Finite Group Databasebeta

← #32157532

Subgroups — #32157532

Order 18176.

2518 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D71C211yesmaximal, characteristic
2#22591232C212yesmaximal, complemented
3#22591224C212yesmaximal, complemented
4#22591216C212yesmaximal, complemented
5#22591208C212yesmaximal, complemented
6#22591198C214yesmaximal, complemented
7#22591187C214yesmaximal
8#22590963C211yesmaximal, characteristic, complemented
9#22590950C212yesmaximal, complemented
10#22590948C212yesmaximal, complemented
11#22590745C212yesmaximal, complemented
12#22590733C212yesmaximal, complemented
13#22590719C211yesmaximal, characteristic
14C2×#17985856C211yesmaximal, characteristic
15#22590697C211yesmaximal, characteristic, complemented
16#22590696C211yesmaximal, characteristic, complemented
17C71×#2317C211yesmaximal, characteristic, complemented
18C23×C4×D71C2211yescharacteristic
19C2×#14556087C2211yescharacteristic
20C2×#14556087C2211yescharacteristic
21C2×#14556086C2214yes—
22C2×#14556086C2211yescharacteristic
23C2×#14556086C2211yescharacteristic
24C2×#14556085C2212yes—
25C2×#14556084C2212yes—
26#117×D71C4116yescomplemented
27C22×C4⋊Dic71C2211yescharacteristic
28C2×C4⋊C4×D71C2211yescharacteristic
29C2×C4⋊C4×D71C2211yescharacteristic
30C22×(C2×D71)⋊C4C2212yes—
31C2×C22⋊C4×D71C2212yes—
32C2×C42×D71C2212yes—
33#17985898C2212yescomplemented
34#17985898C2212yescomplemented
35#17985891C2214yes—
36#17985891C2214yes—
37#17985889C2214yes—
38#17985889C2214yes—
39#17985886C2214yescomplemented
40#17985886C2214yescomplemented
41#17985880C2214yescomplemented
42#17985880C2214yescomplemented
43#17985874C2214yes—
44#17985869C2212yescomplemented
45#17985866C2214yescomplemented
46#17985865C2212yescomplemented
47#17985864C2214yescomplemented
48#17985861C2214yes—
49#17985860C2212yes—
50#17985856C2212yes—
51#17985856C2211yescharacteristic
52#17985856C2212yes—
53#17985856C2211yescharacteristic
54#17985856C2214yes—
55#17985856C2211yescharacteristic
56#17985856C2212yes—
57#17985856C2211yescharacteristic
58#17985856C2212yes—
59#17985854C2212yes—
60C4⋊C4×Dic71C2214yescomplemented
61C4⋊C4×Dic71C2212yescomplemented
62C4⋊C4×Dic71C2212yescomplemented
63C4⋊C4×Dic71C2212yescomplemented
64C4⋊C4×Dic71C2212yescomplemented
65C4⋊C4×Dic71C2212yescomplemented
66C4⋊C4×Dic71C2212yescomplemented
67C4×C4⋊Dic71C2212yescomplemented
68C4×C4⋊Dic71C2212yescomplemented
69C22⋊C4×Dic71C2214yes—
70C4×(C2×D71)⋊C4C2212yes—
71C4×(C2×D71)⋊C4C2212yes—
72C4×C22⋊Dic71C2214yes—
73#17985846C2214yes—
74#17985844C2214yescomplemented
75C2×C71⋊#95C2212yes—
76C2×#117×C71C2211yescharacteristic
77C2×#117×C71C2211yescharacteristic
78C22×C4⋊C4×C71C2211yescharacteristic
79#389×C71C2212yescomplemented
80#389×C71C2212yescomplemented
