Finite Group Databasebeta

← #32013815

Subgroups — #32013815

Order 18176.

1122 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986071C211yesmaximal, characteristic
2#22591289C211yesmaximal, characteristic
3#22589310C211yesmaximal, characteristic, complemented
4#22589298C211yesmaximal, characteristic, complemented
5#22588774C211yesmaximal, characteristic, complemented
6#22588764C211yesmaximal, characteristic, complemented
7#22588653C211yesmaximal, characteristic, complemented
8#22588653C211yesmaximal, characteristic, complemented
9#22588435C211yesmaximal, characteristic, complemented
10#22588430C211yesmaximal, characteristic, complemented
11#22588345C211yesmaximal, characteristic, complemented
12#22588170C211yesmaximal, characteristic, complemented
13#22588059C211yesmaximal, characteristic, complemented
14#22588056C211yesmaximal, characteristic, complemented
15C2×#552×C71C211yesmaximal, characteristic
16C22×#11765849C2211yescharacteristic
17C23×C71⋊C8C2211yescharacteristic
18C2×#14556087C2211yescharacteristic
19C2×#14556087C2211yescharacteristic
20#17986071—24no—
21C2×C4⋊(C71⋊C8)C2211yescharacteristic
22C2×#14556052C2211yescharacteristic
23C2×#14556052C2211yescharacteristic
24C2×#14556052C2211yescharacteristic
25C2×#14556052C2211yescharacteristic
26C2×C22⋊(C71⋊C8)C2211yescharacteristic
27C2×C22⋊(C71⋊C8)C2211yescharacteristic
28C2×#14556039C2211yescharacteristic
29#17985902—21no—
30#17985892—21no—
31#17985892—21no—
32#17985869C2211yescharacteristic
33#17985859C2211yescharacteristic
34#17985859C2211yescharacteristic
35C4⋊C4×Dic71—21no—
36C4×C4⋊Dic71C2211yescharacteristic
37#17985761C2211yescharacteristic
38#17985761C2211yescharacteristic
39#17985761C2211yescharacteristic
40#17985761C2211yescharacteristic
41#17985761C2211yescharacteristic
42#17985761C2211yescharacteristic
43#17985761C2211yescharacteristic
44#17985761C2211yescharacteristic
45#17985761C2211yescharacteristic
46#17985761C2211yescharacteristic
47#17985761C2211yescharacteristic
48#17985761C2211yescharacteristic
49#552×C71—24no—
50#552×C71C418yescomplemented
51C2×#126×C71—21no—
52C2×#125×C71—21no—
53C2×#125×C71C2211yescharacteristic
54C2×#123×C71—21no—
55C2×C22⋊Q8×C71C2211yescharacteristic
56C2×C22⋊Q8×C71C2211yescharacteristic
57C2×C4×Q8×C71C2211yescharacteristic
58C2×C4×D4×C71C2211yescharacteristic
59C2×#117×C71—21no—
60C2×#117×C71C2211yescharacteristic
61C22×C4⋊C4×C71C2211yescharacteristic
62C2×#11765849—22no—
63C2×#11765849—22no—
64C2×#11765849—41no—
65C22×C71⋊C8—22no—
66C22×C71⋊C8—22no—
67C22×C71⋊C8—41no—
68C22×C71⋊C8C2311yescharacteristic
69C22×C71⋊C8C2311yescharacteristic
70C22×C71⋊C8C2311yescharacteristic
