Subgroups — #49148832

Order 36928.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22604428	C₂	1	1	yes	maximal, characteristic
2	#32914743	C₂	1	1	yes	maximal, characteristic
3	M₁₆×D₅₇₇	C₂	1	1	yes	maximal, characteristic
4	#22604428	—	2	1	no	—
5	#22604428	—	2	1	no	—
6	C₂×#17987237	C₄	1	2	yes	complemented
7	C₄⋊#14556313	—	2	1	no	—
8	C₂²⋊#14556313	C₄	1	2	yes	—
9	C₄×#14556313	—	2	1	no	—
10	C₂×C₄×D₅₇₇	C₂²	1	1	yes	characteristic
11	#22604402	C₄	1	1	yes	characteristic, complemented
12	#22604401	—	2	1	no	—
13	C₈×D₅₇₇	—	2	1	no	—
14	M₁₆×C₅₇₇	C₄	1	1	yes	characteristic, complemented
15	C₂×#14556313	—	2	2	no	—
16	#17987237	—	2	2	no	—
17	C₂²×D₅₇₇	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₅₇₇	C₂×C₄	1	1	yes	characteristic
19	C₄×D₅₇₇	D₄	1	1	yes	characteristic
20	C₄×D₅₇₇	D₄	1	1	yes	characteristic
21	C₄×D₅₇₇	D₄	1	1	yes	characteristic
22	C₄×D₅₇₇	Q₈	1	1	yes	characteristic
23	#17987230	—	2	1	no	—
24	C₂×C₄×C₅₇₇	C₂×C₄	1	1	yes	characteristic
25	C₈×C₅₇₇	—	2	1	no	—
26	C₂²×C₅₇₇	C₄²	1	1	yes	characteristic
27	C₂×D₅₇₇	—	4	1	no	—
28	C₂×D₅₇₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×D₅₇₇	C₄⋊C₄	1	1	yes	characteristic
30	#14556313	—	4	2	no	—
31	C₄×C₅₇₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₄×C₅₇₇	C₄⋊C₄	1	1	yes	characteristic
33	Dic₅₇₇	C₂²⋊C₄	1	1	yes	characteristic
34	Dic₅₇₇	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₅₇₇	—	2	1	no	—
36	C₂×C₅₇₇	#95	1	1	yes	characteristic
37	D₅₇₇	—	2	1	no	—
38	D₅₇₇	—	2	1	no	—
39	C₅₇₇	#344	1	1	yes	characteristic, complemented, Sylow
40	#344	—	577	1	no	maximal, Sylow
41	C₂×M₁₆	—	577	1	no	—
42	C₂×M₁₆	—	577	1	no	—
43	#117	—	577	1	no	—
44	C₂²×C₄	—	577	1	no	—
45	M₁₆	—	577	1	no	—
46	M₁₆	—	1154	1	no	—
47	M₁₆	—	1154	1	no	—
48	M₁₆	—	1154	1	no	—
49	M₁₆	#14556313	1	1	yes	characteristic, complemented
50	C₂×C₈	—	577	2	no	—
51	C₂×C₈	—	1154	1	no	—
52	C₄⋊C₄	—	1154	1	no	—
53	C₂²⋊C₄	—	577	2	no	—
54	C₄²	—	1154	1	no	—
55	C₂³	—	577	1	no	—
56	C₂×C₄	—	577	1	no	—
57	C₂×C₄	—	577	1	no	—
58	C₂×C₄	—	577	1	no	—
59	C₂×C₄	—	577	1	no	—
60	C₂×C₄	—	577	1	no	—
61	C₂×C₄	—	1154	2	no	—
62	C₂×C₄	C₂×#14556313	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	1154	2	no	—
65	C₈	—	1154	1	no	—
66	C₂²	—	2308	1	no	—
67	C₂²	—	577	1	no	—
68	C₂²	—	577	1	no	—
69	C₂²	C₄×#14556313	1	1	yes	characteristic
70	C₄	—	2308	2	no	—
71	C₄	—	577	1	no	—
72	C₄	—	577	1	no	—
73	C₄	C₂²⋊#14556313	1	1	yes	characteristic
74	C₄	C₄⋊#14556313	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	1154	1	no	—
77	C₂	—	1154	1	no	—
78	C₂	(C₂×#14556313)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	(C₂×#14556313)⋊C₄
commutator	C₂²×C₅₇₇	C₄²
Frattini	C₂×C₄	C₂×#14556313
Fitting	M₁₆×C₅₇₇	C₄
socle	C₂×C₅₇₇	#95
prime radical	C₂²×D₅₇₇	C₂×C₄
cosocle	C₂×C₄×D₅₇₇	C₂²
hypercenter	M₁₆	#14556313
hypocenter	C₅₇₇	#344
LCS	G ▷ C₂²×C₅₇₇ ▷ C₂×C₅₇₇ ▷ C₅₇₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
6. C₂×#17987237	C₄	semidirect
11. #22604402	C₄	semidirect
14. M₁₆×C₅₇₇	C₄	semidirect
39. C₅₇₇	#344	semidirect
49. M₁₆	#14556313	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22604428	2
#32914743	2
M₁₆×D₅₇₇	2
#344	577