Subgroups — #49148319

Order 36928.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#32914664	C₂	1	1	yes	maximal, characteristic
2	#32914587	C₂	1	4	yes	maximal
3	#32914575	C₂	1	1	yes	maximal, characteristic
4	#125×C₅₇₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₁₅₄	C₂²	1	2	yes	—
6	C₂×#17987230	C₂²	1	2	yes	—
7	C₄⋊Dic₅₇₇	—	2	2	no	—
8	C₄⋊C₄×C₅₇₇	—	2	2	no	—
9	C₄⋊C₄×C₅₇₇	C₂²	1	2	yes	—
10	C₄²×C₅₇₇	C₂²	1	1	yes	characteristic
11	Dic₁₁₅₄	—	2	4	no	—
12	C₂×Dic₅₇₇	—	2	2	no	—
13	#17987230	—	2	2	no	—
14	C₂×C₄×C₅₇₇	—	2	2	no	—
15	C₂×C₄×C₅₇₇	D₄	1	2	yes	—
16	C₂×C₄×C₅₇₇	C₂³	1	1	yes	characteristic
17	C₂²×C₅₇₇	C₂×D₄	1	1	yes	characteristic
18	C₄×C₅₇₇	—	2	2	no	—
19	C₄×C₅₇₇	—	4	2	no	—
20	C₄×C₅₇₇	#41	1	2	yes	—
21	Dic₅₇₇	—	4	2	no	—
22	C₂×C₅₇₇	#124	1	1	yes	characteristic
23	C₂×C₅₇₇	#137	1	2	yes	—
24	C₅₇₇	#491	1	1	yes	characteristic, complemented, Sylow
25	#491	—	577	1	no	maximal, Sylow
26	C₄⋊Q₈	—	577	1	no	—
27	#125	D₅₇₇	1	1	yes	characteristic
28	#103	—	577	4	no	—
29	#97	—	577	1	no	—
30	C₂×Q₈	—	577	2	no	—
31	C₂×C₈	—	577	2	no	—
32	C₄⋊C₄	—	2	2	no	—
33	C₄⋊C₄	—	1154	2	no	—
34	C₄⋊C₄	C₂×D₅₇₇	1	2	yes	—
35	C₄²	C₂×D₅₇₇	1	1	yes	characteristic
36	Q₈	—	1154	4	no	—
37	C₂×C₄	—	2	2	no	—
38	C₂×C₄	—	1154	2	no	—
39	C₂×C₄	C₂²⋊D₅₇₇	1	2	yes	—
40	C₂×C₄	C₂²×D₅₇₇	1	1	yes	characteristic
41	C₈	—	1154	2	no	—
42	C₂²	C₂×C₂²⋊D₅₇₇	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	4	2	no	—
45	C₄	—	2308	2	no	—
46	C₄	#22604419	1	2	yes	—
47	C₂	#32914653	1	1	yes	characteristic
48	C₂	#32914694	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₅₇₇
commutator, cosocle	C₂×C₄×C₅₇₇	C₂³
Frattini	C₂×C₄	C₂²×D₅₇₇
Fitting	#125×C₅₇₇	C₂
socle, prime radical	C₂²×C₅₇₇	C₂×D₄
hypercenter	#125	D₅₇₇
hypocenter	C₅₇₇	#491
LCS	G ▷ C₂×C₄×C₅₇₇ ▷ C₂×C₅₇₇ ▷ C₅₇₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
24. C₅₇₇	#491	semidirect

Maximal subgroups

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

subgroup	index
#32914664	2
#32914587	2
#32914575	2
#125×C₅₇₇	2
#491	577