Finite Group Databasebeta

← C2×#21444393 #29647331

Subgroups — C2×#21444393 #29647331

Order 15616.

1074 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840293C211yesmaximal, characteristic
2C2×#16839812C211yesmaximal, characteristic, complemented
3C2×#16839629C211yesmaximal, characteristic, complemented
4#21444393C218yesmaximal, direct product factor
5C2×#16839500C211yesmaximal, characteristic, complemented
6C2×#16839498C211yesmaximal, characteristic, complemented
7C2×#16839496C211yesmaximal, characteristic
8C2×C61×#327C211yesmaximal, characteristic
9#16840293—22no—
10#16840293—22no—
11#16840293C414yescomplemented
12#16840293C2214yes—
13C2×#14519770—21no—
14C2×#14519768C411yescharacteristic, complemented
15C2×#14519764C411yescharacteristic, complemented
16C2×#14519758—21no—
17C2×#14519756C2211yescharacteristic
18C2×#14519742C411yescharacteristic, complemented
19C2×D4×Dic61—21no—
20C2×D4×Dic61C411yescharacteristic, complemented
21C2×#14519733—21no—
22C22×C4×Dic61C2211yescharacteristic
23#16839812—22no—
24#16839812C2214yescomplemented
25C2×#14519706—21no—
26C2×C22⋊#92418C2211yescharacteristic
27C2×C8×Dic61—21no—
28#16839629—22no—
29#16839629C2214yescomplemented
30C2×#14519684—21no—
31C2×#14519684—21no—
32C2×#14519684C2211yescharacteristic
33#16839500C2214yescomplemented
34#16839498C2214yescomplemented
35#16839496C2214yes—
36C2×#121×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×#95×C61C2211yescharacteristic
39C61×#327C2214yes—
40C22×Dic122C2×C411yescharacteristic
41C23×Dic61—21no—
42C23×Dic61—21no—
43C23×Dic61D411yescharacteristic
44C23×Dic61D411yescharacteristic
45C22×#92418—21no—
46#14519770—24no—
47#14519770—24no—
48#14519768—22no—
49#14519768C2×C414yescomplemented
50#14519764—22no—
51#14519764C2×C414yescomplemented
52#14519758—24no—
53#14519758—24no—
54#14519756—21no—
55#14519756—21no—
56#14519756C2×C412yes—
57#14519756C2312yes—
58#14519742—22no—
59#14519742C2×C414yescomplemented
60D4×Dic61—24no—
61D4×Dic61—24no—
62D4×Dic61—22no—
63D4×Dic61C2×C414yescomplemented
64#14519733—24no—
65#14519733—24no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61C2×C411yescharacteristic
68C2×#11758196—21no—
69C2×#11758196—21no—
70C2×#11758196—21no—
71C2×C22⋊Dic61—21no—
72C2×C22⋊Dic61—21no—
73C2×C22⋊Dic61—21no—
74C2×C22⋊Dic61—21no—
75C2×C4×Dic61—21no—
76C2×C4×Dic61C2×C411yescharacteristic
77C2×C4×Dic61C2×C411yescharacteristic
78C2×C4×Dic61C2×C412yes—
79C2×C4×Dic61D412yes—
80C2×C4×Dic61D411yescharacteristic
81C2×C4×Dic61D411yescharacteristic
82C2×C4×Dic61D412yes—
83C2×C4×Dic61C2312yes—
84#14519706—24no—
85C22⋊#92418—21no—
86C22⋊#92418C2312yes—
87C8×Dic61—24no—
88#14519684—21no—
89#14519684—24no—
90#14519684—24no—
91#14519684C2312yes—
92C22×D4×C61—21no—
93C22×D4×C61C2×C411yescharacteristic
94C23×C4×C61—21no—
95C23×C4×C61C2311yescharacteristic
96C22×C8×C61—21no—
97#121×C61—21no—
98#121×C61—21no—
99#121×C61C2×C412yes—
100#121×C61C2312yes—
101C2×C4⋊C4×C61C2×C411yescharacteristic
102C2×C22⋊C4×C61—21no—
103C22⋊C8×C61—21no—
104C22⋊C8×C61C2312yes—
105#95×C61—21no—
106#95×C61C2312yes—
107C24×C61—21no—
108C24×C61C2×D411yescharacteristic
109C2×D4×C61—22no—
110C2×D4×C61—22no—
