Finite Group Databasebeta

← #17241416

Subgroups — #17241416

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×#11763391C211yesmaximal, characteristic, complemented
2C2×#11763322C211yesmaximal, characteristic, complemented
3#14537073C211yesmaximal, characteristic, complemented
4#14537065C211yesmaximal, characteristic, complemented
5#14535462C211yesmaximal, characteristic, complemented
6#14535419C211yesmaximal, characteristic, complemented
7#14535378C211yesmaximal, characteristic, complemented
8#14535373C211yesmaximal, characteristic, complemented
9#14535198C211yesmaximal, characteristic, complemented
10#14535150C211yesmaximal, characteristic, complemented
11#14535132C211yesmaximal, characteristic, complemented
12#14535117C211yesmaximal, characteristic, complemented
13#14535116C211yesmaximal, characteristic, complemented
14#14535106C211yesmaximal, characteristic, complemented
15#14535103C211yesmaximal, characteristic, complemented
16#14535032C211yesmaximal, characteristic, complemented
17#14535008C211yesmaximal, characteristic, complemented
18#14535000C211yesmaximal, characteristic, complemented
19#14534996C211yesmaximal, characteristic, complemented
20#14534670C211yesmaximal, characteristic, complemented
21#14534624C211yesmaximal, characteristic, complemented
22#14534474C211yesmaximal, characteristic, complemented
23#14534412C211yesmaximal, characteristic, complemented
24#14534380C211yesmaximal, characteristic, complemented
25#14534370C211yesmaximal, characteristic, complemented
26#14533758C211yesmaximal, characteristic, complemented
27#14533675C211yesmaximal, characteristic, complemented
28#14532131C211yesmaximal, characteristic, complemented
29#14532104C211yesmaximal, characteristic, complemented
30#14531425C211yesmaximal, characteristic, complemented
31C17×#2681C211yesmaximal, characteristic, complemented
32C22×#63256C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic, complemented
34#11763391—28no—
35C2×#10587626C2211yescharacteristic
36C2×#10587584C2211yescharacteristic, complemented
37C2×#10587565C2211yescharacteristic, complemented
38C2×#10587561C2211yescharacteristic, complemented
39C2×#10587622C2211yescharacteristic, complemented
40C2×#10587571C2211yescharacteristic
41#11763322—28no—
42C2×#10587580C2211yescharacteristic
43C2×#10587580C2211yescharacteristic
44C2×#10587580C2211yescharacteristic, complemented
45C2×#10587615C2211yescharacteristic, complemented
46C2×#10587621C2211yescharacteristic
47C2×#10587582C2211yescharacteristic, complemented
48C2×#10587632C2211yescharacteristic, complemented
49C2×#10587581C2211yescharacteristic
50C2×#10587616C2211yescharacteristic
51C2×#10587616C2211yescharacteristic, complemented
52C2×#10587570C2211yescharacteristic
53C2×#10587570C2211yescharacteristic
54C2×#10587625C2211yescharacteristic
55C2×#10587624C2211yescharacteristic
56C2×#10587568C2211yescharacteristic
57C2×#10587568C2211yescharacteristic
58C2×#10587568C2211yescharacteristic
59C2×#10587568C2211yescharacteristic
60C2×#10587568C2211yescharacteristic, complemented
61C2×#10587568C2211yescharacteristic, complemented
62C2×#10587623C2211yescharacteristic
63C2×#10587623C2211yescharacteristic
64C2×#10587623C2211yescharacteristic, complemented
65C2×#10587623C2211yescharacteristic, complemented
66C2×#10587579C2211yescharacteristic
67C2×#10587579C2211yescharacteristic, complemented
68C2×C4×C22⋊D17C2211yescharacteristic, complemented
69C2×#10587567C2211yescharacteristic
