Finite Group Databasebeta

← #32156720

Subgroups — #32156720

Order 18176.

2630 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556086C211yesmaximal, characteristic
2#22591232C212yesmaximal, complemented
3#22591221C212yesmaximal, complemented
4#22591219C211yesmaximal, characteristic, complemented
5#22591215C211yesmaximal, characteristic, complemented
6#22591209C211yesmaximal, characteristic, complemented
7#22591195C214yesmaximal, complemented
8#22591190C212yesmaximal
9#22591182C212yesmaximal
10#22590832C214yesmaximal, complemented
11#22590821C212yesmaximal, complemented
12#22590731C212yesmaximal, complemented
13#22590722C211yesmaximal, characteristic
14#117×Dic71C212yesmaximal, complemented
15C4×#14556086C212yesmaximal, complemented
16C4×C22⋊C4×D71C211yesmaximal, characteristic
17C71×#2344C211yesmaximal, characteristic, complemented
18C23×C4×D71C2211yescharacteristic
19C2×#14556087C2212yes—
20C2×#14556086C4116yescomplemented
21C2×#14556086C2212yes—
22C2×#14556086C2211yescharacteristic
23C2×#14556086C2211yescharacteristic
24C2×#14556086C2212yes—
25C2×#14556086C2211yescharacteristic
26C2×#14556086C2212yes—
27C2×#14556086C2211yescharacteristic
28C22×C4⋊Dic71C2211yescharacteristic
29C22×(C2×D71)⋊C4C2212yes—
30C2×C22⋊C4×D71C2211yescharacteristic
31C2×C22⋊C4×D71C2211yescharacteristic
32C22×C4×Dic71C2212yes—
33C2×C42×D71C2212yes—
34#17985898C2212yescomplemented
35#17985897C2212yescomplemented
36#17985895C2212yescomplemented
37#17985891C2214yes—
38#17985890C2214yes—
39#17985889C2214yes—
40#17985888C2214yes—
41#17985885C2214yescomplemented
42#17985884C2214yescomplemented
43#17985882C2214yescomplemented
44#17985873C2214yes—
45#17985870C2214yes—
46#17985866C2214yescomplemented
47#17985863C2214yescomplemented
48#17985862C2212yes—
49#17985861C2212yes—
50#17985859C2211yescharacteristic
51#17985857C2212yes—
52#17985857C2212yes—
53#17985856C2212yes—
54#17985854C2212yes—
55C4⋊C4×Dic71C2212yescomplemented
56C4⋊C4×Dic71C2214yescomplemented
57C4⋊C4×Dic71C2214yescomplemented
58C4⋊C4×Dic71C2212yescomplemented
59C4×C4⋊Dic71C2212yescomplemented
60#17985850C2214yescomplemented
61C22⋊C4×Dic71C2212yes—
62C22⋊C4×Dic71C2211yescharacteristic
63C22⋊C4×Dic71C2211yescharacteristic
64C22⋊C4×Dic71C2212yes—
65C22⋊C4×Dic71C2212yes—
66C4×(C2×D71)⋊C4C2212yes—
67C4×(C2×D71)⋊C4C2214yes—
68C4×C22⋊Dic71C2211yescharacteristic
69#17985846C2212yes—
70#17985846C2212yes—
71#17985846C2214yes—
72#17985845C2214yescomplemented
73#17985844C2214yescomplemented
74#95×D71C2212yes—
75C42×Dic71C2214yescomplemented
76C2×#117×C71C2212yes—
77C22×C4⋊C4×C71C2211yescharacteristic
78#389×C71C2212yescomplemented
79#387×C71C2214yescomplemented
80#381×C71C2212yes—
81#380×C71C2211yescharacteristic
82C4×C4⋊C4×C71C2212yescomplemented
83C4×C22⋊C4×C71C2211yescharacteristic
84C24×D71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2312yes—
87C22×C4×D71—28no—
88C22×C4×D71C2×C418yes—
