Subgroups — C₂×#26010855 #36348814

Order 22112.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₃₈₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₂₇₆₄	C₂	1	1	yes	maximal, characteristic
3	#26010855	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₈×C₆₉₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₆₉₁	—	2	1	no	—
6	Dic₁₃₈₂	—	2	1	no	—
7	Dic₁₃₈₂	C₂²	1	2	yes	complemented
8	D₂₇₆₄	—	2	1	no	—
9	D₂₇₆₄	C₂²	1	2	yes	—
10	C₂×Dic₆₉₁	—	2	1	no	—
11	C₂×C₄×C₆₉₁	C₂²	1	1	yes	characteristic
12	C₈×C₆₉₁	C₂²	1	2	yes	complemented
13	C₂²×C₆₉₁	D₄	1	1	yes	characteristic
14	C₂×D₆₉₁	—	2	2	no	—
15	C₂×D₆₉₁	—	4	2	no	—
16	C₄×C₆₉₁	D₄	1	1	yes	characteristic
17	C₄×C₆₉₁	C₂³	1	1	yes	characteristic
18	Dic₆₉₁	—	2	2	no	—
19	C₂×C₆₉₁	SD₁₆	1	2	yes	complemented
20	C₂×C₆₉₁	C₂×D₄	1	1	yes	characteristic
21	D₆₉₁	—	4	2	no	—
22	C₆₉₁	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
23	C₂×SD₁₆	—	691	1	no	maximal, Sylow
24	C₂×Q₈	—	691	1	no	—
25	C₂×D₄	—	691	1	no	—
26	SD₁₆	—	691	4	no	—
27	C₂×C₈	D₆₉₁	1	1	yes	characteristic, complemented
28	C₂³	—	1382	1	no	—
29	Q₈	—	1382	1	no	—
30	Q₈	—	691	2	no	—
31	D₄	—	1382	1	no	—
32	D₄	—	691	2	no	—
33	C₂×C₄	—	1382	1	no	—
34	C₂×C₄	C₂×D₆₉₁	1	1	yes	characteristic
35	C₈	C₂×D₆₉₁	1	2	yes	complemented
36	C₂²	—	1382	2	no	—
37	C₂²	—	2764	2	no	—
38	C₂²	D₂₇₆₄	1	1	yes	characteristic
39	C₄	—	1382	2	no	—
40	C₄	D₂₇₆₄	1	1	yes	characteristic
41	C₄	C₂²×D₆₉₁	1	1	yes	characteristic
42	C₂	—	2764	2	no	—
43	C₂	#26010855	1	2	yes	direct product factor
44	C₂	C₂×D₂₇₆₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₇₆₄
commutator, cosocle	C₄×C₆₉₁	C₂³
Frattini	C₄	C₂²×D₆₉₁
Fitting	C₂×C₈×C₆₉₁	C₂
socle	C₂²×C₆₉₁	D₄
prime radical	C₂×D₂₇₆₄	C₂
hypercenter	C₂×C₈	D₆₉₁
hypocenter	C₆₉₁	C₂×SD₁₆
LCS	G ▷ C₄×C₆₉₁ ▷ C₂×C₆₉₁ ▷ C₆₉₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₁₃₈₂	C₂	semidirect
3. #26010855	C₂	direct (N × H)
4. C₂×C₈×C₆₉₁	C₂	semidirect
7. Dic₁₃₈₂	C₂²	semidirect
12. C₈×C₆₉₁	C₂²	semidirect
19. C₂×C₆₉₁	SD₁₆	semidirect
22. C₆₉₁	C₂×SD₁₆	semidirect
27. C₂×C₈	D₆₉₁	semidirect
35. C₈	C₂×D₆₉₁	semidirect
43. C₂	#26010855	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×Dic₁₃₈₂	2
C₂×D₂₇₆₄	2
#26010855	2
C₂×C₈×C₆₉₁	2
C₂×SD₁₆	691

Subgroups — C2×#26010855 #36348814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26010855 #36348814