Finite Group Databasebeta

← #31965241

Subgroups — #31965241

Order 18176.

1014 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22597381C211yesmaximal, characteristic, complemented
2#22591280C211yesmaximal, characteristic, complemented
3#22586917C212yesmaximal, complemented
4#22586883C212yesmaximal, complemented
5#22586873C211yesmaximal, characteristic, complemented
6#22586869C211yesmaximal, characteristic, complemented
7#22586860C211yesmaximal, characteristic, complemented
8#22586856C211yesmaximal, characteristic, complemented
9#22586844C212yesmaximal, complemented
10#22586826C212yesmaximal, complemented
11C71×#3505C211yesmaximal, characteristic
12#17986077—22no—
13#17986077—22no—
14#17986052C2212yescomplemented
15#17985963C2211yescharacteristic
16#17985963C2211yescharacteristic
17#17985963C2212yescomplemented
18#17985892—21no—
19#17985885—21no—
20#17985879—21no—
21#17985867C2211yescharacteristic, complemented
22#17985862C2211yescharacteristic
23#17985859C2211yescharacteristic, complemented
24C22⋊C4×Dic71—21no—
25C4×C22⋊Dic71C2211yescharacteristic
26#17985845C2211yescharacteristic, complemented
27C2×C71⋊#95C2211yescharacteristic, complemented
28#17985736C2212yescomplemented
29#17985736C2212yescomplemented
30#17985736C2212yescomplemented
31#17985736C2212yescomplemented
32#17985733C2212yes—
33#17985733C2212yes—
34#17985733C2212yes—
35#17985733C2212yes—
36#553×C71—22no—
37#553×C71C412yescomplemented
38#552×C71C412yescomplemented
39#551×C71—22no—
40#548×C71C412yescomplemented
41#546×C71C412yescomplemented
42#539×C71—21no—
43#538×C71—21no—
44#534×C71—21no—
45#529×C71C2212yes—
46#525×C71C2212yes—
47C2×C22⋊Q8×C71C2211yescharacteristic
48C2×#121×C71C2211yescharacteristic
49#518×C71—21no—
50C2×C4×D4×C71C2211yescharacteristic
51C23×Dic71—21no—
52C2×#11765849—21no—
53C2×#11765849—21no—
54C2×#11765849—22no—
55C2×C4⋊Dic71—21no—
56C2×C22⋊Dic71—21no—
57C2×C22⋊Dic71—21no—
58C2×C22⋊Dic71—21no—
59C2×C4×Dic71—21no—
60C2×C4×Dic71—21no—
61C4⋊(C71⋊C8)—22no—
62C22⋊(C71⋊C8)—21no—
63C22⋊(C71⋊C8)—21no—
64C22⋊(C71⋊C8)—22no—
65C22⋊(C71⋊C8)C2312yes—
66C22⋊(C71⋊C8)C2312yes—
67C4×C71⋊C8—22no—
68C71⋊#95—21no—
69C71⋊#95—21no—
70C71⋊#95—21no—
71C71⋊#95—21no—
72C71⋊#95—21no—
73C71⋊#95C2311yescharacteristic
74C71⋊#95C2311yescharacteristic
75C71⋊#95C2311yescharacteristic
76C71⋊#95C2311yescharacteristic
77C2×#41×C71C2×C412yes—
78C22×Q8×C71C2×C411yescharacteristic, complemented
79C22×D4×C71—21no—
80C22×D4×C71C2×C411yescharacteristic, complemented
81C22×D4×C71D411yescharacteristic
82C23×C4×C71C2311yescharacteristic
83C23×C4×C71C2311yescharacteristic
84#126×C71—22no—
85#126×C71—22no—
86#126×C71—22no—
87#125×C71—22no—
