Group #11767118 — subgroups

Subgroups — C₉×#2397 #11767118

Order 1152.

1260 conjugacy classes of subgroups; only the 372 normal subgroups are shown.

normal subgroups only

This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 372 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₄×C₉	C₂	1	6	yes	maximal, complemented
2	C₉×#399	C₂	1	4	yes	maximal, complemented
3	C₉×#392	C₂	1	4	yes	maximal, complemented
4	C₉×#376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2397	C₃	1	1	yes	maximal, characteristic
6	C₂²×D₄×C₉	C₂²	1	6	yes	—
7	C₂³×C₄×C₉	C₂²	1	4	yes	—
8	C₄×D₄×C₉	—	2	24	no	—
9	C₂×C₉×C₄⋊C₄	C₂²	1	6	yes	—
10	C₂×C₉×C₂²⋊C₄	C₂²	1	12	yes	—
11	C₂×C₄²×C₉	C₂²	1	3	yes	—
12	C₉×#95	C₂²	1	4	yes	—
13	C₂×C₃×C₄×D₄	C₂×C₃	1	6	yes	—
14	C₃×#399	C₂×C₃	1	4	yes	—
15	C₃×#392	C₂×C₃	1	4	yes	—
16	C₃×#376	C₂×C₃	1	1	yes	characteristic
17	C₂⁴×C₉	C₂³	1	4	yes	—
18	C₂×D₄×C₉	—	2	24	no	—
19	C₂×D₄×C₉	—	2	12	no	—
20	C₂²×C₄×C₉	—	2	24	no	—
21	C₂²×C₄×C₉	C₂³	1	4	yes	—
22	C₂²×C₄×C₉	C₂³	1	6	yes	—
23	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
24	C₉×C₄⋊C₄	—	2	12	no	—
25	C₉×C₂²⋊C₄	—	2	24	no	—
26	C₄²×C₉	D₄	1	12	yes	complemented
27	#2397	C₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²×C₃×D₄	C₂²×C₃	1	6	yes	—
29	C₂³×C₃×C₄	C₂²×C₃	1	4	yes	—
30	C₃×C₄×D₄	—	2	24	no	—
31	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	6	yes	—
32	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	12	yes	—
33	C₂×C₃×C₄²	C₂²×C₃	1	3	yes	—
34	C₃×#95	C₂²×C₃	1	4	yes	—
35	C₂³×C₉	—	2	12	no	—
36	C₂³×C₉	—	2	12	no	—
37	C₂³×C₉	#41	1	8	yes	—
38	C₂³×C₉	C₂⁴	1	1	yes	characteristic
39	D₄×C₉	—	2	48	no	—
40	C₂×C₄×C₉	—	2	12	no	—
41	C₂×C₄×C₉	—	2	12	no	—
42	C₂×C₄×C₉	—	4	16	no	—
43	C₂×C₄×C₉	C₂×D₄	1	12	yes	—
44	C₂×C₄×C₉	C₂×D₄	1	6	yes	—
45	C₂×C₄×D₄	C₂×C₉	1	6	yes	complemented
46	#399	C₂×C₉	1	4	yes	complemented
47	#392	C₂×C₉	1	4	yes	complemented
48	#376	C₂×C₉	1	1	yes	characteristic, complemented
49	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
50	C₂×C₃×D₄	—	2	24	no	—
51	C₂×C₃×D₄	—	2	12	no	—
52	C₂²×C₃×C₄	—	2	24	no	—
53	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
54	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
