Subgroups — #364×C₃₅₉ #37525939

Order 22976.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₃₂×C₃₅₉	C₂	1	2	yes	maximal
2	C₄×C₈×C₃₅₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₃₅₉	C₄	1	1	yes	characteristic
4	C₂×C₈×C₃₅₉	C₂²	1	1	yes	characteristic
5	C₄²×C₃₅₉	C₄	1	1	yes	characteristic
6	C₁₆×C₃₅₉	—	2	2	no	—
7	C₂×C₄×C₃₅₉	—	2	1	no	—
8	C₂×C₄×C₃₅₉	C₂×C₄	1	1	yes	characteristic
9	C₈×C₃₅₉	C₈	1	2	yes	—
10	C₈×C₃₅₉	D₄	1	1	yes	characteristic
11	C₈×C₃₅₉	Q₈	1	1	yes	characteristic
12	C₂²×C₃₅₉	M₁₆	1	1	yes	characteristic
13	C₄×C₃₅₉	—	2	2	no	—
14	C₄×C₃₅₉	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₃₅₉	C₂×C₈	1	1	yes	characteristic
16	C₂×C₃₅₉	—	2	1	no	—
17	C₂×C₃₅₉	C₄⋊C₈	1	1	yes	characteristic
18	C₃₅₉	#364	1	1	yes	characteristic, direct product factor, Sylow
19	#364	C₃₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	M₃₂	C₂×C₃₅₉	1	2	yes	—
21	C₄×C₈	C₂×C₃₅₉	1	1	yes	characteristic
22	C₂×C₈	C₄×C₃₅₉	1	1	yes	characteristic
23	C₂×C₈	C₂²×C₃₅₉	1	1	yes	characteristic
24	C₄²	C₄×C₃₅₉	1	1	yes	characteristic
25	C₁₆	—	2	2	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	C₂×C₄×C₃₅₉	1	1	yes	characteristic
28	C₈	C₈×C₃₅₉	1	2	yes	—
29	C₈	D₄×C₃₅₉	1	1	yes	characteristic
30	C₈	Q₈×C₃₅₉	1	1	yes	characteristic
31	C₂²	M₁₆×C₃₅₉	1	1	yes	characteristic
32	C₄	—	2	2	no	—
33	C₄	C₄⋊C₄×C₃₅₉	1	1	yes	characteristic
34	C₄	C₂×C₈×C₃₅₉	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	C₄⋊C₈×C₃₅₉	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₃₅₉	D₄
commutator	C₄	C₂×C₈×C₃₅₉
Frattini, cosocle	C₂×C₈	C₂²×C₃₅₉
socle	C₂×C₃₅₉	C₄⋊C₈
prime radical	C₂²×C₃₅₉	M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₃₅₉ ◁ C₂×C₈×C₃₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
18. C₃₅₉	#364	direct (N × H)
19. #364	C₃₅₉	direct (N × H)

Maximal subgroups

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

subgroup	index
M₃₂×C₃₅₉	2
C₄×C₈×C₃₅₉	2
#364	359

Subgroups — #364×C359 #37525939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #364×C₃₅₉ #37525939