88#125×C71C2×C412yescomplemented
89#124×C71—22no—
90#124×C71C2×C412yescomplemented
91#123×C71—22no—
92#123×C71—22no—
93#123×C71—22no—
94#123×C71—22no—
95#123×C71—22no—
96C22⋊Q8×C71—21no—
97C22⋊Q8×C71—21no—
98C22⋊Q8×C71—22no—
99C22⋊Q8×C71C2×C412yes—
100C22⋊Q8×C71C2×C412yescomplemented
101C22⋊Q8×C71C2312yes—
102#121×C71—22no—
103#121×C71—22no—
104#121×C71—21no—
105#121×C71—21no—
106#121×C71—22no—
107#121×C71C2×C412yes—
108#121×C71C2×C412yescomplemented
109#121×C71C2312yes—
110#120×C71—22no—
111#120×C71—22no—
112C4×Q8×C71C2×C412yescomplemented
113C4×D4×C71—22no—
114C4×D4×C71—22no—
115C4×D4×C71—22no—
116C4×D4×C71—22no—
117C4×D4×C71—22no—
118C4×D4×C71C2×C412yes—
119C4×D4×C71C2×C412yes—
120C4×D4×C71C2×C412yescomplemented
121C4×D4×C71D412yes—
122C4×D4×C71D412yes—
123#117×C71—22no—
124#117×C71—22no—
125#117×C71C2×C412yes—
126C2×C4⋊C4×C71—21no—
127C2×C4⋊C4×C71C2×C411yescharacteristic, complemented
128C2×C4⋊C4×C71C2×C411yescharacteristic, complemented
129C2×C4⋊C4×C71D411yescharacteristic
130C2×C22⋊C4×C71—21no—
131C2×C22⋊C4×C71—21no—
132C2×C22⋊C4×C71—22no—
133C2×C22⋊C4×C71D411yescharacteristic
134C2×C22⋊C4×C71D411yescharacteristic
135C2×C42×C71C2311yescharacteristic
136C22×Dic71—21no—
137C22×Dic71—21no—
138C22×Dic71—21no—
139C22×Dic71—21no—
140C22×Dic71—42no—
141C22×Dic71—42no—
142C22×Dic71—81no—
143#11765849—81no—
144#11765849—81no—
145#11765849—82no—
146C2×C71⋊C8—22no—
147C2×C71⋊C8—22no—
148C4⋊Dic71—81no—
149C22⋊Dic71—42no—
150C22⋊Dic71—42no—
151C22⋊Dic71—81no—
152C4×Dic71—42no—
153C4×Dic71—81no—
154C24×C71—21no—
155C24×C71C2×D411yescharacteristic
156C24×C71C2×D411yescharacteristic
157#41×C71—82no—
158C2×Q8×C71—21no—
159C2×Q8×C71—81no—
160C2×Q8×C71C22×C412yes—
161C2×D4×C71—22no—
162C2×D4×C71—22no—
163C2×D4×C71—22no—
164C2×D4×C71—22no—
165C2×D4×C71—21no—
166C2×D4×C71—41no—
167C2×D4×C71—41no—
168C2×D4×C71—42no—
169C2×D4×C71—42no—
170C2×D4×C71—81no—
171C2×D4×C71C22⋊C412yes—
172C2×D4×C71C22⋊C412yes—
173C2×D4×C71C22×C412yes—
174C22×C4×C71—21no—
175C22×C4×C71—21no—
176C22×C4×C71—21no—
177C22×C4×C71—22no—
178C22×C4×C71—22no—
179C22×C4×C71—81no—
180C22×C4×C71—81no—
181C22×C4×C71C22×C411yescharacteristic
182C22×C4×C71C22×C411yescharacteristic
183C22×C4×C71C22×C412yes—
184C22×C4×C71C2×D411yescharacteristic
185C22×C4×C71C2×D411yescharacteristic
186C22×C4×C71C2×D411yescharacteristic
187C22×C4×C71C2×D411yescharacteristic
188C22×C4×C71C2×D411yescharacteristic
189C22×C4×C71C2×D411yescharacteristic
190C22×C4×C71C2×D412yes—
191C22×C4×C71C2411yescharacteristic
192C4⋊C4×C71—22no—
193C4⋊C4×C71—21no—
194C4⋊C4×C71—21no—
195C4⋊C4×C71—22no—
196C4⋊C4×C71—22no—
197C4⋊C4×C71—22no—
198C4⋊C4×C71—22no—
199C4⋊C4×C71—22no—
200C4⋊C4×C71C22⋊C412yes—