71C22×C71⋊C8C2311yescharacteristic
72#14556087—22no—
73#14556087—22no—
74#14556087—41no—
75#14556087—41no—
76C2×C4⋊Dic71—21no—
77C2×C4⋊Dic71—21no—
78C2×C4⋊Dic71C2311yescharacteristic
79C2×C4⋊Dic71C2311yescharacteristic
80C2×C4⋊Dic71C2311yescharacteristic
81C2×C4⋊Dic71C2311yescharacteristic
82C2×C22⋊Dic71—21no—
83C2×C22⋊Dic71—21no—
84C2×C22⋊Dic71—21no—
85C2×C22⋊Dic71—21no—
86C2×C4×Dic71—21no—
87C2×C4×Dic71—21no—
88C2×C4×Dic71—21no—
89C4⋊(C71⋊C8)—22no—
90#14556052—22no—
91#14556052—22no—
92#14556052—41no—
93#14556052—41no—
94C22⋊(C71⋊C8)—22no—
95C22⋊(C71⋊C8)—22no—
96#14556039—22no—
97C71⋊#95—21no—
98C71⋊#95—21no—
99C71⋊#95—21no—
100C22×Q8×C71C2311yescharacteristic
101C22×D4×C71D411yescharacteristic
102C23×C4×C71—21no—
103C23×C4×C71C2311yescharacteristic
104C23×C4×C71C2311yescharacteristic
105#126×C71—28no—
106#125×C71—28no—
107#125×C71—22no—
108#125×C71C2×C414yes—
109#123×C71—28no—
110C22⋊Q8×C71—22no—
111C22⋊Q8×C71—22no—
112C22⋊Q8×C71C2×C414yes—
113C22⋊Q8×C71C2×C414yes—
114C4×Q8×C71—22no—
115C4×Q8×C71C2×C414yes—
116C4×D4×C71C2×C414yes—
117C4×D4×C71D414yes—
118#117×C71—22no—
119#117×C71—28no—
120#117×C71C2×C414yes—
121C2×C4⋊C4×C71—21no—
122C2×C4⋊C4×C71—22no—
123C2×C4⋊C4×C71—21no—
124C2×C4⋊C4×C71—21no—
125C2×C4⋊C4×C71—21no—
126C2×C4⋊C4×C71—21no—
127C2×C4⋊C4×C71—21no—
128C2×C4⋊C4×C71C2×C414yes—
129C2×C4⋊C4×C71D411yescharacteristic
130C2×C4⋊C4×C71C2311yescharacteristic
131C2×C4⋊C4×C71C2311yescharacteristic
132C2×C4⋊C4×C71C2311yescharacteristic
133C2×C22⋊C4×C71—21no—
134C2×C22⋊C4×C71—21no—
135C2×C22⋊C4×C71—21no—
136C2×C22⋊C4×C71D411yescharacteristic
137C2×C22⋊C4×C71D411yescharacteristic
138C2×C42×C71—21no—
139C2×C42×C71—21no—
140C2×C42×C71C2311yescharacteristic
141C22×Dic71—21no—
142C22×Dic71—21no—
143C22×Dic71—21no—
144C22×Dic71—21no—
145#11765849—44no—
146C2×C71⋊C8—21no—
147C2×C71⋊C8—21no—
148C2×C71⋊C8—21no—
149C2×C71⋊C8—21no—
150C2×C71⋊C8—21no—
151C2×C71⋊C8—21no—
152C2×C71⋊C8—21no—
153C2×C71⋊C8—21no—
154C2×C71⋊C8—21no—
155C2×C71⋊C8—21no—
156C2×C71⋊C8—21no—
157C2×C71⋊C8—44no—
158C2×C71⋊C8#4112yes—
159C4⋊Dic71—21no—
160C4⋊Dic71—21no—
161C4⋊Dic71—21no—
162C4⋊Dic71—21no—
163C4⋊Dic71—21no—
164C4⋊Dic71—21no—
165C4⋊Dic71—21no—
166C4⋊Dic71—42no—
167C4⋊Dic71—81no—
168C4⋊Dic71#4112yes—
169C22⋊Dic71—42no—
170C22⋊Dic71—42no—
171C22⋊Dic71—81no—
172C22⋊Dic71—81no—
173C4×Dic71—42no—
174C4×Dic71—42no—
175C4×Dic71—42no—
176C24×C71C2×D411yescharacteristic
177C24×C71C2×D411yescharacteristic
178C2×Q8×C71—21no—
179C2×Q8×C71—21no—
180C2×Q8×C71—21no—
181C2×Q8×C71—21no—
182C2×Q8×C71—21no—
183C2×Q8×C71C22×C412yes—
184C2×D4×C71—41no—
185C2×D4×C71—41no—
186C2×D4×C71C22⋊C414yes—
