Finite Group Databasebeta

← #2851×D71 #32203317

Subgroups — #2851×D71 #32203317

Order 18176.

3182 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D71C211yesmaximal, characteristic, complemented
2C22×C42×D71C211yesmaximal, characteristic
3#22596651C211yesmaximal, characteristic, complemented
4#22596650C211yesmaximal, characteristic, complemented
5#22596649C212yesmaximal, complemented
6#22596648C212yesmaximal, complemented
7#22596647C214yesmaximal, complemented
8#22596646C214yesmaximal, complemented
9#22596645C211yesmaximal, characteristic, complemented
10#389×D71C212yesmaximal, complemented
11#387×D71C214yesmaximal, complemented
12#385×D71C214yesmaximal
13#382×D71C211yesmaximal, characteristic, complemented
14#380×D71C212yesmaximal
15C71×#2851C211yesmaximal, characteristic, complemented
16C23×C4×D71C2212yes—
17C23×C4×D71C2211yescharacteristic
18C2×#14556120C2211yescharacteristic, complemented
19C2×#14556119C2212yescomplemented
20C2×#14556118C2214yescomplemented
21#125×D71—28no—
22C2×C4⋊C4×D71C2212yes—
23C2×C4⋊C4×D71C2214yes—
24C2×C4⋊C4×D71C2214yes—
25C2×C4⋊C4×D71C2212yes—
26C2×C22⋊C4×D71C2214yes—
27C22×C4×Dic71C2212yes—
28C22×C4×Dic71C2211yescharacteristic
29C2×C42×D71—28no—
30C2×C42×D71C2211yescharacteristic
31C2×C42×D71C2212yes—
32C2×C42×D71C2212yes—
33C2×C42×D71C2211yescharacteristic
34C2×C42×D71C2211yescharacteristic
35C2×C42×D71C2211yescharacteristic
36#17985898C2212yescomplemented
37#17985897C2212yescomplemented
38#17985896C2214yescomplemented
39#17985895C2212yescomplemented
40#17985894C2214yescomplemented
41#17985886C2214yescomplemented
42#17985885C2214yescomplemented
43#17985884C2214yescomplemented
44#17985883C2214yescomplemented
45#17985882C2214yescomplemented
46#17985881C2214yescomplemented
47#17985880C2214yescomplemented
48#17985874C2214yes—
49#17985873C2214yes—
50#17985873C2214yes—
51#17985872C2214yes—
52#17985871C2214yes—
53#17985870C2214yes—
54#17985870C2214yes—
55#17985865C2211yescharacteristic, complemented
56#17985864C2212yescomplemented
57#17985863C2214yescomplemented
58#17985859C2212yes—
59#17985858C2214yes—
60#17985857C2214yes—
61#17985856C2212yes—
62#17985856C2212yes—
63#95×D71C2214yes—
64#95×D71C2214yes—
65#95×D71C2214yes—
66C2×#125×C71C2211yescharacteristic, complemented
67C22×C42×C71C2211yescharacteristic
68#389×C71C2212yescomplemented
69#387×C71C2214yescomplemented
70#385×C71C2214yes—
71#382×C71C2211yescharacteristic, complemented
72#380×C71C2212yes—
73C24×D71C2311yescharacteristic
74C23×Dic71C2312yes—
75C23×Dic71C2311yescharacteristic
76C22×C4×D71—28no—
77C22×C4×D71—28no—
78C22×C4×D71—24no—
79C22×C4×D71—28no—
80C22×C4×D71—24no—
81C22×C4×D71Q818yes—
82C22×C4×D71C2312yes—
83C22×C4×D71C2312yes—
84C22×C4×D71C2314yes—
85C22×C4×D71C2314yes—
86C22×C4×D71C2312yes—
87C22×C4×D71C2311yescharacteristic
