Subgroups — #365×C₃₈₉ #38733596

Order 24896.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₃₂×C₃₈₉	C₂	1	1	yes	maximal, characteristic
2	#108×C₃₈₉	C₂	1	1	yes	maximal, characteristic
3	#106×C₃₈₉	C₂	1	1	yes	maximal, characteristic
4	M₁₆×C₃₈₉	—	2	1	no	—
5	C₂×C₈×C₃₈₉	C₂²	1	1	yes	characteristic
6	C₄⋊C₄×C₃₈₉	—	2	1	no	—
7	C₁₆×C₃₈₉	C₄	1	2	yes	complemented
8	C₂×C₄×C₃₈₉	—	4	1	no	—
9	C₂×C₄×C₃₈₉	D₄	1	1	yes	characteristic
10	C₈×C₃₈₉	—	4	1	no	—
11	C₈×C₃₈₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₈₉	Q₈	1	1	yes	characteristic
13	C₂²×C₃₈₉	SD₁₆	1	1	yes	characteristic
14	C₄×C₃₈₉	—	8	1	no	—
15	C₄×C₃₈₉	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₃₈₉	SD₁₆	1	1	yes	characteristic
17	C₂×C₃₈₉	—	2	1	no	—
18	C₂×C₃₈₉	#106	1	1	yes	characteristic
19	C₃₈₉	#365	1	1	yes	characteristic, direct product factor, Sylow
20	#365	C₃₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	M₃₂	C₂×C₃₈₉	1	1	yes	characteristic
22	#108	C₂×C₃₈₉	1	1	yes	characteristic
23	#106	C₂×C₃₈₉	1	1	yes	characteristic
24	M₁₆	—	2	1	no	—
25	C₂×C₈	C₂²×C₃₈₉	1	1	yes	characteristic
26	C₄⋊C₄	—	2	1	no	—
27	C₁₆	C₄×C₃₈₉	1	2	yes	complemented
28	C₂×C₄	—	4	1	no	—
29	C₂×C₄	D₄×C₃₈₉	1	1	yes	characteristic
30	C₈	—	4	1	no	—
31	C₈	C₂×C₄×C₃₈₉	1	1	yes	characteristic
32	C₈	Q₈×C₃₈₉	1	1	yes	characteristic
33	C₂²	SD₁₆×C₃₈₉	1	1	yes	characteristic
34	C₄	—	8	1	no	—
35	C₄	C₄⋊C₄×C₃₈₉	1	1	yes	characteristic
36	C₄	SD₁₆×C₃₈₉	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#106×C₃₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃₈₉	#106
commutator	C₈	C₂×C₄×C₃₈₉
Frattini, cosocle	C₂×C₈	C₂²×C₃₈₉
prime radical	C₂²×C₃₈₉	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₈₉ ◁ C₂×C₄×C₃₈₉ ◁ C₂×C₈×C₃₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₁₆×C₃₈₉	C₄	semidirect
19. C₃₈₉	#365	direct (N × H)
20. #365	C₃₈₉	direct (N × H)
27. C₁₆	C₄×C₃₈₉	semidirect

Maximal subgroups

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

subgroup	index
M₃₂×C₃₈₉	2
#108×C₃₈₉	2
#106×C₃₈₉	2
#365	389

Subgroups — #365×C389 #38733596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #365×C₃₈₉ #38733596