Finite Group Databasebeta

← #32160473

Subgroups — #32160473

Order 18176.

2190 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986536C211yesmaximal, characteristic
2#22591485C214yesmaximal, complemented
3#22591435C212yesmaximal, complemented
4#22591407C212yesmaximal, complemented
5#22591297C211yesmaximal, characteristic, complemented
6#22591291C212yesmaximal, complemented
7#22591287C211yesmaximal, characteristic, complemented
8#22591272C212yesmaximal, complemented
9#22591240C211yesmaximal, characteristic, complemented
10#22591108C214yesmaximal, complemented
11#22591031C212yesmaximal
12#22591016C212yesmaximal, complemented
13#22590961C212yesmaximal, complemented
14#22590945C212yesmaximal, complemented
15#22590745C211yesmaximal, characteristic, complemented
16#22590744C211yesmaximal, characteristic, complemented
17Q8×C4⋊C4×C71C211yesmaximal, characteristic, complemented
18#17986536C4116yescomplemented
19C2×#14556123C2212yes—
20C2×#14556119C2211yescharacteristic
21C2×#14556117C2211yescharacteristic
22C2×#14556113C2212yes—
23C2×#14556104C2211yescharacteristic
24C2×#14556103C2211yescharacteristic
25C2×C4×D284C2211yescharacteristic
26C2×C4×D284C2212yes—
27C2×#14556090C2212yes—
28C2×#14556086C2212yes—
29C2×#14556086C2212yes—
30C2×#14556085C2212yes—
31C2×#14556085C2212yes—
32C2×C4⋊C4×D71C2212yes—
33C2×C42×D71C2211yescharacteristic
34#17985906C2212yes—
35#17985901C2212yes—
36#17985900C2214yes—
37#17985895C2212yes—
38#17985894C2214yes—
39#17985894C2214yes—
40#17985891C2214yes—
41#17985890C2214yes—
42#17985890C2214yes—
43#17985889C2214yes—
44#17985889C2214yes—
45#17985888C2214yes—
46#17985885C2214yes—
47#17985884C2214yes—
48#17985883C2214yes—
49#17985881C2214yes—
50#17985877C2214yes—
51#17985870C2214yes—
52#17985870C2214yes—
53#17985870C2214yes—
54#17985869C2211yescharacteristic
55#17985868C2211yescharacteristic
56#17985868C2211yescharacteristic
57#17985865C2212yes—
58#17985864C2212yes—
59#17985863C2212yes—
60#17985858C2212yes—
61#17985856C2212yes—
62#17985856C2211yescharacteristic
63#17985856C2211yescharacteristic
64#17985856C2212yes—
65#17985856C2212yes—
66#17985856C2212yes—
67C4⋊C4×Dic71C2212yes—
68C4⋊C4×Dic71C2212yes—
69C4⋊C4×Dic71C2212yes—
70C4⋊C4×Dic71C2214yes—
71C4×Dic71⋊C4C2212yes—
72C4×C4⋊Dic71C2211yescharacteristic
73C4×C4⋊Dic71C2212yes—
74C4×C4⋊Dic71C2212yes—
75C4×(C2×D71)⋊C4C2214yes—
76C2×C4×Q8×C71C2212yes—
77C2×C4×Q8×C71C2211yescharacteristic
78#389×C71C2212yes—
79#389×C71C2214yes—
80#384×C71C2211yescharacteristic
81#384×C71C2212yes—
82C4×C4⋊C4×C71C2211yescharacteristic
83C4×C4⋊C4×C71C2212yes—
84C22×D284C2311yescharacteristic
85C22×D284C2312yes—
86C22×C4×D71C2311yescharacteristic
87C22×C4×D71C2311yescharacteristic
88C22×C4×D71C2312yes—
89C22×C4×D71C2314yes—
90C22×C4×D71C2311yescharacteristic
91#14556123C2×C4116yescomplemented
