Finite Group Databasebeta

← #32157517

Subgroups — #32157517

Order 18176.

2390 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D71C211yesmaximal, characteristic
2#22591235C211yesmaximal, characteristic, complemented
3#22591234C212yesmaximal, complemented
4#22591233C211yesmaximal, characteristic, complemented
5#22591231C211yesmaximal, characteristic, complemented
6#22591228C212yesmaximal, complemented
7#22591224C212yesmaximal, complemented
8#22591222C214yesmaximal, complemented
9#22591221C212yesmaximal, complemented
10#22590955C212yesmaximal, complemented
11#22590934C214yesmaximal
12#22590737C212yesmaximal, complemented
13#22590736C212yesmaximal, complemented
14#22590722C211yesmaximal, characteristic
15#22590721C211yesmaximal, characteristic
16#22590694C212yesmaximal, complemented
17C71×#2347C211yesmaximal, characteristic, complemented
18C23×C4×D71C2211yescharacteristic
19C2×#14556087C2211yescharacteristic
20C2×#14556086C2212yes—
21C2×#14556086C2211yescharacteristic
22C2×#14556086C2211yescharacteristic
23C2×#14556085C2212yes—
24C2×#14556085C2212yes—
25C2×#14556084C2212yes—
26#117×D71C4116yescomplemented
27C2×C4⋊C4×D71C2211yescharacteristic
28C2×C4⋊C4×D71C2211yescharacteristic
29C2×C22⋊C4×D71C2212yes—
30C2×C42×D71C2212yes—
31#17985898C2212yescomplemented
32#17985897C2212yescomplemented
33#17985896C2214yescomplemented
34#17985895C2212yescomplemented
35#17985894C2214yescomplemented
36#17985893C2214yes—
37#17985892C2214yes—
38#17985891C2214yes—
39#17985890C2214yes—
40#17985889C2214yes—
41#17985888C2214yes—
42#17985887C2214yes—
43#17985867C2212yescomplemented
44#17985866C2212yescomplemented
45#17985866C2212yescomplemented
46#17985864C2214yescomplemented
47#17985863C2214yescomplemented
48#17985861C2211yescharacteristic
49#17985861C2211yescharacteristic
50#17985861C2212yes—
51#17985859C2211yescharacteristic
52#17985858C2211yescharacteristic
53#17985858C2211yescharacteristic
54#17985858C2214yes—
55#17985857C2212yes—
56#17985856C2212yes—
57#17985856C2214yes—
58#17985854C2212yes—
59#17985854C2212yes—
60C4⋊C4×Dic71C2212yescomplemented
61C4⋊C4×Dic71C2212yescomplemented
62C4×Dic71⋊C4C2214yescomplemented
63C4×C4⋊Dic71C2212yescomplemented
64C4×C4⋊Dic71C2212yescomplemented
65#17985850C2212yescomplemented
66#17985850C2212yescomplemented
67#17985850C2214yescomplemented
68C22⋊C4×Dic71C2212yes—
69C4×(C2×D71)⋊C4C2212yes—
70C4×(C2×D71)⋊C4C2214yes—
71C4×C22⋊Dic71C2211yescharacteristic
72#17985846C2212yes—
73#17985846C2214yes—
74#17985845C2214yescomplemented
75#17985844C2214yescomplemented
76C2×#117×C71C2211yescharacteristic
77#389×C71C2212yescomplemented
78#388×C71C2214yes—
79#383×C71C2212yescomplemented
80#380×C71C2211yescharacteristic
81C4×C4⋊C4×C71C2212yescomplemented
82C4×C4⋊C4×C71C2212yescomplemented
83C4×C22⋊C4×C71C2211yescharacteristic
