Finite Group Databasebeta

← #2629×D71 #32164513

Subgroups — #2629×D71 #32164513

Order 18176.

2614 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D71C211yesmaximal, characteristic, complemented
2C2×#117×D71C211yesmaximal, characteristic
3#22594175C212yesmaximal, complemented
4#22594174C212yesmaximal, complemented
5#22594173C211yesmaximal, characteristic, complemented
6#22594172C214yesmaximal, complemented
7#22594171C211yesmaximal, characteristic, complemented
8#22594170C211yesmaximal, characteristic, complemented
9#22594169C214yesmaximal, complemented
10#398×D71C214yesmaximal, complemented
11#396×D71C214yesmaximal
12#389×D71C212yesmaximal, complemented
13#384×D71C211yesmaximal, characteristic, complemented
14#380×D71C212yesmaximal
15C71×#2629C211yesmaximal, characteristic, complemented
16C23×C4×D71C2211yescharacteristic
17C2×#14556120C2211yescharacteristic, complemented
18C2×#14556119C2212yescomplemented
19C2×#14556118C2214yescomplemented
20#125×D71—28no—
21C2×#14556087C2211yescharacteristic
22C2×#14556086C2212yes—
23C2×#14556085C2211yescharacteristic
24C2×#14556085C2211yescharacteristic
25C2×#14556084C2212yes—
26#117×D71—28no—
27C2×C4⋊C4×D71C2212yes—
28C2×C4⋊C4×D71C2212yes—
29C2×C4⋊C4×D71C2212yes—
30C2×C4⋊C4×D71C2214yes—
31C2×C4⋊C4×D71C2214yes—
32C2×C4⋊C4×D71C2214yes—
33C2×C22⋊C4×D71C2212yes—
34C2×C22⋊C4×D71C2214yes—
35C2×C42×D71C2211yescharacteristic
36C2×C42×D71C2211yescharacteristic
37#17985933C2214yescomplemented
38#17985933C2214yescomplemented
39#17985932C2214yescomplemented
40#17985932C2214yescomplemented
41#17985931C2214yescomplemented
42#17985930C2214yescomplemented
43#17985929C2214yescomplemented
44#17985923C2214yes—
45#17985922C2214yes—
46#17985922C2214yes—
47#17985922C2214yes—
48#17985921C2214yes—
49#17985921C2214yes—
50#17985921C2214yes—
51#17985898C2212yescomplemented
52#17985897C2212yescomplemented
53#17985896C2214yescomplemented
54#17985895C2212yescomplemented
55#17985894C2214yescomplemented
56#17985869C2211yescharacteristic, complemented
57#17985868C2214yescomplemented
58#17985868C2212yescomplemented
59#17985859C2212yes—
60#17985858C2214yes—
61#17985857C2214yes—
62#17985856C2212yes—
63#17985856C2212yes—
64#95×D71C2214yes—
65#95×D71C2214yes—
66C2×#125×C71C2211yescharacteristic, complemented
67C2×#117×C71C2211yescharacteristic
68#398×C71C2214yescomplemented
69#396×C71C2214yes—
70#389×C71C2212yescomplemented
71#384×C71C2211yescharacteristic, complemented
72#380×C71C2212yes—
73C24×D71C2311yescharacteristic
74C23×Dic71C2311yescharacteristic
75C22×C4×D71—24no—
76C22×C4×D71—24no—
77C22×C4×D71Q818yes—
78C22×C4×D71C2312yes—
79C22×C4×D71C2314yes—
80C22×C4×D71C2314yes—
81C22×C4×D71C2312yes—
82C22×C4×D71C2311yescharacteristic
