Subgroups — #49148146

Order 36928.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22604406	C₂	1	2	yes	maximal, complemented
2	C₄×Dic₁₁₅₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊#17987230	C₂	1	1	yes	maximal, characteristic, complemented
4	#32914585	C₂	1	2	yes	maximal, complemented
5	#127×C₅₇₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₁₅₄	C₂²	1	1	yes	characteristic
7	#22604406	—	2	4	no	—
8	C₂×#17987230	C₂²	1	2	yes	—
9	C₄⋊Dic₅₇₇	C₂²	1	1	yes	characteristic
10	#22604397	—	2	1	no	—
11	C₄×Dic₅₇₇	—	2	1	no	—
12	C₂×D₄×C₅₇₇	—	2	1	no	—
13	C₂×D₄×C₅₇₇	—	2	1	no	—
14	C₂×D₄×C₅₇₇	C₂²	1	2	yes	—
15	C₄²×C₅₇₇	C₂²	1	1	yes	characteristic
16	Dic₁₁₅₄	—	2	1	no	—
17	Dic₁₁₅₄	D₄	1	2	yes	complemented
18	C₂×Dic₅₇₇	—	2	1	no	—
19	C₂×Dic₅₇₇	—	2	1	no	—
20	#17987230	—	2	2	no	—
21	C₂³×C₅₇₇	—	2	2	no	—
22	D₄×C₅₇₇	—	2	2	no	—
23	D₄×C₅₇₇	—	2	2	no	—
24	D₄×C₅₇₇	—	4	2	no	—
25	D₄×C₅₇₇	—	4	2	no	—
26	C₂×C₄×C₅₇₇	D₄	1	1	yes	characteristic
27	C₂×C₄×C₅₇₇	D₄	1	1	yes	characteristic
28	C₂×C₄×C₅₇₇	C₂³	1	1	yes	characteristic
29	C₂²×C₅₇₇	—	4	2	no	—
30	C₂²×C₅₇₇	—	4	2	no	—
31	C₂²×C₅₇₇	—	4	2	no	—
32	C₂²×C₅₇₇	C₂×D₄	1	1	yes	characteristic
33	C₄×C₅₇₇	—	2	1	no	—
34	C₄×C₅₇₇	SD₁₆	1	2	yes	complemented
35	C₄×C₅₇₇	C₂×D₄	1	1	yes	characteristic
36	C₄×C₅₇₇	#41	1	1	yes	characteristic
37	Dic₅₇₇	—	2	2	no	—
38	Dic₅₇₇	—	4	1	no	—
39	C₂×C₅₇₇	—	8	2	no	—
40	C₂×C₅₇₇	#121	1	1	yes	characteristic
41	C₂×C₅₇₇	C₂×SD₁₆	1	1	yes	characteristic
42	C₂×C₅₇₇	AGL(1,ℤ/8)	1	1	yes	characteristic
43	C₅₇₇	#460	1	1	yes	characteristic, complemented, Sylow
44	#460	—	577	1	no	maximal, Sylow
45	C₂×SD₁₆	—	577	2	no	—
46	#127	D₅₇₇	1	1	yes	characteristic
47	C₄×Q₈	—	577	1	no	—
48	C₄⋊C₈	—	577	1	no	—
49	#102	—	577	2	no	—
50	C₂×Q₈	—	577	1	no	—
51	C₂×D₄	—	2	1	no	—
52	C₂×D₄	—	2	1	no	—
53	C₂×D₄	C₂×D₅₇₇	1	2	yes	—
54	SD₁₆	—	1154	4	no	—
55	C₂×C₈	—	577	2	no	—
56	C₄⋊C₄	—	577	1	no	—
57	C₄⋊C₄	—	1154	1	no	—
58	C₄²	—	1154	1	no	—
59	C₄²	C₂×D₅₇₇	1	1	yes	characteristic
60	C₂³	—	2	2	no	—
61	Q₈	—	577	2	no	—
62	Q₈	—	1154	1	no	—
63	D₄	—	2	2	no	—
64	D₄	—	2	2	no	—
65	D₄	—	4	2	no	—
66	D₄	—	4	2	no	—
67	C₂×C₄	—	1154	1	no	—
68	C₂×C₄	—	1154	1	no	—
69	C₂×C₄	C₂²⋊D₅₇₇	1	1	yes	characteristic
70	C₂×C₄	C₂²⋊D₅₇₇	1	1	yes	characteristic
71	C₂×C₄	C₂²×D₅₇₇	1	1	yes	characteristic
72	C₈	—	1154	2	no	—
73	C₂²	—	4	2	no	—
74	C₂²	—	4	2	no	—
75	C₂²	—	4	2	no	—
76	C₂²	C₂×C₂²⋊D₅₇₇	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	2308	1	no	—
79	C₄	—	1154	2	no	—
80	C₄	#22604406	1	2	yes	complemented
81	C₄	D₄×D₅₇₇	1	1	yes	characteristic
82	C₄	#22604417	1	1	yes	characteristic
83	C₂	—	8	2	no	—
84	C₂	#32914635	1	1	yes	characteristic
85	C₂	C₂×#22604406	1	1	yes	characteristic
86	C₂	#32914690	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₅₇₇
commutator, cosocle	C₂×C₄×C₅₇₇	C₂³
Frattini	C₂×C₄	C₂²×D₅₇₇
Fitting, prime radical	#127×C₅₇₇	C₂
socle	C₂²×C₅₇₇	C₂×D₄
hypercenter	#127	D₅₇₇
hypocenter	C₅₇₇	#460
LCS	G ▷ C₂×C₄×C₅₇₇ ▷ C₂×C₅₇₇ ▷ C₅₇₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂×#22604406	C₂	semidirect
2. C₄×Dic₁₁₅₄	C₂	semidirect
3. C₄⋊#17987230	C₂	semidirect
4. #32914585	C₂	semidirect
17. Dic₁₁₅₄	D₄	semidirect
34. C₄×C₅₇₇	SD₁₆	semidirect
43. C₅₇₇	#460	semidirect
80. C₄	#22604406	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22604406	2
C₄×Dic₁₁₅₄	2
C₄⋊#17987230	2
#32914585	2
#127×C₅₇₇	2
#460	577