Finite Group Databasebeta

← #17194599

Subgroups — #17194599

Order 4352.

3534 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763315C211yesmaximal, characteristic
2C2×#11763288C211yesmaximal, characteristic, complemented
3C23×#63225C211yesmaximal, characteristic, complemented
4#14531801C212yesmaximal, complemented
5#14531795C212yesmaximal, complemented
6#14531790C212yesmaximal, complemented
7#14531784C212yesmaximal, complemented
8#14531711C212yesmaximal, complemented
9#14531707C212yesmaximal, complemented
10#14531682C212yesmaximal, complemented
11D4×#63225C212yesmaximal, complemented
12#14531458C211yesmaximal, characteristic, complemented
13#14531455C211yesmaximal, characteristic, complemented
14#14531452C211yesmaximal, characteristic, complemented
15#14531449C211yesmaximal, characteristic, complemented
16#14531403C211yesmaximal, characteristic, complemented
17#14531371C211yesmaximal, characteristic, complemented
18#120×Dic17C211yesmaximal, characteristic, complemented
19C4×#10587639C211yesmaximal, characteristic, complemented
20#14531283C211yesmaximal, characteristic, complemented
21#14531162C211yesmaximal, characteristic, complemented
22#14531139C211yesmaximal, characteristic, complemented
23C4×C17×#120C211yesmaximal, characteristic, complemented
24C22×#63254C2211yescharacteristic
25C24×Dic17C2211yescharacteristic
26C24×Dic17C2211yescharacteristic
27#11763315C4116yescomplemented
28C2×#10587572C2211yescharacteristic
29C2×#10587621C2211yescharacteristic
30C2×#10587564C2212yes—
31C2×#10587625C2212yes—
32C2×#10587639C2211yescharacteristic
33#11763288—28no—
34C2×C4×Dic34C2211yescharacteristic, complemented
35C2×#10587573C2211yescharacteristic, complemented
36C2×D4×Dic17C2211yescharacteristic
37C2×D4×Dic17C2212yes—
38C2×D4×Dic17C2212yes—
39C2×C4×C22⋊D17C2211yescharacteristic
40C2×C4×C22⋊D17C2212yes—
41C2×C4×C22⋊D17C2211yescharacteristic, complemented
42C2×#10587567C2211yescharacteristic
43C2×#10587567C2212yes—
44C2×#10587567C2212yes—
45C2×#10587567C2211yescharacteristic, complemented
46C2×#10587558C2211yescharacteristic, complemented
47C2×#10587563C2211yescharacteristic
48C2×#10587563C2211yescharacteristic
49C2×#10587563C2211yescharacteristic
50C2×#10587563C2211yescharacteristic, complemented
51C22×#63225—28no—
52C22×#63225C2211yescharacteristic
53C22×#63225C2212yes—
54C22×#63225C2212yes—
55C22×#63225C2211yescharacteristic
56C22×#63225C2211yescharacteristic
57C22×#63225C2212yes—
58C22×#63225C2212yes—
59C22×#63225C2211yescharacteristic
60C22×#63225C2211yescharacteristic, complemented
61C2×C4⋊C4×D17C2211yescharacteristic, complemented
62#11762713C2212yescomplemented
63#11762709C2212yescomplemented
64#11762707C2212yescomplemented
65#11762706C2212yescomplemented
66#11762706C2212yescomplemented
67#11762705C2212yescomplemented
68#11762704C2212yescomplemented
69#11762704C2212yescomplemented
70#11762703C2212yescomplemented
71#11762700C2212yescomplemented
72#11762698C2212yescomplemented
73#11762697C2212yescomplemented
74#11762694C2212yescomplemented
75#11762693C2212yescomplemented
76#11762692C2212yescomplemented
77#11762691C2212yescomplemented
78#11762689C2211yescharacteristic
79#11762689C2212yes—
80#11762688C2211yescharacteristic
81#11762688C2212yes—
82#11762686C2211yescharacteristic
83#11762686C2212yes—
84#11762684C2211yescharacteristic
85#11762684C2212yes—
86#11762683C2212yescomplemented
87#11762682C2211yescharacteristic
88#11762682C2212yes—
89#11762682C2212yescomplemented
90#11762681C2211yescharacteristic
91#11762681C2212yes—
92#11762681C2212yescomplemented
