Finite Group Databasebeta

← #32157905

Subgroups — #32157905

Order 18176.

2110 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986551C211yesmaximal, characteristic
2#22591425C211yesmaximal, characteristic
3#22591423C211yesmaximal, characteristic
4#22591421C212yesmaximal
5#22591420C211yesmaximal, characteristic
6#22591418C212yesmaximal
7#22591296C212yesmaximal, complemented
8#22591294C212yesmaximal, complemented
9#22591294C212yesmaximal, complemented
10#22591293C212yesmaximal, complemented
11#22591085C212yesmaximal, complemented
12#22591083C212yesmaximal, complemented
13#22590959C212yesmaximal
14#22590897C212yesmaximal, complemented
15C4×#14556118C212yesmaximal, complemented
16C2×#17985863C211yesmaximal, characteristic
17#22590695C212yesmaximal
18C4×#14556084C211yesmaximal, characteristic
19C71×#2368C211yesmaximal, characteristic
20#17986551C4116yescomplemented
21C2×#14556127C2211yescharacteristic
22C2×#14556126C2211yescharacteristic
23C2×#14556118C2212yes—
24C2×#14556107C2211yescharacteristic
25C2×#14556105C2212yes—
26C2×Q8×Dic71C2211yescharacteristic
27C2×#14556093C2212yes—
28C2×#14556093C2211yescharacteristic
29C2×#14556084C2211yescharacteristic
30C2×#14556084C2212yes—
31C2×#14556084C2211yescharacteristic
32C22×Dic71⋊C4C2212yes—
33C22×C4×Dic71C2211yescharacteristic
34#17985906C2212yes—
35#17985905C2212yes—
36#17985904C2212yes—
37#17985903C2212yes—
38#17985903C2212yes—
39#17985903C2212yes—
40#17985903C2212yes—
41#17985896C2212yes—
42#17985896C2212yes—
43#17985894C2212yes—
44#17985894C2212yes—
45#17985886C2212yes—
46#17985886C2212yes—
47#17985885C2212yes—
48#17985885C2212yes—
49#17985884C2212yes—
50#17985884C2212yes—
51#17985883C2212yes—
52#17985883C2212yes—
53#17985882C2212yes—
54#17985882C2212yes—
55#17985881C2212yes—
56#17985881C2212yes—
57#17985880C2212yes—
58#17985880C2212yes—
59#17985874C2212yes—
60#17985872C2212yes—
61#17985871C2212yes—
62#17985868C2212yes—
63#17985868C2212yes—
64#17985863C2211yescharacteristic
65#17985863C2211yescharacteristic
66#17985863C2212yes—
67#17985863C2212yes—
68#17985863C2211yescharacteristic
69#17985863C2211yescharacteristic
70#17985863C2212yes—
71#17985863C2212yes—
72C4⋊C4×Dic71C2212yes—
73C4⋊C4×Dic71C2212yes—
74C4×Dic71⋊C4C2212yes—
75C4×Dic71⋊C4C2212yes—
76C4×Dic71⋊C4C2212yes—
77C4×Dic71⋊C4C2212yes—
78C4×Dic71⋊C4C2212yes—
79C4×Dic71⋊C4C2212yes—
80C4×Dic71⋊C4C2212yes—
81C4×C4⋊Dic71C2212yes—
82#17985850C2212yes—
83#17985850C2212yes—
84#17985850C2212yes—
85#17985850C2212yes—
86#17985850C2212yes—
87#17985850C2212yes—
