Finite Group Databasebeta

← #32158248

Subgroups — #32158248

Order 18176.

2742 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556113C211yesmaximal, characteristic
2#22591472C214yesmaximal, complemented
3#22591325C214yesmaximal, complemented
4#22591212C212yesmaximal, complemented
5#22591182C212yesmaximal, complemented
6#22591182C212yesmaximal, complemented
7#22591160C212yesmaximal
8#22591136C214yesmaximal, complemented
9#22590935C211yesmaximal, characteristic, complemented
10#22590861C214yesmaximal, complemented
11#22590721C211yesmaximal, characteristic, complemented
12#22590697C211yesmaximal, characteristic, complemented
13#22590692C211yesmaximal, characteristic, complemented
14C4×C22⋊C4×D71C211yesmaximal, characteristic, complemented
15C71×#2313C211yesmaximal, characteristic, complemented
16C23×D284C2211yescharacteristic
17C23×C4×D71C2211yescharacteristic
18C2×#14556113C4116yescomplemented
19C2×#14556113C2212yes—
20C2×#14556113C2212yes—
21C2×#14556113C2212yes—
22C2×#14556113C2212yes—
23C2×#14556090C2214yes—
24C2×#14556087C2212yes—
25C2×#14556085C2212yescomplemented
26C22×Dic71⋊C4C2211yescharacteristic
27C22×(C2×D71)⋊C4C2211yescharacteristic
28C22×(C2×D71)⋊C4C2211yescharacteristic
29C22×(C2×D71)⋊C4C2211yescharacteristic
30C2×C22⋊C4×D71C2212yes—
31C2×C22⋊C4×D71C2212yes—
32C2×C42×D71C2212yescomplemented
33#17985900C2214yes—
34#17985894C2214yescomplemented
35#17985891C2214yescomplemented
36#17985891C2214yescomplemented
37#17985890C2214yescomplemented
38#17985888C2214yescomplemented
39#17985888C2214yescomplemented
40#17985888C2214yescomplemented
41#17985881C2214yescomplemented
42#17985880C2214yescomplemented
43#17985877C2214yes—
44#17985877C2214yes—
45#17985873C2214yescomplemented
46#17985873C2214yescomplemented
47#17985861C2212yescomplemented
48#17985858C2212yescomplemented
49#17985857C2212yes—
50#17985857C2212yes—
51#17985854C2212yes—
52#17985854C2212yes—
53C4⋊C4×Dic71C2214yescomplemented
54C4⋊C4×Dic71C2214yescomplemented
55#17985850C2214yescomplemented
56C22⋊C4×Dic71C2212yes—
57C22⋊C4×Dic71C2212yes—
58C4×(C2×D71)⋊C4C2212yescomplemented
59C4×(C2×D71)⋊C4C2214yescomplemented
60C4×(C2×D71)⋊C4C2212yescomplemented
61C4×C22⋊Dic71C2211yescharacteristic
62C4×C22⋊Dic71C2212yes—
63C4×C22⋊Dic71C2211yescharacteristic
64#17985846C2214yescomplemented
65#17985846C2214yescomplemented
66#17985846C2214yescomplemented
67#17985846C2212yescomplemented
68#95×D71C2212yescomplemented
69C22×C4⋊C4×C71C2211yescharacteristic
70#387×C71C2214yescomplemented
71#387×C71C2214yescomplemented
72#381×C71C2212yes—
73#380×C71C2212yes—
74C4×C22⋊C4×C71C2211yescharacteristic
75C4×C22⋊C4×C71C2211yescharacteristic
76C24×D71C2311yescharacteristic
77C24×D71C2311yescharacteristic
78C22×D284—44no—
79C22×D284C2×C418yes—
80C22×D284C2312yes—
81C22×D284C2312yes—
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C22×C4×D71—44no—