84C24×D71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C22×C4×D71—28no—
87C22×C4×D71C2×C418yes—
88C22×C4×D71C2311yescharacteristic
89C22×C4×D71C2311yescharacteristic
90C22×C4×D71C2311yescharacteristic
91C22×C4×D71C2312yes—
92C22×C4×D71C2312yes—
93C22×C4×D71C2311yescharacteristic
94#14556087C2×C418yes—
95#14556086—28no—
96#14556086C2×C418yes—
97#14556086C2×C418yes—
98#14556085—28no—
99#14556085C2×C4116yes—
100#14556084C2×C4116yes—
101C2×C4⋊Dic71C2312yes—
102C2×C4⋊Dic71C2314yes—
103C2×C4⋊Dic71C2311yescharacteristic
104C2×C4⋊Dic71C2311yescharacteristic
105C2×Dic71⋊C4C2312yes—
106C2×Dic71⋊C4C2312yes—
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×Dic71⋊C4C2312yes—
110C2×Dic71⋊C4C2312yes—
111C4⋊C4×D71C2×C418yes—
112C4⋊C4×D71C2×C418yes—
113C2×C22⋊Dic71C2312yes—
114C2×C22⋊Dic71C2312yes—
115C2×C22⋊Dic71C2312yes—
116C2×(C2×D71)⋊C4C2312yes—
117C2×(C2×D71)⋊C4C2314yes—
118C2×(C2×D71)⋊C4C2312yes—
119C2×(C2×D71)⋊C4C2314yes—
120C2×(C2×D71)⋊C4C2312yes—
121C2×(C2×D71)⋊C4C2312yes—
122C2×(C2×D71)⋊C4C2312yes—
123C2×(C2×D71)⋊C4C2312yes—
124C22⋊C4×D71C2×C4116yes—
125C2×C4×Dic71C2314yes—
126C2×C4×Dic71C2312yes—
127C2×C4×Dic71C2314yes—
128C2×C4×Dic71C2314yes—
129C2×C4×Dic71C2314yes—
130C2×C4×Dic71C2312yes—
131C2×C4×Dic71C2312yes—
132C2×C4×Dic71C2312yes—
133C42×D71C2×C4116yes—
134C71⋊#95C2312yes—
135C71⋊#95C2314yes—
136C71⋊#95C2314yes—
137C71⋊#95C2312yes—
138C71⋊#95C2314yes—
139C71⋊#95C2314yes—
140C71⋊#95C2312yes—
141C71⋊#95C2314yes—
142C71⋊#95C2311yescharacteristic
143C71⋊#95C2311yescharacteristic
144C71⋊#95C2314yes—
145C71⋊#95C2314yes—
146C23×C4×C71C2311yescharacteristic
147#117×C71C2×C418yes—
148C2×C4⋊C4×C71C2312yes—
149C2×C4⋊C4×C71C2314yes—
150C2×C4⋊C4×C71C2311yescharacteristic
151C2×C4⋊C4×C71C2311yescharacteristic
152C2×C22⋊C4×C71C2312yes—
153C2×C22⋊C4×C71C2312yes—
154C2×C22⋊C4×C71C2312yes—
155C2×C42×C71C2312yes—
156C2×C42×C71C2314yes—
157C2×C42×C71C2312yes—
158#95×C71C2314yes—
159#95×C71C2312yes—
160#95×C71C2314yes—
161#95×C71C2311yescharacteristic
162#95×C71C2311yescharacteristic
163C23×D71—24no—
164C23×D71—41no—
165C23×D71—42no—
166C23×D71—41no—
167C23×D71C22×C414yes—
168C23×D71C2411yescharacteristic
169C23×D71C2411yescharacteristic
170C22×Dic71—24no—
171C22×Dic71C22×C414yes—
172C22×Dic71C2412yes—
173C22×Dic71C2412yes—
174C22×Dic71C2414yes—
175C22×Dic71C2411yescharacteristic
176C22×Dic71C2412yes—
177C22×Dic71C2412yes—
178C22×Dic71C2411yescharacteristic
179C2×C4×D71—24no—
180C2×C4×D71—24no—
181C2×C4×D71—24no—
182C2×C4×D71—232no—
183C2×C4×D71—42no—
184C2×C4×D71—42no—
185C2×C4×D71—44no—
186C2×C4×D71C22×C414yes—
187C2×C4×D71C22×C414yes—
188C2×C4×D71C22×C414yes—
189C2×C4×D71C22×C418yes—
190C2×C4×D71C22×C418yes—
191C2×C4×D71C22×C414yes—
192C2×C4×D71#4118yes—
193C4⋊Dic71—24no—
194C4⋊Dic71—44no—
195C4⋊Dic71C22×C414yes—
196C4⋊Dic71C22×C414yes—
197Dic71⋊C4—24no—