70C2×#10587567C2211yescharacteristic, complemented
71C2×#10587578C2211yescharacteristic, complemented
72C2×C22⋊C4×D17C2211yescharacteristic, complemented
73#11762750C2211yescharacteristic, complemented
74#11762744C2211yescharacteristic, complemented
75#11762741C2211yescharacteristic, complemented
76#11762740C2211yescharacteristic, complemented
77#11762737C2211yescharacteristic, complemented
78#11762735C2211yescharacteristic, complemented
79#11762735C2211yescharacteristic, complemented
80#11762733C2211yescharacteristic, complemented
81#11762732C2211yescharacteristic, complemented
82#11762731C2211yescharacteristic, complemented
83#11762731C2211yescharacteristic, complemented
84#11762731C2211yescharacteristic, complemented
85#11762729C2211yescharacteristic, complemented
86#11762727C2211yescharacteristic
87#11762727C2211yescharacteristic
88#11762726C2211yescharacteristic
89#11762726C2211yescharacteristic
90#11762726C2211yescharacteristic, complemented
91#11762726C2211yescharacteristic, complemented
92#11762725C2211yescharacteristic
93#11762725C2211yescharacteristic, complemented
94#11762725C2211yescharacteristic, complemented
95#11762724C2211yescharacteristic
96#11762724C2211yescharacteristic
97#11762724C2211yescharacteristic, complemented
98#11762724C2211yescharacteristic, complemented
99#11762724C2211yescharacteristic, complemented
100#11762724C2211yescharacteristic, complemented
101#11762724C2211yescharacteristic, complemented
102#11762722C2211yescharacteristic, complemented
103#11762720C2211yescharacteristic, complemented
104#11762719C2211yescharacteristic
105#11762719C2211yescharacteristic
106#11762718C2211yescharacteristic
107#11762718C2211yescharacteristic
108#11762718C2211yescharacteristic
109#11762718C2211yescharacteristic
110#11762718C2211yescharacteristic, complemented
111#11762718C2211yescharacteristic, complemented
112#11762717C2211yescharacteristic
113#11762717C2211yescharacteristic
114#11762717C2211yescharacteristic, complemented
115#11762716C2211yescharacteristic, complemented
116#11762714C2211yescharacteristic, complemented
117#11762711C2211yescharacteristic
118#11762710C2211yescharacteristic
119#11762710C2211yescharacteristic, complemented
120#11762710C2211yescharacteristic, complemented
121#11762709C2211yescharacteristic
122#11762709C2211yescharacteristic
123#11762709C2211yescharacteristic
124#11762709C2211yescharacteristic, complemented
125#11762706C2211yescharacteristic, complemented
126#11762704C2211yescharacteristic, complemented
127#11762703C2211yescharacteristic, complemented
128#11762703C2211yescharacteristic, complemented
129#11762702C2211yescharacteristic, complemented
130#11762702C2211yescharacteristic, complemented
131#11762702C2211yescharacteristic, complemented
132#11762701C2211yescharacteristic, complemented
133#11762701C2211yescharacteristic, complemented
134#11762701C2211yescharacteristic, complemented
135#11762700C2211yescharacteristic, complemented
136#11762699C2211yescharacteristic, complemented
137#11762699C2211yescharacteristic, complemented
138#11762699C2211yescharacteristic, complemented
139#11762698C2211yescharacteristic, complemented
140#11762692C2211yescharacteristic, complemented
141#11762690C2211yescharacteristic, complemented
142#11762688C2211yescharacteristic
143#11762688C2211yescharacteristic, complemented
144#11762687C2211yescharacteristic
145#11762687C2211yescharacteristic
146#11762687C2211yescharacteristic
147#11762687C2211yescharacteristic, complemented
