Subgroups — #44416698

Order 29248.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₉₁₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₄₅₇	C₂	1	2	yes	maximal
3	C₂×#20300720	C₂	1	1	yes	maximal, characteristic
4	#28410459	C₂	1	2	yes	maximal
5	#95×C₄₅₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₁₄	—	2	4	no	—
7	C₂×Dic₉₁₄	—	2	2	no	—
8	C₂²×Dic₄₅₇	C₂²	1	1	yes	characteristic
9	C₂²×Dic₄₅₇	C₂²	1	2	yes	—
10	C₂²×Dic₄₅₇	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₄₅₇	—	2	4	no	—
12	#20300720	—	2	2	no	—
13	C₂²×C₄×C₄₅₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₄₅₇	C₂²	1	2	yes	—
15	Dic₉₁₄	—	2	8	no	—
16	C₂×Dic₄₅₇	—	2	1	no	—
17	C₂×Dic₄₅₇	—	2	2	no	—
18	C₂×Dic₄₅₇	—	2	2	no	—
19	C₂×Dic₄₅₇	—	2	1	no	—
20	C₂×Dic₄₅₇	—	2	1	no	—
21	C₂×Dic₄₅₇	—	2	2	no	—
22	C₂×Dic₄₅₇	D₄	1	4	yes	—
23	C₂×Dic₄₅₇	Q₈	1	2	yes	complemented
24	C₂³×C₄₅₇	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₄₅₇	—	2	2	no	—
26	C₂×C₄×C₄₅₇	—	2	2	no	—
27	C₂×C₄×C₄₅₇	—	2	2	no	—
28	C₂×C₄×C₄₅₇	D₄	1	2	yes	—
29	C₂×C₄×C₄₅₇	Q₈	1	4	yes	complemented
30	C₂²×C₄₅₇	C₂×D₄	1	2	yes	—
31	C₂²×C₄₅₇	C₂×D₄	1	1	yes	characteristic
32	C₂²×C₄₅₇	C₂×Q₈	1	1	yes	characteristic
33	C₂²×C₄₅₇	C₂×Q₈	1	2	yes	—
34	C₂²×C₄₅₇	#41	1	1	yes	characteristic
35	C₄×C₄₅₇	—	2	2	no	—
36	C₄×C₄₅₇	—	2	4	no	—
37	Dic₄₅₇	—	2	4	no	—
38	Dic₄₅₇	—	2	2	no	—
39	Dic₄₅₇	—	4	1	no	—
40	C₂×C₄₅₇	#120	1	1	yes	characteristic
41	C₂×C₄₅₇	C₂²⋊Q₈	1	2	yes	—
42	C₂×C₄₅₇	C₂²⋊Q₈	1	1	yes	characteristic
43	C₂×C₄₅₇	C₄⋊Q₈	1	2	yes	—
44	C₂×C₄₅₇	C₄⋊Q₈	1	1	yes	characteristic
45	C₄₅₇	#395	1	1	yes	characteristic, complemented, Sylow
46	#395	—	457	1	no	maximal, Sylow
47	C₂²×Q₈	—	457	1	no	—
48	C₂×C₄⋊C₄	—	457	1	no	—
49	C₂×C₄⋊C₄	—	457	2	no	—
50	#95	—	457	2	no	—
51	#95	D₄₅₇	1	1	yes	characteristic
52	C₂×Q₈	—	914	4	no	—
53	C₂×Q₈	—	914	2	no	—
54	C₂²×C₄	—	457	1	no	—
55	C₂²×C₄	—	457	1	no	—
56	C₂²×C₄	—	457	2	no	—
57	C₂²×C₄	C₂×D₄₅₇	1	1	yes	characteristic
58	C₂²×C₄	C₂×D₄₅₇	1	2	yes	—
59	C₄⋊C₄	—	914	4	no	—
60	C₄⋊C₄	—	914	2	no	—
61	C₂³	C₂²×D₄₅₇	1	1	yes	characteristic
62	Q₈	—	914	8	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	2	2	no	—
66	C₂×C₄	—	914	2	no	—
67	C₂×C₄	—	914	1	no	—
68	C₂×C₄	—	914	2	no	—
69	C₂×C₄	—	914	1	no	—
70	C₂×C₄	—	914	2	no	—
71	C₂×C₄	—	914	1	no	—
72	C₂×C₄	—	457	4	no	—
73	C₂×C₄	—	457	2	no	—
74	C₂×C₄	D₁₈₂₈	1	2	yes	—
75	C₂×C₄	Dic₉₁₄	1	4	yes	complemented
76	C₂²	D₄×D₄₅₇	1	2	yes	—
77	C₂²	C₂×D₁₈₂₈	1	1	yes	characteristic
78	C₂²	Q₈×D₄₅₇	1	1	yes	characteristic
79	C₂²	C₂×Dic₉₁₄	1	2	yes	—
80	C₂²	#20300740	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	2	4	no	—
83	C₄	—	1828	1	no	—
84	C₄	—	914	4	no	—
85	C₄	—	914	2	no	—
86	C₂	#28410522	1	1	yes	characteristic
87	C₂	#28410529	1	2	yes	—
88	C₂	#28410532	1	1	yes	characteristic
89	C₂	#28410551	1	2	yes	—
90	C₂	#28410552	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₅₇
commutator, socle, prime radical, cosocle	C₂³×C₄₅₇	C₂³
Fitting	#95×C₄₅₇	C₂
hypercenter	#95	D₄₅₇
hypocenter	C₄₅₇	#395
LCS	G ▷ C₂³×C₄₅₇ ▷ C₄₅₇
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
23. C₂×Dic₄₅₇	Q₈	semidirect
29. C₂×C₄×C₄₅₇	Q₈	semidirect
45. C₄₅₇	#395	semidirect
75. C₂×C₄	Dic₉₁₄	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₉₁₄	2
C₂×C₄⋊Dic₄₅₇	2
C₂×#20300720	2
#28410459	2
#95×C₄₅₇	2
#395	457