Subgroups — #37588754

Order 24512.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27133841	C₂	1	1	yes	maximal, characteristic
2	#27133774	C₂	1	4	yes	maximal
3	C₄×C₃₈₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Q₈×C₃₈₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₇₆₆	—	2	1	no	—
6	C₂×C₃₈₃⋊C₈	C₂²	1	2	yes	—
7	C₄⋊Dic₃₈₃	—	2	1	no	—
8	C₄⋊Dic₃₈₃	C₂²	1	2	yes	—
9	C₂×Q₈×C₃₈₃	—	2	1	no	—
10	C₄⋊C₄×C₃₈₃	—	2	1	no	—
11	C₄⋊C₄×C₃₈₃	C₂²	1	2	yes	—
12	C₄²×C₃₈₃	C₂²	1	1	yes	characteristic
13	Dic₇₆₆	—	4	2	no	—
14	C₂×Dic₃₈₃	—	2	2	no	—
15	C₃₈₃⋊C₈	Q₈	1	4	yes	complemented
16	Q₈×C₃₈₃	—	4	2	no	—
17	C₂×C₄×C₃₈₃	—	2	2	no	—
18	C₂×C₄×C₃₈₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₃₈₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₃₈₃	C₂³	1	1	yes	characteristic
21	C₂²×C₃₈₃	C₂×D₄	1	1	yes	characteristic
22	C₄×C₃₈₃	—	4	2	no	—
23	C₄×C₃₈₃	D₈	1	2	yes	—
24	C₄×C₃₈₃	Q₁₆	1	2	yes	—
25	C₄×C₃₈₃	C₂×Q₈	1	2	yes	—
26	Dic₃₈₃	—	4	2	no	—
27	C₂×C₃₈₃	C₄⋊Q₈	1	1	yes	characteristic
28	C₂×C₃₈₃	C₂×D₈	1	1	yes	characteristic
29	C₂×C₃₈₃	C₂×Q₁₆	1	1	yes	characteristic
30	C₃₈₃	#500	1	1	yes	characteristic, complemented, Sylow
31	#500	—	383	1	no	maximal, Sylow
32	C₄⋊Q₈	—	383	1	no	—
33	C₄⋊Q₈	D₃₈₃	1	1	yes	characteristic
34	#107	—	383	4	no	—
35	C₄×C₈	—	383	1	no	—
36	C₂×Q₈	—	2	1	no	—
37	C₂×Q₈	—	766	1	no	—
38	C₂×C₈	—	383	2	no	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	383	2	no	—
41	C₄⋊C₄	—	766	1	no	—
42	C₄⋊C₄	C₂×D₃₈₃	1	2	yes	—
43	C₄²	C₂×D₃₈₃	1	1	yes	characteristic
44	Q₈	—	4	2	no	—
45	Q₈	—	1532	2	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	766	2	no	—
48	C₂×C₄	C₂²⋊D₃₈₃	1	1	yes	characteristic
49	C₂×C₄	C₂²⋊D₃₈₃	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₃₈₃	1	1	yes	characteristic
51	C₈	—	383	4	no	—
52	C₂²	C₂×C₂²⋊D₃₈₃	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	1532	2	no	—
55	C₄	#20259442	1	2	yes	—
56	C₄	#20259447	1	2	yes	—
57	C₄	Q₈×D₃₈₃	1	2	yes	—
58	C₂	#27133839	1	1	yes	characteristic
59	C₂	C₂×#20259442	1	1	yes	characteristic
60	C₂	C₂×#20259447	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₈₃
commutator, cosocle	C₂×C₄×C₃₈₃	C₂³
Frattini	C₂×C₄	C₂²×D₃₈₃
Fitting	C₄⋊Q₈×C₃₈₃	C₂
socle, prime radical	C₂²×C₃₈₃	C₂×D₄
hypercenter	C₄⋊Q₈	D₃₈₃
hypocenter	C₃₈₃	#500
LCS	G ▷ C₂×C₄×C₃₈₃ ▷ C₂×C₃₈₃ ▷ C₃₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
15. C₃₈₃⋊C₈	Q₈	semidirect
30. C₃₈₃	#500	semidirect

Maximal subgroups

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

subgroup	index
#27133841	2
#27133774	2
C₄×C₃₈₃⋊C₈	2
C₄⋊Q₈×C₃₈₃	2
#500	383