85C22×C4×D71C2×C418yescomplemented
86C22×C4×D71C2314yes—
87C22×C4×D71C2311yescharacteristic
88C22×C4×D71C2311yescharacteristic
89C22×C4×D71C2314yes—
90C22×C4×D71C2311yescharacteristic
91C22×C4×D71C2311yescharacteristic
92#14556113C2×C4116yescomplemented
93#14556113C2×C4116yescomplemented
94#14556113C2×C4116yescomplemented
95#14556113C2×C4116yescomplemented
96#14556090—48no—
97#14556087—28no—
98#14556085—44no—
99C2×C4⋊Dic71C2314yes—
100C2×Dic71⋊C4C2×C418yescomplemented
101C2×Dic71⋊C4C2314yes—
102C2×Dic71⋊C4C2314yes—
103C2×Dic71⋊C4C2312yes—
104C2×Dic71⋊C4C2312yes—
105C2×C22⋊Dic71C2312yes—
106C2×C22⋊Dic71C2312yes—
107C2×(C2×D71)⋊C4C2×C418yescomplemented
108C2×(C2×D71)⋊C4C2×C418yescomplemented
109C2×(C2×D71)⋊C4C2×C418yescomplemented
110C2×(C2×D71)⋊C4C2314yes—
111C2×(C2×D71)⋊C4C2314yes—
112C2×(C2×D71)⋊C4C2314yes—
113C2×(C2×D71)⋊C4C2314yes—
114C2×(C2×D71)⋊C4C2314yes—
115C2×(C2×D71)⋊C4C2314yes—
116C2×(C2×D71)⋊C4C2312yes—
117C2×(C2×D71)⋊C4C2312yes—
118C2×(C2×D71)⋊C4C2312yes—
119C2×(C2×D71)⋊C4C2312yes—
120C2×(C2×D71)⋊C4C2312yes—
121C2×(C2×D71)⋊C4C2312yes—
122C22⋊C4×D71—28no—
123C22⋊C4×D71—28no—
124C2×C4×Dic71C2314yes—
125C2×C4×Dic71C2312yes—
126C2×C4×Dic71C2314yes—
127C2×C4×Dic71C2314yes—
128C2×C4×Dic71C2312yes—
129C2×C4×Dic71C2314yes—
130C42×D71—44no—
131C71⋊#95C2312yes—
132C71⋊#95C2314yes—
133C71⋊#95C2314yes—
134C71⋊#95C2314yes—
135C71⋊#95C2314yes—
136C71⋊#95C2312yes—
137C71⋊#95C2314yes—
138C23×C4×C71C2311yescharacteristic
139C23×C4×C71C2311yescharacteristic
140C23×C4×C71C2311yescharacteristic
141C2×C4⋊C4×C71C2×C418yescomplemented
142C2×C4⋊C4×C71C2314yes—
143C2×C4⋊C4×C71C2312yes—
144C2×C4⋊C4×C71C2312yes—
145C2×C22⋊C4×C71C2312yes—
146C2×C22⋊C4×C71C2312yes—
147C2×C42×C71C2312yes—
148C2×C42×C71C2312yes—
149#95×C71C2312yes—
150#95×C71C2312yes—
151#95×C71C2314yes—
152#95×C71C2314yes—
153#95×C71C2314yes—
154C23×D71—24no—
155C23×D71—24no—
156C23×D71—24no—
157C23×D71—42no—
158C23×D71—42no—
159C23×D71—42no—
160C23×D71C22×C414yes—
161C23×D71C22×C414yes—
162C23×D71C2411yescharacteristic
163C23×D71C2412yes—
164C23×D71C2411yescharacteristic
165C2×D284—28no—
166C2×D284—416no—
167C2×D284—44no—
168C2×D284C22×C418yes—
169C2×D284C22×C418yes—
170C22×Dic71—42no—
171C22×Dic71—42no—
172C22×Dic71C22×C414yes—
173C22×Dic71C22×C414yes—
174C22×Dic71C2414yes—
175C22×Dic71C2411yescharacteristic
176C22×Dic71C2411yescharacteristic
177C22×Dic71C2412yes—
178C22×Dic71C2414yes—
179C2×C4×D71—24no—
180C2×C4×D71—24no—
181C2×C4×D71—28no—
182C2×C4×D71—28no—
183C2×C4×D71—28no—
184C2×C4×D71—416no—
185C2×C4×D71—42no—
186C2×C4×D71—42no—
187C2×C4×D71—44no—
188C2×C4×D71—44no—
189C2×C4×D71—44no—
190C2×C4×D71C22×C414yes—
191C2×C4×D71C22×C414yes—
192C2×C4×D71C22×C414yes—
193C2×C4×D71C22×C414yes—
194C4⋊Dic71—28no—
195Dic71⋊C4—44no—
196Dic71⋊C4—44no—
197Dic71⋊C4C22×C418yes—
198Dic71⋊C4C22×C418yes—
199C22⋊Dic71—24no—