88C22×C4×D71C2311yescharacteristic
89C22×C4×D71C2311yescharacteristic
90C22×C4×D71C2312yes—
91C22×C4×D71C2311yescharacteristic
92#14556120—24no—
93#14556119—28no—
94#14556118—216no—
95C2×C4⋊Dic71C2312yes—
96C2×C4⋊Dic71C2312yes—
97C2×C4⋊Dic71C2314yes—
98C2×C4⋊Dic71C2314yes—
99C2×Dic71⋊C4C2314yes—
100C2×Dic71⋊C4C2314yes—
101C2×Dic71⋊C4C2314yes—
102C2×Dic71⋊C4C2314yes—
103C2×Dic71⋊C4C2314yes—
104C2×Dic71⋊C4C2314yes—
105C4⋊C4×D71—216no—
106C4⋊C4×D71—28no—
107C4⋊C4×D71—216no—
108C4⋊C4×D71—28no—
109C2×C22⋊Dic71C2314yes—
110C2×(C2×D71)⋊C4C2314yes—
111C2×(C2×D71)⋊C4C2314yes—
112C22⋊C4×D71—216no—
113C2×C4×Dic71—28no—
114C2×C4×Dic71—24no—
115C2×C4×Dic71C2312yes—
116C2×C4×Dic71C2312yes—
117C2×C4×Dic71C2312yes—
118C2×C4×Dic71C2312yes—
119C2×C4×Dic71C2311yescharacteristic
120C2×C4×Dic71C2312yes—
121C2×C4×Dic71C2311yescharacteristic
122C42×D71—28no—
123C42×D71—24no—
124C42×D71—28no—
125C42×D71—24no—
126C42×D71—24no—
127C42×D71D418yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C71⋊#95C2314yes—
131C71⋊#95C2314yes—
132C71⋊#95C2314yes—
133C71⋊#95C2314yes—
134C71⋊#95C2314yes—
135C71⋊#95C2314yes—
136C71⋊#95C2314yes—
137C23×C4×C71C2312yes—
138C23×C4×C71C2311yescharacteristic
139#125×C71—24no—
140C2×C4⋊C4×C71C2312yes—
141C2×C4⋊C4×C71C2312yes—
142C2×C4⋊C4×C71C2314yes—
143C2×C4⋊C4×C71C2314yes—
144C2×C22⋊C4×C71C2314yes—
145C2×C42×C71—24no—
146C2×C42×C71C2312yes—
147C2×C42×C71C2311yescharacteristic
148C2×C42×C71C2311yescharacteristic
149#95×C71C2314yes—
150#95×C71C2314yes—
151#95×C71C2314yes—
152C23×D71—22no—
153C23×D71—22no—
154C23×D71—24no—
155C23×D71C2×Q814yes—
156C23×D71#4118yes—
157C23×D71C2411yescharacteristic
158C23×D71C2411yescharacteristic
159C22×Dic71—24no—
160C22×Dic71—24no—
161C22×Dic71—22no—
162C22×Dic71—24no—
163C22×Dic71—22no—
164C22×Dic71C2×Q814yes—
165C22×Dic71C2414yes—
166C22×Dic71C2414yes—
167C22×Dic71C2412yes—
168C22×Dic71C2411yescharacteristic
169C22×Dic71C2412yes—
170C22×Dic71C2411yescharacteristic
171C2×C4×D71—264no—
172C2×C4×D71—22no—
173C2×C4×D71—24no—
174C2×C4×D71—24no—
175C2×C4×D71—24no—
176C2×C4×D71—22no—
177C2×C4×D71—24no—
178C2×C4×D71—24no—
179C2×C4×D71—24no—
180C2×C4×D71—24no—
181C2×C4×D71—22no—
182C2×C4×D71—24no—
183C2×C4×D71—22no—
184C2×C4×D71—24no—
185C2×C4×D71—22no—
186C2×C4×D71—24no—
187C2×C4×D71—22no—
188C2×C4×D71—232no—
189C2×C4×D71—28no—
190C2×C4×D71—28no—
191C2×C4×D71—28no—
192C2×C4×D71—28no—
193C2×C4×D71—28no—
194C2×C4×D71—28no—
195C2×C4×D71C2×D418yes—
196C2×C4×D71C2×D414yes—
197C2×C4×D71C2×Q814yes—
198C2×C4×D71C2×Q814yes—
199C2×C4×D71C2×Q814yes—
200C2×C4×D71C2×Q814yes—
201C2×C4×D71#4118yes—
202C2×C4×D71#4114yes—
203C4⋊Dic71—24no—
204C4⋊Dic71—24no—
205C4⋊Dic71—28no—
206C4⋊Dic71—28no—
207Dic71⋊C4—28no—
208Dic71⋊C4—28no—
209Dic71⋊C4—28no—
210Dic71⋊C4—28no—
211Dic71⋊C4—28no—
212Dic71⋊C4—28no—