81#385×C71C2214yes—
82#384×C71C2212yescomplemented
83#382×C71C2212yescomplemented
84C24×D71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2312yes—
87C22×C4×D71—24no—
88C22×C4×D71—24no—
89C22×C4×D71C2×C418yes—
90C22×C4×D71C2311yescharacteristic
91C22×C4×D71C2311yescharacteristic
92C22×C4×D71C2311yescharacteristic
93C22×C4×D71C2311yescharacteristic
94C22×C4×D71C2312yes—
95C22×C4×D71C2312yes—
96#14556087—24no—
97#14556087C2×C418yes—
98#14556086—48no—
99#14556086C2×C418yescomplemented
100#14556086C2×C418yescomplemented
101#14556085C2×C4116yescomplemented
102#14556084C2×C4116yes—
103C2×C4⋊Dic71—24no—
104C2×C4⋊Dic71C2312yes—
105C2×C4⋊Dic71C2311yescharacteristic
106C2×C4⋊Dic71C2312yes—
107C2×C4⋊Dic71C2311yescharacteristic
108C2×C4⋊Dic71C2314yes—
109C2×C4⋊Dic71C2314yes—
110C2×C4⋊Dic71C2311yescharacteristic
111C2×C4⋊Dic71C2311yescharacteristic
112C2×Dic71⋊C4C2312yes—
113C2×Dic71⋊C4C2312yes—
114C4⋊C4×D71C2×C418yescomplemented
115C4⋊C4×D71C2×C418yescomplemented
116C2×C22⋊Dic71C2312yes—
117C2×C22⋊Dic71C2312yes—
118C2×(C2×D71)⋊C4—44no—
119C2×(C2×D71)⋊C4C2312yes—
120C2×(C2×D71)⋊C4C2314yes—
121C2×(C2×D71)⋊C4C2312yes—
122C2×(C2×D71)⋊C4C2312yes—
123C2×(C2×D71)⋊C4C2312yes—
124C2×(C2×D71)⋊C4C2314yes—
125C2×(C2×D71)⋊C4C2312yes—
126C2×(C2×D71)⋊C4C2312yes—
127C22⋊C4×D71C2×C4116yes—
128C2×C4×Dic71C2312yes—
129C2×C4×Dic71C2314yes—
130C2×C4×Dic71C2314yes—
131C2×C4×Dic71C2314yes—
132C2×C4×Dic71C2314yes—
133C2×C4×Dic71C2312yes—
134C2×C4×Dic71C2312yes—
135C2×C4×Dic71C2312yes—
136C42×D71C2×C4116yescomplemented
137C71⋊#95C2314yes—
138C71⋊#95C2314yes—
139C71⋊#95C2312yes—
140C71⋊#95C2314yes—
141C71⋊#95C2314yes—
142C71⋊#95C2314yes—
143C71⋊#95C2314yes—
144C71⋊#95C2312yes—
145C71⋊#95C2312yes—
146C71⋊#95C2312yes—
147C71⋊#95C2314yes—
148C71⋊#95C2314yes—
149C23×C4×C71C2312yes—
150C23×C4×C71C2311yescharacteristic
151#117×C71—24no—
152#117×C71C2×C418yes—
153C2×C4⋊C4×C71—24no—
154C2×C4⋊C4×C71C2312yes—
155C2×C4⋊C4×C71C2312yes—
156C2×C4⋊C4×C71C2311yescharacteristic
157C2×C4⋊C4×C71C2311yescharacteristic
158C2×C4⋊C4×C71C2314yes—
159C2×C4⋊C4×C71C2314yes—
160C2×C4⋊C4×C71C2311yescharacteristic
161C2×C4⋊C4×C71C2311yescharacteristic
162C2×C22⋊C4×C71C2312yes—
163C2×C22⋊C4×C71C2312yes—
164C2×C42×C71C2312yes—
165C2×C42×C71C2312yes—
166#95×C71C2314yes—
167#95×C71C2314yes—
168C23×D71—22no—
169C23×D71—22no—
170C23×D71—22no—
171C23×D71—22no—
172C23×D71—41no—
173C23×D71—41no—
174C23×D71C22×C414yes—
175C23×D71C2411yescharacteristic
176C23×D71C2411yescharacteristic
177C22×Dic71—22no—
178C22×Dic71—22no—
179C22×Dic71—24no—
180C22×Dic71—42no—
181C22×Dic71—42no—
182C22×Dic71C22×C414yes—
183C22×Dic71C2414yes—
184C22×Dic71C2412yes—
185C22×Dic71C2412yes—
186C22×Dic71C2411yescharacteristic