111C2×D4×C61—21no—
112C2×D4×C61—42no—
113C2×D4×C61—42no—
114C2×D4×C61—42no—
115C2×D4×C61C22×C412yes—
116C22×C4×C61—21no—
117C22×C4×C61—22no—
118C22×C4×C61—42no—
119C22×C4×C61—42no—
120C22×C4×C61—42no—
121C22×C4×C61—42no—
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C22×C411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2411yescharacteristic
128C22×Dic61—22no—
129C22×Dic61—22no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—24no—
133C22×Dic61—22no—
134C22×Dic61—42no—
135C22×Dic61—44no—
136C22×Dic61—42no—
137C22×Dic61—42no—
138C22×Dic61—42no—
139C22×Dic61C22⋊C411yescharacteristic
140C22×Dic61C22⋊C411yescharacteristic
141C22×Dic61C22⋊C411yescharacteristic
142C22×Dic61C22⋊C411yescharacteristic
143C22×Dic61C22⋊C412yes—
144C22×Dic61C22⋊C412yes—
145C22×Dic61C2×D412yes—
146C22×Dic61C2×D412yes—
147C2×Dic122—21no—
148C2×Dic122—42no—
149C2×Dic122C22×C412yes—
150C2×C8×C61—22no—
151C2×C8×C61—42no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61C22×C412yes—
154C22⋊C4×C61—22no—
155C22⋊C4×C61—22no—
156C22⋊Dic61—22no—
157C22⋊Dic61—22no—
158C22⋊Dic61—24no—
159C22⋊Dic61—24no—
160C22⋊Dic61—24no—
161C4⋊Dic61—21no—
162C4⋊Dic61—24no—
163C4⋊Dic61C22×C412yes—
164#11758196—22no—
165#11758196—22no—
166#11758196—24no—
167#11758196—24no—
168C4×Dic61—24no—
169C4×Dic61C22⋊C412yes—
170C4×Dic61C22⋊C412yes—
171C4×Dic61C22⋊C412yes—
172C4×Dic61C22⋊C412yes—
173C4×Dic61C22×C412yes—
174C4×Dic61C22×C412yes—
175C4×Dic61C2×D412yes—
176C4×Dic61C2×D412yes—
177C2×#92418—22no—
178C2×#92418—42no—
179C23×C61—22no—
180C23×C61—22no—
181C23×C61—22no—
182C23×C61—42no—
183C23×C61—42no—
184C23×C61—42no—
185C23×C61C2×C22⋊C411yescharacteristic
186C23×C61C2×C22⋊C411yescharacteristic
187C23×C61#13512yes—
188C23×C61#13512yes—
189C23×C61C22×D411yescharacteristic
190D4×C61—42no—
191D4×C61—42no—
192D4×C61—42no—
193D4×C61—42no—
194D4×C61—44no—
195C2×C4×C61—22no—
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—42no—
203C2×C4×C61—42no—
204C2×C4×C61—42no—
205C2×C4×C61—42no—
206C2×C4×C61—84no—
207C2×C4×C61C2×C22⋊C411yescharacteristic
208C2×C4×C61C2×C22⋊C411yescharacteristic
209C2×C4×C61C23×C411yescharacteristic
210C2×C4×C61C22×D411yescharacteristic
211C2×Dic61—22no—
212C2×Dic61—22no—
213C2×Dic61—24no—
214C2×Dic61—22no—
215C2×Dic61—22no—
216C2×Dic61—22no—
217C2×Dic61—22no—
218C2×Dic61—22no—
219C2×Dic61—22no—
220C2×Dic61—42no—
221C2×Dic61—42no—
222C2×Dic61—48no—
223C2×Dic61—42no—
224C2×Dic61—42no—
225C2×Dic61—42no—
226C2×Dic61—42no—
227C2×Dic61—42no—
228C2×Dic61—84no—
229C2×Dic61C2×C22⋊C412yes—
230C2×Dic61C2×C22⋊C412yes—
231C2×Dic61C2×C22⋊C412yes—
232C2×Dic61C2×C22⋊C412yes—
233Dic122—42no—
234Dic122—42no—
235C8×C61—42no—
236#92418—42no—
237C2×#1521—611nomaximal, Sylow
238C22×C61—21no—
239C22×C61—21no—
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—24no—
243C22×C61—24no—
244C22×C61—42no—
245C22×C61—42no—
246C22×C61—42no—
247C22×C61—84no—
248C22×C61#41012yes—
249C22×C61#41612yes—
250C22×C61#41612yes—
251C22×C61#42112yes—
252C22×C61C22×C22⋊C411yescharacteristic
253C22×C61C2×#13511yescharacteristic
254C22×C61C2×#13511yescharacteristic
255C4×C61—21no—
256C4×C61—21no—
