Finite Group Databasebeta

← #32160374

Subgroups — #32160374

Order 18176.

2630 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556110C211yesmaximal, characteristic
2#22591489C214yesmaximal, complemented
3#22591335C214yesmaximal, complemented
4#22591219C212yesmaximal, complemented
5#22591186C212yesmaximal, complemented
6#22591185C212yesmaximal, complemented
7C22⋊C4×C22⋊D71C212yesmaximal
8#22591125C214yesmaximal, complemented
9#22591007C214yesmaximal, complemented
10#22590957C211yesmaximal, characteristic, complemented
11#22590942C211yesmaximal, characteristic, complemented
12#22590938C211yesmaximal, characteristic, complemented
13#22590722C211yesmaximal, characteristic, complemented
14#380×D71C211yesmaximal, characteristic, complemented
15C71×#2315C211yesmaximal, characteristic, complemented
16C23×C22⋊D71C2211yescharacteristic
17C23×C4×D71C2211yescharacteristic
18C2×#14556110C4116yescomplemented
19C2×#14556110C2212yes—
20C2×#14556110C2212yes—
21C2×#14556110C2212yes—
22C2×#14556110C2212yes—
23C2×C4×C22⋊D71C2214yes—
24C2×#14556086C2212yescomplemented
25C2×#14556084C2212yes—
26C22×C4⋊Dic71C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C2×C4⋊C4×D71C2212yescomplemented
29C22×C22⋊Dic71C2211yescharacteristic
30C22×(C2×D71)⋊C4C2211yescharacteristic
31C2×C22⋊C4×D71C2212yes—
32#17985899C2214yes—
33#17985896C2214yescomplemented
34#17985895C2214yescomplemented
35#17985894C2214yescomplemented
36#17985893C2214yescomplemented
37#17985892C2214yescomplemented
38#17985892C2214yescomplemented
39#17985889C2214yescomplemented
40#17985888C2214yescomplemented
41#17985887C2214yescomplemented
42#17985886C2214yescomplemented
43#17985884C2214yescomplemented
44#17985884C2214yescomplemented
45#17985880C2214yescomplemented
46#17985878C2214yes—
47#17985875C2214yes—
48#17985872C2214yescomplemented
49#17985870C2214yescomplemented
50#17985861C2212yescomplemented
51#17985860C2212yes—
52#17985859C2211yescharacteristic
53#17985859C2211yescharacteristic
54#17985858C2212yescomplemented
55#17985857C2212yes—
56#17985857C2212yes—
57#17985856C2212yescomplemented
58#17985856C2212yescomplemented
59#17985855C2212yes—
60#17985854C2212yes—
61C4⋊C4×Dic71C2214yescomplemented
62C22⋊C4×Dic71C2212yes—
63C22⋊C4×Dic71C2212yes—
64C4×C22⋊Dic71C2212yes—
65C4×C22⋊Dic71C2214yescomplemented
66#17985846C2212yescomplemented
67#17985846C2214yescomplemented
68#95×D71C2212yescomplemented
69C22×C22⋊C4×C71C2212yes—
70C22×C22⋊C4×C71C2211yescharacteristic
71#385×C71C2214yescomplemented
72#385×C71C2214yescomplemented
73#380×C71C2211yescharacteristic
74#380×C71C2212yes—
75#380×C71C2211yescharacteristic
76C24×D71C2311yescharacteristic
77C22×C22⋊D71—44no—
78C22×C22⋊D71C2×C418yes—
79C22×C22⋊D71C2312yes—
80C22×C22⋊D71C2312yes—
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C22×C4×D71—44no—
85C22×C4×D71C2×C418yescomplemented
86C22×C4×D71C2311yescharacteristic
