Finite Group Databasebeta

← #2552×D71 #32169268

Subgroups — #2552×D71 #32169268

Order 18176.

2446 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×D71C212yesmaximal
2#22593377C212yesmaximal, complemented
3#22593376C211yesmaximal, characteristic, complemented
4#22593375C211yesmaximal, characteristic, complemented
5#22593374C212yesmaximal, complemented
6#22593373C212yesmaximal, complemented
7#22593372C212yesmaximal, complemented
8#22593371C211yesmaximal, characteristic, complemented
9#22593370C214yesmaximal, complemented
10#398×D71C214yesmaximal
11#389×D71C212yesmaximal
12#389×D71C212yesmaximal
13#384×D71C211yesmaximal, characteristic
14#384×D71C212yesmaximal
15C4×C4⋊C4×D71C211yesmaximal, characteristic
16C4×C4⋊C4×D71C211yesmaximal, characteristic
17C71×#2552C211yesmaximal, characteristic, complemented
18C2×#14556120C2212yes—
19C2×#14556119C2212yes—
20C2×#14556119C2212yes—
21C2×#14556118C2214yes—
22C2×#14556118C2214yes—
23#125×D71—216no—
24C2×C4⋊C4×D71C2212yes—
25C2×C4⋊C4×D71C2211yescharacteristic
26C2×C4⋊C4×D71C2212yes—
27C2×C4⋊C4×D71C2214yes—
28C2×C4⋊C4×D71C2211yescharacteristic
29C2×C4⋊C4×D71C2214yes—
30C2×C4⋊C4×D71C2214yes—
31C2×C4⋊C4×D71C2212yes—
32C2×C4⋊C4×D71C2211yescharacteristic
33C2×C4⋊C4×D71C2211yescharacteristic
34C2×C42×D71C2212yes—
35C2×C42×D71C2212yes—
36C2×C42×D71C2211yescharacteristic
37#17985933C2214yes—
38#17985933C2214yes—
39#17985932C2214yes—
40#17985932C2214yes—
41#17985931C2214yes—
42#17985930C2214yes—
43#17985929C2214yes—
44#17985898C2212yes—
45#17985898C2212yes—
46#17985897C2212yes—
47#17985897C2212yes—
48#17985896C2214yes—
49#17985896C2214yes—
50#17985895C2212yes—
51#17985895C2212yes—
52#17985894C2214yes—
53#17985894C2214yes—
54#17985869C2212yes—
55#17985869C2211yescharacteristic
56#17985868C2212yes—
57#17985868C2214yes—
58#17985868C2214yes—
59#17985868C2212yes—
60#17985868C2212yes—
61#17985868C2212yes—
62#17985868C2212yes—
63C4⋊C4×Dic71C2211yescharacteristic
64C4⋊C4×Dic71C2211yescharacteristic
65C4⋊C4×Dic71C2211yescharacteristic
66C4⋊C4×Dic71C2211yescharacteristic
67C4×Dic71⋊C4C2212yes—
68C4×Dic71⋊C4C2212yes—
69C4×C4⋊Dic71C2211yescharacteristic
70C4×C4⋊Dic71C2211yescharacteristic
71#17985850C2212yes—
72#17985850C2212yes—
73#95×D71C2214yes—
74#95×D71C2212yes—
75#95×D71C2212yes—
76C2×#125×C71C2212yes—
77#398×C71C2214yes—
78#389×C71C2212yes—
79#389×C71C2212yes—
80#384×C71C2212yes—
81#384×C71C2211yescharacteristic
82C4×C4⋊C4×C71C2211yescharacteristic
83C4×C4⋊C4×C71C2211yescharacteristic
84C22×C4×D71C2312yes—
85C22×C4×D71C2312yes—
86C22×C4×D71C2314yes—
87C22×C4×D71C2312yes—
88C22×C4×D71C2311yescharacteristic
89C22×C4×D71C2312yes—
90C22×C4×D71C2311yescharacteristic
91C22×C4×D71C2311yescharacteristic
92#14556120—28no—
