Finite Group Databasebeta

← C2×#20256342 #27096815

Subgroups — C2×#20256342 #27096815

Order 12032.

1898 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689833C211yesmaximal, characteristic, complemented
2#20256342C2116yesmaximal, direct product factor
3C2×#15689533C211yesmaximal, characteristic, complemented
4C2×#15689529C211yesmaximal, characteristic, complemented
5C2×#15689522C211yesmaximal, characteristic, complemented
6C2×#15689423C211yesmaximal, characteristic, complemented
7C2×#15689423C211yesmaximal, characteristic, complemented
8C2×#15689420C211yesmaximal, characteristic, complemented
9C2×#15689420C211yesmaximal, characteristic, complemented
10C2×#15689403C211yesmaximal, characteristic, complemented
11C2×#15689400C211yesmaximal, characteristic, complemented
12C2×#15689254C211yesmaximal, characteristic, complemented
13C2×#15689233C211yesmaximal, characteristic
14C2×#15689233C211yesmaximal, characteristic
15C2×C4×#10625334C211yesmaximal, characteristic
16C2×C47×#554C211yesmaximal, characteristic, complemented
17C22×#10625334C2211yescharacteristic
18#15689833—24no—
19#15689833C2218yescomplemented
20C2×#13094024C2211yescharacteristic
21C2×#13094016C2211yescharacteristic
22C2×#13094016C2211yescharacteristic
23C2×#13094002—21no—
24C2×#13094002—21no—
25C2×#13094000—21no—
26C2×C4×D188C2211yescharacteristic
27C2×C4×D188C2211yescharacteristic
28C2×C4×D188C2211yescharacteristic
29C2×C4⋊C4×D47—21no—
30#15689533C2218yescomplemented
31#15689529C2218yescomplemented
32#15689522C2218yescomplemented
33#15689423C2218yescomplemented
34#15689423C2218yescomplemented
35#15689420C2218yescomplemented
36#15689420C2218yescomplemented
37#15689403C2218yescomplemented
38#15689400C2218yescomplemented
39#15689254C2218yescomplemented
40#15689233C2218yes—
41#15689233C2218yes—
42C4×#10625334C2218yes—
43C2×#13093957C2211yescharacteristic
44C2×#13093957C2211yescharacteristic
45C2×#13093957C2211yescharacteristic
46C2×#13093957C2211yescharacteristic
47C2×#13093957C2211yescharacteristic
48C2×#13093955C2211yescharacteristic
49C2×#13093955C2211yescharacteristic
50C2×#13093955C2211yescharacteristic
51C2×#13093955C2211yescharacteristic
52C2×C4⋊(C47⋊C8)C2211yescharacteristic
53C2×C4⋊(C47⋊C8)C2211yescharacteristic
54C2×C4⋊(C47⋊C8)C2211yescharacteristic
55C2×#13093945C2211yescharacteristic
56C2×#13093945C2211yescharacteristic
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×Dic94—21no—
78C22×D188C2311yescharacteristic
79C22×C4×D47—21no—
80C22×C4×D47—21no—
81C22×C4×D47—21no—
82C2×#10625334Q818yescomplemented
83C2×#10625334C2314yes—
84C22×C47⋊C8C2311yescharacteristic
85C22×C47⋊C8C2311yescharacteristic
86C22×C47⋊C8C2311yescharacteristic
87C22×C47⋊C8C2311yescharacteristic
88#13094024—22no—
89#13094024C2314yes—
90#13094016—22no—
91#13094016—22no—
92#13094016C2314yes—
93#13094016C2314yes—
94#13094002—28no—
95#13094002—28no—
96#13094000—28no—
97C4×D188—22no—
98C4×D188—22no—
99C4×D188—22no—
100C4×D188C2314yes—
101C4×D188C2314yes—
102C4×D188C2314yes—
103C2×C4⋊Dic47—21no—
104C2×C4⋊Dic47C2311yescharacteristic
105C2×C4⋊Dic47C2311yescharacteristic
106C2×C4⋊Dic47C2311yescharacteristic
107C2×Dic47⋊C4—21no—