83C22×C4×D71C2311yescharacteristic
84C22×C4×D71C2311yescharacteristic
85C22×C4×D71C2311yescharacteristic
86#14556120—24no—
87#14556119—28no—
88#14556118—216no—
89#14556087—24no—
90#14556086—28no—
91#14556085—24no—
92#14556085—24no—
93#14556084—28no—
94C2×C4⋊Dic71C2312yes—
95C2×C4⋊Dic71C2312yes—
96C2×C4⋊Dic71C2314yes—
97C2×C4⋊Dic71C2312yes—
98C2×C4⋊Dic71C2314yes—
99C2×C4⋊Dic71C2314yes—
100C2×Dic71⋊C4C2314yes—
101C2×Dic71⋊C4C2314yes—
102C2×Dic71⋊C4C2314yes—
103C2×Dic71⋊C4C2314yes—
104C2×Dic71⋊C4C2312yes—
105C2×Dic71⋊C4C2312yes—
106C2×Dic71⋊C4C2314yes—
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×Dic71⋊C4C2314yes—
110C4⋊C4×D71—28no—
111C4⋊C4×D71—216no—
112C4⋊C4×D71—28no—
113C4⋊C4×D71—28no—
114C4⋊C4×D71—48no—
115C4⋊C4×D71—48no—
116C2×C22⋊Dic71C2312yes—
117C2×C22⋊Dic71C2314yes—
118C2×(C2×D71)⋊C4C2312yes—
119C2×(C2×D71)⋊C4C2312yes—
120C2×(C2×D71)⋊C4C2314yes—
121C2×(C2×D71)⋊C4C2314yes—
122C22⋊C4×D71—28no—
123C22⋊C4×D71—48no—
124C2×C4×Dic71C2312yes—
125C2×C4×Dic71C2311yescharacteristic
126C2×C4×Dic71C2312yes—
127C2×C4×Dic71C2311yescharacteristic
128C42×D71—24no—
129C42×D71D418yes—
130C71⋊#95C2314yes—
131C71⋊#95C2314yes—
132C71⋊#95C2314yes—
133C71⋊#95C2314yes—
134C71⋊#95C2314yes—
135C71⋊#95C2314yes—
136C23×C4×C71C2311yescharacteristic
137#125×C71—24no—
138#117×C71—24no—
139C2×C4⋊C4×C71C2312yes—
140C2×C4⋊C4×C71C2312yes—
141C2×C4⋊C4×C71C2312yes—
142C2×C4⋊C4×C71C2314yes—
143C2×C4⋊C4×C71C2314yes—
144C2×C4⋊C4×C71C2314yes—
145C2×C22⋊C4×C71C2312yes—
146C2×C22⋊C4×C71C2314yes—
147C2×C42×C71C2311yescharacteristic
148C2×C42×C71C2311yescharacteristic
149#95×C71C2314yes—
150#95×C71C2314yes—
151C23×D71—22no—
152C23×D71—22no—
153C23×D71—24no—
154C23×D71—24no—
155C23×D71C2×Q814yes—
156C23×D71C2411yescharacteristic
157C23×D71C2411yescharacteristic
158C22×Dic71—22no—
159C22×Dic71—22no—
160C22×Dic71C2×Q814yes—
161C22×Dic71C2412yes—
162C22×Dic71C2414yes—
163C22×Dic71C2414yes—
164C22×Dic71C2412yes—
165C22×Dic71C2411yescharacteristic
166C22×Dic71C2411yescharacteristic
167C2×C4×D71—22no—
168C2×C4×D71—22no—
169C2×C4×D71—24no—
170C2×C4×D71—24no—
171C2×C4×D71—22no—
172C2×C4×D71—22no—
173C2×C4×D71—22no—
174C2×C4×D71—22no—
175C2×C4×D71—232no—
176C2×C4×D71—24no—
177C2×C4×D71—28no—
178C2×C4×D71—28no—
179C2×C4×D71—28no—
180C2×C4×D71—28no—
181C2×C4×D71—24no—
182C2×C4×D71—28no—
183C2×C4×D71—24no—
184C2×C4×D71—28no—
185C2×C4×D71C2×D418yes—
186C2×C4×D71C2×D414yes—
187C2×C4×D71C2×Q814yes—
188C2×C4×D71C2×Q814yes—
189C2×C4×D71C2×Q814yes—
190C2×C4×D71C2×Q814yes—
191C2×C4×D71#4114yes—
192C4⋊Dic71—24no—
193C4⋊Dic71—24no—
194C4⋊Dic71—24no—
195C4⋊Dic71—28no—
196C4⋊Dic71—44no—
197C4⋊Dic71—44no—
198Dic71⋊C4—24no—
199Dic71⋊C4—28no—
200Dic71⋊C4—24no—