187C22×Dic71C2411yescharacteristic
188C22×Dic71C2412yes—
189C22×Dic71C2412yes—
190C2×C4×D71—24no—
191C2×C4×D71—24no—
192C2×C4×D71—232no—
193C2×C4×D71—22no—
194C2×C4×D71—22no—
195C2×C4×D71—22no—
196C2×C4×D71—22no—
197C2×C4×D71—22no—
198C2×C4×D71—22no—
199C2×C4×D71—22no—
200C2×C4×D71—22no—
201C2×C4×D71—42no—
202C2×C4×D71—42no—
203C2×C4×D71C22×C414yes—
204C2×C4×D71C22×C414yes—
205C2×C4×D71C22×C414yes—
206C2×C4×D71C22×C414yes—
207C2×C4×D71C22×C418yes—
208C2×C4×D71C22×C418yes—
209C4⋊Dic71—24no—
210C4⋊Dic71—24no—
211C4⋊Dic71—22no—
212C4⋊Dic71—22no—
213C4⋊Dic71—44no—
214C4⋊Dic71—44no—
215C4⋊Dic71C22×C414yes—
216C4⋊Dic71C22×C414yes—
217Dic71⋊C4C22×C418yes—
218Dic71⋊C4C22×C418yes—
219C22⋊Dic71—24no—
220C22⋊Dic71C22×C418yes—
221(C2×D71)⋊C4—28no—
222(C2×D71)⋊C4—24no—
223(C2×D71)⋊C4—24no—
224(C2×D71)⋊C4—44no—
225(C2×D71)⋊C4—42no—
226(C2×D71)⋊C4—42no—
227(C2×D71)⋊C4C22×C418yes—
228(C2×D71)⋊C4C22×C418yes—
229C4×Dic71—24no—
230C4×Dic71—44no—
231C4×Dic71—44no—
232C4×Dic71—44no—
233C4×Dic71—44no—
234C4×Dic71C22×C418yes—
235C4×Dic71C22×C418yes—
236C4×Dic71C22×C418yes—
237C24×C71C2411yescharacteristic
238C22×C4×C71—24no—
239C22×C4×C71—42no—
240C22×C4×C71—42no—
241C22×C4×C71C22×C414yes—
242C22×C4×C71#4114yes—
243C22×C4×C71#4114yes—
244C22×C4×C71C2412yes—
245C22×C4×C71C2414yes—
246C22×C4×C71C2412yes—
247C22×C4×C71C2412yes—
248C22×C4×C71C2412yes—
249C22×C4×C71C2411yescharacteristic
250C22×C4×C71C2411yescharacteristic
251C4⋊C4×C71—24no—
252C4⋊C4×C71—24no—
253C4⋊C4×C71—22no—
254C4⋊C4×C71—22no—
255C4⋊C4×C71—44no—
256C4⋊C4×C71—44no—
257C4⋊C4×C71C22×C414yes—
258C4⋊C4×C71C22×C414yes—
259C22⋊C4×C71—24no—
260C22⋊C4×C71C22×C418yes—
261C42×C71—24no—
262C42×C71C22×C418yes—
263C23×C71—21no—
264C23×C71—21no—
265C23×C71—21no—
266C23×C71—21no—
267C23×C71C23×C412yes—
268C23×C71C2×#4112yes—
269C23×C71C2×#4112yes—
270C23×C71C2511yescharacteristic
271C22×D71—21no—
272C22×D71—21no—
273C22×D71—21no—
274C22×D71—21no—
275C22×D71—28no—
276C22×D71—21no—
277C22×D71—21no—
278C22×D71—21no—
279C22×D71—21no—
280C22×D71—21no—
281C22×D71—21no—
282C22×D71—28no—
283C22×D71—44no—
284C22×D71—44no—
285C22×D71—44no—
286C22×D71—44no—
287C22×D71—44no—
288C22×D71C23×C412yes—
289C22×D71C23×C412yes—
290C22×D71H(5,𝔽2)12yes—
291C22×D712−1+412yes—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—24no—
299C2×C4×C71—22no—
300C2×C4×C71—24no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—24no—
304C2×C4×C71—22no—
305C2×C4×C71—84no—
306C2×C4×C71#117116yescomplemented
307C2×C4×C71C23×C414yes—
308C2×C4×C71C23×C414yes—
309C2×C4×C71C23×C412yes—
310C2×C4×C71C23×C412yes—
311C2×C4×C71C2×#4112yes—
312C2×C4×C71C2×#4112yes—
313C2×C4×C71C2×#4112yes—
314C2×C4×C71C2×#4112yes—
315C2×Dic71—28no—
316C2×Dic71—21no—
317C2×Dic71—21no—
