Finite Group Databasebeta

← #32158302

Subgroups — #32158302

Order 18176.

2286 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986536C211yesmaximal, characteristic
2#22591463C214yesmaximal, complemented
3#22591377C212yesmaximal
4#22591363C212yesmaximal, complemented
5#22591297C211yesmaximal, characteristic, complemented
6#22591291C211yesmaximal, characteristic, complemented
7#22591291C212yesmaximal, complemented
8#22591272C212yesmaximal, complemented
9C4⋊C4×D284C211yesmaximal, characteristic, complemented
10#22591133C214yesmaximal, complemented
11#22590948C212yesmaximal, complemented
12#22590899C212yesmaximal, complemented
13C4×#14556117C212yesmaximal, complemented
14#22590745C211yesmaximal, characteristic, complemented
15#22590694C212yesmaximal, complemented
16C4×#14556086C211yesmaximal, characteristic, complemented
17Q8×C4⋊C4×C71C211yesmaximal, characteristic, complemented
18#17986536C4116yescomplemented
19C2×#14556123C2212yes—
20C2×#14556119C2211yescharacteristic
21C2×#14556117C2211yescharacteristic
22C2×#14556113C2212yes—
23C2×#14556104C2211yescharacteristic
24C2×#14556103C2211yescharacteristic
25C2×C4×D284C2212yes—
26C2×C4×D284C2211yescharacteristic
27C2×C4×D284C2212yes—
28C2×#14556086C2211yescharacteristic
29C2×#14556086C2211yescharacteristic
30C2×#14556086C2212yes—
31C2×#14556086C2212yes—
32C2×#14556085C2212yes—
33C2×C4⋊C4×D71C2212yes—
34C2×C42×D71C2211yescharacteristic
35#17985906C2212yes—
36#17985900C2214yes—
37#17985900C2212yes—
38#17985897C2212yes—
39#17985890C2214yes—
40#17985889C2214yes—
41#17985889C2214yes—
42#17985889C2214yes—
43#17985889C2214yes—
44#17985889C2214yes—
45#17985885C2214yes—
46#17985884C2214yes—
47#17985880C2214yes—
48#17985880C2214yes—
49#17985877C2214yes—
50#17985873C2214yes—
51#17985869C2211yescharacteristic
52#17985865C2212yes—
53#17985864C2212yes—
54#17985856C2212yes—
55#17985856C2212yes—
56#17985856C2212yes—
57#17985856C2212yes—
58C4⋊C4×Dic71C2212yes—
59C4⋊C4×Dic71C2212yes—
60C4⋊C4×Dic71C2212yes—
61C4⋊C4×Dic71C2214yes—
62C4⋊C4×Dic71C2212yes—
63C4⋊C4×Dic71C2211yescharacteristic
64C4⋊C4×Dic71C2211yescharacteristic
65C4×Dic71⋊C4C2214yes—
66C4×C4⋊Dic71C2211yescharacteristic
67C4×C4⋊Dic71C2212yes—
68#17985850C2214yes—
69C4×(C2×D71)⋊C4C2214yes—
70C4×(C2×D71)⋊C4C2212yes—
71C4×(C2×D71)⋊C4C2214yes—
72#17985846C2214yes—
73#17985846C2212yes—
74#17985844C2212yes—
75C42×Dic71C2212yes—
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×D284—44no—
98C4×D284C2×C418yes—
99C4×D284C2×C4116yescomplemented
100#14556086—24no—
101#14556086—28no—
102#14556086—24no—
103#14556086—44no—
104#14556085C2×C4116yescomplemented
105C2×C4⋊Dic71C2311yescharacteristic
106C2×C4⋊Dic71C2312yes—
107C2×C4⋊Dic71C2312yes—
108C2×C4⋊Dic71C2312yes—