148#11762687C2211yescharacteristic, complemented
149#11762685C2211yescharacteristic
150#11762685C2211yescharacteristic
151#11762685C2211yescharacteristic
152#11762685C2211yescharacteristic
153#11762685C2211yescharacteristic, complemented
154#11762685C2211yescharacteristic, complemented
155#11762685C2211yescharacteristic, complemented
156#11762685C2211yescharacteristic, complemented
157#11762680C2211yescharacteristic, complemented
158#11762680C2211yescharacteristic, complemented
159#11762680C2211yescharacteristic, complemented
160#11762680C2211yescharacteristic, complemented
161#11762680C2211yescharacteristic, complemented
162#11762672C2211yescharacteristic, complemented
163#11762671C2211yescharacteristic, complemented
164#11762671C2211yescharacteristic, complemented
165#11762670C2211yescharacteristic, complemented
166#11762668C2211yescharacteristic, complemented
167#11762668C2211yescharacteristic, complemented
168#11762667C2211yescharacteristic, complemented
169#11762666C2211yescharacteristic, complemented
170#11762664C2211yescharacteristic, complemented
171#11762664C2211yescharacteristic, complemented
172C4×#63225C2211yescharacteristic, complemented
173#11762654C2211yescharacteristic, complemented
174C2×C17×#123C2211yescharacteristic
175C2×C17×C22⋊Q8C2211yescharacteristic, complemented
176C2×C17×C22⋊Q8C2211yescharacteristic, complemented
177C2×C17×#121C2211yescharacteristic
178C17×#398C2211yescharacteristic, complemented
179C17×#396C2211yescharacteristic, complemented
180C17×#394C2211yescharacteristic
181C17×#394C2211yescharacteristic, complemented
182C17×#394C2211yescharacteristic, complemented
183C17×#393C2211yescharacteristic, complemented
184C17×#390C2211yescharacteristic, complemented
185C17×#389C2211yescharacteristic, complemented
186C17×#388C2211yescharacteristic, complemented
187C17×#386C2211yescharacteristic, complemented
188C17×#385C2211yescharacteristic, complemented
189C24×D17C2311yescharacteristic
190C24×D17C2311yescharacteristic
191C22×Q8×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C22×D4×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
209C2×#63256—24no—
210C2×#63256—42no—
211C2×#63256—42no—
212C22×D68C2311yescharacteristic
213C22×D68C2311yescharacteristic
214C22×D68C2311yescharacteristic
215C22×D68C2311yescharacteristic
216C22×D68C2311yescharacteristic
217C22×D68C2311yescharacteristic
218C22×D68C2311yescharacteristic
219C22×D68C2311yescharacteristic
220C22×C4×D17—24no—
221C22×C4×D17—42no—
222C22×C4×D17—42no—
223C22×C4×D17C2311yescharacteristic
224C22×C4×D17C2311yescharacteristic
225C22×C4×D17C2311yescharacteristic
226C22×C4×D17C2311yescharacteristic
227C22×C4×D17C2311yescharacteristic
228C22×C4×D17C2311yescharacteristic
229C22×C4×D17C2311yescharacteristic
230C22×Dic34C2311yescharacteristic
231C17×#123—42no—
232C17×C22⋊Q8—24no—
233C17×C22⋊Q8—42no—
234C17×#121—24no—
235C2×C4⋊C4×C17C2311yescharacteristic
236C2×C4⋊C4×C17C2311yescharacteristic
237C2×C4⋊C4×C17C2311yescharacteristic
238C2×C4⋊C4×C17C2311yescharacteristic
239C2×C4⋊C4×C17C2311yescharacteristic
240C2×C4⋊C4×C17C2311yescharacteristic
241C2×C4⋊C4×C17C2311yescharacteristic
242C2×C4⋊C4×C17C2311yescharacteristic
243C2×C4⋊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×C22⋊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×C42×C17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×C22⋊Dic17C2311yescharacteristic
263C2×C22⋊Dic17C2311yescharacteristic
264C2×C22⋊Dic17C2311yescharacteristic
265C2×C22⋊Dic17C2311yescharacteristic