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—42no—
260C4×C61—82no—
261Dic61—22no—
262Dic61—22no—
263Dic61—22no—
264Dic61—22no—
265Dic61—42no—
266Dic61—42no—
267Dic61—82no—
268C2×#529—611no—
269C2×#431—611no—
270C2×#383—611no—
271#1521—618no—
272C2×#328—611no—
273C2×#328—611no—
274C2×#327—611no—
275C2×#327D6111yescharacteristic
276C2×C61—21no—
277C2×C61—21no—
278C2×C61—22no—
279C2×C61—82no—
280C2×C61#152114yescomplemented
281C2×C61C2×#41011yescharacteristic
282C2×C61C2×#41611yescharacteristic
283C2×C61C2×#42111yescharacteristic
284#529—614no—
285#529—614no—
286#529—1222no—
287#529—1222no—
288C2×#126—1221no—
289C2×#125—611no—
290C2×#124—611no—
291C2×#123—1221no—
292C2×C22⋊Q8—611no—
293C2×#121C2×D6111yescharacteristic
294C2×C4×Q8—611no—
295C2×C4×D4—611no—
296C2×C4×D4—1221no—
297C2×#117—1221no—
298C22×C42—611no—
299#431—614no—
300#431—1222no—
301C2×C4⋊C8—1221no—
302C2×C22⋊C8—611no—
303C2×C22⋊C8C2×D6111yescharacteristic
304C2×C4×C8—1221no—
305#383—614no—
306#383—1222no—
307C2×#95—611no—
308C2×#95—1221no—
309C2×#95—1221no—
310C2×#95C2×D6111yescharacteristic
311#328—614no—
312#328—614no—
313#327—614no—
314#327C2×D6114yes—
315C61C2×#152111yescharacteristic, complemented, Sylow
316C22×Q8—611no—
317C22×D4—21no—
318C22×D4C4×D6111yescharacteristic
319C23×C4—21no—
320C23×C4—611no—
321C23×C4—611no—
322C23×C4—1221no—
323C23×C4—1221no—
324C23×C4C22×D6111yescharacteristic
325C22×C8—21no—
326C22×C8—1221no—
327#126—1224no—
328#126—1224no—
329#125—614no—
330#125—1222no—
331#124—614no—
332#124—1222no—
333#123—1224no—
334#123—1224no—
335C22⋊Q8—612no—
336C22⋊Q8—612no—
337C22⋊Q8—1221no—
338C22⋊Q8—1221no—
339#121—21no—
340#121—21no—
341#121C4×D6112yes—
342#121C22×D6112yes—
343C4×Q8—614no—
344C4×Q8—1222no—
345C4×D4—614no—
346C4×D4—1222no—
347C4×D4—1224no—
348C4×D4—1224no—
349#117—1224no—
350#117—1224no—
351C2×C4⋊C4—611no—
352C2×C4⋊C4—1221no—
353C2×C4⋊C4—1221no—
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1221no—
356C2×C4⋊C4C4×D6111yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—1221no—
359C2×C22⋊C4—1221no—
360C2×C22⋊C4—1221no—
361C2×C22⋊C4—1221no—
362C2×C42—611no—
363C2×C42—611no—
364C2×C42—612no—
365C2×C42—611no—
366C2×C42—611no—
367C2×C42—612no—
368C2×C42—612no—
369C2×C42—612no—
370C2×C42—1221no—
371C4⋊C8—1224no—
372C22⋊C8—21no—
373C22⋊C8—612no—
374C22⋊C8—1221no—
375C22⋊C8C22×D6112yes—
376C4×C8—1224no—
377#95—21no—
378#95—612no—
379#95—1224no—
380#95—1224no—
381#95—1221no—
382#95C22×D6112yes—
383C24—21no—
384C24D4×D6111yescharacteristic
385C2×Q8—612no—
386C2×Q8—1221no—
387C2×Q8—2442no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—21no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4C2×C4×D6112yes—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—612no—
402C22×C4—612no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—612no—
408C22×C4—612no—
409C22×C4—1224no—
410C22×C4—1222no—
411C22×C4—1222no—
412C22×C4—1221no—
413C22×C4—1221no—
414C22×C4—1222no—
415C22×C4—2442no—
416C22×C4—2444no—
417C22×C4—2442no—
418C22×C4—2442no—
419C22×C4—2442no—
420C22×C4C2×C4×D6111yescharacteristic
421C22×C4C2×C4×D6111yescharacteristic
422C22×C4D4×D6111yescharacteristic
423C22×C4D4×D6111yescharacteristic