89C22×C4×D71C2312yes—
90C22×C4×D71C2312yes—
91C22×C4×D71C2311yescharacteristic
92C22×C4×D71C2311yescharacteristic
93C22×C4×D71C2311yescharacteristic
94C22×C4×D71C2311yescharacteristic
95#14556087—28no—
96#14556086—28no—
97#14556086C2×C4116yes—
98#14556086C2×C418yes—
99#14556086C2×C418yes—
100#14556086C2×C418yescomplemented
101#14556086C2×C4116yescomplemented
102#14556086C2×C418yescomplemented
103C2×C4⋊Dic71C2×C418yescomplemented
104C2×C4⋊Dic71C2312yes—
105C2×C4⋊Dic71C2314yes—
106C2×C4⋊Dic71C2311yescharacteristic
107C2×C4⋊Dic71C2312yes—
108C2×C4⋊Dic71C2311yescharacteristic
109C2×Dic71⋊C4C2314yes—
110C2×Dic71⋊C4C2314yes—
111C2×C22⋊Dic71C2311yescharacteristic
112C2×C22⋊Dic71C2312yes—
113C2×C22⋊Dic71C2311yescharacteristic
114C2×(C2×D71)⋊C4C2×C4116yes—
115C2×(C2×D71)⋊C4C2314yes—
116C2×(C2×D71)⋊C4C2312yes—
117C2×(C2×D71)⋊C4C2312yes—
118C2×(C2×D71)⋊C4C2314yes—
119C2×(C2×D71)⋊C4C2312yes—
120C2×(C2×D71)⋊C4C2312yes—
121C2×(C2×D71)⋊C4C2312yes—
122C2×(C2×D71)⋊C4C2312yes—
123C22⋊C4×D71—24no—
124C22⋊C4×D71—24no—
125C2×C4×Dic71C2×C4116yescomplemented
126C2×C4×Dic71C2312yes—
127C2×C4×Dic71C2314yes—
128C2×C4×Dic71C2314yes—
129C2×C4×Dic71C2312yes—
130C2×C4×Dic71C2312yes—
131C2×C4×Dic71C2314yes—
132C2×C4×Dic71C2314yes—
133C2×C4×Dic71C2312yes—
134C2×C4×Dic71C2312yes—
135C2×C4×Dic71C2312yes—
136C2×C4×Dic71C2312yes—
137C42×D71—28no—
138C71⋊#95C2312yes—
139C71⋊#95C2312yes—
140C71⋊#95C2312yes—
141C71⋊#95C2314yes—
142C71⋊#95C2314yes—
143C71⋊#95C2314yes—
144C71⋊#95C2314yes—
145C71⋊#95C2314yes—
146C71⋊#95C2314yes—
147C71⋊#95C2312yes—
148C71⋊#95C2314yes—
149C23×C4×C71C2311yescharacteristic
150C23×C4×C71C2312yes—
151#117×C71—28no—
152C2×C4⋊C4×C71C2×C418yescomplemented
153C2×C4⋊C4×C71C2314yes—
154C2×C4⋊C4×C71C2312yes—
155C2×C4⋊C4×C71C2311yescharacteristic
156C2×C4⋊C4×C71C2312yes—
157C2×C4⋊C4×C71C2311yescharacteristic
158C2×C22⋊C4×C71C2312yes—
159C2×C22⋊C4×C71C2311yescharacteristic
160C2×C22⋊C4×C71C2311yescharacteristic
161C2×C42×C71C2314yes—
162C2×C42×C71C2312yes—
163#95×C71C2312yes—
164#95×C71C2314yes—
165#95×C71C2312yes—
166#95×C71C2314yes—
167C23×D71—22no—
168C23×D71—22no—
169C23×D71—24no—
170C23×D71—42no—
171C23×D71C22×C414yes—
172C23×D71C2411yescharacteristic
173C23×D71C2411yescharacteristic
174C22×Dic71—24no—
175C22×Dic71—44no—
176C22×Dic71C22×C414yes—
177C22×Dic71C22×C418yes—
178C22×Dic71C2412yes—
179C22×Dic71C2414yes—
180C22×Dic71C2411yescharacteristic
181C22×Dic71C2412yes—
182C22×Dic71C2412yes—
183C22×Dic71C2412yes—
184C22×Dic71C2411yescharacteristic
185C2×C4×D71—24no—
186C2×C4×D71—24no—
187C2×C4×D71—24no—
188C2×C4×D71—232no—
189C2×C4×D71—24no—
190C2×C4×D71—24no—
191C2×C4×D71—24no—
192C2×C4×D71—24no—
193C2×C4×D71—42no—
194C2×C4×D71—42no—
195C2×C4×D71C22×C414yes—
196C2×C4×D71C22×C414yes—
197C2×C4×D71C22×C414yes—
198C2×C4×D71C22×C414yes—
199C2×C4×D71#4118yes—
200C4⋊Dic71—24no—
201C4⋊Dic71—28no—
202C4⋊Dic71C22×C418yes—
203C4⋊Dic71C22×C414yes—
