Subgroups — #49148239

Order 36928.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#32914664	C₂	1	1	yes	maximal, characteristic, complemented
2	#32914595	C₂	1	2	yes	maximal, complemented
3	C₄⋊#17987230	C₂	1	1	yes	maximal, characteristic, complemented
4	#32914585	C₂	1	2	yes	maximal
5	C₄×D₄×C₅₇₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₁₅₄	—	2	1	no	—
7	C₂×#17987230	C₂²	1	2	yes	—
8	C₄⋊Dic₅₇₇	—	2	1	no	—
9	C₄⋊Dic₅₇₇	C₂²	1	2	yes	—
10	C₂×D₄×C₅₇₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₅₇₇	—	2	1	no	—
12	C₄⋊C₄×C₅₇₇	C₂²	1	1	yes	characteristic
13	C₂²⋊C₄×C₅₇₇	—	2	1	no	—
14	C₄²×C₅₇₇	C₂²	1	1	yes	characteristic
15	Dic₁₁₅₄	—	4	2	no	—
16	C₂×Dic₅₇₇	—	2	2	no	—
17	#17987230	—	2	2	no	—
18	C₂³×C₅₇₇	—	2	1	no	—
19	D₄×C₅₇₇	—	2	1	no	—
20	D₄×C₅₇₇	Q₈	1	2	yes	complemented
21	C₂×C₄×C₅₇₇	—	2	1	no	—
22	C₂×C₄×C₅₇₇	—	4	2	no	—
23	C₂×C₄×C₅₇₇	D₄	1	1	yes	characteristic
24	C₂×C₄×C₅₇₇	D₄	1	1	yes	characteristic
25	C₂×C₄×C₅₇₇	C₂³	1	1	yes	characteristic
26	C₂²×C₅₇₇	—	2	2	no	—
27	C₂²×C₅₇₇	—	4	1	no	—
28	C₂²×C₅₇₇	—	4	1	no	—
29	C₂²×C₅₇₇	C₂×D₄	1	1	yes	characteristic
30	C₄×C₅₇₇	—	2	1	no	—
31	C₄×C₅₇₇	—	4	1	no	—
32	C₄×C₅₇₇	SD₁₆	1	2	yes	—
33	C₄×C₅₇₇	C₂×Q₈	1	1	yes	characteristic
34	C₄×C₅₇₇	#41	1	1	yes	characteristic
35	Dic₅₇₇	—	4	2	no	—
36	C₂×C₅₇₇	—	4	2	no	—
37	C₂×C₅₇₇	C₂²⋊Q₈	1	1	yes	characteristic
38	C₂×C₅₇₇	C₂×SD₁₆	1	1	yes	characteristic
39	C₂×C₅₇₇	AGL(1,ℤ/8)	1	1	yes	characteristic
40	C₅₇₇	#476	1	1	yes	characteristic, complemented, Sylow
41	#476	—	577	1	no	maximal, Sylow
42	C₄⋊Q₈	—	577	1	no	—
43	C₄×D₄	D₅₇₇	1	1	yes	characteristic
44	#106	—	577	2	no	—
45	C₄⋊C₈	—	577	1	no	—
46	#102	—	577	2	no	—
47	C₂×Q₈	—	1154	1	no	—
48	C₂×D₄	C₂×D₅₇₇	1	1	yes	characteristic
49	C₂²×C₄	—	2	1	no	—
50	C₂×C₈	—	577	2	no	—
51	C₄⋊C₄	—	577	2	no	—
52	C₄⋊C₄	—	1154	1	no	—
53	C₄⋊C₄	C₂×D₅₇₇	1	1	yes	characteristic
54	C₂²⋊C₄	—	2	1	no	—
55	C₄²	C₂×D₅₇₇	1	1	yes	characteristic
56	C₂³	—	2	1	no	—
57	Q₈	—	2308	2	no	—
58	D₄	—	2	1	no	—
59	D₄	Dic₁₁₅₄	1	2	yes	complemented
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	4	2	no	—
62	C₂×C₄	—	1154	2	no	—
63	C₂×C₄	C₂²⋊D₅₇₇	1	1	yes	characteristic
64	C₂×C₄	C₂²⋊D₅₇₇	1	1	yes	characteristic
65	C₂×C₄	C₂²×D₅₇₇	1	1	yes	characteristic
66	C₈	—	1154	2	no	—
67	C₂²	—	2	2	no	—
68	C₂²	—	4	1	no	—
69	C₂²	—	4	1	no	—
70	C₂²	C₂×C₂²⋊D₅₇₇	1	1	yes	characteristic
71	C₄	—	2	1	no	—
72	C₄	—	4	1	no	—
73	C₄	—	2308	2	no	—
74	C₄	#22604406	1	2	yes	—
75	C₄	C₂×Dic₁₁₅₄	1	1	yes	characteristic
76	C₄	#22604418	1	1	yes	characteristic
77	C₂	—	4	2	no	—
78	C₂	#32914643	1	1	yes	characteristic
79	C₂	C₂×#22604406	1	1	yes	characteristic
80	C₂	#32914689	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₅₇₇
commutator, cosocle	C₂×C₄×C₅₇₇	C₂³
Frattini	C₂×C₄	C₂²×D₅₇₇
Fitting	C₄×D₄×C₅₇₇	C₂
socle	C₂²×C₅₇₇	C₂×D₄
prime radical	C₂×D₄×C₅₇₇	C₂²
hypercenter	C₄×D₄	D₅₇₇
hypocenter	C₅₇₇	#476
LCS	G ▷ C₂×C₄×C₅₇₇ ▷ C₂×C₅₇₇ ▷ C₅₇₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #32914664	C₂	semidirect
2. #32914595	C₂	semidirect
3. C₄⋊#17987230	C₂	semidirect
20. D₄×C₅₇₇	Q₈	semidirect
40. C₅₇₇	#476	semidirect
59. D₄	Dic₁₁₅₄	semidirect

Maximal subgroups

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

subgroup	index
#32914664	2
#32914595	2
C₄⋊#17987230	2
#32914585	2
C₄×D₄×C₅₇₇	2
#476	577