424C22×C4D4×D6111yescharacteristic
425C22×C4C23×D6111yescharacteristic
426C2×C8—22no—
427C2×C8—42no—
428C2×C8—1222no—
429C2×C8—2442no—
430C4⋊C4—21no—
431C4⋊C4—612no—
432C4⋊C4—1224no—
433C4⋊C4—1224no—
434C4⋊C4—1224no—
435C4⋊C4—1222no—
436C4⋊C4—1221no—
437C4⋊C4—1222no—
438C4⋊C4C2×C4×D6112yes—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—1224no—
442C22⋊C4—1224no—
443C22⋊C4—1224no—
444C22⋊C4—1222no—
445C22⋊C4—1222no—
446C42—612no—
447C42—612no—
448C42—612no—
449C42—612no—
450C42—612no—
451C42—612no—
452C42—612no—
453C42—612no—
454C42—1224no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23C22⋊C4×D6111yescharacteristic
462C23C22⋊C4×D6111yescharacteristic
463C23#1451979612yes—
464C23#1451979812yes—
465C23C2×D4×D6111yescharacteristic
466Q8—2442no—
467Q8—2442no—
468D4—42no—
469D4—42no—
470D4—44no—
471D4—42no—
472D4—42no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—84no—
485C2×C4—612no—
486C2×C4—612no—
487C2×C4—612no—
488C2×C4—612no—
489C2×C4—1224no—
490C2×C4—1222no—
491C2×C4—1222no—
492C2×C4—1222no—
493C2×C4—1222no—
494C2×C4—1222no—
495C2×C4—1222no—
496C2×C4—1222no—
497C2×C4—1222no—
498C2×C4—4884no—
499C2×C4—2442no—
500C2×C4—2442no—
501C2×C4—2448no—
502C2×C4—2442no—
503C2×C4—2442no—
504C2×C4—2442no—
505C2×C4—2442no—
506C2×C4—2442no—
507C2×C4C22⋊C4×D6111yescharacteristic
508C2×C4C22⋊C4×D6111yescharacteristic
509C2×C4C22×C4×D6111yescharacteristic
510C2×C4C2×D4×D6111yescharacteristic
511C8—42no—
512C8—2442no—
513C22—21no—
514C22—21no—
515C22—24no—
516C22—24no—
517C22—21no—
518C22—21no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—84no—
523C22#1683973412yes—
524C22#1683975512yes—
525C22#1683975512yes—
526C22#1683977712yes—
527C22C2×C22⋊C4×D6111yescharacteristic
528C22C2×#1451979611yescharacteristic
529C22C2×#1451979811yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—21no—
534C4—42no—
535C4—82no—
536C4—1222no—
537C4—1222no—
538C4—1222no—
539C4—1222no—
540C4—4882no—
541C4—2442no—
542C4—2442no—
543C2—21no—
544C2—21no—
545C2—22no—
546C2—82no—
547C2#2144439314yesdirect product factor
548C2C2×#1683973411yescharacteristic
549C2C2×#1683975511yescharacteristic
550C2C2×#1683977711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#327C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#121×C61C22
cosocleC22×C4×C61C24
hypercenterC2×#327D61
hypocenterC61C2×#1521
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#16839812C2semidirect
3. C2×#16839629C2semidirect
4. #21444393C2direct (N × H)
5. C2×#16839500C2semidirect
6. C2×#16839498C2semidirect
11. #16840293C4semidirect
14. C2×#14519768C4semidirect
15. C2×#14519764C4semidirect
18. C2×#14519742C4semidirect
20. C2×D4×Dic61C4semidirect
24. #16839812C22semidirect
29. #16839629C22semidirect
33. #16839500C22semidirect
34. #16839498C22semidirect
49. #14519768C2×C4semidirect
51. #14519764C2×C4semidirect
59. #14519742C2×C4semidirect
63. D4×Dic61C2×C4semidirect
280. C2×C61#1521semidirect
315. C61C2×#1521semidirect
547. C2#21444393direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402932
C2×#168398122
C2×#168396292
#214443932
C2×#168395002
C2×#168394982
C2×#168394962
C2×C61×#3272
C2×#152161