213C22⋊Dic71—28no—
214(C2×D71)⋊C4—28no—
215(C2×D71)⋊C4—28no—
216C4×Dic71—24no—
217C4×Dic71—22no—
218C4×Dic71—24no—
219C4×Dic71—24no—
220C4×Dic71—24no—
221C4×Dic71C2×D418yes—
222C4×Dic71C2×D414yes—
223C24×C71C2411yescharacteristic
224C22×C4×C71—24no—
225C22×C4×C71—24no—
226C22×C4×C71—22no—
227C22×C4×C71—24no—
228C22×C4×C71—22no—
229C22×C4×C71C2×Q814yes—
230C22×C4×C71C2414yes—
231C22×C4×C71C2414yes—
232C22×C4×C71C2412yes—
233C22×C4×C71C2411yescharacteristic
234C22×C4×C71C2412yes—
235C22×C4×C71C2411yescharacteristic
236C4⋊C4×C71—28no—
237C4⋊C4×C71—24no—
238C4⋊C4×C71—24no—
239C4⋊C4×C71—28no—
240C22⋊C4×C71—28no—
241C42×C71—24no—
242C42×C71—22no—
243C42×C71C2×D414yes—
244C23×C71—21no—
245C23×C71—21no—
246C23×C71—22no—
247C23×C71C22×Q812yes—
248C23×C71C2×#4114yes—
249C23×C71C2511yescharacteristic
250C22×D71—21no—
251C22×D71—21no—
252C22×D71—22no—
253C22×D71—28no—
254C22×D71—216no—
255C22×D71—216no—
256C22×D71—28no—
257C22×D71#125116yescomplemented
258C22×D71C22×D412yes—
259C22×D71C22×Q812yes—
260C22×D71C22×Q812yes—
261C22×D71C2×#4114yes—
262C22×D71C2×#4112yes—
263C22×D71C2×#4114yes—
264C22×D71C2×#4114yes—
265C2×C4×C71—216no—
266C2×C4×C71—21no—
267C2×C4×C71—22no—
268C2×C4×C71—21no—
269C2×C4×C71—22no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—28no—
273C2×C4×C71—24no—
274C2×C4×C71—24no—
275C2×C4×C71—24no—
276C2×C4×C71—24no—
277C2×C4×C71—24no—
278C2×C4×C71—24no—
279C2×C4×C71C22×D414yes—
280C2×C4×C71C22×D412yes—
281C2×C4×C71C22×Q812yes—
282C2×C4×C71C22×Q812yes—
283C2×C4×C71C2×#4114yes—
284C2×C4×C71C2×#4112yes—
285C2×Dic71—216no—
286C2×Dic71—21no—
287C2×Dic71—22no—
288C2×Dic71—21no—
289C2×Dic71—22no—
290C2×Dic71—22no—
291C2×Dic71—22no—
292C2×Dic71—28no—
293C2×Dic71—24no—
294C2×Dic71—24no—
295C2×Dic71—24no—
296C2×Dic71—24no—
297C2×Dic71—24no—
298C2×Dic71—24no—
299C2×Dic71C22×D414yes—
300C2×Dic71C22×D412yes—
301C2×Dic71C22×Q812yes—
302C2×Dic71C22×Q812yes—
303C2×Dic71C2×#4114yes—
304C2×Dic71C2×#4112yes—
305C4×D71—216no—
306C4×D71—216no—
307C4×D71—28no—
308C4×D71—216no—
309C4×D71—216no—
310C4×D71—28no—
311C4×D71—28no—
312C4×D71—416no—
313C4×D71—416no—
314C4×D71C22⋊Q8116yes—
315C22×C71—22no—
316C22×C71—24no—
317C22×C71—24no—
318C22×C71—22no—
319C22×C71C2×#12514yescomplemented
320C22×C71C23×D411yescharacteristic
321C22×C71C23×Q811yescharacteristic
322C22×C71C22×#4111yescharacteristic
323C22×C71C22×#4112yes—
324C22×C71C22×#4112yes—
325C2×D71—22no—
326C2×D71—24no—
327C2×D71—24no—
328C2×D71—22no—
329C2×D71—232no—
330C2×D71C2×C22⋊Q814yes—
331C2×D71#52518yes—
332C2×D71C2×#12514yes—
333C2×D71C2×#12514yescomplemented
334C2×D71#52918yes—
335C2×D71#53314yes—
336C4×C71—22no—
337C4×C71—24no—
338C4×C71—24no—
339C4×C71—44no—
340C4×C71—44no—
341C4×C71C2×C22⋊Q814yes—
342Dic71—22no—
343Dic71—24no—
344Dic71—24no—
345Dic71—44no—
346Dic71—44no—
