—
689C22×D17—44no—
690C22×D17—44no—
691C22×D17—44no—
692C22×D17—44no—
693C22×D17—44no—
694C22×D17—44no—
695C22×D17—82no—
696C22×D17—82no—
697C22×D17—82no—
698C22×D17—82no—
699C22×D17—82no—
700C22×D17—82no—
701C22×D17C22×D412yes—
702C22×D17H(5,𝔽2)12yes—
703D4×C17—44no—
704D4×C17—44no—
705D4×C17—82no—
706C2×C4×C17—21no—
707C2×C4×C17—21no—
708C2×C4×C17—21no—
709C2×C4×C17—21no—
710C2×C4×C17—21no—
711C2×C4×C17—21no—
712C2×C4×C17—21no—
713C2×C4×C17—21no—
714C2×C4×C17—21no—
715C2×C4×C17—21no—
716C2×C4×C17—21no—
717C2×C4×C17—21no—
718C2×C4×C17—21no—
719C2×C4×C17—21no—
720C2×C4×C17—21no—
721C2×C4×C17—21no—
722C2×C4×C17—21no—
723C2×C4×C17—21no—
724C2×C4×C17—21no—
725C2×C4×C17—21no—
726C2×C4×C17—21no—
727C2×C4×C17—21no—
728C2×C4×C17—21no—
729C2×C4×C17—21no—
730C2×C4×C17—21no—
731C2×C4×C17—21no—
732C2×C4×C17—21no—
733C2×C4×C17—21no—
734C2×C4×C17—21no—
735C2×C4×C17—21no—
736C2×C4×C17—21no—
737C2×C4×C17—21no—
738C2×C4×C17—21no—
739C2×C4×C17—21no—
740C2×C4×C17—44no—
741C2×C4×C17—44no—
742C2×C4×C17—82no—
743C2×C4×C17C22×D412yes—
744C2×C4×C17C22×D412yes—
745C22⋊D17—44no—
746C22⋊D17—44no—
747C22⋊D17—44no—
748C22⋊D17—44no—
749C22⋊D17—82no—
750C22⋊D17—82no—
751C22⋊D17—82no—
752C22⋊D17—82no—
753C22⋊D17—82no—
754C22⋊D17—82no—
755C22⋊D17—82no—
756C2×Dic17—21no—
757C2×Dic17—21no—
758C2×Dic17—21no—
759C2×Dic17—21no—
760C2×Dic17—21no—
761C2×Dic17—21no—
762C2×Dic17—21no—
763C2×Dic17—21no—
764C2×Dic17—21no—
765C2×Dic17—21no—
766C2×Dic17—21no—
767C2×Dic17—21no—
768C2×Dic17—21no—
769C2×Dic17—21no—
770C2×Dic17—21no—
771C2×Dic17—21no—
772C2×Dic17—21no—
773C2×Dic17—21no—
774C2×Dic17—21no—
775C2×Dic17—21no—
776C2×Dic17—21no—
777C2×Dic17—21no—
778C2×Dic17—21no—
779C2×Dic17—21no—
780C2×Dic17—21no—
781C2×Dic17—21no—
782C2×Dic17—21no—
783C2×Dic17—21no—
784C2×Dic17—21no—
785C2×Dic17—44no—
786C2×Dic17—82no—
787C2×Dic17C22×D412yes—
788C2×Dic17C22×D412yes—
789C2×Dic17C22×D412yes—
790C2×Dic17H(5,𝔽2)12yes—
791D68—44no—
792D68—44no—
793D68—82no—
794D68—82no—
795D68—82no—
796D68—82no—
797D68—82no—
798D68—82no—
799C4×D17—28no—
800C4×D17—44no—
801C4×D17—44no—
802C4×D17—44no—
803C4×D17—44no—
804Dic34—44no—
805Dic34—82no—
806C2×#538—171no—
807C2×#525—171no—
808#2849—171no—
809#2847—171no—
810#2705—171no—
811#2702—171no—
812#2700—171no—
813#2699—171no—
814#2687—171no—
815#2682—171no—
816#2681—171no—
817#2681—171no—
818#2679—171no—
819#2678—171no—
820#2678—171no—
821#2678—171no—
822#2672—171no—
823#2670—171no—
824#2669—171no—
825#2669—171no—
826#2635—171no—
827#2630—171no—
828#2610—171no—
829#2603—171no—
830#2601—171no—
831#2600D1711yescharacteristic, complemented
832#2544—171no—
833#2534—171no—
834#2407—171no—
835#2404—171no—
836#2319—171no—
837C22×C17—22no—
838C22×C17—22no—
839C22×C17—22no—
840C22×C17—22no—
841C22×C17—22no—
842C22×C17—22no—
843C22×C17—41no—
844C22×C17—41no—
845C22×C17—41no—
846C22×C17—41no—
847C22×C17—41no—
848C22×C17—41no—
849C22×C17—41no—
850C22×C17—41no—
851C22×C17—41no—
852C22×C17—41no—
853C22×C17—41no—
854C22×C17—41no—
855C22×C17—41no—
856C22×C17—41no—
857C22×C17—41no—
858C22×C17C23×D411yescharacteristic
859C22×C17C2×H(5,𝔽2)11yescharacteristic
860C22×C17C2×H(5,𝔽2)11yescharacteristic
861C22×C17C2×H(5,𝔽2)11yescharacteristic