200C22⋊Dic71#4118yes—
201(C2×D71)⋊C4—28no—
202(C2×D71)⋊C4—28no—
203(C2×D71)⋊C4—28no—
204(C2×D71)⋊C4—44no—
205(C2×D71)⋊C4—44no—
206(C2×D71)⋊C4—44no—
207(C2×D71)⋊C4C22×C418yes—
208(C2×D71)⋊C4C22×C418yes—
209(C2×D71)⋊C4C22×C418yes—
210(C2×D71)⋊C4C22×C418yes—
211(C2×D71)⋊C4C22×C418yes—
212(C2×D71)⋊C4C22×C418yes—
213C4×Dic71—28no—
214C4×Dic71—42no—
215C4×Dic71—44no—
216C4×Dic71—44no—
217C4×Dic71—42no—
218C4×Dic71—44no—
219C24×C71C2411yescharacteristic
220C22×C4×C71—24no—
221C22×C4×C71—42no—
222C22×C4×C71—42no—
223C22×C4×C71C22×C414yes—
224C22×C4×C71C22×C414yes—
225C22×C4×C71C22×C414yes—
226C22×C4×C71C2414yes—
227C22×C4×C71C2414yes—
228C22×C4×C71C2411yescharacteristic
229C22×C4×C71C2411yescharacteristic
230C22×C4×C71C2412yes—
231C22×C4×C71C2412yes—
232C4⋊C4×C71—44no—
233C4⋊C4×C71C22×C418yes—
234C4⋊C4×C71C22×C418yes—
235C22⋊C4×C71—24no—
236C22⋊C4×C71—24no—
237C42×C71—42no—
238C42×C71—42no—
239C23×C71—22no—
240C23×C71—22no—
241C23×C71C23×C412yes—
242C23×C71C2×#4114yes—
243C23×C71C2511yescharacteristic
244C22×D71—22no—
245C22×D71—22no—
246C22×D71—28no—
247C22×D71—22no—
248C22×D71—22no—
249C22×D71—22no—
250C22×D71—24no—
251C22×D71—22no—
252C22×D71—22no—
253C22×D71—24no—
254C22×D71—28no—
255C22×D71—28no—
256C22×D71—44no—
257C22×D71—44no—
258C22×D71—44no—
259C22×D71—416no—
260C22×D71—88no—
261C22×D71C23×C414yes—
262C22×D71C23×C412yes—
263C22×D71C23×C412yes—
264C22×D71H(5,𝔽2)14yes—
265C2×C4×C71—28no—
266C2×C4×C71—22no—
267C2×C4×C71—22no—
268C2×C4×C71—22no—
269C2×C4×C71—22no—
270C2×C4×C71—24no—
271C2×C4×C71—24no—
272C2×C4×C71—24no—
273C2×C4×C71—24no—
274C2×C4×C71—24no—
275C2×C4×C71—24no—
276C2×C4×C71—24no—
277C2×C4×C71—44no—
278C2×C4×C71—44no—
279C2×C4×C71C23×C414yes—
280C2×C4×C71C23×C412yes—
281C2×C4×C71C23×C412yes—
282C2×C4×C71C23×C414yes—
283C2×Dic71—24no—
284C2×Dic71—22no—
285C2×Dic71—22no—
286C2×Dic71—24no—
287C2×Dic71—24no—
288C2×Dic71—24no—
289C2×Dic71—24no—
290C2×Dic71—24no—
291C2×Dic71—44no—
292C2×Dic71—44no—
293C2×Dic71C23×C414yes—
294C2×Dic71C23×C412yes—
295C2×Dic71C23×C412yes—
296C2×Dic71C2×#4118yes—
297D284—216no—
298D284—48no—
299C4×D71—28no—
300C4×D71—28no—
301C4×D71—44no—
302C4×D71—44no—
303C4×D71—416no—
304C4×D71—88no—
305C22×C71—22no—
306C22×C71—22no—
307C22×C71—28no—
308C22×C71C4×#4114yes—
309C22×C71C24×C411yescharacteristic
310C22×C71C22×#4112yes—
311C22×C71C2×H(5,𝔽2)12yes—
312C22×C71#58512yes—
313C2×D71—22no—
314C2×D71—22no—
315C2×D71—28no—
316C2×D71—22no—
317C2×D71—24no—
318C2×D71—22no—
319C2×D71—24no—
320C2×D71—22no—
321C2×D71—24no—
322C2×D71—416no—
323C2×D71—44no—
324C2×D71—44no—
325C2×D71—44no—
326C2×D71—88no—
327C2×D71#51814yes—
328C4×C71—24no—
329C4×C71—22no—
330C4×C71—22no—
331C4×C71—24no—
332C4×C71—44no—
333C4×C71—44no—
334Dic71—22no—
335Dic71—22no—
336Dic71—24no—
337Dic71—28no—
338Dic71—44no—
339#34238—711nomaximal, Sylow
340C2×C71—24no—
341C2×C71C2×C4×#4111yescharacteristic