109C2×C4⋊Dic71C2312yes—
110C2×C4⋊Dic71C2311yescharacteristic
111C2×C4⋊Dic71C2311yescharacteristic
112C2×Dic71⋊C4C2314yes—
113C2×Dic71⋊C4C2312yes—
114C2×Dic71⋊C4C2312yes—
115C4⋊C4×D71—28no—
116C2×(C2×D71)⋊C4C2312yes—
117C2×(C2×D71)⋊C4C2314yes—
118C2×(C2×D71)⋊C4C2312yes—
119C2×(C2×D71)⋊C4C2314yes—
120C2×(C2×D71)⋊C4C2314yes—
121C2×(C2×D71)⋊C4C2314yes—
122C2×(C2×D71)⋊C4C2312yes—
123C2×(C2×D71)⋊C4C2312yes—
124C2×(C2×D71)⋊C4C2312yes—
125C2×(C2×D71)⋊C4C2312yes—
126C2×(C2×D71)⋊C4C2312yes—
127C2×C4×Dic71C2312yes—
128C2×C4×Dic71C2312yes—
129C2×C4×Dic71C2312yes—
130C2×C4×Dic71C2314yes—
131C2×C4×Dic71C2312yes—
132C2×C4×Dic71C2312yes—
133C2×C4×Dic71C2314yes—
134C2×C4×Dic71C2314yes—
135C2×C4×Dic71C2311yescharacteristic
136C2×C4×Dic71C2311yescharacteristic
137C2×C4×Dic71C2311yescharacteristic
138C42×D71C2×C418yescomplemented
139C71⋊#95C2312yes—
140C71⋊#95C2312yes—
141C71⋊#95C2312yes—
142C71⋊#95C2314yes—
143C71⋊#95C2314yes—
144C71⋊#95C2314yes—
145C71⋊#95C2314yes—
146C71⋊#95C2314yes—
147C71⋊#95C2314yes—
148C71⋊#95C2314yes—
149C22×Q8×C71C2311yescharacteristic
150C4×Q8×C71—44no—
151C4×Q8×C71C2×C418yescomplemented
152C2×C4⋊C4×C71C2312yes—
153C2×C4⋊C4×C71C2311yescharacteristic
154C2×C4⋊C4×C71C2312yes—
155C2×C4⋊C4×C71C2312yes—
156C2×C4⋊C4×C71C2314yes—
157C2×C4⋊C4×C71C2314yes—
158C2×C4⋊C4×C71C2311yescharacteristic
159C2×C4⋊C4×C71C2312yes—
160C2×C4⋊C4×C71C2311yescharacteristic
161C2×C42×C71C2312yes—
162C2×C42×C71C2314yes—
163C2×C42×C71C2312yes—
164C2×C42×C71C2311yescharacteristic
165#95×C71C2312yes—
166#95×C71C2314yes—
167C23×D71C2411yescharacteristic
168C23×D71C2412yes—
169C2×D284—22no—
170C2×D284—22no—
171C2×D284—42no—
172C2×D284—42no—
173C2×D284C22×C414yes—
174C2×D284C22×C418yes—
175C22×Dic71C2414yes—
176C22×Dic71C2412yes—
177C22×Dic71C2411yescharacteristic
178C22×Dic71C2411yescharacteristic
179C22×Dic71C2411yescharacteristic
180C22×Dic71C2412yes—
181C22×Dic71C2412yes—
182C2×C4×D71—24no—
183C2×C4×D71—22no—
184C2×C4×D71—24no—
185C2×C4×D71—22no—
186C2×C4×D71—22no—
187C2×C4×D71—22no—
188C2×C4×D71—28no—
189C2×C4×D71—41no—
190C2×C4×D71—41no—
191C2×C4×D71—44no—
192C2×C4×D71—44no—
193C2×C4×D71C22×C414yes—
194C2×C4×D71C22×C414yes—
195C2×C4×D71C22×C418yes—
196C2×C4×D71C22×C414yes—
197C4⋊Dic71—24no—
198C4⋊Dic71—22no—
199C4⋊Dic71—24no—
200C4⋊Dic71—42no—
201C4⋊Dic71C22×C414yes—
202C4⋊Dic71C22×C418yes—
203C4⋊Dic71#4114yes—
204Dic71⋊C4—28no—
205Dic71⋊C4C22×C418yes—
206Dic71⋊C4C22×C418yes—
207(C2×D71)⋊C4—24no—
208(C2×D71)⋊C4—28no—
209(C2×D71)⋊C4—24no—
210(C2×D71)⋊C4—44no—
211(C2×D71)⋊C4—44no—
212(C2×D71)⋊C4—44no—
213(C2×D71)⋊C4C22×C418yes—
214(C2×D71)⋊C4C22×C418yes—
215(C2×D71)⋊C4C22×C418yes—
216(C2×D71)⋊C4C22×C418yes—
217(C2×D71)⋊C4C22×C418yes—
218C4×Dic71—24no—
219C4×Dic71—24no—
