Subgroups — C₄⋊#92216 #14516151

Order 1944.

179 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#92216	C₂	1	2	yes	maximal, complemented
2	C₄×#6879	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊#4178	—	3	3	no	maximal
4	C₉×D₃₆	—	3	1	no	maximal
5	C₂×#6879	C₂²	1	1	yes	characteristic
6	#92216	—	2	2	no	—
7	C₂×#4178	—	3	6	no	—
8	C₂×C₉×D₉	—	3	2	no	—
9	C₄×#732	D₃	1	3	yes	complemented
10	C₄×C₉²	D₃	1	1	yes	characteristic, complemented
11	#6879	D₄	1	1	yes	characteristic, complemented, Sylow
12	C₄⋊#272	—	3	3	no	—
13	C₉×D₁₂	—	9	1	no	—
14	C₃×D₃₆	—	3	1	no	—
15	C₂×#732	C₂×D₃	1	3	yes	—
16	C₂×C₉²	C₂×D₃	1	1	yes	characteristic
17	#4178	—	6	6	no	—
18	C₉×D₉	—	6	2	no	—
19	C₂×#272	—	3	6	no	—
20	C₂×D₃×C₉	—	9	2	no	—
21	C₂×C₃×D₉	—	3	2	no	—
22	C₄×H(3,𝔽₃)	—	3	3	no	—
23	C₃×C₄×C₉	—	3	1	no	—
24	C₃×C₄×C₉	C₃⋊D₃	1	1	yes	characteristic
25	#732	D₁₂	1	3	yes	complemented
26	C₉²	D₁₂	1	1	yes	characteristic, complemented
27	C₃×D₁₂	—	9	1	no	—
28	C₃×D₁₂	—	27	3	no	—
29	D₄×C₉	—	27	1	no	—
30	D₃₆	—	3	1	no	—
31	C₂×H(3,𝔽₃)	—	3	3	no	—
32	C₂×C₃×C₉	—	3	1	no	—
33	C₂×C₃×C₉	C₂×C₃⋊D₃	1	1	yes	characteristic
34	#272	—	6	6	no	—
35	D₃×C₉	—	18	2	no	—
36	C₃×D₉	—	6	2	no	—
37	C₂×C₃×D₃	—	9	2	no	—
38	C₂×C₃×D₃	—	27	6	no	—
39	C₃²×C₄	—	9	3	no	—
40	C₃²×C₄	#272	1	1	yes	characteristic
41	C₂²×C₉	—	27	2	no	—
42	C₂×D₉	—	3	2	no	—
43	C₄×C₉	—	3	1	no	—
44	C₄×C₉	—	3	1	no	—
45	C₄×C₉	—	6	1	no	—
46	H(3,𝔽₃)	—	3	3	no	—
47	C₃×C₉	—	3	1	no	—
48	C₃×C₉	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
49	C₃×D₄	—	27	1	no	—
50	D₁₂	—	9	1	no	—
51	D₁₂	—	27	3	no	—
52	C₂×C₃²	—	9	3	no	—
53	C₂×C₃²	C₂×#272	1	1	yes	characteristic
54	C₃×D₃	—	18	2	no	—
55	C₃×D₃	—	54	6	no	—
56	C₂×C₉	—	3	1	no	—
57	C₂×C₉	—	3	1	no	—
58	C₂×C₉	—	6	1	no	—
59	C₂×C₉	—	54	2	no	—
60	D₉	—	6	2	no	—
61	C₂²×C₃	—	27	2	no	—
62	C₂×D₃	—	9	2	no	—
63	C₂×D₃	—	27	6	no	—
64	C₃×C₄	—	3	1	no	—
65	C₃×C₄	—	27	3	no	—
66	C₃×C₄	#4185	1	1	yes	characteristic
67	C₃²	—	9	3	no	—
68	C₃²	C₄⋊#272	1	1	yes	characteristic
69	C₉	—	3	1	no	—
70	C₉	—	3	1	no	—
71	C₉	—	6	1	no	—
72	D₄	—	27	1	no	Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	27	3	no	—
75	C₂×C₃	—	54	2	no	—
76	C₂×C₃	C₂×#4185	1	1	yes	characteristic
77	D₃	—	18	2	no	—
78	D₃	—	54	6	no	—
79	C₂²	—	27	2	no	—
80	C₄	#92216	1	1	yes	characteristic, complemented
81	C₃	—	3	1	no	—
82	C₃	—	27	3	no	—
83	C₃	C₄⋊#4185	1	1	yes	characteristic
84	C₂	—	54	2	no	—
85	C₂	C₂×#92216	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	C₂×#4185
commutator, cosocle	C₂×#6879	C₂²
Frattini	C₂×C₃×C₉	C₂×C₃⋊D₃
Fitting	C₄×#6879	C₂
hypercenter	C₃×C₄	#4185
hypocenter	#6879	D₄
LCS	G ▷ C₂×#6879 ▷ #6879
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#92216	C₂	semidirect
2. C₄×#6879	C₂	semidirect
9. C₄×#732	D₃	semidirect
10. C₄×C₉²	D₃	semidirect
11. #6879	D₄	semidirect
25. #732	D₁₂	semidirect
26. C₉²	D₁₂	semidirect
80. C₄	#92216	semidirect

Maximal subgroups

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

subgroup	index
C₂×#92216	2
C₄×#6879	2
C₄⋊#4178	3
C₉×D₃₆	3

Subgroups — C4⋊#92216 #14516151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊#92216 #14516151