87C22×C4×D71C2311yescharacteristic
88C22×C4×D71C2314yes—
89C22×C4×D71C2311yescharacteristic
90C22×C4×D71C2311yescharacteristic
91#14556110C2×C4116yescomplemented
92#14556110C2×C4116yescomplemented
93#14556110C2×C4116yescomplemented
94#14556110C2×C4116yescomplemented
95C4×C22⋊D71—48no—
96#14556086—44no—
97#14556084—44no—
98C2×C4⋊Dic71C2×C418yescomplemented
99C2×C4⋊Dic71C2312yes—
100C2×C4⋊Dic71C2312yes—
101C2×C4⋊Dic71C2312yes—
102C2×C4⋊Dic71C2312yes—
103C2×Dic71⋊C4C2×C418yescomplemented
104C2×Dic71⋊C4C2314yes—
105C2×Dic71⋊C4C2314yes—
106C2×Dic71⋊C4C2314yes—
107C2×Dic71⋊C4C2312yes—
108C2×Dic71⋊C4C2312yes—
109C4⋊C4×D71—44no—
110C2×C22⋊Dic71C2×C418yescomplemented
111C2×C22⋊Dic71C2312yes—
112C2×C22⋊Dic71C2312yes—
113C2×C22⋊Dic71C2314yes—
114C2×C22⋊Dic71C2314yes—
115C2×C22⋊Dic71C2312yes—
116C2×C22⋊Dic71C2312yes—
117C2×(C2×D71)⋊C4C2×C418yescomplemented
118C2×(C2×D71)⋊C4C2314yes—
119C2×(C2×D71)⋊C4C2314yes—
120C2×(C2×D71)⋊C4C2314yes—
121C2×(C2×D71)⋊C4C2312yes—
122C2×(C2×D71)⋊C4C2312yes—
123C22⋊C4×D71—44no—
124C2×C4×Dic71C2314yes—
125C2×C4×Dic71C2314yes—
126C2×C4×Dic71C2314yes—
127C2×C4×Dic71C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2312yes—
130C71⋊#95C2312yes—
131C71⋊#95C2314yes—
132C71⋊#95C2314yes—
133C71⋊#95C2314yes—
134C71⋊#95C2314yes—
135C71⋊#95C2314yes—
136C71⋊#95C2314yes—
137C25×C71C2311yescharacteristic
138C23×C4×C71C2314yes—
139C23×C4×C71C2311yescharacteristic
140C23×C4×C71C2311yescharacteristic
141C2×C4⋊C4×C71C2314yes—
142C2×C4⋊C4×C71C2312yes—
143C2×C4⋊C4×C71C2312yes—
144C2×C22⋊C4×C71—44no—
145C2×C22⋊C4×C71C2×C418yescomplemented
146C2×C22⋊C4×C71C2312yes—
147C2×C22⋊C4×C71C2312yes—
148C2×C22⋊C4×C71C2314yes—
149C2×C22⋊C4×C71C2312yes—
150C2×C22⋊C4×C71C2312yes—
151#95×C71C2312yes—
152#95×C71C2312yes—
153#95×C71C2314yes—
154C23×D71—22no—
155C23×D71—22no—
156C23×D71—24no—
157C23×D71—42no—
158C23×D71C22×C414yes—
159C23×D71C2411yescharacteristic
160C23×D71C2411yescharacteristic
161C2×C22⋊D71—28no—
162C2×C22⋊D71—44no—
163C2×C22⋊D71—416no—
164C2×C22⋊D71C22×C418yes—
165C2×C22⋊D71C22×C418yes—
166C22×Dic71—22no—
167C22×Dic71—22no—
168C22×Dic71—42no—
169C22×Dic71—42no—
170C22×Dic71C22×C414yes—
171C22×Dic71C22×C414yes—
172C22×Dic71C22×C414yes—
173C22×Dic71C2414yes—
174C22×Dic71C2414yes—
175C22×Dic71C2411yescharacteristic
176C22×Dic71C2411yescharacteristic
177C22×Dic71C2412yes—
178C22×Dic71C2412yes—
179C2×C4×D71—24no—
180C2×C4×D71—24no—
181C2×C4×D71—28no—
182C2×C4×D71—416no—
183C2×C4×D71—42no—
184C2×C4×D71—42no—
185C2×C4×D71—44no—
186C2×C4×D71—44no—
187C2×C4×D71C22×C414yes—
188C2×C4×D71C22×C414yes—
189C2×C4×D71C22×C414yes—
190C2×C4×D71C22×C414yes—
191C4⋊Dic71—42no—
192C4⋊Dic71—42no—
193C4⋊Dic71C22×C418yes—
194C4⋊Dic71C22×C418yes—
195Dic71⋊C4—44no—
196Dic71⋊C4—44no—
197Dic71⋊C4—44no—
198Dic71⋊C4C22×C418yes—
199Dic71⋊C4C22×C418yes—
200C22⋊Dic71—24no—
201C22⋊Dic71—24no—
202C22⋊Dic71—44no—
203C22⋊Dic71—44no—
204C22⋊Dic71C22×C418yes—
