Subgroups — #49148993

Order 36928.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#32914752	C₂	1	2	yes	maximal, complemented
2	#32914735	C₂	1	1	yes	maximal, characteristic, complemented
3	#32914729	C₂	1	2	yes	maximal, complemented
4	C₈×#14556313	C₂	1	1	yes	maximal, characteristic, complemented
5	#32914687	C₂	1	1	yes	maximal, characteristic
6	#22604428	—	2	2	no	—
7	#22604428	C₂²	1	2	yes	—
8	#22604426	—	2	2	no	—
9	#22604426	C₂²	1	1	yes	characteristic
10	C₄×#14556313	C₂²	1	1	yes	characteristic
11	#22604419	C₂²	1	2	yes	—
12	#22604405	C₄	1	2	yes	complemented
13	D₄₆₁₆	C₄	1	1	yes	characteristic, complemented
14	C₈×D₅₇₇	C₂²	1	1	yes	characteristic
15	Q₁₆×C₅₇₇	C₄	1	1	yes	characteristic, complemented
16	C₂×#14556313	—	2	1	no	—
17	#17987237	—	2	2	no	—
18	#17987237	D₄	1	1	yes	characteristic
19	#17987237	D₄	1	1	yes	characteristic
20	D₂₃₀₈	—	2	2	no	—
21	D₂₃₀₈	C₂×C₄	1	2	yes	—
22	C₄×D₅₇₇	—	2	2	no	—
23	C₄×D₅₇₇	C₂³	1	1	yes	characteristic
24	#17987230	C₂×C₄	1	1	yes	characteristic
25	Q₈×C₅₇₇	C₂×C₄	1	2	yes	—
26	C₈×C₅₇₇	C₂×C₄	1	1	yes	characteristic
27	C₂×D₅₇₇	—	2	2	no	—
28	C₂×D₅₇₇	#41	1	1	yes	characteristic
29	#14556313	—	2	2	no	—
30	C₄×C₅₇₇	—	2	2	no	—
31	C₄×C₅₇₇	C₂²×C₄	1	1	yes	characteristic
32	Dic₅₇₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₅₇₇	C₄×D₄	1	1	yes	characteristic
34	D₅₇₇	—	2	1	no	—
35	D₅₇₇	—	4	2	no	—
36	C₅₇₇	#443	1	1	yes	characteristic, complemented, Sylow
37	#443	—	577	1	no	maximal, Sylow
38	#135	—	577	1	no	—
39	#131	—	577	2	no	—
40	#108	—	577	1	no	—
41	#104	—	577	2	no	—
42	C₄×C₈	—	577	1	no	—
43	#41	—	577	2	no	—
44	Q₁₆	#14556313	1	1	yes	characteristic, complemented
45	SD₁₆	—	577	2	no	—
46	D₈	—	577	1	no	—
47	M₁₆	—	577	2	no	—
48	M₁₆	—	1154	2	no	—
49	C₂×C₈	—	577	1	no	—
50	C₂×C₈	—	577	1	no	—
51	C₂×C₈	—	1154	2	no	—
52	C₄²	—	577	1	no	—
53	Q₈	C₂×#14556313	1	2	yes	—
54	D₄	—	577	2	no	—
55	D₄	—	1154	2	no	—
56	C₂×C₄	—	577	1	no	—
57	C₂×C₄	—	1154	2	no	—
58	C₂×C₄	—	1154	1	no	—
59	C₈	—	577	1	no	—
60	C₈	—	577	1	no	—
61	C₈	—	577	1	no	—
62	C₈	—	1154	2	no	—
63	C₈	C₂×#14556313	1	1	yes	characteristic
64	C₂²	—	577	1	no	—
65	C₂²	—	1154	2	no	—
66	C₄	—	2	2	no	—
67	C₄	—	577	1	no	—
68	C₄	—	1154	2	no	—
69	C₄	C₂²×#14556313	1	1	yes	characteristic
70	C₂	—	2308	2	no	—
71	C₂	—	1154	1	no	—
72	C₂	D₄×#14556313	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#14556313
commutator	C₄×C₅₇₇	C₂²×C₄
Frattini	C₄	C₂²×#14556313
Fitting	Q₁₆×C₅₇₇	C₄
socle	C₂×C₅₇₇	C₄×D₄
prime radical	#32914687	C₂
cosocle	C₄×D₅₇₇	C₂³
hypercenter	Q₁₆	#14556313
hypocenter	C₅₇₇	#443
LCS	G ▷ C₄×C₅₇₇ ▷ C₂×C₅₇₇ ▷ C₅₇₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #32914752	C₂	semidirect
2. #32914735	C₂	semidirect
3. #32914729	C₂	semidirect
4. C₈×#14556313	C₂	semidirect
12. #22604405	C₄	semidirect
13. D₄₆₁₆	C₄	semidirect
15. Q₁₆×C₅₇₇	C₄	semidirect
36. C₅₇₇	#443	semidirect
44. Q₁₆	#14556313	semidirect

Maximal subgroups

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

subgroup	index
#32914752	2
#32914735	2
#32914729	2
C₈×#14556313	2
#32914687	2
#443	577