Subgroups — C₂²⋊#14519827 #21460932

Order 7808.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519827	C₂	1	2	yes	maximal, complemented
2	C₂²×#11758185	C₂	1	1	yes	maximal, characteristic
3	#14519827	—	2	2	no	—
4	C₂×#11758185	—	2	2	no	—
5	C₂×#11758185	C₄	1	1	yes	characteristic
6	C₂×#11758185	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
8	C₂²×C₄×C₆₁	C₈	1	1	yes	characteristic
9	C₂×C₈×C₆₁	—	2	1	no	—
10	C₂×C₈×C₆₁	—	2	1	no	—
11	C₂×C₈×C₆₁	C₈	1	1	yes	characteristic
12	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
13	#11758185	—	2	1	no	—
14	#11758185	D₄	1	2	yes	—
15	C₂³×C₆₁	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₆₁	—	2	1	no	—
17	C₂×C₄×C₆₁	—	2	1	no	—
18	C₂×C₄×C₆₁	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
20	C₈×C₆₁	—	2	1	no	—
21	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₆₁	M₁₆	1	1	yes	characteristic
23	C₂²×C₆₁	—	2	1	no	—
24	C₂²×C₆₁	—	2	1	no	—
25	C₂²×C₆₁	C₃₂	1	2	yes	complemented
26	C₂²×C₆₁	C₂×C₁₆	1	1	yes	characteristic
27	C₄×C₆₁	—	2	1	no	—
28	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
29	C₄×C₆₁	M₃₂	1	1	yes	characteristic
30	C₂²⋊C₃₂	—	61	1	no	maximal, Sylow
31	C₂×C₆₁	—	2	2	no	—
32	C₂×C₆₁	C₂²⋊C₁₆	1	1	yes	characteristic
33	C₂×C₆₁	C₂×C₃₂	1	1	yes	characteristic
34	C₂×C₆₁	M₆₄	1	1	yes	characteristic
35	C₂²×C₁₆	—	61	1	no	—
36	C₂×C₃₂	—	61	2	no	—
37	C₆₁	C₂²⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₈	#6923	1	1	yes	characteristic
39	C₂×C₁₆	—	61	1	no	—
40	C₂×C₁₆	—	61	1	no	—
41	C₂×C₁₆	—	122	2	no	—
42	C₃₂	—	122	2	no	—
43	C₂²×C₄	#92420	1	1	yes	characteristic
44	C₂×C₈	—	2	1	no	—
45	C₂×C₈	—	2	1	no	—
46	C₂×C₈	#92420	1	1	yes	characteristic
47	C₂×C₈	C₂×#6923	1	1	yes	characteristic
48	C₁₆	—	61	2	no	—
49	C₁₆	—	122	1	no	—
50	C₂³	#11758187	1	1	yes	characteristic
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	#11758187	1	1	yes	characteristic
54	C₂×C₄	C₂×#92420	1	1	yes	characteristic
55	C₈	—	2	1	no	—
56	C₈	#11758217	1	1	yes	characteristic
57	C₈	C₂²⋊#6923	1	1	yes	characteristic
58	C₂²	—	2	1	no	—
59	C₂²	—	2	1	no	—
60	C₂²	#14519827	1	2	yes	complemented
61	C₂²	C₂×#11758187	1	1	yes	characteristic
62	C₄	—	2	1	no	—
63	C₄	C₂²⋊#92420	1	1	yes	characteristic
64	C₄	#14519851	1	1	yes	characteristic
65	C₂	—	2	2	no	—
66	C₂	C₂²⋊#11758187	1	1	yes	characteristic
67	C₂	C₂×#14519827	1	1	yes	characteristic
68	C₂	#16840694	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#6923
commutator	C₂×C₆₁	C₂×C₃₂
Fitting	C₂²×C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₁₆
hypercenter	C₂²×C₈	#6923
hypocenter	C₆₁	C₂²⋊C₃₂
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. C₂×#14519827	C₂	semidirect
25. C₂²×C₆₁	C₃₂	semidirect
37. C₆₁	C₂²⋊C₃₂	semidirect
60. C₂²	#14519827	semidirect

Subgroups — C22⋊#14519827 #21460932

Conjugacy classes of subgroups

Complements

Subgroups — C₂²⋊#14519827 #21460932