Subgroups — #37565059

Order 24256.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₅₁₆	C₂	1	1	yes	maximal, characteristic
2	#27131271	C₂	1	1	yes	maximal, characteristic
3	#108×C₃₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₅₈	—	2	1	no	—
5	Dic₁₅₁₆	—	2	1	no	—
6	Dic₁₅₁₆	C₄	1	2	yes	—
7	C₃₇₉⋊C₁₆	—	2	1	no	—
8	M₁₆×C₃₇₉	—	2	1	no	—
9	C₂×C₈×C₃₇₉	C₂²	1	1	yes	characteristic
10	Dic₇₅₈	—	2	2	no	—
11	Dic₇₅₈	—	4	1	no	—
12	C₂×Dic₃₇₉	—	4	1	no	—
13	C₂×C₄×C₃₇₉	D₄	1	1	yes	characteristic
14	C₈×C₃₇₉	—	4	1	no	—
15	C₈×C₃₇₉	C₂×C₄	1	1	yes	characteristic
16	C₈×C₃₇₉	D₄	1	1	yes	characteristic
17	C₂²×C₃₇₉	SD₁₆	1	1	yes	characteristic
18	C₄×C₃₇₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₃₇₉	D₈	1	1	yes	characteristic
20	Dic₃₇₉	—	4	2	no	—
21	C₂×C₃₇₉	—	2	1	no	—
22	C₂×C₃₇₉	#102	1	1	yes	characteristic
23	C₃₇₉	#362	1	1	yes	characteristic, complemented, Sylow
24	#362	—	379	1	no	maximal, Sylow
25	C₂×Q₁₆	—	379	1	no	—
26	M₃₂	—	379	1	no	—
27	#108	D₃₇₉	1	1	yes	characteristic
28	C₂×Q₈	—	758	1	no	—
29	Q₁₆	—	379	2	no	—
30	Q₁₆	—	758	1	no	—
31	M₁₆	—	2	1	no	—
32	C₂×C₈	C₂×D₃₇₉	1	1	yes	characteristic
33	C₁₆	—	758	1	no	—
34	Q₈	—	1516	1	no	—
35	Q₈	—	758	2	no	—
36	C₂×C₄	—	1516	1	no	—
37	C₂×C₄	C₂²⋊D₃₇₉	1	1	yes	characteristic
38	C₈	—	4	1	no	—
39	C₈	C₄×D₃₇₉	1	1	yes	characteristic
40	C₈	D₁₅₁₆	1	1	yes	characteristic
41	C₂²	#20258593	1	1	yes	characteristic
42	C₄	—	1516	2	no	—
43	C₄	(C₂×D₃₇₉)⋊C₄	1	1	yes	characteristic
44	C₄	#20258591	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#27131251	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#27131251
commutator	C₈×C₃₇₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₃₇₉
Fitting	#108×C₃₇₉	C₂
socle	C₂×C₃₇₉	#102
prime radical	C₂²×C₃₇₉	SD₁₆
cosocle	C₂×C₈×C₃₇₉	C₂²
hypercenter	#108	D₃₇₉
hypocenter	C₃₇₉	#362
LCS	G ▷ C₈×C₃₇₉ ▷ C₄×C₃₇₉ ▷ C₂×C₃₇₉ ▷ C₃₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

Complements

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

N	H ≅ G/N	type
23. C₃₇₉	#362	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₅₁₆	2
#27131271	2
#108×C₃₇₉	2
#362	379