204C4⋊Dic71C22×C414yes—
205Dic71⋊C4—44no—
206Dic71⋊C4—44no—
207C22⋊Dic71—22no—
208C22⋊Dic71—24no—
209C22⋊Dic71#4114yes—
210(C2×D71)⋊C4—28no—
211(C2×D71)⋊C4—24no—
212(C2×D71)⋊C4—24no—
213(C2×D71)⋊C4—44no—
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—28no—
223C4×Dic71—44no—
224C4×Dic71—44no—
225C4×Dic71C22×C418yes—
226C4×Dic71C22×C418yes—
227C4×Dic71C22×C418yes—
228C4×Dic71C22×C418yes—
229C24×C71C2411yescharacteristic
230C22×C4×C71—24no—
231C22×C4×C71—24no—
232C22×C4×C71—24no—
233C22×C4×C71C22×C414yes—
234C22×C4×C71C22×C418yes—
235C22×C4×C71C2412yes—
236C22×C4×C71C2414yes—
237C22×C4×C71C2411yescharacteristic
238C22×C4×C71C2412yes—
239C22×C4×C71C2412yes—
240C22×C4×C71C2412yes—
241C22×C4×C71C2411yescharacteristic
242C4⋊C4×C71—28no—
243C4⋊C4×C71—24no—
244C4⋊C4×C71C22×C418yes—
245C4⋊C4×C71C22×C414yes—
246C4⋊C4×C71C22×C414yes—
247C22⋊C4×C71—24no—
248C22⋊C4×C71—22no—
249C22⋊C4×C71#4114yes—
250C42×C71—28no—
251C42×C71—24no—
252C23×C71—22no—
253C23×C71—22no—
254C23×C71C23×C412yes—
255C23×C71C2×#4112yes—
256C23×C71C2×#4112yes—
257C23×C71C2511yescharacteristic
258C22×D71—21no—
259C22×D71—21no—
260C22×D71—22no—
261C22×D71—28no—
262C22×D71—21no—
263C22×D71—21no—
264C22×D71—22no—
265C22×D71—22no—
266C22×D71—28no—
267C22×D71—44no—
268C22×D71—48no—
269C22×D71—48no—
270C22×D71C23×C412yes—
271C22×D71C23×C412yes—
272C22×D71C2×#4114yes—
273C2×C4×C71—216no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—28no—
282C2×C4×C71—24no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—24no—
286C2×C4×C71—24no—
287C2×C4×C71—22no—
288C2×C4×C71C23×C414yes—
289C2×C4×C71C23×C414yes—
290C2×C4×C71C23×C412yes—
291C2×C4×C71C23×C412yes—
292C2×C4×C71C2×#4114yes—
293C2×C4×C71C2×#4114yes—
294C2×Dic71—22no—
295C2×Dic71—22no—
296C2×Dic71—22no—
297C2×Dic71—24no—
298C2×Dic71—24no—
299C2×Dic71—28no—
300C2×Dic71—22no—
301C2×Dic71—24no—
302C2×Dic71—24no—
303C2×Dic71—22no—
304C2×Dic71—24no—
305C2×Dic71—22no—
306C2×Dic71—48no—
307C2×Dic71C23×C412yes—
308C2×Dic71C23×C414yes—
309C2×Dic71C23×C414yes—
310C2×Dic71C23×C412yes—
311C2×Dic71C2×#4114yes—
312C2×Dic71C2×#4114yes—
313C4×D71—28no—
314C4×D71—28no—
315C4×D71—28no—
316C4×D71—48no—
317C4×D71—48no—
318C4×D71#117116yescomplemented
319C22×C71—22no—
320C22×C71—22no—
321C22×C71—24no—
322C22×C71—24no—
323C22×C71C4×#4114yes—
324C22×C71C24×C411yescharacteristic
325C22×C71C22×#4112yes—
326C22×C71C22×#4111yescharacteristic
327C22×C71C22×#4111yescharacteristic
328C22×C71#58512yes—
329C2×D71—22no—
330C2×D71—22no—
331C2×D71—24no—
332C2×D71—24no—
333C2×D71—22no—
334C2×D71—22no—
335C2×D71—22no—
336C2×D71—416no—
337C2×D71—42no—
338C2×D71—42no—
339C2×D71C2×#11714yes—
340C4×C71—22no—
341C4×C71—24no—
342C4×C71—24no—
343C4×C71—24no—
344C4×C71—42no—
345C4×C71—44no—
346C4×C71C2×#11714yes—
347Dic71—22no—
348Dic71—24no—
349Dic71—24no—
350Dic71—24no—
351Dic71—42no—
352Dic71—44no—
353Dic71C2×#11714yes—
354#34109—711nomaximal, Sylow
