Subgroups — C₂×#31772682 #46831132

Order 34624.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₄₁⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#14524194	C₂	1	1	yes	maximal, characteristic
3	#31772682	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₈×D₅₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#14524194	C₄	1	2	yes	—
6	D₅₄₁⋊C₈	C₄	1	2	yes	complemented
7	D₅₄₁⋊C₈	C₂²	1	2	yes	—
8	C₂×#16864520	C₄	1	2	yes	complemented
9	C₄×#14524194	C₄	1	2	yes	—
10	C₄×#14524194	C₂²	1	2	yes	—
11	C₂×C₄×D₅₄₁	C₂²	1	1	yes	characteristic
12	C₂×#16864513	C₄	1	1	yes	characteristic, complemented
13	C₈×D₅₄₁	C₄	1	2	yes	complemented
14	C₈×D₅₄₁	C₂²	1	2	yes	—
15	C₂×C₈×C₅₄₁	C₄	1	1	yes	characteristic, complemented
16	C₂×#14524194	—	2	4	no	—
17	C₂×#14524194	C₂×C₄	1	4	yes	—
18	#16864520	C₂×C₄	1	4	yes	complemented
19	C₂²×D₅₄₁	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₅₄₁	C₂×C₄	1	1	yes	characteristic
21	C₄×D₅₄₁	C₂×C₄	1	1	yes	characteristic
22	C₄×D₅₄₁	C₂×C₄	1	1	yes	characteristic
23	C₄×D₅₄₁	C₂×C₄	1	1	yes	characteristic
24	C₄×D₅₄₁	C₂³	1	1	yes	characteristic
25	#16864513	C₂×C₄	1	2	yes	complemented
26	C₂×C₄×C₅₄₁	C₂×C₄	1	1	yes	characteristic
27	C₈×C₅₄₁	C₂×C₄	1	2	yes	complemented
28	C₂²×C₅₄₁	C₄²	1	1	yes	characteristic
29	C₂×D₅₄₁	C₄²	1	1	yes	characteristic
30	C₂×D₅₄₁	M₁₆	1	4	yes	—
31	C₂×D₅₄₁	C₂²×C₄	1	1	yes	characteristic
32	#14524194	—	2	4	no	—
33	C₄×C₅₄₁	C₄²	1	1	yes	characteristic
34	C₄×C₅₄₁	C₂²×C₄	1	1	yes	characteristic
35	Dic₅₄₁	C₄²	1	1	yes	characteristic
36	Dic₅₄₁	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₅₄₁	#97	1	2	yes	complemented
38	C₂×C₅₄₁	C₂×C₄²	1	1	yes	characteristic
39	D₅₄₁	#97	1	2	yes	complemented
40	D₅₄₁	C₂×M₁₆	1	2	yes	—
41	C₅₄₁	C₂×#97	1	1	yes	characteristic, complemented, Sylow
42	C₂×#97	—	541	1	no	maximal, Sylow
43	C₂²×C₈	—	541	1	no	—
44	C₂²×C₈	—	541	1	no	—
45	C₂×C₄²	—	541	1	no	—
46	#97	—	541	4	no	—
47	C₂²×C₄	—	541	1	no	—
48	C₂²×C₄	—	541	2	no	—
49	C₂×C₈	—	541	2	no	—
50	C₂×C₈	—	541	2	no	—
51	C₂×C₈	—	541	2	no	—
52	C₂×C₈	—	541	1	no	—
53	C₂×C₈	—	541	2	no	—
54	C₂×C₈	—	541	2	no	—
55	C₂×C₈	#14524194	1	1	yes	characteristic, complemented
56	C₄²	—	541	2	no	—
57	C₄²	—	541	2	no	—
58	C₂³	—	541	1	no	—
59	C₂×C₄	—	541	1	no	—
60	C₂×C₄	—	541	1	no	—
61	C₂×C₄	—	541	1	no	—
62	C₂×C₄	—	541	1	no	—
63	C₂×C₄	—	541	1	no	—
64	C₂×C₄	—	541	4	no	—
65	C₂×C₄	—	1082	4	no	—
66	C₂×C₄	C₂×#14524194	1	1	yes	characteristic
67	C₈	—	541	4	no	—
68	C₈	—	541	2	no	—
69	C₈	C₂×#14524194	1	2	yes	complemented
70	C₂²	—	541	4	no	—
71	C₂²	—	541	1	no	—
72	C₂²	—	541	1	no	—
73	C₂²	C₄×#14524194	1	1	yes	characteristic
74	C₄	—	541	1	no	—
75	C₄	—	541	1	no	—
76	C₄	—	1082	4	no	—
77	C₄	C₄×#14524194	1	1	yes	characteristic
78	C₄	C₂²×#14524194	1	1	yes	characteristic
79	C₂	—	541	2	no	—
80	C₂	—	541	2	no	—
81	C₂	#31772682	1	2	yes	direct product factor
82	C₂	C₂×C₄×#14524194	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#14524194
commutator	C₂×C₅₄₁	C₂×C₄²
Frattini	C₄	C₂²×#14524194
Fitting	C₂×C₈×C₅₄₁	C₄
socle	C₂²×C₅₄₁	C₄²
prime radical	C₂²×D₅₄₁	C₂×C₄
cosocle	C₄×D₅₄₁	C₂³
hypercenter	C₂×C₈	#14524194
hypocenter	C₅₄₁	C₂×#97
LCS	G ▷ C₂×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
3. #31772682	C₂	direct (N × H)
6. D₅₄₁⋊C₈	C₄	semidirect
8. C₂×#16864520	C₄	semidirect
12. C₂×#16864513	C₄	semidirect
13. C₈×D₅₄₁	C₄	semidirect
15. C₂×C₈×C₅₄₁	C₄	semidirect
18. #16864520	C₂×C₄	semidirect
25. #16864513	C₂×C₄	semidirect
27. C₈×C₅₄₁	C₂×C₄	semidirect
37. C₂×C₅₄₁	#97	semidirect
39. D₅₄₁	#97	semidirect
41. C₅₄₁	C₂×#97	semidirect
55. C₂×C₈	#14524194	semidirect
69. C₈	C₂×#14524194	semidirect
81. C₂	#31772682	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×D₅₄₁⋊C₈	2
C₂×C₄×#14524194	2
#31772682	2
C₂×C₈×D₅₄₁	2
C₂×#97	541

Subgroups — C2×#31772682 #46831132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#31772682 #46831132