266C2×C22⋊Dic17C2311yescharacteristic
267C2×C22⋊Dic17C2311yescharacteristic
268#10587632—24no—
269#10587626—42no—
270#10587625—24no—
271#10587624—24no—
272#10587623—24no—
273#10587623—24no—
274#10587623—42no—
275#10587623—42no—
276#10587622—24no—
277#10587621—24no—
278#10587616—24no—
279#10587616—42no—
280#10587615—24no—
281C4×C22⋊D17—24no—
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×#63227C2311yescharacteristic
316C2×#63227C2311yescharacteristic
317C2×#63227C2311yescharacteristic
318C2×#63227C2311yescharacteristic
319C2×C4⋊Dic17C2311yescharacteristic
320C2×C4⋊Dic17C2311yescharacteristic
321C2×C4⋊Dic17C2311yescharacteristic
322C2×C4⋊Dic17C2311yescharacteristic
323C2×#63225C2311yescharacteristic
324C2×#63225C2311yescharacteristic
325C2×#63225C2311yescharacteristic
326C2×#63225C2311yescharacteristic
327C2×#63225C2311yescharacteristic
328C2×#63225C2311yescharacteristic
329C2×#63225C2311yescharacteristic
330C2×#63225C2311yescharacteristic
331C2×#63225C2311yescharacteristic
332C2×#63225C2311yescharacteristic
333C2×#63225C2311yescharacteristic
334C2×C4×Dic17C2311yescharacteristic
335C2×C4×Dic17C2311yescharacteristic
336C2×C4×Dic17C2311yescharacteristic
337C2×C4×Dic17C2311yescharacteristic
338C2×C4×Dic17C2311yescharacteristic
339C2×C4×Dic17C2311yescharacteristic
340#10587584—24no—
341#10587582—24no—
342#10587581—24no—
343#10587580—24no—
344#10587580—24no—
345#10587580—42no—
346#10587579—24no—
347#10587579—24no—
348#10587578—24no—
349#10587571—24no—
350#10587570—42no—
351#10587570—42no—
352#10587568—24no—
353#10587568—24no—
354#10587568—42no—
355#10587568—42no—
356#10587568—42no—
357#10587568—42no—
358#10587567—24no—
359#10587567D418yescomplemented
360C22⋊C4×D17—24no—
361#10587565—24no—
362#10587561—42no—
363C17×#95C2311yescharacteristic
364C17×#95C2311yescharacteristic
365C17×#95C2311yescharacteristic
366C17×#95C2311yescharacteristic
367C17×#95C2311yescharacteristic
368C17×#95C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
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×Q8×C17—22no—
414C2×Q8×C17—22no—
415C2×Q8×C17—41no—
416C2×D4×C17—22no—
417C2×D4×C17—22no—
418C2×D4×C17—22no—
419C2×D4×C17—41no—
420C2×D4×C17—41no—
421C2×D4×C17—41no—
422C2×D4×C17—41no—
423C2×D4×C17—41no—
424C2×D4×C17—41no—
425C22×C4×C17—22no—
426C22×C4×C17—22no—
427C22×C4×C17—22no—
428C22×C4×C17—41no—
429C22×C4×C17—41no—
430C22×C4×C17—41no—
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—41no—
452C2×C22⋊D17—41no—
453C2×C22⋊D17—41no—
454C2×C22⋊D17—41no—
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—41no—
477C22×Dic17—41no—
478C22×Dic17C2×D414yes—
479C22×Dic17C2411yescharacteristic
480C22×Dic17C2411yescharacteristic
481C22×Dic17C2411yescharacteristic
482C22×Dic17C2411yescharacteristic
483C22×Dic17C2411yescharacteristic
484C22×Dic17C2411yescharacteristic
485C22×Dic17C2411yescharacteristic
486C22×Dic17C2411yescharacteristic
487C22×Dic17C2411yescharacteristic
488C22×Dic17C2411yescharacteristic
489C22×Dic17C2411yescharacteristic
490#63256—416no—
491C2×D68—22no—
492C2×D68—22no—
493C2×D68—22no—
494C2×D68—22no—
495C2×D68—22no—
496C2×D68—22no—
497C2×D68—22no—
498C2×D68—22no—
499C2×D68—22no—
500C2×D68—22no—
501C2×D68—22no—
502C2×D68—22no—
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×C4×D17—22no—
516C2×C4×D17—22no—
517C2×C4×D17—22no—
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—416no—
526C2×C4×D17—41no—
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×D17—41no—