198Dic71⋊C4—24no—
199Dic71⋊C4—44no—
200Dic71⋊C4—44no—
201Dic71⋊C4C22×C418yes—
202Dic71⋊C4C22×C418yes—
203C22⋊Dic71—42no—
204C22⋊Dic71—42no—
205C22⋊Dic71C22×C418yes—
206(C2×D71)⋊C4—24no—
207(C2×D71)⋊C4—24no—
208(C2×D71)⋊C4—28no—
209(C2×D71)⋊C4—42no—
210(C2×D71)⋊C4—42no—
211(C2×D71)⋊C4—44no—
212(C2×D71)⋊C4C22×C418yes—
213(C2×D71)⋊C4C22×C418yes—
214C4×Dic71—24no—
215C4×Dic71—28no—
216C4×Dic71—44no—
217C4×Dic71—44no—
218C4×Dic71—44no—
219C4×Dic71C22×C418yes—
220C4×Dic71C22×C418yes—
221C4×Dic71C22×C418yes—
222C24×C71C2411yescharacteristic
223C22×C4×C71—24no—
224C22×C4×C71C22×C414yes—
225C22×C4×C71C2412yes—
226C22×C4×C71C2414yes—
227C22×C4×C71C2412yes—
228C22×C4×C71C2411yescharacteristic
229C22×C4×C71C2412yes—
230C22×C4×C71C2412yes—
231C22×C4×C71C2411yescharacteristic
232C4⋊C4×C71—24no—
233C4⋊C4×C71—44no—
234C4⋊C4×C71C22×C414yes—
235C4⋊C4×C71C22×C414yes—
236C22⋊C4×C71—42no—
237C22⋊C4×C71—42no—
238C22⋊C4×C71C22×C418yes—
239C42×C71—24no—
240C42×C71—44no—
241C42×C71C22×C418yes—
242C23×C71—22no—
243C23×C71—21no—
244C23×C71—22no—
245C23×C71—21no—
246C23×C71C23×C412yes—
247C23×C71C2511yescharacteristic
248C22×D71—21no—
249C22×D71—22no—
250C22×D71—21no—
251C22×D71—22no—
252C22×D71—21no—
253C22×D71—22no—
254C22×D71—21no—
255C22×D71—28no—
256C22×D71—44no—
257C22×D71—44no—
258C22×D71—48no—
259C22×D71—48no—
260C22×D71C23×C412yes—
261C22×D71C23×C412yes—
262C22×D71C2×#4114yes—
263C2×C4×C71—22no—
264C2×C4×C71—22no—
265C2×C4×C71—24no—
266C2×C4×C71—22no—
267C2×C4×C71—28no—
268C2×C4×C71—22no—
269C2×C4×C71—22no—
270C2×C4×C71—24no—
271C2×C4×C71—22no—
272C2×C4×C71—24no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—24no—
276C2×C4×C71—22no—
277C2×C4×C71C23×C412yes—
278C2×C4×C71C23×C414yes—
279C2×C4×C71C23×C414yes—
280C2×C4×C71C23×C412yes—
281C2×C4×C71C2×#4114yes—
282C2×Dic71—22no—
283C2×Dic71—22no—
284C2×Dic71—22no—
285C2×Dic71—24no—
286C2×Dic71—28no—
287C2×Dic71—22no—
288C2×Dic71—22no—
289C2×Dic71—24no—
290C2×Dic71—22no—
291C2×Dic71—22no—
292C2×Dic71—24no—
293C2×Dic71—24no—
294C2×Dic71—22no—
295C2×Dic71—22no—
296C2×Dic71C23×C412yes—
297C2×Dic71C23×C414yes—
298C2×Dic71C23×C414yes—
299C2×Dic71C23×C412yes—
300C2×Dic71C2×#4114yes—
301C4×D71—28no—
302C4×D71—28no—
303C4×D71—28no—
304C4×D71—48no—
305C4×D71—48no—
306C4×D71#117116yes—
307C22×C71—22no—
308C22×C71—22no—
309C22×C71—22no—
310C22×C71—42no—
311C22×C71—42no—
312C22×C71C24×C411yescharacteristic
313C22×C71C22×#4112yes—
314C22×C71#58511yescharacteristic
315C22×C71#58512yes—
316C22×C71#58511yescharacteristic
317C2×D71—22no—
318C2×D71—22no—
319C2×D71—24no—
320C2×D71—24no—
321C2×D71—22no—
322C2×D71—22no—
323C2×D71—22no—
324C2×D71—416no—
325C2×D71—42no—
326C2×D71—42no—
327C2×D71C2×#11714yes—
328C4×C71—22no—
329C4×C71—24no—
330C4×C71—24no—
331C4×C71—42no—
332C4×C71—42no—
333C4×C71—44no—
334C4×C71C2×#11714yes—