88#17985850C2212yes—
89C22⋊C4×Dic71C2211yescharacteristic
90C22⋊C4×Dic71C2212yes—
91C22⋊C4×Dic71C2211yescharacteristic
92C22⋊C4×Dic71C2212yes—
93C4×C22⋊Dic71C2212yes—
94C4×C22⋊Dic71C2211yescharacteristic
95#17985844C2212yes—
96C2×C71⋊#95C2212yes—
97C2×C71⋊#95C2211yescharacteristic
98C42×Dic71C2212yes—
99C2×C22⋊Q8×C71C2211yescharacteristic
100#391×C71C2212yes—
101#387×C71C2212yes—
102#387×C71C2212yes—
103#385×C71C2212yes—
104C4×C4⋊C4×C71C2212yes—
105C4×C22⋊C4×C71C2212yes—
106C4×C22⋊C4×C71C2211yescharacteristic
107C2×#95×C71C2211yescharacteristic
108C22×Dic142C2311yescharacteristic
109C22×Dic142C2312yes—
110C23×Dic71C2312yes—
111C23×Dic71C2311yescharacteristic
112C23×Dic71C2311yescharacteristic
113#14556127C2×C418yescomplemented
114#14556126C2×C418yescomplemented
115#14556118C2×C4116yescomplemented
116#14556107C2×C418yes—
117#14556105C2×C4116yes—
118Q8×Dic71C2×C418yescomplemented
119#14556093C2×C4116yescomplemented
120#14556093C2×C418yescomplemented
121#14556084—24no—
122#14556084C2×C4116yes—
123#14556084Q818yescomplemented
124C2×C4⋊Dic71C2312yes—
125C2×C4⋊Dic71C2312yes—
126C2×C4⋊Dic71C2312yes—
127C2×C4⋊Dic71C2311yescharacteristic
128C2×Dic71⋊C4—28no—
129C2×Dic71⋊C4C2312yes—
130C2×Dic71⋊C4C2312yes—
131C2×Dic71⋊C4C2312yes—
132C2×Dic71⋊C4C2312yes—
133C2×Dic71⋊C4C2312yes—
134C2×Dic71⋊C4C2312yes—
135C2×Dic71⋊C4C2312yes—
136C2×Dic71⋊C4C2312yes—
137C2×Dic71⋊C4C2312yes—
138C2×Dic71⋊C4C2312yes—
139C2×Dic71⋊C4C2312yes—
140C2×Dic71⋊C4C2312yes—
141C2×Dic71⋊C4C2312yes—
142C2×Dic71⋊C4C2312yes—
143C2×Dic71⋊C4C2312yes—
144C2×C22⋊Dic71C2311yescharacteristic
145C2×C22⋊Dic71C2312yes—
146C2×C22⋊Dic71C2311yescharacteristic
147C2×C4×Dic71C2×C418yes—
148C2×C4×Dic71C2312yes—
149C2×C4×Dic71C2312yes—
150C2×C4×Dic71C2312yes—
151C2×C4×Dic71C2312yes—
152C2×C4×Dic71C2312yes—
153C2×C4×Dic71C2312yes—
154C2×C4×Dic71C2312yes—
155C2×C4×Dic71C2312yes—
156C2×C4×Dic71C2312yes—
157C2×C4×Dic71C2312yes—
158C2×C4×Dic71C2311yescharacteristic
159C2×C4×Dic71C2311yescharacteristic
160C2×C4×Dic71C2311yescharacteristic
161C2×C4×Dic71C2312yes—
162C2×C4×Dic71C2312yes—
163C2×C4×Dic71C2311yescharacteristic
164C2×C4×Dic71C2312yes—
165C71⋊#95C2312yes—
166C71⋊#95C2312yes—
167C71⋊#95C2311yescharacteristic
168C71⋊#95C2311yescharacteristic
169C71⋊#95C2312yes—
170C71⋊#95C2312yes—
171C71⋊#95C2312yes—
172C71⋊#95C2312yes—
173C71⋊#95C2312yes—
174C71⋊#95C2312yes—
175C71⋊#95C2312yes—
176C71⋊#95C2312yes—
177C71⋊#95C2312yes—
178C71⋊#95C2312yes—
179C71⋊#95C2312yes—
180C71⋊#95C2312yes—
181C71⋊#95C2312yes—
182C71⋊#95C2312yes—
183C71⋊#95C2312yes—
