Subgroups — #46831222

Order 34624.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31772715	C₂	1	2	yes	maximal, complemented
2	#31772698	C₂	1	1	yes	maximal, characteristic, complemented
3	#31772692	C₂	1	2	yes	maximal, complemented
4	#31772682	C₂	1	1	yes	maximal, characteristic, complemented
5	#31772647	C₂	1	1	yes	maximal, characteristic
6	#22575846	C₂²	1	2	yes	—
7	#22575845	—	2	2	no	—
8	D₅₄₁⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×#16864520	—	2	2	no	—
10	C₄×#14524194	C₂²	1	1	yes	characteristic
11	#22575835	C₂²	1	2	yes	—
12	Dic₂₁₆₄	C₄	1	1	yes	characteristic, complemented
13	#22575824	C₄	1	2	yes	complemented
14	C₈×D₅₄₁	C₂²	1	1	yes	characteristic
15	D₈×C₅₄₁	C₄	1	1	yes	characteristic, complemented
16	C₂×#14524194	—	2	1	no	—
17	#16864520	—	2	2	no	—
18	#16864520	D₄	1	2	yes	—
19	Dic₁₀₈₂	C₂×C₄	1	2	yes	—
20	C₂²⋊D₅₄₁	—	2	2	no	—
21	C₂×Dic₅₄₁	—	2	2	no	—
22	C₄×D₅₄₁	C₂³	1	1	yes	characteristic
23	#16864513	C₂×C₄	1	1	yes	characteristic
24	D₄×C₅₄₁	C₂×C₄	1	2	yes	—
25	C₈×C₅₄₁	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₅₄₁	—	2	2	no	—
27	C₂×D₅₄₁	#41	1	1	yes	characteristic
28	#14524194	—	4	1	no	—
29	C₄×C₅₄₁	C₂²×C₄	1	1	yes	characteristic
30	Dic₅₄₁	—	2	2	no	—
31	Dic₅₄₁	C₂×D₄	1	1	yes	characteristic
32	C₂×C₅₄₁	—	4	2	no	—
33	C₂×C₅₄₁	C₄×D₄	1	1	yes	characteristic
34	D₅₄₁	—	2	1	no	—
35	C₅₄₁	#444	1	1	yes	characteristic, complemented, Sylow
36	#444	—	541	1	no	maximal, Sylow
37	#135	—	541	1	no	—
38	#131	—	541	2	no	—
39	#108	—	541	1	no	—
40	#104	—	541	2	no	—
41	#97	—	541	1	no	—
42	#41	—	541	2	no	—
43	Q₁₆	—	541	1	no	—
44	SD₁₆	—	541	2	no	—
45	D₈	#14524194	1	1	yes	characteristic, complemented
46	M₁₆	—	541	2	no	—
47	M₁₆	—	1082	2	no	—
48	C₂×C₈	—	541	1	no	—
49	C₂×C₈	—	541	1	no	—
50	C₂×C₈	—	1082	2	no	—
51	C₄²	—	541	1	no	—
52	Q₈	—	541	2	no	—
53	D₄	—	1082	2	no	—
54	D₄	C₂×#14524194	1	2	yes	—
55	C₂×C₄	—	541	1	no	—
56	C₂×C₄	—	1082	2	no	—
57	C₂×C₄	—	1082	1	no	—
58	C₈	—	541	2	no	—
59	C₈	—	541	1	no	—
60	C₈	—	1082	2	no	—
61	C₈	C₂×#14524194	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	—	541	1	no	—
64	C₄	—	541	1	no	—
65	C₄	—	1082	2	no	—
66	C₄	—	2164	1	no	—
67	C₄	C₂²×#14524194	1	1	yes	characteristic
68	C₂	—	4	2	no	—
69	C₂	—	1082	1	no	—
70	C₂	D₄×#14524194	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#14524194
commutator	C₄×C₅₄₁	C₂²×C₄
Frattini	C₄	C₂²×#14524194
Fitting	D₈×C₅₄₁	C₄
socle	C₂×C₅₄₁	C₄×D₄
prime radical	#31772647	C₂
cosocle	C₄×D₅₄₁	C₂³
hypercenter	D₈	#14524194
hypocenter	C₅₄₁	#444
LCS	G ▷ C₄×C₅₄₁ ▷ C₂×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #31772715	C₂	semidirect
2. #31772698	C₂	semidirect
3. #31772692	C₂	semidirect
4. #31772682	C₂	semidirect
12. Dic₂₁₆₄	C₄	semidirect
13. #22575824	C₄	semidirect
15. D₈×C₅₄₁	C₄	semidirect
35. C₅₄₁	#444	semidirect
45. D₈	#14524194	semidirect

Maximal subgroups

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

subgroup	index
#31772715	2
#31772698	2
#31772692	2
#31772682	2
#31772647	2
#444	541