Finite Group Databasebeta

← #32013740

Subgroups — #32013740

Order 18176.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986071C211yesmaximal, characteristic
2D4×C4⋊Dic71C211yesmaximal, characteristic
3#22589310C211yesmaximal, characteristic, complemented
4#22589298C211yesmaximal, characteristic, complemented
5#22588774C211yesmaximal, characteristic, complemented
6#22588764C211yesmaximal, characteristic, complemented
7#22588648C211yesmaximal, characteristic, complemented
8#22588648C211yesmaximal, characteristic, complemented
9#22588435C211yesmaximal, characteristic, complemented
10#22588426C211yesmaximal, characteristic, complemented
11#22588345C211yesmaximal, characteristic, complemented
12#22588170C211yesmaximal, characteristic, complemented
13#22588061C211yesmaximal, characteristic, complemented
14C2×#17985761C211yesmaximal, characteristic, complemented
15C2×#552×C71C211yesmaximal, characteristic
16C22×#11765849C2211yescharacteristic
17C23×C71⋊C8C2211yescharacteristic
18C2×D4×Dic71—21no—
19C22×C4⋊Dic71C2211yescharacteristic
20C22×C4⋊Dic71C2211yescharacteristic
21#17986071—24no—
22C2×C4⋊(C71⋊C8)C2211yescharacteristic
23C2×#14556052C2211yescharacteristic
24C2×#14556052C2211yescharacteristic
25C2×#14556052C2211yescharacteristic
26C2×#14556052C2211yescharacteristic
27C2×C22⋊(C71⋊C8)C2211yescharacteristic
28C2×C22⋊(C71⋊C8)C2211yescharacteristic
29C2×#14556039C2211yescharacteristic
30#17985898—21no—
31#17985874—21no—
32#17985874—21no—
33#17985869C2211yescharacteristic
34#17985859C2211yescharacteristic
35#17985859C2211yescharacteristic
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
62C23×Dic71—21no—
63C23×Dic71—21no—
64C2×#11765849—22no—
65C2×#11765849—22no—
66C2×#11765849—41no—
67C22×C71⋊C8—22no—
68C22×C71⋊C8—22no—
69C22×C71⋊C8—41no—
70C22×C71⋊C8C2311yescharacteristic
71C22×C71⋊C8C2311yescharacteristic
72C22×C71⋊C8C2311yescharacteristic
73C22×C71⋊C8C2311yescharacteristic
74D4×Dic71—44no—
75C2×C4⋊Dic71—22no—
76C2×C4⋊Dic71—22no—
77C2×C4⋊Dic71—21no—
78C2×C4⋊Dic71—21no—
79C2×C4⋊Dic71—21no—
80C2×C4⋊Dic71—21no—
81C2×C4⋊Dic71—41no—
82C2×C4⋊Dic71—41no—
83C2×C4⋊Dic71C2311yescharacteristic
84C2×C4⋊Dic71C2311yescharacteristic
85C2×C4⋊Dic71C2311yescharacteristic
86C2×C4⋊Dic71C2311yescharacteristic
87C2×C22⋊Dic71—21no—
88C2×C22⋊Dic71—21no—
89C2×C4×Dic71—21no—
90C4⋊(C71⋊C8)—22no—
91#14556052—22no—
92#14556052—22no—
93#14556052—41no—
94#14556052—41no—
95C22⋊(C71⋊C8)—22no—
96C22⋊(C71⋊C8)—22no—
97#14556039—22no—
98C71⋊#95—21no—
99C71⋊#95—21no—
100C71⋊#95—21no—
101C22×Q8×C71C2311yescharacteristic
102C22×D4×C71D411yescharacteristic