55	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
56	C₃×C₄⋊C₄	—	2	12	no	—
57	C₃×C₂²⋊C₄	—	2	24	no	—
58	C₃×C₄²	C₃×D₄	1	12	yes	—
59	C₂²×C₉	—	2	24	no	—
60	C₂²×C₉	—	4	12	no	—
61	C₂²×C₉	—	4	4	no	—
62	C₂²×C₉	C₂²×D₄	1	3	yes	—
63	C₂²×C₉	C₂×#41	1	4	yes	—
64	C₄×C₉	—	2	12	no	—
65	C₄×C₉	—	4	4	no	—
66	C₄×C₉	#127	1	4	yes	—
67	C₂²×D₄	C₂²×C₉	1	6	yes	—
68	C₂³×C₄	C₂²×C₉	1	4	yes	—
69	C₄×D₄	—	2	24	no	—
70	C₂×C₄⋊C₄	C₂²×C₉	1	6	yes	—
71	C₂×C₂²⋊C₄	C₂²×C₉	1	12	yes	—
72	C₂×C₄²	C₂²×C₉	1	3	yes	—
73	#95	C₂²×C₉	1	4	yes	—
74	C₂³×C₃	—	2	12	no	—
75	C₂³×C₃	—	2	12	no	—
76	C₂³×C₃	C₃×#41	1	8	yes	—
77	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
78	C₃×D₄	—	2	48	no	—
79	C₂×C₃×C₄	—	2	12	no	—
80	C₂×C₃×C₄	—	2	12	no	—
81	C₂×C₃×C₄	—	4	16	no	—
82	C₂×C₃×C₄	C₂×C₃×D₄	1	12	yes	—
83	C₂×C₃×C₄	C₂×C₃×D₄	1	6	yes	—
84	C₂×C₉	—	4	8	no	—
85	C₂×C₉	#525	1	6	yes	—
86	C₂×C₉	C₂×#127	1	1	yes	characteristic
87	C₂⁴	C₂³×C₉	1	4	yes	—
88	C₂×D₄	—	2	24	no	—
89	C₂×D₄	—	2	12	no	—
90	C₂²×C₄	—	2	24	no	—
91	C₂²×C₄	C₂³×C₉	1	4	yes	—
92	C₂²×C₄	C₂³×C₉	1	6	yes	—
93	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
94	C₄⋊C₄	—	2	12	no	—
95	C₂²⋊C₄	—	2	24	no	—
96	C₄²	D₄×C₉	1	12	yes	complemented
97	C₂²×C₃	—	2	24	no	—
98	C₂²×C₃	—	4	12	no	—
99	C₂²×C₃	—	4	4	no	—
100	C₂²×C₃	C₂²×C₃×D₄	1	3	yes	—
101	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
102	C₃×C₄	—	2	12	no	—
103	C₃×C₄	—	4	4	no	—
104	C₃×C₄	C₃×#127	1	4	yes	—
105	C₉	#2397	1	1	yes	characteristic, direct product factor, Sylow
106	C₂³	—	2	12	no	—
107	C₂³	—	2	12	no	—
108	C₂³	C₉×#41	1	8	yes	—
109	C₂³	C₂⁴×C₉	1	1	yes	characteristic
110	D₄	—	2	48	no	—
111	C₂×C₄	—	2	12	no	—
112	C₂×C₄	—	2	12	no	—
113	C₂×C₄	—	4	16	no	—
114	C₂×C₄	C₂×D₄×C₉	1	12	yes	—
115	C₂×C₄	C₂×D₄×C₉	1	6	yes	—
116	C₂×C₃	—	4	8	no	—
117	C₂×C₃	C₃×#525	1	6	yes	—
118	C₂×C₃	C₂×C₃×#127	1	1	yes	characteristic
119	C₂²	—	2	24	no	—
120	C₂²	—	4	12	no	—
121	C₂²	—	4	4	no	—
122	C₂²	C₂²×D₄×C₉	1	3	yes	—
123	C₂²	C₂×C₉×#41	1	4	yes	—
124	C₄	—	2	12	no	—
125	C₄	—	4	4	no	—
126	C₄	C₉×#127	1	4	yes	—
127	C₃	C₃×#2397	1	1	yes	characteristic
128	C₂	—	4	8	no	—
129	C₂	C₉×#525	1	6	yes	—
130	C₂	C₂×C₉×#127	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×D₄×C₉

