Finite Group Databasebeta

← C2×#20256215 #27096043

Subgroups — C2×#20256215 #27096043

Order 12032.

1886 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×#15689846C211yesmaximal, characteristic, complemented
2#20256215C2116yesmaximal, direct product factor
3C2×#15689493C211yesmaximal, characteristic, complemented
4C2×#15689485C211yesmaximal, characteristic, complemented
5C2×#15689480C211yesmaximal, characteristic, complemented
6C2×#15689427C211yesmaximal, characteristic, complemented
7C2×#15689405C211yesmaximal, characteristic, complemented
8C2×#15689420C211yesmaximal, characteristic, complemented
9C2×#15689338C211yesmaximal, characteristic
10C2×#15689338C211yesmaximal, characteristic
11C2×#15689328C211yesmaximal, characteristic, complemented
12C2×#15689254C211yesmaximal, characteristic, complemented
13C2×#15689233C211yesmaximal, characteristic
14C2×#15689223C211yesmaximal, characteristic, complemented
15C2×C4×#10625335C211yesmaximal, characteristic, complemented
16C2×C47×#554C211yesmaximal, characteristic, complemented
17C22×#10625335C2211yescharacteristic
18C22×#10625335C2211yescharacteristic
19C22×#10625334C2211yescharacteristic
20#15689846—24no—
21#15689846C2218yescomplemented
22C2×#13094024C2211yescharacteristic
23C2×#13094019—21no—
24C2×#13094019—21no—
25C2×#13094012C2211yescharacteristic
26C2×#13094012C2211yescharacteristic
27C2×#13094000—21no—
28C2×C4×Dic94C2211yescharacteristic
29C2×C4×Dic94C2211yescharacteristic
30C2×C4×D188C2211yescharacteristic
31C2×#13093982—21no—
32#15689493C2218yescomplemented
33#15689485C2218yescomplemented
34#15689480C2218yescomplemented
35#15689427C2218yescomplemented
36#15689420C2218yescomplemented
37#15689405C2218yescomplemented
38#15689338C2218yes—
39#15689338C2218yes—
40#15689328C2218yescomplemented
41#15689254C2218yescomplemented
42#15689233C2218yes—
43#15689223C2218yescomplemented
44C4×#10625335C2218yescomplemented
45C2×#13093957C2211yescharacteristic
46C2×#13093955C2211yescharacteristic
47C2×#13093955C2211yescharacteristic
48C2×C4⋊(C47⋊C8)C2211yescharacteristic
49C2×C4⋊(C47⋊C8)C2211yescharacteristic
50C2×C4⋊(C47⋊C8)C2211yescharacteristic
51C2×#13093947C2211yescharacteristic
52C2×#13093947C2211yescharacteristic
53C2×#13093947C2211yescharacteristic
54C2×#13093947C2211yescharacteristic
55C2×#13093947C2211yescharacteristic
56C2×#13093947C2211yescharacteristic
57C2×#13093945C2211yescharacteristic
58C2×#13093944C2211yescharacteristic
59C2×#13093944C2211yescharacteristic
60C2×#13093944C2211yescharacteristic
61C2×#13093935C2211yescharacteristic
62C2×#13093935C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C47×#554—24no—
65C47×#554C2218yescomplemented
66C2×C4⋊Q8×C47C2211yescharacteristic
67C2×#125×C47C2211yescharacteristic
68C2×#125×C47C2211yescharacteristic
