Subgroups — C₂×#32914737 #49149003

Order 36928.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#32914737	C₂	1	4	yes	maximal, direct product factor
2	C₂×#22604421	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×D₅₇₇	C₂	1	1	yes	maximal, characteristic
4	#22604421	C₂²	1	4	yes	complemented
5	C₂×C₄×D₅₇₇	C₄	1	1	yes	characteristic
6	C₂×#17987230	C₂²	1	1	yes	characteristic
7	C₈×D₅₇₇	C₄	1	2	yes	—
8	C₈×D₅₇₇	C₂²	1	2	yes	—
9	C₂×C₈×C₅₇₇	C₄	1	1	yes	characteristic
10	C₂²×D₅₇₇	C₈	1	1	yes	characteristic
11	C₂×Dic₅₇₇	C₈	1	1	yes	characteristic
12	C₄×D₅₇₇	C₈	1	2	yes	—
13	C₄×D₅₇₇	C₂×C₄	1	2	yes	—
14	#17987230	C₂×C₄	1	1	yes	characteristic
15	#17987230	C₂³	1	1	yes	characteristic
16	C₂×C₄×C₅₇₇	C₂×C₄	1	1	yes	characteristic
17	C₈×C₅₇₇	C₂×C₄	1	2	yes	—
18	C₂²×C₅₇₇	C₂×C₈	1	1	yes	characteristic
19	C₂×D₅₇₇	C₁₆	1	4	yes	complemented
20	C₂×D₅₇₇	C₂×C₈	1	2	yes	—
21	C₄×C₅₇₇	C₂×C₈	1	1	yes	characteristic
22	C₄×C₅₇₇	C₂²×C₄	1	1	yes	characteristic
23	Dic₅₇₇	C₂×C₈	1	2	yes	—
24	C₂×C₅₇₇	C₂×C₁₆	1	2	yes	complemented
25	C₂×C₅₇₇	C₂²×C₈	1	1	yes	characteristic
26	D₅₇₇	C₂×C₁₆	1	4	yes	complemented
27	C₅₇₇	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
28	C₂²×C₁₆	—	577	1	no	maximal, Sylow
29	C₂²×C₈	—	577	1	no	—
30	C₂×C₁₆	—	577	2	no	—
31	C₂×C₁₆	—	577	4	no	—
32	C₂²×C₄	—	577	1	no	—
33	C₂×C₈	—	577	1	no	—
34	C₂×C₈	—	577	2	no	—
35	C₂×C₈	—	577	2	no	—
36	C₂×C₈	#14556313	1	1	yes	characteristic
37	C₁₆	—	577	4	no	—
38	C₂³	—	577	1	no	—
39	C₂×C₄	—	577	1	no	—
40	C₂×C₄	—	577	2	no	—
41	C₂×C₄	—	577	2	no	—
42	C₂×C₄	C₂×#14556313	1	1	yes	characteristic
43	C₈	—	577	1	no	—
44	C₈	—	577	1	no	—
45	C₈	C₂×#14556313	1	2	yes	—
46	C₂²	—	577	4	no	—
47	C₂²	—	577	2	no	—
48	C₂²	#22604426	1	1	yes	characteristic
49	C₄	—	577	2	no	—
50	C₄	#22604426	1	1	yes	characteristic
51	C₄	C₂²×#14556313	1	1	yes	characteristic
52	C₂	—	577	4	no	—
53	C₂	#32914737	1	2	yes	direct product factor
54	C₂	C₂×#22604426	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₈	#14556313
commutator, hypocenter	C₅₇₇	C₂²×C₁₆
Frattini	C₄	C₂²×#14556313
Fitting	C₂×C₈×C₅₇₇	C₄
socle	C₂²×C₅₇₇	C₂×C₈
prime radical	C₂²×D₅₇₇	C₈
cosocle	#17987230	C₂³
LCS	G ▷ C₅₇₇
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. #32914737	C₂	direct (N × H)
2. C₂×#22604421	C₂	semidirect
4. #22604421	C₂²	semidirect
19. C₂×D₅₇₇	C₁₆	semidirect
24. C₂×C₅₇₇	C₂×C₁₆	semidirect
26. D₅₇₇	C₂×C₁₆	semidirect
27. C₅₇₇	C₂²×C₁₆	semidirect
53. C₂	#32914737	direct (N × H)

Maximal subgroups

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

subgroup	index
#32914737	2
C₂×#22604421	2
C₂×C₈×D₅₇₇	2
C₂²×C₁₆	577

Subgroups — C2×#32914737 #49149003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#32914737 #49149003