220C4×Dic71—24no—
221C4×Dic71—28no—
222C4×Dic71—42no—
223C4×Dic71—44no—
224C4×Dic71—42no—
225C4×Dic71—44no—
226C4×Dic71C22×C414yes—
227C4×Dic71C22×C414yes—
228C4×Dic71C22×C414yes—
229C2×Q8×C71—22no—
230C2×Q8×C71—22no—
231C2×Q8×C71C22×C414yes—
232C22×C4×C71C2412yes—
233C22×C4×C71C2414yes—
234C22×C4×C71C2411yescharacteristic
235C22×C4×C71C2412yes—
236C22×C4×C71C2412yes—
237C22×C4×C71C2412yes—
238C22×C4×C71C2411yescharacteristic
239C22×C4×C71C2411yescharacteristic
240C4⋊C4×C71—24no—
241C4⋊C4×C71—22no—
242C4⋊C4×C71—24no—
243C4⋊C4×C71—42no—
244C4⋊C4×C71—44no—
245C4⋊C4×C71—44no—
246C4⋊C4×C71C22×C414yes—
247C4⋊C4×C71C22×C418yes—
248C4⋊C4×C71#4114yes—
249C42×C71—24no—
250C42×C71—44no—
251C42×C71C22×C414yes—
252C42×C71C22×C418yes—
253C23×C71C2511yescharacteristic
254C22×D71—21no—
255C22×D71—22no—
256C22×D71—21no—
257C22×D71—22no—
258C22×D71—21no—
259C22×D71—22no—
260C22×D71—21no—
261C22×D71—22no—
262C22×D71—22no—
263C22×D71—22no—
264C22×D71—21no—
265C22×D71—21no—
266C22×D71C23×C414yes—
267C22×D71C23×C412yes—
268Q8×C71—28no—
269C2×C4×C71—22no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—21no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—21no—
277C2×C4×C71—22no—
278C2×C4×C71—24no—
279C2×C4×C71—22no—
280C2×C4×C71—24no—
281C2×C4×C71—22no—
282C2×C4×C71—24no—
283C2×C4×C71C23×C412yes—
284C2×C4×C71C23×C414yes—
285C2×C4×C71C23×C414yes—
286C2×C4×C71C23×C412yes—
287C2×C4×C71C23×C412yes—
288C2×C4×C71C2×#4112yes—
289C2×C4×C71C2×#4114yes—
290C2×C4×C71C2×#4112yes—
291C2×C4×C71H(5,𝔽2)12yes—
292C2×C4×C712−1+412yes—
293C2×Dic71—21no—
294C2×Dic71—22no—
295C2×Dic71—21no—
296C2×Dic71—22no—
297C2×Dic71—21no—
298C2×Dic71—22no—
299C2×Dic71—21no—
300C2×Dic71—22no—
301C2×Dic71—21no—
302C2×Dic71—21no—
303C2×Dic71—22no—
304C2×Dic71—24no—
305C2×Dic71—24no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—24no—
309C2×Dic71C23×C412yes—
310C2×Dic71C23×C412yes—
311C2×Dic71C23×C412yes—
312C2×Dic71C23×C414yes—
313C2×Dic71C2×#4114yes—
314D284—28no—
315D284—48no—
316C4×D71—216no—
317C4×D71—28no—
318C4×D71—28no—
319C4×D71—44no—
320C4×D71—88no—
321C22×C71C24×C411yescharacteristic
322C22×C71C22×#4111yescharacteristic
323C22×C71C22×#4111yescharacteristic
324C22×C71C2×H(5,𝔽2)11yescharacteristic
325C22×C71C2×2−1+411yescharacteristic
326C22×C71#58511yescharacteristic
327C22×C71#58511yescharacteristic
328C2×D71—22no—
329C2×D71—24no—
330C2×D71—22no—
331C2×D71—24no—
332C2×D71—22no—
333C2×D71—24no—
334C2×D71—42no—
335C2×D71—41no—
336C2×D71—41no—
337C2×D71—42no—
338C2×D71—41no—
339C2×D71—42no—
340C2×D71—41no—
341C2×D71—42no—
342C4×C71—24no—
343C4×C71—22no—
344C4×C71—24no—
345C4×C71—24no—
346C4×C71—42no—
347C4×C71—44no—
348C4×C71C4×#4114yes—
349C4×C71#52014yes—
350Dic71—22no—
351Dic71—24no—
