Subgroups — #46829914

Order 34624.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31772616	C₂	1	1	yes	maximal, characteristic
2	#31772539	C₂	1	1	yes	maximal, characteristic, complemented
3	#97×C₅₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Dic₁₀₈₂	C₄	1	1	yes	characteristic
5	C₂×D₂₁₆₄	C₄	1	1	yes	characteristic
6	C₂×#16864513	—	2	1	no	—
7	#22575813	—	2	1	no	—
8	#22575813	—	2	1	no	—
9	C₂×C₈×C₅₄₁	—	2	1	no	—
10	C₄²×C₅₄₁	C₂²	1	1	yes	characteristic
11	C₂²×D₅₄₁	—	2	1	no	—
12	Dic₁₀₈₂	—	4	1	no	—
13	D₂₁₆₄	—	4	1	no	—
14	C₂×Dic₅₄₁	—	2	1	no	—
15	#16864513	—	2	2	no	—
16	C₂×C₄×C₅₄₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₅₄₁	D₄	1	1	yes	characteristic
18	C₂×C₄×C₅₄₁	D₄	1	1	yes	characteristic
19	C₈×C₅₄₁	—	2	2	no	—
20	C₂²×C₅₄₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×D₅₄₁	—	4	1	no	—
22	C₂×D₅₄₁	—	4	1	no	—
23	C₂×D₅₄₁	—	4	1	no	—
24	C₄×C₅₄₁	—	2	1	no	—
25	C₄×C₅₄₁	—	2	1	no	—
26	C₄×C₅₄₁	—	2	1	no	—
27	Dic₅₄₁	—	4	1	no	—
28	C₂×C₅₄₁	#100	1	1	yes	characteristic
29	C₂×C₅₄₁	#104	1	1	yes	characteristic
30	C₂×C₅₄₁	#104	1	1	yes	characteristic
31	D₅₄₁	—	8	1	no	—
32	C₅₄₁	#329	1	1	yes	characteristic, complemented, Sylow
33	#329	—	541	1	no	maximal, Sylow
34	#124	—	541	1	no	—
35	#97	—	541	1	no	—
36	#97	D₅₄₁	1	1	yes	characteristic, complemented
37	C₂×Q₈	—	541	1	no	—
38	C₂×D₄	—	541	1	no	—
39	C₂×C₈	—	2	1	no	—
40	C₂×C₈	—	1082	1	no	—
41	C₂²⋊C₄	—	1082	1	no	—
42	C₂²⋊C₄	—	1082	1	no	—
43	C₄²	C₂×D₅₄₁	1	1	yes	characteristic
44	C₂³	—	1082	1	no	—
45	Q₈	—	2164	1	no	—
46	D₄	—	2164	1	no	—
47	C₂×C₄	—	1082	1	no	—
48	C₂×C₄	C₄×D₅₄₁	1	1	yes	characteristic
49	C₂×C₄	C₂²⋊D₅₄₁	1	1	yes	characteristic
50	C₂×C₄	D₂₁₆₄	1	1	yes	characteristic
51	C₈	—	2	2	no	—
52	C₈	—	1082	2	no	—
53	C₂²	—	2164	1	no	—
54	C₂²	—	2164	1	no	—
55	C₂²	—	2164	1	no	—
56	C₂²	#22575813	1	1	yes	characteristic
57	C₄	—	2	1	no	—
58	C₄	—	2	1	no	—
59	C₄	—	2	1	no	—
60	C₄	—	2164	1	no	—
61	C₂	—	4328	1	no	—
62	C₂	#31772544	1	1	yes	characteristic
63	C₂	#31772554	1	1	yes	characteristic
64	C₂	#31772556	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22575813
commutator	C₂×C₄×C₅₄₁	C₂×C₄
Frattini	C₄²	C₂×D₅₄₁
Fitting	#97×C₅₄₁	C₂
socle	C₂²×C₅₄₁	C₂²⋊C₄
prime radical	C₂×D₂₁₆₄	C₄
cosocle	C₄²×C₅₄₁	C₂²
hypercenter	#97	D₅₄₁
hypocenter	C₅₄₁	#329
LCS	G ▷ C₂×C₄×C₅₄₁ ▷ C₂²×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
2. #31772539	C₂	semidirect
3. #97×C₅₄₁	C₂	semidirect
32. C₅₄₁	#329	semidirect
36. #97	D₅₄₁	semidirect

Maximal subgroups

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

subgroup	index
#31772616	2
#31772539	2
#97×C₅₄₁	2
#329	541