347Dic71C2×C22⋊Q814yes—
348C2×#2851—711nomaximal, Sylow
349C2×C71—24no—
350C2×C71C22×C22⋊Q811yescharacteristic
351C2×C71C2×#52512yes—
352C2×C71C22×#12511yescharacteristic
353C2×C71C2×#52912yes—
354C2×C71C2×#53311yescharacteristic
355D71—24no—
356D71#285118yesdirect product factor
357C22×#125—711no—
358C23×C42—711no—
359#2851—711no—
360#2851—712no—
361#2851—714no—
362#2851—714no—
363#2851—711no—
364#2851—712no—
365#2851—711no—
366#2851D7111yescharacteristic, direct product factor
367C2×#389—712no—
368C2×#387—714no—
369C2×#385—714no—
370C2×#382—711no—
371C2×#380—712no—
372C71C2×#285111yescharacteristic, complemented, Sylow
373C24×C4—711no—
374C24×C4—712no—
375C2×#125—714no—
376C2×#125—712no—
377C2×#125—711no—
378C2×#125—1428no—
379C2×#125C2×D7111yescharacteristic, complemented
380C22×C4⋊C4—712no—
381C22×C4⋊C4—714no—
382C22×C4⋊C4—712no—
383C22×C4⋊C4—714no—
384C22×C22⋊C4—714no—
385C22×C42—711no—
386C22×C42—712no—
387C22×C42—711no—
388C22×C42—711no—
389C22×C42—712no—
390C22×C42—711no—
391C22×C42—712no—
392C22×C42—711no—
393C22×C42—1428no—
394C22×C42C2×D7111yescharacteristic
395#389—714no—
396#389—712no—
397#389—712no—
398#389—712no—
399#389—714no—
400#389C2×D7112yescomplemented
401#387—714no—
402#387—714no—
403#387—714no—
404#387—714no—
405#387—714no—
406#387—714no—
407#387—714no—
408#387C2×D7114yescomplemented
409#385—714no—
410#385—714no—
411#385—714no—
412#385—714no—
413#385—714no—
414#385—714no—
415#385—714no—
416#385C2×D7114yes—
417#382—712no—
418#382—711no—
419#382—714no—
420#382C2×D7111yescharacteristic, complemented
421#380—712no—
422#380—712no—
423#380—712no—
424#380—714no—
425#380—714no—
426#380C2×D7112yes—
427C2×#95—714no—
428C2×#95—714no—
429C2×#95—714no—
430C25—711no—
431C23×C4—711no—
432C23×C4—711no—
433C23×C4—718no—
434C23×C4—712no—
435C23×C4—712no—
436C23×C4—711no—
437C23×C4—711no—
438C23×C4—711no—
439C23×C4—712no—
440C23×C4—714no—
441C23×C4—714no—
442C23×C4—712no—
443C23×C4—712no—
444C23×C4—1424no—
445C23×C4—1428no—
446C23×C4—1424no—
447C23×C4—1428no—
448C23×C4—1428no—
449C23×C4C22×D7112yes—
450C23×C4C22×D7111yescharacteristic
451#125—24no—
452#125—14216no—
453#125—1428no—
454#125—1424no—
455C2×C4⋊C4—714no—
456C2×C4⋊C4—712no—
457C2×C4⋊C4—714no—
458C2×C4⋊C4—714no—
459C2×C4⋊C4—714no—
460C2×C4⋊C4—714no—
461C2×C4⋊C4—712no—
462C2×C4⋊C4—714no—
463C2×C4⋊C4—714no—
464C2×C4⋊C4—714no—
465C2×C4⋊C4—1428no—
466C2×C4⋊C4—14216no—
467C2×C4⋊C4—1428no—
468C2×C4⋊C4—14216no—
469C2×C4⋊C4C22×D7112yes—
470C2×C4⋊C4C22×D7114yes—
471C2×C4⋊C4C22×D7112yes—
472C2×C4⋊C4C22×D7114yes—
473C2×C22⋊C4—714no—
474C2×C22⋊C4—714no—
475C2×C22⋊C4—714no—
476C2×C22⋊C4—14216no—
477C2×C22⋊C4C22×D7114yes—
478C2×C42—24no—
479C2×C42—712no—
480C2×C42—711no—
481C2×C42—718no—
482C2×C42—712no—
483C2×C42—712no—
484C2×C42—712no—
485C2×C42—712no—
486C2×C42—711no—