69C2×C22⋊Q8×C47—21no—
70C2×C22⋊Q8×C47—21no—
71C2×C22⋊Q8×C47—21no—
72C2×C4×Q8×C47C2211yescharacteristic
73C2×C4×D4×C47C2211yescharacteristic
74C2×C4×D4×C47C2211yescharacteristic
75C2×C4×D4×C47C2211yescharacteristic
76C22×C4⋊C4×C47—21no—
77C22×Dic94C2311yescharacteristic
78C22×Dic94C2311yescharacteristic
79C22×D188C2311yescharacteristic
80C22×C4×D47—21no—
81C2×#10625335—24no—
82C2×#10625335—24no—
83C2×#10625335C2314yes—
84C2×#10625335C2314yes—
85C2×#10625334—24no—
86C2×#10625334C2314yes—
87C22×C47⋊C8C2311yescharacteristic
88C22×C47⋊C8C2311yescharacteristic
89C22×C47⋊C8C2311yescharacteristic
90C22×C47⋊C8C2311yescharacteristic
91#13094024—22no—
92#13094024C2314yes—
93#13094019—28no—
94#13094019—28no—
95#13094012—22no—
96#13094012—22no—
97#13094012C2314yes—
98#13094012C2314yes—
99#13094000—28no—
100C4×Dic94—22no—
101C4×Dic94—22no—
102C4×Dic94C2314yes—
103C4×Dic94C2314yes—
104C4×D188—22no—
105C4×D188C2314yes—
106#13093982—28no—
107C2×C4⋊Dic47—21no—
108C2×C4⋊Dic47—21no—
109C2×C4⋊Dic47C2311yescharacteristic
110C2×Dic47⋊C4—21no—
111C2×Dic47⋊C4—21no—
112C2×(C2×D47)⋊C4—21no—
113C2×(C2×D47)⋊C4—21no—
114C2×(C2×D47)⋊C4—21no—
115C2×(C2×D47)⋊C4—21no—
116C2×(C2×D47)⋊C4—21no—
117C2×C4×Dic47—21no—
118C2×C4×Dic47—21no—
119#13093957C2314yes—
120#13093955C2314yes—
121#13093955C2314yes—
122C4⋊(C47⋊C8)C2314yes—
123C4⋊(C47⋊C8)C2314yes—
124C4⋊(C47⋊C8)C2314yes—
125#13093947C2314yes—
126#13093947C2314yes—
127#13093947C2314yes—
128#13093947C2314yes—
129#13093947C2314yes—
130#13093947C2314yes—
131#13093945C2314yes—
132#13093944C2314yes—
133#13093944C2314yes—
134#13093944C2314yes—
135#13093935C2314yes—
136#13093935C2314yes—
137C4×C47⋊C8C2314yes—
138C22×Q8×C47—21no—
139C22×Q8×C47D411yescharacteristic
140C22×D4×C47C2311yescharacteristic
141C23×C4×C47—21no—
142C23×C4×C47—21no—
143C23×C4×C47—21no—
144C4⋊Q8×C47—22no—
145C4⋊Q8×C47C2314yes—
146#125×C47—22no—
147#125×C47—22no—
148#125×C47C2314yes—
149#125×C47C2314yes—
150C22⋊Q8×C47—28no—
151C22⋊Q8×C47—28no—
152C22⋊Q8×C47—28no—
153C4×Q8×C47D414yes—
154C4×Q8×C47C2314yes—
155C4×D4×C47—22no—
156C4×D4×C47—22no—
157C4×D4×C47—22no—
158C4×D4×C47C2314yes—
159C4×D4×C47C2314yes—
160C4×D4×C47C2314yes—
161C2×C4⋊C4×C47—21no—
162C2×C4⋊C4×C47—21no—
163C2×C4⋊C4×C47—21no—
164C2×C4⋊C4×C47—21no—
165C2×C4⋊C4×C47—21no—
166C2×C4⋊C4×C47—28no—
167C2×C4⋊C4×C47D411yescharacteristic
168C2×C4⋊C4×C47D411yescharacteristic
169C2×C4⋊C4×C47D411yescharacteristic
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C22⋊C4×C47—21no—
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176C2×C42×C47C2311yescharacteristic
177C2×C42×C47C2311yescharacteristic
178C2×C42×C47C2311yescharacteristic
179C24×C47—21no—
180C23×D47—21no—
181C2×Q8×C47—24no—
182C2×Q8×C47—42no—
183C2×Q8×C47—82no—
184C2×Q8×C47C2×D414yes—
