Subgroups — C₄⋊((C₂²⋊C₉)⋊C₂) #63686

Order 288.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×(C₂²⋊C₉)⋊C₂	C₂	1	2	yes	maximal, complemented
2	C₄×C₂²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#930	—	3	1	no	maximal
4	C₂×C₂²⋊C₉	C₂²	1	1	yes	characteristic
5	(C₂²⋊C₉)⋊C₂	—	2	2	no	—
6	D₃₆	—	4	1	no	maximal
7	C₂²×C₃×C₄	D₃	1	1	yes	characteristic
8	C₂×#67	—	3	2	no	—
9	C₂×D₁₂	—	3	1	no	—
10	(C₂×D₃)⋊C₄	—	3	2	no	—
11	C₄⋊Dic₃	—	3	1	no	—
12	C₂×D₉	—	4	2	no	—
13	C₂²⋊C₉	D₄	1	1	yes	characteristic, complemented
14	C₄×C₉	—	4	1	no	—
15	#121	—	9	1	no	Sylow
16	C₂³×C₃	C₂×D₃	1	1	yes	characteristic
17	C₂²×D₃	—	3	2	no	—
18	C₂×C₃×C₄	—	3	1	no	—
19	C₂×C₃×C₄	—	3	1	no	—
20	#67	—	6	2	no	—
21	#67	—	6	2	no	—
22	C₂×Dic₃	—	3	2	no	—
23	D₁₂	—	6	1	no	—
24	D₁₂	—	6	1	no	—
25	C₂×C₉	—	4	1	no	—
26	D₉	—	8	2	no	—
27	C₂×D₄	—	9	1	no	—
28	C₂×D₄	—	9	2	no	—
29	C₂²×C₄	D₉	1	1	yes	characteristic, complemented
30	C₄⋊C₄	—	9	1	no	—
31	C₂²⋊C₄	—	9	2	no	—
32	C₂²×C₃	—	3	1	no	—
33	C₂²×C₃	—	3	1	no	—
34	C₂²×C₃	D₁₂	1	1	yes	characteristic
35	C₂×D₃	—	6	2	no	—
36	C₂×D₃	—	6	2	no	—
37	C₂×D₃	—	6	2	no	—
38	C₃×C₄	—	3	1	no	—
39	C₃×C₄	S₄	1	1	yes	characteristic
40	Dic₃	—	6	2	no	—
41	C₉	—	4	1	no	Sylow
42	C₂³	—	9	2	no	—
43	C₂³	C₂×D₉	1	1	yes	characteristic
44	D₄	—	18	1	no	—
45	D₄	—	18	2	no	—
46	D₄	—	18	2	no	—
47	D₄	—	18	1	no	—
48	C₂×C₄	—	3	1	no	—
49	C₂×C₄	—	3	1	no	—
50	C₂×C₄	—	9	2	no	—
51	C₂×C₃	—	3	1	no	—
52	C₂×C₃	—	3	1	no	—
53	C₂×C₃	C₂×S₄	1	1	yes	characteristic
54	D₃	—	12	2	no	—
55	C₂²	—	3	1	no	—
56	C₂²	—	3	1	no	—
57	C₂²	—	18	2	no	—
58	C₂²	—	18	2	no	—
59	C₂²	—	18	2	no	—
60	C₂²	D₃₆	1	1	yes	characteristic, complemented
61	C₄	—	3	1	no	—
62	C₄	—	18	2	no	—
63	C₄	(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic, complemented
64	C₃	C₄⋊S₄	1	1	yes	characteristic
65	C₂	—	3	1	no	—
66	C₂	—	3	1	no	—
67	C₂	—	36	2	no	—
68	C₂	C₂×(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×(C₂²⋊C₉)⋊C₂
commutator, cosocle	C₂×C₂²⋊C₉	C₂²
Frattini	C₂×C₃	C₂×S₄
Fitting	C₂²×C₃×C₄	D₃
socle	C₂³×C₃	C₂×D₃
hypercenter	C₄	(C₂²⋊C₉)⋊C₂
hypocenter	C₂²⋊C₉	D₄
LCS	G ▷ C₂×C₂²⋊C₉ ▷ C₂²⋊C₉
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. C₂×(C₂²⋊C₉)⋊C₂	C₂	semidirect
2. C₄×C₂²⋊C₉	C₂	semidirect
13. C₂²⋊C₉	D₄	semidirect
29. C₂²×C₄	D₉	semidirect
60. C₂²	D₃₆	semidirect
63. C₄	(C₂²⋊C₉)⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×(C₂²⋊C₉)⋊C₂	2
C₄×C₂²⋊C₉	2
#930	3
D₃₆	4

Subgroups — C4⋊((C22⋊C9)⋊C2) #63686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊((C₂²⋊C₉)⋊C₂) #63686