Finite Group Databasebeta

← C2×#20256230 #27096075

Subgroups — C2×#20256230 #27096075

Order 12032.

1810 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689846C211yesmaximal, characteristic
2#20256230C2116yesmaximal, direct product factor
3C2×#15689493C211yesmaximal, characteristic, complemented
4C2×#15689485C211yesmaximal, characteristic
5C2×#15689480C211yesmaximal, characteristic
6C2×#15689427C211yesmaximal, characteristic, complemented
7C2×#15689415C211yesmaximal, characteristic, complemented
8C2×#15689420C211yesmaximal, characteristic
9C2×#15689345C211yesmaximal, characteristic
10C2×#15689345C211yesmaximal, characteristic
11C2×#15689333C211yesmaximal, characteristic, complemented
12C2×#15689254C211yesmaximal, characteristic, complemented
13C2×#15689228C211yesmaximal, characteristic, complemented
14C2×#15689221C211yesmaximal, characteristic
15C2×C4×#10625337C211yesmaximal, characteristic, complemented
16C2×C47×#557C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625336C2211yescharacteristic
20#15689846—24no—
21#15689846C2218yes—
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#15689485C2218yes—
34#15689480C2218yes—
35#15689427C2218yescomplemented
36#15689420C2218yes—
37#15689415C2218yescomplemented
38#15689345C2218yes—
39#15689345C2218yes—
40#15689333C2218yescomplemented
41#15689254C2218yescomplemented
42#15689228C2218yescomplemented
43#15689221C2218yes—
44C4×#10625337C2218yescomplemented
45C2×#13093957C2211yescharacteristic
46C2×#13093957C2211yescharacteristic
47C2×#13093955C2211yescharacteristic
48C2×C4⋊(C47⋊C8)C2211yescharacteristic
49C2×C4⋊(C47⋊C8)C2211yescharacteristic
50C2×C4⋊(C47⋊C8)C2211yescharacteristic
51C2×#13093948C2211yescharacteristic
52C2×#13093947C2211yescharacteristic
53C2×#13093947C2211yescharacteristic
54C2×#13093947C2211yescharacteristic
55C2×#13093947C2211yescharacteristic
56C2×#13093947C2211yescharacteristic
57C2×#13093947C2211yescharacteristic
58C2×#13093944C2211yescharacteristic
59C2×#13093944C2211yescharacteristic
60C2×#13093944C2211yescharacteristic
61C2×#13093935C2211yescharacteristic
62C2×#13093935C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C47×#557—24no—
65C47×#557C2218yescomplemented
66C2×C4⋊Q8×C47—21no—
67C2×C4⋊Q8×C47C2211yescharacteristic
68C2×#125×C47—21no—
69C2×#125×C47—21no—
70C2×#125×C47C2211yescharacteristic
71C2×#125×C47C2211yescharacteristic
72C2×C4×Q8×C47—21no—
73C2×C4×Q8×C47C2211yescharacteristic
74C2×C4×Q8×C47C2211yescharacteristic
75C2×C4×Q8×C47C2211yescharacteristic
76C2×C4×Q8×C47C2211yescharacteristic
77C22×Dic94C2311yescharacteristic
78C22×Dic94C2311yescharacteristic
79C22×D188C2311yescharacteristic
80C22×C4×D47—21no—
81C2×#10625337—24no—
82C2×#10625337—24no—
83C2×#10625337C2314yes—
84C2×#10625337C2314yes—
85C2×#10625336—24no—
86C2×#10625336C2314yes—
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#13093957C2314yes—
121#13093955C2314yes—
