Subgroups — #44417053

Order 29248.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28410585	C₂	1	2	yes	maximal
2	C₂×Dic₁₈₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#28410558	C₂	1	1	yes	maximal, characteristic
4	#28410470	C₂	1	2	yes	maximal, complemented
5	#108×C₄₅₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#20300741	C₂²	1	1	yes	characteristic
7	C₂×Dic₉₁₄	C₂²	1	2	yes	—
8	Dic₁₈₂₈	—	2	2	no	—
9	Dic₁₈₂₈	—	2	1	no	—
10	Dic₁₈₂₈	—	2	1	no	—
11	#20300730	—	2	2	no	—
12	#20300725	C₂²	1	1	yes	characteristic
13	#20300724	—	2	1	no	—
14	C₈×D₄₅₇	—	2	1	no	—
15	M₁₆×C₄₅₇	C₂²	1	2	yes	—
16	C₂×C₈×C₄₅₇	C₂²	1	1	yes	characteristic
17	Dic₉₁₄	—	2	2	no	—
18	Dic₉₁₄	—	2	2	no	—
19	Dic₉₁₄	D₄	1	1	yes	characteristic
20	D₁₈₂₈	D₄	1	1	yes	characteristic
21	C₂²⋊D₄₅₇	—	2	1	no	—
22	C₂×Dic₄₅₇	—	2	2	no	—
23	C₄×D₄₅₇	—	2	1	no	—
24	#16814532	—	2	1	no	—
25	C₂×C₄×C₄₅₇	C₂³	1	1	yes	characteristic
26	C₈×C₄₅₇	—	2	2	no	—
27	C₈×C₄₅₇	D₄	1	1	yes	characteristic
28	C₈×C₄₅₇	D₄	1	1	yes	characteristic
29	C₂²×C₄₅₇	#41	1	1	yes	characteristic
30	C₂×D₄₅₇	—	2	1	no	—
31	C₄×C₄₅₇	C₂×D₄	1	1	yes	characteristic
32	C₄×C₄₅₇	C₂×D₄	1	1	yes	characteristic
33	Dic₄₅₇	—	2	1	no	—
34	Dic₄₅₇	—	4	2	no	—
35	C₂×C₄₅₇	—	2	1	no	—
36	C₂×C₄₅₇	#121	1	1	yes	characteristic
37	D₄₅₇	—	4	1	no	—
38	C₄₅₇	#473	1	1	yes	characteristic, complemented, Sylow
39	#473	—	457	1	no	maximal, Sylow
40	#137	—	457	2	no	—
41	C₂×Q₁₆	—	457	1	no	—
42	#131	—	457	1	no	—
43	#108	D₄₅₇	1	1	yes	characteristic, complemented
44	#101	—	457	2	no	—
45	#41	—	457	1	no	—
46	C₂×Q₈	—	457	2	no	—
47	Q₁₆	—	914	2	no	—
48	Q₁₆	—	914	1	no	—
49	Q₁₆	—	914	1	no	—
50	SD₁₆	—	914	2	no	—
51	M₁₆	—	914	1	no	—
52	M₁₆	—	457	1	no	—
53	M₁₆	C₂×D₄₅₇	1	2	yes	—
54	C₂×C₈	—	914	1	no	—
55	C₂×C₈	C₂×D₄₅₇	1	1	yes	characteristic
56	Q₈	—	914	2	no	—
57	Q₈	—	914	2	no	—
58	Q₈	—	457	1	no	—
59	D₄	—	914	1	no	—
60	D₄	—	457	1	no	—
61	C₂×C₄	—	914	2	no	—
62	C₂×C₄	—	914	1	no	—
63	C₂×C₄	C₂²×D₄₅₇	1	1	yes	characteristic
64	C₈	—	2	2	no	—
65	C₈	—	914	1	no	—
66	C₈	D₁₈₂₈	1	1	yes	characteristic
67	C₈	D₁₈₂₈	1	1	yes	characteristic
68	C₂²	—	914	1	no	—
69	C₂²	#20300742	1	1	yes	characteristic
70	C₄	—	1828	2	no	—
71	C₄	—	914	1	no	—
72	C₄	D₄×D₄₅₇	1	1	yes	characteristic
73	C₄	C₂×D₁₈₂₈	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	1828	1	no	—
76	C₂	#28410527	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#28410527
commutator, cosocle	C₂×C₄×C₄₅₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₅₇
Fitting	#108×C₄₅₇	C₂
socle	C₂×C₄₅₇	#121
prime radical	#20300741	C₂²
hypercenter	#108	D₄₅₇
hypocenter	C₄₅₇	#473
LCS	G ▷ C₂×C₄×C₄₅₇ ▷ C₂×C₄₅₇ ▷ C₄₅₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₁₈₂₈	C₂	semidirect
4. #28410470	C₂	semidirect
5. #108×C₄₅₇	C₂	semidirect
38. C₄₅₇	#473	semidirect
43. #108	D₄₅₇	semidirect

Maximal subgroups

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

subgroup	index
#28410585	2
C₂×Dic₁₈₂₈	2
#28410558	2
#28410470	2
#108×C₄₅₇	2
#473	457