Finite Group Databasebeta

← C2×#22592415 #32165658

Subgroups — C2×#22592415 #32165658

Order 18176.

2594 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
1C22×#14556123C211yesmaximal, characteristic
2#22592415C2116yesmaximal, direct product factor
3C2×#17985938C211yesmaximal, characteristic, complemented
4C2×#17985921C211yesmaximal, characteristic
5C2×#17985918C211yesmaximal, characteristic, complemented
6C2×#17985910C211yesmaximal, characteristic
7C2×#17985897C211yesmaximal, characteristic, complemented
8C2×#17985890C211yesmaximal, characteristic
9C2×#17985890C211yesmaximal, characteristic
10C2×#17985890C211yesmaximal, characteristic
11C2×#17985889C211yesmaximal, characteristic
12C2×#17985885C211yesmaximal, characteristic, complemented
13C2×#17985883C211yesmaximal, characteristic, complemented
14C2×#17985880C211yesmaximal, characteristic, complemented
15C2×C4×Dic71⋊C4C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C71C211yesmaximal, characteristic, complemented
17C2×#14556123—28no—
18C2×#14556123C2218yes—
19C22×C4⋊Dic71C2211yescharacteristic
20C22×C4⋊Dic71C2211yescharacteristic
21C22×Dic71⋊C4C2211yescharacteristic
22C22×Dic71⋊C4C2211yescharacteristic
23C22×Dic71⋊C4C2211yescharacteristic
24C22×Dic71⋊C4C2211yescharacteristic
25C22×Dic71⋊C4C2211yescharacteristic
26C22×(C2×D71)⋊C4C2211yescharacteristic
27C22×(C2×D71)⋊C4C2211yescharacteristic
28C22×(C2×D71)⋊C4C2211yescharacteristic
29C22×(C2×D71)⋊C4C2211yescharacteristic
30C22×(C2×D71)⋊C4C2211yescharacteristic
31C22×(C2×D71)⋊C4C2211yescharacteristic
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×C4×Dic71C2211yescharacteristic
34C22×C4×Dic71C2211yescharacteristic
35#17985938C2218yescomplemented
36#17985921C2218yes—
37#17985918C2218yescomplemented
38#17985910C2218yes—
39#17985897C2218yescomplemented
40#17985890C2218yes—
41#17985890C2218yes—
42#17985890C2218yes—
43#17985889C2218yes—
44#17985885C2218yescomplemented
45#17985883C2218yescomplemented
46#17985880C2218yescomplemented
47C4×Dic71⋊C4C2218yescomplemented
48C2×C71⋊#95C2211yescharacteristic
49C2×C71⋊#95C2211yescharacteristic
50C2×C71⋊#95C2211yescharacteristic
51C2×C71⋊#95C2211yescharacteristic
52C2×C71⋊#95C2211yescharacteristic
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C23×Q8×C71C2211yescharacteristic
61C2×C4×Q8×C71—28no—
62C2×C4×Q8×C71C2218yescomplemented
63C22×C4⋊C4×C71C2211yescharacteristic
64C22×C4⋊C4×C71C2211yescharacteristic
65C22×C4⋊C4×C71C2211yescharacteristic
66C22×C42×C71C2211yescharacteristic
67C22×C42×C71C2211yescharacteristic
68C22×C42×C71C2211yescharacteristic
69C24×D71C2311yescharacteristic
70C23×Dic71C2311yescharacteristic
71C23×Dic71C2311yescharacteristic
72C23×Dic71C2311yescharacteristic
73C23×Dic71C2311yescharacteristic