93#11762680C2212yescomplemented
94#11762678C2212yescomplemented
95#11762673C2212yescomplemented
96#11762670C2211yescharacteristic
97#11762670C2211yescharacteristic
98#11762668C2212yescomplemented
99#11762667C2212yes—
100#11762667C2212yes—
101#11762667C2212yescomplemented
102#11762665C2211yescharacteristic
103C4×#63225C2212yescomplemented
104C4×#63225C2212yescomplemented
105#11762660C2212yescomplemented
106#11762660C2212yescomplemented
107C22⋊C4×Dic17C2211yescharacteristic
108C22⋊C4×Dic17C2211yescharacteristic
109C22⋊C4×Dic17C2212yes—
110C22⋊C4×Dic17C2212yes—
111C22⋊C4×Dic17C2212yes—
112C22⋊C4×Dic17C2212yes—
113C4×C22⋊Dic17C2211yescharacteristic
114C4×C22⋊Dic17C2212yes—
115C24×C4×C17C2211yescharacteristic
116C2×C17×#120C2211yescharacteristic
117C2×C4×D4×C17C2211yescharacteristic
118C2×C4×D4×C17C2212yes—
119C17×#386C2211yescharacteristic
120C17×#386C2212yes—
121C17×#385C2211yescharacteristic
122C17×#385C2212yes—
123C17×#379C2211yescharacteristic
124C4×C22⋊C4×C17C2211yescharacteristic
125C4×C22⋊C4×C17C2212yes—
126C25×C17C2311yescharacteristic
127C22×D4×C17C2312yes—
128C22×D4×C17C2311yescharacteristic
129C23×C4×C17—24no—
130C23×C4×C17—44no—
131C23×C4×C17C2312yes—
132C23×C4×C17C2312yes—
133C23×C4×C17C2311yescharacteristic
134C23×C4×C17C2311yescharacteristic
135C23×C4×C17C2311yescharacteristic
136C22×C22⋊D17C2312yes—
137C22×C22⋊D17C2311yescharacteristic
138C22×C22⋊D17C2311yescharacteristic
139C23×Dic17—24no—
140C23×Dic17—24no—
141C23×Dic17—24no—
142C23×Dic17—44no—
143C23×Dic17C2×C418yescomplemented
144C23×Dic17C2312yes—
145C23×Dic17C2312yes—
146C23×Dic17C2312yes—
147C23×Dic17C2312yes—
148C23×Dic17C2311yescharacteristic
149C23×Dic17C2311yescharacteristic
150C23×Dic17C2311yescharacteristic
151C23×Dic17C2311yescharacteristic
152C23×Dic17C2311yescharacteristic
153C23×Dic17C2311yescharacteristic
154C2×#63254—24no—
155C2×#63254—24no—
156C2×#63254C2×C418yescomplemented
157C22×C4×D17C2311yescharacteristic
158C22×C4×D17C2311yescharacteristic
159C22×C4×D17C2311yescharacteristic
160C22×Dic34C2311yescharacteristic
161C17×#120C2×C418yescomplemented
162C4×D4×C17—24no—
163C4×D4×C17—44no—
164C2×C4⋊C4×C17C2311yescharacteristic
165C2×C4⋊C4×C17C2312yes—
166C2×C22⋊C4×C17C2311yescharacteristic
167C2×C22⋊C4×C17C2311yescharacteristic
168C2×C22⋊C4×C17C2312yes—
169C2×C22⋊C4×C17C2311yescharacteristic
170C2×C22⋊C4×C17C2312yes—
171C2×C22⋊C4×C17C2312yes—
172C2×C22⋊C4×C17C2311yescharacteristic
173C2×C22⋊C4×C17C2312yes—
174C2×C42×C17C2311yescharacteristic
175C2×C42×C17C2312yes—
176#10587639C2×C418yescomplemented
177C2×C22⋊Dic17C2311yescharacteristic
178C2×C22⋊Dic17C2312yes—
179C2×C22⋊Dic17C2311yescharacteristic
180C2×C22⋊Dic17C2311yescharacteristic
181C2×C22⋊Dic17C2312yes—
182C2×C22⋊Dic17C2312yes—
183C2×C22⋊Dic17C2311yescharacteristic
184C2×C22⋊Dic17C2312yes—
185C2×C22⋊Dic17C2312yes—
186#10587625C2×C4116yescomplemented
187#10587621C2×C418yescomplemented
188D4×Dic17—24no—
189D4×Dic17—44no—
190D4×Dic17C2×C4116yescomplemented
191C4×C22⋊D17—24no—
192C4×C22⋊D17—24no—
193C4×C22⋊D17—44no—
194C2×#63227C2311yescharacteristic
195C2×#63227C2311yescharacteristic
196C2×#63227C2312yes—
197C2×#63227C2312yes—
198C2×#63227C2312yes—
199C2×C4⋊Dic17C2311yescharacteristic
200C2×C4⋊Dic17C2312yes—
201C2×C4⋊Dic17C2312yes—
202C2×#63225—28no—
203C2×#63225—28no—
204C2×#63225—28no—
205C2×#63225—28no—
206C2×#63225—24no—
207C2×#63225—24no—
208C2×#63225—24no—
209C2×#63225—24no—
210C2×#63225D418yescomplemented
211C2×#63225C2312yes—
212C2×#63225C2312yes—
213C2×#63225C2312yes—
214C2×#63225C2312yes—
215C2×#63225C2312yes—