201C4⋊C4×C71C22⋊C412yes—
202C4⋊C4×C71C22×C412yes—
203C4⋊C4×C71C22×C412yes—
204C22⋊C4×C71—22no—
205C22⋊C4×C71—22no—
206C22⋊C4×C71—22no—
207C22⋊C4×C71—22no—
208C22⋊C4×C71—22no—
209C22⋊C4×C71—22no—
210C22⋊C4×C71—22no—
211C22⋊C4×C71—22no—
212C22⋊C4×C71—22no—
213C22⋊C4×C71—22no—
214C22⋊C4×C71C22⋊C412yes—
215C22⋊C4×C71C22⋊C412yes—
216C22⋊C4×C71C22⋊C412yes—
217C22⋊C4×C71C22⋊C412yes—
218C42×C71—22no—
219C42×C71—22no—
220C42×C71C22×C412yes—
221C42×C71C2×D412yes—
222C23×C71—21no—
223C23×C71—21no—
224C23×C71—21no—
225C23×C71—21no—
226C23×C71—22no—
227C23×C71—41no—
228C23×C71—41no—
229C23×C71—41no—
230C23×C71—41no—
231C23×C71—42no—
232C23×C71—81no—
233C23×C71—81no—
234C23×C71C2×C22⋊C411yescharacteristic
235C23×C71C2×C22⋊C412yes—
236C23×C71C2×C22⋊C411yescharacteristic
237C23×C71C22×D411yescharacteristic
238Q8×C71—42no—
239Q8×C71—81no—
240D4×C71—42no—
241D4×C71—42no—
242D4×C71—42no—
243D4×C71—44no—
244D4×C71—42no—
245D4×C71—42no—
246D4×C71—81no—
247D4×C71—82no—
248D4×C71—82no—
249C2×C4×C71—21no—
250C2×C4×C71—21no—
251C2×C4×C71—22no—
252C2×C4×C71—22no—
253C2×C4×C71—22no—
254C2×C4×C71—41no—
255C2×C4×C71—41no—
256C2×C4×C71—41no—
257C2×C4×C71—42no—
258C2×C4×C71—41no—
259C2×C4×C71—41no—
260C2×C4×C71—42no—
261C2×C4×C71—41no—
262C2×C4×C71—41no—
263C2×C4×C71—41no—
264C2×C4×C71—42no—
265C2×C4×C71—82no—
266C2×C4×C71—82no—
267C2×C4×C71—81no—
268C2×C4×C71—81no—
269C2×C4×C71C2×C22⋊C412yes—
270C2×C4×C71C2×C22⋊C412yes—
271C2×C4×C71C2×C22⋊C412yes—
272C2×C4×C71C2×C22⋊C411yescharacteristic
273C2×C4×C71C2×C22⋊C411yescharacteristic
274C2×C4×C71C23×C411yescharacteristic
275C2×C4×C71C22×D411yescharacteristic
276C2×Dic71—22no—
277C2×Dic71—41no—
278C2×Dic71—41no—
279C2×Dic71—41no—
280C2×Dic71—41no—
281C2×Dic71—41no—
282C2×Dic71—41no—
283C2×Dic71—41no—
284C2×Dic71—41no—
285C2×Dic71—41no—
286C2×Dic71—41no—
287C2×Dic71—41no—
288C2×Dic71—84no—
289C71⋊C8—42no—
290C71⋊C8—42no—
291C22×C71—21no—
292C22×C71—21no—
293C22×C71—21no—
294C22×C71—22no—
295C22×C71—21no—
296C22×C71—21no—
297C22×C71—21no—
298C22×C71—22no—
299C22×C71—21no—
300C22×C71—22no—
301C22×C71—21no—
302C22×C71—42no—
303C22×C71—42no—
304C22×C71—42no—
305C22×C71—42no—
306C22×C71—42no—
307C22×C71—81no—
308C22×C71—81no—
309C22×C71—162no—
310C22×C71C22×C22⋊C411yescharacteristic
311C22×C71#57511yescharacteristic
312C22×C71#57511yescharacteristic
313C4×C71—21no—
314C4×C71—21no—
315C4×C71—22no—
316C4×C71—21no—
317C4×C71—21no—
318C4×C71—22no—
319C4×C71—22no—
320C4×C71—42no—
321C4×C71—42no—
322C4×C71—42no—
323Dic71—42no—
324Dic71—81no—
325Dic71—81no—
326Dic71—81no—
327#17623—711nomaximal, Sylow
328C2×C71—21no—
329C2×C71—21no—
330C2×C71—42no—
331C2×C71—41no—
332C2×C71—41no—
