Group #11807926 — subgroups

Subgroups — #11807926

Order 1152.

972 conjugacy classes of subgroups; only the 214 normal subgroups are shown.

normal subgroups only

This group has 972 conjugacy classes of subgroups — too many to draw. Only its 214 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×#63436	C₂	1	1	yes	maximal, characteristic
2	C₉×#383	C₂	1	1	yes	maximal, characteristic, complemented
3	#10588617	C₂	1	1	yes	maximal, characteristic, complemented
4	#10588345	C₂	1	12	yes	maximal, complemented
5	#74298	—	3	1	no	maximal
6	C₂²×D₃₆	C₂²	1	6	yes	—
7	C₂²×C₄×D₉	C₂²	1	4	yes	—
8	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
9	C₂×(C₂×D₉)⋊C₄	C₂²	1	12	yes	—
10	#63436	C₄	1	8	yes	complemented
11	C₉×#95	C₂²	1	6	yes	—
12	C₉⋊#95	C₂²	1	6	yes	—
13	C₂×#874	—	3	1	no	—
14	C₃×#383	D₃	1	1	yes	characteristic
15	#4937	—	3	1	no	—
16	#4665	—	3	12	no	—
17	C₂³×D₉	C₂³	1	4	yes	—
18	C₂²×C₄×C₉	C₂³	1	4	yes	—
19	C₂²×C₄×C₉	C₂³	1	3	yes	—
20	C₂²×Dic₉	C₂³	1	4	yes	—
21	C₂×D₃₆	—	4	6	no	—
22	C₂×D₃₆	—	4	6	no	—
23	C₂×D₃₆	C₂×C₄	1	24	yes	complemented
24	C₂×C₄×D₉	—	4	12	no	—
25	C₄²×C₉	C₂×C₄	1	4	yes	complemented
26	(C₂×D₉)⋊C₄	—	4	12	no	—
27	#2380	—	9	1	no	Sylow
28	C₂²×D₁₂	—	3	6	no	—
29	C₂²×C₄×D₃	—	3	4	no	—
30	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
31	C₂×(C₂×D₃)⋊C₄	—	3	12	no	—
32	#874	—	3	8	no	—
33	C₃×#95	C₂×D₃	1	6	yes	—
34	C₃⋊#95	—	3	6	no	—
35	C₂³×C₉	C₂⁴	1	1	yes	characteristic
36	C₂²×D₉	—	2	12	no	—
37	C₂²×D₉	—	2	12	no	—
38	C₂²×D₉	C₂²×C₄	1	8	yes	—
39	C₂×C₄×C₉	—	2	6	no	—
40	C₂×C₄×C₉	—	2	12	no	—
41	C₂×C₄×C₉	C₂²×C₄	1	6	yes	—
42	C₂×Dic₉	—	2	12	no	—
43	D₃₆	—	4	24	no	—
44	C₄×D₉	—	4	16	no	—
45	C₂×#127	—	9	1	no	—
46	#386	—	9	12	no	—
47	#383	—	9	1	no	—
48	#383	D₉	1	1	yes	characteristic, complemented
49	C₂³×D₃	—	3	4	no	—
50	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
51	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
52	C₂²×Dic₃	—	3	4	no	—
53	C₂×D₁₂	—	3	24	no	—
54	C₂×D₁₂	—	12	6	no	—
55	C₂×D₁₂	—	12	6	no	—
56	C₂×C₄×D₃	—	12	12	no	—