487C2×C42—1428no—
488C2×C42—1424no—
489C2×C42—1424no—
490C2×C42—1428no—
491C2×C42—1428no—
492C2×C42—1424no—
493C2×C42—1424no—
494C2×C42C22×D7112yes—
495C2×C42C22×D7111yescharacteristic
496C2×C42C22×D7111yescharacteristic
497#95—714no—
498#95—714no—
499#95—714no—
500#95—714no—
501#95—714no—
502#95—714no—
503#95—714no—
504#95—714no—
505#95—714no—
506#95C22×D7114yes—
507#95C22×D7114yes—
508#95C22×D7114yes—
509C24—711no—
510C24—714no—
511C24—718no—
512C24—711no—
513C24—1422no—
514C24—1422no—
515C24—1424no—
516C24C23×D7111yescharacteristic
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—711no—
523C22×C4—714no—
524C22×C4—714no—
525C22×C4—714no—
526C22×C4—714no—
527C22×C4—711no—
528C22×C4—712no—
529C22×C4—712no—
530C22×C4—718no—
531C22×C4—714no—
532C22×C4—714no—
533C22×C4—714no—
534C22×C4—718no—
535C22×C4—714no—
536C22×C4—714no—
537C22×C4—1428no—
538C22×C4—1428no—
539C22×C4—1428no—
540C22×C4—1428no—
541C22×C4—1428no—
542C22×C4—1428no—
543C22×C4—1422no—
544C22×C4—1424no—
545C22×C4—1422no—
546C22×C4—1424no—
547C22×C4—14232no—
548C22×C4—1424no—
549C22×C4—1422no—
550C22×C4—1424no—
551C22×C4—1422no—
552C22×C4—1424no—
553C22×C4—1424no—
554C22×C4—1424no—
555C22×C4—1424no—
556C22×C4—14264no—
557C22×C4—1422no—
558C22×C4—1424no—
559C22×C4—1422no—
560C22×C4—1424no—
561C22×C4—1424no—
562C22×C4—1424no—
563C22×C4—1422no—
564C22×C4—1424no—
565C22×C4—1422no—
566C22×C4Q8×D7114yes—
567C22×C4C23×D7114yes—
568C22×C4C23×D7114yes—
569C22×C4C23×D7112yes—
570C22×C4C23×D7111yescharacteristic
571C22×C4C23×D7112yes—
572C22×C4C23×D7111yescharacteristic
573C4⋊C4—28no—
574C4⋊C4—24no—
575C4⋊C4—28no—
576C4⋊C4—24no—
577C4⋊C4—1428no—
578C4⋊C4—1428no—
579C4⋊C4—1428no—
580C4⋊C4—1428no—
581C4⋊C4—1428no—
582C4⋊C4—1428no—
583C4⋊C4—1428no—
584C4⋊C4—1424no—
585C4⋊C4—1428no—
586C4⋊C4—1424no—
587C22⋊C4—28no—
588C22⋊C4—1428no—
589C22⋊C4—1428no—
590C22⋊C4—1428no—
591C42—24no—
592C42—22no—
593C42—718no—
594C42—714no—
595C42—1424no—
596C42—1424no—
597C42—1424no—
598C42—1424no—
599C42—1422no—
600C42D4×D7114yes—
601C23—21no—
602C23—21no—
603C23—22no—
604C23—712no—
605C23—712no—
606C23—712no—
607C23—714no—
608C23—714no—
609C23—712no—
610C23—714no—
611C23—7116no—
612C23—1428no—
613C23—14216no—
614C23—14216no—
615C23—1428no—
616C23—1421no—
617C23—1421no—
618C23—1422no—
619C23C2×Q8×D7112yes—
620C23#41×D7114yes—
621C23C24×D7111yescharacteristic
622C2×C4—216no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—28no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—28416no—
637C2×C4—28416no—
638C2×C4—712no—
639C2×C4—712no—
640C2×C4—712no—
641C2×C4—7116no—
642C2×C4—714no—
643C2×C4—712no—
644C2×C4—714no—
645C2×C4—1428no—
646C2×C4—1428no—
647C2×C4—14216no—
648C2×C4—14216no—
649C2×C4—14216no—
650C2×C4—14216no—
651C2×C4—1424no—
652C2×C4—1424no—
653C2×C4—1424no—