352Dic71—22no—
353Dic71—22no—
354Dic71—24no—
355Dic71—44no—
356Dic71—42no—
357#34242—711nomaximal, Sylow
358C2×C71C2×C4×#4111yescharacteristic
359C2×C71C2×#52011yescharacteristic
360C2×C71#342811yescharacteristic
361C2×C71#351411yescharacteristic
362C2×C71#351511yescharacteristic
363C2×C71#351711yescharacteristic
364C2×C71#351811yescharacteristic
365D71—42no—
366D71—44no—
367C2×#529—711no—
368#2373—714no—
369#2363—712no—
370#2362—712no—
371#2355—711no—
372#2354—712no—
373#2354—711no—
374#2352—712no—
375Q8×C4⋊C4D7111yescharacteristic, complemented
376D4×C4⋊C4—711no—
377#2335—714no—
378#2314—712no—
379C4×#125—712no—
380C4×#124—712no—
381#2285—711no—
382#2274—712no—
383C4×#117—711no—
384C71#3424211yescharacteristic, complemented, Sylow
385#529—7116no—
386C2×#126—712no—
387C2×#125—711no—
388C2×#124—711no—
389C2×#123—712no—
390C2×C22⋊Q8—711no—
391C2×#121—711no—
392C2×C4×Q8C2×D7112yes—
393C2×C4×Q8C2×D7111yescharacteristic
394C2×C4×D4—712no—
395C2×C4×D4—711no—
396C2×C4×D4—712no—
397C2×#117—712no—
398C2×#117—711no—
399C2×#117—711no—
400C2×#117—712no—
401C2×#117—712no—
402C22×C4⋊C4—712no—
403C22×C42—711no—
404#391—712no—
405#390—714no—
406#390—712no—
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#384—711no—
423#384C2×D7112yes—
424#384C2×D7111yescharacteristic
425#382—712no—
426#382—712no—
427#380—712no—
428#380—712no—
429#380—712no—
430#380—712no—
431C4×C4⋊C4—712no—
432C4×C4⋊C4—714no—
433C4×C4⋊C4—712no—
434C4×C4⋊C4—711no—
435C4×C4⋊C4—712no—
436C4×C4⋊C4—712no—
437C4×C4⋊C4—711no—
438C4×C4⋊C4—711no—
439C4×C4⋊C4—712no—
440C4×C4⋊C4—714no—
441C4×C4⋊C4—714no—
442C4×C4⋊C4C2×D7111yescharacteristic
443C4×C4⋊C4C2×D7112yes—
444C4×C22⋊C4—714no—
445C4×C22⋊C4—714no—
446C4×C22⋊C4—712no—
447C4×C22⋊C4—712no—
448C4×C22⋊C4—714no—
449#376—712no—
450C43—712no—
451C22×Q8C22×D7111yescharacteristic
452C22×D4—712no—
453C22×D4—711no—
454C23×C4—711no—
455C23×C4—714no—
456C23×C4—712no—
457C23×C4—711no—
458C23×C4—711no—
459#126—7116no—
460#125—718no—
461#124—718no—
462#123—7116no—
463C22⋊Q8—718no—
464#121—718no—
465C4×Q8—44no—
466C4×Q8C4×D7118yescomplemented
467C4×D4—2844no—
468C4×D4—718no—
469C4×D4—7116no—
470#117—2844no—
471#117—7116no—
472#117—1424no—
473#117—1428no—
474#117—1424no—
475C2×C4⋊C4—712no—
476C2×C4⋊C4—711no—
477C2×C4⋊C4—712no—
478C2×C4⋊C4—712no—
479C2×C4⋊C4—711no—
480C2×C4⋊C4—712no—
481C2×C4⋊C4—712no—
482C2×C4⋊C4—714no—
483C2×C4⋊C4—712no—
484C2×C4⋊C4—711no—
485C2×C4⋊C4—1428no—
486C2×C4⋊C4C22×D7112yes—
487C2×C4⋊C4C22×D7111yescharacteristic
488C2×C4⋊C4C22×D7112yes—
489C2×C4⋊C4C22×D7114yes—
490C2×C4⋊C4C22×D7112yes—
491C2×C4⋊C4C22×D7114yes—
492C2×C4⋊C4C22×D7111yescharacteristic
493C2×C4⋊C4C22×D7112yes—
494C2×C4⋊C4C22×D7111yescharacteristic
495C2×C22⋊C4—714no—