74C23×Dic71C2311yescharacteristic
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2311yescharacteristic
77#14556123—232no—
78C2×C4⋊Dic71—24no—
79C2×C4⋊Dic71—24no—
80C2×C4⋊Dic71C2314yes—
81C2×C4⋊Dic71C2314yes—
82C2×Dic71⋊C4—24no—
83C2×Dic71⋊C4—24no—
84C2×Dic71⋊C4—24no—
85C2×Dic71⋊C4—24no—
86C2×Dic71⋊C4—24no—
87C2×Dic71⋊C4C2314yes—
88C2×Dic71⋊C4C2314yes—
89C2×Dic71⋊C4C2314yes—
90C2×Dic71⋊C4C2314yes—
91C2×Dic71⋊C4C2314yes—
92C2×(C2×D71)⋊C4—24no—
93C2×(C2×D71)⋊C4—24no—
94C2×(C2×D71)⋊C4—24no—
95C2×(C2×D71)⋊C4—24no—
96C2×(C2×D71)⋊C4—24no—
97C2×(C2×D71)⋊C4—24no—
98C2×(C2×D71)⋊C4—24no—
99C2×(C2×D71)⋊C4C2314yes—
100C2×(C2×D71)⋊C4C2314yes—
101C2×(C2×D71)⋊C4C2314yes—
102C2×(C2×D71)⋊C4C2314yes—
103C2×(C2×D71)⋊C4C2314yes—
104C2×(C2×D71)⋊C4C2314yes—
105C2×(C2×D71)⋊C4C2314yes—
106C2×C4×Dic71—24no—
107C2×C4×Dic71—24no—
108C2×C4×Dic71C2314yes—
109C2×C4×Dic71C2314yes—
110C71⋊#95C2314yes—
111C71⋊#95C2314yes—
112C71⋊#95C2314yes—
113C71⋊#95C2314yes—
114C71⋊#95C2314yes—
115C71⋊#95C2314yes—
116C71⋊#95C2314yes—
117C71⋊#95C2314yes—
118C71⋊#95C2314yes—
119C71⋊#95C2314yes—
120C71⋊#95C2314yes—
121C71⋊#95C2314yes—
122C22×Q8×C71—24no—
123C22×Q8×C71—24no—
124C22×Q8×C71—24no—
125C22×Q8×C71C2314yes—
126C23×C4×C71C2311yescharacteristic
127C23×C4×C71C2311yescharacteristic
128C23×C4×C71C2311yescharacteristic
129C23×C4×C71C2311yescharacteristic
130C23×C4×C71C2311yescharacteristic
131C23×C4×C71C2311yescharacteristic
132C23×C4×C71C2311yescharacteristic
133C4×Q8×C71—232no—
134C2×C4⋊C4×C71—24no—
135C2×C4⋊C4×C71—24no—
136C2×C4⋊C4×C71D418yes—
137C2×C4⋊C4×C71C2314yes—
138C2×C4⋊C4×C71C2314yes—
139C2×C4⋊C4×C71C2314yes—
140C2×C42×C71—24no—
141C2×C42×C71—24no—
142C2×C42×C71—24no—
143C2×C42×C71C2314yes—
144C2×C42×C71C2314yes—
145C2×C42×C71C2314yes—
146C23×D71—22no—
147C23×D71—22no—
148C23×D71—22no—
149C23×D71—22no—
150C23×D71—22no—
151C23×D71—22no—
152C23×D71—22no—
153C23×D71C2412yes—
154C22×Dic71—22no—
155C22×Dic71—22no—
156C22×Dic71—22no—
157C22×Dic71—22no—
158C22×Dic71—22no—
159C22×Dic71—22no—
160C22×Dic71—22no—
161C22×Dic71—22no—
162C22×Dic71—22no—
163C22×Dic71—22no—
164C22×Dic71—22no—
165C22×Dic71—22no—
166C22×Dic71—22no—
167C22×Dic71—22no—
168C22×Dic71—22no—
169C22×Dic71—22no—
170C22×Dic71—22no—
171C22×Dic71—22no—
172C22×Dic71—22no—
173C22×Dic71—22no—
174C22×Dic71#4114yes—
175C22×Dic71C2412yes—
176C22×Dic71C2412yes—
177C22×Dic71C2412yes—
178C22×Dic71C2412yes—
179C22×Dic71C2412yes—
180C22×Dic71C2412yes—
181C22×Dic71C2412yes—
182C4⋊Dic71—28no—
183C4⋊Dic71—28no—
184Dic71⋊C4—28no—
185Dic71⋊C4—28no—
186Dic71⋊C4—28no—
187Dic71⋊C4—28no—
188Dic71⋊C4—28no—
189(C2×D71)⋊C4—28no—
190(C2×D71)⋊C4—28no—
191(C2×D71)⋊C4—28no—
192(C2×D71)⋊C4—28no—
193(C2×D71)⋊C4—28no—
194(C2×D71)⋊C4—28no—
195(C2×D71)⋊C4—28no—