201Dic71⋊C4—28no—
202Dic71⋊C4—28no—
203Dic71⋊C4—28no—
204Dic71⋊C4—44no—
205Dic71⋊C4—44no—
206Dic71⋊C4—44no—
207Dic71⋊C4—44no—
208C22⋊Dic71—24no—
209C22⋊Dic71—44no—
210(C2×D71)⋊C4—24no—
211(C2×D71)⋊C4—24no—
212(C2×D71)⋊C4—44no—
213(C2×D71)⋊C4—44no—
214C4×Dic71—22no—
215C4×Dic71—24no—
216C4×Dic71C2×D418yes—
217C4×Dic71C2×D414yes—
218C24×C71C2411yescharacteristic
219C22×C4×C71—22no—
220C22×C4×C71—22no—
221C22×C4×C71C2×Q814yes—
222C22×C4×C71C2412yes—
223C22×C4×C71C2414yes—
224C22×C4×C71C2414yes—
225C22×C4×C71C2412yes—
226C22×C4×C71C2411yescharacteristic
227C22×C4×C71C2411yescharacteristic
228C4⋊C4×C71—24no—
229C4⋊C4×C71—28no—
230C4⋊C4×C71—24no—
231C4⋊C4×C71—24no—
232C4⋊C4×C71—44no—
233C4⋊C4×C71—44no—
234C22⋊C4×C71—24no—
235C22⋊C4×C71—44no—
236C42×C71—22no—
237C42×C71C2×D414yes—
238C23×C71—21no—
239C23×C71—21no—
240C23×C71—22no—
241C23×C71—22no—
242C23×C71C22×Q812yes—
243C23×C71C2511yescharacteristic
244C22×D71—21no—
245C22×D71—21no—
246C22×D71—22no—
247C22×D71—22no—
248C22×D71—28no—
249C22×D71—216no—
250C22×D71—48no—
251C22×D71—44no—
252C22×D71—44no—
253C22×D71C22×D412yes—
254C22×D71C22×Q812yes—
255C22×D71C22×Q812yes—
256C22×D71C2×#4112yes—
257C22×D71H(5,𝔽2)14yes—
258C22×D712−1+414yes—
259C2×C4×C71—21no—
260C2×C4×C71—21no—
261C2×C4×C71—22no—
262C2×C4×C71—22no—
263C2×C4×C71—28no—
264C2×C4×C71—22no—
265C2×C4×C71—24no—
266C2×C4×C71—24no—
267C2×C4×C71—24no—
268C2×C4×C71—24no—
269C2×C4×C71—22no—
270C2×C4×C71—24no—
271C2×C4×C71—22no—
272C2×C4×C71—24no—
273C2×C4×C71C22×D414yes—
274C2×C4×C71C22×D412yes—
275C2×C4×C71C22×Q812yes—
276C2×C4×C71C22×Q812yes—
277C2×C4×C71C2×#4112yes—
278C2×Dic71—21no—
279C2×Dic71—21no—
280C2×Dic71—22no—
281C2×Dic71—22no—
282C2×Dic71—28no—
283C2×Dic71—22no—
284C2×Dic71—24no—
285C2×Dic71—24no—
286C2×Dic71—24no—
287C2×Dic71—24no—
288C2×Dic71—24no—
289C2×Dic71—22no—
290C2×Dic71—22no—
291C2×Dic71—24no—
292C2×Dic71C22×D414yes—
293C2×Dic71C22×D412yes—
294C2×Dic71C22×Q812yes—
295C2×Dic71C22×Q812yes—
296C2×Dic71C2×#4112yes—
297C4×D71—28no—
298C4×D71—216no—
299C4×D71—28no—
300C4×D71—28no—
301C4×D71—48no—
302C4×D71—416no—
303C4×D71—416no—
304C4×D71C22⋊Q8116yes—
305C22×C71—22no—
306C22×C71—24no—
307C22×C71—42no—
308C22×C71—41no—
309C22×C71—41no—
310C22×C71C23×D411yescharacteristic
311C22×C71C23×Q811yescharacteristic
312C22×C71C22×#4111yescharacteristic
313C22×C71C2×H(5,𝔽2)12yes—
314C22×C71C2×2−1+412yes—
315C2×D71—22no—
316C2×D71—24no—
317C2×D71—42no—
318C2×D71—41no—
319C2×D71—41no—
320C2×D71—416no—
321C2×D71C2×C22⋊Q814yes—
322C2×D71#53718yes—
323C2×D71#54014yes—
324C2×D71#54114yes—
325C2×D71#54418yes—
326C4×C71—22no—
327C4×C71—24no—
328C4×C71—42no—
329C4×C71—44no—
330C4×C71—44no—
331C4×C71C2×C22⋊Q814yes—
332Dic71—22no—
333Dic71—24no—