187C22×C4×C71—21no—
188C22×C4×C71—21no—
189C22×C4×C71—21no—
190C22×C4×C71—21no—
191C22×C4×C71—21no—
192C22×C4×C71—21no—
193C22×C4×C71—21no—
194C22×C4×C71—21no—
195C22×C4×C71—24no—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—21no—
200C22×C4×C71—42no—
201C22×C4×C71—42no—
202C22×C4×C71C22×C412yes—
203C22×C4×C71C22×C412yes—
204C22×C4×C71C2×D411yescharacteristic
205C22×C4×C71C2×D411yescharacteristic
206C22×C4×C71C2×D411yescharacteristic
207C22×C4×C71C2×D411yescharacteristic
208C22×C4×C71C2×D412yes—
209C22×C4×C71C2×D412yes—
210C22×C4×C71C2411yescharacteristic
211C4⋊C4×C71—24no—
212C4⋊C4×C71—24no—
213C4⋊C4×C71—24no—
214C4⋊C4×C71—24no—
215C4⋊C4×C71—24no—
216C4⋊C4×C71—24no—
217C4⋊C4×C71—21no—
218C4⋊C4×C71—21no—
219C4⋊C4×C71—21no—
220C4⋊C4×C71C22⋊C414yes—
221C4⋊C4×C71C22×C412yes—
222C4⋊C4×C71C22×C412yes—
223C4⋊C4×C71C22×C412yes—
224C22⋊C4×C71—24no—
225C22⋊C4×C71—24no—
226C22⋊C4×C71—24no—
227C22⋊C4×C71C22⋊C414yes—
228C22⋊C4×C71C22⋊C414yes—
229C42×C71—24no—
230C42×C71—24no—
231C42×C71C22×C412yes—
232C42×C71C2×D412yes—
233C23×C71—21no—
234C23×C71—21no—
235C23×C71—21no—
236C23×C71—21no—
237C23×C71—21no—
238C23×C71—21no—
239C23×C71—21no—
240C23×C71—21no—
241C23×C71—21no—
242C23×C71—21no—
243C23×C71—21no—
244C23×C71—21no—
245C23×C71C2×C22⋊C412yes—
246C23×C71C2×C22⋊C412yes—
247C23×C71C22×D411yescharacteristic
248Q8×C71—22no—
249Q8×C71—22no—
250Q8×C71—41no—
251Q8×C71—41no—
252D4×C71—44no—
253C2×C4×C71—21no—
254C2×C4×C71—21no—
255C2×C4×C71—21no—
256C2×C4×C71—21no—
257C2×C4×C71—21no—
258C2×C4×C71—21no—
259C2×C4×C71—21no—
260C2×C4×C71—21no—
261C2×C4×C71—22no—
262C2×C4×C71—22no—
263C2×C4×C71—22no—
264C2×C4×C71—22no—
265C2×C4×C71—22no—
266C2×C4×C71—22no—
267C2×C4×C71—22no—
268C2×C4×C71—22no—
269C2×C4×C71—22no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—48no—
274C2×C4×C71—41no—
275C2×C4×C71—41no—
276C2×C4×C71—41no—
277C2×C4×C71—41no—
278C2×C4×C71—41no—
279C2×C4×C71—41no—
280C2×C4×C71—41no—
281C2×C4×C71—41no—
282C2×C4×C71C2×C22⋊C412yes—
283C2×C4×C71C2×C22⋊C412yes—
284C2×C4×C71C2×C22⋊C412yes—
285C2×C4×C71C2×C22⋊C412yes—
286C2×C4×C71C23×C411yescharacteristic
287C2×C4×C71C22×D411yescharacteristic
288C2×C4×C71C2×#4111yescharacteristic
289C2×C4×C71C2×#4111yescharacteristic
290C2×C4×C71H(5,𝔽2)11yescharacteristic
291C2×C4×C712−1+411yescharacteristic
292C2×Dic71—22no—
293C2×Dic71—41no—
294C2×Dic71—41no—
295C2×Dic71—41no—
296C2×Dic71—41no—
297C2×Dic71—41no—
298C2×Dic71—41no—
299C2×Dic71—41no—
300C2×Dic71—41no—
301C2×Dic71—41no—
302C2×Dic71—41no—
303C2×Dic71—41no—
304C71⋊C8—22no—
305C71⋊C8—41no—
306C71⋊C8—41no—
307C71⋊C8—41no—
308C22×C71—22no—
309C22×C71—22no—
310C22×C71—22no—
