Subgroups — #11757436⋊C₂ #14516440

Order 1944.

103 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11757436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉⋊((C₂²⋊C₉)⋊C₂)	C₃	1	1	yes	maximal, characteristic, complemented
3	#10619650	—	3	1	no	maximal
4	#6878⋊C₂	—	4	1	no	maximal
5	C₂²×#732	D₃	1	1	yes	characteristic
6	C₂×#4179	—	3	1	no	—
7	#66359	—	2	1	no	—
8	C₉×C₂²⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
9	#66326	—	3	1	no	—
10	#6878	—	4	1	no	Sylow
11	C₃⋊((C₂²⋊C₉)⋊C₂)	—	9	1	no	—
12	#6233	—	3	1	no	—
13	#638⋊C₃	—	9	1	no	—
14	C₂×#732	—	3	1	no	—
15	C₉⋊D₉	—	4	1	no	—
16	#4179	—	6	1	no	—
17	C₂²×H(3,𝔽₃)	—	3	1	no	—
18	C₂²×C₃×C₉	C₃×D₃	1	1	yes	characteristic
19	C₂×C₃⋊D₉	—	3	1	no	—
20	C₂×(C₃⋊D₃)⋊C₃	—	9	1	no	—
21	#1094	—	6	1	no	—
22	C₃×C₂²⋊C₉	—	3	1	no	—
23	C₃⋊Dic₉	—	3	1	no	—
24	(C₃⋊Dic₃)⋊C₃	—	9	1	no	—
25	#733	—	8	1	no	—
26	#732	S₄	1	1	yes	characteristic
27	C₉²	—	4	1	no	—
28	#638	—	9	1	no	—
29	C₃×#67	—	27	1	no	—
30	(C₂²⋊C₉)⋊C₂	—	27	3	no	—
31	#611	—	27	1	no	—
32	C₂×H(3,𝔽₃)	—	3	1	no	—
33	C₂×H(3,𝔽₃)	—	6	1	no	—
34	C₂×C₃×C₉	—	3	1	no	—
35	C₃⋊D₉	—	6	1	no	—
36	C₃⋊D₉	—	36	1	no	—
37	(C₃⋊D₃)⋊C₃	—	18	1	no	—
38	C₂²×C₃²	—	9	1	no	—
39	C₂²×C₃²	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
40	C₂×C₃⋊D₃	—	9	1	no	—
41	C₂×C₃×D₃	—	27	1	no	—
42	C₃⋊Dic₃	—	9	1	no	—
43	C₃×Dic₃	—	27	1	no	—
44	C₂²×C₉	—	3	1	no	—
45	C₂×D₉	—	27	1	no	—
46	C₂²⋊C₉	—	3	3	no	—
47	C₂²⋊C₉	—	18	1	no	—
48	Dic₉	—	27	1	no	—
49	3₋¹⁺²	—	24	1	no	—
50	H(3,𝔽₃)	—	3	1	no	—
51	C₃×C₉	—	12	1	no	—
52	C₃×C₉	C₃×S₄	1	1	yes	characteristic
53	C₃×D₄	—	81	1	no	—
54	#67	—	27	1	no	—
55	#67	—	81	1	no	—
56	C₂×C₃²	—	3	1	no	—
57	C₂×C₃²	—	9	1	no	—
58	C₂×C₃²	—	18	1	no	—
59	C₃⋊D₃	—	18	1	no	—
60	C₃×D₃	—	54	1	no	—
61	C₂×C₉	—	9	1	no	—
62	D₉	—	54	1	no	—
63	D₉	—	108	3	no	—
64	C₂²×C₃	—	3	1	no	—
65	C₂²×C₃	—	27	1	no	—
66	C₂²×C₃	—	81	1	no	—
67	C₂²×C₃	#4179	1	1	yes	characteristic
68	C₂×D₃	—	27	1	no	—
69	C₂×D₃	—	81	1	no	—
70	C₃×C₄	—	81	1	no	—
71	Dic₃	—	27	1	no	—
72	Dic₃	—	81	1	no	—
73	C₃²	—	9	1	no	—
74	C₃²	(C₃⋊S₄)⋊C₃	1	1	yes	characteristic
75	C₉	—	3	1	no	—
76	C₉	—	12	3	no	—
77	C₉	—	72	1	no	—
78	D₄	—	81	1	no	Sylow
79	C₂×C₃	—	3	1	no	—
80	C₂×C₃	—	9	1	no	—
81	C₂×C₃	—	27	1	no	—
82	C₂×C₃	—	54	1	no	—
83	C₂×C₃	—	162	1	no	—
84	D₃	—	54	1	no	—
85	D₃	—	162	1	no	—
86	C₂²	—	81	1	no	—
87	C₂²	#6878⋊C₂	1	1	yes	characteristic, complemented
88	C₄	—	81	1	no	—
89	C₃	—	3	1	no	—
90	C₃	—	27	1	no	—
91	C₃	#10619743	1	1	yes	characteristic
92	C₂	—	3	1	no	—
93	C₂	—	162	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₉×C₂²⋊C₉	C₂×C₃
Frattini	C₃×C₉	C₃×S₄
Fitting	C₂²×#732	D₃
socle	C₂²×C₃	#4179
LCS	G ▷ C₉×C₂²⋊C₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #11757436	C₂	semidirect
2. C₉⋊((C₂²⋊C₉)⋊C₂)	C₃	semidirect
8. C₉×C₂²⋊C₉	C₂×C₃	semidirect
87. C₂²	#6878⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
#11757436	2
C₉⋊((C₂²⋊C₉)⋊C₂)	3
#10619650	3
#6878⋊C₂	4

Subgroups — #11757436⋊C2 #14516440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #11757436⋊C₂ #14516440