Subgroups — C₂×C₃⋊((C₂²⋊C₉)⋊C₂) #88890

Order 432.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊((C₂²⋊C₉)⋊C₂)	C₂	1	2	yes	maximal, direct product factor
3	C₂×#638	—	3	1	no	maximal
4	C₂×(C₂²⋊C₉)⋊C₂	—	3	3	no	maximal
5	C₂×C₃⋊D₉	—	4	1	no	maximal
6	C₃×C₂²⋊C₉	C₂²	1	1	yes	characteristic, complemented
7	C₂³×C₃²	D₃	1	1	yes	characteristic
8	C₂²×C₃⋊D₃	—	3	1	no	—
9	#638	—	3	2	no	—
10	#638	—	3	2	no	—
11	C₂×C₃⋊Dic₃	—	3	1	no	—
12	C₂×C₂²⋊C₉	D₃	1	3	yes	complemented
13	(C₂²⋊C₉)⋊C₂	—	3	6	no	—
14	C₂×C₃×C₉	—	4	1	no	—
15	C₃⋊D₉	—	4	2	no	—
16	C₂×#67	—	9	3	no	—
17	C₂×#67	—	9	1	no	—
18	C₂²×C₃²	—	3	1	no	—
19	C₂²×C₃²	—	3	1	no	—
20	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
21	C₂×C₃⋊D₃	—	3	2	no	—
22	C₂×C₃⋊D₃	—	6	1	no	—
23	C₂×C₃⋊D₃	—	6	1	no	—
24	C₃⋊Dic₃	—	3	2	no	—
25	C₂×D₉	—	12	3	no	—
26	C₂²⋊C₉	C₂×D₃	1	3	yes	complemented
27	C₃×C₉	—	4	1	no	Sylow
28	C₂³×C₃	D₉	1	3	yes	complemented
29	C₂³×C₃	C₃⋊D₃	1	1	yes	characteristic
30	C₂²×D₃	—	9	3	no	—
31	C₂²×D₃	—	9	1	no	—
32	#67	—	9	6	no	—
33	#67	—	9	2	no	—
34	#67	—	9	6	no	—
35	#67	—	9	2	no	—
36	C₂×Dic₃	—	9	3	no	—
37	C₂×Dic₃	—	9	1	no	—
38	C₂×C₃²	—	3	1	no	—
39	C₂×C₃²	—	3	1	no	—
40	C₂×C₃²	S₄	1	1	yes	characteristic
41	C₃⋊D₃	—	6	2	no	—
42	C₂×C₉	—	4	3	no	—
43	D₉	—	12	6	no	—
44	C₂×D₄	—	27	1	no	Sylow
45	C₂²×C₃	—	3	3	no	—
46	C₂²×C₃	—	3	1	no	—
47	C₂²×C₃	—	3	3	no	—
48	C₂²×C₃	—	3	1	no	—
49	C₂²×C₃	C₂×D₉	1	3	yes	complemented
50	C₂²×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
51	C₂×D₃	—	9	2	no	—
52	C₂×D₃	—	9	6	no	—
53	C₂×D₃	—	18	1	no	—
54	C₂×D₃	—	18	3	no	—
55	C₂×D₃	—	18	3	no	—
56	C₂×D₃	—	18	1	no	—
57	Dic₃	—	9	2	no	—
58	Dic₃	—	9	6	no	—
59	C₃²	C₂×S₄	1	1	yes	characteristic
60	C₉	—	4	3	no	—
61	C₂³	—	27	1	no	—
62	C₂³	C₃⋊D₉	1	1	yes	characteristic, complemented
63	D₄	—	27	2	no	—
64	D₄	—	27	2	no	—
65	C₂×C₄	—	27	1	no	—
66	C₂×C₃	—	3	1	no	—
67	C₂×C₃	—	3	1	no	—
68	C₂×C₃	—	3	3	no	—
69	C₂×C₃	—	3	3	no	—
70	C₂×C₃	(C₂²⋊C₉)⋊C₂	1	3	yes	complemented
71	C₂×C₃	C₃⋊S₄	1	1	yes	characteristic
72	D₃	—	18	2	no	—
73	D₃	—	18	6	no	—
74	C₂²	—	3	1	no	—
75	C₂²	—	3	1	no	—
76	C₂²	—	27	2	no	—
77	C₂²	—	54	1	no	—
78	C₂²	—	54	1	no	—
79	C₂²	C₂×C₃⋊D₉	1	1	yes	characteristic, complemented
80	C₄	—	27	2	no	—
81	C₃	C₂×(C₂²⋊C₉)⋊C₂	1	3	yes	complemented
82	C₃	C₂×C₃⋊S₄	1	1	yes	characteristic
83	C₂	—	3	1	no	—
84	C₂	—	3	1	no	—
85	C₂	—	54	2	no	—
86	C₂	C₃⋊((C₂²⋊C₉)⋊C₂)	1	1	yes	characteristic, direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₂²⋊C₉	C₂	semidirect
2. C₃⋊((C₂²⋊C₉)⋊C₂)	C₂	direct (N × H)
6. C₃×C₂²⋊C₉	C₂²	semidirect
12. C₂×C₂²⋊C₉	D₃	semidirect
26. C₂²⋊C₉	C₂×D₃	semidirect
28. C₂³×C₃	D₉	semidirect
49. C₂²×C₃	C₂×D₉	semidirect
62. C₂³	C₃⋊D₉	semidirect
70. C₂×C₃	(C₂²⋊C₉)⋊C₂	semidirect
79. C₂²	C₂×C₃⋊D₉	semidirect
81. C₃	C₂×(C₂²⋊C₉)⋊C₂	semidirect
86. C₂	C₃⋊((C₂²⋊C₉)⋊C₂)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₂²⋊C₉	2
C₃⋊((C₂²⋊C₉)⋊C₂)	2
C₂×#638	3
C₂×(C₂²⋊C₉)⋊C₂	3
C₂×C₃⋊D₉	4

Subgroups — C2×C3⋊((C22⋊C9)⋊C2) #88890

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊((C₂²⋊C₉)⋊C₂) #88890