Subgroups — #6869⋊C₈ #14515670

Order 1944.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6869	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃⋊(C₉⋊C₈)	—	3	1	no	maximal
3	(C₂₇⋊C₃)⋊C₈	—	3	3	no	maximal
4	C₂×#6869	C₄	1	1	yes	characteristic
5	C₃²×C₄×C₉	D₃	1	1	yes	characteristic
6	C₄×C₂₇⋊C₃	D₃	1	3	yes	—
7	#6869	C₈	1	1	yes	characteristic, complemented, Sylow
8	C₃×C₃⋊(C₃⋊C₈)	—	9	1	no	—
9	C₃⋊(C₉⋊C₈)	—	3	1	no	—
10	C₃×C₉⋊C₈	—	9	2	no	—
11	C₃×C₉⋊C₈	—	9	1	no	—
12	C₂₇⋊C₈	—	3	3	no	—
13	C₂×C₃²×C₉	Dic₃	1	1	yes	characteristic
14	C₂×C₂₇⋊C₃	Dic₃	1	3	yes	—
15	C₃³×C₄	D₉	1	1	yes	characteristic
16	C₃×C₄×C₉	—	3	1	no	—
17	C₃×C₄×C₉	—	6	1	no	—
18	C₃×C₄×C₉	D₉	1	2	yes	—
19	C₃×C₄×C₉	C₃⋊D₃	1	1	yes	characteristic
20	C₄×C₂₇	—	3	3	no	—
21	C₃²×C₉	C₃⋊C₈	1	1	yes	characteristic
22	C₂₇⋊C₃	C₃⋊C₈	1	3	yes	complemented
23	C₃⋊(C₃⋊C₈)	—	9	1	no	—
24	C₃×C₃⋊C₈	—	27	3	no	—
25	C₃×C₃⋊C₈	—	27	1	no	—
26	C₉⋊C₈	—	9	2	no	—
27	C₉⋊C₈	—	9	1	no	—
28	C₂×C₃³	Dic₉	1	1	yes	characteristic
29	C₂×C₃×C₉	—	3	1	no	—
30	C₂×C₃×C₉	—	6	1	no	—
31	C₂×C₃×C₉	Dic₉	1	2	yes	—
32	C₂×C₃×C₉	C₃⋊Dic₃	1	1	yes	characteristic
33	C₂×C₂₇	—	3	3	no	—
34	C₃²×C₄	—	3	1	no	—
35	C₃²×C₄	—	3	3	no	—
36	C₃²×C₄	C₃⋊D₉	1	1	yes	characteristic
37	C₄×C₉	—	2	1	no	—
38	C₄×C₉	—	3	2	no	—
39	C₄×C₉	#272	1	1	yes	characteristic
40	C₃³	C₉⋊C₈	1	1	yes	characteristic
41	C₃×C₉	—	3	1	no	—
42	C₃×C₉	—	6	1	no	—
43	C₃×C₉	C₉⋊C₈	1	2	yes	—
44	C₃×C₉	C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
45	C₂₇	—	3	3	no	—
46	C₃×C₈	—	81	1	no	—
47	C₃⋊C₈	—	27	3	no	—
48	C₃⋊C₈	—	27	1	no	—
49	C₂×C₃²	—	3	1	no	—
50	C₂×C₃²	—	3	3	no	—
51	C₂×C₃²	C₃⋊Dic₉	1	1	yes	characteristic
52	C₂×C₉	—	2	1	no	—
53	C₂×C₉	—	3	2	no	—
54	C₂×C₉	#1084	1	1	yes	characteristic
55	C₃×C₄	—	3	3	no	—
56	C₃×C₄	—	3	1	no	—
57	C₃×C₄	#4181	1	1	yes	characteristic
58	C₃²	—	3	3	no	—
59	C₃²	—	3	1	no	—
60	C₃²	C₃⋊(C₉⋊C₈)	1	1	yes	characteristic
61	C₉	—	2	1	no	—
62	C₉	—	3	2	no	—
63	C₉	#6180	1	1	yes	characteristic
64	C₈	—	81	1	no	Sylow
65	C₂×C₃	—	3	3	no	—
66	C₂×C₃	—	3	1	no	—
67	C₂×C₃	#66328	1	1	yes	characteristic
68	C₄	#6869⋊C₂	1	1	yes	characteristic
69	C₃	—	3	3	no	—
70	C₃	—	3	1	no	—
71	C₃	#10619507	1	1	yes	characteristic
72	C₂	#6869⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	#6869⋊C₂
commutator, hypocenter	#6869	C₈
Frattini	C₃×C₄×C₉	C₃⋊D₃
Fitting, cosocle	C₄×#6869	C₂
socle	C₂×C₃	#66328
prime radical	C₂×C₃³	Dic₉
LCS	G ▷ #6869
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
7. #6869	C₈	semidirect
22. C₂₇⋊C₃	C₃⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6869	2
C₃×C₃⋊(C₉⋊C₈)	3
(C₂₇⋊C₃)⋊C₈	3

Subgroups — #6869⋊C8 #14515670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #6869⋊C₈ #14515670