355C2×C71—24no—
356C2×C71C22×#11711yescharacteristic
357C2×C71C2×C4×#4111yescharacteristic
358C2×C71#342811yescharacteristic
359C2×C71#347512yes—
360C2×C71#347512yes—
361D71—24no—
362D71—42no—
363C22×#117—711no—
364#2347—712no—
365#2346—712no—
366#2345—711no—
367#2345—711no—
368#2344—711no—
369#2344D7111yescharacteristic, complemented
370#2343—714no—
371#2342—712no—
372#2342—712no—
373#2298—714no—
374#2296—712no—
375#2283—712no—
376#2280—711no—
377C4×#117—712no—
378C4×#117—712no—
379C2×C4×C22⋊C4—711no—
380C71#3410911yescharacteristic, complemented, Sylow
381C24×C4—711no—
382C2×#117—712no—
383C2×#117—7116no—
384C2×#117—712no—
385C2×#117—711no—
386C2×#117—711no—
387C2×#117—711no—
388C2×#117—711no—
389C2×#117—712no—
390C2×#117—712no—
391C2×#117C2×D7112yes—
392C22×C4⋊C4—711no—
393C22×C4⋊C4C2×D7111yescharacteristic
394C22×C22⋊C4—712no—
395C22×C22⋊C4—711no—
396C22×C22⋊C4—711no—
397C22×C42—712no—
398C22×C42—712no—
399#389—712no—
400#389—712no—
401#389—712no—
402#389C2×D7112yescomplemented
403#388—714no—
404#388—714no—
405#388—714no—
406#388—714no—
407#387—714no—
408#387—714no—
409#387—714no—
410#387C2×D7114yescomplemented
411#385—714no—
412#385—714no—
413#383—714no—
414#382—714no—
415#381—712no—
416#381—712no—
417#381C2×D7112yes—
418#380—711no—
419#380—712no—
420#380—712no—
421#380—712no—
422#380C2×D7111yescharacteristic
423#379—712no—
424C4×C4⋊C4—714no—
425C4×C4⋊C4—712no—
426C4×C4⋊C4—712no—
427C4×C4⋊C4—714no—
428C4×C4⋊C4—712no—
429C4×C4⋊C4—714no—
430C4×C4⋊C4C2×D7112yescomplemented
431C4×C22⋊C4—711no—
432C4×C22⋊C4—712no—
433C4×C22⋊C4—712no—
434C4×C22⋊C4—711no—
435C4×C22⋊C4—711no—
436C4×C22⋊C4—712no—
437C4×C22⋊C4—714no—
438C4×C22⋊C4—712no—
439C4×C22⋊C4—714no—
440C4×C22⋊C4—712no—
441C4×C22⋊C4—712no—
442C4×C22⋊C4C2×D7111yescharacteristic
443#376—714no—
444#376—714no—
445C2×#95—712no—
446C43—714no—
447C25—711no—
448C23×C4—712no—
449C23×C4—712no—
450C23×C4—712no—
451C23×C4—711no—
452C23×C4—711no—
453C23×C4—718no—
454C23×C4—711no—
455C23×C4—711no—
456C23×C4—711no—
457C23×C4—1428no—
458C23×C4C22×D7112yes—
459C23×C4C22×D7111yescharacteristic
460#117—28no—
461#117—718no—
462#117—718no—
463#117—7116no—
464#117—718no—
465#117—718no—
466#117—7116no—
467#117—1428no—
468#117—1428no—
469C2×C4⋊C4—714no—
470C2×C4⋊C4—714no—
471C2×C4⋊C4—718no—
472C2×C4⋊C4—711no—
473C2×C4⋊C4—712no—
474C2×C4⋊C4—711no—
475C2×C4⋊C4—712no—
476C2×C4⋊C4—714no—
477C2×C4⋊C4C4×D7118yescomplemented
478C2×C4⋊C4C22×D7112yes—
479C2×C4⋊C4C22×D7114yes—
480C2×C4⋊C4C22×D7111yescharacteristic
481C2×C4⋊C4C22×D7112yes—
482C2×C4⋊C4C22×D7111yescharacteristic
483C2×C22⋊C4—714no—
484C2×C22⋊C4—711no—
485C2×C22⋊C4—7116no—
486C2×C22⋊C4—712no—
487C2×C22⋊C4—712no—
488C2×C22⋊C4—712no—
489C2×C22⋊C4—712no—
490C2×C22⋊C4—711no—
491C2×C22⋊C4—712no—
492C2×C22⋊C4—712no—
493C2×C22⋊C4—712no—
494C2×C22⋊C4—714no—
495C2×C22⋊C4—1424no—
496C2×C22⋊C4—1424no—
497C2×C22⋊C4C22×D7111yescharacteristic
498C2×C22⋊C4C22×D7112yes—