108C2×Dic47⋊C4—21no—
109C2×Dic47⋊C4—21no—
110C2×Dic47⋊C4—21no—
111C4⋊C4×D47—28no—
112C2×(C2×D47)⋊C4—21no—
113C2×(C2×D47)⋊C4—21no—
114C2×(C2×D47)⋊C4—21no—
115#13093957C2314yes—
116#13093957C2314yes—
117#13093957C2314yes—
118#13093957C2314yes—
119#13093957C2314yes—
120#13093955C2314yes—
121#13093955C2314yes—
122#13093955C2314yes—
123#13093955C2314yes—
124C4⋊(C47⋊C8)C2314yes—
125C4⋊(C47⋊C8)C2314yes—
126C4⋊(C47⋊C8)C2314yes—
127#13093945C2314yes—
128#13093945C2314yes—
129#13093945C2314yes—
130#13093944C2314yes—
131#13093944C2314yes—
132#13093944C2314yes—
133#13093935C2314yes—
134#13093935C2314yes—
135C4×C47⋊C8C2314yes—
136C22×Q8×C47—21no—
137C22×Q8×C47D411yescharacteristic
138C22×D4×C47C2311yescharacteristic
139C23×C4×C47—21no—
140C23×C4×C47—21no—
141C23×C4×C47—21no—
142C4⋊Q8×C47—22no—
143C4⋊Q8×C47C2314yes—
144#125×C47—22no—
145#125×C47—22no—
146#125×C47C2314yes—
147#125×C47C2314yes—
148C22⋊Q8×C47—28no—
149C22⋊Q8×C47—28no—
150C22⋊Q8×C47—28no—
151C4×Q8×C47D414yes—
152C4×Q8×C47C2314yes—
153C4×D4×C47—22no—
154C4×D4×C47—22no—
155C4×D4×C47—22no—
156C4×D4×C47C2314yes—
157C4×D4×C47C2314yes—
158C4×D4×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—28no—
165C2×C4⋊C4×C47D411yescharacteristic
166C2×C4⋊C4×C47D411yescharacteristic
167C2×C4⋊C4×C47D411yescharacteristic
168C2×C4⋊C4×C47C2311yescharacteristic
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C22⋊C4×C47—21no—
172C2×C22⋊C4×C47—21no—
173C2×C22⋊C4×C47—21no—
174C2×C42×C47C2311yescharacteristic
175C2×C42×C47C2311yescharacteristic
176C2×C42×C47C2311yescharacteristic
177C24×C47—21no—
178C23×D47—21no—
179C2×Q8×C47—24no—
180C2×Q8×C47—42no—
181C2×Q8×C47—82no—
182C2×Q8×C47C2×D414yes—
183C2×D4×C47—21no—
184C2×D4×C47—22no—
185C2×D4×C47C2×Q814yes—
186C2×D4×C47C2412yes—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—24no—
191C22×C4×C47—24no—
192C22×C4×C47—24no—
193C22×C4×C47—44no—
194C22×C4×C47—82no—
195C22×C4×C47—82no—
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2411yescharacteristic
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C2×D188—21no—
207C2×D188—22no—
208C2×D188C2×Q814yes—
209C2×D188C2412yes—
210C2×C4×D47—24no—
211C2×C4×D47—24no—
212C2×C4×D47—24no—
213C2×C4×D47—44no—
214C2×C4×D47—82no—
215C2×C4×D47—82no—
216C2×Dic94—24no—
217C2×Dic94—82no—
218C4⋊C4×C47—24no—
219C4⋊C4×C47—24no—
220C4⋊C4×C47—24no—
221C4⋊C4×C47—24no—
222C4⋊C4×C47—24no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47C2×D414yes—
227C4⋊C4×C47C2×D414yes—
228C4⋊C4×C47C2×D414yes—
229C4⋊C4×C47C2412yes—
230C4⋊C4×C47C2412yes—
231C4⋊C4×C47C2412yes—
232C22⋊C4×C47—24no—
233C22⋊C4×C47—24no—
234C22⋊C4×C47—24no—
235C42×C47C2×D412yes—
236C42×C47C2×D412yes—
237C42×C47C2×D412yes—
238C42×C47C2412yes—
239C42×C47C2412yes—
240C42×C47C2412yes—
241#10625334C2×Q8116yescomplemented
242(C2×D47)⋊C4—24no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245C4⋊Dic47—24no—
246C4⋊Dic47—21no—
247C4⋊Dic47—21no—
248C4⋊Dic47—21no—
249C4⋊Dic47C2412yes—
250C4⋊Dic47C2412yes—
251C4⋊Dic47C2412yes—
252Dic47⋊C4—24no—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256C2×C47⋊C8—22no—
257C2×C47⋊C8—22no—
258C2×C47⋊C8—22no—
259C2×C47⋊C8C2×Q814yes—
260C2×C47⋊C8C2412yes—