103C23×C4×C71—21no—
104C23×C4×C71C2311yescharacteristic
105C23×C4×C71C2311yescharacteristic
106#126×C71—28no—
107#125×C71—28no—
108#125×C71—22no—
109#125×C71C2×C414yescomplemented
110#123×C71—28no—
111C22⋊Q8×C71—22no—
112C22⋊Q8×C71—22no—
113C22⋊Q8×C71C2×C414yescomplemented
114C22⋊Q8×C71C2×C414yescomplemented
115C4×Q8×C71—22no—
116C4×Q8×C71C2×C414yescomplemented
117C4×D4×C71C2×C414yes—
118C4×D4×C71D414yes—
119#117×C71—22no—
120#117×C71—28no—
121#117×C71C2×C414yescomplemented
122C2×C4⋊C4×C71—21no—
123C2×C4⋊C4×C71—22no—
124C2×C4⋊C4×C71—21no—
125C2×C4⋊C4×C71—21no—
126C2×C4⋊C4×C71—21no—
127C2×C4⋊C4×C71—21no—
128C2×C4⋊C4×C71—21no—
129C2×C4⋊C4×C71C2×C414yescomplemented
130C2×C4⋊C4×C71D411yescharacteristic
131C2×C4⋊C4×C71C2311yescharacteristic
132C2×C4⋊C4×C71C2311yescharacteristic
133C2×C4⋊C4×C71C2311yescharacteristic
134C2×C22⋊C4×C71—21no—
135C2×C22⋊C4×C71—21no—
136C2×C22⋊C4×C71—21no—
137C2×C22⋊C4×C71D411yescharacteristic
138C2×C22⋊C4×C71D411yescharacteristic
139C2×C42×C71—21no—
140C2×C42×C71—21no—
141C2×C42×C71C2311yescharacteristic
142C22×Dic71—21no—
143C22×Dic71—21no—
144C22×Dic71—21no—
145C22×Dic71—21no—
146C22×Dic71—42no—
147C22×Dic71—42no—
148C22×Dic71—42no—
149C22×Dic71—42no—
150C22×Dic71—81no—
151C22×Dic71—81no—
152#11765849—44no—
153C2×C71⋊C8—21no—
154C2×C71⋊C8—21no—
155C2×C71⋊C8—21no—
156C2×C71⋊C8—21no—
157C2×C71⋊C8—21no—
158C2×C71⋊C8—21no—
159C2×C71⋊C8—21no—
160C2×C71⋊C8—21no—
161C2×C71⋊C8—21no—
162C2×C71⋊C8—21no—
163C2×C71⋊C8—21no—
164C2×C71⋊C8—44no—
165C2×C71⋊C8#4112yes—
166C4⋊Dic71—21no—
167C4⋊Dic71—21no—
168C4⋊Dic71—21no—
169C4⋊Dic71—21no—
170C4⋊Dic71—21no—
171C4⋊Dic71—21no—
172C4⋊Dic71—21no—
173C4⋊Dic71—42no—
174C4⋊Dic71—42no—
175C4⋊Dic71—42no—
176C4⋊Dic71—81no—
177C4⋊Dic71#4112yes—
178C22⋊Dic71—42no—
179C22⋊Dic71—42no—
180C4×Dic71—42no—
181C24×C71C2×D411yescharacteristic
182C24×C71C2×D411yescharacteristic
183C2×Q8×C71—21no—
184C2×Q8×C71—21no—
185C2×Q8×C71—21no—
186C2×Q8×C71—21no—
187C2×Q8×C71—21no—
188C2×Q8×C71C22×C412yes—
189C2×D4×C71—22no—
190C2×D4×C71—22no—
191C2×D4×C71C22⋊C414yes—
192C22×C4×C71—21no—
193C22×C4×C71—21no—
194C22×C4×C71—21no—
195C22×C4×C71—21no—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—21no—
200C22×C4×C71—24no—
201C22×C4×C71—21no—
202C22×C4×C71—21no—
203C22×C4×C71—21no—
204C22×C4×C71—21no—
205C22×C4×C71—42no—
206C22×C4×C71—42no—
207C22×C4×C71C22×C412yes—
208C22×C4×C71C22×C412yes—
209C22×C4×C71C2×D411yescharacteristic
210C22×C4×C71C2×D411yescharacteristic
211C22×C4×C71C2×D411yescharacteristic
212C22×C4×C71C2×D411yescharacteristic
213C22×C4×C71C2×D412yes—
214C22×C4×C71C2×D412yes—