185C2×D4×C47—21no—
186C2×D4×C47—22no—
187C2×D4×C47#4114yes—
188C2×D4×C47C2412yes—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—24no—
193C22×C4×C47—24no—
194C22×C4×C47—24no—
195C22×C4×C47—44no—
196C22×C4×C47—82no—
197C22×C4×C47—82no—
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2411yescharacteristic
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C2×D188—22no—
209C2×D188—22no—
210C2×D188—21no—
211C2×D188C2412yes—
212C2×C4×D47—24no—
213C2×C4×D47—44no—
214C2×Dic94—22no—
215C2×Dic94—22no—
216C2×Dic94—22no—
217C2×Dic94—22no—
218C2×Dic94—21no—
219C2×Dic94—21no—
220C2×Dic94C2412yes—
221C2×Dic94C2412yes—
222C4⋊C4×C47—24no—
223C4⋊C4×C47—24no—
224C4⋊C4×C47—24no—
225C4⋊C4×C47—24no—
226C4⋊C4×C47—24no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47C2×D414yes—
231C4⋊C4×C47C2×D414yes—
232C4⋊C4×C47C2×D414yes—
233C4⋊C4×C47C2412yes—
234C4⋊C4×C47C2412yes—
235C4⋊C4×C47C2412yes—
236C22⋊C4×C47—24no—
237C22⋊C4×C47—24no—
238C22⋊C4×C47—24no—
239C42×C47C2×D412yes—
240C42×C47C2×D412yes—
241C42×C47C2×D412yes—
242C42×C47C2412yes—
243C42×C47C2412yes—
244C42×C47C2412yes—
245#10625335—28no—
246#10625335—28no—
247#10625334—28no—
248(C2×D47)⋊C4—24no—
249(C2×D47)⋊C4—24no—
250(C2×D47)⋊C4—24no—
251(C2×D47)⋊C4—24no—
252(C2×D47)⋊C4—24no—
253C4⋊Dic47—24no—
254C4⋊Dic47—24no—
255C4⋊Dic47—21no—
256C4⋊Dic47C2412yes—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259C4×Dic47—24no—
260C4×Dic47—24no—
261C2×C47⋊C8—22no—
262C2×C47⋊C8—22no—
263C2×C47⋊C8—22no—
264C2×C47⋊C8—22no—
265C2×C47⋊C8C2412yes—
266C2×C47⋊C8C2412yes—
267C2×C47⋊C8C2412yes—
268C2×C47⋊C8C2412yes—
269C23×C47—24no—
270C23×C47—22no—
271C23×C47—42no—
272C23×C47—42no—
273C23×C47C22×D411yescharacteristic
274C22×D47—22no—
275C22×D47—42no—
276C22×D47—42no—
277C22×D47—42no—
278Q8×C47—44no—
279Q8×C47—84no—
280D4×C47—24no—
281D4×C47—22no—
282D4×C47C2×#4114yes—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—48no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—84no—
297C2×C4×C47—84no—
298C2×C4×C47C22×D412yes—
299C2×C4×C47C22×D412yes—
300C2×C4×C47C22×D412yes—
301C2×C4×C47C22×D412yes—
302C2×C4×C47C22×D412yes—
303C2×C4×C47C22×D412yes—
304C2×C4×C47C22×D411yescharacteristic
305C2×C4×C47C2×#4112yes—
306C2×C4×C472−1+412yes—
307C2×C4×C47C2511yescharacteristic
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314D188—22no—
315D188—22no—
316D188—42no—
317C4×D47—48no—
318Dic94—22no—
319Dic94—22no—
320Dic94—22no—
321Dic94—22no—
322Dic94—42no—
323Dic94—42no—
324C47⋊C8—22no—
325C47⋊C8—22no—
326C47⋊C8—22no—
327C47⋊C8—22no—
328C2×#3376—471nomaximal, Sylow
329C22×C47—24no—
330C22×C47—48no—
331C22×C47—42no—
332C22×C47—42no—
333C22×C47#54812yes—
334C22×C47#57512yes—
335C22×C47#57712yes—
336C22×C47C23×D411yescharacteristic
337C2×D47—42no—
338C2×D47—42no—
