Subgroups — #6880⋊C₈ #14515653

Order 1944.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6880	C₂	1	1	yes	maximal, characteristic
2	#733⋊C₈	C₃	1	1	yes	maximal, characteristic
3	C₉×C₉⋊C₈	—	3	1	no	maximal
4	C₂×#6880	C₄	1	1	yes	characteristic
5	C₄×#733	—	2	1	no	—
6	C₄×#733	C₂×C₃	1	1	yes	characteristic
7	C₄×C₉²	D₃	1	1	yes	characteristic
8	#6880	C₈	1	1	yes	characteristic, complemented, Sylow
9	3₋¹⁺²⋊C₈	—	9	1	no	—
10	C₉×C₃⋊C₈	—	9	1	no	—
11	C₃×C₉⋊C₈	—	3	1	no	—
12	C₂×#733	—	2	1	no	—
13	C₂×#733	C₃×C₄	1	1	yes	characteristic
14	C₂×C₉²	Dic₃	1	1	yes	characteristic
15	C₄×3₋¹⁺²	—	3	1	no	—
16	C₄×3₋¹⁺²	—	6	1	no	—
17	C₃×C₄×C₉	—	3	1	no	—
18	C₃×C₄×C₉	C₃×D₃	1	1	yes	characteristic
19	#733	—	2	1	no	—
20	#733	C₃×C₈	1	1	yes	characteristic
21	C₉²	C₃⋊C₈	1	1	yes	characteristic
22	C₃×C₃⋊C₈	—	9	1	no	—
23	C₈×C₉	—	27	1	no	—
24	C₉⋊C₈	—	3	1	no	—
25	C₉⋊C₈	—	9	1	no	—
26	C₂×3₋¹⁺²	—	3	1	no	—
27	C₂×3₋¹⁺²	—	6	1	no	—
28	C₂×C₃×C₉	—	3	1	no	—
29	C₂×C₃×C₉	C₃×Dic₃	1	1	yes	characteristic
30	C₃²×C₄	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
31	C₄×C₉	—	3	1	no	—
32	C₄×C₉	—	3	1	no	—
33	C₄×C₉	—	6	1	no	—
34	C₄×C₉	—	9	1	no	—
35	C₄×C₉	—	18	1	no	—
36	3₋¹⁺²	—	3	1	no	—
37	3₋¹⁺²	—	6	1	no	—
38	C₃×C₉	—	3	1	no	—
39	C₃×C₉	C₃×C₃⋊C₈	1	1	yes	characteristic
40	C₃×C₈	—	27	1	no	—
41	C₃⋊C₈	—	9	1	no	—
42	C₂×C₃²	(C₃⋊Dic₃)⋊C₃	1	1	yes	characteristic
43	C₂×C₉	—	3	1	no	—
44	C₂×C₉	—	3	1	no	—
45	C₂×C₉	—	6	1	no	—
46	C₂×C₉	—	9	1	no	—
47	C₂×C₉	—	18	1	no	—
48	C₃×C₄	—	3	1	no	—
49	C₃×C₄	#4178	1	1	yes	characteristic
50	C₃²	(C₃⋊(C₃⋊C₈))⋊C₃	1	1	yes	characteristic
51	C₉	—	3	1	no	—
52	C₉	—	3	1	no	—
53	C₉	—	6	1	no	—
54	C₉	—	9	1	no	—
55	C₉	—	18	1	no	—
56	C₈	—	27	1	no	Sylow
57	C₂×C₃	—	3	1	no	—
58	C₂×C₃	#66325	1	1	yes	characteristic
59	C₄	#6880⋊C₂	1	1	yes	characteristic
60	C₃	—	3	1	no	—
61	C₃	#10619504	1	1	yes	characteristic
62	C₂	#6880⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	#6880⋊C₂
commutator, hypocenter	#733	C₃×C₈
Frattini	C₃×C₄×C₉	C₃×D₃
Fitting	C₄×#6880	C₂
socle	C₂×C₃	#66325
prime radical	C₂×C₃²	(C₃⋊Dic₃)⋊C₃
cosocle	C₄×#733	C₂×C₃
LCS	G ▷ #733
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
8. #6880	C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6880	2
#733⋊C₈	3
C₉×C₉⋊C₈	3

Subgroups — #6880⋊C8 #14515653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #6880⋊C₈ #14515653