Subgroups — #37588389

Order 24512.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27133800	C₂	1	2	yes	maximal
2	#27133775	C₂	1	2	yes	maximal, complemented
3	#27133773	C₂	1	2	yes	maximal, complemented
4	C₂²×C₈×C₃₈₃	C₂	1	1	yes	maximal, characteristic
5	C₄⋊Dic₃₈₃	C₂²	1	4	yes	—
6	C₂²⋊Dic₃₈₃	—	2	2	no	—
7	C₄×Dic₃₈₃	—	2	2	no	—
8	C₂²×C₄×C₃₈₃	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₃₈₃	C₄	1	4	yes	complemented
10	C₂×C₈×C₃₈₃	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₃₈₃	C₂²	1	1	yes	characteristic
12	C₂×Dic₃₈₃	—	2	4	no	—
13	C₂³×C₃₈₃	D₄	1	1	yes	characteristic
14	C₂×C₄×C₃₈₃	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₃₈₃	D₄	1	1	yes	characteristic
16	C₂×C₄×C₃₈₃	Q₈	1	2	yes	—
17	C₂×C₄×C₃₈₃	C₂³	1	1	yes	characteristic
18	C₈×C₃₈₃	C₂×C₄	1	2	yes	—
19	C₈×C₃₈₃	C₂×C₄	1	2	yes	—
20	C₂²×C₃₈₃	—	2	2	no	—
21	C₂²×C₃₈₃	C₄⋊C₄	1	2	yes	—
22	C₂²×C₃₈₃	C₂×D₄	1	1	yes	characteristic
23	C₄×C₃₈₃	C₄⋊C₄	1	2	yes	—
24	C₄×C₃₈₃	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₃₈₃	C₂×Q₈	1	1	yes	characteristic
26	Dic₃₈₃	—	4	4	no	—
27	C₂×C₃₈₃	—	2	2	no	—
28	C₂×C₃₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₃₈₃	#135	1	2	yes	—
30	C₃₈₃	#427	1	1	yes	characteristic, complemented, Sylow
31	#427	—	383	1	no	maximal, Sylow
32	C₂²×C₈	D₃₈₃	1	1	yes	characteristic
33	#117	—	383	2	no	—
34	#107	—	383	2	no	—
35	#106	—	383	2	no	—
36	C₂²×C₄	C₂×D₃₈₃	1	1	yes	characteristic
37	C₂×C₈	Dic₃₈₃	1	4	yes	complemented
38	C₂×C₈	C₂×D₃₈₃	1	1	yes	characteristic
39	C₂×C₈	C₂×D₃₈₃	1	1	yes	characteristic
40	C₄⋊C₄	—	383	4	no	—
41	C₂²⋊C₄	—	766	2	no	—
42	C₄²	—	766	2	no	—
43	C₂³	D₁₅₃₂	1	1	yes	characteristic
44	C₂×C₄	—	766	4	no	—
45	C₂×C₄	C₂×Dic₃₈₃	1	2	yes	—
46	C₂×C₄	D₁₅₃₂	1	1	yes	characteristic
47	C₂×C₄	Dic₇₆₆	1	2	yes	—
48	C₂×C₄	C₂²×D₃₈₃	1	1	yes	characteristic
49	C₈	C₂×Dic₃₈₃	1	2	yes	—
50	C₈	C₂×Dic₃₈₃	1	2	yes	—
51	C₂²	—	2	2	no	—
52	C₂²	C₄⋊Dic₃₈₃	1	2	yes	—
53	C₂²	C₂×D₁₅₃₂	1	1	yes	characteristic
54	C₄	—	1532	4	no	—
55	C₄	C₄⋊Dic₃₈₃	1	2	yes	—
56	C₄	C₂²×Dic₃₈₃	1	1	yes	characteristic
57	C₄	C₂×Dic₇₆₆	1	1	yes	characteristic
58	C₂	—	2	2	no	—
59	C₂	C₂×C₄⋊Dic₃₈₃	1	1	yes	characteristic
60	C₂	#27133863	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₁₅₃₂
commutator	C₄×C₃₈₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₈₃
Fitting	C₂²×C₈×C₃₈₃	C₂
socle	C₂²×C₃₈₃	C₂×D₄
prime radical	C₂³×C₃₈₃	D₄
cosocle	C₂×C₄×C₃₈₃	C₂³
hypercenter	C₂²×C₈	D₃₈₃
hypocenter	C₃₈₃	#427
LCS	G ▷ C₄×C₃₈₃ ▷ C₂×C₃₈₃ ▷ C₃₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #27133775	C₂	semidirect
3. #27133773	C₂	semidirect
9. C₂×C₈×C₃₈₃	C₄	semidirect
30. C₃₈₃	#427	semidirect
37. C₂×C₈	Dic₃₈₃	semidirect

Maximal subgroups

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

subgroup	index
#27133800	2
#27133775	2
#27133773	2
C₂²×C₈×C₃₈₃	2
#427	383