Subgroups — #49148848

Order 36928.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#32914738	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#22604421	C₂	1	1	yes	maximal, characteristic, complemented
3	#32914672	C₂	1	1	yes	maximal, characteristic
4	#22604421	—	2	1	no	—
5	#22604421	—	2	1	no	—
6	#22604418	C₄	1	1	yes	characteristic
7	#22604401	—	2	1	no	—
8	C₂×#17987230	C₂²	1	1	yes	characteristic
9	C₈×D₅₇₇	—	2	1	no	—
10	M₁₆×C₅₇₇	C₄	1	1	yes	characteristic
11	Dic₁₁₅₄	C₈	1	1	yes	characteristic
12	D₂₃₀₈	C₈	1	1	yes	characteristic
13	C₂²⋊D₅₇₇	—	2	1	no	—
14	C₄×D₅₇₇	—	2	1	no	—
15	#17987230	D₄	1	1	yes	characteristic
16	#17987230	D₄	1	1	yes	characteristic
17	C₂×C₄×C₅₇₇	C₂×C₄	1	1	yes	characteristic
18	C₈×C₅₇₇	—	2	1	no	—
19	C₂²×C₅₇₇	M₁₆	1	1	yes	characteristic
20	C₂×D₅₇₇	—	2	1	no	—
21	C₄×C₅₇₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₅₇₇	C₂×C₈	1	1	yes	characteristic
23	Dic₅₇₇	—	2	1	no	—
24	C₂×C₅₇₇	—	2	1	no	—
25	C₂×C₅₇₇	C₂²⋊C₈	1	1	yes	characteristic
26	D₅₇₇	—	4	1	no	—
27	C₅₇₇	#350	1	1	yes	characteristic, complemented, Sylow
28	#350	—	577	1	no	maximal, Sylow
29	#131	—	577	1	no	—
30	M₃₂	—	577	1	no	—
31	C₂×C₁₆	—	577	1	no	—
32	#41	—	577	1	no	—
33	M₁₆	—	1154	1	no	—
34	M₁₆	#14556313	1	1	yes	characteristic
35	C₂×C₈	—	577	1	no	—
36	C₂×C₈	—	1154	1	no	—
37	C₁₆	—	1154	1	no	—
38	C₁₆	—	1154	1	no	—
39	Q₈	—	577	1	no	—
40	D₄	—	577	1	no	—
41	D₄	—	1154	1	no	—
42	C₂×C₄	—	1154	1	no	—
43	C₂×C₄	C₂×#14556313	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	—	577	1	no	—
46	C₈	—	577	1	no	—
47	C₂²	—	1154	1	no	—
48	C₂²	#22604428	1	1	yes	characteristic
49	C₄	—	1154	1	no	—
50	C₄	C₂²⋊#14556313	1	1	yes	characteristic
51	C₄	#22604426	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	2308	1	no	—
54	C₂	#32914721	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#14556313
commutator	C₄×C₅₇₇	C₂×C₈
Frattini	C₂×C₄	C₂×#14556313
Fitting	M₁₆×C₅₇₇	C₄
socle	C₂×C₅₇₇	C₂²⋊C₈
prime radical	#22604418	C₄
cosocle	C₂×#17987230	C₂²
hypercenter	M₁₆	#14556313
hypocenter	C₅₇₇	#350
LCS	G ▷ C₄×C₅₇₇ ▷ C₂×C₅₇₇ ▷ C₅₇₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
1. #32914738	C₂	semidirect
2. C₂×#22604421	C₂	semidirect
27. C₅₇₇	#350	semidirect

Maximal subgroups

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

subgroup	index
#32914738	2
C₂×#22604421	2
#32914672	2
#350	577