Subgroups — C₄⋊(#6897⋊C₂) #14517552

Order 1944.

244 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#6897⋊C₂	C₂	1	2	yes	maximal, complemented
2	C₄×#6897	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₉⋊D₉)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₄⋊#4169	—	3	4	no	maximal
5	C₂×#6897	C₂²	1	1	yes	characteristic
6	#6897⋊C₂	—	2	2	no	—
7	C₂×C₉⋊D₉	C₂×C₃	1	2	yes	complemented
8	C₂×#4169	—	3	8	no	—
9	C₄×C₉⋊C₉	—	2	4	no	—
10	C₄×C₃²⋊C₉	D₃	1	4	yes	—
11	C₄×C₉²	C₂×C₃	1	1	yes	characteristic, complemented
12	#6897	D₄	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₄⋊(C₃⋊D₃)	—	9	1	no	—
14	C₄⋊(C₃⋊D₉)	—	3	4	no	—
15	C₂×C₉⋊C₉	—	2	4	no	—
16	C₂×C₃²⋊C₉	C₂×D₃	1	4	yes	—
17	C₂×C₉²	C₂²×C₃	1	1	yes	characteristic
18	C₉⋊D₉	—	2	2	no	—
19	#4169	—	6	8	no	—
20	C₂×C₃×C₃⋊D₃	—	9	2	no	—
21	C₃³×C₄	C₃⋊D₃	1	1	yes	characteristic
22	C₂×C₃⋊D₉	—	3	8	no	—
23	C₃×C₄×C₉	—	2	4	no	—
24	C₃×C₄×C₉	C₃×D₃	1	4	yes	—
25	C₉⋊C₉	—	2	4	no	—
26	C₃²⋊C₉	D₁₂	1	4	yes	—
27	C₉²	C₃×D₄	1	1	yes	characteristic, complemented
28	C₄⋊(C₃⋊D₃)	—	9	1	no	—
29	C₃×D₁₂	—	27	4	no	—
30	D₃₆	—	27	4	no	—
31	C₂×C₃³	C₂×C₃⋊D₃	1	1	yes	characteristic
32	C₃×C₃⋊D₃	—	18	2	no	—
33	C₂×C₃×C₉	—	2	4	no	—
34	C₂×C₃×C₉	C₂×C₃×D₃	1	4	yes	—
35	C₃⋊D₉	—	6	8	no	—
36	C₂×C₃⋊D₃	—	9	2	no	—
37	C₂×C₃×D₃	—	27	8	no	—
38	C₃²×C₄	—	3	4	no	—
39	C₃²×C₄	C₃×C₃⋊D₃	1	1	yes	characteristic
40	C₂×D₉	—	27	8	no	—
41	C₄×C₉	—	3	4	no	—
42	C₄×C₉	—	6	4	no	—
43	C₃³	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
44	C₃×C₉	—	2	4	no	—
45	C₃×C₉	C₃×D₁₂	1	4	yes	—
46	C₃×D₄	—	81	1	no	—
47	D₁₂	—	27	4	no	—
48	C₂×C₃²	—	3	4	no	—
49	C₂×C₃²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
50	C₃⋊D₃	—	18	2	no	—
51	C₃×D₃	—	54	8	no	—
52	C₂×C₉	—	3	4	no	—
53	C₂×C₉	—	6	4	no	—
54	D₉	—	54	8	no	—
55	C₂²×C₃	—	81	2	no	—
56	C₂×D₃	—	27	8	no	—
57	C₃×C₄	—	9	1	no	—
58	C₃×C₄	#4207	1	4	yes	—
59	C₃²	—	3	4	no	—
60	C₃²	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
61	C₉	—	3	4	no	—
62	C₉	—	6	4	no	—
63	D₄	—	81	1	no	Sylow
64	C₂×C₃	—	9	1	no	—
65	C₂×C₃	—	162	2	no	—
66	C₂×C₃	C₂×#4207	1	4	yes	—
67	D₃	—	54	8	no	—
68	C₂²	—	81	2	no	—
69	C₄	#6897⋊C₂	1	1	yes	characteristic, complemented
70	C₃	—	9	1	no	—
71	C₃	C₄⋊#4207	1	4	yes	—
72	C₂	—	162	2	no	—
73	C₂	C₂×#6897⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#6897⋊C₂
commutator, cosocle	C₂×C₉²	C₂²×C₃
Frattini, socle	C₂×C₃²	C₂×C₃×C₃⋊D₃
Fitting	C₄×#6897	C₂
hypercenter	C₄	#6897⋊C₂
hypocenter	C₉²	C₃×D₄
LCS	G ▷ C₂×C₉² ▷ C₉²
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#6897⋊C₂	C₂	semidirect
2. C₄×#6897	C₂	semidirect
3. C₄⋊(C₉⋊D₉)	C₃	semidirect
7. C₂×C₉⋊D₉	C₂×C₃	semidirect
11. C₄×C₉²	C₂×C₃	semidirect
12. #6897	D₄	semidirect
27. C₉²	C₃×D₄	semidirect
69. C₄	#6897⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#6897⋊C₂	2
C₄×#6897	2
C₄⋊(C₉⋊D₉)	3
C₄⋊#4169	3

Subgroups — C4⋊(#6897⋊C2) #14517552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊(#6897⋊C₂) #14517552