205C22⋊Dic71C22×C418yes—
206(C2×D71)⋊C4—28no—
207(C2×D71)⋊C4—44no—
208(C2×D71)⋊C4—44no—
209(C2×D71)⋊C4C22×C418yes—
210(C2×D71)⋊C4C22×C418yes—
211C4×Dic71—44no—
212C4×Dic71—44no—
213C4×Dic71—44no—
214C4×Dic71—44no—
215C24×C71—22no—
216C24×C71—22no—
217C24×C71—42no—
218C24×C71—42no—
219C24×C71C22×C414yes—
220C24×C71C2412yes—
221C24×C71C2411yescharacteristic
222C22×C4×C71—42no—
223C22×C4×C71—42no—
224C22×C4×C71—44no—
225C22×C4×C71—44no—
226C22×C4×C71—44no—
227C22×C4×C71C22×C414yes—
228C22×C4×C71C22×C414yes—
229C22×C4×C71C2414yes—
230C22×C4×C71C2414yes—
231C22×C4×C71C2411yescharacteristic
232C22×C4×C71C2411yescharacteristic
233C22×C4×C71C2412yes—
234C4⋊C4×C71—44no—
235C4⋊C4×C71—42no—
236C4⋊C4×C71—42no—
237C22⋊C4×C71—24no—
238C22⋊C4×C71—24no—
239C22⋊C4×C71—44no—
240C22⋊C4×C71C22×C418yes—
241C22⋊C4×C71C22×C418yes—
242C23×C71—22no—
243C23×C71—22no—
244C23×C71—22no—
245C23×C71—24no—
246C23×C71—22no—
247C23×C71—24no—
248C23×C71—28no—
249C23×C71—44no—
250C23×C71—44no—
251C23×C71—84no—
252C23×C71—84no—
253C23×C71C23×C414yes—
254C23×C71C23×C412yes—
255C23×C71H(5,𝔽2)12yes—
256C23×C712−1+412yes—
257C23×C71C2511yescharacteristic
258C22×D71—21no—
259C22×D71—21no—
260C22×D71—22no—
261C22×D71—28no—
262C22×D71—21no—
263C22×D71—22no—
264C22×D71—21no—
265C22×D71—22no—
266C22×D71—28no—
267C22×D71—44no—
268C22×D71—48no—
269C22×D71—48no—
270C22×D71C23×C412yes—
271C22×D71C23×C412yes—
272C22×D71H(5,𝔽2)14yes—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—24no—
276C2×C4×C71—24no—
277C2×C4×C71—24no—
278C2×C4×C71—24no—
279C2×C4×C71—24no—
280C2×C4×C71—24no—
281C2×C4×C71—24no—
282C2×C4×C71—44no—
283C2×C4×C71—44no—
284C2×C4×C71—88no—
285C2×C4×C71C23×C414yes—
286C2×C4×C71C23×C412yes—
287C2×C4×C71C23×C412yes—
288C22⋊D71—216no—
289C22⋊D71—48no—
290C2×Dic71—28no—
291C2×Dic71—22no—
292C2×Dic71—22no—
293C2×Dic71—24no—
294C2×Dic71—22no—
295C2×Dic71—22no—
296C2×Dic71—24no—
297C2×Dic71—24no—
298C2×Dic71—24no—
299C2×Dic71—24no—
300C2×Dic71—24no—
301C2×Dic71—24no—
302C2×Dic71—44no—
303C2×Dic71—44no—
304C2×Dic71C23×C414yes—
305C2×Dic71C23×C412yes—
306C2×Dic71C23×C412yes—
307C2×Dic71C23×C414yes—
308C4×D71—28no—
309C4×D71—28no—
310C4×D71—44no—
311C4×D71—44no—
312C4×D71—88no—
313C22×C71—22no—
314C22×C71—22no—
315C22×C71—24no—
316C22×C71—24no—
317C22×C71—24no—
318C22×C71—24no—
319C22×C71—24no—
320C22×C71—44no—
321C22×C71—44no—
322C22×C71—88no—
323C22×C71#52014yes—
324C22×C71C24×C411yescharacteristic
325C22×C71C2×H(5,𝔽2)12yes—
326C22×C71C2×H(5,𝔽2)11yescharacteristic
327C22×C71C2×2−1+411yescharacteristic
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×D71#51814yes—
340C4×C71—22no—
341C4×C71—22no—
342C4×C71—24no—
343C4×C71—44no—
344C4×C71—44no—
345Dic71—22no—
346Dic71—22no—
347Dic71—24no—
348Dic71—24no—
349Dic71—44no—
350Dic71—44no—
351#34376—711nomaximal, Sylow
352C2×C71—24no—
353C2×C71—44no—
354C2×C71C2×#51811yescharacteristic