215C22×C4×C71C2411yescharacteristic
216C4⋊C4×C71—24no—
217C4⋊C4×C71—24no—
218C4⋊C4×C71—24no—
219C4⋊C4×C71—24no—
220C4⋊C4×C71—24no—
221C4⋊C4×C71—24no—
222C4⋊C4×C71—21no—
223C4⋊C4×C71—21no—
224C4⋊C4×C71—21no—
225C4⋊C4×C71C22⋊C414yes—
226C4⋊C4×C71C22×C412yes—
227C4⋊C4×C71C22×C412yes—
228C4⋊C4×C71C22×C412yes—
229C22⋊C4×C71—24no—
230C22⋊C4×C71—24no—
231C22⋊C4×C71—24no—
232C22⋊C4×C71C22⋊C414yes—
233C22⋊C4×C71C22⋊C414yes—
234C42×C71—24no—
235C42×C71—24no—
236C42×C71C22×C412yes—
237C42×C71C2×D412yes—
238C23×C71—21no—
239C23×C71—21no—
240C23×C71—21no—
241C23×C71—21no—
242C23×C71—21no—
243C23×C71—21no—
244C23×C71—21no—
245C23×C71—21no—
246C23×C71—21no—
247C23×C71—21no—
248C23×C71C2×C22⋊C412yes—
249C23×C71C2×C22⋊C412yes—
250C23×C71AGL(1,ℤ/8)12yes—
251C23×C71#13712yes—
252C23×C71C22×D411yescharacteristic
253Q8×C71—22no—
254Q8×C71—22no—
255Q8×C71—41no—
256Q8×C71—41no—
257D4×C71—28no—
258C2×C4×C71—21no—
259C2×C4×C71—21no—
260C2×C4×C71—21no—
261C2×C4×C71—21no—
262C2×C4×C71—21no—
263C2×C4×C71—21no—
264C2×C4×C71—21no—
265C2×C4×C71—21no—
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—22no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—41no—
279C2×C4×C71—41no—
280C2×C4×C71—41no—
281C2×C4×C71—41no—
282C2×C4×C71—41no—
283C2×C4×C71—41no—
284C2×C4×C71—41no—
285C2×C4×C71—41no—
286C2×C4×C71—48no—
287C2×C4×C71C2×C22⋊C412yes—
288C2×C4×C71C2×C22⋊C412yes—
289C2×C4×C71C2×C22⋊C412yes—
290C2×C4×C71C2×C22⋊C412yes—
291C2×C4×C71C23×C411yescharacteristic
292C2×C4×C71C22×D411yescharacteristic
293C2×C4×C71C2×#4111yescharacteristic
294C2×C4×C71C2×#4111yescharacteristic
295C2×C4×C71H(5,𝔽2)11yescharacteristic
296C2×C4×C712−1+411yescharacteristic
297C2×Dic71—22no—
298C2×Dic71—41no—
299C2×Dic71—41no—
300C2×Dic71—41no—
301C2×Dic71—41no—
302C2×Dic71—41no—
303C2×Dic71—41no—
304C2×Dic71—41no—
305C2×Dic71—41no—
306C2×Dic71—41no—
307C2×Dic71—41no—
308C2×Dic71—41no—
309C2×Dic71—84no—
310C2×Dic71—84no—
311C71⋊C8—22no—
312C71⋊C8—41no—
313C71⋊C8—41no—
314C71⋊C8—41no—
315C22×C71—22no—
316C22×C71—22no—
317C22×C71—22no—
318C22×C71—22no—
319C22×C71—22no—
320C22×C71—22no—
321C22×C71—22no—
322C22×C71—22no—
323C22×C71—22no—
324C22×C71—41no—
325C22×C71—41no—
326C22×C71—41no—
327C22×C71—41no—
328C22×C71#41714yes—
329C22×C71C22×C22⋊C411yescharacteristic
330C22×C71#54611yescharacteristic
331C22×C71#54711yescharacteristic
332C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C71C2×#13711yescharacteristic
334C22×C71#57711yescharacteristic
335C22×C71#57811yescharacteristic
336C4×C71—22no—
337C4×C71—22no—
338C4×C71—22no—
339C4×C71—22no—
340C4×C71—42no—