261C2×C47⋊C8C2412yes—
262C2×C47⋊C8C2412yes—
263C2×C47⋊C8C2412yes—
264C23×C47—24no—
265C23×C47—22no—
266C23×C47—42no—
267C23×C47—42no—
268C23×C47C22×D411yescharacteristic
269C22×D47—24no—
270C22×D47—22no—
271C22×D47—42no—
272C22×D47—42no—
273Q8×C47—44no—
274Q8×C47—84no—
275D4×C47—24no—
276D4×C47—22no—
277D4×C47C22×Q814yes—
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—48no—
288C2×C4×C47—42no—
289C2×C4×C47—42no—
290C2×C4×C47—42no—
291C2×C4×C47—84no—
292C2×C4×C47—84no—
293C2×C4×C47C22×D412yes—
294C2×C4×C47C22×D412yes—
295C2×C4×C47C22×D412yes—
296C2×C4×C47C22×D412yes—
297C2×C4×C47C22×D412yes—
298C2×C4×C47C22×D412yes—
299C2×C4×C47C22×D411yescharacteristic
300C2×C4×C47C22×Q812yes—
301C2×C4×C472−1+412yes—
302C2×C4×C47C2511yescharacteristic
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309D188—24no—
310D188—22no—
311D188C22×Q814yes—
312C4×D47—48no—
313C4×D47—84no—
314C4×D47—84no—
315Dic94—84no—
316C47⋊C8—22no—
317C47⋊C8—22no—
318C47⋊C8—22no—
319C47⋊C8C22×Q814yes—
320C2×#3389—471nomaximal, Sylow
321C22×C47—24no—
322C22×C47—48no—
323C22×C47—42no—
324C22×C47—42no—
325C22×C47D4×Q812yes—
326C22×C47#57512yes—
327C22×C47#57612yes—
328C22×C47C23×D411yescharacteristic
329C2×D47—24no—
330C2×D47—48no—
331C2×D47—42no—
332C2×D47—42no—
333C4×C47—22no—
334C4×C47—22no—
335C4×C47—22no—
336C4×C47—22no—
337C4×C47—22no—
338C4×C47—22no—
339C4×C47—42no—
340C4×C47—42no—
341C4×C47—42no—
342C4×C47D4×Q812yes—
343C4×C47C23×Q811yescharacteristic
344C4×C47C2×2−1+411yescharacteristic
345Dic47—42no—
346Dic47—42no—
347Dic47—42no—
348C2×#554—471no—
349C2×#554D4711yescharacteristic, complemented
350#3389—4716no—
351C2×#501—471no—
352C2×#501—471no—
353C2×#499—471no—
354C2×#478—471no—
355C2×#478—471no—
356C2×#478—471no—
357C2×#478—471no—
358C2×#474—471no—
359C2×#474—471no—
360C2×#446—471no—
361C2×#442—471no—
362C2×#442—471no—
363C2×C4×D8—471no—
364C2×C47—44no—
365C2×C47#338914yescomplemented
366C2×C47C2×D4×Q811yescharacteristic
367C2×C47C2×#57511yescharacteristic
368C2×C47C2×#57611yescharacteristic
369D47—44no—
370C22×D8—471no—
371#554—24no—
372#554—478no—
373#554—944no—
374#554C2×D4718yescomplemented
375C2×C4⋊Q8—471no—
376C2×C4⋊Q8C2×D4711yescharacteristic
377C2×#125—471no—
378C2×#125—471no—
379C2×#125C2×D4711yescharacteristic
380C2×#125C2×D4711yescharacteristic
381C2×C22⋊Q8—21no—
382C2×C22⋊Q8—21no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—941no—
385C2×C22⋊Q8—941no—
386C2×C22⋊Q8—941no—
387C2×C4×Q8C2×D4711yescharacteristic
388C2×C4×D4—471no—
389C2×C4×D4—471no—
390C2×C4×D4—471no—
391C2×C4×D4C2×D4711yescharacteristic
392C2×C4×D4C2×D4711yescharacteristic
393C2×C4×D4C2×D4711yescharacteristic
394C22×C4⋊C4—21no—
395C22×C4⋊C4—941no—
396#501—478no—
397#501—478no—
398#499—478no—
399#478—478no—
400#478—478no—
401#478—478no—
402#478—478no—
403#474—478no—
404#474—478no—
405#446—478no—
406#442—478no—
407#442—478no—
408C4×D8—478no—
409C2×#107—471no—
410C2×#107—471no—
411C2×#107—471no—
412C2×#107—471no—
413C2×#107—471no—
414C2×#106—471no—
415C2×#106—471no—
416C2×#106—471no—
417C2×#106—471no—
418C2×C4⋊C8—471no—
419C2×C4⋊C8—471no—
420C2×C4⋊C8—471no—
421C2×#102—471no—
422C2×#102—471no—
423C2×#102—471no—
424C2×#102—471no—