355C2×C71C2×#52011yescharacteristic
356C2×C71#342811yescharacteristic
357C2×C71#353412yes—
358C2×C71#353512yes—
359D71—24no—
360D71—42no—
361C22×#123—711no—
362#2376—714no—
363#2359—714no—
364#2345—712no—
365#2342—712no—
366#2342—712no—
367D4×C22⋊C4—712no—
368#2335—714no—
369#2322—714no—
370#2316—711no—
371#2315D7111yescharacteristic, complemented
372#2313—711no—
373#2312—711no—
374#2280—711no—
375C2×#380—711no—
376C71#3437611yescharacteristic, complemented, Sylow
377C23×D4—711no—
378C24×C4—711no—
379C2×#123—7116no—
380C2×#123—712no—
381C2×#123—712no—
382C2×#123—712no—
383C2×#123—712no—
384C2×C4×D4—714no—
385C2×#117—712no—
386C2×#117—712no—
387C22×C4⋊C4—712no—
388C22×C4⋊C4—711no—
389C22×C4⋊C4—711no—
390C22×C22⋊C4—712no—
391C22×C22⋊C4—711no—
392C22×C22⋊C4—711no—
393C22×C22⋊C4C2×D7112yes—
394C22×C22⋊C4C2×D7111yescharacteristic
395#390—714no—
396#389—714no—
397#389—714no—
398#389—714no—
399#388—714no—
400#388—714no—
401#388—714no—
402#388—714no—
403#388—714no—
404#388—714no—
405#387—714no—
406#387—714no—
407#387—714no—
408#387—714no—
409#386—714no—
410#386—714no—
411#385—714no—
412#385—714no—
413#385C2×D7114yescomplemented
414#385C2×D7114yescomplemented
415#381—712no—
416#381—712no—
417#380—711no—
418#380—711no—
419#380—712no—
420#380—712no—
421#380—712no—
422#380—712no—
423#380—712no—
424#380C2×D7111yescharacteristic
425#380C2×D7111yescharacteristic
426#380C2×D7112yes—
427#379—712no—
428#379—712no—
429C4×C4⋊C4—714no—
430C4×C22⋊C4—712no—
431C4×C22⋊C4—714no—
432C4×C22⋊C4—712no—
433C4×C22⋊C4—712no—
434C4×C22⋊C4—714no—
435C4×C22⋊C4—712no—
436C2×#95—712no—
437C25—711no—
438C25C22×D7111yescharacteristic
439C22×D4—2844no—
440C22×D4—718no—
441C22×D4—712no—
442C22×D4—712no—
443C23×C4—2844no—
444C23×C4—711no—
445C23×C4—711no—
446C23×C4—718no—
447C23×C4—711no—
448C23×C4—711no—
449C23×C4—714no—
450C23×C4—711no—
451C23×C4—711no—
452C23×C4—711no—
453C23×C4C22×D7114yes—
454C23×C4C22×D7111yescharacteristic
455C23×C4C22×D7111yescharacteristic
456#123—7116no—
457#123—7116no—
458#123—7116no—
459#123—7116no—
460C4×D4—2848no—
461#117—2844no—
462#117—2844no—
463C2×C4⋊C4—2844no—
464C2×C4⋊C4—714no—
465C2×C4⋊C4—712no—
466C2×C4⋊C4—712no—
467C2×C4⋊C4—714no—
468C2×C4⋊C4—714no—
469C2×C4⋊C4—718no—
470C2×C4⋊C4—718no—
471C2×C4⋊C4—712no—
472C2×C4⋊C4—712no—
473C2×C4⋊C4—712no—
474C2×C4⋊C4—712no—
475C2×C4⋊C4C22×D7112yes—
476C2×C4⋊C4C22×D7112yes—
477C2×C4⋊C4C22×D7114yes—
478C2×C22⋊C4—44no—
479C2×C22⋊C4—2844no—
480C2×C22⋊C4—714no—
481C2×C22⋊C4—714no—
482C2×C22⋊C4—714no—
483C2×C22⋊C4—714no—
484C2×C22⋊C4—718no—
485C2×C22⋊C4—712no—
486C2×C22⋊C4—712no—
487C2×C22⋊C4—718no—
488C2×C22⋊C4—712no—
489C2×C22⋊C4—712no—
490C2×C22⋊C4—712no—
491C2×C22⋊C4—712no—
492C2×C22⋊C4—714no—
493C2×C22⋊C4C4×D7118yescomplemented
494C2×C22⋊C4C22×D7112yes—
495C2×C22⋊C4C22×D7112yes—
496C2×C22⋊C4C22×D7114yes—
497C2×C22⋊C4C22×D7112yes—
498C2×C22⋊C4C22×D7112yes—
499C2×C42—714no—