57	C₃×C₄²	C₄×D₃	1	4	yes	—
58	(C₂×D₃)⋊C₄	—	12	12	no	—
59	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
60	C₂²×C₉	H(5,𝔽₂)	1	6	yes	—
61	C₂×D₉	—	2	24	no	—
62	C₂×D₉	—	4	4	no	—
63	C₂×D₉	—	4	12	no	—
64	C₄×C₉	—	2	6	no	—
65	C₄×C₉	—	4	4	no	—
66	Dic₉	—	4	4	no	—
67	C₂²×D₄	—	9	6	no	—
68	C₂³×C₄	—	9	4	no	—
69	#127	—	9	8	no	—
70	C₂×C₂²⋊C₄	—	9	12	no	—
71	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
72	#95	—	9	6	no	—
73	#95	C₂×D₉	1	6	yes	—
74	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
75	C₂²×D₃	—	3	8	no	—
76	C₂²×D₃	—	6	12	no	—
77	C₂²×D₃	—	6	12	no	—
78	C₂×C₃×C₄	—	2	6	no	—
79	C₂×C₃×C₄	—	2	12	no	—
80	C₂×C₃×C₄	C₂×C₄×D₃	1	6	yes	—
81	C₂×Dic₃	—	6	12	no	—
82	D₁₂	—	12	24	no	—
83	C₄×D₃	—	12	16	no	—
84	C₂×C₉	#518	1	3	yes	—
85	C₂×C₉	#560	1	4	yes	—
86	D₉	—	4	8	no	—
87	C₂⁴	—	9	4	no	—
88	C₂×D₄	—	9	24	no	—
89	C₂×D₄	—	36	6	no	—
90	C₂×D₄	—	36	6	no	—
91	C₂²×C₄	—	9	4	no	—
92	C₂²×C₄	—	36	12	no	—
93	C₂²×C₄	C₂²×D₉	1	4	yes	—
94	C₂²×C₄	C₂²×D₉	1	3	yes	—
95	C₂²⋊C₄	—	36	12	no	—
96	C₄²	C₄×D₉	1	4	yes	complemented
97	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
98	C₂²×C₃	#1009	1	6	yes	—
99	C₂×D₃	—	6	24	no	—
100	C₂×D₃	—	12	4	no	—
101	C₂×D₃	—	12	12	no	—
102	C₃×C₄	—	2	6	no	—
103	C₃×C₄	—	4	4	no	—
104	Dic₃	—	12	4	no	—
105	C₉	#2380	1	1	yes	characteristic, complemented, Sylow
106	C₂³	—	9	8	no	—
107	C₂³	—	18	12	no	—
108	C₂³	—	18	12	no	—
109	C₂³	C₂³×D₉	1	1	yes	characteristic
110	D₄	—	36	24	no	—
111	C₂×C₄	—	2	6	no	—
112	C₂×C₄	—	2	12	no	—
113	C₂×C₄	—	18	12	no	—
114	C₂×C₄	—	36	16	no	—
115	C₂×C₄	C₂×C₄×D₉	1	6	yes	—
116	C₂×C₃	#5521	1	3	yes	—
117	C₂×C₃	#5711	1	4	yes	—
118	D₃	—	12	8	no	—
119	C₂²	—	18	24	no	—
120	C₂²	—	36	4	no	—
121	C₂²	—	36	12	no	—
122	C₂²	C₂²×C₄×D₉	1	1	yes	characteristic
123	C₂²	#63715	1	6	yes	—
124	C₄	—	2	6	no	—
125	C₄	—	4	4	no	—
126	C₄	—	36	4	no	—
127	C₃	#74298	1	1	yes	characteristic
128	C₂	—	36	8	no	—
129	C₂	#10589623	1	3	yes	—
130	C₂	#10589813	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#63436