184C71⋊#95C2312yes—
185C71⋊#95C2312yes—
186C71⋊#95C2312yes—
187C22×Q8×C71C2311yescharacteristic
188C23×C4×C71C2312yes—
189C23×C4×C71C2311yescharacteristic
190C22⋊Q8×C71C2×C418yes—
191C2×C4⋊C4×C71C2312yes—
192C2×C4⋊C4×C71C2312yes—
193C2×C4⋊C4×C71C2312yes—
194C2×C4⋊C4×C71C2311yescharacteristic
195C2×C22⋊C4×C71C2311yescharacteristic
196C2×C22⋊C4×C71C2312yes—
197C2×C22⋊C4×C71C2311yescharacteristic
198C2×C42×C71C2312yes—
199C2×C42×C71C2312yes—
200C2×C42×C71C2312yes—
201#95×C71C2312yes—
202#95×C71C2311yescharacteristic
203#95×C71C2312yes—
204#95×C71C2312yes—
205#95×C71C2312yes—
206#95×C71C2311yescharacteristic
207#95×C71C2312yes—
208#95×C71C2312yes—
209C2×Dic142—42no—
210C2×Dic142—42no—
211C2×Dic142—42no—
212C2×Dic142C22×C418yes—
213C2×Dic142C22×C414yes—
214C22×Dic71—24no—
215C22×Dic71—42no—
216C22×Dic71—42no—
217C22×Dic71—42no—
218C22×Dic71C22×C414yes—
219C22×Dic71C22×C414yes—
220C22×Dic71C2×Q814yes—
221C22×Dic71#4114yes—
222C22×Dic71C2412yes—
223C22×Dic71C2412yes—
224C22×Dic71C2412yes—
225C22×Dic71C2411yescharacteristic
226C22×Dic71C2411yescharacteristic
227C22×Dic71C2412yes—
228C22×Dic71C2412yes—
229C22×Dic71C2412yes—
230C22×Dic71C2411yescharacteristic
231C22×Dic71C2411yescharacteristic
232C4⋊Dic71—42no—
233C4⋊Dic71—42no—
234C4⋊Dic71C22×C418yes—
235C4⋊Dic71C22×C414yes—
236Dic71⋊C4—24no—
237Dic71⋊C4—24no—
238Dic71⋊C4—24no—
239Dic71⋊C4—24no—
240Dic71⋊C4—24no—
241Dic71⋊C4—42no—
242Dic71⋊C4—42no—
243Dic71⋊C4—42no—
244Dic71⋊C4—42no—
245Dic71⋊C4C22×C418yes—
246Dic71⋊C4C22×C418yes—
247Dic71⋊C4C22×C418yes—
248Dic71⋊C4C22×C418yes—
249Dic71⋊C4C22×C418yes—
250Dic71⋊C4C2×Q818yes—
251C22⋊Dic71—22no—
252C22⋊Dic71C22×C418yes—
253C22⋊Dic71C2×Q814yes—
254C4×Dic71—24no—
255C4×Dic71—42no—
256C4×Dic71—42no—
257C4×Dic71—42no—
258C4×Dic71—42no—
259C4×Dic71—42no—
260C4×Dic71—42no—
261C4×Dic71—42no—
262C4×Dic71—42no—
263C4×Dic71—42no—
264C4×Dic71C22×C414yes—
265C4×Dic71C22×C414yes—
266C4×Dic71C22×C414yes—
267C4×Dic71C22×C414yes—
268C4×Dic71C22×C418yes—
269C4×Dic71C22×C418yes—
270C4×Dic71C2×Q818yes—
271C24×C71C2411yescharacteristic
272C2×Q8×C71—42no—
273C2×Q8×C71C22×C414yes—
274C22×C4×C71—24no—
275C22×C4×C71—42no—
276C22×C4×C71—42no—
277C22×C4×C71—42no—
278C22×C4×C71C22×C414yes—
279C22×C4×C71C2412yes—
280C22×C4×C71C2412yes—
281C22×C4×C71C2412yes—
282C22×C4×C71C2411yescharacteristic
283C22×C4×C71C2412yes—
284C22×C4×C71C2411yescharacteristic
285C22×C4×C71C2412yes—
286C22×C4×C71C2412yes—
287C4⋊C4×C71—42no—
288C4⋊C4×C71—42no—
289C4⋊C4×C71C22×C418yes—
290C4⋊C4×C71C22×C414yes—
291C22⋊C4×C71—22no—