342C2×C71C2×#51811yescharacteristic
343C2×C71#342811yescharacteristic
344C2×C71#351314yes—
345D71—24no—
346D71—42no—
347D71—44no—
348C22×#123—711no—
349#2374—714no—
350#2359—714no—
351#2345—712no—
352#2342—712no—
353#2342—712no—
354D4×C22⋊C4—712no—
355#2335—714no—
356#2313D7111yescharacteristic, complemented
357#2312—711no—
358C4×#123—714no—
359#2280—711no—
360#2274—711no—
361#2273—711no—
362C2×C4×C22⋊C4—711no—
363C71#3423811yescharacteristic, complemented, Sylow
364C23×D4—711no—
365C24×C4—711no—
366C2×#123—7116no—
367C2×#123—712no—
368C2×#123—712no—
369C2×#123—712no—
370C2×#123—712no—
371C2×C4×D4—714no—
372C2×#117—712no—
373C2×#117—712no—
374C22×C4⋊C4—711no—
375C22×C4⋊C4C2×D7111yescharacteristic
376C22×C22⋊C4—711no—
377C22×C22⋊C4—711no—
378C22×C22⋊C4—711no—
379C22×C22⋊C4—712no—
380C22×C22⋊C4—712no—
381C22×C42—712no—
382#390—714no—
383#389—714no—
384#388—714no—
385#388—714no—
386#388—714no—
387#388—714no—
388#388—714no—
389#388—714no—
390#387—714no—
391#387—714no—
392#387C2×D7114yescomplemented
393#387C2×D7114yescomplemented
394#386—714no—
395#386—714no—
396#385—714no—
397#385—714no—
398#381—712no—
399#381C2×D7112yes—
400#380—712no—
401#380—712no—
402#380—712no—
403#380C2×D7112yes—
404#379—712no—
405#379—712no—
406C4×C4⋊C4—714no—
407C4×C4⋊C4—714no—
408C4×C4⋊C4—714no—
409C4×C22⋊C4—711no—
410C4×C22⋊C4—712no—
411C4×C22⋊C4—711no—
412C4×C22⋊C4—712no—
413C4×C22⋊C4—712no—
414C4×C22⋊C4—712no—
415C4×C22⋊C4—714no—
416C4×C22⋊C4—712no—
417C4×C22⋊C4—714no—
418C4×C22⋊C4—714no—
419C4×C22⋊C4—714no—
420C4×C22⋊C4—712no—
421C4×C22⋊C4C2×D7111yescharacteristic
422C4×C22⋊C4C2×D7111yescharacteristic
423C2×#95—712no—
424C25—711no—
425C25—711no—
426C22×D4—2844no—
427C22×D4—718no—
428C22×D4—712no—
429C22×D4—712no—
430C23×C4—2844no—
431C23×C4—711no—
432C23×C4—711no—
433C23×C4—718no—
434C23×C4—711no—
435C23×C4—711no—
436C23×C4—714no—
437C23×C4—714no—
438C23×C4—711no—
439C23×C4—711no—
440C23×C4C22×D7111yescharacteristic
441C23×C4C22×D7111yescharacteristic
442C23×C4C22×D7111yescharacteristic
443#123—7116no—
444#123—7116no—
445#123—7116no—
446#123—7116no—
447C4×D4—2848no—
448#117—2844no—
449#117—1428no—
450C2×C4⋊C4—714no—
451C2×C4⋊C4—714no—
452C2×C4⋊C4—718no—
453C2×C4⋊C4—712no—
454C2×C4⋊C4—712no—
455C2×C4⋊C4—714no—
456C2×C4⋊C4C4×D7118yescomplemented
457C2×C4⋊C4C22×D7114yes—
458C2×C4⋊C4C22×D7112yes—
459C2×C4⋊C4C22×D7112yes—
460C2×C22⋊C4—714no—
461C2×C22⋊C4—714no—
462C2×C22⋊C4—714no—
463C2×C22⋊C4—712no—
464C2×C22⋊C4—718no—
465C2×C22⋊C4—718no—
466C2×C22⋊C4—718no—
467C2×C22⋊C4—712no—
468C2×C22⋊C4—712no—
469C2×C22⋊C4—712no—
470C2×C22⋊C4—712no—
471C2×C22⋊C4—712no—
472C2×C22⋊C4—712no—
473C2×C22⋊C4—712no—
474C2×C22⋊C4—714no—
475C2×C22⋊C4—714no—
476C2×C22⋊C4—714no—
477C2×C22⋊C4—1428no—
478C2×C22⋊C4—1428no—
479C2×C22⋊C4C22×D7112yes—
480C2×C22⋊C4C22×D7112yes—
481C2×C42—2844no—
482C2×C42—712no—