93#14556119—28no—
94#14556119—28no—
95#14556118—216no—
96#14556118—216no—
97C2×C4⋊Dic71C2311yescharacteristic
98C2×C4⋊Dic71C2311yescharacteristic
99C2×C4⋊Dic71C2312yes—
100C2×C4⋊Dic71C2312yes—
101C2×C4⋊Dic71C2314yes—
102C2×C4⋊Dic71C2314yes—
103C2×C4⋊Dic71C2314yes—
104C2×C4⋊Dic71C2312yes—
105C2×C4⋊Dic71C2311yescharacteristic
106C2×C4⋊Dic71C2311yescharacteristic
107C2×Dic71⋊C4C2312yes—
108C2×Dic71⋊C4C2312yes—
109C2×Dic71⋊C4C2314yes—
110C2×Dic71⋊C4C2314yes—
111C2×Dic71⋊C4C2314yes—
112C2×Dic71⋊C4C2314yes—
113C2×Dic71⋊C4C2314yes—
114C2×Dic71⋊C4C2314yes—
115C2×Dic71⋊C4C2314yes—
116C2×Dic71⋊C4C2314yes—
117C2×Dic71⋊C4C2314yes—
118C2×Dic71⋊C4C2312yes—
119C2×Dic71⋊C4C2312yes—
120C4⋊C4×D71—216no—
121C4⋊C4×D71—216no—
122C4⋊C4×D71—28no—
123C4⋊C4×D71—24no—
124C4⋊C4×D71—28no—
125C4⋊C4×D71—24no—
126C4⋊C4×D71—48no—
127C4⋊C4×D71—44no—
128C4⋊C4×D71D418yes—
129C4⋊C4×D71Q818yes—
130C2×C4×Dic71C2312yes—
131C2×C4×Dic71C2312yes—
132C2×C4×Dic71C2312yes—
133C2×C4×Dic71C2312yes—
134C2×C4×Dic71C2312yes—
135C2×C4×Dic71C2312yes—
136C2×C4×Dic71C2311yescharacteristic
137C2×C4×Dic71C2311yescharacteristic
138C2×C4×Dic71C2311yescharacteristic
139C42×D71—28no—
140C42×D71—28no—
141C42×D71Q818yes—
142C71⋊#95C2312yes—
143C71⋊#95C2312yes—
144C71⋊#95C2312yes—
145C71⋊#95C2312yes—
146C71⋊#95C2312yes—
147C71⋊#95C2312yes—
148C71⋊#95C2314yes—
149C71⋊#95C2314yes—
150C71⋊#95C2314yes—
151#125×C71—28no—
152C2×C4⋊C4×C71C2311yescharacteristic
153C2×C4⋊C4×C71C2311yescharacteristic
154C2×C4⋊C4×C71C2312yes—
155C2×C4⋊C4×C71C2312yes—
156C2×C4⋊C4×C71C2314yes—
157C2×C4⋊C4×C71C2314yes—
158C2×C4⋊C4×C71C2314yes—
159C2×C4⋊C4×C71C2312yes—
160C2×C4⋊C4×C71C2311yescharacteristic
161C2×C4⋊C4×C71C2311yescharacteristic
162C2×C42×C71C2312yes—
163C2×C42×C71C2312yes—
164C2×C42×C71C2311yescharacteristic
165#95×C71C2312yes—
166#95×C71C2312yes—
167#95×C71C2314yes—
168C23×D71C2411yescharacteristic
169C22×Dic71C2412yes—
170C22×Dic71C2412yes—
171C22×Dic71C2414yes—
172C22×Dic71C2412yes—
173C22×Dic71C2411yescharacteristic
174C22×Dic71C2412yes—
175C22×Dic71C2411yescharacteristic
176C22×Dic71C2411yescharacteristic
177C2×C4×D71—24no—
178C2×C4×D71—24no—
179C2×C4×D71—22no—
180C2×C4×D71—24no—
181C2×C4×D71—22no—
182C2×C4×D71—24no—
183C2×C4×D71—24no—
184C2×C4×D71—24no—
185C2×C4×D71—28no—
186C2×C4×D71—24no—
187C2×C4×D71—24no—
188C2×C4×D71—28no—
189C2×C4×D71—24no—
190C2×C4×D71—28no—
191C2×C4×D71—24no—
192C2×C4×D71C2×D418yes—
193C2×C4×D71C2×D414yes—
194C2×C4×D71C2×Q814yes—
195C2×C4×D71C2×Q818yes—
196C2×C4×D71C2×Q814yes—
197C2×C4×D71C2×Q814yes—
198C2×C4×D71C2×Q814yes—
199C2×C4×D71#4114yes—
200C2×C4×D71#4114yes—
201C4⋊Dic71—28no—
202C4⋊Dic71—24no—
203C4⋊Dic71—22no—
204C4⋊Dic71—22no—
205C4⋊Dic71—24no—
206C4⋊Dic71—28no—