196C4×Dic71—28no—
197C4×Dic71—28no—
198C24×C71C2411yescharacteristic
199C2×Q8×C71—232no—
200C2×Q8×C71—28no—
201C2×Q8×C71—28no—
202C2×Q8×C71—28no—
203C22×C4×C71—22no—
204C22×C4×C71—22no—
205C22×C4×C71—22no—
206C22×C4×C71—22no—
207C22×C4×C71—22no—
208C22×C4×C71—22no—
209C22×C4×C71—22no—
210C22×C4×C71—22no—
211C22×C4×C71—22no—
212C22×C4×C71—22no—
213C22×C4×C71—22no—
214C22×C4×C71—22no—
215C22×C4×C71—22no—
216C22×C4×C71—22no—
217C22×C4×C71—22no—
218C22×C4×C71C2×D414yes—
219C22×C4×C71C2×D414yes—
220C22×C4×C71C2×D414yes—
221C22×C4×C71#4114yes—
222C22×C4×C71#4114yes—
223C22×C4×C71#4114yes—
224C22×C4×C71C2412yes—
225C22×C4×C71C2412yes—
226C22×C4×C71C2412yes—
227C22×C4×C71C2412yes—
228C22×C4×C71C2412yes—
229C22×C4×C71C2412yes—
230C22×C4×C71C2412yes—
231C4⋊C4×C71—28no—
232C4⋊C4×C71—28no—
233C4⋊C4×C71C2×D4116yes—
234C42×C71—28no—
235C42×C71—28no—
236C42×C71—28no—
237C23×C71C22×D412yes—
238C23×C71C2×#4112yes—
239C23×C71C2×#4112yes—
240C23×C71C2×#4112yes—
241C23×C71C2×#4112yes—
242C23×C712−1+412yes—
243C23×C712−1+412yes—
244C23×C71C2511yescharacteristic
245C22×D71—22no—
246C22×D71—22no—
247C22×D71—22no—
248C22×D71—22no—
249C22×D71—22no—
250C22×D71—22no—
251C22×D71—22no—
252C22×D71—44no—
253C22×D71—44no—
254C22×D71—44no—
255C22×D71—44no—
256C22×D71—44no—
257C22×D71—44no—
258C22×D71—44no—
259Q8×C71—232no—
260C2×C4×C71—28no—
261C2×C4×C71—28no—
262C2×C4×C71—28no—
263C2×C4×C71—28no—
264C2×C4×C71—28no—
265C2×C4×C71—28no—
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—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—44no—
282C2×C4×C71C22×D414yes—
283C2×C4×C71C22×D414yes—
284C2×C4×C71C22×D414yes—
285C2×C4×C71C2×#4114yes—
286C2×C4×C71C2×#4114yes—
287C2×C4×C71C2×#4114yes—
288C2×Dic71—28no—
289C2×Dic71—22no—
290C2×Dic71—22no—
291C2×Dic71—22no—
292C2×Dic71—22no—
293C2×Dic71—22no—
294C2×Dic71—22no—
295C2×Dic71—22no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—22no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—44no—
310C2×Dic71—44no—
311C2×Dic71—44no—
312C2×Dic71—44no—
313C2×Dic71—44no—
314C2×Dic71—44no—
315C2×Dic71C2×#4114yes—
316C22×C71#52514yes—
317C22×C71#52914yes—
318C22×C71#54114yes—
319C22×C71#54714yes—
320C22×C71#54814yes—
321C22×C71#55614yes—
322C22×C71#55614yes—
323C22×C71C23×D411yescharacteristic
324C22×C71C22×#4111yescharacteristic
325C22×C71C22×#4111yescharacteristic
326C22×C71C22×#4111yescharacteristic
327C22×C71C22×#4111yescharacteristic
328C22×C71C2×2−1+411yescharacteristic
329C22×C71C2×2−1+411yescharacteristic
330C2×D71—42no—
331C2×D71—42no—
332C2×D71—42no—
333C2×D71—42no—
334C2×D71—42no—
335C2×D71—42no—
336C2×D71—42no—
337C2×D71—88no—
338C4×C71—24no—
339C4×C71—24no—
340C4×C71—24no—
341C4×C71—24no—
342C4×C71—24no—
343C4×C71—24no—
344C4×C71—42no—