318C2×Dic71—21no—
319C2×Dic71—21no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—22no—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—24no—
327C2×Dic71—22no—
328C2×Dic71—24no—
329C2×Dic71—22no—
330C2×Dic71—22no—
331C2×Dic71—24no—
332C2×Dic71—22no—
333C2×Dic71—84no—
334C2×Dic71C23×C412yes—
335C2×Dic71C23×C414yes—
336C2×Dic71C23×C414yes—
337C2×Dic71C23×C412yes—
338C4×D71—216no—
339C4×D71—28no—
340C4×D71—28no—
341C4×D71—28no—
342C4×D71—28no—
343C4×D71—48no—
344C22×C71—22no—
345C22×C71—22no—
346C22×C71—22no—
347C22×C71—22no—
348C22×C71—22no—
349C22×C71—22no—
350C22×C71C2×#11714yes—
351C22×C71C24×C411yescharacteristic
352C22×C71C22×#4111yescharacteristic
353C22×C71C22×#4111yescharacteristic
354C22×C71C2×H(5,𝔽2)11yescharacteristic
355C22×C71C2×2−1+411yescharacteristic
356C22×C71#58511yescharacteristic
357C22×C71#58511yescharacteristic
358C2×D71—22no—
359C2×D71—22no—
360C2×D71—22no—
361C2×D71—22no—
362C2×D71—22no—
363C2×D71—22no—
364C2×D71—22no—
365C2×D71—22no—
366C2×D71—22no—
367C2×D71—416no—
368C2×D71—41no—
369C2×D71—41no—
370C2×D71—41no—
371C2×D71—41no—
372C2×D71#52014yes—
373C4×C71—24no—
374C4×C71—24no—
375C4×C71—42no—
376C4×C71—44no—
377C4×C71—42no—
378C4×C71C2×#11714yes—
379C4×C71C2×#11714yes—
380Dic71—22no—
381Dic71—22no—
382Dic71—24no—
383Dic71—24no—
384Dic71—42no—
385Dic71—44no—
386Dic71—42no—
387#34180—711nomaximal, Sylow
388C2×C71—24no—
389C2×C71C22×#11711yescharacteristic
390C2×C71C2×#52011yescharacteristic
391C2×C71#342811yescharacteristic
392C2×C71#349411yescharacteristic
393C2×C71#349411yescharacteristic
394C2×C71#349511yescharacteristic
395C2×C71#349511yescharacteristic
396D71—24no—
397D71—42no—
398C22×#117—711no—
399#2347—712no—
400#2346—712no—
401#2345—712no—
402#2344—712no—
403#2343—714no—
404#2342—714no—
405#2317—711no—
406#2317D7111yescharacteristic, complemented
407#2314—712no—
408#2314—712no—
409#2285—712no—
410#2283—712no—
411#2280—711no—
412C2×#380—711no—
413#2274—711no—
414#2274—711no—
415C71#3418011yescharacteristic, complemented, Sylow
416C24×C4—711no—
417C2×#117—711no—
418C2×#117—7116no—
419C2×#117—711no—
420C2×#117—714no—
421C2×#117—711no—
422C2×#117—711no—
423C2×#117—712no—
424C2×#117—712no—
425C2×#117C2×D7111yescharacteristic
426C2×#117C2×D7111yescharacteristic
427C22×C4⋊C4—711no—
428C22×C4⋊C4—711no—
429C22×C4⋊C4—711no—
430C22×C4⋊C4C2×D7111yescharacteristic
431C22×C22⋊C4—712no—
432C22×C22⋊C4—712no—
433C22×C42—712no—
434#389—712no—
435#389—712no—
436#389C2×D7112yescomplemented
437#389C2×D7112yescomplemented
438#388—714no—
439#388—714no—
440#388—714no—
441#388—714no—
442#387—714no—
443#387—714no—
444#387—714no—
445#387—714no—
446#385—714no—
447#385C2×D7114yes—
448#384—712no—
449#384C2×D7112yescomplemented