92#14556119C2×C418yescomplemented
93#14556117C2×C418yes—
94#14556113C2×C4116yescomplemented
95#14556104C2×C418yescomplemented
96#14556103C2×C418yes—
97C4×D284C2×C418yes—
98C4×D284C2×C4116yescomplemented
99#14556090—44no—
100#14556086—44no—
101#14556086—44no—
102#14556085—44no—
103#14556085C2×C4116yescomplemented
104C2×C4⋊Dic71C2311yescharacteristic
105C2×C4⋊Dic71C2312yes—
106C2×C4⋊Dic71C2312yes—
107C2×C4⋊Dic71C2311yescharacteristic
108C2×C4⋊Dic71C2312yes—
109C2×C4⋊Dic71C2311yescharacteristic
110C2×C4⋊Dic71C2312yes—
111C2×Dic71⋊C4C2312yes—
112C2×Dic71⋊C4C2312yes—
113C2×Dic71⋊C4C2312yes—
114C2×Dic71⋊C4C2312yes—
115C2×Dic71⋊C4C2314yes—
116C2×Dic71⋊C4C2312yes—
117C2×Dic71⋊C4C2312yes—
118C4⋊C4×D71—44no—
119C2×(C2×D71)⋊C4C2314yes—
120C2×(C2×D71)⋊C4C2314yes—
121C2×(C2×D71)⋊C4C2312yes—
122C2×(C2×D71)⋊C4C2312yes—
123C2×(C2×D71)⋊C4C2314yes—
124C2×(C2×D71)⋊C4C2314yes—
125C2×(C2×D71)⋊C4C2312yes—
126C2×(C2×D71)⋊C4C2312yes—
127C2×(C2×D71)⋊C4C2312yes—
128C2×(C2×D71)⋊C4C2312yes—
129C2×(C2×D71)⋊C4C2312yes—
130C2×C4×Dic71C2312yes—
131C2×C4×Dic71C2314yes—
132C2×C4×Dic71C2314yes—
133C2×C4×Dic71C2314yes—
134C2×C4×Dic71C2311yescharacteristic
135C2×C4×Dic71C2311yescharacteristic
136C2×C4×Dic71C2311yescharacteristic
137C42×D71C2×C418yescomplemented
138C71⋊#95C2312yes—
139C71⋊#95C2314yes—
140C71⋊#95C2314yes—
141C71⋊#95C2312yes—
142C71⋊#95C2314yes—
143C71⋊#95C2312yes—
144C71⋊#95C2314yes—
145C71⋊#95C2314yes—
146C71⋊#95C2314yes—
147C71⋊#95C2314yes—
148C22×Q8×C71C2311yescharacteristic
149C4×Q8×C71—44no—
150C4×Q8×C71C2×C418yescomplemented
151C2×C4⋊C4×C71C2312yes—
152C2×C4⋊C4×C71C2311yescharacteristic
153C2×C4⋊C4×C71C2312yes—
154C2×C4⋊C4×C71C2311yescharacteristic
155C2×C4⋊C4×C71C2312yes—
156C2×C4⋊C4×C71C2314yes—
157C2×C4⋊C4×C71C2314yes—
158C2×C4⋊C4×C71C2311yescharacteristic
159C2×C4⋊C4×C71C2312yes—
160C2×C42×C71C2312yes—
161C2×C42×C71C2314yes—
162C2×C42×C71C2312yes—
163C2×C42×C71C2311yescharacteristic
164#95×C71C2312yes—
165#95×C71C2314yes—
166C23×D71C2411yescharacteristic
167C23×D71C2412yes—
168C2×D284—22no—
169C2×D284—22no—
170C2×D284—42no—
171C2×D284—42no—
172C2×D284C22×C414yes—
173C2×D284C22×C418yes—
174C22×Dic71C2412yes—
175C22×Dic71C2412yes—
176C22×Dic71C2414yes—
177C22×Dic71C2411yescharacteristic
178C22×Dic71C2411yescharacteristic
179C22×Dic71C2411yescharacteristic
180C22×Dic71C2412yes—
181C2×C4×D71—24no—
182C2×C4×D71—22no—
183C2×C4×D71—22no—
184C2×C4×D71—22no—
185C2×C4×D71—24no—
186C2×C4×D71—22no—
187C2×C4×D71—41no—
188C2×C4×D71—41no—
189C2×C4×D71—44no—
190C2×C4×D71—44no—
191C2×C4×D71—44no—
192C2×C4×D71C22×C414yes—
193C2×C4×D71C22×C414yes—
194C2×C4×D71C22×C418yes—
195C2×C4×D71C22×C414yes—
196C4⋊Dic71—22no—
197C4⋊Dic71—24no—
198C4⋊Dic71—22no—
199C4⋊Dic71—24no—
200C4⋊Dic71—42no—
201C4⋊Dic71C22×C414yes—
202C4⋊Dic71C22×C418yes—
203Dic71⋊C4—44no—
204Dic71⋊C4—42no—
205Dic71⋊C4—42no—