334Dic71—42no—
335Dic71—44no—
336Dic71—44no—
337Dic71C2×C22⋊Q814yes—
338C2×#2629—711nomaximal, Sylow
339C2×C71—42no—
340C2×C71C22×C22⋊Q811yescharacteristic
341C2×C71C2×#53712yes—
342C2×C71C2×#54011yescharacteristic
343C2×C71C2×#54111yescharacteristic
344C2×C71C2×#54412yes—
345D71—42no—
346D71#262918yesdirect product factor
347C22×#125—711no—
348C22×#117—711no—
349#2629—714no—
350#2629—714no—
351#2629—712no—
352#2629—711no—
353#2629—712no—
354#2629—711no—
355#2629—711no—
356#2629D7111yescharacteristic, direct product factor
357C2×#398—714no—
358C2×#396—714no—
359C2×#389—712no—
360C2×#384—711no—
361C2×#380—712no—
362C71C2×#262911yescharacteristic, complemented, Sylow
363C24×C4—711no—
364C2×#125—714no—
365C2×#125—712no—
366C2×#125—711no—
367C2×#125—1428no—
368C2×#125C2×D7111yescharacteristic, complemented
369C2×#117—711no—
370C2×#117—712no—
371C2×#117—712no—
372C2×#117—711no—
373C2×#117—711no—
374C2×#117—1428no—
375C2×#117C2×D7111yescharacteristic
376C22×C4⋊C4—714no—
377C22×C4⋊C4—714no—
378C22×C4⋊C4—714no—
379C22×C4⋊C4—712no—
380C22×C4⋊C4—712no—
381C22×C4⋊C4—712no—
382C22×C22⋊C4—714no—
383C22×C22⋊C4—712no—
384C22×C42—711no—
385C22×C42—711no—
386#398—714no—
387#398—714no—
388#398—714no—
389#398—714no—
390#398—714no—
391#398—714no—
392#398—714no—
393#398C2×D7114yescomplemented
394#396—714no—
395#396—714no—
396#396—714no—
397#396—714no—
398#396—714no—
399#396—714no—
400#396—714no—
401#396C2×D7114yes—
402#389—714no—
403#389—712no—
404#389—712no—
405#389—712no—
406#389—714no—
407#389C2×D7112yescomplemented
408#384—712no—
409#384—714no—
410#384—711no—
411#384C2×D7111yescharacteristic, complemented
412#380—712no—
413#380—712no—
414#380—712no—
415#380—714no—
416#380—714no—
417#380C2×D7112yes—
418C2×#95—714no—
419C2×#95—714no—
420C25—711no—
421C23×C4—711no—
422C23×C4—711no—
423C23×C4—718no—
424C23×C4—712no—
425C23×C4—711no—
426C23×C4—711no—
427C23×C4—711no—
428C23×C4—714no—
429C23×C4—714no—
430C23×C4—712no—
431C23×C4—1424no—
432C23×C4—1424no—
433C23×C4C22×D7111yescharacteristic
434#125—24no—
435#125—14216no—
436#125—1428no—
437#125—1424no—
438#117—24no—
439#117—1424no—
440#117—1428no—
441#117—1428no—
442#117—1424no—
443#117—1424no—
444C2×C4⋊C4—2848no—
445C2×C4⋊C4—2848no—
446C2×C4⋊C4—714no—
447C2×C4⋊C4—714no—
448C2×C4⋊C4—714no—
449C2×C4⋊C4—714no—
450C2×C4⋊C4—714no—
451C2×C4⋊C4—714no—
452C2×C4⋊C4—712no—
453C2×C4⋊C4—712no—
454C2×C4⋊C4—712no—
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—1428no—
463C2×C4⋊C4—1428no—
464C2×C4⋊C4—14216no—
465C2×C4⋊C4—1428no—
466C2×C4⋊C4C22×D7112yes—
467C2×C4⋊C4C22×D7112yes—
468C2×C4⋊C4C22×D7114yes—
469C2×C4⋊C4C22×D7112yes—
470C2×C4⋊C4C22×D7114yes—
471C2×C4⋊C4C22×D7114yes—
472C2×C22⋊C4—2848no—