496C2×C22⋊C4—714no—
497C2×C22⋊C4—714no—
498C2×C22⋊C4—712no—
499C2×C22⋊C4—712no—
500C2×C22⋊C4—712no—
501C2×C22⋊C4—712no—
502C2×C22⋊C4—712no—
503C2×C22⋊C4—712no—
504C2×C22⋊C4—712no—
505C2×C22⋊C4—714no—
506C2×C42—714no—
507C2×C42—712no—
508C2×C42—712no—
509C2×C42—714no—
510C2×C42—711no—
511C2×C42—711no—
512C2×C42—711no—
513C2×C42—718no—
514C2×C42—712no—
515C2×C42—712no—
516C2×C42—714no—
517C2×C42—712no—
518C2×C42C22×D7112yes—
519C2×C42C22×D7114yes—
520C2×C42C22×D7112yes—
521C2×C42C22×D7111yescharacteristic
522#95—712no—
523#95—712no—
524#95—712no—
525#95—714no—
526#95—714no—
527#95—714no—
528#95—714no—
529#95—714no—
530#95—714no—
531#95—714no—
532#95C22×D7112yes—
533#95C22×D7114yes—
534C24—712no—
535C24—711no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8C2×C4×D7114yes—
539C2×D4—2842no—
540C2×D4—2842no—
541C2×D4—718no—
542C2×D4—714no—
543C2×D4—1422no—
544C2×D4—1422no—
545C22×C4—2841no—
546C22×C4—2841no—
547C22×C4—2844no—
548C22×C4—2844no—
549C22×C4—714no—
550C22×C4—712no—
551C22×C4—711no—
552C22×C4—711no—
553C22×C4—711no—
554C22×C4—712no—
555C22×C4—714no—
556C22×C4—714no—
557C22×C4—718no—
558C22×C4—712no—
559C22×C4—714no—
560C22×C4—1428no—
561C22×C4—1424no—
562C22×C4—1422no—
563C22×C4—1424no—
564C22×C4—1422no—
565C22×C4—1422no—
566C22×C4—1422no—
567C22×C4C23×D7112yes—
568C22×C4C23×D7114yes—
569C22×C4C23×D7112yes—
570C22×C4C23×D7112yes—
571C22×C4C23×D7111yescharacteristic
572C22×C4C23×D7112yes—
573C22×C4C23×D7111yescharacteristic
574C22×C4C23×D7111yescharacteristic
575C4⋊C4—22no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—42no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—2842no—
582C4⋊C4—718no—
583C4⋊C4—718no—
584C4⋊C4—714no—
585C4⋊C4—718no—
586C4⋊C4—714no—
587C4⋊C4—1428no—
588C4⋊C4—1424no—
589C4⋊C4—1422no—
590C4⋊C4—1424no—
591C4⋊C4C2×C4×D7114yes—
592C4⋊C4C2×C4×D7118yes—
593C4⋊C4#1176586614yes—
594C22⋊C4—2844no—
595C22⋊C4—2844no—
596C22⋊C4—2844no—
597C22⋊C4—718no—
598C22⋊C4—718no—
599C22⋊C4—718no—
600C22⋊C4—718no—
601C22⋊C4—718no—
602C22⋊C4—1424no—
603C22⋊C4—1428no—
604C22⋊C4—1424no—
605C42—24no—
606C42—44no—
607C42—2844no—
608C42—2842no—
609C42—2842no—
610C42—2844no—
611C42—714no—
612C42—714no—
613C42—714no—
614C42—1424no—
615C42—1428no—
616C42—1424no—
617C42—1424no—
618C42C2×C4×D7114yes—
619C42C2×C4×D7118yes—
620C23—714no—
621C23—712no—
622C23—1421no—
623C23—1422no—
624C23—1421no—
625C23—1422no—
626C23—1421no—
627C23—1422no—
628C23—1421no—
629C23—1422no—
630C23—1422no—
631C23—1421no—
632C23—1422no—
633C23—1421no—
634C23C24×D7111yescharacteristic
635Q8—28no—
636D4—2848no—
637D4—1428no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—2844no—
653C2×C4—5688no—
654C2×C4—712no—
655C2×C4—712no—
656C2×C4—712no—
657C2×C4—714no—