345Dic71—24no—
346Dic71—42no—
347Dic71—42no—
348Dic71—42no—
349Dic71—42no—
350Dic71—42no—
351Dic71—42no—
352C2×#2469—711nomaximal, Sylow
353C2×C71#246918yescomplemented
354C2×C71C2×#52511yescharacteristic
355C2×C71C2×#52911yescharacteristic
356C2×C71C2×#54111yescharacteristic
357C2×C71C2×#54711yescharacteristic
358C2×C71C2×#54811yescharacteristic
359C2×C71C2×#55611yescharacteristic
360C2×C71C2×#55611yescharacteristic
361D71—82no—
362C22×#126—711no—
363C22×C4×Q8D7111yescharacteristic, complemented
364#2469—7116no—
365C2×#400—711no—
366C2×#396—711no—
367C2×#395—711no—
368C2×#393—711no—
369C2×#389—711no—
370C2×#388—711no—
371C2×#388—711no—
372C2×#388—711no—
373C2×#388—711no—
374C2×#387—711no—
375C2×#387—711no—
376C2×#387—711no—
377C2×C4×C4⋊C4—711no—
378C71C2×#246911yescharacteristic, complemented, Sylow
379C23×Q8C2×D7111yescharacteristic
380C2×#126—718no—
381C2×#126—1428no—
382C2×C4×Q8—28no—
383C2×C4×Q8C2×D7118yescomplemented
384C22×C4⋊C4—711no—
385C22×C4⋊C4—711no—
386C22×C4⋊C4—711no—
387C22×C4⋊C4—711no—
388C22×C4⋊C4—711no—
389C22×C4⋊C4—711no—
390C22×C4⋊C4—711no—
391C22×C4⋊C4C2×D7111yescharacteristic
392C22×C4⋊C4C2×D7111yescharacteristic
393C22×C4⋊C4C2×D7111yescharacteristic
394C22×C22⋊C4—711no—
395C22×C22⋊C4—711no—
396C22×C22⋊C4—711no—
397C22×C22⋊C4—711no—
398C22×C22⋊C4—711no—
399C22×C22⋊C4—711no—
400C22×C22⋊C4—711no—
401C22×C42—711no—
402C22×C42—711no—
403C22×C42C2×D7111yescharacteristic
404C22×C42C2×D7111yescharacteristic
405C22×C42C2×D7111yescharacteristic
406#400—718no—
407#396—718no—
408#395—718no—
409#393—718no—
410#389—718no—
411#388—718no—
412#388—718no—
413#388—718no—
414#388—718no—
415#387—718no—
416#387—718no—
417#387—718no—
418C4×C4⋊C4—718no—
419C2×#95—711no—
420C2×#95—711no—
421C2×#95—711no—
422C2×#95—711no—
423C2×#95—711no—
424C2×#95—711no—
425C2×#95—711no—
426C2×#95—711no—
427C2×#95—711no—
428C2×#95—711no—
429C2×#95—711no—
430C2×#95—711no—
431C25—711no—
432C22×Q8—24no—
433C22×Q8—24no—
434C22×Q8—24no—
435C22×Q8C22×D7114yes—
436C23×C4—711no—
437C23×C4—711no—
438C23×C4—711no—
439C23×C4—711no—
440C23×C4—711no—
441C23×C4—711no—
442C23×C4—711no—
443C23×C4C22×D7111yescharacteristic
444C23×C4C22×D7111yescharacteristic
445C23×C4C22×D7111yescharacteristic
446C23×C4C22×D7111yescharacteristic
447C23×C4C22×D7111yescharacteristic
448C23×C4C22×D7111yescharacteristic
449C23×C4C22×D7111yescharacteristic
450#126—14232no—
451C4×Q8—232no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—714no—
455C2×C4⋊C4—714no—
456C2×C4⋊C4—714no—
457C2×C4⋊C4—714no—
458C2×C4⋊C4—714no—
459C2×C4⋊C4—714no—
460C2×C4⋊C4—714no—
461C2×C4⋊C4—1424no—
462C2×C4⋊C4—1424no—
463C2×C4⋊C4—1424no—
464C2×C4⋊C4—1424no—
465C2×C4⋊C4—1424no—
466C2×C4⋊C4—1424no—
467C2×C4⋊C4—1424no—
468C2×C4⋊C4C22⋊D7118yes—