862C22×C17#58511yescharacteristic
863C22×C17#58511yescharacteristic
864C22×C17#58511yescharacteristic
865C2×D17—22no—
866C2×D17—22no—
867C2×D17—22no—
868C2×D17—22no—
869C2×D17—22no—
870C2×D17—22no—
871C2×D17—416no—
872C2×D17—41no—
873C2×D17—41no—
874C2×D17—41no—
875C2×D17—41no—
876C2×D17—41no—
877C2×D17—41no—
878C2×D17—41no—
879C2×D17—41no—
880C2×D17—41no—
881C2×D17—41no—
882C2×D17—41no—
883C2×D17—41no—
884C2×D17—41no—
885C2×D17—41no—
886C2×D17—41no—
887C2×D17—41no—
888C2×D17—41no—
889C2×D17—41no—
890C2×D17—41no—
891C2×D17—41no—
892C2×D17—41no—
893C2×D17—41no—
894C2×D17—41no—
895C2×D17—41no—
896C2×D17—41no—
897C2×D17—41no—
898C2×D17—41no—
899C2×D17—41no—
900C2×D17—41no—
901C2×D17—88no—
902C4×C17—22no—
903C4×C17—22no—
904C4×C17—41no—
905C4×C17—41no—
906C4×C17—41no—
907C4×C17—41no—
908C4×C17—41no—
909C4×C17—41no—
910C4×C17—41no—
911C4×C17—41no—
912C4×C17—41no—
913C4×C17—41no—
914Dic17—22no—
915Dic17—22no—
916Dic17—22no—
917Dic17—22no—
918Dic17—41no—
919Dic17—41no—
920Dic17—41no—
921Dic17—41no—
922Dic17—41no—
923Dic17—41no—
924Dic17—41no—
925C22×#41—171no—
926C24×C4—171no—
927#538—348no—
928C2×#127—171no—
929C2×#126—171no—
930C2×#126—171no—
931C2×#124—171no—
932C2×#124—171no—
933C2×#124—171no—
934#525—348no—
935C2×#123—171no—
936C2×#123—171no—
937C2×#123—171no—
938C2×#123—171no—
939C2×#123—171no—
940C2×#123—171no—
941C2×C22⋊Q8—171no—
942C2×C22⋊Q8—171no—
943C2×C22⋊Q8—171no—
944C2×C22⋊Q8—171no—
945C2×#121—171no—
946C2×#121—171no—
947C2×#121—171no—
948C2×#121—171no—
949C2×#121—171no—
950C2×#121—171no—
951C2×#121—171no—
952C2×#121—171no—
953C2×#120—171no—
954C2×#120—171no—
955C2×#120—171no—
956C2×#120—171no—
957C2×#120—171no—
958C2×#120—171no—
959C2×#120—171no—
960C2×#120—171no—
961C2×#120—171no—
962C2×#120—171no—
963C2×C4×D4—171no—
964C2×C4×D4—171no—
965C2×C4×D4—171no—
966C2×C4×D4C2×D1711yescharacteristic
967C2×C4×D4C2×D1711yescharacteristic, complemented
968C2×#117—171no—
969C22×C22⋊C4—171no—
970#400—171no—
971#399—171no—
972#398—171no—
973#398—171no—
974#398—171no—
975#397—171no—
976#397—171no—
977#397C2×D1711yescharacteristic, complemented
978#396—171no—
979#396—171no—
980#396—171no—
981#396—171no—
982#396—171no—
983#396—171no—
984#395—171no—
985#394—171no—
986#394—171no—
987#394—171no—
988#394—171no—
989#394—171no—
990#394—171no—
991#394—171no—
992#394—171no—
993#394—171no—
994#394—171no—
995#394—171no—
996#394—171no—
997#394—171no—
998#394—171no—
999#394—171no—
1000#394—171no—
1001#394—171no—
1002#394C2×D1711yescharacteristic
1003#394C2×D1711yescharacteristic, complemented
1004#393—171no—
1005#393—171no—
1006#393—171no—
1007#392—171no—
1008#392—171no—
1009#392—171no—
1010#392—171no—
1011#392—171no—
1012#392—171no—
1013#392—171no—
1014#392—171no—
1015#392—171no—
1016#392—171no—
1017#392C2×D1711yescharacteristic
1018#391—171no—
1019#391—171no—
1020#390—171no—
1021#390—171no—
1022#390—171no—
1023#390—171no—
1024#390—171no—
1025#390—171no—
1026#390—171no—
1027#390—171no—
1028#390—171no—
1029#389—171no—
1030#389—171no—
1031#389—171no—
1032#388—171no—
1033#388—171no—
1034#388—171no—
1035#388—171no—
1036#388—171no—
1037#388—171no—
1038#388—171no—
1039#388—171no—
1040#388—171no—