292C22⋊C4×C71C22×C418yes—
293C22⋊C4×C71C2×Q814yes—
294C42×C71—42no—
295C42×C71—42no—
296C42×C71—42no—
297C23×C71—22no—
298C23×C71—22no—
299C23×C71C23×C412yes—
300C23×C71C22×Q812yes—
301C23×C71C2×#4112yes—
302C23×C71C2511yescharacteristic
303Q8×C71—44no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—22no—
310C2×C4×C71—22no—
311C2×C4×C71—22no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—22no—
318C2×C4×C71—22no—
319C2×C4×C71—22no—
320C2×C4×C71—22no—
321C2×C4×C71—44no—
322C2×C4×C71—84no—
323C2×C4×C71C23×C414yes—
324C2×C4×C71C23×C414yes—
325C2×C4×C71C23×C412yes—
326C2×C4×C71C23×C412yes—
327C2×C4×C71C22×Q814yes—
328C2×Dic71—22no—
329C2×Dic71—22no—
330C2×Dic71—22no—
331C2×Dic71—22no—
332C2×Dic71—22no—
333C2×Dic71—22no—
334C2×Dic71—22no—
335C2×Dic71—22no—
336C2×Dic71—22no—
337C2×Dic71—22no—
338C2×Dic71—22no—
339C2×Dic71—22no—
340C2×Dic71—22no—
341C2×Dic71—22no—
342C2×Dic71—22no—
343C2×Dic71—22no—
344C2×Dic71—22no—
345C2×Dic71—44no—
346C2×Dic71—84no—
347C2×Dic71C4×Q8116yes—
348C2×Dic71C23×C412yes—
349C2×Dic71C23×C412yes—
350C2×Dic71C23×C414yes—
351C2×Dic71C23×C414yes—
352C2×Dic71C23×C412yes—
353C2×Dic71C23×C412yes—
354C2×Dic71C22×Q814yes—
355C2×Dic71C22×Q812yes—
356C2×Dic71C22×Q812yes—
357C2×Dic71C2×#4112yes—
358C2×Dic71C2×#4112yes—
359Dic142—48no—
360Dic142—44no—
361C22×C71—22no—
362C22×C71—22no—
363C22×C71—24no—
364C22×C71—24no—
365C22×C71C2×C4×Q814yes—
366C22×C71C24×C411yescharacteristic
367C22×C71C23×Q811yescharacteristic
368C22×C71C22×#4111yescharacteristic
369C22×C71#58512yes—
370C22×C71#58512yes—
371C4×C71—22no—
372C4×C71—24no—
373C4×C71—22no—
374C4×C71—24no—
375C4×C71—24no—
376C4×C71—42no—
377C4×C71—42no—
378C4×C71—42no—
379Dic71—22no—
380Dic71—24no—
381Dic71—24no—
382Dic71—22no—
383Dic71—24no—
384Dic71—42no—
385Dic71—42no—
386Dic71—42no—
387Dic71C2×C4×Q814yes—
388Dic71C2×C4×Q814yes—
389#34215—711nomaximal, Sylow
390C2×C71—24no—
391C2×C71C22×C4×Q811yescharacteristic
392C2×C71#342811yescharacteristic
393C2×C71#342811yescharacteristic
394C2×C71#350412yes—
395C2×C71#351012yes—
396C2×#533—711no—
397#2368—712no—
398#2368—712no—
399#2368—711no—
400#2368—711no—
401#2368—711no—
402#2368D7111yescharacteristic
403#2355—712no—
404#2355—712no—
405#2355—712no—
406#2355—712no—
407#2331—712no—
408#2331—712no—
409#2317—712no—
410C4×#125—712no—
411C4×#125—712no—
412C2×#382—711no—
413#2274—712no—
414C4×#117—711no—
415C71#3421511yescharacteristic, complemented, Sylow
416#533—7116no—
417C2×C4⋊Q8—711no—
418C2×C4⋊Q8—711no—
419C2×#125—712no—
420C2×C22⋊Q8—711no—