473C2×C22⋊C4—714no—
474C2×C22⋊C4—714no—
475C2×C22⋊C4—714no—
476C2×C22⋊C4—712no—
477C2×C22⋊C4—712no—
478C2×C22⋊C4—712no—
479C2×C22⋊C4—1428no—
480C2×C22⋊C4C22×D7112yes—
481C2×C22⋊C4C22×D7114yes—
482C2×C42—712no—
483C2×C42—711no—
484C2×C42—718no—
485C2×C42—712no—
486C2×C42—711no—
487C2×C42—1424no—
488C2×C42C22×D7111yescharacteristic
489C2×C42C22×D7111yescharacteristic
490#95—714no—
491#95—714no—
492#95—714no—
493#95—714no—
494#95—714no—
495#95—714no—
496#95C22×D7114yes—
497#95C22×D7114yes—
498C24—711no—
499C24—714no—
500C24—711no—
501C24—1424no—
502C24—1422no—
503C24—1422no—
504C24—1424no—
505C24C23×D7111yescharacteristic
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—711no—
509C22×C4—714no—
510C22×C4—714no—
511C22×C4—714no—
512C22×C4—714no—
513C22×C4—711no—
514C22×C4—712no—
515C22×C4—718no—
516C22×C4—714no—
517C22×C4—714no—
518C22×C4—714no—
519C22×C4—712no—
520C22×C4—714no—
521C22×C4—714no—
522C22×C4—1424no—
523C22×C4—1428no—
524C22×C4—1428no—
525C22×C4—1428no—
526C22×C4—1424no—
527C22×C4—1428no—
528C22×C4—1428no—
529C22×C4—1428no—
530C22×C4—1424no—
531C22×C4—1422no—
532C22×C4—1422no—
533C22×C4—14232no—
534C22×C4—1424no—
535C22×C4—1422no—
536C22×C4—1424no—
537C22×C4—1422no—
538C22×C4—1422no—
539C22×C4—1422no—
540C22×C4—1422no—
541C22×C4—1422no—
542C22×C4Q8×D7114yes—
543C22×C4C23×D7112yes—
544C22×C4C23×D7114yes—
545C22×C4C23×D7114yes—
546C22×C4C23×D7112yes—
547C22×C4C23×D7111yescharacteristic
548C22×C4C23×D7111yescharacteristic
549C4⋊C4—24no—
550C4⋊C4—28no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—2844no—
556C4⋊C4—2844no—
557C4⋊C4—2844no—
558C4⋊C4—2844no—
559C4⋊C4—2844no—
560C4⋊C4—2844no—
561C4⋊C4—1428no—
562C4⋊C4—1424no—
563C4⋊C4—1428no—
564C4⋊C4—1428no—
565C4⋊C4—1424no—
566C4⋊C4—1428no—
567C4⋊C4—1424no—
568C4⋊C4—1428no—
569C4⋊C4—1424no—
570C4⋊C4—1424no—
571C22⋊C4—24no—
572C22⋊C4—44no—
573C22⋊C4—2844no—
574C22⋊C4—2844no—
575C22⋊C4—2844no—
576C22⋊C4—1424no—
577C22⋊C4—1424no—
578C22⋊C4—1424no—
579C42—22no—
580C42—718no—
581C42—714no—
582C42—1424no—
583C42—1422no—
584C42D4×D7114yes—
585C23—21no—
586C23—21no—
587C23—22no—
588C23—22no—
589C23—2848no—
590C23—2844no—
591C23—2844no—
592C23—712no—
593C23—712no—
594C23—712no—
595C23—714no—
596C23—714no—
597C23—712no—
598C23—1428no—
599C23—14216no—
600C23—1421no—
601C23—1421no—
602C23—1422no—
603C23—1422no—
604C23C2×Q8×D7112yes—
605C23C24×D7111yescharacteristic
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—28no—
611C2×C4—22no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—2848no—
621C2×C4—28416no—
622C2×C4—28416no—
623C2×C4—712no—
624C2×C4—712no—
625C2×C4—712no—
626C2×C4—7116no—
627C2×C4—714no—
628C2×C4—712no—
629C2×C4—1428no—
630C2×C4—1428no—
631C2×C4—14216no—