207C4⋊Dic71—44no—
208C4⋊Dic71—42no—
209C4⋊Dic71C2×D414yes—
210C4⋊Dic71C2×Q814yes—
211Dic71⋊C4—28no—
212Dic71⋊C4—28no—
213Dic71⋊C4—28no—
214Dic71⋊C4—28no—
215Dic71⋊C4—28no—
216Dic71⋊C4—24no—
217Dic71⋊C4—24no—
218Dic71⋊C4—28no—
219Dic71⋊C4—44no—
220Dic71⋊C4—44no—
221Dic71⋊C4—44no—
222Dic71⋊C4C2×D418yes—
223Dic71⋊C4C2×Q818yes—
224C4×Dic71—24no—
225C4×Dic71—24no—
226C4×Dic71—24no—
227C4×Dic71—24no—
228C4×Dic71—24no—
229C4×Dic71—24no—
230C4×Dic71C2×Q814yes—
231C4×Dic71C2×Q814yes—
232C4×Dic71C2×Q814yes—
233C22×C4×C71C2412yes—
234C22×C4×C71C2412yes—
235C22×C4×C71C2414yes—
236C22×C4×C71C2412yes—
237C22×C4×C71C2411yescharacteristic
238C22×C4×C71C2412yes—
239C22×C4×C71C2411yescharacteristic
240C22×C4×C71C2411yescharacteristic
241C4⋊C4×C71—28no—
242C4⋊C4×C71—28no—
243C4⋊C4×C71—24no—
244C4⋊C4×C71—22no—
245C4⋊C4×C71—22no—
246C4⋊C4×C71—24no—
247C4⋊C4×C71—44no—
248C4⋊C4×C71—42no—
249C4⋊C4×C71C2×D414yes—
250C4⋊C4×C71C2×Q814yes—
251C42×C71—24no—
252C42×C71—24no—
253C42×C71C2×Q814yes—
254C23×C71C2511yescharacteristic
255C22×D71C22×D412yes—
256C22×D71C22×Q812yes—
257C22×D71C22×Q812yes—
258C22×D71C2×#4112yes—
259C22×D71C2×#4112yes—
260C22×D71H(5,𝔽2)12yes—
261C22×D712−1+412yes—
262C2×C4×C71—22no—
263C2×C4×C71—22no—
264C2×C4×C71—21no—
265C2×C4×C71—22no—
266C2×C4×C71—21no—
267C2×C4×C71—22no—
268C2×C4×C71—22no—
269C2×C4×C71—22no—
270C2×C4×C71—24no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—24no—
274C2×C4×C71—22no—
275C2×C4×C71—24no—
276C2×C4×C71—22no—
277C2×C4×C71C22×D414yes—
278C2×C4×C71C22×D412yes—
279C2×C4×C71C22×Q812yes—
280C2×C4×C71C22×Q814yes—
281C2×C4×C71C22×Q812yes—
282C2×C4×C71C22×Q812yes—
283C2×C4×C71C22×Q812yes—
284C2×C4×C71C2×#4112yes—
285C2×C4×C71C2×#4112yes—
286C2×Dic71—22no—
287C2×Dic71—22no—
288C2×Dic71—21no—
289C2×Dic71—22no—
290C2×Dic71—21no—
291C2×Dic71—22no—
292C2×Dic71—22no—
293C2×Dic71—22no—
294C2×Dic71—24no—
295C2×Dic71—22no—
296C2×Dic71—22no—
297C2×Dic71—24no—
298C2×Dic71—22no—
299C2×Dic71—24no—
300C2×Dic71—22no—
301C2×Dic71C22×D414yes—
302C2×Dic71C22×D412yes—
303C2×Dic71C22×Q812yes—
304C2×Dic71C22×Q814yes—
305C2×Dic71C22×Q812yes—
306C2×Dic71C22×Q812yes—
307C2×Dic71C22×Q812yes—
308C2×Dic71C2×#4112yes—
309C2×Dic71C2×#4112yes—
310C4×D71—28no—
311C4×D71—216no—
312C4×D71—216no—
313C4×D71—48no—
314C4×D71—48no—
315C4×D71—416no—
316C4×D71#125116yescomplemented
317C4×D71C4⋊Q8116yes—
318C22×C71C23×D411yescharacteristic
319C22×C71C23×Q811yescharacteristic
320C22×C71C23×Q811yescharacteristic
321C22×C71C22×#4111yescharacteristic
322C22×C71C22×#4111yescharacteristic
323C22×C71C2×H(5,𝔽2)11yescharacteristic
324C22×C71C2×2−1+411yescharacteristic
325C2×D71C2×#12514yes—
326C2×D71C2×C4⋊Q814yes—
327C2×D71#54414yes—
328C2×D71#54714yes—
329C2×D71#55014yes—