206Dic71⋊C4—42no—
207Dic71⋊C4—42no—
208Dic71⋊C4C22×C418yes—
209Dic71⋊C4C22×C418yes—
210(C2×D71)⋊C4—44no—
211(C2×D71)⋊C4—42no—
212(C2×D71)⋊C4—42no—
213(C2×D71)⋊C4—44no—
214(C2×D71)⋊C4—44no—
215(C2×D71)⋊C4—44no—
216(C2×D71)⋊C4C22×C418yes—
217(C2×D71)⋊C4C22×C418yes—
218(C2×D71)⋊C4C22×C418yes—
219(C2×D71)⋊C4C22×C418yes—
220(C2×D71)⋊C4C22×C418yes—
221C4×Dic71—24no—
222C4×Dic71—44no—
223C4×Dic71—44no—
224C4×Dic71—44no—
225C4×Dic71C22×C414yes—
226C4×Dic71C22×C414yes—
227C4×Dic71C22×C414yes—
228C2×Q8×C71—22no—
229C2×Q8×C71—22no—
230C2×Q8×C71C22×C414yes—
231C22×C4×C71C2414yes—
232C22×C4×C71C2412yes—
233C22×C4×C71C2412yes—
234C22×C4×C71C2411yescharacteristic
235C22×C4×C71C2412yes—
236C22×C4×C71C2412yes—
237C22×C4×C71C2411yescharacteristic
238C22×C4×C71C2411yescharacteristic
239C4⋊C4×C71—24no—
240C4⋊C4×C71—24no—
241C4⋊C4×C71—22no—
242C4⋊C4×C71—22no—
243C4⋊C4×C71—42no—
244C4⋊C4×C71—44no—
245C4⋊C4×C71—44no—
246C4⋊C4×C71C22×C414yes—
247C4⋊C4×C71C22×C418yes—
248C42×C71—24no—
249C42×C71—44no—
250C42×C71C22×C414yes—
251C42×C71C22×C418yes—
252C23×C71C2511yescharacteristic
253C22×D71—21no—
254C22×D71—21no—
255C22×D71—22no—
256C22×D71—22no—
257C22×D71—21no—
258C22×D71—22no—
259C22×D71—21no—
260C22×D71—22no—
261C22×D71—22no—
262C22×D71—22no—
263C22×D71—21no—
264C22×D71—21no—
265C22×D71C23×C414yes—
266C22×D71C23×C412yes—
267Q8×C71—28no—
268C2×C4×C71—22no—
269C2×C4×C71—22no—
270C2×C4×C71—21no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—21no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—24no—
277C2×C4×C71—22no—
278C2×C4×C71—24no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—24no—
282C2×C4×C71—22no—
283C2×C4×C71C23×C412yes—
284C2×C4×C71C23×C414yes—
285C2×C4×C71C23×C414yes—
286C2×C4×C71C23×C412yes—
287C2×C4×C71C23×C412yes—
288C2×C4×C71H(5,𝔽2)12yes—
289C2×C4×C71H(5,𝔽2)12yes—
290C2×C4×C712−1+412yes—
291C2×C4×C712−1+412yes—
292C2×Dic71—21no—
293C2×Dic71—22no—
294C2×Dic71—21no—
295C2×Dic71—21no—
296C2×Dic71—22no—
297C2×Dic71—21no—
298C2×Dic71—21no—
299C2×Dic71—21no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—24no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—24no—
306C2×Dic71—22no—
307C2×Dic71—24no—
308C2×Dic71—22no—
309C2×Dic71C23×C412yes—
310C2×Dic71C23×C412yes—
311C2×Dic71C23×C412yes—
312C2×Dic71C23×C414yes—
313D284—28no—
314D284—48no—
315C4×D71—28no—
316C4×D71—216no—
317C4×D71—28no—
318C4×D71—44no—
319C4×D71—88no—
320C22×C71C24×C411yescharacteristic
321C22×C71C2×H(5,𝔽2)11yescharacteristic
322C22×C71C2×H(5,𝔽2)11yescharacteristic
323C22×C71C2×2−1+411yescharacteristic
324C22×C71C2×2−1+411yescharacteristic
325C22×C71#58511yescharacteristic
326C22×C71#58511yescharacteristic
327C2×D71—22no—
328C2×D71—22no—
329C2×D71—24no—
330C2×D71—24no—
331C2×D71—22no—
332C2×D71—24no—
333C2×D71—42no—
334C2×D71—41no—
335C2×D71—41no—
336C2×D71—42no—
