Subgroups — #38734530

Order 24896.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27159407	C₂	1	1	yes	maximal, characteristic, complemented
2	#27159403	C₂	1	1	yes	maximal, characteristic, complemented
3	#27159330	C₂	1	1	yes	maximal, characteristic, complemented
4	#27159329	C₂	1	1	yes	maximal, characteristic, complemented
5	#27159325	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×D₃₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₃₂×C₃₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#20261967	—	2	1	no	—
9	#20261965	—	2	1	no	—
10	Dic₁₅₅₆	C₂²	1	1	yes	characteristic
11	#20261954	—	2	1	no	—
12	#20261953	—	2	1	no	—
13	D₃₁₁₂	C₂²	1	1	yes	characteristic
14	C₈×D₃₈₉	C₂²	1	1	yes	characteristic
15	#20261941	C₂²	1	1	yes	characteristic
16	Q₁₆×C₃₈₉	C₂²	1	1	yes	characteristic
17	D₈×C₃₈₉	C₂²	1	1	yes	characteristic
18	C₁₆×C₃₈₉	C₂²	1	1	yes	characteristic
19	Dic₇₇₈	—	2	1	no	—
20	D₁₅₅₆	—	2	1	no	—
21	D₁₅₅₆	—	4	1	no	—
22	C₂²⋊D₃₈₉	—	4	1	no	—
23	C₂×Dic₃₈₉	—	4	1	no	—
24	C₄×D₃₈₉	—	4	1	no	—
25	C₄×D₃₈₉	D₄	1	1	yes	characteristic
26	#15691005	D₄	1	1	yes	characteristic
27	Q₈×C₃₈₉	—	2	1	no	—
28	D₄×C₃₈₉	—	2	1	no	—
29	C₈×C₃₈₉	C₂³	1	1	yes	characteristic
30	C₂²×C₃₈₉	—	4	1	no	—
31	C₂×D₃₈₉	—	4	1	no	—
32	C₂×D₃₈₉	D₈	1	1	yes	characteristic
33	C₄×C₃₈₉	—	4	1	no	—
34	C₄×C₃₈₉	C₂×D₄	1	1	yes	characteristic
35	Dic₃₈₉	—	4	1	no	—
36	Dic₃₈₉	D₈	1	1	yes	characteristic
37	C₂×C₃₈₉	—	8	1	no	—
38	C₂×C₃₈₉	C₂×D₈	1	1	yes	characteristic
39	D₃₈₉	—	2	1	no	—
40	D₃₈₉	—	8	1	no	—
41	C₃₈₉	#508	1	1	yes	characteristic, complemented, Sylow
42	#508	—	389	1	no	maximal, Sylow
43	#135	—	389	1	no	—
44	#135	—	389	1	no	—
45	Q₃₂	—	389	1	no	—
46	SD₃₂	—	389	1	no	—
47	SD₃₂	D₃₈₉	1	1	yes	characteristic, complemented
48	D₁₆	—	389	1	no	—
49	C₂×C₁₆	—	389	1	no	—
50	#41	—	778	1	no	—
51	#41	—	778	1	no	—
52	Q₁₆	—	389	1	no	—
53	Q₁₆	C₂×D₃₈₉	1	1	yes	characteristic
54	SD₁₆	—	778	1	no	—
55	SD₁₆	—	778	1	no	—
56	D₈	—	389	1	no	—
57	D₈	C₂×D₃₈₉	1	1	yes	characteristic
58	C₂×C₈	—	389	1	no	—
59	C₁₆	—	389	1	no	—
60	C₁₆	C₂×D₃₈₉	1	1	yes	characteristic
61	Q₈	—	2	1	no	—
62	Q₈	—	778	1	no	—
63	D₄	—	2	1	no	—
64	D₄	—	778	1	no	—
65	D₄	—	1556	1	no	—
66	D₄	—	1556	1	no	—
67	C₂×C₄	—	1556	1	no	—
68	C₂×C₄	—	1556	1	no	—
69	C₂×C₄	—	389	1	no	—
70	C₈	—	389	1	no	—
71	C₈	C₂²×D₃₈₉	1	1	yes	characteristic
72	C₂²	—	4	1	no	—
73	C₂²	—	1556	1	no	—
74	C₂²	—	389	1	no	—
75	C₄	—	4	1	no	—
76	C₄	—	1556	1	no	—
77	C₄	—	389	1	no	—
78	C₄	D₄×D₃₈₉	1	1	yes	characteristic
79	C₂	—	8	1	no	—
80	C₂	—	778	1	no	—
81	C₂	—	3112	1	no	—
82	C₂	D₈×D₃₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₃₈₉
commutator, cosocle	C₈×C₃₈₉	C₂³
Frattini	C₈	C₂²×D₃₈₉
Fitting	SD₃₂×C₃₈₉	C₂
socle	C₂×C₃₈₉	C₂×D₈
hypercenter	SD₃₂	D₃₈₉
hypocenter	C₃₈₉	#508
LCS	G ▷ C₈×C₃₈₉ ▷ C₄×C₃₈₉ ▷ C₂×C₃₈₉ ▷ C₃₈₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ SD₃₂

Complements

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

N	H ≅ G/N	type
1. #27159407	C₂	semidirect
2. #27159403	C₂	semidirect
3. #27159330	C₂	semidirect
4. #27159329	C₂	semidirect
5. #27159325	C₂	semidirect
6. C₁₆×D₃₈₉	C₂	semidirect
7. SD₃₂×C₃₈₉	C₂	semidirect
41. C₃₈₉	#508	semidirect
47. SD₃₂	D₃₈₉	semidirect

Maximal subgroups

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

subgroup	index
#27159407	2
#27159403	2
#27159330	2
#27159329	2
#27159325	2
C₁₆×D₃₈₉	2
SD₃₂×C₃₈₉	2
#508	389