534C2×C4×D17—41no—
535C2×C4×D17—41no—
536C2×C4×D17C2×D414yes—
537C2×Dic34—22no—
538C2×Dic34—41no—
539C2×Dic34—41no—
540C4⋊C4×C17—22no—
541C4⋊C4×C17—22no—
542C4⋊C4×C17—22no—
543C4⋊C4×C17—22no—
544C4⋊C4×C17—22no—
545C4⋊C4×C17—41no—
546C4⋊C4×C17—41no—
547C4⋊C4×C17—41no—
548C4⋊C4×C17—41no—
549C22⋊C4×C17—22no—
550C22⋊C4×C17—22no—
551C22⋊C4×C17—22no—
552C22⋊C4×C17—22no—
553C22⋊C4×C17—41no—
554C22⋊C4×C17—41no—
555C22⋊C4×C17—41no—
556C22⋊C4×C17—41no—
557C22⋊C4×C17—41no—
558C22⋊C4×C17—41no—
559C22⋊C4×C17—41no—
560C22⋊C4×C17—41no—
561C22⋊C4×C17C2×D414yes—
562C42×C17—41no—
563C22⋊Dic17—22no—
564C22⋊Dic17—22no—
565C22⋊Dic17—22no—
566C22⋊Dic17—22no—
567C22⋊Dic17—22no—
568C22⋊Dic17—22no—
569C22⋊Dic17—41no—
570C22⋊Dic17—41no—
571C22⋊Dic17—41no—
572C22⋊Dic17—41no—
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—22no—
586#63227—22no—
587#63227—22no—
588#63227—22no—
589#63227—22no—
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#63227—41no—
607#63227—41no—
608#63227—41no—
609#63227C2×D414yes—
610C4⋊Dic17—22no—
611C4⋊Dic17—22no—
612C4⋊Dic17—41no—
613C4⋊Dic17—41no—
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#63225C2×D414yes—
625C4×Dic17—22no—
626C4×Dic17—22no—
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×C17—21no—
652C23×C17C22×D412yes—
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—44no—
687C22×D17—44no—
688C22×D17—44no—
689C22×D17—44no—
690C22×D17—44no—
691C22×D17—44no—
692C22×D17—44no—
693C22×D17—44no—
694C22×D17—82no—
695C22×D17—82no—
696C22×D17—82no—
697C22×D17—82no—
698C22×D17—82no—
699C22×D17—82no—
700C22×D17C22×D412yes—
701C22×D17H(5,𝔽2)12yes—
702C22×D17H(5,𝔽2)12yes—
703Q8×C17—44no—
704D4×C17—82no—
705D4×C17—82no—
706D4×C17—82no—
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—82no—
742C2×C4×C17C22×D412yes—
743C2×C4×C17C22×D412yes—
744C2×C4×C17H(5,𝔽2)12yes—
745C22⋊D17—44no—
746C22⋊D17—44no—
747C22⋊D17—44no—
748C22⋊D17—82no—
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—21no—
786C2×Dic17—44no—
787C2×Dic17C22×D412yes—
788C2×Dic17C22×D412yes—
789C2×Dic17C22×D412yes—
790D68—44no—
791D68—44no—
792D68—44no—
793D68—44no—
794D68—44no—
795D68—82no—
796D68—82no—
797D68—82no—
798C4×D17—28no—
799C4×D17—44no—
800C4×D17—44no—
801C4×D17—44no—
802C4×D17—44no—
803C4×D17—44no—
804C4×D17—82no—
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#2681D1711yescharacteristic, complemented
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#2600—171no—
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—41no—
841C22×C17—41no—
842C22×C17—41no—
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—22no—
872C2×D17—22no—
873C2×D17—22no—
874C2×D17—416no—
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—22no—
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—41no—
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×#123C2×D1711yescharacteristic
941C2×C22⋊Q8—171no—
942C2×C22⋊Q8—171no—
943C2×C22⋊Q8C2×D1711yescharacteristic, complemented
944C2×C22⋊Q8C2×D1711yescharacteristic, complemented
945C2×#121—171no—
946C2×#121—171no—
947C2×#121—171no—
948C2×#121—171no—
949C2×#121—171no—
950C2×#121—171no—
951C2×#121—171no—
952C2×#121C2×D1711yescharacteristic
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×D4—171no—
967C2×C4×D4—171no—
968C2×#117—171no—
969C22×C22⋊C4—171no—
970#400—171no—
971#399—171no—
972#398—171no—
973#398—171no—
974#398C2×D1711yescharacteristic, complemented
975#397—171no—
976#397—171no—
977#397—171no—
978#396—171no—
979#396—171no—
980#396—171no—
981#396—171no—
