Subgroups — #49148995

Order 36928.

104 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	#32914734	C₂	1	1	yes	maximal, characteristic, complemented
3	#32914729	C₂	1	2	yes	maximal, complemented
4	#32914718	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	2	yes	—
19	D₂₃₀₈	—	2	2	no	—
20	D₂₃₀₈	C₂×C₄	1	2	yes	—
21	C₄×D₅₇₇	—	2	2	no	—
22	C₄×D₅₇₇	C₂³	1	1	yes	characteristic
23	#17987230	C₂×C₄	1	1	yes	characteristic
24	Q₈×C₅₇₇	C₂×C₄	1	2	yes	—
25	C₈×C₅₇₇	C₂×C₄	1	1	yes	characteristic
26	C₂×D₅₇₇	—	2	2	no	—
27	C₂×D₅₇₇	#41	1	1	yes	characteristic
28	#14556313	—	4	1	no	—
29	C₄×C₅₇₇	—	2	2	no	—
30	C₄×C₅₇₇	C₂²×C₄	1	1	yes	characteristic
31	Dic₅₇₇	C₂×D₄	1	1	yes	characteristic
32	C₂×C₅₇₇	C₄×D₄	1	1	yes	characteristic
33	D₅₇₇	—	2	1	no	—
34	D₅₇₇	—	4	2	no	—
35	C₅₇₇	#444	1	1	yes	characteristic, complemented, Sylow
36	#444	—	577	1	no	maximal, Sylow
37	#135	—	577	1	no	—
38	#131	—	577	2	no	—
39	#108	—	577	1	no	—
40	#104	—	577	2	no	—
41	#97	—	577	1	no	—
42	#41	—	577	2	no	—
43	Q₁₆	#14556313	1	1	yes	characteristic, complemented
44	SD₁₆	—	577	2	no	—
45	D₈	—	577	1	no	—
46	M₁₆	—	577	2	no	—
47	M₁₆	—	1154	2	no	—
48	C₂×C₈	—	577	1	no	—
49	C₂×C₈	—	577	1	no	—
50	C₂×C₈	—	1154	2	no	—
51	C₄²	—	577	1	no	—
52	Q₈	C₂×#14556313	1	2	yes	—
53	D₄	—	577	2	no	—
54	D₄	—	1154	2	no	—
55	C₂×C₄	—	577	1	no	—
56	C₂×C₄	—	1154	2	no	—
57	C₂×C₄	—	1154	1	no	—
58	C₈	—	577	2	no	—
59	C₈	—	577	1	no	—
60	C₈	—	1154	2	no	—
61	C₈	C₂×#14556313	1	1	yes	characteristic
62	C₂²	—	577	1	no	—
63	C₂²	—	1154	2	no	—
64	C₄	—	2	2	no	—
65	C₄	—	2308	1	no	—
66	C₄	—	577	1	no	—
67	C₄	C₂²×#14556313	1	1	yes	characteristic
68	C₂	—	2308	2	no	—
69	C₂	—	1154	1	no	—
70	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	#444
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. #32914734	C₂	semidirect
3. #32914729	C₂	semidirect
4. #32914718	C₂	semidirect
12. #22604405	C₄	semidirect
13. D₄₆₁₆	C₄	semidirect
15. Q₁₆×C₅₇₇	C₄	semidirect
35. C₅₇₇	#444	semidirect
43. 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
#32914734	2
#32914729	2
#32914718	2
#32914687	2
#444	577