Subgroups — #46831219

Order 34624.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31772716	C₂	1	2	yes	maximal, complemented
2	#31772699	C₂	1	1	yes	maximal, characteristic, complemented
3	#31772693	C₂	1	2	yes	maximal, complemented
4	C₈×#14524194	C₂	1	1	yes	maximal, characteristic, complemented
5	#31772651	C₂	1	1	yes	maximal, characteristic
6	#22575846	—	2	2	no	—
7	#22575846	C₂²	1	2	yes	—
8	D₅₄₁⋊C₈	—	2	2	no	—
9	D₅₄₁⋊C₈	C₂²	1	1	yes	characteristic
10	C₄×#14524194	C₂²	1	1	yes	characteristic
11	#22575837	C₂²	1	2	yes	—
12	#22575823	C₄	1	2	yes	complemented
13	D₄₃₂₈	C₄	1	1	yes	characteristic, complemented
14	C₈×D₅₄₁	C₂²	1	1	yes	characteristic
15	Q₁₆×C₅₄₁	C₄	1	1	yes	characteristic, complemented
16	C₂×#14524194	—	2	1	no	—
17	#16864520	—	2	2	no	—
18	#16864520	D₄	1	1	yes	characteristic
19	#16864520	D₄	1	1	yes	characteristic
20	D₂₁₆₄	—	2	2	no	—
21	D₂₁₆₄	C₂×C₄	1	2	yes	—
22	C₄×D₅₄₁	—	2	2	no	—
23	C₄×D₅₄₁	C₂³	1	1	yes	characteristic
24	#16864513	C₂×C₄	1	1	yes	characteristic
25	Q₈×C₅₄₁	C₂×C₄	1	2	yes	—
26	C₈×C₅₄₁	C₂×C₄	1	1	yes	characteristic
27	C₂×D₅₄₁	—	2	2	no	—
28	C₂×D₅₄₁	#41	1	1	yes	characteristic
29	#14524194	—	2	2	no	—
30	C₄×C₅₄₁	—	2	2	no	—
31	C₄×C₅₄₁	C₂²×C₄	1	1	yes	characteristic
32	Dic₅₄₁	C₂×D₄	1	1	yes	characteristic
33	C₂×C₅₄₁	C₄×D₄	1	1	yes	characteristic
34	D₅₄₁	—	2	1	no	—
35	D₅₄₁	—	4	2	no	—
36	C₅₄₁	#443	1	1	yes	characteristic, complemented, Sylow
37	#443	—	541	1	no	maximal, Sylow
38	#135	—	541	1	no	—
39	#131	—	541	2	no	—
40	#108	—	541	1	no	—
41	#104	—	541	2	no	—
42	C₄×C₈	—	541	1	no	—
43	#41	—	541	2	no	—
44	Q₁₆	#14524194	1	1	yes	characteristic, complemented
45	SD₁₆	—	541	2	no	—
46	D₈	—	541	1	no	—
47	M₁₆	—	541	2	no	—
48	M₁₆	—	1082	2	no	—
49	C₂×C₈	—	541	1	no	—
50	C₂×C₈	—	541	1	no	—
51	C₂×C₈	—	1082	2	no	—
52	C₄²	—	541	1	no	—
53	Q₈	C₂×#14524194	1	2	yes	—
54	D₄	—	541	2	no	—
55	D₄	—	1082	2	no	—
56	C₂×C₄	—	541	1	no	—
57	C₂×C₄	—	1082	2	no	—
58	C₂×C₄	—	1082	1	no	—
59	C₈	—	541	1	no	—
60	C₈	—	541	1	no	—
61	C₈	—	541	1	no	—
62	C₈	—	1082	2	no	—
63	C₈	C₂×#14524194	1	1	yes	characteristic
64	C₂²	—	541	1	no	—
65	C₂²	—	1082	2	no	—
66	C₄	—	2	2	no	—
67	C₄	—	541	1	no	—
68	C₄	—	1082	2	no	—
69	C₄	C₂²×#14524194	1	1	yes	characteristic
70	C₂	—	1082	1	no	—
71	C₂	—	2164	2	no	—
72	C₂	D₄×#14524194	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#14524194
commutator	C₄×C₅₄₁	C₂²×C₄
Frattini	C₄	C₂²×#14524194
Fitting	Q₁₆×C₅₄₁	C₄
socle	C₂×C₅₄₁	C₄×D₄
prime radical	#31772651	C₂
cosocle	C₄×D₅₄₁	C₂³
hypercenter	Q₁₆	#14524194
hypocenter	C₅₄₁	#443
LCS	G ▷ C₄×C₅₄₁ ▷ C₂×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #31772716	C₂	semidirect
2. #31772699	C₂	semidirect
3. #31772693	C₂	semidirect
4. C₈×#14524194	C₂	semidirect
12. #22575823	C₄	semidirect
13. D₄₃₂₈	C₄	semidirect
15. Q₁₆×C₅₄₁	C₄	semidirect
36. C₅₄₁	#443	semidirect
44. Q₁₆	#14524194	semidirect

Maximal subgroups

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

subgroup	index
#31772716	2
#31772699	2
#31772693	2
C₈×#14524194	2
#31772651	2
#443	541