216C2×#63225C2311yescharacteristic
217C2×#63225C2311yescharacteristic
218C2×#63225C2311yescharacteristic
219C2×#63225C2312yes—
220C2×#63225C2311yescharacteristic
221C2×#63225C2312yes—
222C2×#63225C2312yes—
223C2×#63225C2312yes—
224C2×#63225C2312yes—
225C2×#63225C2312yes—
226C2×#63225C2311yescharacteristic
227C2×#63225C2311yescharacteristic
228C2×#63225C2311yescharacteristic
229C2×#63225C2311yescharacteristic
230C2×C4×Dic17C2311yescharacteristic
231C2×C4×Dic17C2311yescharacteristic
232C2×C4×Dic17C2311yescharacteristic
233C2×C4×Dic17C2311yescharacteristic
234C2×C4×Dic17C2311yescharacteristic
235C2×C4×Dic17C2312yes—
236C2×C4×Dic17C2312yes—
237C2×C4×Dic17C2312yes—
238C2×C4×Dic17C2312yes—
239C2×C4×Dic17C2312yes—
240C4⋊C4×D17—24no—
241#10587573—24no—
242#10587572C2×C418yescomplemented
243#10587567—24no—
244#10587567—24no—
245#10587567—44no—
246#10587567C2×C4116yescomplemented
247#10587564C2×C4116yescomplemented
248#10587563—24no—
249#10587563—24no—
250#10587563—24no—
251#10587563C2×C418yescomplemented
252#10587558—24no—
253C4×Dic34—24no—
254C17×#95C2312yes—
255C17×#95C2312yes—
256C17×#95C2312yes—
257#10587502C2312yes—
258#10587502C2312yes—
259#10587502C2312yes—
260#10587502C2312yes—
261#10587502C2312yes—
262#10587502C2312yes—
263#10587502C2312yes—
264#10587502C2312yes—
265#10587502C2312yes—
266#10587502C2312yes—
267#10587502C2312yes—
268#10587502C2312yes—
269#10587502C2312yes—
270C24×C17—22no—
271C24×C17—22no—
272C24×C17—24no—
273C24×C17—24no—
274C24×C17C22×C414yes—
275C24×C17C2411yescharacteristic
276C24×C17C2411yescharacteristic
277C24×C17C2412yes—
278C23×D17C2411yescharacteristic
279C2×D4×C17—22no—
280C2×D4×C17—22no—
281C2×D4×C17—24no—
282C2×D4×C17—24no—
283C2×D4×C17C22×C414yes—
284C2×D4×C17C22×C418yes—
285C22×C4×C17—22no—
286C22×C4×C17—24no—
287C22×C4×C17—24no—
288C22×C4×C17—24no—
289C22×C4×C17—24no—
290C22×C4×C17—22no—
291C22×C4×C17—42no—
292C22×C4×C17—42no—
293C22×C4×C17—42no—
294C22×C4×C17—42no—
295C22×C4×C17—42no—
296C22×C4×C17—416no—
297C22×C4×C17C2×D414yes—
298C22×C4×C17C2411yescharacteristic
299C22×C4×C17C2412yes—
300C22×C4×C17C2411yescharacteristic
301C22×C4×C17C2412yes—
302C22×C4×C17C2411yescharacteristic
303C22×C4×C17C2412yes—
304C22×C4×C17C2411yescharacteristic
305C22×C4×C17C2411yescharacteristic
306C2×C22⋊D17—22no—
307C2×C22⋊D17—22no—
308C2×C22⋊D17—24no—
309C2×C22⋊D17—24no—
310C2×C22⋊D17—22no—
311C2×C22⋊D17—22no—
312C2×C22⋊D17C22×C414yes—
313C2×C22⋊D17C22×C418yes—
314C2×C22⋊D17C22×C414yescomplemented
315C22×Dic17—22no—
316C22×Dic17—22no—
317C22×Dic17—232no—
318C22×Dic17—22no—
319C22×Dic17—24no—
320C22×Dic17—24no—
321C22×Dic17—22no—
322C22×Dic17—24no—
323C22×Dic17—24no—
324C22×Dic17—22no—
325C22×Dic17—24no—
326C22×Dic17—24no—
327C22×Dic17—24no—
328C22×Dic17—24no—
329C22×Dic17—22no—
330C22×Dic17—42no—
331C22×Dic17—42no—
332C22×Dic17—42no—
333C22×Dic17—42no—
334C22×Dic17—42no—
335C22×Dic17—416no—
336C22×Dic17C22×C418yes—
337C22×Dic17C22×C418yes—
338C22×Dic17C22×C414yes—
339C22×Dic17C22×C414yes—
340C22×Dic17C22×C414yescomplemented
341C22×Dic17C2×D414yes—
342C22×Dic17C2×D414yes—
343C22×Dic17#4114yes—
344C22×Dic17C2411yescharacteristic
345C22×Dic17C2412yes—
346C22×Dic17C2411yescharacteristic
347C22×Dic17C2412yes—
348C22×Dic17C2411yescharacteristic
349C22×Dic17C2412yes—
350C22×Dic17C2412yes—
351C22×Dic17C2411yescharacteristic
352C22×Dic17C2411yescharacteristic
353C22×Dic17C2411yescharacteristic
354C22×Dic17C2411yescharacteristic
355#63254—232no—
356C2×C4×D17—22no—
357C2×C4×D17—22no—
358C2×C4×D17—22no—
359C2×C4×D17—22no—
360C2×C4×D17—42no—
361C2×C4×D17—42no—