425C2×#102—471no—
426C2×#102—471no—
427C2×#97—471no—
428C2×#97—471no—
429C2×C4×C8—471no—
430C47C2×#338911yescharacteristic, complemented, Sylow
431C22×Q8—21no—
432C22×Q8—941no—
433C22×Q8C22⋊D4711yescharacteristic
434C22×D4—471no—
435C22×D4C22×D4711yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—21no—
439C23×C4—941no—
440C23×C4—941no—
441C23×C4—941no—
442C2×D8—478no—
443C2×D8—474no—
444C22×C8—471no—
445C22×C8—471no—
446C22×C8—471no—
447C22×C8—471no—
448C4⋊Q8—22no—
449C4⋊Q8—474no—
450C4⋊Q8—942no—
451C4⋊Q8C22×D4714yes—
452#125—22no—
453#125—22no—
454#125—474no—
455#125—474no—
456#125—942no—
457#125—942no—
458#125C22×D4714yes—
459#125C22×D4714yes—
460C22⋊Q8—28no—
461C22⋊Q8—28no—
462C22⋊Q8—28no—
463C22⋊Q8—948no—
464C22⋊Q8—948no—
465C22⋊Q8—948no—
466C4×Q8C22⋊D4714yes—
467C4×Q8C22×D4714yes—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—474no—
472C4×D4—474no—
473C4×D4—474no—
474C4×D4—942no—
475C4×D4—942no—
476C4×D4—942no—
477C4×D4C22×D4714yes—
478C4×D4C22×D4714yes—
479C4×D4C22×D4714yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—28no—
486C2×C4⋊C4—471no—
487C2×C4⋊C4—471no—
488C2×C4⋊C4—471no—
489C2×C4⋊C4—941no—
490C2×C4⋊C4—941no—
491C2×C4⋊C4—941no—
492C2×C4⋊C4—941no—
493C2×C4⋊C4—941no—
494C2×C4⋊C4—948no—
495C2×C4⋊C4C22⋊D4711yescharacteristic
496C2×C4⋊C4C22⋊D4711yescharacteristic
497C2×C4⋊C4C22⋊D4711yescharacteristic
498C2×C4⋊C4C22×D4711yescharacteristic
499C2×C4⋊C4C22×D4711yescharacteristic
500C2×C4⋊C4C22×D4711yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—941no—
505C2×C22⋊C4—941no—
506C2×C22⋊C4—941no—
507C2×C42C22×D4711yescharacteristic
508C2×C42C22×D4711yescharacteristic
509C2×C42C22×D4711yescharacteristic
510#107—474no—
511#107—474no—
512#107—474no—
513#107—474no—
514#107—474no—
515#106—474no—
516#106—474no—
517#106—474no—
518#106—474no—
519C4⋊C8—474no—
520C4⋊C8—474no—
521C4⋊C8—474no—
522#102—474no—
523#102—474no—
524#102—474no—
525#102—474no—
526#102—474no—
527#102—474no—
528#97—474no—
529#97—474no—
530C4×C8—474no—
531C24—21no—
532C24—941no—
533C2×Q8—24no—
534C2×Q8—42no—
535C2×Q8—82no—
536C2×Q8—944no—
537C2×Q8—3762no—
538C2×Q8C2×C22⋊D4714yes—
539C2×D4—21no—
540C2×D4—22no—
541C2×D4—474no—
542C2×D4—472no—
543C2×D4—941no—
544C2×D4—942no—
545C2×D4Q8×D4714yes—
546C2×D4C23×D4712yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—44no—
554C22×C4—82no—
555C22×C4—82no—
556C22×C4—941no—
557C22×C4—941no—
558C22×C4—941no—
559C22×C4—944no—
560C22×C4—944no—
561C22×C4—944no—
562C22×C4—3762no—
563C22×C4—3762no—
564C22×C4—1884no—
565C22×C4C2×C22⋊D4711yescharacteristic
566C22×C4C2×C22⋊D4711yescharacteristic
567C22×C4C2×C22⋊D4711yescharacteristic
568C22×C4C2×C22⋊D4711yescharacteristic
569C22×C4C2×C22⋊D4711yescharacteristic
570C22×C4C2×C22⋊D4711yescharacteristic
571C22×C4C23×D4711yescharacteristic
572D8—4716no—
573C2×C8—474no—
574C2×C8—472no—
575C2×C8—472no—
576C2×C8—472no—
577C2×C8—472no—
578C2×C8—942no—
579C2×C8—942no—
580C2×C8—942no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—472no—
590C4⋊C4—472no—
591C4⋊C4—472no—
592C4⋊C4—944no—
593C4⋊C4—944no—
594C4⋊C4—944no—
595C4⋊C4—944no—
596C4⋊C4—941no—
597C4⋊C4—941no—
598C4⋊C4—941no—
599C4⋊C4—944no—
