Subgroups — #46830112

Order 34624.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₅₄₁	C₂	1	3	yes	maximal, complemented
2	C₂×#22575813	C₂	1	3	yes	maximal
3	#95×C₅₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₅₄₁	C₂²	1	1	yes	characteristic
5	C₂²×Dic₅₄₁	C₂²	1	3	yes	—
6	C₄⋊Dic₅₄₁	—	2	6	no	—
7	#22575813	—	2	6	no	—
8	C₂²×C₄×C₅₄₁	C₂²	1	3	yes	—
9	C₂²×D₅₄₁	—	2	3	no	—
10	C₂²×D₅₄₁	—	2	3	no	—
11	C₂²×D₅₄₁	Q₈	1	2	yes	—
12	C₂×Dic₅₄₁	—	2	3	no	—
13	C₂×Dic₅₄₁	—	2	6	no	—
14	C₂³×C₅₄₁	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₅₄₁	—	2	6	no	—
16	C₂×C₄×C₅₄₁	D₄	1	6	yes	—
17	C₂²×C₅₄₁	C₂×D₄	1	3	yes	—
18	C₂²×C₅₄₁	C₂×Q₈	1	1	yes	characteristic
19	C₂²×C₅₄₁	#41	1	3	yes	—
20	C₂×D₅₄₁	—	2	6	no	—
21	C₂×D₅₄₁	—	4	3	no	—
22	C₂×D₅₄₁	—	4	1	no	—
23	C₄×C₅₄₁	—	2	6	no	—
24	Dic₅₄₁	—	4	3	no	—
25	C₂×C₅₄₁	C₂²⋊Q₈	1	3	yes	—
26	C₂×C₅₄₁	#123	1	3	yes	—
27	C₂×C₅₄₁	#127	1	1	yes	characteristic
28	D₅₄₁	—	4	2	no	—
29	C₅₄₁	#399	1	1	yes	characteristic, complemented, Sylow
30	#399	—	541	1	no	maximal, Sylow
31	C₂×C₄⋊C₄	—	541	3	no	—
32	C₂×C₂²⋊C₄	—	541	3	no	—
33	#95	D₅₄₁	1	1	yes	characteristic, complemented
34	C₂⁴	—	541	1	no	—
35	C₂²×C₄	—	541	3	no	—
36	C₂²×C₄	C₂×D₅₄₁	1	3	yes	—
37	C₄⋊C₄	—	1082	6	no	—
38	C₂²⋊C₄	—	1082	6	no	—
39	C₂³	—	541	2	no	—
40	C₂³	—	1082	3	no	—
41	C₂³	—	1082	3	no	—
42	C₂³	C₂²×D₅₄₁	1	1	yes	characteristic
43	C₂×C₄	—	2	6	no	—
44	C₂×C₄	—	1082	3	no	—
45	C₂×C₄	—	1082	6	no	—
46	C₂×C₄	D₂₁₆₄	1	6	yes	—
47	C₂²	—	1082	6	no	—
48	C₂²	—	2164	3	no	—
49	C₂²	—	2164	1	no	—
50	C₂²	C₂×D₂₁₆₄	1	3	yes	—
51	C₂²	Q₈×D₅₄₁	1	1	yes	characteristic
52	C₂²	#22575835	1	3	yes	—
53	C₄	—	2	6	no	—
54	C₄	—	2164	3	no	—
55	C₂	—	2164	2	no	—
56	C₂	#31772608	1	3	yes	—
57	C₂	#31772612	1	3	yes	—
58	C₂	#31772625	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₅₄₁
commutator, socle, cosocle	C₂³×C₅₄₁	C₂³
Fitting	#95×C₅₄₁	C₂
prime radical	C₂³×D₅₄₁	C₂²
hypercenter	#95	D₅₄₁
hypocenter	C₅₄₁	#399
LCS	G ▷ C₂³×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
1. C₂×C₄⋊Dic₅₄₁	C₂	semidirect
3. #95×C₅₄₁	C₂	semidirect
29. C₅₄₁	#399	semidirect
33. #95	D₅₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊Dic₅₄₁	2
C₂×#22575813	2
#95×C₅₄₁	2
#399	541