333C2×C71—82no—
334C2×C71#288311yescharacteristic
335C2×C71#289611yescharacteristic
336C2×C71#290111yescharacteristic
337#3505D7111yescharacteristic
338#2975—711no—
339#2353—711no—
340#1521—712no—
341#1513—712no—
342#1511—711no—
343#1510—711no—
344#1508—711no—
345#1507—711no—
346#1504—712no—
347#1500—712no—
348C71#1762311yescharacteristic, complemented, Sylow
349#553—22no—
350#553Dic7112yescomplemented
351#552Dic7112yescomplemented
352#551—22no—
353#548Dic7112yescomplemented
354#546Dic7112yescomplemented
355#539—21no—
356#538—21no—
357#534—21no—
358#529C2×D7112yes—
359#525C2×D7112yes—
360C2×C22⋊Q8C2×D7111yescharacteristic
361C2×#121C2×D7111yescharacteristic
362#518—21no—
363C2×C4×D4C2×D7111yescharacteristic
364#436—1422no—
365#436—1422no—
366#431—712no—
367#407—711no—
368#407—711no—
369#407—712no—
370#388—1421no—
371#387—1421no—
372#386—1421no—
373#383—711no—
374#381—711no—
375#380—711no—
376C4×C22⋊C4—711no—
377C4×C22⋊C4—1421no—
378#376—711no—
379C2×#95—711no—
380#328—712no—
381#328—712no—
382#328—712no—
383#328—712no—
384#327—712no—
385#327—712no—
386#327—712no—
387#327—712no—
388C2×#41C2×Dic7112yes—
389C22×Q8C2×Dic7111yescharacteristic, complemented
390C22×D4—21no—
391C22×D4C2×Dic7111yescharacteristic, complemented
392C22×D4C22⋊D7111yescharacteristic
393C23×C4—1421no—
394C23×C4C22×D7111yescharacteristic
395C23×C4C22×D7111yescharacteristic
396C2×M16—1421no—
397C2×M16—1421no—
398C2×M16—1422no—
399#126—22no—
400#126—22no—
401#126—22no—
402#125—22no—
403#125C2×Dic7112yescomplemented
404#124—22no—
405#124C2×Dic7112yescomplemented
406#123—22no—
407#123—22no—
408#123—22no—
409#123—22no—
410#123—22no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—22no—
414C22⋊Q8C2×Dic7112yes—
415C22⋊Q8C2×Dic7112yescomplemented
416C22⋊Q8C22×D7112yes—
417#121—22no—
418#121—22no—
419#121—21no—
420#121—21no—
421#121—22no—
422#121C2×Dic7112yes—
423#121C2×Dic7112yescomplemented
424#121C22×D7112yes—
425#120—22no—
426#120—22no—
427C4×Q8C2×Dic7112yescomplemented
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4C2×Dic7112yes—
434C4×D4C2×Dic7112yes—
435C4×D4C2×Dic7112yescomplemented
436C4×D4C22⋊D7112yes—
437C4×D4C22⋊D7112yes—
438#117—22no—
439#117—22no—
440#117C2×Dic7112yes—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—1421no—
443C2×C4⋊C4C2×Dic7111yescharacteristic, complemented
444C2×C4⋊C4C2×Dic7111yescharacteristic, complemented
445C2×C4⋊C4C22⋊D7111yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—1421no—
450C2×C22⋊C4—1421no—
451C2×C22⋊C4—1421no—
452C2×C22⋊C4C22⋊D7111yescharacteristic
453C2×C22⋊C4C22⋊D7111yescharacteristic
454C2×C42—1421no—
455C2×C42—1421no—
456C2×C42C22×D7111yescharacteristic