600C4⋊C4C2×C22⋊D4714yes—
601C4⋊C4C2×C22⋊D4714yes—
602C4⋊C4C2×C22⋊D4714yes—
603C4⋊C4C23×D4712yes—
604C4⋊C4C23×D4712yes—
605C4⋊C4C23×D4712yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—944no—
610C22⋊C4—944no—
611C22⋊C4—944no—
612C42C2×C22⋊D4712yes—
613C42C2×C22⋊D4712yes—
614C42C2×C22⋊D4712yes—
615C42C23×D4712yes—
616C42C23×D4712yes—
617C42C23×D4712yes—
618C23—24no—
619C23—22no—
620C23—42no—
621C23—42no—
622C23—944no—
623C23—942no—
624C23—1882no—
625C23—1882no—
626C23C22×C22⋊D4711yescharacteristic
627Q8—44no—
628Q8—84no—
629Q8—3764no—
630D4—24no—
631D4—22no—
632D4—474no—
633D4—944no—
634D4—942no—
635D4C2×Q8×D4714yes—
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—48no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—942no—
652C2×C4—942no—
653C2×C4—942no—
654C2×C4—3764no—
655C2×C4—3764no—
656C2×C4—1888no—
657C2×C4—1882no—
658C2×C4—1882no—
659C2×C4—1882no—
660C2×C4C22×C22⋊D4712yes—
661C2×C4C22×C22⋊D4712yes—
662C2×C4C22×C22⋊D4712yes—
663C2×C4C22×C22⋊D4712yes—
664C2×C4C22×C22⋊D4712yes—
665C2×C4C22×C22⋊D4712yes—
666C2×C4C22×C22⋊D4711yescharacteristic
667C2×C4C2×Q8×D4712yes—
668C2×C4#1309407212yes—
669C2×C4C24×D4711yescharacteristic
670C8—474no—
671C8—942no—
672C8—942no—
673C8—942no—
674C22—24no—
675C22—42no—
676C22—48no—
677C22—42no—
678C22—944no—
679C22—1882no—
680C22—1888no—
681C22—1882no—
682C22Q8×C22⋊D4712yes—
683C22#1568992112yes—
684C22#1568992612yes—
685C22C23×C22⋊D4711yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—22no—
691C4—22no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—1882no—
696C4—1882no—
697C4—1882no—
698C4Q8×C22⋊D4712yes—
699C4C22×Q8×D4711yescharacteristic
700C4C2×#1309407211yescharacteristic
701C2—44no—
702C2—1884no—
703C2#2025634214yesdirect product factor
704C2C2×Q8×C22⋊D4711yescharacteristic
705C2C2×#1568992111yescharacteristic
706C2C2×#1568992611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#554C2
socleC23×C47C22×D4
prime radicalC22×#10625334C22
hypercenterC2×#554D47
hypocenterC47C2×#3389
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×#15689833C2semidirect
2. #20256342C2direct (N × H)
3. C2×#15689533C2semidirect
4. C2×#15689529C2semidirect
5. C2×#15689522C2semidirect
6. C2×#15689423C2semidirect
7. C2×#15689423C2semidirect
8. C2×#15689420C2semidirect
9. C2×#15689420C2semidirect
10. C2×#15689403C2semidirect
11. C2×#15689400C2semidirect
12. C2×#15689254C2semidirect
16. C2×C47×#554C2semidirect
19. #15689833C22semidirect
30. #15689533C22semidirect
31. #15689529C22semidirect
32. #15689522C22semidirect
33. #15689423C22semidirect
34. #15689423C22semidirect
35. #15689420C22semidirect
36. #15689420C22semidirect
37. #15689403C22semidirect
38. #15689400C22semidirect
39. #15689254C22semidirect
65. C47×#554C22semidirect
82. C2×#10625334Q8semidirect
241. #10625334C2×Q8semidirect
349. C2×#554D47semidirect
365. C2×C47#3389semidirect
374. #554C2×D47semidirect
430. C47C2×#3389semidirect
703. C2#20256342direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898332
#202563422
C2×#156895332
C2×#156895292
C2×#156895222
C2×#156894232
C2×#156894202
C2×#156894032
C2×#156894002
C2×#156892542
C2×#156892332
C2×C4×#106253342
C2×C47×#5542
C2×#338947