982#396—171no—
983#396C2×D1711yescharacteristic, complemented
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#394C2×D1711yescharacteristic
1002#394C2×D1711yescharacteristic, complemented
1003#394C2×D1711yescharacteristic, complemented
1004#393—171no—
1005#393—171no—
1006#393C2×D1711yescharacteristic, complemented
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#392—171no—
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#390C2×D1711yescharacteristic, complemented
1029#389—171no—
1030#389—171no—
1031#389C2×D1711yescharacteristic, complemented
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#388—171no—
1045#388C2×D1711yescharacteristic, complemented
1046#387—171no—
1047#387—171no—
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#386—171no—
1063#386C2×D1711yescharacteristic, complemented
1064#385—171no—
1065#385—171no—
1066#385—171no—
1067#385—171no—
1068#385—171no—
1069#385C2×D1711yescharacteristic, complemented
1070#381—171no—
1071#381—171no—
1072#381—171no—
1073#381—171no—
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—81no—
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—42no—
1095D17—81no—
1096D17—81no—
1097C25—171no—
1098C25—171no—
1099C2×#41—344no—
1100C2×#41—682no—
1101C2×#41—682no—
1102C22×Q8—171no—
1103C22×Q8C22×D1711yescharacteristic
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—171no—
1134C23×C4—344no—
1135C23×C4—682no—
1136C23×C4—682no—
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—42no—
1146#123—344no—
1147#123—344no—
1148#123—344no—
1149#123—344no—
1150#123—682no—
1151C22⋊Q8—24no—
1152C22⋊Q8—42no—
1153C22⋊Q8—344no—
1154C22⋊Q8—344no—
1155#121—24no—
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—178no—
1174C4×D4—344no—
1175C4×D4—344no—
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⋊C4C22×D1711yescharacteristic
1195C2×C4⋊C4C22×D1711yescharacteristic
1196C2×C4⋊C4C22×D1711yescharacteristic
1197C2×C4⋊C4C22×D1711yescharacteristic
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—344no—
1251C2×C22⋊C4C22×D1711yescharacteristic
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×C42—171no—
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#95—171no—
1290#95—171no—
1291#95—171no—
1292#95—171no—
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—22no—
1324C2×Q8—22no—
1325C2×Q8—41no—
1326C2×Q8—342no—
1327C2×Q8—681no—
1328C2×Q8—681no—
1329C2×D4—22no—
1330C2×D4—22no—
1331C2×D4—22no—
1332C2×D4—41no—
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—342no—
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—22no—
1398C22×C4—41no—
1399C22×C4—41no—
1400C22×C4—41no—
1401C22×C4—171no—
1402C22×C4—171no—
1403C22×C4—171no—
1404C22×C4—174no—
1405C22×C4—174no—
1406C22×C4—171no—
1407C22×C4—171no—
1408C22×C4—171no—
1409C22×C4—171no—
1410C22×C4—171no—
1411C22×C4—171no—
1412C22×C4—171no—
1413C22×C4—171no—
1414C22×C4—342no—
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—681no—
1425C22×C4—681no—
1426C22×C4—681no—
1427C22×C4—681no—
1428C22×C4—681no—
1429C22×C4—681no—
1430C22×C4—681no—
1431C22×C4—681no—
1432C22×C4—681no—
1433C22×C4—681no—
1434C22×C4—6816no—
1435C22×C4—681no—
1436C22×C4—681no—
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—22no—
1452C4⋊C4—22no—
1453C4⋊C4—22no—
1454C4⋊C4—41no—
1455C4⋊C4—41no—
1456C4⋊C4—41no—
1457C4⋊C4—41no—
1458C4⋊C4—174no—
1459C4⋊C4—342no—
1460C4⋊C4—342no—
1461C4⋊C4—342no—
1462C4⋊C4—342no—
1463C4⋊C4—342no—
1464C4⋊C4—342no—
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—41no—