500C2×C42—714no—
501C2×C42—714no—
502C2×C42—714no—
503#95—714no—
504#95—712no—
505#95—714no—
506#95—712no—
507#95—714no—
508#95—714no—
509#95—714no—
510#95—714no—
511#95—714no—
512#95C22×D7112yes—
513#95C22×D7112yes—
514#95C22×D7114yes—
515C24—22no—
516C24—22no—
517C24—42no—
518C24—42no—
519C24—2842no—
520C24—714no—
521C24—711no—
522C24—711no—
523C24—1424no—
524C24—1422no—
525C24—1422no—
526C24C2×C4×D7114yes—
527C24C23×D7112yes—
528C24C23×D7111yescharacteristic
529C2×D4—28416no—
530C2×D4—2844no—
531C2×D4—718no—
532C2×D4—718no—
533C2×D4—1428no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—2842no—
540C22×C4—2842no—
541C22×C4—2844no—
542C22×C4—2844no—
543C22×C4—28416no—
544C22×C4—2842no—
545C22×C4—2842no—
546C22×C4—714no—
547C22×C4—714no—
548C22×C4—714no—
549C22×C4—714no—
550C22×C4—714no—
551C22×C4—711no—
552C22×C4—712no—
553C22×C4—712no—
554C22×C4—711no—
555C22×C4—714no—
556C22×C4—714no—
557C22×C4—714no—
558C22×C4—714no—
559C22×C4—1428no—
560C22×C4—1424no—
561C22×C4—1424no—
562C22×C4—1422no—
563C22×C4—1422no—
564C22×C4C2×C4×D7114yes—
565C22×C4C2×C4×D7114yes—
566C22×C4C23×D7114yes—
567C22×C4C23×D7114yes—
568C22×C4C23×D7112yes—
569C22×C4C23×D7111yescharacteristic
570C22×C4C23×D7111yescharacteristic
571C4⋊C4—42no—
572C4⋊C4—44no—
573C4⋊C4—42no—
574C4⋊C4—2844no—
575C4⋊C4—2844no—
576C4⋊C4—2844no—
577C4⋊C4—2842no—
578C4⋊C4—2842no—
579C4⋊C4—718no—
580C4⋊C4—718no—
581C4⋊C4—718no—
582C4⋊C4—718no—
583C22⋊C4—24no—
584C22⋊C4—24no—
585C22⋊C4—44no—
586C22⋊C4—2844no—
587C22⋊C4—2844no—
588C22⋊C4—2844no—
589C22⋊C4—2844no—
590C22⋊C4—718no—
591C22⋊C4—718no—
592C22⋊C4—718no—
593C22⋊C4—718no—
594C22⋊C4—1428no—
595C22⋊C4—1424no—
596C22⋊C4—1424no—
597C22⋊C4C2×C4×D7118yes—
598C22⋊C4C2×C4×D7118yes—
599C42—2844no—
600C42—2844no—
601C42—2844no—
602C42—2844no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—28no—
610C23—44no—
611C23—44no—
612C23—84no—
613C23—84no—
614C23—2848no—
615C23—2848no—
616C23—2844no—
617C23—712no—
618C23—714no—
619C23—712no—
620C23—1428no—
621C23—1422no—
622C23—1421no—
623C23—1421no—
624C23—1422no—
625C23—1428no—
626C23—1421no—
627C23—1421no—
628C23—1422no—
629C23C22×C4×D7114yes—
630C23C22×C4×D7112yes—
631C23#1455617312yes—
632C23#1455617612yes—
633C23C24×D7111yescharacteristic
634D4—2848no—
635D4—14216no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—88no—
648C2×C4—2844no—
649C2×C4—2844no—
650C2×C4—2844no—
651C2×C4—2844no—
652C2×C4—5688no—
653C2×C4—714no—
654C2×C4—712no—
655C2×C4—712no—
656C2×C4—714no—
657C2×C4—1428no—
658C2×C4—1428no—
659C2×C4—1424no—
660C2×C4—1424no—
661C2×C4—1424no—
662C2×C4—1424no—
663C2×C4—1424no—
664C2×C4—1424no—
665C2×C4—1422no—
666C2×C4—1424no—
667C2×C4—1422no—
668C2×C4—1422no—
669C2×C4—1422no—
670C2×C4—1428no—
671C2×C4C22×C4×D7114yes—
672C2×C4C22×C4×D7112yes—
673C2×C4C22×C4×D7112yes—
674C22—24no—
675C22—22no—
676C22—24no—
677C22—22no—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—44no—