421C2×C22⋊Q8—712no—
422C2×C22⋊Q8C2×D7111yescharacteristic
423C2×C4×Q8—711no—
424C2×C4×Q8—711no—
425C2×C4×Q8—712no—
426C2×#117—712no—
427C2×#117—711no—
428C2×#117—711no—
429C22×C4⋊C4—712no—
430C22×C42—711no—
431#391—712no—
432#391—712no—
433#391—712no—
434#391—712no—
435#391—712no—
436#391—712no—
437#391—712no—
438#391C2×D7112yes—
439#389—712no—
440#389—712no—
441#389—712no—
442#389—712no—
443#387—712no—
444#387—712no—
445#387—712no—
446#387—712no—
447#387—712no—
448#387—712no—
449#387—712no—
450#387—712no—
451#387—712no—
452#387—712no—
453#387—712no—
454#387—712no—
455#387—712no—
456#387—712no—
457#387C2×D7112yes—
458#387C2×D7112yes—
459#385—712no—
460#385—712no—
461#385—712no—
462#385C2×D7112yes—
463#384—712no—
464#384—712no—
465#382—711no—
466#382—711no—
467#382—712no—
468#382—712no—
469#382—712no—
470#382—712no—
471#382—711no—
472#382—711no—
473C4×C4⋊C4—712no—
474C4×C4⋊C4—712no—
475C4×C4⋊C4—712no—
476C4×C4⋊C4—712no—
477C4×C4⋊C4—712no—
478C4×C4⋊C4—712no—
479C4×C4⋊C4—712no—
480C4×C4⋊C4—712no—
481C4×C4⋊C4—712no—
482C4×C4⋊C4—712no—
483C4×C4⋊C4—712no—
484C4×C4⋊C4—712no—
485C4×C4⋊C4—712no—
486C4×C4⋊C4—712no—
487C4×C4⋊C4—712no—
488C4×C4⋊C4—712no—
489C4×C4⋊C4—712no—
490C4×C4⋊C4C2×D7112yes—
491C4×C22⋊C4—711no—
492C4×C22⋊C4—712no—
493C4×C22⋊C4—711no—
494C4×C22⋊C4—711no—
495C4×C22⋊C4—712no—
496C4×C22⋊C4—712no—
497C4×C22⋊C4C2×D7111yescharacteristic
498C4×C22⋊C4C2×D7112yes—
499#376—712no—
500C2×#95—712no—
501C2×#95—711no—
502C2×#95C2×D7111yescharacteristic
503C43—712no—
504C22×Q8—712no—
505C22×Q8—711no—
506C22×Q8C22×D7111yescharacteristic
507C23×C4—711no—
508C23×C4—712no—
509C23×C4—711no—
510C23×C4C22×D7112yes—
511C23×C4C22×D7111yescharacteristic
512C4⋊Q8—718no—
513C4⋊Q8—718no—
514#125—7116no—
515C22⋊Q8—718no—
516C22⋊Q8—7116no—
517C22⋊Q8C4×D7118yes—
518C4×Q8—718no—
519C4×Q8—718no—
520C4×Q8—7116no—
521#117—7116no—
522#117—718no—
523#117—1424no—
524C2×C4⋊C4—712no—
525C2×C4⋊C4—712no—
526C2×C4⋊C4—712no—
527C2×C4⋊C4—712no—
528C2×C4⋊C4—712no—
529C2×C4⋊C4—712no—
530C2×C4⋊C4—712no—
531C2×C4⋊C4—712no—
532C2×C4⋊C4—712no—
533C2×C4⋊C4—712no—
534C2×C4⋊C4—712no—
535C2×C4⋊C4—712no—
536C2×C4⋊C4—712no—
537C2×C4⋊C4—711no—
538C2×C4⋊C4—712no—
539C2×C4⋊C4—712no—
540C2×C4⋊C4—712no—
541C2×C4⋊C4—712no—
542C2×C4⋊C4—712no—
543C2×C4⋊C4—1428no—
544C2×C4⋊C4C22×D7112yes—
545C2×C4⋊C4C22×D7112yes—
546C2×C4⋊C4C22×D7112yes—
547C2×C4⋊C4C22×D7111yescharacteristic
548C2×C22⋊C4—712no—
549C2×C22⋊C4—711no—
550C2×C22⋊C4—711no—
551C2×C22⋊C4C22×D7111yescharacteristic
552C2×C22⋊C4C22×D7112yes—
553C2×C22⋊C4C22×D7111yescharacteristic