311C22×C71—22no—
312C22×C71—22no—
313C22×C71—22no—
314C22×C71—41no—
315C22×C71—41no—
316C22×C71—41no—
317C22×C71—41no—
318C22×C71—41no—
319C22×C71—41no—
320C22×C71—41no—
321C22×C71—41no—
322C22×C71C22×C22⋊C411yescharacteristic
323C22×C71#54611yescharacteristic
324C22×C71#54711yescharacteristic
325C22×C71#57511yescharacteristic
326C22×C71#57511yescharacteristic
327C22×C71#57711yescharacteristic
328C22×C71#57811yescharacteristic
329C4×C71—22no—
330C4×C71—22no—
331C4×C71—22no—
332C4×C71—22no—
333C4×C71—42no—
334C4×C71—42no—
335C4×C71—42no—
336C4×C71—42no—
337C4×C71C4×#4111yescharacteristic
338C4×C71#52011yescharacteristic
339C4×C71#54611yescharacteristic
340C4×C71#54711yescharacteristic
341Dic71—42no—
342Dic71—81no—
343Dic71—81no—
344Dic71—81no—
345#22496—711nomaximal, Sylow
346C2×C71—42no—
347C2×C71—42no—
348C2×C71#233911yescharacteristic
349C2×C71#289611yescharacteristic
350C2×C71#289811yescharacteristic
351C2×C71#331511yescharacteristic
352C2×C71#331711yescharacteristic
353C2×C71#334811yescharacteristic
354C2×C71#334911yescharacteristic
355C2×#552D7111yescharacteristic
356C2×#435—711no—
357#2354—711no—
358#1992—711no—
359#1989—711no—
360#1894—711no—
361#1892—711no—
362#1873—711no—
363#1873—711no—
364#1825—711no—
365#1824—711no—
366#1803—711no—
367#1763—711no—
368#1736—711no—
369#1735—711no—
370C71#2249611yescharacteristic, complemented, Sylow
371C22×M16—711no—
372C23×C8—711no—
373#552—24no—
374#552Dic7118yescomplemented
375C2×#126—21no—
376C2×#125—21no—
377C2×#125C2×D7111yescharacteristic
378C2×#123—21no—
379C2×C22⋊Q8C2×D7111yescharacteristic
380C2×C22⋊Q8C2×D7111yescharacteristic
381C2×C4×Q8C2×D7111yescharacteristic
382C2×C4×D4C2×D7111yescharacteristic
383C2×#117—21no—
384C2×#117—711no—
385C2×#117—711no—
386C2×#117C2×D7111yescharacteristic
387C22×C4⋊C4C2×D7111yescharacteristic
388#435—1424no—
389C2×C4⋊C8—711no—
390C2×#103—711no—
391C2×#103—711no—
392C2×#103—711no—
393C2×#103—711no—
394C2×C22⋊C8—711no—
395C2×C22⋊C8—711no—
396C2×#97—711no—
397#390—1421no—
398#388—1421no—
399#388—1421no—
400#384—711no—
401#380—711no—
402#380—711no—
403C4×C4⋊C4—711no—
404C4×C4⋊C4—1421no—
405#340—711no—
406#340—711no—
407#340—711no—
408#340—711no—
409#340—711no—
410#340—711no—
411#340—711no—
412#340—711no—
413#340—711no—
414#340—711no—
415#340—711no—
416#340—711no—
417C22×Q8C22×D7111yescharacteristic
418C22×D4C22⋊D7111yescharacteristic
419C23×C4—21no—
420C23×C4C22×D7111yescharacteristic
421C23×C4C22×D7111yescharacteristic
422C2×M16—2841no—
423C2×M16—1422no—
424C2×M16—1422no—
425C22×C8—2841no—
426C22×C8—711no—
427C22×C8—711no—
428C22×C8—711no—
429C22×C8—711no—
430C22×C8—1422no—