335Dic71—22no—
336Dic71—24no—
337Dic71—24no—
338Dic71—42no—
339Dic71—44no—
340Dic71—42no—
341Dic71C2×#11714yes—
342#34179—711nomaximal, Sylow
343C2×C71—42no—
344C2×C71C22×#11711yescharacteristic
345C2×C71#342811yescharacteristic
346C2×C71#342811yescharacteristic
347C2×C71#349312yes—
348C2×C71#349312yes—
349D71—24no—
350D71—42no—
351C22×#117—711no—
352#2347—712no—
353#2347—711no—
354#2347—712no—
355#2347—711no—
356#2347—711no—
357#2347D7111yescharacteristic, complemented
358#2346—712no—
359#2346—714no—
360#2346—712no—
361#2316—712no—
362#2312—714no—
363#2283—712no—
364#2283—712no—
365#2280—711no—
366#2280—711no—
367#2274—712no—
368C71#3417911yescharacteristic, complemented, Sylow
369C24×C4—711no—
370C2×#117—711no—
371C2×#117—7116no—
372C2×#117—711no—
373C2×#117—711no—
374C2×#117—712no—
375C2×#117—712no—
376C2×#117—712no—
377C2×#117—712no—
378C2×#117C2×D7111yescharacteristic
379C22×C4⋊C4—711no—
380C22×C4⋊C4—711no—
381C22×C22⋊C4—712no—
382C22×C42—712no—
383#389—714no—
384#389—712no—
385#389—712no—
386#389—712no—
387#389—714no—
388#389C2×D7112yescomplemented
389#388—714no—
390#388—714no—
391#388—714no—
392#388—714no—
393#388—714no—
394#388—714no—
395#388—714no—
396#388C2×D7114yes—
397#383—712no—
398#383—712no—
399#383—712no—
400#383C2×D7112yescomplemented
401#382—714no—
402#382—714no—
403#381—712no—
404#381—711no—
405#381—711no—
406#380—711no—
407#380—714no—
408#380—712no—
409#380—712no—
410#380—714no—
411#380—711no—
412#380—711no—
413#380C2×D7111yescharacteristic
414#379—712no—
415#379—712no—
416C4×C4⋊C4—712no—
417C4×C4⋊C4—712no—
418C4×C4⋊C4—712no—
419C4×C4⋊C4—714no—
420C4×C4⋊C4—712no—
421C4×C4⋊C4—714no—
422C4×C4⋊C4—712no—
423C4×C4⋊C4—712no—
424C4×C4⋊C4C2×D7112yescomplemented
425C4×C4⋊C4C2×D7112yescomplemented
426C4×C22⋊C4—711no—
427C4×C22⋊C4—712no—
428C4×C22⋊C4—714no—
429C4×C22⋊C4—712no—
430C4×C22⋊C4—714no—
431C4×C22⋊C4—712no—
432C4×C22⋊C4C2×D7111yescharacteristic
433#376—714no—
434#376—714no—
435C25—711no—
436C23×C4—712no—
437C23×C4—712no—
438C23×C4—711no—
439C23×C4—711no—
440C23×C4—718no—
441C23×C4—711no—
442C23×C4—711no—
443C23×C4—711no—
444C23×C4—1428no—
445C23×C4C22×D7111yescharacteristic
446#117—718no—
447#117—718no—
448#117—718no—
449#117—7116no—
450#117—7116no—
451#117—1428no—
452#117—1428no—
453#117C4×D7118yes—
454C2×C4⋊C4—714no—
455C2×C4⋊C4—714no—
456C2×C4⋊C4—714no—
457C2×C4⋊C4—712no—
458C2×C4⋊C4—711no—
459C2×C4⋊C4—712no—
460C2×C4⋊C4—711no—
461C2×C4⋊C4—718no—
462C2×C4⋊C4—718no—
463C2×C4⋊C4—712no—
464C2×C4⋊C4—712no—
465C2×C4⋊C4—712no—
466C2×C4⋊C4C22×D7112yes—
467C2×C4⋊C4C22×D7114yes—
468C2×C4⋊C4C22×D7111yescharacteristic
469C2×C4⋊C4C22×D7111yescharacteristic
470C2×C22⋊C4—712no—
471C2×C22⋊C4—712no—
472C2×C22⋊C4—712no—
473C2×C22⋊C4—714no—
474C2×C22⋊C4—712no—
475C2×C22⋊C4—712no—
476C2×C22⋊C4—712no—
477C2×C22⋊C4—712no—