499C2×C22⋊C4C22×D7111yescharacteristic
500C2×C42—714no—
501C2×C42—714no—
502C2×C42—7116no—
503C2×C42—712no—
504C2×C42—712no—
505C2×C42—712no—
506C2×C42—712no—
507C2×C42—714no—
508C2×C42—714no—
509C2×C42—712no—
510C2×C42—712no—
511C2×C42—712no—
512C2×C42—1428no—
513C2×C42C22×D7114yes—
514C2×C42C22×D7112yes—
515#95—712no—
516#95—712no—
517#95—712no—
518#95—714no—
519#95—714no—
520#95—714no—
521#95—714no—
522#95—714no—
523#95—714no—
524#95—712no—
525#95—714no—
526#95C22×D7112yes—
527#95C22×D7114yes—
528#95C22×D7112yes—
529#95C22×D7114yes—
530C24—2842no—
531C24—714no—
532C24—711no—
533C24—711no—
534C24—1424no—
535C24—1422no—
536C24—1422no—
537C24C23×D7111yescharacteristic
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—2842no—
542C22×C4—2842no—
543C22×C4—2844no—
544C22×C4—718no—
545C22×C4—711no—
546C22×C4—714no—
547C22×C4—718no—
548C22×C4—714no—
549C22×C4—711no—
550C22×C4—712no—
551C22×C4—712no—
552C22×C4—712no—
553C22×C4—714no—
554C22×C4—714no—
555C22×C4—714no—
556C22×C4—712no—
557C22×C4—714no—
558C22×C4—1424no—
559C22×C4—1424no—
560C22×C4—1424no—
561C22×C4—1424no—
562C22×C4—14232no—
563C22×C4—1424no—
564C22×C4—1424no—
565C22×C4—1424no—
566C22×C4—1424no—
567C22×C4C2×C4×D7118yes—
568C22×C4C2×C4×D7114yes—
569C22×C4C23×D7112yes—
570C22×C4C23×D7114yes—
571C22×C4C23×D7111yescharacteristic
572C22×C4C23×D7112yes—
573C22×C4C23×D7112yes—
574C22×C4C23×D7112yes—
575C22×C4C23×D7111yescharacteristic
576C4⋊C4—24no—
577C4⋊C4—28no—
578C4⋊C4—2844no—
579C4⋊C4—2844no—
580C4⋊C4—718no—
581C4⋊C4—714no—
582C4⋊C4—714no—
583C4⋊C4—1428no—
584C4⋊C4—1424no—
585C4⋊C4C2×C4×D7118yes—
586C4⋊C4C2×C4×D7114yes—
587C4⋊C4C2×C4×D7114yes—
588C22⋊C4—22no—
589C22⋊C4—24no—
590C22⋊C4—2844no—
591C22⋊C4—714no—
592C22⋊C4—718no—
593C22⋊C4—718no—
594C22⋊C4—718no—
595C22⋊C4—718no—
596C22⋊C4—1424no—
597C22⋊C4—1428no—
598C22⋊C4—1424no—
599C22⋊C4—1422no—
600C22⋊C4—1424no—
601C22⋊C4#1176586414yes—
602C42—24no—
603C42—28no—
604C42—2844no—
605C42—2844no—
606C42—718no—
607C42—718no—
608C42—718no—
609C42—718no—
610C42—1424no—
611C42—1424no—
612C42—1428no—
613C42—1428no—
614C42—1424no—
615C23—22no—
616C23—22no—
617C23—2848no—
618C23—2848no—
619C23—2844no—
620C23—712no—
621C23—714no—
622C23—712no—
623C23—1428no—
624C23—1421no—
625C23—1422no—
626C23—1421no—
627C23—1422no—
628C23—1428no—
629C23—1421no—
630C23—1421no—
631C23—1422no—
632C23C22×C4×D7112yes—
633C23#41×D7112yes—
634C23C2×#1176586412yes—
635C23C24×D7111yescharacteristic
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—216no—
644C2×C4—28no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—2848no—
652C2×C4—2848no—
653C2×C4—2848no—
654C2×C4—712no—
655C2×C4—714no—
656C2×C4—7116no—
657C2×C4—712no—
658C2×C4—714no—
659C2×C4—714no—
660C2×C4—714no—
661C2×C4—1428no—
662C2×C4—1428no—
663C2×C4—1422no—
664C2×C4—1424no—
665C2×C4—1424no—
666C2×C4—1422no—
667C2×C4—1424no—
668C2×C4—1422no—
669C2×C4—1428no—