431C22×C8—1422no—
432#126—28no—
433#125—28no—
434#125—22no—
435#125C2×Dic7114yes—
436#123—28no—
437C22⋊Q8—22no—
438C22⋊Q8—22no—
439C22⋊Q8C2×Dic7114yes—
440C22⋊Q8C2×Dic7114yes—
441C4×Q8—22no—
442C4×Q8C2×Dic7114yes—
443C4×D4C2×Dic7114yes—
444C4×D4C22⋊D7114yes—
445#117—22no—
446#117—28no—
447#117—2841no—
448#117—2841no—
449#117—1422no—
450#117—1422no—
451#117C2×Dic7114yes—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—711no—
460C2×C4⋊C4—711no—
461C2×C4⋊C4—711no—
462C2×C4⋊C4—711no—
463C2×C4⋊C4—1421no—
464C2×C4⋊C4—1421no—
465C2×C4⋊C4C2×Dic7114yes—
466C2×C4⋊C4C22⋊D7111yescharacteristic
467C2×C4⋊C4C22×D7111yescharacteristic
468C2×C4⋊C4C22×D7111yescharacteristic
469C2×C4⋊C4C22×D7111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—1421no—
474C2×C22⋊C4—1421no—
475C2×C22⋊C4—1421no—
476C2×C22⋊C4—1421no—
477C2×C22⋊C4C22⋊D7111yescharacteristic
478C2×C22⋊C4C22⋊D7111yescharacteristic
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—1421no—
482C2×C42—1421no—
483C2×C42—1421no—
484C2×C42C22×D7111yescharacteristic
485C4⋊C8—1422no—
486#103—2841no—
487#103—2841no—
488#103—1422no—
489#103—1422no—
490C22⋊C8—1422no—
491C22⋊C8—1422no—
492#97—1422no—
493#95—1421no—
494#95—1421no—
495#95—1421no—
496C24C2×C22⋊D7111yescharacteristic
497C24C2×C22⋊D7111yescharacteristic
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8C22×Dic7112yes—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4C22⋊Dic7114yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—24no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—1421no—
523C22×C4—1421no—
524C22×C4—1421no—
525C22×C4—1421no—
526C22×C4C22×Dic7112yes—
527C22×C4C22×Dic7112yes—
528C22×C4C2×C22⋊D7112yes—
529C22×C4C2×C22⋊D7112yes—
530C22×C4C2×C22⋊D7111yescharacteristic
531C22×C4C2×C22⋊D7111yescharacteristic
532C22×C4C2×C22⋊D7111yescharacteristic
533C22×C4C2×C22⋊D7111yescharacteristic
534C22×C4C23×D7111yescharacteristic
535M16—2844no—
536C2×C8—2844no—
537C2×C8—712no—
538C2×C8—1421no—
539C2×C8—1421no—
540C2×C8—1421no—
541C2×C8—1421no—
542C2×C8—1421no—
543C2×C8—1421no—
544C2×C8—1421no—
545C2×C8—1421no—
546C2×C8—1421no—
547C2×C8—1421no—
548C2×C8—1421no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—2842no—
559C4⋊C4—5681no—
560C4⋊C4—712no—
561C4⋊C4—1421no—
562C4⋊C4—1421no—
563C4⋊C4—1421no—
564C4⋊C4—1421no—
565C4⋊C4—1421no—
566C4⋊C4—1421no—
567C4⋊C4—1421no—
568C4⋊C4C22⋊Dic7114yes—
569C4⋊C4C22×Dic7112yes—
570C4⋊C4C22×Dic7112yes—
571C4⋊C4C22×Dic7112yes—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—2842no—
576C22⋊C4—2842no—
577C22⋊C4—5681no—
578C22⋊C4—5681no—
579C22⋊C4C22⋊Dic7114yes—
580C22⋊C4C22⋊Dic7114yes—
581C42—24no—
582C42—24no—