362C2×C4×D17C22×C414yescomplemented
363C2×Dic34—22no—
364C2×Dic34—22no—
365C2×Dic34C22×C414yescomplemented
366C4⋊C4×C17—22no—
367C4⋊C4×C17—42no—
368C22⋊C4×C17—22no—
369C22⋊C4×C17—22no—
370C22⋊C4×C17—24no—
371C22⋊C4×C17—24no—
372C22⋊C4×C17—22no—
373C22⋊C4×C17—42no—
374C22⋊C4×C17C22×C414yes—
375C22⋊C4×C17C22×C418yes—
376C42×C17—22no—
377C42×C17—42no—
378C22⋊Dic17—22no—
379C22⋊Dic17—22no—
380C22⋊Dic17—24no—
381C22⋊Dic17—24no—
382C22⋊Dic17—22no—
383C22⋊Dic17—42no—
384C22⋊Dic17C22×C414yes—
385C22⋊Dic17C22×C418yes—
386C22⋊Dic17C22×C418yescomplemented
387#63227—22no—
388#63227—22no—
389#63227—42no—
390#63227—42no—
391#63227C22×C418yescomplemented
392C4⋊Dic17—22no—
393C4⋊Dic17—42no—
394C4⋊Dic17C22×C418yescomplemented
395#63225—22no—
396#63225—24no—
397#63225—24no—
398#63225—22no—
399#63225—22no—
400#63225—22no—
401#63225—24no—
402#63225—24no—
403#63225—24no—
404#63225—24no—
405#63225—24no—
406#63225—42no—
407#63225—42no—
408#63225C22×C418yescomplemented
409#63225C22×C418yescomplemented
410#63225C2×D414yes—
411#63225C2×D414yes—
412#63225C2×D414yes—
413#63225C2×D414yes—
414C4×Dic17—22no—
415C4×Dic17—22no—
416C4×Dic17—22no—
417C4×Dic17—22no—
418C4×Dic17—22no—
419C4×Dic17—24no—
420C4×Dic17—42no—
421C4×Dic17—42no—
422C4×Dic17—42no—
423C4×Dic17C22×C418yescomplemented
424#34200—171nomaximal, Sylow
425C23×C17—28no—
426C23×C17—28no—
427C23×C17—216no—
428C23×C17—28no—
429C23×C17—216no—
430C23×C17—22no—
431C23×C17—22no—
432C23×C17—22no—
433C23×C17—22no—
434C23×C17—22no—
435C23×C17—22no—
436C23×C17—21no—
437C23×C17—21no—
438C23×C17—22no—
439C23×C17—22no—
440C23×C17C23×C412yes—
441C23×C17C23×C412yes—
442C23×C17C23×C414yes—
443C23×C17C22×D412yes—
444C23×C17C2×#4112yes—
445C23×C17H(5,𝔽2)14yes—
446C23×C172−1+414yes—
447C23×C17C2511yescharacteristic
448C22×D17—21no—
449C22×D17—21no—
450C22×D17—22no—
451C22×D17—22no—
452C22×D17C23×C412yes—
453D4×C17—28no—
454D4×C17—216no—
455C2×C4×C17—21no—
456C2×C4×C17—21no—
457C2×C4×C17—22no—
458C2×C4×C17—22no—
459C2×C4×C17—22no—
460C2×C4×C17—22no—
461C2×C4×C17—21no—
462C2×C4×C17—21no—
463C2×C4×C17—22no—
464C2×C4×C17—22no—
465C2×C4×C17—22no—
466C2×C4×C17—22no—
467C2×C4×C17—22no—
468C2×C4×C17—22no—
469C2×C4×C17—22no—
470C2×C4×C17—22no—
471C2×C4×C17—44no—
472C2×C4×C17—48no—
473C2×C4×C17—48no—
474C2×C4×C17—44no—
475C2×C4×C17—82no—
476C2×C4×C17C23×C412yes—
477C2×C4×C17C23×C414yes—
478C2×C4×C17C22×D412yes—
479C2×C4×C17C22×D412yes—
480C22⋊D17—28no—
481C22⋊D17—216no—
482C22⋊D17—28no—
483C2×Dic17—28no—
484C2×Dic17—21no—
485C2×Dic17—22no—
486C2×Dic17—21no—
487C2×Dic17—22no—
488C2×Dic17—22no—
489C2×Dic17—22no—
490C2×Dic17—22no—
491C2×Dic17—22no—
492C2×Dic17—28no—
493C2×Dic17—216no—
494C2×Dic17—216no—
495C2×Dic17—21no—
496C2×Dic17—21no—
497C2×Dic17—22no—
498C2×Dic17—22no—
499C2×Dic17—22no—
500C2×Dic17—22no—
501C2×Dic17—22no—
502C2×Dic17—22no—
503C2×Dic17—22no—
504C2×Dic17—22no—
505C2×Dic17—44no—
506C2×Dic17—48no—
507C2×Dic17—48no—
508C2×Dic17—44no—
509C2×Dic17—82no—
510C2×Dic17C4×D4116yescomplemented
511C2×Dic17C23×C414yes—
512C2×Dic17C23×C412yes—
513C2×Dic17C23×C414yes—
514C2×Dic17C23×C412yes—
515C2×Dic17C23×C412yes—
516C2×Dic17C22×D412yes—
517C2×Dic17C22×D412yes—
518C2×Dic17C22×D412yes—
519C2×Dic17C22×D412yes—
520C2×Dic17C2×#4112yes—
521C2×Dic17C2×#4112yes—
522C4×D17—28no—
523C4×D17—82no—
524C4×D17—82no—
525Dic34—28no—
526C2×#525—171no—
527C2×#520—171no—
528C23×C4⋊C4—171no—
529#2361—172no—
530#2361—172no—
531#2360—172no—
532#2360—172no—
533#2352—172no—
534#2352—172no—
535D4×C4⋊C4—172no—
536D4×C4⋊C4—172no—
537#2322—171no—
538#2322—171no—
539#2322—171no—
540#2322—171no—