C₂

yes

maximal, characteristic

C₉×#383

C₂

yes

maximal, characteristic, complemented

#10588617

C₂

yes

maximal, characteristic, complemented

#10588345

C₂

yes

maximal, complemented

#74298

—

maximal

C₂²×D₃₆

C₂²

yes

—

C₂²×C₄×D₉

C₂²

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₂×(C₂×D₉)⋊C₄

C₂²

yes

—

#63436

C₄

yes

complemented

C₉×#95

C₂²

yes

—

C₉⋊#95

C₂²

yes

—

C₂×#874

—

C₃×#383

D₃

yes

characteristic

#4937

—

#4665

—

C₂³×D₉

C₂³

yes

—

C₂²×C₄×C₉

C₂³

yes

—

C₂²×C₄×C₉

C₂³

yes

—

C₂²×Dic₉

C₂³

yes

—

C₂×D₃₆

—

C₂×D₃₆

—

C₂×D₃₆

C₂×C₄

yes

complemented

C₂×C₄×D₉

—

C₄²×C₉

C₂×C₄

yes

complemented

(C₂×D₉)⋊C₄

—

#2380

—

Sylow

C₂²×D₁₂

—

C₂²×C₄×D₃

—

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

C₂×(C₂×D₃)⋊C₄

—

#874

—

C₃×#95

C₂×D₃

yes

—

C₃⋊#95

—

C₂³×C₉

C₂⁴

yes

characteristic

C₂²×D₉

—

C₂²×D₉

—

C₂²×D₉

C₂²×C₄

yes

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂²×C₄

yes

—

C₂×Dic₉

—

D₃₆

—

C₄×D₉

—

—

—

—

D₉

yes

characteristic, complemented

C₂³×D₃

—

C₂²×C₃×C₄

C₂²×D₃

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

—

C₂²×Dic₃

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×C₄×D₃

—

C₃×C₄²

C₄×D₃

yes

—

(C₂×D₃)⋊C₄

—

C₂²×C₉

C₂³×C₄

yes

characteristic

C₂²×C₉

H(5,𝔽₂)

yes

—

C₂×D₉

—

C₂×D₉

—

C₂×D₉

—

C₄×C₉

—

C₄×C₉

—

Dic₉

—

C₂²×D₄

—

C₂³×C₄

—

#127

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₉

yes

characteristic

#95

—

#95

C₂×D₉

yes

—

C₂³×C₃

C₂³×D₃

yes

characteristic

C₂²×D₃

—

C₂²×D₃

—

C₂²×D₃

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂×C₄×D₃

yes

—

C₂×Dic₃

—

D₁₂

—

C₄×D₃

—

C₂×C₉

#518

yes

—

C₂×C₉

#560

yes

—

D₉

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₉

yes

—

C₂²×C₄

C₂²×D₉

yes

—

C₂²⋊C₄

—

C₄²

C₄×D₉

yes

complemented

C₂²×C₃

C₂²×C₄×D₃

yes

characteristic

C₂²×C₃

#1009

yes

—

C₂×D₃

—

100

C₂×D₃

—

101

C₂×D₃

—

102

C₃×C₄

—

103

C₃×C₄

—

104

Dic₃

—

105

C₉

#2380

yes

characteristic, complemented, Sylow

106

C₂³

—

107

C₂³

—

108

C₂³

—

109

C₂³

C₂³×D₉

yes

characteristic

110

D₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

C₂×C₄×D₉

yes

—

116

C₂×C₃

#5521

yes

—

117

C₂×C₃

#5711

yes

—

118

D₃

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

C₂²×C₄×D₉

yes

characteristic

123

C₂²

#63715

yes

—

124

C₄

—

125

C₄

—

126

C₄

—

127

C₃

#74298

yes

characteristic

128

C₂

—

129

C₂

#10589623

yes

—

130

C₂

#10589813

yes

—

	subgroup	G/H
center	C₂³	C₂³×D₉
commutator	C₂²×C₉	C₂³×C₄
Frattini, socle	C₂³×C₃	C₂³×D₃
Fitting	C₉×#383	C₂
prime radical	C₂×#63436	C₂
cosocle	C₂³×C₉	C₂⁴
hypercenter	#383	D₉
hypocenter	C₉	#2380
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ #383

subgroup

G/H

center

C₂³

C₂³×D₉

commutator

C₂²×C₉

C₂³×C₄

Frattini, socle

C₂³×C₃

C₂³×D₃

C₂

C₂

C₂³×C₉

C₂⁴

D₉

C₉

G ▷ C₂²×C₉ ▷ C₉

C₁ ◁ C₂³ ◁ #383

N	H ≅ G/N	type
2. C₉×#383	C₂	semidirect
3. #10588617	C₂	semidirect
4. #10588345	C₂	semidirect
10. #63436	C₄	semidirect
23. C₂×D₃₆	C₂×C₄	semidirect
25. C₄²×C₉	C₂×C₄	semidirect
48. #383	D₉	semidirect
96. C₄²	C₄×D₉	semidirect
105. C₉	#2380	semidirect

H ≅ G/N

type

2. C₉×#383

C₂

semidirect

3. #10588617

C₂

semidirect

4. #10588345

C₂

semidirect

10. #63436

C₄

semidirect

23. C₂×D₃₆

C₂×C₄

semidirect

25. C₄²×C₉

C₂×C₄

semidirect

48. #383

D₉

semidirect

96. C₄²

C₄×D₉

semidirect

105. C₉

#2380

semidirect

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

subgroup	index
C₂×#63436	2
C₉×#383	2
#10588617	2
#10588345	2
#74298	3

subgroup

index

Subgroups — #11807926

Conjugacy classes of subgroups

Complements

Maximal subgroups