122C4⋊(C47⋊C8)C2314yes—
123C4⋊(C47⋊C8)C2314yes—
124C4⋊(C47⋊C8)C2314yes—
125#13093948C2314yes—
126#13093947C2314yes—
127#13093947C2314yes—
128#13093947C2314yes—
129#13093947C2314yes—
130#13093947C2314yes—
131#13093947C2314yes—
132#13093944C2314yes—
133#13093944C2314yes—
134#13093944C2314yes—
135#13093935C2314yes—
136#13093935C2314yes—
137C4×C47⋊C8C2314yes—
138C22×Q8×C47—21no—
139C22×Q8×C47D411yescharacteristic
140C22×Q8×C47C2311yescharacteristic
141C4⋊Q8×C47—28no—
142C4⋊Q8×C47—22no—
143C4⋊Q8×C47C2314yes—
144#125×C47—28no—
145#125×C47—28no—
146#125×C47—22no—
147#125×C47—22no—
148#125×C47C2314yes—
149#125×C47C2314yes—
150C4×Q8×C47—28no—
151C4×Q8×C47—22no—
152C4×Q8×C47—22no—
153C4×Q8×C47—22no—
154C4×Q8×C47D414yes—
155C4×Q8×C47C2314yes—
156C4×Q8×C47C2314yes—
157C4×Q8×C47C2314yes—
158C4×Q8×C47C2314yes—
159C2×C4⋊C4×C47—21no—
160C2×C4⋊C4×C47—21no—
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—21no—
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×C42×C47—21no—
174C2×C42×C47—21no—
175C2×C42×C47—21no—
176C2×C42×C47C2311yescharacteristic
177C2×C42×C47C2311yescharacteristic
178C2×C42×C47C2311yescharacteristic
179C23×D47—21no—
180C2×Q8×C47—21no—
181C2×Q8×C47—24no—
182C2×Q8×C47—22no—
183C2×Q8×C47—42no—
184C2×Q8×C47—44no—
185C2×Q8×C47C2×D414yes—
186C2×Q8×C47#4114yes—
187C2×Q8×C47C2412yes—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2411yescharacteristic
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C2×D188—22no—
203C2×D188—22no—
204C2×D188—21no—
205C2×D188C2412yes—
206C2×C4×D47—24no—
207C2×C4×D47—44no—
208C2×Dic94—22no—
209C2×Dic94—22no—
210C2×Dic94—22no—
211C2×Dic94—22no—
212C2×Dic94—21no—
213C2×Dic94—21no—
214C2×Dic94C2412yes—
215C2×Dic94C2412yes—
216C4⋊C4×C47—24no—
217C4⋊C4×C47—24no—
218C4⋊C4×C47—24no—
219C4⋊C4×C47—24no—
220C4⋊C4×C47—24no—
221C4⋊C4×C47—24no—
222C4⋊C4×C47—24no—
223C4⋊C4×C47—24no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47C2×D414yes—
228C4⋊C4×C47C2×D414yes—
229C4⋊C4×C47C2×D414yes—
230C4⋊C4×C47C2412yes—
231C4⋊C4×C47C2412yes—
232C4⋊C4×C47C2412yes—
233C42×C47—24no—
234C42×C47—24no—
235C42×C47—24no—
236C42×C47C2×D412yes—
237C42×C47C2×D412yes—
238C42×C47C2×D412yes—
239C42×C47C2412yes—
240C42×C47C2412yes—
241C42×C47C2412yes—
242#10625337—28no—
243#10625337—28no—
244#10625336—28no—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4—24no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4—24no—
249(C2×D47)⋊C4—24no—
250C4⋊Dic47—24no—
251C4⋊Dic47—24no—
252C4⋊Dic47—21no—
253C4⋊Dic47C2412yes—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256C4×Dic47—24no—
257C4×Dic47—24no—
258C2×C47⋊C8—22no—
259C2×C47⋊C8—22no—
260C2×C47⋊C8—22no—
261C2×C47⋊C8—22no—
262C2×C47⋊C8C2412yes—
263C2×C47⋊C8C2412yes—
264C2×C47⋊C8C2412yes—
265C2×C47⋊C8C2412yes—
266C23×C47C22×D411yescharacteristic
267C22×D47—22no—
268C22×D47—42no—
269C22×D47—42no—
270C22×D47—42no—
271Q8×C47—24no—
272Q8×C47—22no—
273Q8×C47—44no—