541#2317—171no—
542#2311—171no—
543C4×#120—171no—
544C4×#120—171no—
545C4×#120—171no—
546C4×#120D1711yescharacteristic, complemented
547#2280—171no—
548#2274—171no—
549C22×C17—232no—
550C22×C17—24no—
551C22×C17—24no—
552C22×C17—24no—
553C22×C17—22no—
554C22×C17—24no—
555C22×C17—22no—
556C22×C17—24no—
557C22×C17—24no—
558C22×C17—24no—
559C22×C17—24no—
560C22×C17—22no—
561C22×C17—24no—
562C22×C17—41no—
563C22×C17—41no—
564C22×C17—42no—
565C22×C17C2×C4×D414yes—
566C22×C17#52018yescomplemented
567C22×C17C24×C411yescharacteristic
568C22×C17C23×D411yescharacteristic
569C22×C17C22×#4111yescharacteristic
570C22×C17C2×H(5,𝔽2)12yes—
571C22×C17C2×2−1+412yes—
572C2×D17—22no—
573C2×D17—24no—
574C2×D17—41no—
575C2×D17—41no—
576C2×D17—42no—
577C4×C17—22no—
578C4×C17—24no—
579C4×C17—22no—
580C4×C17—22no—
581C4×C17—41no—
582C4×C17—42no—
583C4×C17—41no—
584C4×C17—42no—
585Dic17—22no—
586Dic17—24no—
587Dic17—24no—
588Dic17—22no—
589Dic17—22no—
590Dic17—41no—
591Dic17—42no—
592Dic17—41no—
593Dic17—42no—
594Dic17C2×C4×D414yes—
595Dic17C2×C4×D414yes—
596C22×#41—171no—
597C24×C4—171no—
598C24×C4—171no—
599C24×C4C2×D1711yescharacteristic
600#525—1716no—
601C2×#123—171no—
602C2×#123—171no—
603C2×C22⋊Q8—172no—
604C2×#121—172no—
605C2×#120—171no—
606C2×#120C2×D1711yescharacteristic
607#520—348no—
608C2×C4×Q8—171no—
609C2×C4×Q8—171no—
610C2×C4×D4—172no—
611C2×C4×D4—171no—
612C2×C4×D4—171no—
613C2×C4×D4—171no—
614C2×C4×D4—172no—
615C2×C4×D4—172no—
616C2×C4×D4—172no—
617C2×C4×D4—171no—
618C2×C4×D4—171no—
619C2×C4×D4—172no—
620C2×C4×D4C2×D1711yescharacteristic
621C2×C4×D4C2×D1712yes—
622C2×#117—171no—
623C2×#117—171no—
624C2×#117—171no—
625C2×#117—171no—
626C2×#117—171no—
627C22×C4⋊C4—171no—
628C22×C4⋊C4—171no—
629C22×C4⋊C4—171no—
630C22×C4⋊C4—171no—
631C22×C4⋊C4—171no—
632C22×C4⋊C4—172no—
633C22×C4⋊C4—172no—
634C22×C4⋊C4—172no—
635C22×C4⋊C4—172no—
636C22×C4⋊C4—171no—
637C22×C4⋊C4—348no—
638#391—172no—
639#390—172no—
640#389—172no—
641#389—172no—
642#389—172no—
643#389—172no—
644#389—172no—
645#389—172no—
646#388—172no—
647#388—172no—
648#388—172no—
649#388—172no—
650#387—172no—
651#387—172no—
652#387—172no—
653#387—172no—
654#386—171no—
655#386—172no—
656#386—171no—
657#386—172no—
658#386—171no—
659#386—172no—
660#386C2×D1711yescharacteristic
661#386C2×D1712yes—
662#385—171no—
663#385—172no—
664#385—172no—
665#385—172no—
666#385—171no—
667#385—171no—
668#385—172no—
669#385—172no—
670#385—172no—
671#385—172no—
672#385C2×D1711yescharacteristic
673#385C2×D1712yes—
674#384—172no—
675#382—172no—
676#381—171no—
677#381—171no—
678#380—172no—
679#380—172no—
680#380—172no—
681#380—172no—
682#379—171no—
683#379C2×D1711yescharacteristic
684C4×C4⋊C4—172no—
685C4×C4⋊C4—172no—
686C4×C4⋊C4—172no—
687C4×C4⋊C4—172no—
688C4×C22⋊C4—171no—
689C4×C22⋊C4—172no—
690C4×C22⋊C4—171no—
691C4×C22⋊C4—171no—
692C4×C22⋊C4—172no—
693C4×C22⋊C4—172no—
694C4×C22⋊C4—172no—
695C4×C22⋊C4—172no—
696C4×C22⋊C4C2×D1711yescharacteristic
697C4×C22⋊C4C2×D1712yes—
698C2×C17—24no—
699C2×C17—28no—
700C2×C17—42no—
701C2×C17C22×C4×D411yescharacteristic
702C2×C17C2×#52012yes—
703C2×C17#348411yescharacteristic
704C2×C17#348611yescharacteristic
705C2×C17#349212yes—
706D17—42no—
707C25C22×D1711yescharacteristic
708C2×#41—178no—
709C2×#41—344no—
710C2×#41—344no—
711C22×Q8—171no—
712C22×D4—172no—
713C22×D4—171no—
714C22×D4—171no—
715C22×D4C22×D1712yes—
716C22×D4C22×D1711yescharacteristic
717C23×C4—24no—
718C23×C4—44no—
719C23×C4—171no—
720C23×C4—178no—
721C23×C4—172no—
722C23×C4—172no—
723C23×C4—171no—
724C23×C4—171no—
725C23×C4—171no—