339C2×D47—42no—
340C2×D47—84no—
341C4×C47—22no—
342C4×C47—22no—
343C4×C47—22no—
344C4×C47—22no—
345C4×C47—22no—
346C4×C47—22no—
347C4×C47—42no—
348C4×C47—42no—
349C4×C47—42no—
350C4×C47#54812yes—
351C4×C47C22×#4111yescharacteristic
352C4×C47C2×2−1+411yescharacteristic
353Dic47—42no—
354Dic47—42no—
355Dic47—42no—
356C2×#556—471no—
357C2×#554D4711yescharacteristic, complemented
358#3376—4716no—
359C2×#491—471no—
360C2×#489—471no—
361C2×#488—471no—
362C2×#479—471no—
363C2×#475—471no—
364C2×#478—471no—
365C2×#463—471no—
366C2×#463—471no—
367C2×#461—471no—
368C2×#446—471no—
369C2×#442—471no—
370C2×#440—471no—
371C2×C4×SD16—471no—
372C2×C47—44no—
373C2×C47#337614yescomplemented
374C2×C47C2×#54811yescharacteristic
375C2×C47C2×#57511yescharacteristic
376C2×C47C2×#57711yescharacteristic
377D47—82no—
378C22×SD16—471no—
379C22×SD16—471no—
380C22×D8—471no—
381#556—478no—
382#556—944no—
383#554—24no—
384#554C2×D4718yescomplemented
385C2×C4⋊Q8—471no—
386C2×C4⋊Q8C2×D4711yescharacteristic
387C2×#126—941no—
388C2×#126—941no—
389C2×#125C2×D4711yescharacteristic
390C2×#125C2×D4711yescharacteristic
391C2×#124—471no—
392C2×#124—471no—
393C2×C22⋊Q8—21no—
394C2×C22⋊Q8—21no—
395C2×C22⋊Q8—21no—
396C2×C22⋊Q8—941no—
397C2×C4×Q8—471no—
398C2×C4×Q8—471no—
399C2×C4×Q8C2×D4711yescharacteristic
400C2×C4×D4—471no—
401C2×C4×D4C2×D4711yescharacteristic
402C2×C4×D4C2×D4711yescharacteristic
403C2×C4×D4C2×D4711yescharacteristic
404C2×#117—941no—
405C22×C4⋊C4—21no—
406#491—478no—
407#489—478no—
408#488—478no—
409#479—478no—
410#478—478no—
411#475—478no—
412#463—478no—
413#463—478no—
414#461—478no—
415#446—478no—
416#442—478no—
417#440—478no—
418C4×SD16—478no—
419C2×#107—471no—
420C2×#106—471no—
421C2×#106—471no—
422C2×C4⋊C8—471no—
423C2×C4⋊C8—471no—
424C2×C4⋊C8—471no—
425C2×#103—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#103—471no—
429C2×#103—471no—
430C2×#103—471no—
431C2×#102—471no—
432C2×#102—471no—
433C2×#102—471no—
434C2×#102—471no—
435C2×#97—471no—
436C2×#97—471no—
437C2×C4×C8—471no—
438C47C2×#337611yescharacteristic, complemented, Sylow
439C22×Q8—21no—
440C22×Q8—471no—
441C22×Q8—471no—
442C22×Q8C22⋊D4711yescharacteristic
443C22×D4—471no—
444C22×D4C22×D4711yescharacteristic
445C23×C4—21no—
446C23×C4—21no—
447C23×C4—21no—
448C23×C4—941no—
449C2×SD16—474no—
450C2×SD16—474no—
451C2×SD16—944no—
452C2×SD16—944no—
453C2×D8—474no—
454C2×D8—944no—
455C22×C8—471no—
456C22×C8—471no—
457C22×C8—471no—
458C22×C8—471no—
459C4⋊Q8—22no—
460C4⋊Q8—474no—
461C4⋊Q8—942no—
462C4⋊Q8C22×D4714yes—
463#126—948no—
464#126—948no—
465#125—22no—
466#125—22no—
467#125C22×D4714yes—
468#125C22×D4714yes—
469#124—474no—
470#124—474no—
471#124—942no—
472#124—942no—
473C22⋊Q8—28no—
474C22⋊Q8—28no—
475C22⋊Q8—28no—
476C22⋊Q8—948no—
477C4×Q8—474no—
478C4×Q8—474no—