330C2×D71#55414yes—
331C2×D71#55714yes—
332C4×C71—22no—
333C4×C71—24no—
334C4×C71—24no—
335C4×C71—42no—
336C4×C71—42no—
337C4×C71—44no—
338C4×C71C2×#12514yescomplemented
339C4×C71C2×C4⋊Q814yes—
340Dic71—22no—
341Dic71—24no—
342Dic71—24no—
343Dic71—42no—
344Dic71—42no—
345Dic71—44no—
346Dic71C2×#12514yescomplemented
347Dic71C2×C4⋊Q814yes—
348C2×#2552—711nomaximal, Sylow
349C2×C71C22×#12511yescharacteristic
350C2×C71C22×C4⋊Q811yescharacteristic
351C2×C71C2×#54411yescharacteristic
352C2×C71C2×#54711yescharacteristic
353C2×C71C2×#55011yescharacteristic
354C2×C71C2×#55411yescharacteristic
355C2×C71C2×#55711yescharacteristic
356D71#255218yesdirect product factor
357C22×#125—712no—
358#2552—714no—
359#2552—712no—
360#2552—712no—
361#2552—712no—
362#2552—711no—
363#2552—711no—
364#2552—711no—
365#2552—712no—
366#2552D7111yescharacteristic, direct product factor
367C2×#398—714no—
368C2×#389—712no—
369C2×#389—712no—
370C2×#384—711no—
371C2×#384—712no—
372C2×C4×C4⋊C4—711no—
373C2×C4×C4⋊C4—711no—
374C71C2×#255211yescharacteristic, complemented, Sylow
375C2×#125—714no—
376C2×#125—714no—
377C2×#125—712no—
378C2×#125—712no—
379C2×#125—712no—
380C2×#125—14216no—
381C2×#125C2×D7112yes—
382C22×C4⋊C4—712no—
383C22×C4⋊C4—714no—
384C22×C4⋊C4—711no—
385C22×C4⋊C4—711no—
386C22×C4⋊C4—714no—
387C22×C4⋊C4—714no—
388C22×C4⋊C4—712no—
389C22×C4⋊C4—711no—
390C22×C4⋊C4—711no—
391C22×C4⋊C4—712no—
392C22×C42—711no—
393C22×C42—712no—
394C22×C42—712no—
395#398—714no—
396#398—714no—
397#398—714no—
398#398—714no—
399#398—714no—
400#398—714no—
401#398—714no—
402#398C2×D7114yes—
403#389—714no—
404#389—714no—
405#389—712no—
406#389—712no—
407#389—712no—
408#389—712no—
409#389—712no—
410#389—712no—
411#389—714no—
412#389—714no—
413#389C2×D7112yes—
414#389C2×D7112yes—
415#384—712no—
416#384—712no—
417#384—712no—
418#384—712no—
419#384—712no—
420#384—714no—
421#384—714no—
422#384—712no—
423#384—711no—
424#384C2×D7112yes—
425#384C2×D7111yescharacteristic
426C4×C4⋊C4—711no—
427C4×C4⋊C4—711no—
428C4×C4⋊C4—711no—
429C4×C4⋊C4—711no—
430C4×C4⋊C4—711no—
431C4×C4⋊C4—711no—
432C4×C4⋊C4—712no—
433C4×C4⋊C4—712no—
434C4×C4⋊C4—712no—
435C4×C4⋊C4—712no—
436C4×C4⋊C4C2×D7111yescharacteristic
437C4×C4⋊C4C2×D7111yescharacteristic
438C2×#95—712no—
439C2×#95—712no—
440C2×#95—714no—
441C23×C4—711no—
442C23×C4—711no—
443C23×C4—712no—
444C23×C4—712no—
445C23×C4—711no—
446C23×C4—714no—
447C23×C4—712no—
448C23×C4—712no—
449#125—28no—
450#125—1428no—
451#125—14216no—
452#125—14216no—
453#125—1428no—
454#125—1428no—
455C2×C4⋊C4—2844no—
456C2×C4⋊C4—2848no—
457C2×C4⋊C4—714no—
458C2×C4⋊C4—714no—
459C2×C4⋊C4—714no—
460C2×C4⋊C4—714no—
461C2×C4⋊C4—712no—
462C2×C4⋊C4—712no—
463C2×C4⋊C4—711no—
464C2×C4⋊C4—712no—