1041#388—171no—
1042#388—171no—
1043#388—171no—
1044#388C2×D1711yescharacteristic, complemented
1045#388C2×D1711yescharacteristic, complemented
1046#387C2×D1711yescharacteristic, complemented
1047#387C2×D1711yescharacteristic, complemented
1048#386—171no—
1049#386—171no—
1050#386—171no—
1051#386—171no—
1052#386—171no—
1053#386—171no—
1054#386—171no—
1055#386—171no—
1056#386—171no—
1057#386—171no—
1058#386—171no—
1059#386—171no—
1060#386—171no—
1061#386—171no—
1062#386C2×D1711yescharacteristic, complemented
1063#386C2×D1711yescharacteristic, complemented
1064#385—171no—
1065#385—171no—
1066#385—171no—
1067#385—171no—
1068#385C2×D1711yescharacteristic, complemented
1069#385C2×D1711yescharacteristic, complemented
1070#381—171no—
1071#381—171no—
1072#381—171no—
1073#381C2×D1711yescharacteristic, complemented
1074#380—171no—
1075#380—171no—
1076#380—171no—
1077#380—171no—
1078#379—171no—
1079#379—171no—
1080C4×C4⋊C4—171no—
1081#376—171no—
1082C2×C17—42no—
1083C2×C17—42no—
1084C2×C17—81no—
1085C2×C17#344911yescharacteristic
1086C2×C17#348411yescharacteristic
1087C2×C17#348811yescharacteristic
1088C2×C17#353311yescharacteristic
1089C2×C17#353411yescharacteristic
1090C2×C17#354011yescharacteristic
1091C2×C17#354211yescharacteristic
1092D17—42no—
1093D17—42no—
1094D17—81no—
1095D17—81no—
1096D17—81no—
1097C25—171no—
1098C25—171no—
1099C2×#41—344no—
1100C2×#41—682no—
1101C2×#41—682no—
1102C22×Q8—171no—
1103C22×Q8—171no—
1104C22×D4—171no—
1105C22×D4—171no—
1106C22×D4—171no—
1107C22×D4—171no—
1108C22×D4—171no—
1109C22×D4—171no—
1110C22×D4—171no—
1111C22×D4—171no—
1112C22×D4—171no—
1113C22×D4—171no—
1114C22×D4—171no—
1115C22×D4—171no—
1116C22×D4—171no—
1117C22×D4—171no—
1118C22×D4—171no—
1119C22×D4—171no—
1120C22×D4—171no—
1121C22×D4—171no—
1122C22×D4—171no—
1123C22×D4C22×D1711yescharacteristic
1124C22×D4C22×D1711yescharacteristic
1125C22×D4C22×D1711yescharacteristic
1126C23×C4—171no—
1127C23×C4—171no—
1128C23×C4—171no—
1129C23×C4—171no—
1130C23×C4—171no—
1131C23×C4—171no—
1132C23×C4—171no—
1133C23×C4—344no—
1134C23×C4—682no—
1135C23×C4—682no—
1136C23×C4C22×D1711yescharacteristic
1137C23×C4C22×D1711yescharacteristic
1138C23×C4C22×D1711yescharacteristic
1139#127—682no—
1140#126—344no—
1141#126—344no—
1142#124—344no—
1143#124—344no—
1144#124—682no—
1145#123—344no—
1146#123—344no—
1147#123—344no—
1148#123—344no—
1149#123—682no—
1150#123—682no—
1151C22⋊Q8—344no—
1152C22⋊Q8—344no—
1153C22⋊Q8—344no—
1154C22⋊Q8—682no—
1155#121—344no—
1156#121—344no—
1157#121—344no—
1158#121—344no—
1159#121—344no—
1160#121—682no—
1161#121—682no—
1162#121—682no—
1163#120—344no—
1164#120—344no—
1165#120—344no—
1166#120—344no—
1167#120—682no—
1168#120—682no—
1169#120—682no—
1170#120—682no—
1171#120—682no—
1172#120—682no—
1173C4×D4—24no—
1174C4×D4—24no—
1175C4×D4—178no—
1176C4×D4—344no—
1177C4×D4—344no—
1178#117—344no—
1179C2×C4⋊C4—171no—
1180C2×C4⋊C4—171no—
1181C2×C4⋊C4—171no—
1182C2×C4⋊C4—171no—
1183C2×C4⋊C4—171no—
1184C2×C4⋊C4—171no—
1185C2×C4⋊C4—171no—
1186C2×C4⋊C4—171no—
1187C2×C4⋊C4—171no—
1188C2×C4⋊C4—171no—
1189C2×C4⋊C4—171no—
1190C2×C4⋊C4—171no—
1191C2×C4⋊C4—171no—
1192C2×C4⋊C4—171no—
1193C2×C4⋊C4—171no—
1194C2×C4⋊C4—171no—
