Subgroups — #44417210

Order 29248.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28410575	C₂	1	2	yes	maximal, complemented
2	#28410495	C₂	1	2	yes	maximal, complemented
3	D₇₃₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₄₅₇	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₃₂×C₄₅₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#20300742	—	2	2	no	—
7	#20300728	—	2	2	no	—
8	D₃₆₅₆	C₂²	1	2	yes	—
9	C₈×D₄₅₇	C₂²	1	1	yes	characteristic
10	#20300716	C₂²	1	1	yes	characteristic
11	Q₁₆×C₄₅₇	C₂²	1	2	yes	—
12	C₁₆×C₄₅₇	C₂²	1	1	yes	characteristic
13	D₁₈₂₈	—	2	2	no	—
14	D₁₈₂₈	—	4	2	no	—
15	C₄×D₄₅₇	—	4	2	no	—
16	C₄×D₄₅₇	D₄	1	1	yes	characteristic
17	#16814532	D₄	1	1	yes	characteristic
18	Q₈×C₄₅₇	—	2	2	no	—
19	C₈×C₄₅₇	C₂³	1	1	yes	characteristic
20	C₂×D₄₅₇	—	4	2	no	—
21	C₂×D₄₅₇	D₈	1	1	yes	characteristic
22	C₄×C₄₅₇	—	4	2	no	—
23	C₄×C₄₅₇	C₂×D₄	1	1	yes	characteristic
24	Dic₄₅₇	D₈	1	1	yes	characteristic
25	C₂×C₄₅₇	C₂×D₈	1	1	yes	characteristic
26	D₄₅₇	—	2	1	no	—
27	D₄₅₇	—	8	2	no	—
28	C₄₅₇	#508	1	1	yes	characteristic, complemented, Sylow
29	#508	—	457	1	no	maximal, Sylow
30	#135	—	457	2	no	—
31	Q₃₂	D₄₅₇	1	1	yes	characteristic, complemented
32	SD₃₂	—	457	2	no	—
33	D₁₆	—	457	1	no	—
34	C₂×C₁₆	—	457	1	no	—
35	#41	—	914	2	no	—
36	Q₁₆	C₂×D₄₅₇	1	2	yes	—
37	SD₁₆	—	914	2	no	—
38	D₈	—	457	2	no	—
39	C₂×C₈	—	457	1	no	—
40	C₁₆	—	457	1	no	—
41	C₁₆	C₂×D₄₅₇	1	1	yes	characteristic
42	Q₈	—	2	2	no	—
43	D₄	—	1828	2	no	—
44	D₄	—	914	2	no	—
45	C₂×C₄	—	1828	2	no	—
46	C₂×C₄	—	457	1	no	—
47	C₈	—	457	1	no	—
48	C₈	C₂²×D₄₅₇	1	1	yes	characteristic
49	C₂²	—	1828	2	no	—
50	C₂²	—	457	1	no	—
51	C₄	—	4	2	no	—
52	C₄	—	457	1	no	—
53	C₄	D₄×D₄₅₇	1	1	yes	characteristic
54	C₂	—	3656	2	no	—
55	C₂	—	914	1	no	—
56	C₂	D₈×D₄₅₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₄₅₇
commutator, cosocle	C₈×C₄₅₇	C₂³
Frattini	C₈	C₂²×D₄₅₇
Fitting	Q₃₂×C₄₅₇	C₂
socle	C₂×C₄₅₇	C₂×D₈
hypercenter	Q₃₂	D₄₅₇
hypocenter	C₄₅₇	#508
LCS	G ▷ C₈×C₄₅₇ ▷ C₄×C₄₅₇ ▷ C₂×C₄₅₇ ▷ C₄₅₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
1. #28410575	C₂	semidirect
2. #28410495	C₂	semidirect
3. D₇₃₁₂	C₂	semidirect
4. C₁₆×D₄₅₇	C₂	semidirect
5. Q₃₂×C₄₅₇	C₂	semidirect
28. C₄₅₇	#508	semidirect
31. Q₃₂	D₄₅₇	semidirect

Maximal subgroups

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

subgroup	index
#28410575	2
#28410495	2
D₇₃₁₂	2
C₁₆×D₄₅₇	2
Q₃₂×C₄₅₇	2
#508	457