670C2×C4—1422no—
671C2×C4—1422no—
672C2×C4—1424no—
673C2×C4—1422no—
674C2×C4—1424no—
675C2×C4—1428no—
676C2×C4C22×C4×D7114yes—
677C2×C4C22×C4×D7114yes—
678C2×C4C22×C4×D7112yes—
679C2×C4C22×C4×D7112yes—
680C2×C4#41×D7114yes—
681C2×C4C2×#1176586414yes—
682C22—22no—
683C22—22no—
684C22—24no—
685C22—24no—
686C22—28416no—
687C22—2842no—
688C22—2842no—
689C22—714no—
690C22—1422no—
691C22—1422no—
692C22—1422no—
693C22—1422no—
694C22—1422no—
695C22—1424no—
696C22—1424no—
697C22C4×#1176586414yes—
698C22C23×C4×D7111yescharacteristic
699C22C2×#41×D7112yes—
700C22C2×#41×D7111yescharacteristic
701C22C22×#1176586411yescharacteristic
702C22#1798683612yes—
703C4—22no—
704C4—24no—
705C4—24no—
706C4—24no—
707C4—42no—
708C4—44no—
709C4—2844no—
710C4—2842no—
711C4—714no—
712C4—1422no—
713C4—1424no—
714C4—1424no—
715C4—1424no—
716C4#117×D7114yes—
717C2—24no—
718C2—2842no—
719C2—1424no—
720C2C2×#117×D7111yescharacteristic
721C2C2×C4×#1176586411yescharacteristic
722C2#2260154211yescharacteristic
723C2#2260189312yes—
724C2#2260190312yes—
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2344C2
socle, cosocleC23×C71C25
prime radicalC24×D71C23
hypercenter#2344D71
hypocenterC71#34109
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2344

Complements

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

NH ≅ G/Ntype
2. #22591232C2semidirect
3. #22591221C2semidirect
4. #22591219C2semidirect
5. #22591215C2semidirect
6. #22591209C2semidirect
7. #22591195C2semidirect
10. #22590832C2semidirect
11. #22590821C2semidirect
12. #22590731C2semidirect
14. #117×Dic71C2semidirect
15. C4×#14556086C2semidirect
17. C71×#2344C2semidirect
20. C2×#14556086C4semidirect
34. #17985898C22semidirect
35. #17985897C22semidirect
36. #17985895C22semidirect
41. #17985885C22semidirect
42. #17985884C22semidirect
43. #17985882C22semidirect
46. #17985866C22semidirect
47. #17985863C22semidirect
55. C4⋊C4×Dic71C22semidirect
56. C4⋊C4×Dic71C22semidirect
57. C4⋊C4×Dic71C22semidirect
58. C4⋊C4×Dic71C22semidirect
59. C4×C4⋊Dic71C22semidirect
60. #17985850C22semidirect
72. #17985845C22semidirect
73. #17985844C22semidirect
75. C42×Dic71C22semidirect
78. #389×C71C22semidirect
79. #387×C71C22semidirect
82. C4×C4⋊C4×C71C22semidirect
100. #14556086C2×C4semidirect
101. #14556086C2×C4semidirect
102. #14556086C2×C4semidirect
103. C2×C4⋊Dic71C2×C4semidirect
125. C2×C4×Dic71C2×C4semidirect
152. C2×C4⋊C4×C71C2×C4semidirect
318. C4×D71#117semidirect
369. #2344D71semidirect
380. C71#34109semidirect
402. #389C2×D71semidirect
410. #387C2×D71semidirect
430. C4×C4⋊C4C2×D71semidirect
477. C2×C4⋊C4C4×D71semidirect

Maximal subgroups

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

subgroupindex
C22×#145560862
#225912322
#225912212
#225912192
#225912152
#225912092
#225911952
#225911902
#225911822
#225908322
#225908212
#225907312
#225907222
#117×Dic712
C4×#145560862
C4×C22⋊C4×D712
C71×#23442
#3410971