1195C2×C4⋊C4—171no—
1196C2×C4⋊C4—171no—
1197C2×C4⋊C4—171no—
1198C2×C4⋊C4C22×D1711yescharacteristic
1199C2×C4⋊C4C22×D1711yescharacteristic
1200C2×C4⋊C4C22×D1711yescharacteristic
1201C2×C4⋊C4C22×D1711yescharacteristic
1202C2×C4⋊C4C22×D1711yescharacteristic
1203C2×C22⋊C4—171no—
1204C2×C22⋊C4—171no—
1205C2×C22⋊C4—171no—
1206C2×C22⋊C4—171no—
1207C2×C22⋊C4—171no—
1208C2×C22⋊C4—171no—
1209C2×C22⋊C4—171no—
1210C2×C22⋊C4—171no—
1211C2×C22⋊C4—171no—
1212C2×C22⋊C4—171no—
1213C2×C22⋊C4—171no—
1214C2×C22⋊C4—171no—
1215C2×C22⋊C4—171no—
1216C2×C22⋊C4—171no—
1217C2×C22⋊C4—171no—
1218C2×C22⋊C4—171no—
1219C2×C22⋊C4—171no—
1220C2×C22⋊C4—171no—
1221C2×C22⋊C4—171no—
1222C2×C22⋊C4—171no—
1223C2×C22⋊C4—171no—
1224C2×C22⋊C4—171no—
1225C2×C22⋊C4—171no—
1226C2×C22⋊C4—171no—
1227C2×C22⋊C4—171no—
1228C2×C22⋊C4—171no—
1229C2×C22⋊C4—171no—
1230C2×C22⋊C4—171no—
1231C2×C22⋊C4—171no—
1232C2×C22⋊C4—171no—
1233C2×C22⋊C4—171no—
1234C2×C22⋊C4—171no—
1235C2×C22⋊C4—171no—
1236C2×C22⋊C4—171no—
1237C2×C22⋊C4—171no—
1238C2×C22⋊C4—171no—
1239C2×C22⋊C4—171no—
1240C2×C22⋊C4—171no—
1241C2×C22⋊C4—171no—
1242C2×C22⋊C4—171no—
1243C2×C22⋊C4—171no—
1244C2×C22⋊C4—171no—
1245C2×C22⋊C4—171no—
1246C2×C22⋊C4—171no—
1247C2×C22⋊C4—171no—
1248C2×C22⋊C4—171no—
1249C2×C22⋊C4—171no—
1250C2×C22⋊C4—171no—
1251C2×C22⋊C4—344no—
1252C2×C22⋊C4C22×D1711yescharacteristic
1253C2×C22⋊C4C22×D1711yescharacteristic
1254C2×C22⋊C4C22×D1711yescharacteristic
1255C2×C22⋊C4C22×D1711yescharacteristic
1256C2×C22⋊C4C22×D1711yescharacteristic
1257C2×C22⋊C4C22×D1711yescharacteristic
1258C2×C22⋊C4C22×D1711yescharacteristic
1259C2×C22⋊C4C22×D1711yescharacteristic
1260C2×C22⋊C4C22×D1711yescharacteristic
1261C2×C22⋊C4C22×D1711yescharacteristic
1262C2×C22⋊C4C22×D1711yescharacteristic
1263C2×C22⋊C4C22×D1711yescharacteristic
1264C2×C42—171no—
1265C2×C42—171no—
1266C2×C42—171no—
1267C2×C42—171no—
1268C2×C42—171no—
1269C2×C42C22×D1711yescharacteristic
1270C2×C42C22×D1711yescharacteristic
1271#95—171no—
1272#95—171no—
1273#95—171no—
1274#95—171no—
1275#95—171no—
1276#95—171no—
1277#95—171no—
1278#95—171no—
1279#95—171no—
1280#95—171no—
1281#95—171no—
1282#95—171no—
1283#95—171no—
1284#95—171no—
1285#95—171no—
1286#95—171no—
1287#95—171no—
1288#95—171no—
1289#95C22×D1711yescharacteristic
1290#95C22×D1711yescharacteristic
1291#95C22×D1711yescharacteristic
1292#95C22×D1711yescharacteristic
1293#95C22×D1711yescharacteristic
1294#95C22×D1711yescharacteristic
1295#95C22×D1711yescharacteristic
1296#95C22×D1711yescharacteristic
1297#95C22×D1711yescharacteristic
1298#95C22×D1711yescharacteristic
1299C17#3672411yescharacteristic, complemented, Sylow
1300C24—171no—
1301C24—171no—
1302C24—171no—
1303C24—171no—
1304C24—171no—
1305C24—342no—
1306C24—342no—
1307C24—342no—
1308C24—342no—
1309C24—681no—
1310C24—681no—
1311C24—681no—
1312C24—681no—
1313C24—681no—
1314C24—681no—
1315C24—681no—
1316C24—681no—
1317C24—681no—
1318C24—681no—
1319C24C23×D1711yescharacteristic
1320C24C23×D1711yescharacteristic
1321C24C23×D1711yescharacteristic
1322#41—6816no—
1323C2×Q8—342no—
1324C2×Q8—342no—
1325C2×Q8—342no—
1326C2×Q8—681no—
1327C2×Q8—681no—
1328C2×Q8—681no—
1329C2×D4—22no—
1330C2×D4—22no—
1331C2×D4—22no—