632C2×C4—1422no—
633C2×C4—1424no—
634C2×C4—1424no—
635C2×C4—1424no—
636C2×C4—1424no—
637C2×C4—1422no—
638C2×C4—1424no—
639C2×C4—1422no—
640C2×C4—1424no—
641C2×C4—1428no—
642C2×C4—1421no—
643C2×C4—1421no—
644C2×C4—1422no—
645C2×C4—1422no—
646C2×C4—1428no—
647C2×C4C2×D4×D7114yes—
648C2×C4C2×D4×D7112yes—
649C2×C4C2×Q8×D7112yes—
650C2×C4C2×Q8×D7112yes—
651C2×C4#41×D7112yes—
652C22—24no—
653C22—22no—
654C22—42no—
655C22—41no—
656C22—41no—
657C22—28416no—
658C22—2842no—
659C22—2841no—
660C22—2841no—
661C22—718no—
662C22—714no—
663C22—718no—
664C22—714no—
665C22—714no—
666C22—1424no—
667C22—1422no—
668C22C22×D4×D7111yescharacteristic
669C22C22×Q8×D7111yescharacteristic
670C22C2×#41×D7111yescharacteristic
671C22H(5,𝔽2)×D7112yes—
672C222−1+4×D7112yes—
673C4—22no—
674C4—24no—
675C4—42no—
676C4—44no—
677C4—44no—
678C4—2842no—
679C4—2844no—
680C4—2844no—
681C4—714no—
682C4—1422no—
683C4—1424no—
684C4C22⋊Q8×D7114yes—
685C2—42no—
686C2—2842no—
687C2—718no—
688C2C2×C22⋊Q8×D7111yescharacteristic
689C2#537×D7112yes—
690C2#540×D7111yescharacteristic
691C2#541×D7111yescharacteristic
692C2#544×D7112yes—
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC71×#2629C2
prime radicalC24×D71C23
hypercenter#2629D71
hypocenterC71C2×#2629
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2629

Complements

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

NH ≅ G/Ntype
1. C2×#125×D71C2semidirect
3. #22594175C2semidirect
4. #22594174C2semidirect
5. #22594173C2semidirect
6. #22594172C2semidirect
7. #22594171C2semidirect
8. #22594170C2semidirect
9. #22594169C2semidirect
10. #398×D71C2semidirect
12. #389×D71C2semidirect
13. #384×D71C2semidirect
15. C71×#2629C2semidirect
17. C2×#14556120C22semidirect
18. C2×#14556119C22semidirect
19. C2×#14556118C22semidirect
37. #17985933C22semidirect
38. #17985933C22semidirect
39. #17985932C22semidirect
40. #17985932C22semidirect
41. #17985931C22semidirect
42. #17985930C22semidirect
43. #17985929C22semidirect
51. #17985898C22semidirect
52. #17985897C22semidirect
53. #17985896C22semidirect
54. #17985895C22semidirect
55. #17985894C22semidirect
56. #17985869C22semidirect
57. #17985868C22semidirect
58. #17985868C22semidirect
66. C2×#125×C71C22semidirect
68. #398×C71C22semidirect
70. #389×C71C22semidirect
71. #384×C71C22semidirect
346. D71#2629direct (N × H)
356. #2629D71direct (N × H)
362. C71C2×#2629semidirect
368. C2×#125C2×D71semidirect
393. #398C2×D71semidirect
407. #389C2×D71semidirect
411. #384C2×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D712
C2×#117×D712
#225941752
#225941742
#225941732
#225941722
#225941712
#225941702
#225941692
#398×D712
#396×D712
#389×D712
#384×D712
#380×D712
C71×#26292
C2×#262971