Subgroups — #37565026

Order 24256.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27131271	C₂	1	2	yes	maximal, complemented
2	C₂×M₁₆×C₃₇₉	C₂	1	1	yes	maximal, characteristic
3	C₃₇₉⋊C₁₆	—	2	2	no	—
4	C₂²×C₄×C₃₇₉	C₄	1	1	yes	characteristic
5	M₁₆×C₃₇₉	—	2	2	no	—
6	C₂×C₈×C₃₇₉	C₄	1	1	yes	characteristic
7	C₂×C₈×C₃₇₉	C₂²	1	1	yes	characteristic
8	C₂³×C₃₇₉	C₈	1	1	yes	characteristic
9	C₂×C₄×C₃₇₉	—	2	1	no	—
10	C₂×C₄×C₃₇₉	—	2	1	no	—
11	C₂×C₄×C₃₇₉	C₈	1	1	yes	characteristic
12	C₂×C₄×C₃₇₉	C₂×C₄	1	1	yes	characteristic
13	C₈×C₃₇₉	—	2	1	no	—
14	C₈×C₃₇₉	D₄	1	2	yes	—
15	C₂²×C₃₇₉	—	2	1	no	—
16	C₂²×C₃₇₉	—	4	1	no	—
17	C₂²×C₃₇₉	C₂×C₈	1	1	yes	characteristic
18	C₄×C₃₇₉	—	2	1	no	—
19	C₄×C₃₇₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₃₇₉	M₁₆	1	1	yes	characteristic
21	C₂×C₃₇₉	—	2	1	no	—
22	C₂×C₃₇₉	—	4	1	no	—
23	C₂×C₃₇₉	C₂²⋊C₈	1	1	yes	characteristic
24	C₃₇₉	#349	1	1	yes	characteristic, complemented, Sylow
25	#349	—	379	1	no	maximal, Sylow
26	C₂×M₁₆	D₃₇₉	1	1	yes	characteristic
27	M₃₂	—	379	2	no	—
28	C₂²×C₄	Dic₃₇₉	1	1	yes	characteristic
29	M₁₆	—	2	2	no	—
30	C₂×C₈	Dic₃₇₉	1	1	yes	characteristic
31	C₂×C₈	C₂×D₃₇₉	1	1	yes	characteristic
32	C₁₆	—	758	2	no	—
33	C₂³	C₃₇₉⋊C₈	1	1	yes	characteristic
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	C₃₇₉⋊C₈	1	1	yes	characteristic
37	C₂×C₄	C₂×Dic₃₇₉	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	C₂²⋊D₃₇₉	1	2	yes	—
40	C₂²	—	2	1	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂×C₃₇₉⋊C₈	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	C₂²⋊Dic₃₇₉	1	1	yes	characteristic
45	C₄	#20258590	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂²⋊(C₃₇₉⋊C₈)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊Dic₃₇₉
commutator	C₂²×C₃₇₉	C₂×C₈
Frattini	C₂×C₈	C₂×D₃₇₉
Fitting	C₂×M₁₆×C₃₇₉	C₂
socle	C₂×C₃₇₉	C₂²⋊C₈
prime radical	C₂³×C₃₇₉	C₈
cosocle	C₂×C₈×C₃₇₉	C₂²
hypercenter	C₂×M₁₆	D₃₇₉
hypocenter	C₃₇₉	#349
LCS	G ▷ C₂²×C₃₇₉ ▷ C₂×C₃₇₉ ▷ C₃₇₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. #27131271	C₂	semidirect
24. C₃₇₉	#349	semidirect

Maximal subgroups

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

subgroup	index
#27131271	2
C₂×M₁₆×C₃₇₉	2
#349	379