1332C2×D4—22no—
1333C2×D4—41no—
1334C2×D4—41no—
1335C2×D4—41no—
1336C2×D4—41no—
1337C2×D4—41no—
1338C2×D4—174no—
1339C2×D4—342no—
1340C2×D4—342no—
1341C2×D4—342no—
1342C2×D4—342no—
1343C2×D4—342no—
1344C2×D4—342no—
1345C2×D4—342no—
1346C2×D4—342no—
1347C2×D4—342no—
1348C2×D4—342no—
1349C2×D4—342no—
1350C2×D4—342no—
1351C2×D4—342no—
1352C2×D4—342no—
1353C2×D4—342no—
1354C2×D4—342no—
1355C2×D4—342no—
1356C2×D4—342no—
1357C2×D4—342no—
1358C2×D4—681no—
1359C2×D4—681no—
1360C2×D4—681no—
1361C2×D4—681no—
1362C2×D4—681no—
1363C2×D4—681no—
1364C2×D4—681no—
1365C2×D4—681no—
1366C2×D4—681no—
1367C2×D4—681no—
1368C2×D4—681no—
1369C2×D4—681no—
1370C2×D4—681no—
1371C2×D4—681no—
1372C2×D4—681no—
1373C2×D4—681no—
1374C2×D4—681no—
1375C2×D4—681no—
1376C2×D4—681no—
1377C2×D4—681no—
1378C2×D4—681no—
1379C2×D4—681no—
1380C2×D4—681no—
1381C2×D4—681no—
1382C2×D4—681no—
1383C2×D4—681no—
1384C2×D4—681no—
1385C2×D4—681no—
1386C2×D4—681no—
1387C2×D4—681no—
1388C2×D4—681no—
1389C2×D4—681no—
1390C2×D4—681no—
1391C2×D4—681no—
1392C2×D4—681no—
1393C2×D4—681no—
1394C2×D4—681no—
1395C22×C4—22no—
1396C22×C4—22no—
1397C22×C4—41no—
1398C22×C4—41no—
1399C22×C4—41no—
1400C22×C4—41no—
1401C22×C4—41no—
1402C22×C4—41no—
1403C22×C4—171no—
1404C22×C4—171no—
1405C22×C4—171no—
1406C22×C4—171no—
1407C22×C4—174no—
1408C22×C4—171no—
1409C22×C4—171no—
1410C22×C4—171no—
1411C22×C4—171no—
1412C22×C4—171no—
1413C22×C4—171no—
1414C22×C4—171no—
1415C22×C4—342no—
1416C22×C4—342no—
1417C22×C4—342no—
1418C22×C4—342no—
1419C22×C4—342no—
1420C22×C4—342no—
1421C22×C4—342no—
1422C22×C4—342no—
1423C22×C4—342no—
1424C22×C4—342no—
1425C22×C4—342no—
1426C22×C4—681no—
1427C22×C4—681no—
1428C22×C4—681no—
1429C22×C4—681no—
1430C22×C4—681no—
1431C22×C4—681no—
1432C22×C4—6816no—
1433C22×C4—681no—
1434C22×C4—681no—
1435C22×C4—681no—
1436C22×C4D4×D1714yes—
1437C22×C4C23×D1711yescharacteristic
1438C22×C4C23×D1711yescharacteristic
1439C22×C4C23×D1711yescharacteristic
1440C22×C4C23×D1711yescharacteristic
1441C22×C4C23×D1711yescharacteristic
1442C22×C4C23×D1711yescharacteristic
1443C22×C4C23×D1711yescharacteristic
1444C22×C4C23×D1711yescharacteristic
1445C22×C4C23×D1711yescharacteristic
1446C22×C4C23×D1711yescharacteristic
1447C22×C4C23×D1711yescharacteristic
1448C22×C4C23×D1711yescharacteristic
1449C4⋊C4—22no—
1450C4⋊C4—22no—
1451C4⋊C4—41no—
1452C4⋊C4—41no—
1453C4⋊C4—41no—
1454C4⋊C4—174no—
1455C4⋊C4—342no—
1456C4⋊C4—342no—
1457C4⋊C4—342no—
1458C4⋊C4—342no—
1459C4⋊C4—342no—
1460C4⋊C4—342no—
1461C4⋊C4—342no—
1462C4⋊C4—342no—
1463C4⋊C4—342no—
1464C4⋊C4—681no—
1465C4⋊C4—681no—
1466C4⋊C4—681no—
1467C4⋊C4—681no—
1468C4⋊C4—681no—
1469C4⋊C4—681no—
1470C4⋊C4—681no—
1471C4⋊C4—681no—
1472C4⋊C4—681no—
1473C22⋊C4—22no—
1474C22⋊C4—22no—
1475C22⋊C4—22no—
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—174no—
1486C22⋊C4—174no—
1487C22⋊C4—342no—
1488C22⋊C4—342no—
1489C22⋊C4—342no—
1490C22⋊C4—342no—
1491C22⋊C4—342no—
1492C22⋊C4—342no—
1493C22⋊C4—342no—
1494C22⋊C4—342no—
1495C22⋊C4—342no—
1496C22⋊C4—342no—
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—681no—
1510C22⋊C4—681no—
1511C22⋊C4—681no—
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—681no—