450#383—714no—
451#382—714no—
452#382—712no—
453#382C2×D7112yescomplemented
454#381—712no—
455#381—714no—
456#380—712no—
457#380—711no—
458#380—711no—
459#380—714no—
460#380—712no—
461#380—712no—
462#380—712no—
463#380—711no—
464#380—711no—
465#379—712no—
466C4×C4⋊C4—712no—
467C4×C4⋊C4—712no—
468C4×C4⋊C4—712no—
469C4×C4⋊C4—712no—
470C4×C4⋊C4—714no—
471C4×C4⋊C4—712no—
472C4×C4⋊C4—712no—
473C4×C4⋊C4—712no—
474C4×C4⋊C4—712no—
475C4×C22⋊C4—714no—
476C4×C22⋊C4—714no—
477C4×C22⋊C4—712no—
478C4×C22⋊C4—712no—
479C4×C22⋊C4—714no—
480#376—714no—
481C2×#95—712no—
482C25—711no—
483C23×C4—712no—
484C23×C4—712no—
485C23×C4—711no—
486C23×C4—718no—
487C23×C4—712no—
488C23×C4—711no—
489C23×C4—711no—
490C23×C4—711no—
491C23×C4—711no—
492C23×C4—1424no—
493C23×C4—1424no—
494C23×C4C22×D7112yes—
495C23×C4C22×D7111yescharacteristic
496#117—24no—
497#117—2848no—
498#117—718no—
499#117—718no—
500#117—718no—
501#117—7116no—
502#117—7116no—
503#117—1424no—
504#117C4×D7118yes—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—714no—
507C2×C4⋊C4—714no—
508C2×C4⋊C4—711no—
509C2×C4⋊C4—711no—
510C2×C4⋊C4—712no—
511C2×C4⋊C4—712no—
512C2×C4⋊C4—718no—
513C2×C4⋊C4—718no—
514C2×C4⋊C4—712no—
515C2×C4⋊C4—712no—
516C2×C4⋊C4—711no—
517C2×C4⋊C4—711no—
518C2×C4⋊C4—1424no—
519C2×C4⋊C4C22×D7112yes—
520C2×C4⋊C4C22×D7112yes—
521C2×C4⋊C4C22×D7111yescharacteristic
522C2×C4⋊C4C22×D7111yescharacteristic
523C2×C4⋊C4C22×D7114yes—
524C2×C4⋊C4C22×D7114yes—
525C2×C4⋊C4C22×D7111yescharacteristic
526C2×C4⋊C4C22×D7111yescharacteristic
527C2×C22⋊C4—2844no—
528C2×C22⋊C4—714no—
529C2×C22⋊C4—712no—
530C2×C22⋊C4—712no—
531C2×C22⋊C4—712no—
532C2×C22⋊C4—712no—
533C2×C22⋊C4—712no—
534C2×C22⋊C4—7116no—
535C2×C22⋊C4—712no—
536C2×C22⋊C4—714no—
537C2×C22⋊C4—712no—
538C2×C22⋊C4—712no—
539C2×C22⋊C4C22×D7112yes—
540C2×C22⋊C4C22×D7112yes—
541C2×C42—714no—
542C2×C42—714no—
543C2×C42—714no—
544C2×C42—714no—
545C2×C42—712no—
546C2×C42—712no—
547C2×C42—712no—
548C2×C42—7116no—
549C2×C42—712no—
550C2×C42C22×D7112yes—
551C2×C42C22×D7112yes—
552#95—714no—
553#95—714no—
554#95—712no—
555#95—714no—
556#95—712no—
557#95—714no—
558#95—714no—
559#95—714no—
560#95—714no—
561#95—712no—
562#95—712no—
563#95—714no—
564#95C22×D7114yes—
565#95C22×D7114yes—
566C24—2841no—
567C24—2841no—
568C24—714no—
569C24—711no—
570C24—711no—
571C24—1422no—
572C24—1422no—
573C24—1422no—
574C24—1422no—
575C24C23×D7111yescharacteristic
576C22×C4—24no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—2842no—
580C22×C4—2842no—
581C22×C4—2842no—
582C22×C4—2842no—
583C22×C4—718no—
584C22×C4—714no—
585C22×C4—711no—
586C22×C4—711no—
587C22×C4—712no—
588C22×C4—712no—
589C22×C4—714no—
590C22×C4—718no—
591C22×C4—714no—
592C22×C4—714no—
593C22×C4—714no—
594C22×C4—712no—
