Subgroups — C₂×#16840694 #21462239

Order 7808.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840694	C₂	1	4	yes	maximal, direct product factor
2	C₂×#14519827	C₂	1	2	yes	maximal, complemented
3	C₂²×#11758185	C₂	1	1	yes	maximal, characteristic
4	#14519827	C₂²	1	4	yes	complemented
5	C₂×#11758185	C₄	1	2	yes	—
6	C₂×#11758185	C₄	1	1	yes	characteristic
7	C₂×#11758185	C₂²	1	1	yes	characteristic
8	C₂×#11758185	C₂²	1	2	yes	—
9	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₆₁	C₈	1	1	yes	characteristic
11	C₂×C₈×C₆₁	C₈	1	1	yes	characteristic
12	C₂×C₈×C₆₁	C₈	1	2	yes	—
13	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
15	#11758185	C₂×C₄	1	1	yes	characteristic
16	#11758185	C₂×C₄	1	2	yes	—
17	#11758185	C₂³	1	1	yes	characteristic
18	C₂³×C₆₁	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₆₁	C₁₆	1	2	yes	—
20	C₂×C₄×C₆₁	C₁₆	1	1	yes	characteristic
21	C₂×C₄×C₆₁	C₂×C₈	1	2	yes	—
22	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
23	C₈×C₆₁	C₂×C₈	1	2	yes	—
24	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
25	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₆₁	—	2	2	no	—
27	C₂²×C₆₁	C₂×C₁₆	1	2	yes	—
28	C₂²×C₆₁	C₂×C₁₆	1	1	yes	characteristic
29	C₄×C₆₁	C₂×C₁₆	1	2	yes	—
30	C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
31	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
32	C₂×M₆₄	—	61	1	no	maximal, Sylow
33	C₂×C₆₁	—	2	2	no	—
34	C₂×C₆₁	M₆₄	1	2	yes	complemented
35	C₂×C₆₁	C₂²×C₁₆	1	1	yes	characteristic
36	C₂²×C₁₆	—	61	1	no	—
37	M₆₄	—	61	4	no	—
38	C₂×C₃₂	—	61	2	no	—
39	C₆₁	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₈	#6923	1	1	yes	characteristic
41	C₂×C₁₆	—	61	2	no	—
42	C₂×C₁₆	—	61	2	no	—
43	C₂×C₁₆	—	61	1	no	—
44	C₂×C₁₆	—	61	1	no	—
45	C₃₂	—	61	4	no	—
46	C₂²×C₄	#92420	1	1	yes	characteristic
47	C₂×C₈	#92420	1	1	yes	characteristic
48	C₂×C₈	#92420	1	2	yes	—
49	C₂×C₈	C₂×#6923	1	2	yes	—
50	C₂×C₈	C₂×#6923	1	1	yes	characteristic
51	C₁₆	—	61	1	no	—
52	C₁₆	—	61	2	no	—
53	C₁₆	—	61	1	no	—
54	C₂³	#11758187	1	1	yes	characteristic
55	C₂×C₄	#11758187	1	2	yes	—
56	C₂×C₄	#11758187	1	1	yes	characteristic
57	C₂×C₄	C₂×#92420	1	2	yes	—
58	C₂×C₄	C₂×#92420	1	1	yes	characteristic
59	C₈	C₂×#92420	1	2	yes	—
60	C₈	C₂×#92420	1	1	yes	characteristic
61	C₈	C₂²×#6923	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	C₂×#11758187	1	2	yes	—
64	C₂²	C₂×#11758187	1	1	yes	characteristic
65	C₄	C₂×#11758187	1	2	yes	—
66	C₄	C₂×#11758187	1	1	yes	characteristic
67	C₄	C₂²×#92420	1	1	yes	characteristic
68	C₂	—	2	2	no	—
69	C₂	#16840694	1	2	yes	direct product factor
70	C₂	C₂²×#11758187	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×#6923
commutator	C₂×C₆₁	C₂²×C₁₆
Frattini	C₈	C₂²×#6923
Fitting	C₂²×C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₁₆
hypercenter	C₂²×C₈	#6923
hypocenter	C₆₁	C₂×M₆₄
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. #16840694	C₂	direct (N × H)
2. C₂×#14519827	C₂	semidirect
4. #14519827	C₂²	semidirect
34. C₂×C₆₁	M₆₄	semidirect
39. C₆₁	C₂×M₆₄	semidirect
69. C₂	#16840694	direct (N × H)

Subgroups — C2×#16840694 #21462239

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16840694 #21462239