654C2×C4—1424no—
655C2×C4—1424no—
656C2×C4—1424no—
657C2×C4—1428no—
658C2×C4—14216no—
659C2×C4—1421no—
660C2×C4—1422no—
661C2×C4—1421no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4—1422no—
665C2×C4—1428no—
666C2×C4C2×D4×D7114yes—
667C2×C4C2×D4×D7112yes—
668C2×C4C2×Q8×D7112yes—
669C2×C4C2×Q8×D7112yes—
670C2×C4#41×D7114yes—
671C2×C4#41×D7112yes—
672C22—22no—
673C22—24no—
674C22—24no—
675C22—22no—
676C22—714no—
677C22—718no—
678C22—714no—
679C22—718no—
680C22—714no—
681C22—714no—
682C22—14232no—
683C22—1422no—
684C22—1424no—
685C22—1424no—
686C22—1422no—
687C22#125×D7114yescomplemented
688C22C22×D4×D7111yescharacteristic
689C22C22×Q8×D7111yescharacteristic
690C22C2×#41×D7111yescharacteristic
691C22C2×#41×D7112yes—
692C22C2×#41×D7112yes—
693C4—22no—
694C4—24no—
695C4—24no—
696C4—44no—
697C4—44no—
698C4—2844no—
699C4—2844no—
700C4—714no—
701C4—1422no—
702C4—1424no—
703C4—1424no—
704C4C22⋊Q8×D7114yes—
705C2—24no—
706C2—718no—
707C2—1424no—
708C2C2×C22⋊Q8×D7111yescharacteristic
709C2#525×D7112yes—
710C2C2×#125×D7111yescharacteristic
711C2#529×D7112yes—
712C2#533×D7111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC71×#2851C2
prime radicalC24×D71C23
hypercenter#2851D71
hypocenterC71C2×#2851
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2851

Complements

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

NH ≅ G/Ntype
1. C2×#125×D71C2semidirect
3. #22596651C2semidirect
4. #22596650C2semidirect
5. #22596649C2semidirect
6. #22596648C2semidirect
7. #22596647C2semidirect
8. #22596646C2semidirect
9. #22596645C2semidirect
10. #389×D71C2semidirect
11. #387×D71C2semidirect
13. #382×D71C2semidirect
15. C71×#2851C2semidirect
18. C2×#14556120C22semidirect
19. C2×#14556119C22semidirect
20. C2×#14556118C22semidirect
36. #17985898C22semidirect
37. #17985897C22semidirect
38. #17985896C22semidirect
39. #17985895C22semidirect
40. #17985894C22semidirect
41. #17985886C22semidirect
42. #17985885C22semidirect
43. #17985884C22semidirect
44. #17985883C22semidirect
45. #17985882C22semidirect
46. #17985881C22semidirect
47. #17985880C22semidirect
55. #17985865C22semidirect
56. #17985864C22semidirect
57. #17985863C22semidirect
66. C2×#125×C71C22semidirect
68. #389×C71C22semidirect
69. #387×C71C22semidirect
71. #382×C71C22semidirect
257. C22×D71#125semidirect
319. C22×C71C2×#125semidirect
333. C2×D71C2×#125semidirect
356. D71#2851direct (N × H)
366. #2851D71direct (N × H)
372. C71C2×#2851semidirect
379. C2×#125C2×D71semidirect
400. #389C2×D71semidirect
408. #387C2×D71semidirect
420. #382C2×D71semidirect
687. C22#125×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D712
C22×C42×D712
#225966512
#225966502
#225966492
#225966482
#225966472
#225966462
#225966452
#389×D712
#387×D712
#385×D712
#382×D712
#380×D712
C71×#28512
C2×#285171