726C23×C4—171no—
727C23×C4—172no—
728C23×C4—172no—
729C23×C4—171no—
730C23×C4—171no—
731C23×C4—171no—
732C23×C4—171no—
733C23×C4—344no—
734C23×C4—344no—
735C23×C4—344no—
736C23×C4—684no—
737C23×C4C22×D1712yes—
738C23×C4C22×D1712yes—
739C23×C4C22×D1711yescharacteristic
740C23×C4C22×D1711yescharacteristic
741C23×C4C22×D1711yescharacteristic
742#123—178no—
743#123—178no—
744C22⋊Q8—1716no—
745#121—1716no—
746#120—178no—
747#120C4×D1718yescomplemented
748C4×Q8—344no—
749C4×Q8—344no—
750C4×D4—24no—
751C4×D4—44no—
752C4×D4—1716no—
753C4×D4—1716no—
754C4×D4—344no—
755C4×D4—344no—
756C4×D4—344no—
757C4×D4—344no—
758C4×D4—344no—
759C4×D4—684no—
760C4×D4—684no—
761C4×D4—684no—
762#117—178no—
763#117—344no—
764#117—344no—
765#117—344no—
766#117—344no—
767C2×C4⋊C4—178no—
768C2×C4⋊C4—171no—
769C2×C4⋊C4—171no—
770C2×C4⋊C4—171no—
771C2×C4⋊C4—171no—
772C2×C4⋊C4—172no—
773C2×C4⋊C4—172no—
774C2×C4⋊C4—172no—
775C2×C4⋊C4—172no—
776C2×C4⋊C4—172no—
777C2×C4⋊C4—172no—
778C2×C4⋊C4—172no—
779C2×C4⋊C4—172no—
780C2×C4⋊C4—172no—
781C2×C4⋊C4—171no—
782C2×C4⋊C4—171no—
783C2×C4⋊C4—171no—
784C2×C4⋊C4—171no—
785C2×C4⋊C4—171no—
786C2×C4⋊C4—172no—
787C2×C4⋊C4—172no—
788C2×C4⋊C4—172no—
789C2×C4⋊C4—172no—
790C2×C4⋊C4—344no—
791C2×C4⋊C4—348no—
792C2×C4⋊C4—348no—
793C2×C4⋊C4—348no—
794C2×C4⋊C4—348no—
795C2×C4⋊C4—344no—
796C2×C4⋊C4—344no—
797C2×C4⋊C4—344no—
798C2×C4⋊C4—344no—
799C2×C4⋊C4C22×D1711yescharacteristic
800C2×C4⋊C4C22×D1712yes—
801C2×C22⋊C4—171no—
802C2×C22⋊C4—172no—
803C2×C22⋊C4—172no—
804C2×C22⋊C4—172no—
805C2×C22⋊C4—171no—
806C2×C22⋊C4—171no—
807C2×C22⋊C4—171no—
808C2×C22⋊C4—172no—
809C2×C22⋊C4—172no—
810C2×C22⋊C4—171no—
811C2×C22⋊C4—171no—
812C2×C22⋊C4—172no—
813C2×C22⋊C4—172no—
814C2×C22⋊C4—172no—
815C2×C22⋊C4C22×D1711yescharacteristic
816C2×C22⋊C4C22×D1711yescharacteristic
817C2×C22⋊C4C22×D1711yescharacteristic
818C2×C22⋊C4C22×D1712yes—
819C2×C22⋊C4C22×D1712yes—
820C2×C22⋊C4C22×D1712yes—
821C2×C22⋊C4C22×D1711yescharacteristic
822C2×C22⋊C4C22×D1712yes—
823C2×C42—172no—
824C2×C42—171no—
825C2×C42—171no—
826C2×C42—171no—
827C2×C42—171no—
828C2×C42—171no—
829C2×C42—172no—
830C2×C42—172no—
831C2×C42—172no—
832C2×C42—172no—
833C2×C42C22×D1711yescharacteristic
834C2×C42C22×D1712yes—
835#95—172no—
836#95—172no—
837#95—172no—
838#95—172no—
839#95—172no—
840#95—172no—
841#95—172no—
842#95—172no—
843#95—172no—
844#95—172no—
845#95—172no—
846#95—172no—
847#95—172no—
848#95C22×D1712yes—
849#95C22×D1712yes—
850#95C22×D1712yes—
851C17#3420011yescharacteristic, complemented, Sylow
852C24—22no—
853C24—24no—
854C24—22no—
855C24—24no—
856C24—171no—
857C24C2×C4×D1714yes—
858C24C23×D1711yescharacteristic
859C24C23×D1711yescharacteristic
860C24C23×D1712yes—
861#41—3432no—
862C2×Q8—174no—
863C2×Q8—342no—
864C2×Q8—342no—
865C2×D4—22no—
866C2×D4—24no—
867C2×D4—22no—
868C2×D4—24no—
869C2×D4—178no—
870C2×D4—174no—
871C2×D4—174no—
872C2×D4—342no—
873C2×D4—342no—
874C2×D4—342no—
875C2×D4—344no—
876C2×D4—342no—
877C2×D4—344no—
878C2×D4C2×C4×D1718yes—
879C2×D4C2×C4×D1714yes—
880C22×C4—22no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—22no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—416no—
892C22×C4—174no—
893C22×C4—174no—
894C22×C4—174no—
895C22×C4—171no—
896C22×C4—171no—
897C22×C4—178no—
898C22×C4—178no—
899C22×C4—174no—
900C22×C4—174no—
901C22×C4—172no—
902C22×C4—171no—
903C22×C4—172no—
904C22×C4—171no—
905C22×C4—171no—
906C22×C4—174no—
907C22×C4—174no—
908C22×C4—171no—
909C22×C4—172no—
910C22×C4—172no—
911C22×C4—171no—
912C22×C4—342no—
913C22×C4—342no—
914C22×C4—342no—
915C22×C4—344no—
