Subgroups — #37588748

Order 24512.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27133840	C₂	1	2	yes	maximal
2	#27133773	C₂	1	1	yes	maximal, characteristic
3	#27133772	C₂	1	2	yes	maximal
4	C₈×Dic₃₈₃	C₂	1	1	yes	maximal, characteristic
5	#106×C₃₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₇₆₆	—	2	2	no	—
7	C₂×C₃₈₃⋊C₈	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₃₈₃	C₂²	1	2	yes	—
9	Dic₃₈₃⋊C₄	—	2	2	no	—
10	C₄×Dic₃₈₃	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₃₈₃	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₃₈₃	C₂²	1	2	yes	—
13	Dic₇₆₆	—	4	4	no	—
14	C₂×Dic₃₈₃	—	2	2	no	—
15	C₂×Dic₃₈₃	D₄	1	2	yes	—
16	C₃₈₃⋊C₈	Q₈	1	2	yes	complemented
17	C₂×C₄×C₃₈₃	—	2	2	no	—
18	C₂×C₄×C₃₈₃	C₂³	1	1	yes	characteristic
19	C₈×C₃₈₃	Q₈	1	2	yes	complemented
20	C₂²×C₃₈₃	C₂×D₄	1	1	yes	characteristic
21	C₄×C₃₈₃	—	4	2	no	—
22	C₄×C₃₈₃	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₃₈₃	C₂×Q₈	1	1	yes	characteristic
24	Dic₃₈₃	—	4	2	no	—
25	Dic₃₈₃	SD₁₆	1	4	yes	—
26	C₂×C₃₈₃	C₄⋊Q₈	1	1	yes	characteristic
27	C₂×C₃₈₃	C₂×SD₁₆	1	2	yes	—
28	C₃₈₃	#498	1	1	yes	characteristic, complemented, Sylow
29	#498	—	383	1	no	maximal, Sylow
30	C₄⋊Q₈	—	383	2	no	—
31	#106	—	383	1	no	—
32	#106	—	383	2	no	—
33	#106	D₃₈₃	1	1	yes	characteristic
34	C₄×C₈	—	383	1	no	—
35	C₂×Q₈	—	766	2	no	—
36	C₂×C₈	—	383	1	no	—
37	C₂×C₈	C₂×D₃₈₃	1	1	yes	characteristic
38	C₄⋊C₄	—	383	2	no	—
39	C₄⋊C₄	—	766	2	no	—
40	C₄⋊C₄	C₂×D₃₈₃	1	2	yes	—
41	C₄²	—	383	1	no	—
42	Q₈	—	1532	4	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	—	383	2	no	—
45	C₂×C₄	—	766	2	no	—
46	C₂×C₄	C₂²×D₃₈₃	1	1	yes	characteristic
47	C₈	—	383	2	no	—
48	C₈	Dic₇₆₆	1	2	yes	complemented
49	C₂²	D₄×D₃₈₃	1	1	yes	characteristic
50	C₄	—	4	2	no	—
51	C₄	—	383	4	no	—
52	C₄	—	1532	2	no	—
53	C₄	Q₈×D₃₈₃	1	1	yes	characteristic
54	C₄	C₂×Dic₇₆₆	1	1	yes	characteristic
55	C₂	#27133840	1	1	yes	characteristic
56	C₂	SD₁₆×D₃₈₃	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₃₈₃
commutator, cosocle	C₂×C₄×C₃₈₃	C₂³
Frattini	C₂×C₄	C₂²×D₃₈₃
Fitting	#106×C₃₈₃	C₂
socle, prime radical	C₂²×C₃₈₃	C₂×D₄
hypercenter	#106	D₃₈₃
hypocenter	C₃₈₃	#498
LCS	G ▷ C₂×C₄×C₃₈₃ ▷ C₂×C₃₈₃ ▷ C₃₈₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
16. C₃₈₃⋊C₈	Q₈	semidirect
19. C₈×C₃₈₃	Q₈	semidirect
28. C₃₈₃	#498	semidirect
48. C₈	Dic₇₆₆	semidirect

Maximal subgroups

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

subgroup	index
#27133840	2
#27133773	2
#27133772	2
C₈×Dic₃₈₃	2
#106×C₃₈₃	2
#498	383