341C4×C71—42no—
342C4×C71—42no—
343C4×C71—42no—
344C4×C71C4×#4111yescharacteristic
345C4×C71#52011yescharacteristic
346C4×C71#54611yescharacteristic
347C4×C71#54711yescharacteristic
348Dic71—42no—
349Dic71—81no—
350Dic71—81no—
351Dic71—81no—
352#22491—711nomaximal, Sylow
353C2×C71—24no—
354C2×C71—42no—
355C2×C71#233911yescharacteristic
356C2×C71C2×#41711yescharacteristic
357C2×C71#289811yescharacteristic
358C2×C71#331011yescharacteristic
359C2×C71#331211yescharacteristic
360C2×C71#334311yescharacteristic
361C2×C71#334411yescharacteristic
362C2×#552D7111yescharacteristic
363C2×#435—711no—
364D4×C4⋊C4—711no—
365#1992—711no—
366#1989—711no—
367#1894—711no—
368#1892—711no—
369#1872—711no—
370#1872—711no—
371#1825—711no—
372#1823—711no—
373#1803—711no—
374#1763—711no—
375#1736—711no—
376C2×#340—711no—
377C71#2249111yescharacteristic, complemented, Sylow
378C22×M16—711no—
379C23×C8—711no—
380#552—24no—
381#552Dic7118yescomplemented
382C2×#126—21no—
383C2×#125—21no—
384C2×#125C2×D7111yescharacteristic
385C2×#123—21no—
386C2×C22⋊Q8C2×D7111yescharacteristic
387C2×C22⋊Q8C2×D7111yescharacteristic
388C2×C4×Q8C2×D7111yescharacteristic
389C2×C4×D4—1421no—
390C2×C4×D4C2×D7111yescharacteristic
391C2×#117—21no—
392C2×#117C2×D7111yescharacteristic
393C22×C4⋊C4—711no—
394C22×C4⋊C4—711no—
395C22×C4⋊C4C2×D7111yescharacteristic
396#435—1424no—
397C2×C4⋊C8—711no—
398C2×#103—711no—
399C2×#103—711no—
400C2×#103—711no—
401C2×#103—711no—
402C2×C22⋊C8—711no—
403C2×C22⋊C8—711no—
404C2×#97—711no—
405#389—1421no—
406#385—1421no—
407#385—1421no—
408#384—711no—
409#380—711no—
410#380—711no—
411C4×C4⋊C4—711no—
412#340—711no—
413#340—711no—
414#340—711no—
415#340—711no—
416#340—711no—
417#340—711no—
418#340—711no—
419#340—711no—
420#340—711no—
421#340—711no—
422#340—711no—
423#340—711no—
424C22×Q8C22×D7111yescharacteristic
425C22×D4C22⋊D7111yescharacteristic
426C23×C4—21no—
427C23×C4—1421no—
428C23×C4—1421no—
429C23×C4C22×D7111yescharacteristic
430C23×C4C22×D7111yescharacteristic
431C2×M16—2841no—
432C2×M16—1422no—
433C2×M16—1422no—
434C22×C8—2841no—
435C22×C8—711no—
436C22×C8—711no—
437C22×C8—711no—
438C22×C8—711no—
439C22×C8—1422no—
440C22×C8—1422no—
441#126—28no—
442#125—28no—
443#125—22no—
444#125C2×Dic7114yescomplemented
445#123—28no—
446C22⋊Q8—22no—
447C22⋊Q8—22no—
448C22⋊Q8C2×Dic7114yescomplemented
449C22⋊Q8C2×Dic7114yescomplemented
450C4×Q8—22no—
451C4×Q8C2×Dic7114yescomplemented
452C4×D4—2844no—
453C4×D4C2×Dic7114yes—
454C4×D4C22⋊D7114yes—
455#117—22no—
456#117—28no—
457#117C2×Dic7114yescomplemented
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—2841no—