658C2×C4—714no—
659C2×C4—1422no—
660C2×C4—1424no—
661C2×C4—1424no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4—1424no—
665C2×C4—1421no—
666C2×C4—1422no—
667C2×C4—1421no—
668C2×C4—1422no—
669C2×C4—1421no—
670C2×C4—1422no—
671C2×C4—1421no—
672C2×C4—1421no—
673C2×C4—1422no—
674C2×C4—1421no—
675C2×C4—1428no—
676C2×C4—14216no—
677C2×C4—1428no—
678C2×C4C22×C4×D7112yes—
679C2×C4C22×C4×D7114yes—
680C2×C4C22×C4×D7114yes—
681C2×C4C22×C4×D7112yes—
682C2×C4C22×C4×D7112yes—
683C2×C4#41×D7112yes—
684C2×C4C2×#1176586614yes—
685C2×C4C2×#1176586612yes—
686C2×C4#1455617312yes—
687C2×C4#1455617612yes—
688C22—2842no—
689C22—2841no—
690C22—2841no—
691C22—2842no—
692C22—2841no—
693C22—2842no—
694C22—2841no—
695C22—2842no—
696C22—1424no—
697C22—1422no—
698C22—1422no—
699C22—1424no—
700C22—1422no—
701C22—1424no—
702C22C23×C4×D7111yescharacteristic
703C22C2×#41×D7111yescharacteristic
704C22C22×#1176586611yescharacteristic
705C22C2×#1455617311yescharacteristic
706C22C2×#1455617611yescharacteristic
707C22#1798683411yescharacteristic
708C22#1798683611yescharacteristic
709C4—24no—
710C4—24no—
711C4—22no—
712C4—24no—
713C4—42no—
714C4—44no—
715C4—2844no—
716C4—2842no—
717C4—1422no—
718C4—1424no—
719C4—1422no—
720C4—1422no—
721C4—1424no—
722C4C4×#1176586614yes—
723C4#1798648014yes—
724C2—2844no—
725C2—2842no—
726C2C2×C4×#1176586611yescharacteristic
727C2C2×#1798648011yescharacteristic
728C2#2260154011yescharacteristic
729C2#2260230211yescharacteristic
730C2#2260231711yescharacteristic
731C2#2260234311yescharacteristic
732C2#2260235811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingQ8×C4⋊C4×C71C2
socle, cosocleC23×C71C25
prime radicalC2×#14556103C22
hypercenterQ8×C4⋊C4D71
hypocenterC71#34242
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #22591463C2semidirect
4. #22591363C2semidirect
5. #22591297C2semidirect
6. #22591291C2semidirect
7. #22591291C2semidirect
8. #22591272C2semidirect
9. C4⋊C4×D284C2semidirect
10. #22591133C2semidirect
11. #22590948C2semidirect
12. #22590899C2semidirect
13. C4×#14556117C2semidirect
14. #22590745C2semidirect
15. #22590694C2semidirect
16. C4×#14556086C2semidirect
17. Q8×C4⋊C4×C71C2semidirect
18. #17986536C4semidirect
91. #14556123C2×C4semidirect
92. #14556119C2×C4semidirect
94. #14556113C2×C4semidirect
95. #14556104C2×C4semidirect
99. C4×D284C2×C4semidirect
104. #14556085C2×C4semidirect
138. C42×D71C2×C4semidirect
151. C4×Q8×C71C2×C4semidirect
375. Q8×C4⋊C4D71semidirect
384. C71#34242semidirect
466. 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
#225914632
#225913772
#225913632
#225912972
#225912912
#225912722
C4⋊C4×D2842
#225911332
#225909482
#225908992
C4×#145561172
#225907452
#225906942
C4×#145560862
Q8×C4⋊C4×C712
#3424271