337C2×D71—41no—
338C2×D71—42no—
339C2×D71—41no—
340C2×D71—42no—
341C4×C71—24no—
342C4×C71—22no—
343C4×C71—24no—
344C4×C71—44no—
345C4×C71—42no—
346C4×C71—42no—
347C4×C71#52014yes—
348C4×C71#52014yes—
349Dic71—22no—
350Dic71—22no—
351Dic71—24no—
352Dic71—22no—
353Dic71—42no—
354Dic71—42no—
355Dic71—44no—
356#34383—711nomaximal, Sylow
357C2×C71C2×#52011yescharacteristic
358C2×C71C2×#52011yescharacteristic
359C2×C71#342811yescharacteristic
360C2×C71#354611yescharacteristic
361C2×C71#354711yescharacteristic
362C2×C71#355411yescharacteristic
363C2×C71#355511yescharacteristic
364D71—42no—
365D71—44no—
366C2×#529—711no—
367#2376—714no—
368#2370—712no—
369#2367—712no—
370#2355—711no—
371#2354—712no—
372#2354—711no—
373#2352—712no—
374Q8×C4⋊C4D7111yescharacteristic, complemented
375D4×C4⋊C4—711no—
376#2334—714no—
377#2324—712no—
378#2323—712no—
379#2317—712no—
380#2314—712no—
381#2285—711no—
382#2285—711no—
383C71#3438311yescharacteristic, complemented, Sylow
384#529—7116no—
385C2×#126—712no—
386C2×#125—711no—
387C2×#124—711no—
388C2×#123—712no—
389C2×C22⋊Q8—711no—
390C2×#121—711no—
391C2×C4×Q8C2×D7112yes—
392C2×C4×Q8C2×D7111yescharacteristic
393C2×C4×D4—712no—
394C2×C4×D4—711no—
395C2×C4×D4—712no—
396C2×#117—712no—
397C2×#117—712no—
398C2×#117—712no—
399C2×#117—712no—
400C22×C4⋊C4—712no—
401C22×C42—711no—
402#391—712no—
403#390—714no—
404#390—712no—
405#389—714no—
406#389—714no—
407#389—712no—
408#389C2×D7112yes—
409#389C2×D7114yes—
410#388—714no—
411#388—714no—
412#388—714no—
413#388—714no—
414#388—714no—
415#388—714no—
416#387—714no—
417#387—714no—
418#387—714no—
419#387—714no—
420#386—714no—
421#385—714no—
422#385—714no—
423#385—714no—
424#384—711no—
425#384—711no—
426#384—711no—
427#384C2×D7112yes—
428#384C2×D7111yescharacteristic
429#382—712no—
430#382—712no—
431#382—712no—
432#380—712no—
433#380—712no—
434#380—712no—
435#380—711no—
436#380—711no—
437#380—712no—
438#380—712no—
439C4×C4⋊C4—712no—
440C4×C4⋊C4—712no—
441C4×C4⋊C4—714no—
442C4×C4⋊C4—712no—
443C4×C4⋊C4—712no—
444C4×C4⋊C4—712no—
445C4×C4⋊C4—711no—
446C4×C4⋊C4—712no—
447C4×C4⋊C4C2×D7112yes—
448C4×C4⋊C4C2×D7111yescharacteristic
449C4×C22⋊C4—714no—
450C22×Q8C22×D7111yescharacteristic
451C22×D4—712no—
452C22×D4—711no—
453C23×C4—714no—
454C23×C4—711no—
455C23×C4—712no—
456C23×C4—711no—
457C23×C4—711no—
458#126—7116no—
459#125—718no—
460#124—718no—
461#123—7116no—
462C22⋊Q8—718no—
463#121—718no—
464C4×Q8—44no—
465C4×Q8C4×D7118yescomplemented
466C4×D4—2844no—
467C4×D4—718no—
468C4×D4—7116no—
469#117—2844no—
470#117—2844no—
471#117—2844no—
472#117—7116no—
473C2×C4⋊C4—2844no—
474C2×C4⋊C4—714no—
475C2×C4⋊C4—712no—
476C2×C4⋊C4—712no—
477C2×C4⋊C4—712no—
478C2×C4⋊C4—712no—
479C2×C4⋊C4—712no—
480C2×C4⋊C4—712no—
481C2×C4⋊C4—712no—
482C2×C4⋊C4—711no—
483C2×C4⋊C4—712no—
484C2×C4⋊C4—711no—
485C2×C4⋊C4—712no—