1527C22⋊C4—681no—
1528C22⋊C4—681no—
1529C22⋊C4—681no—
1530C22⋊C4—681no—
1531C22⋊C4—681no—
1532C22⋊C4—681no—
1533C42—22no—
1534C42—22no—
1535C42—174no—
1536C42—681no—
1537C42—681no—
1538C42—681no—
1539C42—681no—
1540C23—21no—
1541C23—21no—
1542C23—21no—
1543C23—21no—
1544C23—21no—
1545C23—21no—
1546C23—21no—
1547C23—21no—
1548C23—21no—
1549C23—21no—
1550C23—21no—
1551C23—21no—
1552C23—21no—
1553C23—21no—
1554C23—21no—
1555C23—21no—
1556C23—21no—
1557C23—21no—
1558C23—21no—
1559C23—172no—
1560C23—172no—
1561C23—341no—
1562C23—341no—
1563C23—341no—
1564C23—341no—
1565C23—341no—
1566C23—341no—
1567C23—341no—
1568C23—341no—
1569C23—341no—
1570C23—341no—
1571C23—341no—
1572C23—341no—
1573C23—341no—
1574C23—341no—
1575C23—341no—
1576C23—341no—
1577C23—341no—
1578C23—341no—
1579C23—341no—
1580C23—341no—
1581C23—341no—
1582C23—341no—
1583C23—341no—
1584C23—341no—
1585C23—341no—
1586C23—341no—
1587C23—341no—
1588C23—341no—
1589C23—341no—
1590C23—341no—
1591C23—341no—
1592C23—341no—
1593C23—341no—
1594C23—684no—
1595C23—684no—
1596C23—684no—
1597C23—684no—
1598C23—684no—
1599C23—684no—
1600C23—684no—
1601C23—684no—
1602C23—1362no—
1603C23—1362no—
1604C23—1362no—
1605C23—1362no—
1606C23—1362no—
1607C23—1362no—
1608C23C2×D4×D1712yes—
1609C23#1058769612yes—
1610C23C24×D1711yescharacteristic
1611Q8—684no—
1612Q8—1362no—
1613D4—44no—
1614D4—44no—
1615D4—82no—
1616D4—684no—
1617D4—684no—
1618D4—684no—
1619D4—684no—
1620D4—684no—
1621D4—684no—
1622D4—1362no—
1623D4—1362no—
1624D4—1362no—
1625D4—1362no—
1626D4—1362no—
1627D4—1362no—
1628D4—1362no—
1629D4—1362no—
1630D4—1362no—
1631D4—1362no—
1632D4—1362no—
1633D4—1362no—
1634D4—1362no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—21no—
1646C2×C4—21no—
1647C2×C4—21no—
1648C2×C4—21no—
1649C2×C4—21no—
1650C2×C4—21no—
1651C2×C4—21no—
1652C2×C4—21no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—21no—
1656C2×C4—21no—
1657C2×C4—21no—
1658C2×C4—21no—
1659C2×C4—21no—
1660C2×C4—21no—
1661C2×C4—21no—
1662C2×C4—21no—
1663C2×C4—21no—
1664C2×C4—21no—
1665C2×C4—21no—
1666C2×C4—21no—
1667C2×C4—21no—
1668C2×C4—21no—
1669C2×C4—44no—
1670C2×C4—44no—
1671C2×C4—82no—
1672C2×C4—172no—
1673C2×C4—172no—
1674C2×C4—172no—
1675C2×C4—172no—
1676C2×C4—348no—
1677C2×C4—341no—
1678C2×C4—341no—
1679C2×C4—341no—
1680C2×C4—341no—
1681C2×C4—341no—
1682C2×C4—341no—
1683C2×C4—341no—
1684C2×C4—341no—
1685C2×C4—341no—
1686C2×C4—341no—
1687C2×C4—341no—
1688C2×C4—341no—
1689C2×C4—341no—
1690C2×C4—341no—
1691C2×C4—341no—
1692C2×C4—341no—
1693C2×C4—341no—
1694C2×C4—341no—
1695C2×C4—341no—
1696C2×C4—341no—
1697C2×C4—341no—
1698C2×C4—341no—
1699C2×C4—341no—
1700C2×C4—341no—
1701C2×C4—341no—
1702C2×C4—341no—
1703C2×C4—341no—
1704C2×C4—341no—
1705C2×C4—341no—
1706C2×C4—684no—
1707C2×C4—684no—
1708C2×C4—684no—
1709C2×C4—684no—
1710C2×C4—684no—
1711C2×C4—1362no—
1712C2×C4C2×D4×D1712yes—
1713C2×C4C2×D4×D1712yes—
1714C22—22no—
1715C22—22no—
1716C22—22no—
1717C22—22no—
1718C22—22no—
1719C22—22no—
1720C22—41no—
1721C22—41no—
1722C22—41no—
1723C22—41no—
1724C22—41no—
1725C22—41no—
1726C22—41no—
1727C22—41no—
1728C22—41no—
1729C22—41no—
1730C22—41no—
1731C22—41no—
1732C22—41no—
1733C22—41no—