466C2×C4⋊C4—2841no—
467C2×C4⋊C4—711no—
468C2×C4⋊C4—711no—
469C2×C4⋊C4—711no—
470C2×C4⋊C4—711no—
471C2×C4⋊C4—1421no—
472C2×C4⋊C4—1421no—
473C2×C4⋊C4—1421no—
474C2×C4⋊C4—1422no—
475C2×C4⋊C4—1422no—
476C2×C4⋊C4—1421no—
477C2×C4⋊C4C2×Dic7114yescomplemented
478C2×C4⋊C4C22⋊D7111yescharacteristic
479C2×C4⋊C4C22×D7111yescharacteristic
480C2×C4⋊C4C22×D7111yescharacteristic
481C2×C4⋊C4C22×D7111yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—1421no—
486C2×C22⋊C4—1421no—
487C2×C22⋊C4C22⋊D7111yescharacteristic
488C2×C22⋊C4C22⋊D7111yescharacteristic
489C2×C42—21no—
490C2×C42—21no—
491C2×C42—1421no—
492C2×C42C22×D7111yescharacteristic
493C4⋊C8—1422no—
494#103—2841no—
495#103—2841no—
496#103—1422no—
497#103—1422no—
498C22⋊C8—1422no—
499C22⋊C8—1422no—
500#97—1422no—
501#95—1421no—
502#95—1421no—
503#95—1421no—
504C24C2×C22⋊D7111yescharacteristic
505C24C2×C22⋊D7111yescharacteristic
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8C22×Dic7112yes—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4C22⋊Dic7114yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—24no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—2842no—
531C22×C4—2842no—
532C22×C4—2842no—
533C22×C4—2842no—
534C22×C4—5681no—
535C22×C4—5681no—
536C22×C4—1421no—
537C22×C4—1421no—
538C22×C4—1421no—
539C22×C4—1421no—
540C22×C4C22×Dic7112yes—
541C22×C4C22×Dic7112yes—
542C22×C4C2×C22⋊D7112yes—
543C22×C4C2×C22⋊D7112yes—
544C22×C4C2×C22⋊D7111yescharacteristic
545C22×C4C2×C22⋊D7111yescharacteristic
546C22×C4C2×C22⋊D7111yescharacteristic
547C22×C4C2×C22⋊D7111yescharacteristic
548C22×C4C23×D7111yescharacteristic
549M16—2844no—
550C2×C8—2844no—
551C2×C8—712no—
552C2×C8—1421no—
553C2×C8—1421no—
554C2×C8—1421no—
555C2×C8—1421no—
556C2×C8—1421no—
557C2×C8—1421no—
558C2×C8—1421no—
559C2×C8—1421no—
560C2×C8—1421no—
561C2×C8—1421no—
562C2×C8—1421no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—2842no—
573C4⋊C4—2842no—
574C4⋊C4—2842no—
575C4⋊C4—5681no—
576C4⋊C4—712no—
577C4⋊C4—1421no—
578C4⋊C4—1421no—
579C4⋊C4—1421no—
580C4⋊C4—1421no—
581C4⋊C4—1421no—
582C4⋊C4—1421no—
583C4⋊C4—1421no—
584C4⋊C4C22⋊Dic7114yes—
585C4⋊C4C22×Dic7112yes—
586C4⋊C4C22×Dic7112yes—
587C4⋊C4C22×Dic7112yes—
588C22⋊C4—24no—
589C22⋊C4—24no—
590C22⋊C4—24no—
591C22⋊C4—2842no—
592C22⋊C4—2842no—
593C22⋊C4C22⋊Dic7114yes—
594C22⋊C4C22⋊Dic7114yes—
595C42—24no—
596C42—24no—
597C42—2842no—
598C42C22×Dic7112yes—
599C42C2×C22⋊D7112yes—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23C2×C22⋊Dic7112yes—
611C23C2×C22⋊Dic7112yes—
612C23#1455615312yes—
613C23#1455615812yes—