486C2×C4⋊C4—711no—
487C2×C4⋊C4—712no—
488C2×C4⋊C4C22×D7112yes—
489C2×C4⋊C4C22×D7111yescharacteristic
490C2×C4⋊C4C22×D7112yes—
491C2×C4⋊C4C22×D7111yescharacteristic
492C2×C4⋊C4C22×D7114yes—
493C2×C4⋊C4C22×D7112yes—
494C2×C4⋊C4C22×D7114yes—
495C2×C4⋊C4C22×D7111yescharacteristic
496C2×C4⋊C4C22×D7112yes—
497C2×C22⋊C4—712no—
498C2×C22⋊C4—714no—
499C2×C22⋊C4—712no—
500C2×C22⋊C4—714no—
501C2×C22⋊C4—714no—
502C2×C22⋊C4—714no—
503C2×C22⋊C4—712no—
504C2×C22⋊C4—712no—
505C2×C22⋊C4—712no—
506C2×C22⋊C4—712no—
507C2×C22⋊C4—712no—
508C2×C42—714no—
509C2×C42—714no—
510C2×C42—714no—
511C2×C42—711no—
512C2×C42—711no—
513C2×C42—711no—
514C2×C42—718no—
515C2×C42—712no—
516C2×C42C22×D7112yes—
517C2×C42C22×D7114yes—
518C2×C42C22×D7112yes—
519C2×C42C22×D7111yescharacteristic
520#95—712no—
521#95—714no—
522#95—712no—
523#95—712no—
524#95—714no—
525#95—714no—
526#95—714no—
527#95—714no—
528#95—714no—
529#95—714no—
530#95C22×D7112yes—
531#95C22×D7114yes—
532C24—712no—
533C24—711no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8C2×C4×D7114yes—
537C2×D4—2842no—
538C2×D4—2842no—
539C2×D4—718no—
540C2×D4—714no—
541C2×D4—1422no—
542C2×D4—1422no—
543C22×C4—2841no—
544C22×C4—2841no—
545C22×C4—2844no—
546C22×C4—2844no—
547C22×C4—2844no—
548C22×C4—714no—
549C22×C4—711no—
550C22×C4—711no—
551C22×C4—711no—
552C22×C4—712no—
553C22×C4—714no—
554C22×C4—714no—
555C22×C4—718no—
556C22×C4—712no—
557C22×C4—714no—
558C22×C4—712no—
559C22×C4—1422no—
560C22×C4—1424no—
561C22×C4—1422no—
562C22×C4—1422no—
563C22×C4—1424no—
564C22×C4—1422no—
565C22×C4C23×D7112yes—
566C22×C4C23×D7114yes—
567C22×C4C23×D7112yes—
568C22×C4C23×D7112yes—
569C22×C4C23×D7112yes—
570C22×C4C23×D7111yescharacteristic
571C22×C4C23×D7111yescharacteristic
572C22×C4C23×D7111yescharacteristic
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—42no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—2844no—
581C4⋊C4—2842no—
582C4⋊C4—2842no—
583C4⋊C4—2842no—
584C4⋊C4—2842no—
585C4⋊C4—2842no—
586C4⋊C4—718no—
587C4⋊C4—718no—
588C4⋊C4—714no—
589C4⋊C4—718no—
590C4⋊C4—1422no—
591C4⋊C4—1424no—
592C4⋊C4—1424no—
593C4⋊C4—1422no—
594C4⋊C4C2×C4×D7114yes—
595C4⋊C4C2×C4×D7118yes—
596C22⋊C4—2844no—
597C22⋊C4—2842no—
598C22⋊C4—2842no—
599C22⋊C4—2844no—
600C22⋊C4—2844no—
601C22⋊C4—2844no—
602C22⋊C4—718no—
603C22⋊C4—718no—
604C22⋊C4—718no—
605C22⋊C4—718no—
606C22⋊C4—718no—
607C42—24no—
608C42—44no—
609C42—2844no—
610C42—2844no—
611C42—2844no—
612C42—714no—
613C42—714no—
614C42—714no—
615C42—1424no—
616C42C2×C4×D7114yes—
617C42C2×C4×D7118yes—
618C23—714no—
619C23—712no—
620C23—1421no—
621C23—1422no—
622C23—1421no—
623C23—1422no—
624C23—1421no—
625C23—1421no—
626C23—1422no—
627C23—1422no—
628C23—1422no—
629C23—1421no—
630C23—1422no—
631C23—1421no—
632C23C24×D7111yescharacteristic
633Q8—28no—
634D4—2848no—
635D4—1428no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—2844no—