465C2×C4⋊C4—711no—
466C2×C4⋊C4—718no—
467C2×C4⋊C4—718no—
468C2×C4⋊C4—714no—
469C2×C4⋊C4—712no—
470C2×C4⋊C4—714no—
471C2×C4⋊C4—714no—
472C2×C4⋊C4—714no—
473C2×C4⋊C4—714no—
474C2×C4⋊C4—714no—
475C2×C4⋊C4—714no—
476C2×C4⋊C4—712no—
477C2×C4⋊C4—711no—
478C2×C4⋊C4—712no—
479C2×C4⋊C4—711no—
480C2×C4⋊C4—714no—
481C2×C4⋊C4—712no—
482C2×C4⋊C4—1428no—
483C2×C4⋊C4—14216no—
484C2×C4⋊C4—14216no—
485C2×C4⋊C4—1424no—
486C2×C4⋊C4—1424no—
487C2×C4⋊C4—1428no—
488C2×C4⋊C4C22×D7112yes—
489C2×C4⋊C4C22×D7114yes—
490C2×C4⋊C4C22×D7114yes—
491C2×C4⋊C4C22×D7111yescharacteristic
492C2×C4⋊C4C22×D7111yescharacteristic
493C2×C4⋊C4C22×D7112yes—
494C2×C4⋊C4C22×D7114yes—
495C2×C4⋊C4C22×D7112yes—
496C2×C4⋊C4C22×D7111yescharacteristic
497C2×C4⋊C4C22×D7111yescharacteristic
498C2×C42—711no—
499C2×C42—711no—
500C2×C42—711no—
501C2×C42—718no—
502C2×C42—712no—
503C2×C42—712no—
504C2×C42—712no—
505C2×C42—712no—
506C2×C42—712no—
507C2×C42—712no—
508C2×C42—1428no—
509C2×C42—1428no—
510C2×C42C22×D7112yes—
511C2×C42C22×D7112yes—
512C2×C42C22×D7111yescharacteristic
513#95—712no—
514#95—712no—
515#95—712no—
516#95—712no—
517#95—712no—
518#95—712no—
519#95—714no—
520#95—714no—
521#95—714no—
522#95C22×D7112yes—
523#95C22×D7112yes—
524#95C22×D7114yes—
525C24—711no—
526C22×C4—711no—
527C22×C4—711no—
528C22×C4—714no—
529C22×C4—714no—
530C22×C4—714no—
531C22×C4—714no—
532C22×C4—714no—
533C22×C4—714no—
534C22×C4—711no—
535C22×C4—712no—
536C22×C4—712no—
537C22×C4—718no—
538C22×C4—714no—
539C22×C4—718no—
540C22×C4—712no—
541C22×C4—712no—
542C22×C4—714no—
543C22×C4—1424no—
544C22×C4—1424no—
545C22×C4—1428no—
546C22×C4—1424no—
547C22×C4—1428no—
548C22×C4—1428no—
549C22×C4—1424no—
550C22×C4—1424no—
551C22×C4—1424no—
552C22×C4—1424no—
553C22×C4—1424no—
554C22×C4—1424no—
555C22×C4—1422no—
556C22×C4—1424no—
557C22×C4—1422no—
558C22×C4C23×D7112yes—
559C22×C4C23×D7112yes—
560C22×C4C23×D7114yes—
561C22×C4C23×D7112yes—
562C22×C4C23×D7111yescharacteristic
563C22×C4C23×D7112yes—
564C22×C4C23×D7111yescharacteristic
565C22×C4C23×D7111yescharacteristic
566C4⋊C4—28no—
567C4⋊C4—28no—
568C4⋊C4—24no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—24no—
572C4⋊C4—44no—
573C4⋊C4—42no—
574C4⋊C4—2844no—
575C4⋊C4—2844no—
576C4⋊C4—2844no—
577C4⋊C4—2844no—
578C4⋊C4—2842no—
579C4⋊C4—718no—
580C4⋊C4—714no—
581C4⋊C4—718no—
582C4⋊C4—714no—
583C4⋊C4—1424no—
584C4⋊C4—1424no—
585C4⋊C4—1428no—
586C4⋊C4—1428no—
587C4⋊C4—1428no—
588C4⋊C4—1428no—
589C4⋊C4—1428no—
590C4⋊C4—1428no—
591C4⋊C4—1428no—
592C4⋊C4—1428no—
593C4⋊C4—1424no—
594C4⋊C4—1422no—
595C4⋊C4—1422no—
596C4⋊C4—1424no—
597C4⋊C4D4×D7114yes—
598C4⋊C4Q8×D7114yes—
599C42—24no—
600C42—24no—
601C42—714no—
602C42—714no—
603C42—714no—
604C42—1424no—
605C42—1424no—
606C42—1424no—