916C22×C4—344no—
917C22×C4—342no—
918C22×C4—3432no—
919C22×C4—344no—
920C22×C4—344no—
921C22×C4—342no—
922C22×C4—344no—
923C22×C4—344no—
924C22×C4—342no—
925C22×C4—342no—
926C22×C4—342no—
927C22×C4—342no—
928C22×C4—344no—
929C22×C4—344no—
930C22×C4—342no—
931C22×C4—682no—
932C22×C4—682no—
933C22×C4—682no—
934C22×C4—682no—
935C22×C4—682no—
936C22×C4—682no—
937C22×C4—682no—
938C22×C4—6816no—
939C22×C4D4×D1714yes—
940C22×C4C23×D1711yescharacteristic
941C22×C4C23×D1712yes—
942C22×C4C23×D1712yes—
943C22×C4C23×D1711yescharacteristic
944C22×C4C23×D1712yes—
945C22×C4C23×D1711yescharacteristic
946C22×C4C23×D1711yescharacteristic
947C22×C4C23×D1711yescharacteristic
948C4⋊C4—22no—
949C4⋊C4—42no—
950C4⋊C4—178no—
951C4⋊C4—178no—
952C4⋊C4—178no—
953C4⋊C4—174no—
954C4⋊C4—174no—
955C4⋊C4—174no—
956C4⋊C4—174no—
957C4⋊C4—344no—
958C4⋊C4—344no—
959C4⋊C4—344no—
960C4⋊C4—344no—
961C4⋊C4—342no—
962C4⋊C4—342no—
963C4⋊C4—342no—
964C4⋊C4—342no—
965C4⋊C4—344no—
966C4⋊C4—344no—
967C4⋊C4—344no—
968C4⋊C4—342no—
969C4⋊C4—682no—
970C4⋊C4—682no—
971C4⋊C4—682no—
972C22⋊C4—22no—
973C22⋊C4—24no—
974C22⋊C4—22no—
975C22⋊C4—24no—
976C22⋊C4—22no—
977C22⋊C4—42no—
978C22⋊C4—174no—
979C22⋊C4—178no—
980C22⋊C4—178no—
981C22⋊C4—178no—
982C22⋊C4—342no—
983C22⋊C4—342no—
984C22⋊C4—342no—
985C22⋊C4—344no—
986C22⋊C4—342no—
987C22⋊C4—344no—
988C22⋊C4—342no—
989C22⋊C4—682no—
990C22⋊C4—682no—
991C22⋊C4—682no—
992C22⋊C4C2×C4×D1714yes—
993C22⋊C4C2×C4×D1718yes—
994C42—22no—
995C42—42no—
996C42—178no—
997C42—342no—
998C42—342no—
999C42—342no—
1000C42—342no—
1001C42—344no—
1002C42—342no—
1003C42—682no—
1004C42—682no—
1005C42—682no—
1006C23—28no—
1007C23—28no—
1008C23—216no—
1009C23—28no—
1010C23—216no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—21no—
1018C23—21no—
1019C23—22no—
1020C23—22no—
1021C23—172no—
1022C23—341no—
1023C23—341no—
1024C23—342no—
1025C23—342no—
1026C23C22×C4×D1712yes—
1027C23C22×C4×D1712yes—
1028C23C22×C4×D1714yes—
1029C23C2×D4×D1712yes—
1030C23#1058769114yes—
1031C23#41×D1712yes—
1032C23#1058769714yes—
1033C23C24×D1711yescharacteristic
1034Q8—348no—
1035D4—28no—
1036D4—216no—
1037D4—348no—
1038D4—348no—
1039D4—3416no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—44no—
1057C2×C4—48no—
1058C2×C4—48no—
1059C2×C4—44no—
1060C2×C4—82no—
1061C2×C4—1716no—
1062C2×C4—172no—
1063C2×C4—172no—
1064C2×C4—172no—
1065C2×C4—172no—
1066C2×C4—172no—
1067C2×C4—172no—
1068C2×C4—174no—
1069C2×C4—174no—
1070C2×C4—172no—
1071C2×C4—172no—
1072C2×C4—172no—
1073C2×C4—348no—
1074C2×C4—3416no—
1075C2×C4—3416no—
1076C2×C4—348no—
1077C2×C4—348no—
1078C2×C4—341no—
1079C2×C4—342no—
1080C2×C4—342no—
1081C2×C4—341no—
1082C2×C4—342no—
1083C2×C4—342no—
1084C2×C4—342no—
1085C2×C4—342no—
1086C2×C4—341no—
1087C2×C4—341no—
1088C2×C4—342no—
1089C2×C4—342no—
1090C2×C4—342no—
1091C2×C4—342no—
1092C2×C4—342no—
1093C2×C4—342no—
1094C2×C4—342no—
1095C2×C4—342no—
1096C2×C4—684no—
1097C2×C4—688no—
1098C2×C4—688no—
1099C2×C4—684no—
1100C2×C4—1362no—
1101C2×C4—1362no—
1102C2×C4—1362no—
1103C2×C4C22×C4×D1714yes—
1104C2×C4C22×C4×D1712yes—
1105C2×C4C2×D4×D1712yes—
1106C2×C4C2×D4×D1712yes—
1107C22—232no—
1108C22—22no—
1109C22—24no—
1110C22—22no—
1111C22—24no—
1112C22—24no—
1113C22—24no—
1114C22—24no—
1115C22—24no—
1116C22—24no—
1117C22—24no—
1118C22—22no—
1119C22—24no—
1120C22—41no—
1121C22—41no—
1122C22—42no—
1123C22—342no—
1124C22—344no—
1125C22—681no—
1126C22—681no—
1127C22—682no—
1128C22C4×D4×D1714yes—
1129C22#1176328818yescomplemented
1130C22C23×C4×D1711yescharacteristic
1131C22C22×D4×D1711yescharacteristic
1132C22C2×#41×D1711yescharacteristic
