Subgroups — #49148220

Order 36928.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#32914692	C₂	1	2	yes	maximal, complemented
2	C₂×D₄₆₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#32914670	C₂	1	1	yes	maximal, characteristic, complemented
4	#32914580	C₂	1	2	yes	maximal, complemented
5	#108×C₅₇₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#22604418	C₂²	1	1	yes	characteristic
7	C₂×D₂₃₀₈	C₂²	1	2	yes	—
8	#22604407	—	2	2	no	—
9	D₄₆₁₆	—	2	2	no	—
10	D₄₆₁₆	—	2	1	no	—
11	D₄₆₁₆	—	2	1	no	—
12	#22604402	C₂²	1	1	yes	characteristic
13	#22604401	—	2	1	no	—
14	C₈×D₅₇₇	—	2	1	no	—
15	M₁₆×C₅₇₇	C₂²	1	2	yes	—
16	C₂×C₈×C₅₇₇	C₂²	1	1	yes	characteristic
17	C₂²×D₅₇₇	—	2	2	no	—
18	Dic₁₁₅₄	D₄	1	1	yes	characteristic
19	D₂₃₀₈	—	2	2	no	—
20	D₂₃₀₈	—	2	2	no	—
21	D₂₃₀₈	D₄	1	1	yes	characteristic
22	C₂²⋊D₅₇₇	—	2	1	no	—
23	C₄×D₅₇₇	—	2	1	no	—
24	#17987230	—	2	1	no	—
25	C₂×C₄×C₅₇₇	C₂³	1	1	yes	characteristic
26	C₈×C₅₇₇	—	2	2	no	—
27	C₈×C₅₇₇	D₄	1	1	yes	characteristic
28	C₈×C₅₇₇	D₄	1	1	yes	characteristic
29	C₂²×C₅₇₇	#41	1	1	yes	characteristic
30	C₂×D₅₇₇	—	2	1	no	—
31	C₂×D₅₇₇	—	4	2	no	—
32	C₂×D₅₇₇	—	8	2	no	—
33	C₄×C₅₇₇	C₂×D₄	1	1	yes	characteristic
34	C₄×C₅₇₇	C₂×D₄	1	1	yes	characteristic
35	Dic₅₇₇	—	2	1	no	—
36	C₂×C₅₇₇	—	2	1	no	—
37	C₂×C₅₇₇	#121	1	1	yes	characteristic
38	D₅₇₇	—	4	1	no	—
39	D₅₇₇	—	8	2	no	—
40	C₅₇₇	#472	1	1	yes	characteristic, complemented, Sylow
41	#472	—	577	1	no	maximal, Sylow
42	AGL(1,ℤ/8)	—	577	2	no	—
43	C₂×D₈	—	577	1	no	—
44	#131	—	577	1	no	—
45	#108	D₅₇₇	1	1	yes	characteristic, complemented
46	#100	—	577	2	no	—
47	#41	—	577	1	no	—
48	C₂×D₄	—	577	2	no	—
49	SD₁₆	—	1154	2	no	—
50	D₈	—	1154	2	no	—
51	D₈	—	1154	1	no	—
52	D₈	—	1154	1	no	—
53	M₁₆	—	577	1	no	—
54	M₁₆	—	1154	1	no	—
55	M₁₆	C₂×D₅₇₇	1	2	yes	—
56	C₂×C₈	—	1154	1	no	—
57	C₂×C₈	C₂×D₅₇₇	1	1	yes	characteristic
58	C₂³	—	1154	2	no	—
59	Q₈	—	577	1	no	—
60	D₄	—	577	1	no	—
61	D₄	—	1154	1	no	—
62	D₄	—	1154	2	no	—
63	D₄	—	1154	2	no	—
64	C₂×C₄	—	1154	1	no	—
65	C₂×C₄	C₂²×D₅₇₇	1	1	yes	characteristic
66	C₈	—	2	2	no	—
67	C₈	—	1154	1	no	—
68	C₈	D₂₃₀₈	1	1	yes	characteristic
69	C₈	D₂₃₀₈	1	1	yes	characteristic
70	C₂²	—	2308	2	no	—
71	C₂²	—	4616	2	no	—
72	C₂²	—	1154	1	no	—
73	C₂²	#22604419	1	1	yes	characteristic
74	C₄	—	1154	1	no	—
75	C₄	D₄×D₅₇₇	1	1	yes	characteristic
76	C₄	C₂×D₂₃₀₈	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	—	2308	1	no	—
79	C₂	—	4616	2	no	—
80	C₂	#32914639	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#32914639
commutator, cosocle	C₂×C₄×C₅₇₇	C₂³
Frattini	C₂×C₄	C₂²×D₅₇₇
Fitting	#108×C₅₇₇	C₂
socle	C₂×C₅₇₇	#121
hypercenter	#108	D₅₇₇
hypocenter	C₅₇₇	#472
LCS	G ▷ C₂×C₄×C₅₇₇ ▷ C₂×C₅₇₇ ▷ C₅₇₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
1. #32914692	C₂	semidirect
2. C₂×D₄₆₁₆	C₂	semidirect
3. #32914670	C₂	semidirect
4. #32914580	C₂	semidirect
5. #108×C₅₇₇	C₂	semidirect
40. C₅₇₇	#472	semidirect
45. #108	D₅₇₇	semidirect

Maximal subgroups

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

subgroup	index
#32914692	2
C₂×D₄₆₁₆	2
#32914670	2
#32914580	2
#108×C₅₇₇	2
#472	577