607C42—1424no—
608C42—1424no—
609C42—1424no—
610C42Q8×D7114yes—
611C23—712no—
612C23—712no—
613C23—712no—
614C23—712no—
615C23—712no—
616C23—712no—
617C23—712no—
618C23C24×D7111yescharacteristic
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—2848no—
635C2×C4—2848no—
636C2×C4—28416no—
637C2×C4—712no—
638C2×C4—712no—
639C2×C4—712no—
640C2×C4—712no—
641C2×C4—712no—
642C2×C4—712no—
643C2×C4—7116no—
644C2×C4—7116no—
645C2×C4—714no—
646C2×C4—712no—
647C2×C4—714no—
648C2×C4—1428no—
649C2×C4—14216no—
650C2×C4—14216no—
651C2×C4—1422no—
652C2×C4—1422no—
653C2×C4—1424no—
654C2×C4—1422no—
655C2×C4—1422no—
656C2×C4—1424no—
657C2×C4—1422no—
658C2×C4—1424no—
659C2×C4—1422no—
660C2×C4—1422no—
661C2×C4—1422no—
662C2×C4—1421no—
663C2×C4—1422no—
664C2×C4—1421no—
665C2×C4—1422no—
666C2×C4C2×D4×D7114yes—
667C2×C4C2×D4×D7112yes—
668C2×C4C2×Q8×D7112yes—
669C2×C4C2×Q8×D7114yes—
670C2×C4C2×Q8×D7112yes—
671C2×C4C2×Q8×D7112yes—
672C2×C4C2×Q8×D7112yes—
673C2×C4#41×D7112yes—
674C2×C4#41×D7112yes—
675C22—714no—
676C22—714no—
677C22—714no—
678C22—714no—
679C22—714no—
680C22—714no—
681C22—714no—
682C22C22×D4×D7111yescharacteristic
683C22C22×Q8×D7111yescharacteristic
684C22C22×Q8×D7111yescharacteristic
685C22C2×#41×D7111yescharacteristic
686C22C2×#41×D7111yescharacteristic
687C22H(5,𝔽2)×D7111yescharacteristic
688C222−1+4×D7111yescharacteristic
689C4—22no—
690C4—24no—
691C4—24no—
692C4—42no—
693C4—42no—
694C4—44no—
695C4—2842no—
696C4—2842no—
697C4—2844no—
698C4—714no—
699C4—714no—
700C4—1422no—
701C4—1424no—
702C4—1424no—
703C4#125×D7114yescomplemented
704C4C4⋊Q8×D7114yes—
705C2—718no—
706C2C2×#125×D7111yescharacteristic
707C2C2×C4⋊Q8×D7111yescharacteristic
708C2#544×D7111yescharacteristic
709C2#547×D7111yescharacteristic
710C2#550×D7111yescharacteristic
711C2#554×D7111yescharacteristic
712C2#557×D7111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC71×#2552C2
prime radicalC23×D71C24
hypercenter#2552D71
hypocenterC71C2×#2552
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2552

Complements

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

NH ≅ G/Ntype
2. #22593377C2semidirect
3. #22593376C2semidirect
4. #22593375C2semidirect
5. #22593374C2semidirect
6. #22593373C2semidirect
7. #22593372C2semidirect
8. #22593371C2semidirect
9. #22593370C2semidirect
17. C71×#2552C2semidirect
316. C4×D71#125semidirect
338. C4×C71C2×#125semidirect
346. Dic71C2×#125semidirect
356. D71#2552direct (N × H)
366. #2552D71direct (N × H)
374. C71C2×#2552semidirect
703. C4#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
#225933772
#225933762
#225933752
#225933742
#225933732
#225933722
#225933712
#225933702
#398×D712
#389×D712
#384×D712
C4×C4⋊C4×D712
C71×#25522
C2×#255271