583C42—2842no—
584C42—2842no—
585C42—2842no—
586C42C22×Dic7112yes—
587C42C2×C22⋊D7112yes—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23C2×C22⋊Dic7112yes—
601C23C2×C22⋊Dic7112yes—
602C23C22×C22⋊D7111yescharacteristic
603Q8—22no—
604Q8—22no—
605Q8—41no—
606Q8—41no—
607D4—44no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—48no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—2841no—
638C2×C4—2841no—
639C2×C4—2841no—
640C2×C4—2841no—
641C2×C4—2841no—
642C2×C4—2841no—
643C2×C4—2841no—
644C2×C4—2841no—
645C2×C4—2841no—
646C2×C4—2841no—
647C2×C4—2841no—
648C2×C4—1422no—
649C2×C4C2×C22⋊Dic7112yes—
650C2×C4C2×C22⋊Dic7112yes—
651C2×C4C2×C22⋊Dic7112yes—
652C2×C4C2×C22⋊Dic7112yes—
653C2×C4C23×Dic7111yescharacteristic
654C2×C4C22×C22⋊D7111yescharacteristic
655C2×C4#41×D7111yescharacteristic
656C2×C4#41×D7111yescharacteristic
657C2×C4#1455617411yescharacteristic
658C2×C4#1455617511yescharacteristic
659C8—2841no—
660C8—2841no—
661C8—2841no—
662C8—1422no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22C22×C22⋊Dic7111yescharacteristic
678C22#1798663711yescharacteristic
679C22#1798664811yescharacteristic
680C22#1798679711yescharacteristic
681C22#1798679711yescharacteristic
682C22#1798680711yescharacteristic
683C22#1798681411yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—2842no—
693C4—5681no—
694C4—5681no—
695C4—5681no—
696C4#41×Dic7111yescharacteristic
697C4#1798648211yescharacteristic
698C4#1798663711yescharacteristic
699C4#1798664811yescharacteristic
700C2—42no—
701C2—42no—
702C2#2259117011yescharacteristic
703C2#2259685911yescharacteristic
704C2#2259687311yescharacteristic
705C2#2260043011yescharacteristic
706C2#2260046011yescharacteristic
707C2#2260084911yescharacteristic
708C2#2260087011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC2×#552×C71C2
socleC23×C71C22×D4
prime radicalC22×D4×C71D4
cosocleC22×C4×C71C24
hypercenterC2×#552D71
hypocenterC71#22496
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
3. #22589310C2semidirect
4. #22589298C2semidirect
5. #22588774C2semidirect
6. #22588764C2semidirect
7. #22588653C2semidirect
8. #22588653C2semidirect
9. #22588435C2semidirect
10. #22588430C2semidirect
11. #22588345C2semidirect
12. #22588170C2semidirect
13. #22588059C2semidirect
14. #22588056C2semidirect
50. #552×C71C4semidirect
370. C71#22496semidirect
374. #552Dic71semidirect

Maximal subgroups

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

subgroupindex
C2×#179860712
#225912892
#225893102
#225892982
#225887742
#225887642
#225886532
#225884352
#225884302
#225883452
#225881702
#225880592
#225880562
C2×#552×C712
#2249671