469C2×C4⋊C4C22×D7114yes—
470C2×C4⋊C4C22×D7114yes—
471C2×C4⋊C4C22×D7114yes—
472C2×C22⋊C4—714no—
473C2×C22⋊C4—714no—
474C2×C22⋊C4—714no—
475C2×C22⋊C4—714no—
476C2×C22⋊C4—714no—
477C2×C22⋊C4—714no—
478C2×C22⋊C4—714no—
479C2×C22⋊C4—1424no—
480C2×C22⋊C4—1424no—
481C2×C22⋊C4—1424no—
482C2×C22⋊C4—1424no—
483C2×C22⋊C4—1424no—
484C2×C22⋊C4—1424no—
485C2×C22⋊C4—1424no—
486C2×C42—24no—
487C2×C42—24no—
488C2×C42—24no—
489C2×C42—714no—
490C2×C42—714no—
491C2×C42—1424no—
492C2×C42—1424no—
493C2×C42C22×D7114yes—
494C2×C42C22×D7114yes—
495C2×C42C22×D7114yes—
496#95—714no—
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#95—714no—
507#95—714no—
508C24—712no—
509C24—1422no—
510C24—1422no—
511C24—1422no—
512C24—1422no—
513C24—1422no—
514C24—1422no—
515C24—1422no—
516C24C23×D7111yescharacteristic
517C2×Q8—232no—
518C2×Q8—28no—
519C2×Q8—28no—
520C2×Q8—28no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—714no—
537C22×C4—712no—
538C22×C4—712no—
539C22×C4—712no—
540C22×C4—712no—
541C22×C4—712no—
542C22×C4—712no—
543C22×C4—712no—
544C22×C4—1422no—
545C22×C4—1422no—
546C22×C4—1422no—
547C22×C4—1422no—
548C22×C4—1422no—
549C22×C4—1422no—
550C22×C4—1422no—
551C22×C4—1422no—
552C22×C4—1422no—
553C22×C4—1422no—
554C22×C4—1422no—
555C22×C4—1422no—
556C22×C4—1422no—
557C22×C4—1422no—
558C22×C4—1422no—
559C22×C4—1422no—
560C22×C4—1422no—
561C22×C4—1422no—
562C22×C4—1422no—
563C22×C4—1422no—
564C22×C4C2×C22⋊D7114yes—
565C22×C4C2×C22⋊D7114yes—
566C22×C4C2×C22⋊D7114yes—
567C22×C4#1176586514yes—
568C22×C4#1176586514yes—
569C22×C4#1176586614yes—
570C22×C4C23×D7112yes—
571C22×C4C23×D7112yes—
572C22×C4C23×D7112yes—
573C22×C4C23×D7112yes—
574C22×C4C23×D7112yes—
575C22×C4C23×D7112yes—
576C22×C4C23×D7112yes—
577C4⋊C4—28no—
578C4⋊C4—28no—
579C4⋊C4—1428no—
580C4⋊C4—1428no—
581C4⋊C4—1428no—
582C4⋊C4—1428no—
583C4⋊C4—1428no—
584C4⋊C4—1428no—
585C4⋊C4—1428no—
586C4⋊C4C2×C22⋊D71116yes—
587C22⋊C4—1428no—
588C22⋊C4—1428no—
589C22⋊C4—1428no—
590C22⋊C4—1428no—
591C22⋊C4—1428no—
592C22⋊C4—1428no—
593C22⋊C4—1428no—
594C42—28no—
595C42—28no—
596C42—28no—
597C42—1428no—
598C42—1428no—
599C23—2844no—
600C23—2844no—
601C23—2844no—
602C23—2844no—
603C23—2844no—
604C23—2844no—
605C23—2844no—
606C23—1422no—
607C23—1422no—
608C23—1422no—
609C23—1422no—
610C23—1422no—
611C23—1422no—
612C23—1422no—
613C23C22×C22⋊D7112yes—
614C23#41×D7112yes—
615C23C2×#1176586512yes—
616C23C2×#1176586512yes—
617C23C2×#1176586612yes—
618C23#1455617512yes—
619C23#1455617612yes—
620C23C24×D7111yescharacteristic
621Q8—232no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—28no—
635C2×C4—28no—
636C2×C4—28no—
637C2×C4—28no—
638C2×C4—28no—
639C2×C4—28no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—44no—
644C2×C4—2844no—