483C2×C42—714no—
484C2×C42—712no—
485C2×C42—714no—
486C2×C42—714no—
487C2×C42—714no—
488C2×C42C22×D7112yes—
489C2×C42C22×D7112yes—
490#95—712no—
491#95—714no—
492#95—714no—
493#95—714no—
494#95—712no—
495#95—714no—
496#95—714no—
497#95C22×D7112yes—
498#95C22×D7112yes—
499#95C22×D7114yes—
500#95C22×D7114yes—
501#95C22×D7114yes—
502C24—2842no—
503C24—2842no—
504C24—2842no—
505C24—714no—
506C24—714no—
507C24—711no—
508C24—712no—
509C24—711no—
510C24—1424no—
511C24—1424no—
512C24—1424no—
513C24C23×D7111yescharacteristic
514C2×D4—2844no—
515C2×D4—28416no—
516C2×D4—718no—
517C2×D4—718no—
518C2×D4—1428no—
519C22×C4—24no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—2842no—
523C22×C4—2842no—
524C22×C4—2844no—
525C22×C4—2844no—
526C22×C4—2844no—
527C22×C4—28416no—
528C22×C4—2842no—
529C22×C4—2842no—
530C22×C4—714no—
531C22×C4—714no—
532C22×C4—714no—
533C22×C4—714no—
534C22×C4—714no—
535C22×C4—711no—
536C22×C4—712no—
537C22×C4—711no—
538C22×C4—714no—
539C22×C4—714no—
540C22×C4—714no—
541C22×C4—1428no—
542C22×C4—1428no—
543C22×C4—1428no—
544C22×C4—1424no—
545C22×C4—1424no—
546C22×C4C2×C4×D7114yes—
547C22×C4C2×C4×D7114yes—
548C22×C4C2×C4×D7114yes—
549C22×C4C23×D7114yes—
550C22×C4C23×D7114yes—
551C22×C4C23×D7111yescharacteristic
552C22×C4C23×D7111yescharacteristic
553C22×C4C23×D7112yes—
554C22×C4C23×D7112yes—
555C4⋊C4—44no—
556C4⋊C4—2844no—
557C4⋊C4—2844no—
558C4⋊C4—718no—
559C4⋊C4—718no—
560C4⋊C4—1428no—
561C4⋊C4C2×C4×D7118yes—
562C4⋊C4C2×C4×D7118yes—
563C22⋊C4—24no—
564C22⋊C4—24no—
565C22⋊C4—2844no—
566C22⋊C4—2844no—
567C22⋊C4—2844no—
568C22⋊C4—718no—
569C22⋊C4—718no—
570C22⋊C4—718no—
571C22⋊C4—718no—
572C22⋊C4—718no—
573C22⋊C4—718no—
574C22⋊C4—718no—
575C22⋊C4—1428no—
576C22⋊C4—1428no—
577C22⋊C4—1428no—
578C22⋊C4—1424no—
579C42—42no—
580C42—42no—
581C42—2842no—
582C42—2844no—
583C42—2844no—
584C42—2842no—
585C42—2844no—
586C42—1428no—
587C23—22no—
588C23—22no—
589C23—28416no—
590C23—2844no—
591C23—2844no—
592C23—2844no—
593C23—5688no—
594C23—712no—
595C23—714no—
596C23—714no—
597C23—712no—
598C23—1428no—
599C23—1422no—
600C23—1422no—
601C23—1422no—
602C23—1424no—
603C23—1422no—
604C23—1422no—
605C23—1424no—
606C23—1428no—
607C23—1428no—
608C23—1422no—
609C23—1422no—
610C23C22×C4×D7112yes—
611C23#41×D7114yes—
612C23C24×D7111yescharacteristic
613D4—2848no—
614D4—14216no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—28no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—44no—
628C2×C4—44no—
629C2×C4—2844no—
630C2×C4—2844no—
631C2×C4—28416no—
632C2×C4—2844no—
633C2×C4—2844no—
634C2×C4—5688no—
635C2×C4—714no—
636C2×C4—712no—
637C2×C4—712no—
638C2×C4—718no—
639C2×C4—1428no—
640C2×C4—1428no—
641C2×C4—1424no—
642C2×C4—1424no—
643C2×C4—1424no—
644C2×C4—1424no—
645C2×C4—1422no—
646C2×C4—1422no—
647C2×C4—1424no—
648C2×C4—1424no—
649C2×C4C22×C4×D7114yes—
650C2×C4C22×C4×D7112yes—
