Subgroups — C₂×#20259266 #27133087

Order 12224.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₇₆₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#20259266	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₉₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×C₁₉₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₃₈₂	—	2	1	no	—
6	Dic₇₆₄	—	2	1	no	—
7	Dic₇₆₄	C₂²	1	2	yes	complemented
8	C₁₉₁⋊C₁₆	C₂²	1	2	yes	complemented
9	C₂×D₄×C₁₉₁	—	2	1	no	—
10	D₈×C₁₉₁	—	2	1	no	—
11	D₈×C₁₉₁	C₂²	1	2	yes	—
12	C₂×C₈×C₁₉₁	C₂²	1	1	yes	characteristic
13	Dic₃₈₂	—	2	2	no	—
14	Dic₃₈₂	—	4	1	no	—
15	C₂×Dic₁₉₁	—	4	1	no	—
16	C₂³×C₁₉₁	—	4	1	no	—
17	D₄×C₁₉₁	—	2	2	no	—
18	D₄×C₁₉₁	—	4	1	no	—
19	C₂×C₄×C₁₉₁	D₄	1	1	yes	characteristic
20	C₈×C₁₉₁	D₄	1	1	yes	characteristic
21	C₈×C₁₉₁	C₂³	1	1	yes	characteristic
22	C₂²×C₁₉₁	—	4	2	no	—
23	C₂²×C₁₉₁	—	8	2	no	—
24	C₂²×C₁₉₁	D₈	1	1	yes	characteristic
25	C₄×C₁₉₁	D₈	1	1	yes	characteristic
26	C₄×C₁₉₁	C₂×D₄	1	1	yes	characteristic
27	Dic₁₉₁	—	4	2	no	—
28	C₂×C₁₉₁	—	8	2	no	—
29	C₂×C₁₉₁	SD₃₂	1	2	yes	complemented
30	C₂×C₁₉₁	C₂×D₈	1	1	yes	characteristic
31	C₁₉₁	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
32	C₂×SD₃₂	—	191	1	no	maximal, Sylow
33	C₂×Q₁₆	—	191	1	no	—
34	C₂×D₈	D₁₉₁	1	1	yes	characteristic
35	SD₃₂	—	191	4	no	—
36	C₂×C₁₆	—	191	1	no	—
37	C₂×Q₈	—	382	1	no	—
38	C₂×D₄	—	2	1	no	—
39	Q₁₆	—	382	1	no	—
40	Q₁₆	—	191	2	no	—
41	D₈	—	2	1	no	—
42	D₈	C₂×D₁₉₁	1	2	yes	—
43	C₂×C₈	C₂×D₁₉₁	1	1	yes	characteristic
44	C₁₆	—	191	2	no	—
45	C₂³	—	4	1	no	—
46	Q₈	—	382	2	no	—
47	Q₈	—	764	1	no	—
48	D₄	—	2	2	no	—
49	D₄	—	4	1	no	—
50	C₂×C₄	—	764	1	no	—
51	C₂×C₄	C₂²⋊D₁₉₁	1	1	yes	characteristic
52	C₈	C₂²⋊D₁₉₁	1	1	yes	characteristic
53	C₈	C₂²×D₁₉₁	1	1	yes	characteristic
54	C₂²	—	4	2	no	—
55	C₂²	—	8	2	no	—
56	C₂²	#15690272	1	1	yes	characteristic
57	C₄	—	764	2	no	—
58	C₄	#15690272	1	1	yes	characteristic
59	C₄	C₂×C₂²⋊D₁₉₁	1	1	yes	characteristic
60	C₂	—	8	2	no	—
61	C₂	#20259266	1	2	yes	direct product factor
62	C₂	C₂×#15690272	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15690272
commutator, cosocle	C₈×C₁₉₁	C₂³
Frattini	C₈	C₂²×D₁₉₁
Fitting, prime radical	C₂×D₈×C₁₉₁	C₂
socle	C₂²×C₁₉₁	D₈
hypercenter	C₂×D₈	D₁₉₁
hypocenter	C₁₉₁	C₂×SD₃₂
LCS	G ▷ C₈×C₁₉₁ ▷ C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₇₆₄	C₂	semidirect
2. #20259266	C₂	direct (N × H)
3. C₂×C₁₉₁⋊C₁₆	C₂	semidirect
7. Dic₇₆₄	C₂²	semidirect
8. C₁₉₁⋊C₁₆	C₂²	semidirect
29. C₂×C₁₉₁	SD₃₂	semidirect
31. C₁₉₁	C₂×SD₃₂	semidirect
61. C₂	#20259266	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₇₆₄	2
#20259266	2
C₂×C₁₉₁⋊C₁₆	2
C₂×D₈×C₁₉₁	2
C₂×SD₃₂	191

Subgroups — C2×#20259266 #27133087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20259266 #27133087