614C23C22×C22⋊D7111yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—48no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—2841no—
650C2×C4—2841no—
651C2×C4—2841no—
652C2×C4—2841no—
653C2×C4—2841no—
654C2×C4—2841no—
655C2×C4—2841no—
656C2×C4—2841no—
657C2×C4—2841no—
658C2×C4—2841no—
659C2×C4—2841no—
660C2×C4—5684no—
661C2×C4—5684no—
662C2×C4—1422no—
663C2×C4C2×C22⋊Dic7112yes—
664C2×C4C2×C22⋊Dic7112yes—
665C2×C4C2×C22⋊Dic7112yes—
666C2×C4C2×C22⋊Dic7112yes—
667C2×C4C23×Dic7111yescharacteristic
668C2×C4C22×C22⋊D7111yescharacteristic
669C2×C4#41×D7111yescharacteristic
670C2×C4#41×D7111yescharacteristic
671C2×C4#1455617411yescharacteristic
672C2×C4#1455617511yescharacteristic
673C8—2841no—
674C8—2841no—
675C8—2841no—
676C8—1422no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1798600014yes—
691C22C22×C22⋊Dic7111yescharacteristic
692C22#1798663711yescharacteristic
693C22#1798664811yescharacteristic
694C22C2×#1455615311yescharacteristic
695C22C2×#1455615811yescharacteristic
696C22#1798680711yescharacteristic
697C22#1798681411yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—2842no—
707C4—5681no—
708C4—5681no—
709C4—5681no—
710C4#41×Dic7111yescharacteristic
711C4#1798648211yescharacteristic
712C4#1798663711yescharacteristic
713C4#1798664811yescharacteristic
714C2—24no—
715C2—42no—
716C2#2259117011yescharacteristic
717C2C2×#1798600011yescharacteristic
718C2#2259687311yescharacteristic
719C2#2260035511yescharacteristic
720C2#2260038511yescharacteristic
721C2#2260078011yescharacteristic
722C2#2260079511yescharacteristic
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#22491
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. #22588648C2semidirect
8. #22588648C2semidirect
9. #22588435C2semidirect
10. #22588426C2semidirect
11. #22588345C2semidirect
12. #22588170C2semidirect
13. #22588061C2semidirect
14. C2×#17985761C2semidirect
50. #552×C71C4semidirect
109. #125×C71C2×C4semidirect
113. C22⋊Q8×C71C2×C4semidirect
114. C22⋊Q8×C71C2×C4semidirect
116. C4×Q8×C71C2×C4semidirect
121. #117×C71C2×C4semidirect
129. C2×C4⋊C4×C71C2×C4semidirect
377. C71#22491semidirect
381. #552Dic71semidirect
444. #125C2×Dic71semidirect
448. C22⋊Q8C2×Dic71semidirect
449. C22⋊Q8C2×Dic71semidirect
451. C4×Q8C2×Dic71semidirect
457. #117C2×Dic71semidirect
477. C2×C4⋊C4C2×Dic71semidirect

Maximal subgroups

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

subgroupindex
C2×#179860712
D4×C4⋊Dic712
#225893102
#225892982
#225887742
#225887642
#225886482
#225884352
#225884262
#225883452
#225881702
#225880612
C2×#179857612
C2×#552×C712
#2249171