479C4×Q8—942no—
480C4×Q8—942no—
481C4×Q8C22⋊D4714yes—
482C4×Q8C22×D4714yes—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—474no—
487C4×D4—942no—
488C4×D4C22×D4714yes—
489C4×D4C22×D4714yes—
490C4×D4C22×D4714yes—
491#117—948no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—28no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—941no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4C22⋊D4711yescharacteristic
504C2×C4⋊C4C22⋊D4711yescharacteristic
505C2×C4⋊C4C22⋊D4711yescharacteristic
506C2×C4⋊C4C22×D4711yescharacteristic
507C2×C4⋊C4C22×D4711yescharacteristic
508C2×C4⋊C4C22×D4711yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—941no—
513C2×C22⋊C4—941no—
514C2×C22⋊C4—941no—
515C2×C22⋊C4—941no—
516C2×C22⋊C4—941no—
517C2×C42—941no—
518C2×C42—941no—
519C2×C42C22×D4711yescharacteristic
520C2×C42C22×D4711yescharacteristic
521C2×C42C22×D4711yescharacteristic
522#107—474no—
523#106—474no—
524#106—474no—
525C4⋊C8—474no—
526C4⋊C8—474no—
527C4⋊C8—474no—
528#103—474no—
529#103—474no—
530#103—474no—
531#103—474no—
532#103—474no—
533#103—474no—
534#102—474no—
535#102—474no—
536#102—474no—
537#102—474no—
538#97—474no—
539#97—474no—
540C4×C8—474no—
541C24—21no—
542C24—941no—
543C2×Q8—24no—
544C2×Q8—42no—
545C2×Q8—82no—
546C2×Q8—472no—
547C2×Q8—472no—
548C2×Q8—941no—
549C2×Q8—941no—
550C2×Q8—942no—
551C2×Q8—942no—
552C2×Q8—942no—
553C2×Q8—942no—
554C2×Q8C2×C22⋊D4714yes—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—472no—
558C2×D4—941no—
559C2×D4—942no—
560C2×D4—942no—
561C2×D4#1062535414yes—
562C2×D4C23×D4712yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—44no—
570C22×C4—82no—
571C22×C4—82no—
572C22×C4—941no—
573C22×C4—941no—
574C22×C4—941no—
575C22×C4—944no—
576C22×C4—1884no—
577C22×C4C2×C22⋊D4711yescharacteristic
578C22×C4C2×C22⋊D4711yescharacteristic
579C22×C4C2×C22⋊D4711yescharacteristic
580C22×C4C2×C22⋊D4711yescharacteristic
581C22×C4C2×C22⋊D4711yescharacteristic
582C22×C4C2×C22⋊D4711yescharacteristic
583C22×C4C23×D4711yescharacteristic
584SD16—948no—
585SD16—948no—
586D8—948no—
587C2×C8—472no—
588C2×C8—472no—
589C2×C8—472no—
590C2×C8—472no—
591C2×C8—942no—
592C2×C8—942no—
593C2×C8—942no—
594C2×C8—942no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—472no—
604C4⋊C4—944no—
605C4⋊C4—944no—
606C4⋊C4—941no—
607C4⋊C4—944no—
608C4⋊C4—944no—
609C4⋊C4C2×C22⋊D4714yes—
610C4⋊C4C2×C22⋊D4714yes—
611C4⋊C4C2×C22⋊D4714yes—
612C4⋊C4C23×D4712yes—
613C4⋊C4C23×D4712yes—
614C4⋊C4C23×D4712yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—944no—
619C22⋊C4—944no—
620C22⋊C4—944no—
621C22⋊C4—944no—
622C22⋊C4—944no—
623C42—944no—
624C42—944no—
625C42C2×C22⋊D4712yes—
626C42C2×C22⋊D4712yes—
627C42C2×C22⋊D4712yes—
628C42C23×D4712yes—
629C42C23×D4712yes—
630C42C23×D4712yes—
631C23—24no—