595C22×C4—714no—
596C22×C4—712no—
597C22×C4—1424no—
598C22×C4—1424no—
599C22×C4—1424no—
600C22×C4—1422no—
601C22×C4—1422no—
602C22×C4—1422no—
603C22×C4—1422no—
604C22×C4—1422no—
605C22×C4—1422no—
606C22×C4—1422no—
607C22×C4—1422no—
608C22×C4—1422no—
609C22×C4—1422no—
610C22×C4—14232no—
611C22×C4C2×C4×D7114yes—
612C22×C4#1176586414yes—
613C22×C4#1176586614yes—
614C22×C4C23×D7112yes—
615C22×C4C23×D7114yes—
616C22×C4C23×D7112yes—
617C22×C4C23×D7112yes—
618C22×C4C23×D7112yes—
619C22×C4C23×D7111yescharacteristic
620C22×C4C23×D7111yescharacteristic
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—2844no—
628C4⋊C4—2844no—
629C4⋊C4—718no—
630C4⋊C4—718no—
631C4⋊C4—714no—
632C4⋊C4—714no—
633C4⋊C4—1424no—
634C4⋊C4—1424no—
635C4⋊C4—1422no—
636C4⋊C4—1422no—
637C4⋊C4C2×C4×D7114yes—
638C4⋊C4C2×C4×D7114yes—
639C22⋊C4—24no—
640C22⋊C4—2844no—
641C22⋊C4—2842no—
642C22⋊C4—2842no—
643C22⋊C4—718no—
644C22⋊C4—718no—
645C22⋊C4—718no—
646C22⋊C4—1428no—
647C22⋊C4—1424no—
648C22⋊C4—1424no—
649C22⋊C4—1424no—
650C22⋊C4C2×C4×D7118yes—
651C42—24no—
652C42—2844no—
653C42—2844no—
654C42—2844no—
655C42—2844no—
656C42—718no—
657C42—718no—
658C42—718no—
659C42—1424no—
660C42C2×C4×D7118yes—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—2844no—
666C23—2844no—
667C23—2844no—
668C23—2844no—
669C23—2844no—
670C23—712no—
671C23—712no—
672C23—712no—
673C23—712no—
674C23—1428no—
675C23—1421no—
676C23—1421no—
677C23—1421no—
678C23—1421no—
679C23—1421no—
680C23—1421no—
681C23—1428no—
682C23—1421no—
683C23—1421no—
684C23—1421no—
685C23—1421no—
686C23C22×C4×D7112yes—
687C23C2×#1176586412yes—
688C23C2×#1176586612yes—
689C23C24×D7111yescharacteristic
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—84no—
704C2×C4—2848no—
705C2×C4—5684no—
706C2×C4—712no—
707C2×C4—714no—
708C2×C4—714no—
709C2×C4—712no—
710C2×C4—14216no—
711C2×C4—1422no—
712C2×C4—1422no—
713C2×C4—1424no—
714C2×C4—1422no—
715C2×C4—1424no—
716C2×C4—1422no—
717C2×C4—1422no—
718C2×C4—1424no—
719C2×C4—1422no—
720C2×C4—1421no—
721C2×C4—1421no—
722C2×C4—1421no—
723C2×C4—1421no—
724C2×C4—1422no—
725C2×C4—1422no—
726C2×C4—1422no—
727C2×C4—1422no—
728C2×C4—1428no—
729C2×C4—1428no—
730C2×C4—1428no—
731C2×C4—1428no—
732C2×C4—1428no—
733C2×C4#14556086116yescomplemented
734C2×C4C22×C4×D7114yes—
735C2×C4C22×C4×D7114yes—
736C2×C4C22×C4×D7112yes—
737C2×C4C22×C4×D7112yes—
738C2×C4C2×#1176586412yes—
739C2×C4C2×#1176586412yes—
740C2×C4C2×#1176586612yes—
741C2×C4C2×#1176586612yes—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—28416no—
749C22—2841no—
750C22—2841no—
751C22—2841no—
752C22—2841no—
753C22—714no—
754C22—1422no—
755C22—1422no—
756C22—1422no—
757C22—1422no—
758C22—1422no—
759C22—1422no—
760C22—1422no—
761C22—1422no—