C₂

yes

maximal, complemented

C₉×#399

C₂

yes

maximal, complemented

C₉×#392

C₂

yes

maximal, complemented

C₉×#376

C₂

yes

maximal, characteristic, complemented

C₃×#2397

C₃

yes

maximal, characteristic

C₂²×D₄×C₉

C₂²

yes

—

C₂³×C₄×C₉

C₂²

yes

—

C₄×D₄×C₉

—

C₂×C₉×C₄⋊C₄

C₂²

yes

—

C₂×C₉×C₂²⋊C₄

C₂²

yes

—

C₂×C₄²×C₉

C₂²

yes

—

C₉×#95

C₂²

yes

—

C₂×C₃×C₄×D₄

C₂×C₃

yes

—

C₃×#399

C₂×C₃

yes

—

C₃×#392

C₂×C₃

yes

—

C₃×#376

C₂×C₃

yes

characteristic

C₂⁴×C₉

C₂³

yes

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

C₂³

yes

—

C₂²×C₄×C₉

C₂³

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₉×C₄⋊C₄

—

C₉×C₂²⋊C₄

—

C₄²×C₉

D₄

yes

complemented

#2397

C₉

yes

characteristic, direct product factor, Sylow

C₂²×C₃×D₄

C₂²×C₃

yes

—

C₂³×C₃×C₄

C₂²×C₃

yes

—

C₃×C₄×D₄

—

C₂×C₃×C₄⋊C₄

C₂²×C₃

yes

—

C₂×C₃×C₂²⋊C₄

C₂²×C₃

yes

—

C₂×C₃×C₄²

C₂²×C₃

yes

—

C₃×#95

C₂²×C₃

yes

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

#41

yes

—

C₂³×C₉

C₂⁴

yes

characteristic

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×D₄

C₂×C₉

yes

complemented

#399

C₂×C₉

yes

complemented

#392

C₂×C₉

yes

complemented

#376

C₂×C₉

yes

characteristic, complemented

C₂⁴×C₃

C₂³×C₃

yes

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₂³×C₃

yes

—

C₂²×C₃×C₄

C₂³×C₃

yes

—

C₂²×C₃×C₄

C₂³×C₃

yes

characteristic

C₃×C₄⋊C₄

—

C₃×C₂²⋊C₄

—

C₃×C₄²

C₃×D₄

yes

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

C₂²×D₄

yes

—

C₂²×C₉

C₂×#41

yes

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

#127

yes

—

C₂²×D₄

C₂²×C₉

yes

—

C₂³×C₄

C₂²×C₉

yes

—

C₄×D₄

—

C₂×C₄⋊C₄

C₂²×C₉

yes

—

C₂×C₂²⋊C₄

C₂²×C₉

yes

—

C₂×C₄²

C₂²×C₉

yes

—

#95

C₂²×C₉

yes

—

C₂³×C₃

—

C₂³×C₃

—

C₂³×C₃

C₃×#41

yes

—

C₂³×C₃

C₂⁴×C₃

yes

characteristic

C₃×D₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂×C₃×D₄

yes

—

C₂×C₃×C₄

C₂×C₃×D₄

yes

—

C₂×C₉

—

C₂×C₉

#525

yes

—

C₂×C₉

C₂×#127

yes

characteristic

C₂⁴

C₂³×C₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂³×C₉

yes

—

C₂²×C₄

C₂³×C₉

yes

—

C₂²×C₄

C₂³×C₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

D₄×C₉

yes

complemented

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

—

100

C₂²×C₃

C₂²×C₃×D₄

yes

—

101

C₂²×C₃

C₂×C₃×#41

yes

—

102

C₃×C₄

—

103

C₃×C₄

—

104

C₃×C₄

C₃×#127

yes

—

105

C₉

#2397

yes

characteristic, direct product factor, Sylow

106

C₂³

—

107

C₂³

—

108

C₂³

C₉×#41

yes

—

109

C₂³

C₂⁴×C₉

yes

characteristic

110

D₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

C₂×D₄×C₉

yes

—

115

C₂×C₄

C₂×D₄×C₉

yes

—

116

C₂×C₃

—

117

C₂×C₃

C₃×#525

yes

—

118

C₂×C₃

C₂×C₃×#127

yes

characteristic

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

C₂²×D₄×C₉

yes

—

123

C₂²

C₂×C₉×#41

yes

—

124

C₄

—

125

C₄

—

126

C₄

C₉×#127

yes

—

127

C₃

C₃×#2397

yes

characteristic

128

C₂

—

129

C₂

C₉×#525

yes

—

130

C₂

C₂×C₉×#127

yes

characteristic

	subgroup	G/H
center	C₂²×C₄×C₉	C₂³
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₃×#2397	C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₉ ◁ G

subgroup

G/H

center

C₂²×C₄×C₉

C₂³

commutator

C₂³

C₂⁴×C₉

Frattini, socle, cosocle

C₂³×C₃

C₂⁴×C₃

C₃

G ▷ C₂³ ▷ C₁

C₁ ◁ C₂²×C₄×C₉ ◁ G

N	H ≅ G/N	type
1. C₂×C₄×D₄×C₉	C₂	semidirect
2. C₉×#399	C₂	semidirect
3. C₉×#392	C₂	semidirect
4. C₉×#376	C₂	semidirect
26. C₄²×C₉	D₄	semidirect
27. #2397	C₉	direct (N × H)
45. C₂×C₄×D₄	C₂×C₉	semidirect
46. #399	C₂×C₉	semidirect
47. #392	C₂×C₉	semidirect
48. #376	C₂×C₉	semidirect
96. C₄²	D₄×C₉	semidirect
105. C₉	#2397	direct (N × H)

H ≅ G/N

type

1. C₂×C₄×D₄×C₉

C₂

semidirect

2. C₉×#399

C₂

semidirect

3. C₉×#392

C₂

semidirect

4. C₉×#376

C₂

semidirect

26. C₄²×C₉

D₄

semidirect

27. #2397

C₉

direct (N × H)

45. C₂×C₄×D₄

C₂×C₉

semidirect

46. #399

C₂×C₉

semidirect

47. #392

C₂×C₉

semidirect

48. #376

C₂×C₉

semidirect

96. C₄²

D₄×C₉

semidirect

105. C₉

#2397

direct (N × H)

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

subgroup	index
C₂×C₄×D₄×C₉	2
C₉×#399	2
C₉×#392	2
C₉×#376	2
C₃×#2397	3

subgroup

index

C₂×C₄×D₄×C₉

Subgroups — C₉×#2397 #11767118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#2397 #11767118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2397 #11767118