Subgroups — #46831190

Order 34624.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22575846	C₂	1	1	yes	maximal, characteristic
2	D₅₄₁⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	#31772699	C₂	1	2	yes	maximal, complemented
4	#31772698	C₂	1	2	yes	maximal, complemented
5	M₁₆×D₅₄₁	C₂	1	1	yes	maximal, characteristic
6	#22575846	—	2	1	no	—
7	#22575846	C₂²	1	1	yes	characteristic
8	#22575846	C₂²	1	2	yes	—
9	#22575846	C₂²	1	1	yes	characteristic
10	#22575845	—	2	1	no	—
11	D₅₄₁⋊C₈	—	2	1	no	—
12	C₂×#16864520	—	2	1	no	—
13	C₂×C₄×D₅₄₁	C₂²	1	1	yes	characteristic
14	#22575820	C₄	1	1	yes	characteristic
15	#22575819	C₄	1	2	yes	—
16	C₈×D₅₄₁	C₂²	1	2	yes	—
17	M₁₆×C₅₄₁	C₄	1	1	yes	characteristic
18	#16864520	—	2	2	no	—
19	#16864520	—	2	1	no	—
20	#16864520	—	2	1	no	—
21	C₂²×D₅₄₁	Q₈	1	1	yes	characteristic
22	C₂×Dic₅₄₁	D₄	1	1	yes	characteristic
23	C₄×D₅₄₁	C₂×C₄	1	1	yes	characteristic
24	C₄×D₅₄₁	D₄	1	1	yes	characteristic
25	C₄×D₅₄₁	Q₈	1	1	yes	characteristic
26	C₄×D₅₄₁	C₂³	1	1	yes	characteristic
27	#16864513	C₂×C₄	1	2	yes	—
28	C₂×C₄×C₅₄₁	C₂×C₄	1	1	yes	characteristic
29	C₈×C₅₄₁	C₂×C₄	1	2	yes	—
30	C₂²×C₅₄₁	C₄⋊C₄	1	1	yes	characteristic
31	C₂×D₅₄₁	—	4	1	no	—
32	C₂×D₅₄₁	C₄⋊C₄	1	1	yes	characteristic
33	C₂×D₅₄₁	C₂×Q₈	1	1	yes	characteristic
34	C₄×C₅₄₁	C₄⋊C₄	1	1	yes	characteristic
35	C₄×C₅₄₁	C₂²×C₄	1	1	yes	characteristic
36	Dic₅₄₁	C₄⋊C₄	1	1	yes	characteristic
37	Dic₅₄₁	C₂×D₄	1	1	yes	characteristic
38	C₂×C₅₄₁	—	2	1	no	—
39	C₂×C₅₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
40	D₅₄₁	—	2	1	no	—
41	D₅₄₁	—	2	1	no	—
42	C₅₄₁	#430	1	1	yes	characteristic, complemented, Sylow
43	#430	—	541	1	no	maximal, Sylow
44	C₂×M₁₆	—	541	1	no	—
45	C₂×M₁₆	—	541	1	no	—
46	C₂×M₁₆	—	541	1	no	—
47	#108	—	541	2	no	—
48	#108	—	541	2	no	—
49	C₂²×C₄	—	541	1	no	—
50	M₁₆	—	541	1	no	—
51	M₁₆	—	541	2	no	—
52	M₁₆	—	541	1	no	—
53	M₁₆	—	541	2	no	—
54	M₁₆	—	541	1	no	—
55	M₁₆	—	1082	1	no	—
56	M₁₆	—	1082	1	no	—
57	M₁₆	#14524194	1	1	yes	characteristic
58	C₂×C₈	—	541	2	no	—
59	C₂×C₈	—	1082	1	no	—
60	C₂×C₈	—	1082	1	no	—
61	C₂³	—	541	1	no	—
62	C₂×C₄	—	541	1	no	—
63	C₂×C₄	—	541	1	no	—
64	C₂×C₄	—	541	1	no	—
65	C₂×C₄	—	541	1	no	—
66	C₂×C₄	—	541	1	no	—
67	C₂×C₄	C₂×#14524194	1	1	yes	characteristic
68	C₈	—	541	2	no	—
69	C₈	—	1082	2	no	—
70	C₈	—	1082	1	no	—
71	C₈	—	1082	1	no	—
72	C₈	C₂×#14524194	1	2	yes	—
73	C₂²	—	541	1	no	—
74	C₂²	—	541	1	no	—
75	C₂²	—	2164	1	no	—
76	C₂²	C₄⋊#14524194	1	1	yes	characteristic
77	C₄	—	541	1	no	—
78	C₄	—	541	1	no	—
79	C₄	C₄⋊#14524194	1	1	yes	characteristic
80	C₄	C₂²×#14524194	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	—	1082	1	no	—
83	C₂	—	1082	1	no	—
84	C₂	C₂×C₄⋊#14524194	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₄⋊#14524194
commutator	C₄×C₅₄₁	C₂²×C₄
Frattini	C₄	C₂²×#14524194
Fitting	M₁₆×C₅₄₁	C₄
socle	C₂×C₅₄₁	C₂×C₄⋊C₄
prime radical	C₂²×D₅₄₁	Q₈
cosocle	C₄×D₅₄₁	C₂³
hypercenter	M₁₆	#14524194
hypocenter	C₅₄₁	#430
LCS	G ▷ C₄×C₅₄₁ ▷ C₂×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
3. #31772699	C₂	semidirect
4. #31772698	C₂	semidirect
42. C₅₄₁	#430	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22575846	2
D₅₄₁⋊M₁₆	2
#31772699	2
#31772698	2
M₁₆×D₅₄₁	2
#430	541