478C2×C22⋊C4—7116no—
479C2×C22⋊C4—712no—
480C2×C22⋊C4—714no—
481C2×C22⋊C4—712no—
482C2×C22⋊C4C22×D7112yes—
483C2×C22⋊C4C22×D7112yes—
484C2×C22⋊C4C22×D7112yes—
485C2×C42—714no—
486C2×C42—714no—
487C2×C42—714no—
488C2×C42—712no—
489C2×C42—712no—
490C2×C42—712no—
491C2×C42—7116no—
492C2×C42—714no—
493C2×C42—712no—
494C2×C42C22×D7112yes—
495C2×C42C22×D7114yes—
496C2×C42C22×D7112yes—
497#95—712no—
498#95—714no—
499#95—712no—
500#95—714no—
501#95—714no—
502#95—714no—
503#95—711no—
504#95—711no—
505#95—712no—
506#95—714no—
507#95—714no—
508#95—714no—
509#95C22×D7114yes—
510#95C22×D7112yes—
511#95C22×D7114yes—
512#95C22×D7111yescharacteristic
513#95C22×D7111yescharacteristic
514C24—2841no—
515C24—2842no—
516C24—2841no—
517C24—714no—
518C24—711no—
519C24—711no—
520C24—1424no—
521C24C23×D7111yescharacteristic
522C22×C4—24no—
523C22×C4—2842no—
524C22×C4—2844no—
525C22×C4—2842no—
526C22×C4—718no—
527C22×C4—718no—
528C22×C4—711no—
529C22×C4—714no—
530C22×C4—718no—
531C22×C4—714no—
532C22×C4—711no—
533C22×C4—712no—
534C22×C4—712no—
535C22×C4—714no—
536C22×C4—714no—
537C22×C4—714no—
538C22×C4—712no—
539C22×C4—714no—
540C22×C4—712no—
541C22×C4—1424no—
542C22×C4—14232no—
543C22×C4—1424no—
544C22×C4—1424no—
545C22×C4—1424no—
546C22×C4C2×C4×D7114yes—
547C22×C4C23×D7112yes—
548C22×C4C23×D7114yes—
549C22×C4C23×D7112yes—
550C22×C4C23×D7111yescharacteristic
551C22×C4C23×D7112yes—
552C22×C4C23×D7112yes—
553C22×C4C23×D7111yescharacteristic
554C4⋊C4—24no—
555C4⋊C4—44no—
556C4⋊C4—2844no—
557C4⋊C4—2844no—
558C4⋊C4—2844no—
559C4⋊C4—718no—
560C4⋊C4—718no—
561C4⋊C4—714no—
562C4⋊C4—714no—
563C4⋊C4—1424no—
564C4⋊C4—1424no—
565C4⋊C4—1424no—
566C4⋊C4C2×C4×D7114yes—
567C4⋊C4C2×C4×D7114yes—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—2842no—
571C22⋊C4—2844no—
572C22⋊C4—2842no—
573C22⋊C4—2842no—
574C22⋊C4—2842no—
575C22⋊C4—718no—
576C22⋊C4—718no—
577C22⋊C4—718no—
578C22⋊C4—1424no—
579C22⋊C4—1424no—
580C22⋊C4—1428no—
581C22⋊C4C2×C4×D7118yes—
582C42—24no—
583C42—44no—
584C42—2844no—
585C42—2844no—
586C42—2844no—
587C42—718no—
588C42—718no—
589C42—718no—
590C42—1428no—
591C42—1424no—
592C42C2×C4×D7118yes—
593C23—22no—
594C23—21no—
595C23—22no—
596C23—21no—
597C23—2844no—
598C23—2844no—
599C23—2848no—
600C23—2848no—
601C23—712no—
602C23—714no—
603C23—712no—
604C23—1428no—
605C23—1422no—
606C23—1421no—
607C23—1422no—
608C23—1421no—
609C23—1421no—
610C23—1422no—
611C23—1421no—
612C23C22×C4×D7112yes—
613C23C24×D7111yescharacteristic
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—24no—
617C2×C4—22no—
618C2×C4—28no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—2848no—
629C2×C4—2848no—
630C2×C4—712no—
631C2×C4—714no—
632C2×C4—7116no—
633C2×C4—712no—
634C2×C4—714no—
635C2×C4—714no—
636C2×C4—1428no—
637C2×C4—1428no—
638C2×C4—1424no—
639C2×C4—1422no—
640C2×C4—1422no—
