Subgroups — #44416988

Order 29248.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₈₂₈	C₂	1	2	yes	maximal
2	#28410552	C₂	1	1	yes	maximal, characteristic
3	C₄×Dic₉₁₄	C₂	1	1	yes	maximal, characteristic
4	#28410477	C₂	1	2	yes	maximal
5	C₄⋊C₈×C₄₅₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₁₄	C₂²	1	2	yes	—
7	C₂×Dic₉₁₄	C₂²	1	1	yes	characteristic
8	Dic₁₈₂₈	—	2	4	no	—
9	C₄⋊Dic₄₅₇	—	2	1	no	—
10	C₄⋊Dic₄₅₇	—	2	1	no	—
11	C₄⋊Dic₄₅₇	C₂²	1	1	yes	characteristic
12	#20300720	—	2	1	no	—
13	C₄×Dic₄₅₇	—	2	1	no	—
14	C₂×C₈×C₄₅₇	C₂²	1	2	yes	—
15	C₄²×C₄₅₇	C₂²	1	1	yes	characteristic
16	Dic₉₁₄	—	2	1	no	—
17	Dic₉₁₄	—	2	2	no	—
18	Dic₉₁₄	—	2	2	no	—
19	Dic₉₁₄	D₄	1	2	yes	—
20	C₂×Dic₄₅₇	—	2	1	no	—
21	C₂×Dic₄₅₇	—	2	1	no	—
22	C₂×Dic₄₅₇	—	2	2	no	—
23	C₂×C₄×C₄₅₇	D₄	1	1	yes	characteristic
24	C₂×C₄×C₄₅₇	D₄	1	1	yes	characteristic
25	C₂×C₄×C₄₅₇	C₂³	1	1	yes	characteristic
26	C₈×C₄₅₇	—	2	2	no	—
27	C₂²×C₄₅₇	C₂×D₄	1	1	yes	characteristic
28	C₄×C₄₅₇	—	2	1	no	—
29	C₄×C₄₅₇	Q₁₆	1	2	yes	complemented
30	C₄×C₄₅₇	C₂×D₄	1	1	yes	characteristic
31	C₄×C₄₅₇	#41	1	1	yes	characteristic
32	Dic₄₅₇	—	2	2	no	—
33	Dic₄₅₇	—	4	2	no	—
34	Dic₄₅₇	—	4	1	no	—
35	C₂×C₄₅₇	#121	1	1	yes	characteristic
36	C₂×C₄₅₇	C₂×Q₁₆	1	1	yes	characteristic
37	C₂×C₄₅₇	#137	1	1	yes	characteristic
38	C₄₅₇	#462	1	1	yes	characteristic, complemented, Sylow
39	#462	—	457	1	no	maximal, Sylow
40	C₂×Q₁₆	—	457	2	no	—
41	C₄⋊Q₈	—	457	1	no	—
42	C₄×Q₈	—	457	1	no	—
43	C₄⋊C₈	D₄₅₇	1	1	yes	characteristic
44	#103	—	457	2	no	—
45	C₂×Q₈	—	457	2	no	—
46	C₂×Q₈	—	457	1	no	—
47	Q₁₆	—	914	4	no	—
48	C₂×C₈	C₂×D₄₅₇	1	2	yes	—
49	C₄⋊C₄	—	914	1	no	—
50	C₄⋊C₄	—	914	1	no	—
51	C₄⋊C₄	—	914	1	no	—
52	C₄⋊C₄	—	457	1	no	—
53	C₄²	—	914	1	no	—
54	C₄²	C₂×D₄₅₇	1	1	yes	characteristic
55	Q₈	—	914	2	no	—
56	Q₈	—	914	2	no	—
57	Q₈	—	914	1	no	—
58	Q₈	—	457	2	no	—
59	C₂×C₄	—	914	1	no	—
60	C₂×C₄	—	914	2	no	—
61	C₂×C₄	—	914	1	no	—
62	C₂×C₄	D₁₈₂₈	1	1	yes	characteristic
63	C₂×C₄	D₁₈₂₈	1	1	yes	characteristic
64	C₂×C₄	C₂²×D₄₅₇	1	1	yes	characteristic
65	C₈	—	2	2	no	—
66	C₂²	C₂×D₁₈₂₈	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	1828	2	no	—
69	C₄	—	1828	1	no	—
70	C₄	—	914	2	no	—
71	C₄	Dic₁₈₂₈	1	2	yes	complemented
72	C₄	D₄×D₄₅₇	1	1	yes	characteristic
73	C₄	#20300742	1	1	yes	characteristic
74	C₂	#28410527	1	1	yes	characteristic
75	C₂	C₂×Dic₁₈₂₈	1	1	yes	characteristic
76	C₂	#28410585	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₈₂₈
commutator, cosocle	C₂×C₄×C₄₅₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₅₇
Fitting	C₄⋊C₈×C₄₅₇	C₂
socle, prime radical	C₂²×C₄₅₇	C₂×D₄
hypercenter	C₄⋊C₈	D₄₅₇
hypocenter	C₄₅₇	#462
LCS	G ▷ C₂×C₄×C₄₅₇ ▷ C₂×C₄₅₇ ▷ C₄₅₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
29. C₄×C₄₅₇	Q₁₆	semidirect
38. C₄₅₇	#462	semidirect
71. C₄	Dic₁₈₂₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₈₂₈	2
#28410552	2
C₄×Dic₉₁₄	2
#28410477	2
C₄⋊C₈×C₄₅₇	2
#462	457