1734C22—41no—
1735C22—342no—
1736C22—342no—
1737C22—342no—
1738C22—342no—
1739C22—342no—
1740C22—342no—
1741C22—6816no—
1742C22—681no—
1743C22—681no—
1744C22—681no—
1745C22—681no—
1746C22—681no—
1747C22—681no—
1748C22—681no—
1749C22—681no—
1750C22—681no—
1751C22—681no—
1752C22—681no—
1753C22—681no—
1754C22—681no—
1755C22—681no—
1756C22—681no—
1757C22—681no—
1758C22—681no—
1759C22—681no—
1760C22—681no—
1761C22—681no—
1762C22—681no—
1763C22—681no—
1764C22—681no—
1765C22—681no—
1766C22—681no—
1767C22—681no—
1768C22—681no—
1769C22—681no—
1770C22—681no—
1771C22—1368no—
1772C22C22×D4×D1711yescharacteristic
1773C22H(5,𝔽2)×D1711yescharacteristic
1774C22H(5,𝔽2)×D1711yescharacteristic
1775C22C2×#1058769611yescharacteristic
1776C22#1176364511yescharacteristic
1777C22#1176364511yescharacteristic
1778C22#1176364511yescharacteristic
1779C4—22no—
1780C4—22no—
1781C4—41no—
1782C4—41no—
1783C4—41no—
1784C4—41no—
1785C4—41no—
1786C4—41no—
1787C4—41no—
1788C4—41no—
1789C4—41no—
1790C4—41no—
1791C4—342no—
1792C4—342no—
1793C4—342no—
1794C4—342no—
1795C4—681no—
1796C4—681no—
1797C4—681no—
1798C4—681no—
1799C4—681no—
1800C4—681no—
1801C4—681no—
1802C2—42no—
1803C2—42no—
1804C2—81no—
1805C2—682no—
1806C2—682no—
1807C2—1361no—
1808C2—1361no—
1809C2—1361no—
1810C2#1454211411yescharacteristic
1811C2#1454241611yescharacteristic
1812C2#1454244511yescharacteristic
1813C2#1454294211yescharacteristic
1814C2#1454296111yescharacteristic
1815C2#1454304711yescharacteristic
1816C2#1454309311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2600C2
hypercenter#2600D17
hypocenterC17#36724
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2600

Complements

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

NH ≅ G/Ntype
1. C2×#11763392C2semidirect
2. C2×#11763318C2semidirect
3. #14537079C2semidirect
4. #14537065C2semidirect
5. #14535458C2semidirect
6. #14535413C2semidirect
7. #14535383C2semidirect
8. #14535372C2semidirect
9. #14535207C2semidirect
10. #14535150C2semidirect
11. #14535140C2semidirect
12. #14535137C2semidirect
13. #14535117C2semidirect
14. #14535115C2semidirect
15. #14535111C2semidirect
16. #14535108C2semidirect
17. #14535037C2semidirect
18. #14535008C2semidirect
19. #14535002C2semidirect
20. #14534995C2semidirect
21. #14534675C2semidirect
22. #14534633C2semidirect
23. #14534469C2semidirect
24. #14534410C2semidirect
25. #14534379C2semidirect
26. #14533753C2semidirect
27. #14533670C2semidirect
28. #14532129C2semidirect
29. #14532105C2semidirect
30. #14531424C2semidirect
31. C17×#2600C2semidirect
33. C23×C4×D17C22semidirect
36. C2×#10587584C22semidirect
37. C2×#10587562C22semidirect
39. C2×#10587571C22semidirect
40. C2×#10587571C22semidirect
44. C2×#10587580C22semidirect
45. C2×#10587615C22semidirect
48. C2×#10587610C22semidirect
49. C2×#10587582C22semidirect
50. C2×#10587564C22semidirect
51. C2×#10587564C22semidirect
53. C2×#10587616C22semidirect
64. C2×#10587568C22semidirect
65. C2×#10587568C22semidirect
68. C2×#10587623C22semidirect
69. C2×#10587623C22semidirect
70. C2×C4×D68C22semidirect
72. C2×C4×C22⋊D17C22semidirect
73. C2×#10587558C22semidirect
74. C22×#63227C22semidirect
75. #11762751C22semidirect
