Subgroups — #37588479

Order 24512.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₇₆₆	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₃₈₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	Dic₃₈₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	Dic₃₈₃⋊C₈	C₂	1	1	yes	maximal, characteristic
5	#27133751	C₂	1	1	yes	maximal, characteristic
6	C₈×Dic₃₈₃	C₂	1	1	yes	maximal, characteristic
7	#97×C₃₈₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₇₆₆	C₄	1	1	yes	characteristic
9	C₂×C₃₈₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₃₈₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₃₈₃	C₄	1	1	yes	characteristic
12	Dic₃₈₃⋊C₄	C₄	1	1	yes	characteristic
13	Dic₃₈₃⋊C₄	C₄	1	1	yes	characteristic
14	C₄×Dic₃₈₃	C₂²	1	1	yes	characteristic
15	C₄×Dic₃₈₃	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₃₈₃	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₃₈₃	C₂²	1	1	yes	characteristic
18	C₄²×C₃₈₃	C₂²	1	1	yes	characteristic
19	Dic₇₆₆	—	2	2	no	—
20	C₂×Dic₃₈₃	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₃₈₃	C₂×C₄	1	1	yes	characteristic
22	C₂×Dic₃₈₃	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₃₈₃	C₂×C₄	1	1	yes	characteristic
24	C₃₈₃⋊C₈	—	2	1	no	—
25	C₃₈₃⋊C₈	—	2	1	no	—
26	C₂×C₄×C₃₈₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×C₃₈₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×C₃₈₃	C₂³	1	1	yes	characteristic
29	C₈×C₃₈₃	—	2	1	no	—
30	C₈×C₃₈₃	Q₈	1	2	yes	complemented
31	C₂²×C₃₈₃	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₃₈₃	—	2	1	no	—
33	C₄×C₃₈₃	—	2	1	no	—
34	C₄×C₃₈₃	C₂×Q₈	1	1	yes	characteristic
35	C₄×C₃₈₃	#41	1	1	yes	characteristic
36	Dic₃₈₃	—	2	1	no	—
37	Dic₃₈₃	—	2	1	no	—
38	Dic₃₈₃	—	2	1	no	—
39	Dic₃₈₃	M₁₆	1	2	yes	—
40	C₂×C₃₈₃	C₄×Q₈	1	1	yes	characteristic
41	C₂×C₃₈₃	C₂×M₁₆	1	1	yes	characteristic
42	C₂×C₃₈₃	#131	1	1	yes	characteristic
43	C₃₈₃	#446	1	1	yes	characteristic, complemented, Sylow
44	#446	—	383	1	no	maximal, Sylow
45	C₄×Q₈	—	383	1	no	—
46	C₄⋊C₈	—	383	1	no	—
47	C₄⋊C₈	—	383	1	no	—
48	C₄⋊C₈	—	383	1	no	—
49	#97	—	383	1	no	—
50	#97	D₃₈₃	1	1	yes	characteristic
51	C₄×C₈	—	383	1	no	—
52	C₂×Q₈	—	383	1	no	—
53	C₂×C₈	—	383	1	no	—
54	C₂×C₈	—	383	1	no	—
55	C₂×C₈	C₂×D₃₈₃	1	1	yes	characteristic
56	C₂×C₈	C₂×D₃₈₃	1	1	yes	characteristic
57	C₄⋊C₄	—	383	1	no	—
58	C₄⋊C₄	—	383	1	no	—
59	C₄⋊C₄	—	383	1	no	—
60	C₄²	—	383	1	no	—
61	C₄²	—	383	1	no	—
62	C₄²	C₂×D₃₈₃	1	1	yes	characteristic
63	Q₈	—	766	2	no	—
64	C₂×C₄	—	383	1	no	—
65	C₂×C₄	—	383	1	no	—
66	C₂×C₄	—	383	1	no	—
67	C₂×C₄	—	383	1	no	—
68	C₂×C₄	C₄×D₃₈₃	1	1	yes	characteristic
69	C₂×C₄	C₄×D₃₈₃	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₃₈₃	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	—	766	1	no	—
73	C₈	—	766	1	no	—
74	C₈	Dic₇₆₆	1	2	yes	complemented
75	C₂²	C₂×C₄×D₃₈₃	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	2	1	no	—
78	C₄	—	383	2	no	—
79	C₄	—	766	1	no	—
80	C₄	—	766	1	no	—
81	C₄	—	766	1	no	—
82	C₄	C₂×Dic₇₆₆	1	1	yes	characteristic
83	C₄	#20259457	1	1	yes	characteristic
84	C₂	C₄×Dic₇₆₆	1	1	yes	characteristic
85	C₂	M₁₆×D₃₈₃	1	1	yes	characteristic
86	C₂	#27133849	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃₈₃
commutator, socle, prime radical	C₂²×C₃₈₃	C₂²×C₄
Fitting	#97×C₃₈₃	C₂
cosocle	C₂×C₄×C₃₈₃	C₂³
hypercenter	#97	D₃₈₃
hypocenter	C₃₈₃	#446
LCS	G ▷ C₂²×C₃₈₃ ▷ C₃₈₃
UCS	C₁ ◁ C₂×C₄ ◁ #97

Complements

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

N	H ≅ G/N	type
30. C₈×C₃₈₃	Q₈	semidirect
43. C₃₈₃	#446	semidirect
74. C₈	Dic₇₆₆	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₇₆₆	2
C₄⋊(C₃₈₃⋊C₈)	2
Dic₃₈₃⋊C₈	2
#27133751	2
C₈×Dic₃₈₃	2
#97×C₃₈₃	2
#446	383