Subgroups — #37588178

Order 24512.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₈₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#27133775	C₂	1	1	yes	maximal, characteristic
3	#107×C₃₈₃	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₃₈₃	—	2	1	no	—
5	C₃₈₃⋊C₁₆	C₄	1	2	yes	complemented
6	C₂×C₈×C₃₈₃	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₃₈₃	—	2	1	no	—
8	C₂×Dic₃₈₃	—	4	1	no	—
9	C₂×C₄×C₃₈₃	—	4	1	no	—
10	C₂×C₄×C₃₈₃	D₄	1	1	yes	characteristic
11	C₈×C₃₈₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₈₃	Q₈	1	1	yes	characteristic
13	C₂²×C₃₈₃	D₈	1	1	yes	characteristic
14	C₄×C₃₈₃	—	8	1	no	—
15	C₄×C₃₈₃	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₃₈₃	Q₁₆	1	1	yes	characteristic
17	Dic₃₈₃	—	8	1	no	—
18	C₂×C₃₈₃	#107	1	1	yes	characteristic
19	C₂×C₃₈₃	SD₃₂	1	1	yes	characteristic
20	C₂×C₃₈₃	SD₃₂	1	1	yes	characteristic
21	C₃₈₃	#367	1	1	yes	characteristic, complemented, Sylow
22	#367	—	383	1	no	maximal, Sylow
23	C₂×C₁₆	—	383	1	no	—
24	#107	—	383	1	no	—
25	#107	D₃₈₃	1	1	yes	characteristic
26	C₂×C₈	C₂×D₃₈₃	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	766	1	no	—
29	C₁₆	—	383	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	1532	1	no	—
32	C₂×C₄	C₂²⋊D₃₈₃	1	1	yes	characteristic
33	C₈	C₄×D₃₈₃	1	1	yes	characteristic
34	C₈	Dic₇₆₆	1	1	yes	characteristic
35	C₂²	#20259442	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	3064	1	no	—
38	C₄	Dic₃₈₃⋊C₄	1	1	yes	characteristic
39	C₄	#20259447	1	1	yes	characteristic
40	C₂	#27133774	1	1	yes	characteristic
41	C₂	#27133784	1	1	yes	characteristic
42	C₂	#27133785	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#20259442
commutator	C₈×C₃₈₃	C₂×C₄
Frattini	C₂×C₈	C₂×D₃₈₃
Fitting	#107×C₃₈₃	C₂
socle, prime radical	C₂²×C₃₈₃	D₈
cosocle	C₂×C₈×C₃₈₃	C₂²
hypercenter	#107	D₃₈₃
hypocenter	C₃₈₃	#367
LCS	G ▷ C₈×C₃₈₃ ▷ C₄×C₃₈₃ ▷ C₂×C₃₈₃ ▷ C₃₈₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
5. C₃₈₃⋊C₁₆	C₄	semidirect
21. C₃₈₃	#367	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₈₃⋊C₁₆	2
#27133775	2
#107×C₃₈₃	2
#367	383