651C2×C4C22×C4×D7112yes—
652C2×C4C22×C4×D7114yes—
653C22—28no—
654C22—22no—
655C22—22no—
656C22—28416no—
657C22—2844no—
658C22—2844no—
659C22—2844no—
660C22—5688no—
661C22—714no—
662C22—1422no—
663C22—1424no—
664C22—1422no—
665C22—1424no—
666C22—1422no—
667C22—1424no—
668C22—1428no—
669C22—1422no—
670C22—1422no—
671C22#1798646714yes—
672C22C23×C4×D7111yescharacteristic
673C22C2×#41×D7112yes—
674C22H(5,𝔽2)×D7112yes—
675C22#1798683612yes—
676C4—24no—
677C4—22no—
678C4—22no—
679C4—24no—
680C4—44no—
681C4—44no—
682C4—2844no—
683C4—1428no—
684C4—1422no—
685C4—1422no—
686C4—1424no—
687C2—24no—
688C2—2842no—
689C2—2844no—
690C2—1424no—
691C2C2×#1798646711yescharacteristic
692C2#518×D7111yescharacteristic
693C2#2260154211yescharacteristic
694C2#2260227014yes—
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2313C2
socle, cosocleC23×C71C25
prime radicalC23×D284C22
hypercenter#2313D71
hypocenterC71#34238
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2313

Complements

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

NH ≅ G/Ntype
2. #22591472C2semidirect
3. #22591325C2semidirect
4. #22591212C2semidirect
5. #22591182C2semidirect
6. #22591182C2semidirect
8. #22591136C2semidirect
9. #22590935C2semidirect
10. #22590861C2semidirect
11. #22590721C2semidirect
12. #22590697C2semidirect
13. #22590692C2semidirect
14. C4×C22⋊C4×D71C2semidirect
15. C71×#2313C2semidirect
18. C2×#14556113C4semidirect
25. C2×#14556085C22semidirect
32. C2×C42×D71C22semidirect
34. #17985894C22semidirect
35. #17985891C22semidirect
36. #17985891C22semidirect
37. #17985890C22semidirect
38. #17985888C22semidirect
39. #17985888C22semidirect
40. #17985888C22semidirect
41. #17985881C22semidirect
42. #17985880C22semidirect
45. #17985873C22semidirect
46. #17985873C22semidirect
47. #17985861C22semidirect
48. #17985858C22semidirect
53. C4⋊C4×Dic71C22semidirect
54. C4⋊C4×Dic71C22semidirect
55. #17985850C22semidirect
58. C4×(C2×D71)⋊C4C22semidirect
59. C4×(C2×D71)⋊C4C22semidirect
60. C4×(C2×D71)⋊C4C22semidirect
64. #17985846C22semidirect
65. #17985846C22semidirect
66. #17985846C22semidirect
67. #17985846C22semidirect
68. #95×D71C22semidirect
70. #387×C71C22semidirect
71. #387×C71C22semidirect
85. C22×C4×D71C2×C4semidirect
92. #14556113C2×C4semidirect
93. #14556113C2×C4semidirect
94. #14556113C2×C4semidirect
95. #14556113C2×C4semidirect
100. C2×Dic71⋊C4C2×C4semidirect
107. C2×(C2×D71)⋊C4C2×C4semidirect
108. C2×(C2×D71)⋊C4C2×C4semidirect
109. C2×(C2×D71)⋊C4C2×C4semidirect
141. C2×C4⋊C4×C71C2×C4semidirect
356. #2313D71semidirect
363. C71#34238semidirect
392. #387C2×D71semidirect
393. #387C2×D71semidirect
456. 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×#145561132
#225914722
#225913252
#225912122
#225911822
#225911602
#225911362
#225909352
#225908612
#225907212
#225906972
#225906922
C4×C22⋊C4×D712
C71×#23132
#3423871