641C2×C4—1422no—
642C2×C4—1424no—
643C2×C4—1422no—
644C2×C4—1422no—
645C2×C4—1422no—
646C2×C4—1424no—
647C2×C4—1428no—
648C2×C4—1422no—
649C2×C4—1422no—
650C2×C4—1424no—
651C2×C4—1422no—
652C2×C4—1428no—
653C2×C4C22×C4×D7112yes—
654C2×C4C22×C4×D7114yes—
655C2×C4C22×C4×D7114yes—
656C2×C4C22×C4×D7112yes—
657C2×C4#41×D7114yes—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—42no—
662C22—42no—
663C22—28416no—
664C22—2842no—
665C22—2842no—
666C22—714no—
667C22—1422no—
668C22—1422no—
669C22—1422no—
670C22—1422no—
671C22—1422no—
672C22—1424no—
673C22—1424no—
674C22C23×C4×D7111yescharacteristic
675C22C2×#41×D7112yes—
676C22#1798683411yescharacteristic
677C22#1798683512yes—
678C22#1798683611yescharacteristic
679C4—22no—
680C4—24no—
681C4—24no—
682C4—42no—
683C4—42no—
684C4—44no—
685C4—2844no—
686C4—2842no—
687C4—2842no—
688C4—714no—
689C4—1422no—
690C4—1424no—
691C4—1424no—
692C4#117×D7114yes—
693C2—42no—
694C2—2842no—
695C2—1424no—
696C2C2×#117×D7111yescharacteristic
697C2#2260153911yescharacteristic
698C2#2260154011yescharacteristic
699C2#2260205412yes—
700C2#2260205612yes—
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2347C2
socle, cosocleC23×C71C25
prime radicalC24×D71C23
hypercenter#2347D71
hypocenterC71#34179
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2347

Complements

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

NH ≅ G/Ntype
2. #22591235C2semidirect
3. #22591234C2semidirect
4. #22591233C2semidirect
5. #22591231C2semidirect
6. #22591228C2semidirect
7. #22591224C2semidirect
8. #22591222C2semidirect
9. #22591221C2semidirect
10. #22590955C2semidirect
12. #22590737C2semidirect
13. #22590736C2semidirect
16. #22590694C2semidirect
17. C71×#2347C2semidirect
26. #117×D71C4semidirect
31. #17985898C22semidirect
32. #17985897C22semidirect
33. #17985896C22semidirect
34. #17985895C22semidirect
35. #17985894C22semidirect
43. #17985867C22semidirect
44. #17985866C22semidirect
45. #17985866C22semidirect
46. #17985864C22semidirect
47. #17985863C22semidirect
60. C4⋊C4×Dic71C22semidirect
61. C4⋊C4×Dic71C22semidirect
62. C4×Dic71⋊C4C22semidirect
63. C4×C4⋊Dic71C22semidirect
64. C4×C4⋊Dic71C22semidirect
65. #17985850C22semidirect
66. #17985850C22semidirect
67. #17985850C22semidirect
74. #17985845C22semidirect
75. #17985844C22semidirect
77. #389×C71C22semidirect
79. #383×C71C22semidirect
81. C4×C4⋊C4×C71C22semidirect
82. C4×C4⋊C4×C71C22semidirect
357. #2347D71semidirect
368. C71#34179semidirect
388. #389C2×D71semidirect
400. #383C2×D71semidirect
424. C4×C4⋊C4C2×D71semidirect
425. C4×C4⋊C4C2×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D712
#225912352
#225912342
#225912332
#225912312
#225912282
#225912242
#225912222
#225912212
#225909552
#225909342
#225907372
#225907362
#225907222
#225907212
#225906942
C71×#23472
#3417971