457C4⋊C8—1422no—
458C22⋊C8—712no—
459C22⋊C8—712no—
460C22⋊C8—1421no—
461C22⋊C8—1421no—
462C22⋊C8—1422no—
463C4×C8—1422no—
464#95—711no—
465#95—711no—
466#95—711no—
467#95—711no—
468#95—1421no—
469#95—1421no—
470#95—1421no—
471#95—1421no—
472#95—1421no—
473C24—21no—
474C24C2×C22⋊D7111yescharacteristic
475C24C2×C22⋊D7111yescharacteristic
476#41—82no—
477C2×Q8—21no—
478C2×Q8—81no—
479C2×Q8C22×Dic7112yes—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—21no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—81no—
490C2×D4C22⋊Dic7112yes—
491C2×D4C22⋊Dic7112yes—
492C2×D4C22×Dic7112yes—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—81no—
499C22×C4—81no—
500C22×C4—2842no—
501C22×C4—2842no—
502C22×C4—5681no—
503C22×C4—1421no—
504C22×C4—1421no—
505C22×C4—1421no—
506C22×C4—1421no—
507C22×C4C22×Dic7111yescharacteristic
508C22×C4C22×Dic7111yescharacteristic
509C22×C4C22×Dic7112yes—
510C22×C4C2×C22⋊D7111yescharacteristic
511C22×C4C2×C22⋊D7111yescharacteristic
512C22×C4C2×C22⋊D7111yescharacteristic
513C22×C4C2×C22⋊D7112yes—
514C22×C4C2×C22⋊D7111yescharacteristic
515C22×C4C2×C22⋊D7111yescharacteristic
516C22×C4C2×C22⋊D7111yescharacteristic
517C22×C4C23×D7111yescharacteristic
518M16—5682no—
519M16—5681no—
520M16—5681no—
521C2×C8—1422no—
522C2×C8—1422no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—5681no—
532C4⋊C4C22⋊Dic7112yes—
533C4⋊C4C22⋊Dic7112yes—
534C4⋊C4C22×Dic7112yes—
535C4⋊C4C22×Dic7112yes—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—2842no—
547C22⋊C4—2842no—
548C22⋊C4—5681no—
549C22⋊C4C22⋊Dic7112yes—
550C22⋊C4C22⋊Dic7112yes—
551C22⋊C4C22⋊Dic7112yes—
552C22⋊C4C22⋊Dic7112yes—
553C42—22no—
554C42—22no—
555C42—2842no—
556C42—5681no—
557C42C22×Dic7112yes—
558C42C2×C22⋊D7112yes—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—22no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—42no—
569C23—81no—
570C23—81no—
571C23C2×C22⋊Dic7111yescharacteristic
572C23C2×C22⋊Dic7112yes—
573C23C2×C22⋊Dic7111yescharacteristic
574C23C22×C22⋊D7111yescharacteristic
575Q8—42no—
576Q8—81no—
577D4—42no—
578D4—42no—
579D4—42no—
580D4—44no—
581D4—42no—
582D4—42no—
583D4—81no—
584D4—82no—
585D4—82no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—82no—
603C2×C4—82no—
604C2×C4—81no—
605C2×C4—81no—
606C2×C4—2841no—
607C2×C4—2841no—
608C2×C4—2841no—
609C2×C4—2841no—
610C2×C4—2841no—
611C2×C4—2841no—
612C2×C4—2841no—
613C2×C4—2841no—
614C2×C4—2841no—
615C2×C4—2841no—
616C2×C4—2841no—
617C2×C4—5684no—
618C2×C4—1422no—
619C2×C4C2×C22⋊Dic7112yes—
620C2×C4C2×C22⋊Dic7112yes—
621C2×C4C2×C22⋊Dic7112yes—
622C2×C4C2×C22⋊Dic7111yescharacteristic
623C2×C4C2×C22⋊Dic7111yescharacteristic
624C2×C4C23×Dic7111yescharacteristic