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—342no—
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⋊C4D4×D1714yes—
1533C42—41no—
1534C42—174no—
1535C42—342no—
1536C42—342no—
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—21no—
1560C23—172no—
1561C23—172no—
1562C23—172no—
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—341no—
1595C23—684no—
1596C23—684no—
1597C23—684no—
1598C23—684no—
1599C23—684no—
1600C23—684no—
1601C23—684no—
1602C23—684no—
1603C23—1362no—
1604C23—1362no—
1605C23—1362no—
1606C23—1362no—
1607C23—1362no—
1608C23—1362no—
1609C23C2×D4×D1712yes—
1610C23C24×D1711yescharacteristic
1611Q8—44no—
1612Q8—1362no—
1613D4—82no—
1614D4—82no—
1615D4—82no—
1616D4—684no—
1617D4—684no—
1618D4—684no—
1619D4—684no—
1620D4—684no—
1621D4—684no—
1622D4—684no—
1623D4—684no—
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—44no—
1669C2×C4—82no—
1670C2×C4—172no—
1671C2×C4—172no—
1672C2×C4—172no—
1673C2×C4—348no—
1674C2×C4—341no—
1675C2×C4—341no—
1676C2×C4—341no—
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—684no—
1705C2×C4—684no—
1706C2×C4—684no—
1707C2×C4—684no—
1708C2×C4—684no—
1709C2×C4—684no—
1710C2×C4—1362no—
1711C2×C4C2×D4×D1712yes—
1712C2×C4C2×D4×D1712yes—
1713C2×C4#1058769112yes—
1714C22—22no—
1715C22—22no—
1716C22—22no—
1717C22—41no—
1718C22—41no—
1719C22—41no—
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—342no—
1742C22—342no—
1743C22—342no—
1744C22—6816no—
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×#1058769111yescharacteristic
1776C22#1176364511yescharacteristic
1777C22#1176364611yescharacteristic
1778C22#1176364611yescharacteristic
1779C4—22no—
1780C4—22no—
1781C4—22no—
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—681no—
1795C4—681no—
1796C4—681no—
1797C4—681no—
1798C4—681no—
1799C4—681no—
1800C4—681no—
1801C4—681no—
1802C2—42no—
1803C2—81no—
1804C2—81no—
1805C2—682no—
1806C2—682no—
1807C2—682no—
1808C2—1361no—
1809C2—1361no—
1810C2#1454211611yescharacteristic
1811C2#1454241211yescharacteristic
1812C2#1454244711yescharacteristic
1813C2#1454295911yescharacteristic
1814C2#1454297611yescharacteristic
1815C2#1454305811yescharacteristic
1816C2#1454308811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2681C2
hypercenter#2681D17
hypocenterC17#36724
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2681

Complements

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

NH ≅ G/Ntype
1. C2×#11763391C2semidirect
2. C2×#11763322C2semidirect
3. #14537073C2semidirect
4. #14537065C2semidirect
5. #14535462C2semidirect
6. #14535419C2semidirect
7. #14535378C2semidirect
8. #14535373C2semidirect
9. #14535198C2semidirect
10. #14535150C2semidirect
11. #14535132C2semidirect
12. #14535117C2semidirect
13. #14535116C2semidirect
14. #14535106C2semidirect
15. #14535103C2semidirect
16. #14535032C2semidirect
17. #14535008C2semidirect
18. #14535000C2semidirect
19. #14534996C2semidirect
20. #14534670C2semidirect
21. #14534624C2semidirect
22. #14534474C2semidirect
23. #14534412C2semidirect
24. #14534380C2semidirect
25. #14534370C2semidirect
26. #14533758C2semidirect
27. #14533675C2semidirect
28. #14532131C2semidirect
29. #14532104C2semidirect
30. #14531425C2semidirect
31. C17×#2681C2semidirect
33. C23×C4×D17C22semidirect
36. C2×#10587584C22semidirect
37. C2×#10587565C22semidirect
38. C2×#10587561C22semidirect
39. C2×#10587622C22semidirect
44. C2×#10587580C22semidirect
45. C2×#10587615C22semidirect
47. C2×#10587582C22semidirect