274Q8×C47—48no—
275Q8×C47C2×#4114yes—
276C2×C4×C47—24no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47—42no—
290C2×C4×C47C22×D412yes—
291C2×C4×C47C22×D412yes—
292C2×C4×C47C22×D412yes—
293C2×C4×C47C22×D412yes—
294C2×C4×C47C22×D412yes—
295C2×C4×C47C22×D412yes—
296C2×C4×C47C22×D411yescharacteristic
297C2×C4×C47C2×#4112yes—
298C2×C4×C472−1+412yes—
299C2×C4×C47C2511yescharacteristic
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—42no—
304C2×Dic47—42no—
305C2×Dic47—42no—
306D188—22no—
307D188—22no—
308D188—42no—
309C4×D47—48no—
310Dic94—22no—
311Dic94—22no—
312Dic94—22no—
313Dic94—22no—
314Dic94—42no—
315Dic94—42no—
316C47⋊C8—22no—
317C47⋊C8—22no—
318C47⋊C8—22no—
319C47⋊C8—22no—
320C2×#3377—471nomaximal, Sylow
321C22×C47#54812yes—
322C22×C47#57512yes—
323C22×C47#57812yes—
324C22×C47C23×D411yescharacteristic
325C2×D47—42no—
326C2×D47—42no—
327C2×D47—42no—
328C2×D47—84no—
329C4×C47—24no—
330C4×C47—22no—
331C4×C47—22no—
332C4×C47—22no—
333C4×C47—22no—
334C4×C47—22no—
335C4×C47—22no—
336C4×C47—42no—
337C4×C47—42no—
338C4×C47—42no—
339C4×C47#54812yes—
340C4×C47C22×#4111yescharacteristic
341C4×C47C2×2−1+411yescharacteristic
342Dic47—42no—
343Dic47—42no—
344Dic47—42no—
345C2×#557D4711yescharacteristic, complemented
346C2×#556—471no—
347#3377—4716no—
348C2×#491—471no—
349C2×#489—471no—
350C2×#488—471no—
351C2×#479—471no—
352C2×#477—471no—
353C2×#478—471no—
354C2×#464—471no—
355C2×#464—471no—
356C2×#462—471no—
357C2×#446—471no—
358C2×#441—471no—
359C2×#440—471no—
360C2×C4×Q16—471no—
361C2×C47#337714yescomplemented
362C2×C47C2×#54811yescharacteristic
363C2×C47C2×#57511yescharacteristic
364C2×C47C2×#57811yescharacteristic
365D47—82no—
366C22×Q16—471no—
367C22×Q16—471no—
368C22×SD16—471no—
369#557—24no—
370#557C2×D4718yescomplemented
371#556—478no—
372#556—944no—
373C2×C4⋊Q8—21no—
374C2×C4⋊Q8—471no—
375C2×C4⋊Q8C2×D4711yescharacteristic
376C2×#126—941no—
377C2×#126—941no—
378C2×#125—21no—
379C2×#125—21no—
380C2×#125C2×D4711yescharacteristic
381C2×#125C2×D4711yescharacteristic
382C2×#124—471no—
383C2×#124—471no—
384C2×C22⋊Q8—941no—
385C2×C4×Q8—21no—
386C2×C4×Q8—471no—
387C2×C4×Q8—471no—
388C2×C4×Q8C2×D4711yescharacteristic
389C2×C4×Q8C2×D4711yescharacteristic
390C2×C4×Q8C2×D4711yescharacteristic
391C2×C4×Q8C2×D4711yescharacteristic
392C2×C4×D4—471no—
393C2×#117—941no—
394#491—478no—
395#489—478no—
396#488—478no—
397#479—478no—
398#478—478no—
399#477—478no—
400#464—478no—
401#464—478no—
402#462—478no—
403#446—478no—
404#441—478no—
405#440—478no—
406C4×Q16—478no—
407C2×#107—471no—
408C2×#107—471no—
409C2×#106—471no—
410C2×C4⋊C8—471no—
411C2×C4⋊C8—471no—
412C2×C4⋊C8—471no—
413C2×#103—471no—
414C2×#103—471no—
415C2×#103—471no—
416C2×#103—471no—
417C2×#103—471no—
418C2×#103—471no—
419C2×#103—471no—
420C2×#102—471no—
421C2×#102—471no—
422C2×#102—471no—
423C2×#97—471no—
424C2×#97—471no—
425C2×C4×C8—471no—
