Subgroups — #44416854

Order 29248.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20300724	C₂	1	2	yes	maximal, complemented
2	C₄×D₁₈₂₈	C₂	1	1	yes	maximal, characteristic
3	#28410464	C₂	1	2	yes	maximal, complemented
4	C₄×#16814532	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄⋊C₈×C₄₅₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₈₂₈	C₄	1	1	yes	characteristic
7	C₂×C₄×D₄₅₇	C₂²	1	2	yes	—
8	#20300724	—	2	4	no	—
9	C₂×#16814532	C₂²	1	1	yes	characteristic
10	C₂×#16814532	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₄₅₇	C₄	1	1	yes	characteristic
12	#20300718	C₄	1	2	yes	—
13	C₂×C₈×C₄₅₇	C₂²	1	2	yes	—
14	C₄²×C₄₅₇	C₂²	1	1	yes	characteristic
15	C₂²×D₄₅₇	C₂×C₄	1	2	yes	—
16	D₁₈₂₈	—	2	2	no	—
17	C₂×Dic₄₅₇	C₂×C₄	1	2	yes	—
18	C₄×D₄₅₇	—	2	2	no	—
19	C₄×D₄₅₇	—	2	2	no	—
20	#16814532	—	2	1	no	—
21	#16814532	D₄	1	2	yes	complemented
22	C₂×C₄×C₄₅₇	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×C₄₅₇	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×C₄₅₇	C₂³	1	1	yes	characteristic
25	C₈×C₄₅₇	—	2	2	no	—
26	C₂²×C₄₅₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₄₅₇	—	2	2	no	—
28	C₂×D₄₅₇	—	2	2	no	—
29	C₂×D₄₅₇	—	2	2	no	—
30	C₄×C₄₅₇	—	2	1	no	—
31	C₄×C₄₅₇	M₁₆	1	2	yes	complemented
32	C₄×C₄₅₇	C₂×D₄	1	1	yes	characteristic
33	C₄×C₄₅₇	#41	1	1	yes	characteristic
34	Dic₄₅₇	—	2	2	no	—
35	C₂×C₄₅₇	C₄×D₄	1	1	yes	characteristic
36	C₂×C₄₅₇	C₂×M₁₆	1	1	yes	characteristic
37	C₂×C₄₅₇	#131	1	1	yes	characteristic
38	D₄₅₇	—	4	2	no	—
39	C₄₅₇	#436	1	1	yes	characteristic, complemented, Sylow
40	#436	—	457	1	no	maximal, Sylow
41	C₂×M₁₆	—	457	2	no	—
42	C₄×D₄	—	457	1	no	—
43	C₄⋊C₈	D₄₅₇	1	1	yes	characteristic, complemented
44	C₂²⋊C₈	—	457	2	no	—
45	C₄×C₈	—	457	1	no	—
46	C₂×D₄	—	457	1	no	—
47	C₂²×C₄	—	457	2	no	—
48	M₁₆	—	914	4	no	—
49	C₂×C₈	—	457	1	no	—
50	C₂×C₈	—	457	1	no	—
51	C₂×C₈	C₂×D₄₅₇	1	2	yes	—
52	C₄⋊C₄	—	457	1	no	—
53	C₂²⋊C₄	—	457	2	no	—
54	C₄²	C₂×D₄₅₇	1	1	yes	characteristic
55	C₂³	—	457	2	no	—
56	D₄	—	914	2	no	—
57	C₂×C₄	—	914	2	no	—
58	C₂×C₄	—	914	2	no	—
59	C₂×C₄	—	457	2	no	—
60	C₂×C₄	C₄×D₄₅₇	1	1	yes	characteristic
61	C₂×C₄	C₄×D₄₅₇	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₄₅₇	1	1	yes	characteristic
63	C₈	—	2	2	no	—
64	C₈	—	914	1	no	—
65	C₈	—	457	2	no	—
66	C₂²	—	914	2	no	—
67	C₂²	—	914	2	no	—
68	C₂²	—	914	2	no	—
69	C₂²	C₂×C₄×D₄₅₇	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	914	2	no	—
72	C₄	#20300724	1	2	yes	complemented
73	C₄	D₄×D₄₅₇	1	1	yes	characteristic
74	C₄	#20300742	1	1	yes	characteristic
75	C₂	—	1828	2	no	—
76	C₂	#28410514	1	1	yes	characteristic
77	C₂	C₂×#20300724	1	1	yes	characteristic
78	C₂	#28410560	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₅₇
commutator, socle	C₂²×C₄₅₇	C₂²×C₄
Fitting	C₄⋊C₈×C₄₅₇	C₂
prime radical	C₂×D₁₈₂₈	C₄
cosocle	C₂×C₄×C₄₅₇	C₂³
hypercenter	C₄⋊C₈	D₄₅₇
hypocenter	C₄₅₇	#436
LCS	G ▷ C₂²×C₄₅₇ ▷ C₄₅₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#20300724	C₂	semidirect
3. #28410464	C₂	semidirect
4. C₄×#16814532	C₂	semidirect
5. C₄⋊C₈×C₄₅₇	C₂	semidirect
21. #16814532	D₄	semidirect
31. C₄×C₄₅₇	M₁₆	semidirect
39. C₄₅₇	#436	semidirect
43. C₄⋊C₈	D₄₅₇	semidirect
72. C₄	#20300724	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20300724	2
C₄×D₁₈₂₈	2
#28410464	2
C₄×#16814532	2
C₄⋊C₈×C₄₅₇	2
#436	457