Subgroups — #46831028

Order 34624.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31772685	C₂	1	1	yes	maximal, characteristic
2	(C₂×#14524194)⋊C₄	C₂	1	1	yes	maximal, characteristic
3	#31772608	C₂	1	1	yes	maximal, characteristic
4	C₂²×#14524194	—	2	1	no	—
5	C₂×#16864520	—	2	1	no	—
6	C₂×Dic₁₀₈₂	C₄	1	1	yes	characteristic, complemented
7	C₂×C₄×D₅₄₁	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₅₄₁	—	2	1	no	—
9	#22575813	—	2	1	no	—
10	C₄⋊C₄×C₅₄₁	C₄	1	1	yes	characteristic, complemented
11	C₂×#14524194	—	2	2	no	—
12	C₂×#14524194	—	4	1	no	—
13	C₂×#14524194	—	4	1	no	—
14	#16864520	—	4	1	no	—
15	C₂²×D₅₄₁	D₄	1	1	yes	characteristic
16	Dic₁₀₈₂	—	4	1	no	—
17	C₂×Dic₅₄₁	—	2	1	no	—
18	C₂×Dic₅₄₁	D₄	1	1	yes	characteristic
19	C₄×D₅₄₁	—	4	1	no	—
20	C₂×C₄×C₅₄₁	—	2	1	no	—
21	C₂×C₄×C₅₄₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₅₄₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×D₅₄₁	—	2	1	no	—
24	C₂×D₅₄₁	—	2	1	no	—
25	C₂×D₅₄₁	SD₁₆	1	1	yes	characteristic
26	C₂×D₅₄₁	Q₁₆	1	1	yes	characteristic
27	#14524194	—	4	2	no	—
28	C₄×C₅₄₁	—	2	1	no	—
29	C₄×C₅₄₁	—	4	1	no	—
30	Dic₅₄₁	—	2	1	no	—
31	Dic₅₄₁	—	4	1	no	—
32	C₂×C₅₄₁	#99	1	1	yes	characteristic
33	C₂×C₅₄₁	#103	1	1	yes	characteristic
34	C₂×C₅₄₁	#104	1	1	yes	characteristic
35	D₅₄₁	—	2	1	no	—
36	D₅₄₁	—	2	1	no	—
37	C₅₄₁	#328	1	1	yes	characteristic, complemented, Sylow
38	#328	—	541	1	no	maximal, Sylow
39	C₂²⋊Q₈	—	541	1	no	—
40	C₂²⋊C₈	—	541	1	no	—
41	#95	—	541	1	no	—
42	C₂×Q₈	—	541	1	no	—
43	C₂²×C₄	—	541	1	no	—
44	C₂²×C₄	—	1082	1	no	—
45	C₂×C₈	—	1082	1	no	—
46	C₄⋊C₄	—	1082	1	no	—
47	C₄⋊C₄	#14524194	1	1	yes	characteristic, complemented
48	C₂²⋊C₄	—	1082	1	no	—
49	C₂³	—	541	1	no	—
50	Q₈	—	2164	1	no	—
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	541	1	no	—
53	C₂×C₄	—	1082	2	no	—
54	C₂×C₄	—	1082	1	no	—
55	C₂×C₄	—	2164	1	no	—
56	C₂×C₄	—	2164	1	no	—
57	C₂×C₄	—	2164	1	no	—
58	C₂×C₄	C₂×#14524194	1	1	yes	characteristic
59	C₈	—	2164	1	no	—
60	C₂²	—	541	1	no	—
61	C₂²	—	541	1	no	—
62	C₂²	—	1082	1	no	—
63	C₂²	—	1082	1	no	—
64	C₂²	C₂²⋊#14524194	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	—	4	1	no	—
67	C₄	—	1082	1	no	—
68	C₄	—	2164	2	no	—
69	C₄	—	2164	1	no	—
70	C₂	—	1082	1	no	—
71	C₂	—	1082	1	no	—
72	C₂	#31772687	1	1	yes	characteristic
73	C₂	#31772691	1	1	yes	characteristic
74	C₂	#31772692	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#14524194
commutator	C₂×C₄×C₅₄₁	C₂×C₄
Frattini	C₂×C₄	C₂×#14524194
Fitting	C₄⋊C₄×C₅₄₁	C₄
socle	C₂²×C₅₄₁	C₂²⋊C₄
prime radical	C₂²×D₅₄₁	D₄
cosocle	C₂×C₄×D₅₄₁	C₂²
hypercenter	C₄⋊C₄	#14524194
hypocenter	C₅₄₁	#328
LCS	G ▷ C₂×C₄×C₅₄₁ ▷ C₂²×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
6. C₂×Dic₁₀₈₂	C₄	semidirect
10. C₄⋊C₄×C₅₄₁	C₄	semidirect
37. C₅₄₁	#328	semidirect
47. C₄⋊C₄	#14524194	semidirect

Maximal subgroups

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

subgroup	index
#31772685	2
(C₂×#14524194)⋊C₄	2
#31772608	2
#328	541