76. #11762744C22semidirect
77. #11762743C22semidirect
78. #11762742C22semidirect
79. #11762740C22semidirect
80. #11762738C22semidirect
81. #11762738C22semidirect
82. #11762733C22semidirect
83. #11762733C22semidirect
84. #11762733C22semidirect
85. #11762731C22semidirect
86. #11762731C22semidirect
87. #11762731C22semidirect
88. #11762729C22semidirect
91. #11762727C22semidirect
92. #11762727C22semidirect
94. #11762726C22semidirect
97. #11762725C22semidirect
98. #11762725C22semidirect
101. #11762724C22semidirect
102. #11762724C22semidirect
103. #11762724C22semidirect
104. #11762724C22semidirect
105. #11762723C22semidirect
106. #11762722C22semidirect
107. #11762722C22semidirect
108. #11762722C22semidirect
115. #11762718C22semidirect
116. #11762718C22semidirect
118. #11762717C22semidirect
119. #11762715C22semidirect
120. #11762713C22semidirect
121. #11762711C22semidirect
124. #11762710C22semidirect
128. #11762709C22semidirect
129. #11762709C22semidirect
130. #11762706C22semidirect
131. #11762706C22semidirect
132. #11762706C22semidirect
133. #11762703C22semidirect
134. #11762703C22semidirect
135. #11762701C22semidirect
136. #11762701C22semidirect
137. #11762701C22semidirect
138. #11762700C22semidirect
139. #11762700C22semidirect
140. #11762698C22semidirect
141. #11762698C22semidirect
142. #11762698C22semidirect
143. #11762697C22semidirect
144. #11762697C22semidirect
151. #11762687C22semidirect
152. #11762687C22semidirect
155. #11762686C22semidirect
156. #11762685C22semidirect
157. #11762685C22semidirect
158. #11762685C22semidirect
159. #11762681C22semidirect
160. #11762680C22semidirect
161. #11762680C22semidirect
162. #11762680C22semidirect
163. #11762671C22semidirect
164. #11762671C22semidirect
165. #11762670C22semidirect
166. #11762669C22semidirect
167. #11762668C22semidirect
168. #11762668C22semidirect
169. #11762667C22semidirect
170. #11762664C22semidirect
171. #11762664C22semidirect
172. #11762660C22semidirect
173. #11762654C22semidirect
175. C2×C4×D4×C17C22semidirect
176. C17×#397C22semidirect
178. C17×#394C22semidirect
180. C17×#388C22semidirect
181. C17×#388C22semidirect
182. C17×#387C22semidirect
183. C17×#387C22semidirect
184. C17×#386C22semidirect
185. C17×#386C22semidirect
186. C17×#385C22semidirect
187. C17×#385C22semidirect
188. C17×#381C22semidirect
274. C4×C22⋊D17D4semidirect
831. #2600D17semidirect
967. C2×C4×D4C2×D17semidirect
977. #397C2×D17semidirect
1003. #394C2×D17semidirect
1044. #388C2×D17semidirect
1045. #388C2×D17semidirect
1046. #387C2×D17semidirect
1047. #387C2×D17semidirect
1062. #386C2×D17semidirect
1063. #386C2×D17semidirect
1068. #385C2×D17semidirect
1069. #385C2×D17semidirect
1073. #381C2×D17semidirect
1299. C17#36724semidirect

Maximal subgroups

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

subgroupindex
C2×#117633922
C2×#117633182
#145370792
#145370652
#145354582
#145354132
#145353832
#145353722
#145352072
#145351502
#145351402
#145351372
#145351172
#145351152
#145351112
#145351082
#145350372
#145350082
#145350022
#145349952
#145346752
#145346332
#145344692
#145344102
#145343792
#145337532
#145336702
#145321292
#145321052
#145314242
C17×#26002
#3672417