652C2×C4—5688no—
653C2×C4—712no—
654C2×C4—712no—
655C2×C4—712no—
656C2×C4—714no—
657C2×C4—1422no—
658C2×C4—1422no—
659C2×C4—1424no—
660C2×C4—1422no—
661C2×C4—1424no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4—1422no—
665C2×C4—1424no—
666C2×C4—1421no—
667C2×C4—1421no—
668C2×C4—1422no—
669C2×C4—1421no—
670C2×C4—1421no—
671C2×C4—1422no—
672C2×C4—1421no—
673C2×C4—1421no—
674C2×C4—1428no—
675C2×C4—1428no—
676C2×C4—14216no—
677C2×C4C22×C4×D7112yes—
678C2×C4C22×C4×D7114yes—
679C2×C4C22×C4×D7114yes—
680C2×C4C22×C4×D7112yes—
681C2×C4C22×C4×D7112yes—
682C2×C4#1455617312yes—
683C2×C4#1455617412yes—
684C2×C4#1455617612yes—
685C2×C4#1455617612yes—
686C22—2841no—
687C22—2842no—
688C22—2841no—
689C22—2842no—
690C22—2842no—
691C22—2841no—
692C22—2841no—
693C22—2842no—
694C22—1422no—
695C22—1424no—
696C22—1424no—
697C22—1422no—
698C22—1422no—
699C22—1424no—
700C22C23×C4×D7111yescharacteristic
701C22C2×#1455617311yescharacteristic
702C22C2×#1455617411yescharacteristic
703C22C2×#1455617611yescharacteristic
704C22C2×#1455617611yescharacteristic
705C22#1798683411yescharacteristic
706C22#1798683611yescharacteristic
707C4—24no—
708C4—22no—
709C4—24no—
710C4—44no—
711C4—42no—
712C4—42no—
713C4—2844no—
714C4—2842no—
715C4—2842no—
716C4—1422no—
717C4—1422no—
718C4—1424no—
719C4—1422no—
720C4#1798648014yes—
721C4#1798648114yes—
722C2—2844no—
723C2—2842no—
724C2C2×#1798648011yescharacteristic
725C2C2×#1798648111yescharacteristic
726C2#2260154011yescharacteristic
727C2#2260270011yescharacteristic
728C2#2260272511yescharacteristic
729C2#2260281411yescharacteristic
730C2#2260282911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingQ8×C4⋊C4×C71C2
socle, cosocleC23×C71C25
prime radicalC2×#14556103C22
hypercenterQ8×C4⋊C4D71
hypocenterC71#34383
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #22591485C2semidirect
3. #22591435C2semidirect
4. #22591407C2semidirect
5. #22591297C2semidirect
6. #22591291C2semidirect
7. #22591287C2semidirect
8. #22591272C2semidirect
9. #22591240C2semidirect
10. #22591108C2semidirect
12. #22591016C2semidirect
13. #22590961C2semidirect
14. #22590945C2semidirect
15. #22590745C2semidirect
16. #22590744C2semidirect
17. Q8×C4⋊C4×C71C2semidirect
18. #17986536C4semidirect
91. #14556123C2×C4semidirect
92. #14556119C2×C4semidirect
94. #14556113C2×C4semidirect
95. #14556104C2×C4semidirect
98. C4×D284C2×C4semidirect
103. #14556085C2×C4semidirect
137. C42×D71C2×C4semidirect
150. C4×Q8×C71C2×C4semidirect
374. Q8×C4⋊C4D71semidirect
383. C71#34383semidirect
465. C4×Q8C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179865362
#225914852
#225914352
#225914072
#225912972
#225912912
#225912872
#225912722
#225912402
#225911082
#225910312
#225910162
#225909612
#225909452
#225907452
#225907442
Q8×C4⋊C4×C712
#3438371