426C47C2×#337711yescharacteristic, complemented, Sylow
427C22×Q8—21no—
428C22×Q8—471no—
429C22×Q8—471no—
430C22×Q8C22⋊D4711yescharacteristic
431C22×Q8C22×D4711yescharacteristic
432C22×D4—471no—
433C23×C4—941no—
434C2×Q16—474no—
435C2×Q16—474no—
436C2×Q16—944no—
437C2×Q16—944no—
438C2×SD16—474no—
439C2×SD16—944no—
440C22×C8—471no—
441C22×C8—471no—
442C22×C8—471no—
443C22×C8—471no—
444C4⋊Q8—28no—
445C4⋊Q8—22no—
446C4⋊Q8—474no—
447C4⋊Q8—942no—
448C4⋊Q8C22×D4714yes—
449#126—948no—
450#126—948no—
451#125—28no—
452#125—28no—
453#125—22no—
454#125—22no—
455#125C22×D4714yes—
456#125C22×D4714yes—
457#124—474no—
458#124—474no—
459#124—942no—
460#124—942no—
461C22⋊Q8—948no—
462C4×Q8—28no—
463C4×Q8—22no—
464C4×Q8—22no—
465C4×Q8—22no—
466C4×Q8—474no—
467C4×Q8—474no—
468C4×Q8—942no—
469C4×Q8—942no—
470C4×Q8C22⋊D4714yes—
471C4×Q8C22×D4714yes—
472C4×Q8C22×D4714yes—
473C4×Q8C22×D4714yes—
474C4×Q8C22×D4714yes—
475C4×D4—474no—
476C4×D4—942no—
477#117—948no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—471no—
487C2×C4⋊C4—941no—
488C2×C4⋊C4—941no—
489C2×C4⋊C4—941no—
490C2×C4⋊C4—941no—
491C2×C4⋊C4C22⋊D4711yescharacteristic
492C2×C4⋊C4C22⋊D4711yescharacteristic
493C2×C4⋊C4C22⋊D4711yescharacteristic
494C2×C4⋊C4C22×D4711yescharacteristic
495C2×C4⋊C4C22×D4711yescharacteristic
496C2×C4⋊C4C22×D4711yescharacteristic
497C2×C22⋊C4—941no—
498C2×C22⋊C4—941no—
499C2×C22⋊C4—941no—
500C2×C22⋊C4—941no—
501C2×C22⋊C4—941no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42—21no—
505C2×C42—941no—
506C2×C42—941no—
507C2×C42C22×D4711yescharacteristic
508C2×C42C22×D4711yescharacteristic
509C2×C42C22×D4711yescharacteristic
510#107—474no—
511#107—474no—
512#106—474no—
513C4⋊C8—474no—
514C4⋊C8—474no—
515C4⋊C8—474no—
516#103—474no—
517#103—474no—
518#103—474no—
519#103—474no—
520#103—474no—
521#103—474no—
522#103—474no—
523#102—474no—
524#102—474no—
525#102—474no—
526#97—474no—
527#97—474no—
528C4×C8—474no—
529C24—941no—
530C2×Q8—21no—
531C2×Q8—24no—
532C2×Q8—22no—
533C2×Q8—42no—
534C2×Q8—44no—
535C2×Q8—472no—
536C2×Q8—472no—
537C2×Q8—941no—
538C2×Q8—941no—
539C2×Q8—942no—
540C2×Q8—942no—
541C2×Q8—942no—
542C2×Q8—942no—
543C2×Q8#1062535414yes—
544C2×Q8C2×C22⋊D4714yes—
545C2×Q8C23×D4712yes—
546C2×D4—472no—
547C2×D4—941no—
548C2×D4—942no—
549C2×D4—942no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—941no—
555C22×C4—941no—
556C22×C4—941no—
557C22×C4—944no—
558C22×C4—1884no—
559C22×C4C2×C22⋊D4711yescharacteristic
560C22×C4C2×C22⋊D4711yescharacteristic
561C22×C4C2×C22⋊D4711yescharacteristic
562C22×C4C2×C22⋊D4711yescharacteristic
563C22×C4C2×C22⋊D4711yescharacteristic
564C22×C4C2×C22⋊D4711yescharacteristic
565C22×C4C23×D4711yescharacteristic
566Q16—948no—
567Q16—948no—
568SD16—948no—
569C2×C8—472no—
570C2×C8—472no—
571C2×C8—472no—
572C2×C8—472no—
573C2×C8—942no—
574C2×C8—942no—
575C2×C8—942no—
576C2×C8—942no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—472no—
589C4⋊C4—944no—