48. C2×#10587632C22semidirect
51. C2×#10587616C22semidirect
60. C2×#10587568C22semidirect
61. C2×#10587568C22semidirect
64. C2×#10587623C22semidirect
65. C2×#10587623C22semidirect
67. C2×#10587579C22semidirect
68. C2×C4×C22⋊D17C22semidirect
70. C2×#10587567C22semidirect
71. C2×#10587578C22semidirect
72. C2×C22⋊C4×D17C22semidirect
73. #11762750C22semidirect
74. #11762744C22semidirect
75. #11762741C22semidirect
76. #11762740C22semidirect
77. #11762737C22semidirect
78. #11762735C22semidirect
79. #11762735C22semidirect
80. #11762733C22semidirect
81. #11762732C22semidirect
82. #11762731C22semidirect
83. #11762731C22semidirect
84. #11762731C22semidirect
85. #11762729C22semidirect
90. #11762726C22semidirect
91. #11762726C22semidirect
93. #11762725C22semidirect
94. #11762725C22semidirect
97. #11762724C22semidirect
98. #11762724C22semidirect
99. #11762724C22semidirect
100. #11762724C22semidirect
101. #11762724C22semidirect
102. #11762722C22semidirect
103. #11762720C22semidirect
110. #11762718C22semidirect
111. #11762718C22semidirect
114. #11762717C22semidirect
115. #11762716C22semidirect
116. #11762714C22semidirect
119. #11762710C22semidirect
120. #11762710C22semidirect
124. #11762709C22semidirect
125. #11762706C22semidirect
126. #11762704C22semidirect
127. #11762703C22semidirect
128. #11762703C22semidirect
129. #11762702C22semidirect
130. #11762702C22semidirect
131. #11762702C22semidirect
132. #11762701C22semidirect
133. #11762701C22semidirect
134. #11762701C22semidirect
135. #11762700C22semidirect
136. #11762699C22semidirect
137. #11762699C22semidirect
138. #11762699C22semidirect
139. #11762698C22semidirect
140. #11762692C22semidirect
141. #11762690C22semidirect
143. #11762688C22semidirect
147. #11762687C22semidirect
148. #11762687C22semidirect
153. #11762685C22semidirect
154. #11762685C22semidirect
155. #11762685C22semidirect
156. #11762685C22semidirect
157. #11762680C22semidirect
158. #11762680C22semidirect
159. #11762680C22semidirect
160. #11762680C22semidirect
161. #11762680C22semidirect
162. #11762672C22semidirect
163. #11762671C22semidirect
164. #11762671C22semidirect
165. #11762670C22semidirect
166. #11762668C22semidirect
167. #11762668C22semidirect
168. #11762667C22semidirect
169. #11762666C22semidirect
170. #11762664C22semidirect
171. #11762664C22semidirect
172. C4×#63225C22semidirect
173. #11762654C22semidirect
175. C2×C17×C22⋊Q8C22semidirect
176. C2×C17×C22⋊Q8C22semidirect
178. C17×#398C22semidirect
179. C17×#396C22semidirect
181. C17×#394C22semidirect
182. C17×#394C22semidirect
183. C17×#393C22semidirect
184. C17×#390C22semidirect
185. C17×#389C22semidirect
186. C17×#388C22semidirect
187. C17×#386C22semidirect
188. C17×#385C22semidirect
359. #10587567D4semidirect
817. #2681D17semidirect
943. C2×C22⋊Q8C2×D17semidirect
944. C2×C22⋊Q8C2×D17semidirect
974. #398C2×D17semidirect
983. #396C2×D17semidirect
1002. #394C2×D17semidirect
1003. #394C2×D17semidirect
1006. #393C2×D17semidirect
1028. #390C2×D17semidirect
1031. #389C2×D17semidirect
1045. #388C2×D17semidirect
1063. #386C2×D17semidirect
1069. #385C2×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×#117633912
C2×#117633222
#145370732
#145370652
#145354622
#145354192
#145353782
#145353732
#145351982
#145351502
#145351322
#145351172
#145351162
#145351062
#145351032
#145350322
#145350082
#145350002
#145349962
#145346702
#145346242
#145344742
#145344122
#145343802
#145343702
#145337582
#145336752
#145321312
#145321042
#145314252
C17×#26812
#3672417