682C22—44no—
683C22—88no—
684C22—28416no—
685C22—2842no—
686C22—2842no—
687C22—714no—
688C22—1422no—
689C22—1422no—
690C22—1422no—
691C22—1424no—
692C22—1424no—
693C22—1422no—
694C22—1422no—
695C22#1798648014yes—
696C22C23×C4×D7111yescharacteristic
697C22H(5,𝔽2)×D7112yes—
698C22C2×#1455617311yescharacteristic
699C22C2×#1455617611yescharacteristic
700C22#1798683412yes—
701C4—22no—
702C4—22no—
703C4—24no—
704C4—44no—
705C4—44no—
706C4—2844no—
707C4—2844no—
708C4—1422no—
709C4—1422no—
710C4—1424no—
711C4—1424no—
712C2—24no—
713C2—44no—
714C2—2842no—
715C2—1424no—
716C2#518×D7111yescharacteristic
717C2C2×#1798648011yescharacteristic
718C2#2260153811yescharacteristic
719C2#2260252712yes—
720C2#2260255412yes—
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2315C2
socle, cosocleC23×C71C25
prime radicalC23×C22⋊D71C22
hypercenter#2315D71
hypocenterC71#34376
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2315

Complements

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

NH ≅ G/Ntype
2. #22591489C2semidirect
3. #22591335C2semidirect
4. #22591219C2semidirect
5. #22591186C2semidirect
6. #22591185C2semidirect
8. #22591125C2semidirect
9. #22591007C2semidirect
10. #22590957C2semidirect
11. #22590942C2semidirect
12. #22590938C2semidirect
13. #22590722C2semidirect
14. #380×D71C2semidirect
15. C71×#2315C2semidirect
18. C2×#14556110C4semidirect
24. C2×#14556086C22semidirect
28. C2×C4⋊C4×D71C22semidirect
33. #17985896C22semidirect
34. #17985895C22semidirect
35. #17985894C22semidirect
36. #17985893C22semidirect
37. #17985892C22semidirect
38. #17985892C22semidirect
39. #17985889C22semidirect
40. #17985888C22semidirect
41. #17985887C22semidirect
42. #17985886C22semidirect
43. #17985884C22semidirect
44. #17985884C22semidirect
45. #17985880C22semidirect
48. #17985872C22semidirect
49. #17985870C22semidirect
50. #17985861C22semidirect
54. #17985858C22semidirect
57. #17985856C22semidirect
58. #17985856C22semidirect
61. C4⋊C4×Dic71C22semidirect
65. C4×C22⋊Dic71C22semidirect
66. #17985846C22semidirect
67. #17985846C22semidirect
68. #95×D71C22semidirect
71. #385×C71C22semidirect
72. #385×C71C22semidirect
85. C22×C4×D71C2×C4semidirect
91. #14556110C2×C4semidirect
92. #14556110C2×C4semidirect
93. #14556110C2×C4semidirect
94. #14556110C2×C4semidirect
98. C2×C4⋊Dic71C2×C4semidirect
103. C2×Dic71⋊C4C2×C4semidirect
110. C2×C22⋊Dic71C2×C4semidirect
117. C2×(C2×D71)⋊C4C2×C4semidirect
145. C2×C22⋊C4×C71C2×C4semidirect
371. #2315D71semidirect
376. C71#34376semidirect
413. #385C2×D71semidirect
414. #385C2×D71semidirect
493. C2×C22⋊C4C4×D71semidirect

Maximal subgroups

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

subgroupindex
C22×#145561102
#225914892
#225913352
#225912192
#225911862
#225911852
C22⋊C4×C22⋊D712
#225911252
#225910072
#225909572
#225909422
#225909382
#225907222
#380×D712
C71×#23152
#3437671