554C2×C42—712no—
555C2×C42—712no—
556C2×C42—712no—
557C2×C42—712no—
558C2×C42—712no—
559C2×C42—712no—
560C2×C42—712no—
561C2×C42—712no—
562C2×C42—712no—
563C2×C42—718no—
564C2×C42—712no—
565C2×C42—712no—
566C2×C42—712no—
567C2×C42—711no—
568C2×C42—711no—
569C2×C42—711no—
570C2×C42—711no—
571C2×C42—712no—
572C2×C42C22×D7112yes—
573C2×C42C22×D7112yes—
574C2×C42C22×D7112yes—
575#95—712no—
576#95—712no—
577#95—711no—
578#95—711no—
579#95—712no—
580#95—712no—
581#95—712no—
582#95—712no—
583#95—712no—
584#95—712no—
585#95—712no—
586#95—712no—
587#95—712no—
588#95—712no—
589#95—712no—
590#95—712no—
591#95—712no—
592#95—712no—
593#95—712no—
594#95—712no—
595#95—712no—
596#95—712no—
597#95C22×D7111yescharacteristic
598#95C22×D7111yescharacteristic
599#95C22×D7112yes—
600#95C22×D7112yes—
601#95C22×D7112yes—
602#95C22×D7112yes—
603#95C22×D7112yes—
604#95C22×D7112yes—
605C24C23×D7111yescharacteristic
606C2×Q8—42no—
607C2×Q8—2842no—
608C2×Q8—2842no—
609C2×Q8—2842no—
610C2×Q8—718no—
611C2×Q8—714no—
612C2×Q8C2×C4×D7114yes—
613C22×C4—24no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—2842no—
618C22×C4—2842no—
619C22×C4—2842no—
620C22×C4—714no—
621C22×C4—714no—
622C22×C4—714no—
623C22×C4—714no—
624C22×C4—711no—
625C22×C4—711no—
626C22×C4—711no—
627C22×C4—712no—
628C22×C4—711no—
629C22×C4—712no—
630C22×C4—712no—
631C22×C4—712no—
632C22×C4—712no—
633C22×C4—712no—
634C22×C4—1424no—
635C22×C4C2×C4×D7114yes—
636C22×C4C23×D7112yes—
637C22×C4C23×D7112yes—
638C22×C4C23×D7112yes—
639C22×C4C23×D7111yescharacteristic
640C22×C4C23×D7111yescharacteristic
641C22×C4C23×D7112yes—
642C22×C4C23×D7112yes—
643C22×C4C23×D7112yes—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—2842no—
647C4⋊C4—2842no—
648C4⋊C4—2842no—
649C4⋊C4—2842no—
650C4⋊C4—2842no—
651C4⋊C4—2842no—
652C4⋊C4—718no—
653C4⋊C4—718no—
654C4⋊C4—718no—
655C4⋊C4—718no—
656C4⋊C4—718no—
657C4⋊C4—718no—
658C4⋊C4—714no—
659C4⋊C4—718no—
660C4⋊C4—1424no—
661C4⋊C4—1424no—
662C4⋊C4—1424no—
663C4⋊C4—1424no—
664C4⋊C4—1424no—
665C4⋊C4C2×C4×D7118yes—
666C4⋊C4C2×C4×D7114yes—
667C22⋊C4—22no—
668C22⋊C4—718no—
669C22⋊C4—714no—
670C22⋊C4—1422no—
671C22⋊C4C2×C4×D7118yes—
672C22⋊C4Q8×D7114yes—
673C42—42no—
674C42—42no—
675C42—42no—
676C42—2842no—
677C42—2842no—
678C42—2842no—
679C42—2842no—
680C42—2842no—
681C42—2842no—
682C42—2842no—
683C42—2842no—
684C42—2842no—
685C42—714no—
686C42—714no—
687C42—714no—
688C42—714no—
689C42—718no—
690C42—718no—
691C42—718no—
692C42—1424no—
693C23—22no—
694C23—22no—
695C23C22×C4×D7112yes—