645C2×C4—2844no—
646C2×C4—2844no—
647C2×C4—2844no—
648C2×C4—2844no—
649C2×C4—2844no—
650C2×C4—714no—
651C2×C4—1422no—
652C2×C4—1422no—
653C2×C4—1422no—
654C2×C4—1422no—
655C2×C4—1422no—
656C2×C4—1422no—
657C2×C4—1422no—
658C2×C4—1422no—
659C2×C4—1422no—
660C2×C4—1422no—
661C2×C4—1422no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4—1422no—
665C2×C4—1422no—
666C2×C4—1422no—
667C2×C4—1422no—
668C2×C4—1422no—
669C2×C4—1422no—
670C2×C4—1422no—
671C2×C4—1428no—
672C2×C4C22×C22⋊D7114yes—
673C2×C4C22×C22⋊D7114yes—
674C2×C4C22×C22⋊D7114yes—
675C2×C4C2×#1176586514yes—
676C2×C4C2×#1176586514yes—
677C2×C4C2×#1176586614yes—
678C22—2842no—
679C22—2842no—
680C22—2842no—
681C22—2842no—
682C22—2842no—
683C22—2842no—
684C22—2842no—
685C22—5688no—
686C22#1798651014yes—
687C22#1798653614yes—
688C22#1798660714yes—
689C22#1798664814yes—
690C22#1798666014yes—
691C22#1798672114yes—
692C22#1798672214yes—
693C22C23×C22⋊D7111yescharacteristic
694C22C2×#41×D7111yescharacteristic
695C22C22×#1176586511yescharacteristic
696C22C22×#1176586511yescharacteristic
697C22C22×#1176586611yescharacteristic
698C22C2×#1455617511yescharacteristic
699C22C2×#1455617611yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—24no—
704C4—24no—
705C4—24no—
706C4—42no—
707C4—2842no—
708C4—2842no—
709C4—2842no—
710C4—2842no—
711C4—2842no—
712C4—2842no—
713C4—1424no—
714C2—5682no—
715C2#2259241518yesdirect product factor
716C2C2×#1798651011yescharacteristic
717C2C2×#1798653611yescharacteristic
718C2C2×#1798660711yescharacteristic
719C2C2×#1798664811yescharacteristic
720C2C2×#1798666011yescharacteristic
721C2C2×#1798672111yescharacteristic
722C2C2×#1798672211yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×C4×Q8×C71C2
socleC24×C71C24
prime radicalC24×D71C23
hypercenterC22×C4×Q8D71
hypocenterC71C2×#2469
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #22592415C2direct (N × H)
3. C2×#17985938C2semidirect
5. C2×#17985918C2semidirect
7. C2×#17985897C2semidirect
12. C2×#17985885C2semidirect
13. C2×#17985883C2semidirect
14. C2×#17985880C2semidirect
15. C2×C4×Dic71⋊C4C2semidirect
16. C22×C4×Q8×C71C2semidirect
35. #17985938C22semidirect
37. #17985918C22semidirect
39. #17985897C22semidirect
44. #17985885C22semidirect
45. #17985883C22semidirect
46. #17985880C22semidirect
47. C4×Dic71⋊C4C22semidirect
62. C2×C4×Q8×C71C22semidirect
353. C2×C71#2469semidirect
363. C22×C4×Q8D71semidirect
378. C71C2×#2469semidirect
383. C2×C4×Q8C2×D71semidirect
715. C2#22592415direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561232
#225924152
C2×#179859382
C2×#179859212
C2×#179859182
C2×#179859102
C2×#179858972
C2×#179858902
C2×#179858892
C2×#179858852
C2×#179858832
C2×#179858802
C2×C4×Dic71⋊C42
C22×C4×Q8×C712
C2×#246971