1133C22C2×#1058769112yes—
1134C22C2×#1058769712yes—
1135C4—22no—
1136C4—22no—
1137C4—22no—
1138C4—24no—
1139C4—42no—
1140C4—41no—
1141C4—41no—
1142C4—42no—
1143C4—174no—
1144C4—174no—
1145C4—342no—
1146C4—342no—
1147C4—344no—
1148C4—342no—
1149C4—344no—
1150C4—682no—
1151C4—681no—
1152C4—681no—
1153C4—682no—
1154C2—24no—
1155C2—28no—
1156C2—42no—
1157C2—682no—
1158C2C2×C4×D4×D1711yescharacteristic
1159C2C2×#1176328812yes—
1160C2#1454241311yescharacteristic
1161C2#1454243111yescharacteristic
1162C2#1454248512yes—
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC4×C17×#120C2
socle, cosocleC23×C17C25
prime radicalC2×#11763315C2
hypercenterC4×#120D17
hypocenterC17#34200
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
2. C2×#11763288C2semidirect
3. C23×#63225C2semidirect
4. #14531801C2semidirect
5. #14531795C2semidirect
6. #14531790C2semidirect
7. #14531784C2semidirect
8. #14531711C2semidirect
9. #14531707C2semidirect
10. #14531682C2semidirect
11. D4×#63225C2semidirect
12. #14531458C2semidirect
13. #14531455C2semidirect
14. #14531452C2semidirect
15. #14531449C2semidirect
16. #14531403C2semidirect
17. #14531371C2semidirect
18. #120×Dic17C2semidirect
19. C4×#10587639C2semidirect
20. #14531283C2semidirect
21. #14531162C2semidirect
22. #14531139C2semidirect
23. C4×C17×#120C2semidirect
27. #11763315C4semidirect
34. C2×C4×Dic34C22semidirect
35. C2×#10587573C22semidirect
41. C2×C4×C22⋊D17C22semidirect
45. C2×#10587567C22semidirect
46. C2×#10587558C22semidirect
50. C2×#10587563C22semidirect
60. C22×#63225C22semidirect
61. C2×C4⋊C4×D17C22semidirect
62. #11762713C22semidirect
63. #11762709C22semidirect
64. #11762707C22semidirect
65. #11762706C22semidirect
66. #11762706C22semidirect
67. #11762705C22semidirect
68. #11762704C22semidirect
69. #11762704C22semidirect
70. #11762703C22semidirect
71. #11762700C22semidirect
72. #11762698C22semidirect
73. #11762697C22semidirect
74. #11762694C22semidirect
75. #11762693C22semidirect
76. #11762692C22semidirect
77. #11762691C22semidirect
86. #11762683C22semidirect
89. #11762682C22semidirect
92. #11762681C22semidirect
93. #11762680C22semidirect
94. #11762678C22semidirect
95. #11762673C22semidirect
98. #11762668C22semidirect
101. #11762667C22semidirect
103. C4×#63225C22semidirect
104. C4×#63225C22semidirect
105. #11762660C22semidirect
106. #11762660C22semidirect
143. C23×Dic17C2×C4semidirect
156. C2×#63254C2×C4semidirect
161. C17×#120C2×C4semidirect
176. #10587639C2×C4semidirect
186. #10587625C2×C4semidirect
187. #10587621C2×C4semidirect
190. D4×Dic17C2×C4semidirect
210. C2×#63225D4semidirect
242. #10587572C2×C4semidirect
246. #10587567C2×C4semidirect
247. #10587564C2×C4semidirect
251. #10587563C2×C4semidirect
314. C2×C22⋊D17C22×C4semidirect
340. C22×Dic17C22×C4semidirect
362. C2×C4×D17C22×C4semidirect
365. C2×Dic34C22×C4semidirect
386. C22⋊Dic17C22×C4semidirect
391. #63227C22×C4semidirect
394. C4⋊Dic17C22×C4semidirect
408. #63225C22×C4semidirect
409. #63225C22×C4semidirect
423. C4×Dic17C22×C4semidirect
510. C2×Dic17C4×D4semidirect
546. C4×#120D17semidirect
566. C22×C17#520semidirect
747. #120C4×D17semidirect
851. C17#34200semidirect
1129. C22#11763288semidirect

Maximal subgroups

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

subgroupindex
C2×#117633152
C2×#117632882
C23×#632252
#145318012
#145317952
#145317902
#145317842
#145317112
#145317072
#145316822
D4×#632252
#145314582
#145314552
#145314522
#145314492
#145314032
#145313712
#120×Dic172
C4×#105876392
#145312832
#145311622
#145311392
C4×C17×#1202
#3420017