696C23C2×Q8×D7112yes—
697C23#41×D7112yes—
698C23C24×D7111yescharacteristic
699Q8—44no—
700Q8—2844no—
701Q8—2848no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—44no—
720C2×C4—84no—
721C2×C4—2844no—
722C2×C4—5684no—
723C2×C4—712no—
724C2×C4—712no—
725C2×C4—712no—
726C2×C4—712no—
727C2×C4—712no—
728C2×C4—712no—
729C2×C4—7116no—
730C2×C4—712no—
731C2×C4—712no—
732C2×C4—714no—
733C2×C4—714no—
734C2×C4—714no—
735C2×C4—1422no—
736C2×C4—1422no—
737C2×C4—1422no—
738C2×C4—1422no—
739C2×C4—1422no—
740C2×C4—1422no—
741C2×C4—1422no—
742C2×C4—1422no—
743C2×C4—1422no—
744C2×C4—1422no—
745C2×C4—1422no—
746C2×C4—1422no—
747C2×C4—1422no—
748C2×C4—1422no—
749C2×C4—1422no—
750C2×C4—1422no—
751C2×C4—1422no—
752C2×C4C22×C4×D7112yes—
753C2×C4C22×C4×D7112yes—
754C2×C4C22×C4×D7114yes—
755C2×C4C22×C4×D7114yes—
756C2×C4C2×Q8×D7114yes—
757C22—22no—
758C22—22no—
759C22—24no—
760C22—24no—
761C22C4×Q8×D7114yes—
762C22C23×C4×D7111yescharacteristic
763C22C22×Q8×D7111yescharacteristic
764C22C2×#41×D7111yescharacteristic
765C22#1798683412yes—
766C22#1798683512yes—
767C4—22no—
768C4—22no—
769C4—24no—
770C4—24no—
771C4—24no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—2842no—
776C4—2842no—
777C4—2842no—
778C4—714no—
779C4—714no—
780C4—1424no—
781C4—1422no—
782C4—1422no—
783C4—1424no—
784C4—1424no—
785C2—24no—
786C2C2×C4×Q8×D7111yescharacteristic
787C2#2260153811yescharacteristic
788C2#2260153911yescharacteristic
789C2#2260216012yes—
790C2#2260222812yes—
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2368C2
socle, cosocleC23×C71C25
prime radicalC24×C71C24
hypercenter#2368D71
hypocenterC71#34215
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2368

Complements

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

NH ≅ G/Ntype
7. #22591296C2semidirect
8. #22591294C2semidirect
9. #22591294C2semidirect
10. #22591293C2semidirect
11. #22591085C2semidirect
12. #22591083C2semidirect
14. #22590897C2semidirect
15. C4×#14556118C2semidirect
20. #17986551C4semidirect
113. #14556127C2×C4semidirect
114. #14556126C2×C4semidirect
115. #14556118C2×C4semidirect
118. Q8×Dic71C2×C4semidirect
119. #14556093C2×C4semidirect
120. #14556093C2×C4semidirect
123. #14556084Q8semidirect
415. C71#34215semidirect

Maximal subgroups

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

subgroupindex
C2×#179865512
#225914252
#225914232
#225914212
#225914202
#225914182
#225912962
#225912942
#225912932
#225910852
#225910832
#225909592
#225908972
C4×#145561182
C2×#179858632
#225906952
C4×#145560842
C71×#23682
#3421571