625C2×C4C22×C22⋊D7111yescharacteristic
626C8—2842no—
627C8—2842no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—22no—
632C22—21no—
633C22—21no—
634C22—22no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—22no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—81no—
645C22—81no—
646C22—162no—
647C22C22×C22⋊Dic7111yescharacteristic
648C22#1798679711yescharacteristic
649C22#1798679711yescharacteristic
650C4—22no—
651C4—21no—
652C4—21no—
653C4—22no—
654C4—21no—
655C4—21no—
656C4—22no—
657C4—42no—
658C4—42no—
659C4—42no—
660C4—2842no—
661C4—5681no—
662C4—5681no—
663C4—5681no—
664C2—21no—
665C2—21no—
666C2—42no—
667C2—41no—
668C2—41no—
669C2—82no—
670C2#2259680111yescharacteristic
671C2#2259685911yescharacteristic
672C2#2259688711yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
Fitting, prime radicalC71×#3505C2
socleC22×C71C22×C22⋊C4
cosocleC22×C4×C71C24
hypercenter#3505D71
hypocenterC71#17623
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3505

Complements

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

NH ≅ G/Ntype
1. #22597381C2semidirect
2. #22591280C2semidirect
3. #22586917C2semidirect
4. #22586883C2semidirect
5. #22586873C2semidirect
6. #22586869C2semidirect
7. #22586860C2semidirect
8. #22586856C2semidirect
9. #22586844C2semidirect
10. #22586826C2semidirect
14. #17986052C22semidirect
17. #17985963C22semidirect
21. #17985867C22semidirect
23. #17985859C22semidirect
26. #17985845C22semidirect
27. C2×C71⋊#95C22semidirect
28. #17985736C22semidirect
29. #17985736C22semidirect
30. #17985736C22semidirect
31. #17985736C22semidirect
37. #553×C71C4semidirect
38. #552×C71C4semidirect
40. #548×C71C4semidirect
41. #546×C71C4semidirect
78. C22×Q8×C71C2×C4semidirect
80. C22×D4×C71C2×C4semidirect
88. #125×C71C2×C4semidirect
90. #124×C71C2×C4semidirect
100. C22⋊Q8×C71C2×C4semidirect
108. #121×C71C2×C4semidirect
112. C4×Q8×C71C2×C4semidirect
120. C4×D4×C71C2×C4semidirect
127. C2×C4⋊C4×C71C2×C4semidirect
128. C2×C4⋊C4×C71C2×C4semidirect
348. C71#17623semidirect
350. #553Dic71semidirect
351. #552Dic71semidirect
353. #548Dic71semidirect
354. #546Dic71semidirect
389. C22×Q8C2×Dic71semidirect
391. C22×D4C2×Dic71semidirect
403. #125C2×Dic71semidirect
405. #124C2×Dic71semidirect
415. C22⋊Q8C2×Dic71semidirect
423. #121C2×Dic71semidirect
427. C4×Q8C2×Dic71semidirect
435. C4×D4C2×Dic71semidirect
443. C2×C4⋊C4C2×Dic71semidirect
444. C2×C4⋊C4C2×Dic71semidirect

Maximal subgroups

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

subgroupindex
#225973812
#225912802
#225869172
#225868832
#225868732
#225868692
#225868602
#225868562
#225868442
#225868262
C71×#35052
#1762371