762C22—1422no—
763C22C2×#1455608614yes—
764C22C23×C4×D7111yescharacteristic
765C22C22×#1176586411yescharacteristic
766C22C22×#1176586611yescharacteristic
767C22H(5,𝔽2)×D7111yescharacteristic
768C222−1+4×D7111yescharacteristic
769C22#1798683411yescharacteristic
770C22#1798683611yescharacteristic
771C4—24no—
772C4—24no—
773C4—44no—
774C4—42no—
775C4—42no—
776C4—2844no—
777C4—2842no—
778C4—2842no—
779C4—1422no—
780C4—1422no—
781C4—1424no—
782C4—1424no—
783C4C2×#1455608614yes—
784C4C2×#1455608614yes—
785C2—24no—
786C2—2842no—
787C2—1424no—
788C2C22×#1455608611yescharacteristic
789C2#520×D7111yescharacteristic
790C2#2260154011yescharacteristic
791C2#2260207211yescharacteristic
792C2#2260207811yescharacteristic
793C2#2260208911yescharacteristic
794C2#2260209511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2317C2
socle, cosocleC23×C71C25
prime radicalC24×D71C23
hypercenter#2317D71
hypocenterC71#34180
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2317

Complements

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

NH ≅ G/Ntype
2. #22591232C2semidirect
3. #22591224C2semidirect
4. #22591216C2semidirect
5. #22591208C2semidirect
6. #22591198C2semidirect
8. #22590963C2semidirect
9. #22590950C2semidirect
10. #22590948C2semidirect
11. #22590745C2semidirect
12. #22590733C2semidirect
15. #22590697C2semidirect
16. #22590696C2semidirect
17. C71×#2317C2semidirect
26. #117×D71C4semidirect
33. #17985898C22semidirect
34. #17985898C22semidirect
39. #17985886C22semidirect
40. #17985886C22semidirect
41. #17985880C22semidirect
42. #17985880C22semidirect
44. #17985869C22semidirect
45. #17985866C22semidirect
46. #17985865C22semidirect
47. #17985864C22semidirect
60. C4⋊C4×Dic71C22semidirect
61. C4⋊C4×Dic71C22semidirect
62. C4⋊C4×Dic71C22semidirect
63. C4⋊C4×Dic71C22semidirect
64. C4⋊C4×Dic71C22semidirect
65. C4⋊C4×Dic71C22semidirect
66. C4⋊C4×Dic71C22semidirect
67. C4×C4⋊Dic71C22semidirect
68. C4×C4⋊Dic71C22semidirect
74. #17985844C22semidirect
79. #389×C71C22semidirect
80. #389×C71C22semidirect
82. #384×C71C22semidirect
83. #382×C71C22semidirect
99. #14556086C2×C4semidirect
100. #14556086C2×C4semidirect
101. #14556085C2×C4semidirect
114. C4⋊C4×D71C2×C4semidirect
115. C4⋊C4×D71C2×C4semidirect
136. C42×D71C2×C4semidirect
306. C2×C4×C71#117semidirect
406. #2317D71semidirect
415. C71#34180semidirect
436. #389C2×D71semidirect
437. #389C2×D71semidirect
449. #384C2×D71semidirect
453. #382C2×D71semidirect
733. C2×C4#14556086semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D712
#225912322
#225912242
#225912162
#225912082
#225911982
#225911872
#225909632
#225909502
#225909482
#225907452
#225907332
#225907192
C2×#179858562
#225906972
#225906962
C71×#23172
#3418071