Subgroups — #1094⋊C₄ #88602

Order 432.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1094	C₂	1	1	yes	maximal, characteristic
2	C₃×#217	—	3	1	no	maximal
3	(C₂²⋊C₉)⋊C₄	C₃	1	1	yes	maximal, characteristic, complemented
4	#1094	C₄	1	1	yes	characteristic, complemented
5	3₋¹⁺²⋊C₄	—	4	1	no	maximal
6	C₂³×C₃²	D₃	1	1	yes	characteristic
7	C₂×C₃×Dic₃	—	3	1	no	—
8	C₂×C₃×Dic₃	—	3	1	no	—
9	C₂×C₂²⋊C₉	—	2	1	no	—
10	C₂×C₂²⋊C₉	C₂×C₃	1	1	yes	characteristic
11	C₂×3₋¹⁺²	—	4	1	no	—
12	C₃×C₂²⋊C₄	—	9	1	no	—
13	#217	—	3	1	no	—
14	C₂²×C₃²	—	3	1	no	—
15	C₂²×C₃²	—	3	1	no	—
16	C₂²×C₃²	Dic₃	1	1	yes	characteristic
17	C₃×Dic₃	—	6	1	no	—
18	C₃×Dic₃	—	6	1	no	—
19	C₂²⋊C₉	—	2	1	no	—
20	C₂²⋊C₉	C₃×C₄	1	1	yes	characteristic, complemented
21	Dic₉	—	4	1	no	—
22	3₋¹⁺²	—	4	1	no	Sylow
23	C₂³×C₃	—	3	1	no	—
24	C₂³×C₃	C₃×D₃	1	1	yes	characteristic
25	C₂×C₃×C₄	—	9	1	no	—
26	C₂×C₃×C₄	—	9	1	no	—
27	C₂×Dic₃	—	3	1	no	—
28	C₂×Dic₃	—	3	1	no	—
29	C₂×C₃²	—	3	1	no	—
30	C₂×C₃²	—	3	1	no	—
31	C₂×C₃²	S₄	1	1	yes	characteristic
32	C₂×C₉	—	4	1	no	—
33	C₂×C₉	—	8	1	no	—
34	C₂²⋊C₄	—	9	1	no	Sylow
35	C₂²×C₃	—	3	1	no	—
36	C₂²×C₃	—	3	1	no	—
37	C₂²×C₃	—	3	1	no	—
38	C₂²×C₃	—	3	1	no	—
39	C₂²×C₃	—	3	1	no	—
40	C₂²×C₃	—	6	1	no	—
41	C₂²×C₃	—	6	1	no	—
42	C₂²×C₃	C₃×Dic₃	1	1	yes	characteristic
43	C₃×C₄	—	18	1	no	—
44	C₃×C₄	—	18	1	no	—
45	Dic₃	—	6	1	no	—
46	Dic₃	—	6	1	no	—
47	C₃²	SL(2,ℤ/4)	1	1	yes	characteristic
48	C₉	—	4	1	no	—
49	C₉	—	8	1	no	—
50	C₂³	AGL(1,ℤ/9)	1	1	yes	characteristic
51	C₂×C₄	—	9	1	no	—
52	C₂×C₄	—	9	1	no	—
53	C₂×C₃	—	3	1	no	—
54	C₂×C₃	—	3	1	no	—
55	C₂×C₃	—	3	1	no	—
56	C₂×C₃	—	3	1	no	—
57	C₂×C₃	—	3	1	no	—
58	C₂×C₃	—	6	1	no	—
59	C₂×C₃	—	6	1	no	—
60	C₂×C₃	C₃×S₄	1	1	yes	characteristic
61	C₂²	—	3	1	no	—
62	C₂²	—	3	1	no	—
63	C₂²	3₋¹⁺²⋊C₄	1	1	yes	characteristic, complemented
64	C₄	—	18	1	no	—
65	C₄	—	18	1	no	—
66	C₃	—	3	1	no	—
67	C₃	C₃×SL(2,ℤ/4)	1	1	yes	characteristic
68	C₂	—	3	1	no	—
69	C₂	—	3	1	no	—
70	C₂	((C₂²⋊C₉)⋊C₂)⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	((C₂²⋊C₉)⋊C₂)⋊C₃
commutator, hypocenter	C₂²⋊C₉	C₃×C₄
Frattini	C₂×C₃	C₃×S₄
Fitting, prime radical	C₂³×C₃²	D₃
socle	C₂³×C₃	C₃×D₃
cosocle	C₂×C₂²⋊C₉	C₂×C₃
LCS	G ▷ C₂²⋊C₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. (C₂²⋊C₉)⋊C₄	C₃	semidirect
4. #1094	C₄	semidirect
20. C₂²⋊C₉	C₃×C₄	semidirect
63. C₂²	3₋¹⁺²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#1094	2
C₃×#217	3
(C₂²⋊C₉)⋊C₄	3
3₋¹⁺²⋊C₄	4

Subgroups — #1094⋊C4 #88602

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1094⋊C₄ #88602