Subgroups — C₂×#26010851 #36348809

Order 22112.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₇₆₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#26010851	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₆₉₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₆₉₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₆₉₁	—	2	1	no	—
6	D₂₇₆₄	—	2	1	no	—
7	D₂₇₆₄	C₂²	1	2	yes	complemented
8	C₆₉₁⋊C₈	C₂²	1	2	yes	complemented
9	C₂³×C₆₉₁	—	2	1	no	—
10	D₄×C₆₉₁	—	2	1	no	—
11	D₄×C₆₉₁	C₂²	1	2	yes	complemented
12	C₂×C₄×C₆₉₁	C₂²	1	1	yes	characteristic
13	C₂²×C₆₉₁	—	2	2	no	—
14	C₂²×C₆₉₁	—	4	2	no	—
15	C₂²×C₆₉₁	D₄	1	1	yes	characteristic
16	C₂×D₆₉₁	—	2	2	no	—
17	C₂×D₆₉₁	—	4	2	no	—
18	C₄×C₆₉₁	D₄	1	1	yes	characteristic
19	C₄×C₆₉₁	C₂³	1	1	yes	characteristic
20	C₂×C₆₉₁	—	4	2	no	—
21	C₂×C₆₉₁	D₈	1	2	yes	complemented
22	C₂×C₆₉₁	C₂×D₄	1	1	yes	characteristic
23	D₆₉₁	—	4	2	no	—
24	C₆₉₁	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
25	C₂×D₈	—	691	1	no	maximal, Sylow
26	C₂×D₄	—	691	1	no	—
27	C₂×D₄	D₆₉₁	1	1	yes	characteristic, complemented
28	D₈	—	691	4	no	—
29	C₂×C₈	—	691	1	no	—
30	C₂³	—	2	1	no	—
31	C₂³	—	1382	1	no	—
32	D₄	—	2	1	no	—
33	D₄	—	1382	1	no	—
34	D₄	—	691	2	no	—
35	D₄	C₂×D₆₉₁	1	2	yes	complemented
36	C₂×C₄	C₂×D₆₉₁	1	1	yes	characteristic
37	C₈	—	691	2	no	—
38	C₂²	—	2	2	no	—
39	C₂²	—	4	2	no	—
40	C₂²	—	1382	2	no	—
41	C₂²	—	2764	2	no	—
42	C₂²	C₂²⋊D₆₉₁	1	1	yes	characteristic
43	C₄	C₂²⋊D₆₉₁	1	1	yes	characteristic
44	C₄	C₂²×D₆₉₁	1	1	yes	characteristic
45	C₂	—	4	2	no	—
46	C₂	—	2764	2	no	—
47	C₂	#26010851	1	2	yes	direct product factor
48	C₂	C₂×C₂²⋊D₆₉₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊D₆₉₁
commutator, cosocle	C₄×C₆₉₁	C₂³
Frattini	C₄	C₂²×D₆₉₁
Fitting	C₂×D₄×C₆₉₁	C₂
socle	C₂²×C₆₉₁	D₄
hypercenter	C₂×D₄	D₆₉₁
hypocenter	C₆₉₁	C₂×D₈
LCS	G ▷ C₄×C₆₉₁ ▷ C₂×C₆₉₁ ▷ C₆₉₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₂₇₆₄	C₂	semidirect
2. #26010851	C₂	direct (N × H)
3. C₂×C₆₉₁⋊C₈	C₂	semidirect
4. C₂×D₄×C₆₉₁	C₂	semidirect
7. D₂₇₆₄	C₂²	semidirect
8. C₆₉₁⋊C₈	C₂²	semidirect
11. D₄×C₆₉₁	C₂²	semidirect
21. C₂×C₆₉₁	D₈	semidirect
24. C₆₉₁	C₂×D₈	semidirect
27. C₂×D₄	D₆₉₁	semidirect
35. D₄	C₂×D₆₉₁	semidirect
47. C₂	#26010851	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×D₂₇₆₄	2
#26010851	2
C₂×C₆₉₁⋊C₈	2
C₂×D₄×C₆₉₁	2
C₂×D₈	691

Subgroups — C2×#26010851 #36348809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26010851 #36348809