Subgroups — #49148862

Order 36928.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#32914737	C₂	1	1	yes	maximal, characteristic
2	#32914733	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×D₅₇₇	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#14556313	—	2	1	no	—
5	#22604421	—	2	1	no	—
6	Q₈×D₅₇₇	—	2	1	no	—
7	Dic₂₃₀₈	C₄	1	1	yes	characteristic, complemented
8	#22604408	—	2	1	no	—
9	C₈×D₅₇₇	C₂²	1	1	yes	characteristic
10	Q₁₆×C₅₇₇	C₄	1	1	yes	characteristic, complemented
11	C₂×#14556313	—	4	1	no	—
12	Dic₁₁₅₄	—	2	1	no	—
13	Dic₁₁₅₄	—	4	1	no	—
14	C₄×D₅₇₇	—	4	1	no	—
15	C₄×D₅₇₇	D₄	1	1	yes	characteristic
16	#17987230	D₄	1	1	yes	characteristic
17	Q₈×C₅₇₇	—	2	1	no	—
18	C₈×C₅₇₇	C₂×C₄	1	1	yes	characteristic
19	C₂×D₅₇₇	D₈	1	1	yes	characteristic
20	#14556313	—	8	1	no	—
21	C₄×C₅₇₇	—	4	1	no	—
22	C₄×C₅₇₇	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₅₇₇	—	4	1	no	—
24	Dic₅₇₇	SD₁₆	1	1	yes	characteristic
25	C₂×C₅₇₇	#102	1	1	yes	characteristic
26	D₅₇₇	SD₃₂	1	1	yes	characteristic
27	D₅₇₇	Q₃₂	1	1	yes	characteristic
28	C₅₇₇	#358	1	1	yes	characteristic, complemented, Sylow
29	#358	—	577	1	no	maximal, Sylow
30	C₂×Q₁₆	—	577	1	no	—
31	C₂×C₁₆	—	577	1	no	—
32	#107	—	577	1	no	—
33	C₂×Q₈	—	1154	1	no	—
34	Q₁₆	—	577	1	no	—
35	Q₁₆	—	1154	1	no	—
36	Q₁₆	#14556313	1	1	yes	characteristic, complemented
37	C₂×C₈	—	577	1	no	—
38	C₄⋊C₄	—	1154	1	no	—
39	C₁₆	—	1154	1	no	—
40	Q₈	—	2	1	no	—
41	Q₈	—	2308	1	no	—
42	Q₈	—	1154	1	no	—
43	C₂×C₄	—	2308	1	no	—
44	C₂×C₄	—	2308	1	no	—
45	C₂×C₄	—	577	1	no	—
46	C₈	—	577	1	no	—
47	C₈	C₂×#14556313	1	1	yes	characteristic
48	C₂²	—	577	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	2308	1	no	—
51	C₄	—	4616	1	no	—
52	C₄	—	577	1	no	—
53	C₄	C₂²⋊#14556313	1	1	yes	characteristic
54	C₂	—	577	1	no	—
55	C₂	—	577	1	no	—
56	C₂	#32914726	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#32914726
commutator	C₈×C₅₇₇	C₂×C₄
Frattini	C₈	C₂×#14556313
Fitting	Q₁₆×C₅₇₇	C₄
socle	C₂×C₅₇₇	#102
prime radical	C₂×D₅₇₇	D₈
cosocle	C₈×D₅₇₇	C₂²
hypercenter	Q₁₆	#14556313
hypocenter	C₅₇₇	#358
LCS	G ▷ C₈×C₅₇₇ ▷ C₄×C₅₇₇ ▷ C₂×C₅₇₇ ▷ C₅₇₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
7. Dic₂₃₀₈	C₄	semidirect
10. Q₁₆×C₅₇₇	C₄	semidirect
28. C₅₇₇	#358	semidirect
36. Q₁₆	#14556313	semidirect

Maximal subgroups

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

subgroup	index
#32914737	2
#32914733	2
Q₁₆×D₅₇₇	2
#358	577