632C23—22no—
633C23—42no—
634C23—42no—
635C23—942no—
636C23—1882no—
637C23—1882no—
638C23—1882no—
639C23C22×C22⋊D4711yescharacteristic
640Q8—44no—
641Q8—84no—
642Q8—942no—
643Q8—942no—
644Q8—942no—
645Q8—942no—
646Q8—1882no—
647Q8—1882no—
648D4—24no—
649D4—22no—
650D4—942no—
651D4—942no—
652D4—1882no—
653D4C2×#1062535414yes—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—48no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—84no—
668C2×C4—84no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—1888no—
673C2×C4—1882no—
674C2×C4—1882no—
675C2×C4—1882no—
676C2×C4C22×C22⋊D4712yes—
677C2×C4C22×C22⋊D4712yes—
678C2×C4C22×C22⋊D4712yes—
679C2×C4C22×C22⋊D4712yes—
680C2×C4C22×C22⋊D4712yes—
681C2×C4C22×C22⋊D4712yes—
682C2×C4C22×C22⋊D4711yescharacteristic
683C2×C4C2×#1062535412yes—
684C2×C4#1309407212yes—
685C2×C4C24×D4711yescharacteristic
686C8—942no—
687C8—942no—
688C8—942no—
689C8—942no—
690C22—24no—
691C22—42no—
692C22—42no—
693C22—48no—
694C22—3764no—
695C22—1882no—
696C22—1882no—
697C22—1882no—
698C22#1568978412yes—
699C22#1568992112yes—
700C22#1568993412yes—
701C22C23×C22⋊D4711yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—1882no—
712C4—1882no—
713C4—1882no—
714C4#1568978412yes—
715C4C22×#1062535411yescharacteristic
716C4C2×#1309407211yescharacteristic
717C2—44no—
718C2—3762no—
719C2#2025621514yesdirect product factor
720C2C2×#1568978411yescharacteristic
721C2C2×#1568992111yescharacteristic
722C2C2×#1568993411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#554C2
socleC23×C47C22×D4
prime radicalC22×#10625334C22
hypercenterC2×#554D47
hypocenterC47C2×#3376
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#15689846C2semidirect
2. #20256215C2direct (N × H)
3. C2×#15689493C2semidirect
4. C2×#15689485C2semidirect
5. C2×#15689480C2semidirect
6. C2×#15689427C2semidirect
7. C2×#15689405C2semidirect
8. C2×#15689420C2semidirect
11. C2×#15689328C2semidirect
12. C2×#15689254C2semidirect
14. C2×#15689223C2semidirect
15. C2×C4×#10625335C2semidirect
16. C2×C47×#554C2semidirect
21. #15689846C22semidirect
32. #15689493C22semidirect
33. #15689485C22semidirect
34. #15689480C22semidirect
35. #15689427C22semidirect
36. #15689420C22semidirect
37. #15689405C22semidirect
40. #15689328C22semidirect
41. #15689254C22semidirect
43. #15689223C22semidirect
44. C4×#10625335C22semidirect
65. C47×#554C22semidirect
357. C2×#554D47semidirect
373. C2×C47#3376semidirect
384. #554C2×D47semidirect
438. C47C2×#3376semidirect
719. C2#20256215direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898462
#202562152
C2×#156894932
C2×#156894852
C2×#156894802
C2×#156894272
C2×#156894052
C2×#156894202
C2×#156893382
C2×#156893282
C2×#156892542
C2×#156892332
C2×#156892232
C2×C4×#106253352
C2×C47×#5542
C2×#337647