590C4⋊C4—944no—
591C4⋊C4—941no—
592C4⋊C4—944no—
593C4⋊C4—944no—
594C4⋊C4C2×C22⋊D4714yes—
595C4⋊C4C2×C22⋊D4714yes—
596C4⋊C4C2×C22⋊D4714yes—
597C4⋊C4C23×D4712yes—
598C4⋊C4C23×D4712yes—
599C4⋊C4C23×D4712yes—
600C22⋊C4—944no—
601C22⋊C4—944no—
602C22⋊C4—944no—
603C22⋊C4—944no—
604C22⋊C4—944no—
605C42—24no—
606C42—24no—
607C42—24no—
608C42—944no—
609C42—944no—
610C42C2×C22⋊D4712yes—
611C42C2×C22⋊D4712yes—
612C42C2×C22⋊D4712yes—
613C42C23×D4712yes—
614C42C23×D4712yes—
615C42C23×D4712yes—
616C23—942no—
617C23—1882no—
618C23—1882no—
619C23—1882no—
620C23C22×C22⋊D4711yescharacteristic
621Q8—24no—
622Q8—22no—
623Q8—44no—
624Q8—48no—
625Q8—942no—
626Q8—942no—
627Q8—942no—
628Q8—942no—
629Q8—1882no—
630Q8—1882no—
631Q8C2×#1062535414yes—
632D4—942no—
633D4—942no—
634D4—1882no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—942no—
650C2×C4—942no—
651C2×C4—942no—
652C2×C4—1888no—
653C2×C4—1882no—
654C2×C4—1882no—
655C2×C4—1882no—
656C2×C4C22×C22⋊D4712yes—
657C2×C4C22×C22⋊D4712yes—
658C2×C4C22×C22⋊D4712yes—
659C2×C4C22×C22⋊D4712yes—
660C2×C4C22×C22⋊D4712yes—
661C2×C4C22×C22⋊D4712yes—
662C2×C4C22×C22⋊D4711yescharacteristic
663C2×C4C2×#1062535412yes—
664C2×C4#1309407212yes—
665C2×C4C24×D4711yescharacteristic
666C8—942no—
667C8—942no—
668C8—942no—
669C8—942no—
670C22—3764no—
671C22—1882no—
672C22—1882no—
673C22—1882no—
674C22#1568978412yes—
675C22#1568992112yes—
676C22#1568993812yes—
677C22C23×C22⋊D4711yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—24no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—1882no—
689C4—1882no—
690C4—1882no—
691C4#1568978412yes—
692C4C22×#1062535411yescharacteristic
693C4C2×#1309407211yescharacteristic
694C2—3762no—
695C2#2025623014yesdirect product factor
696C2C2×#1568978411yescharacteristic
697C2C2×#1568992111yescharacteristic
698C2C2×#1568993811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#557C2
socleC23×C47C22×D4
prime radicalC22×D188C23
hypercenterC2×#557D47
hypocenterC47C2×#3377
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #20256230C2direct (N × H)
3. C2×#15689493C2semidirect
6. C2×#15689427C2semidirect
7. C2×#15689415C2semidirect
11. C2×#15689333C2semidirect
12. C2×#15689254C2semidirect
13. C2×#15689228C2semidirect
15. C2×C4×#10625337C2semidirect
16. C2×C47×#557C2semidirect
32. #15689493C22semidirect
35. #15689427C22semidirect
37. #15689415C22semidirect
40. #15689333C22semidirect
41. #15689254C22semidirect
42. #15689228C22semidirect
44. C4×#10625337C22semidirect
65. C47×#557C22semidirect
345. C2×#557D47semidirect
361. C2×C47#3377semidirect
370. #557C2×D47semidirect
426. C47C2×#3377semidirect
695. C2#20256230direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898462
#202562302
C2×#156894932
C2×#156894852
C2×#156894802
C2×#156894272
C2×#156894152
C2×#156894202
C2×#156893452
C2×#156893332
C2×#156892542
C2×#156892282
C2×#156892212
C2×C4×#106253372
C2×C47×#5572
C2×#337747