Group #13135570 — subgroups

Subgroups — #10588207⋊C₃ #13135570

Order 1728.

340 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 124 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⋊C₄×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic
2	C₂×#3667⋊C₃	C₂	1	2	yes	maximal
3	C₃×#4530	—	3	1	no	maximal
4	#10588207	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₄×3₋¹⁺²	C₄	1	2	yes	—
6	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×3₋¹⁺²	—	2	2	no	—
8	#3667⋊C₃	—	2	2	no	—
9	#3667⋊C₃	C₄	1	4	yes	complemented
10	C₂×3₋¹⁺²⋊C₈	—	2	2	no	—
11	C₂×C₃²×C₄⋊C₄	D₃	1	1	yes	characteristic
12	C₂×C₃×#208	—	3	2	no	—
13	C₂×C₉×C₄⋊C₄	—	2	1	no	—
14	C₂×C₉×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
15	C₂×#3667	C₂×C₃	1	2	yes	—
16	C₂³×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×3₋¹⁺²	—	2	2	no	—
18	C₂×C₄×3₋¹⁺²	—	4	2	no	—
19	C₂×C₄×3₋¹⁺²	C₂×C₄	1	2	yes	—
20	C₂×C₄×3₋¹⁺²	D₄	1	1	yes	characteristic
21	C₂×C₄×3₋¹⁺²	D₄	1	2	yes	—
22	C₂×C₄×3₋¹⁺²	Q₈	1	1	yes	characteristic
23	3₋¹⁺²⋊C₈	—	2	4	no	—
24	C₃×#343	—	9	1	no	—
25	#4530	—	3	1	no	—
26	C₂²×C₃²×C₄	Dic₃	1	2	yes	—
27	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
28	C₃²×C₄⋊C₄	—	2	2	no	—
29	C₃×#208	—	3	4	no	—
30	C₃×#208	—	6	2	no	—
31	C₂×C₃×C₃⋊C₈	—	6	2	no	—
32	C₂²×C₄×C₉	—	2	1	no	—
33	C₂²×C₄×C₉	—	2	2	no	—
34	C₂²×C₄×C₉	C₃×C₄	1	2	yes	—
35	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
36	C₉×C₄⋊C₄	—	2	4	no	—
37	C₉×C₄⋊C₄	—	2	2	no	—
38	#3667	—	2	2	no	—
39	#3667	C₃×C₄	1	4	yes	complemented
40	C₂×C₉⋊C₈	—	2	2	no	—
41	C₂²×3₋¹⁺²	—	2	1	no	—
42	C₂²×3₋¹⁺²	—	2	1	no	—
43	C₂²×3₋¹⁺²	C₄²	1	1	yes	characteristic
44	C₂²×3₋¹⁺²	C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×3₋¹⁺²	C₄⋊C₄	1	1	yes	characteristic
46	C₄×3₋¹⁺²	—	4	2	no	—
47	C₄×3₋¹⁺²	C₂²⋊C₄	1	2	yes	—
48	C₄×3₋¹⁺²	C₄⋊C₄	1	2	yes	—
49	C₂×C₃×M₁₆	—	9	2	no	—
50	C₂×C₃×C₄⋊C₄	—	3	1	no	—
51	C₂×C₃×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic
52	C₂×#208	—	3	2	no	—
53	C₂³×C₃²	C₂×Dic₃	1	1	yes	characteristic
54	C₂×C₃²×C₄	—	2	2	no	—
55	C₂×C₃²×C₄	—	4	2	no	—
56	C₂×C₃²×C₄	Dic₆	1	1	yes	characteristic
57	C₂×C₃²×C₄	C₄×D₃	1	2	yes	—
58	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
59	C₂×C₃²×C₄	#67	1	2	yes	—
60	C₂³×C₉	—	2	1	no	—
61	C₂³×C₉	C₂×C₃×C₄	1	1	yes	characteristic
62	C₃×C₃⋊C₈	—	6	4	no	—
63	C₂×C₄×C₉	—	2	4	no	—
64	C₂×C₄×C₉	—	2	2	no	—
65	C₂×C₄×C₉	—	2	1	no	—
66	C₂×C₄×C₉	—	2	2	no	—
67	C₂×C₄×C₉	—	2	1	no	—
68	C₂×C₄×C₉	—	2	2	no	—
69	C₂×C₄×C₉	—	4	4	no	—
70	C₂×C₄×C₉	—	4	2	no	—
71	C₂×C₄×C₉	C₂×C₃×C₄	1	2	yes	—
72	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
73	C₂×C₄×C₉	C₃×D₄	1	2	yes	—
74	C₂×C₄×C₉	C₃×Q₈	1	1	yes	characteristic
75	C₉⋊C₈	—	2	4	no	—
76	#343	—	9	1	no	Sylow
77	C₂×3₋¹⁺²	—	2	1	no	—
78	C₂×3₋¹⁺²	—	2	1	no	—
79	C₂×3₋¹⁺²	#95	1	1	yes	characteristic
80	C₂×3₋¹⁺²	#100	1	1	yes	characteristic
81	C₂×3₋¹⁺²	#101	1	1	yes	characteristic
82	C₂²×C₃×C₄	—	3	2	no	—
83	C₂²×C₃×C₄	—	3	1	no	—
84	C₂²×C₃×C₄	C₃×Dic₃	1	2	yes	—
85	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
86	C₃×M₁₆	—	9	4	no	—
87	C₃×M₁₆	—	18	2	no	—
88	C₂×C₃×C₈	—	18	2	no	—
89	C₃×C₄⋊C₄	—	2	2	no	—
90	C₃×C₄⋊C₄	—	6	2	no	—
91	#208	—	3	4	no	—
92	#208	—	6	2	no	—
93	C₂×C₃⋊C₈	—	6	2	no	—
94	C₂²×C₃²	—	2	1	no	—
95	C₂²×C₃²	—	2	1	no	—
96	C₂²×C₃²	C₄×Dic₃	1	1	yes	characteristic
97	C₂²×C₃²	C₄⋊Dic₃	1	1	yes	characteristic
98	C₂²×C₃²	#217	1	1	yes	characteristic
99	C₃²×C₄	—	4	2	no	—
100	C₃²×C₄	Dic₃⋊C₄	1	2	yes	—
101	C₃²×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
102	C₂²×C₉	—	2	2	no	—
103	C₂²×C₉	—	2	2	no	—
104	C₂²×C₉	—	2	1	no	—
105	C₂²×C₉	—	2	1	no	—
106	C₂²×C₉	—	2	1	no	—
107	C₂²×C₉	—	2	1	no	—
108	C₂²×C₉	—	2	1	no	—
109	C₂²×C₉	C₃×C₄²	1	1	yes	characteristic
110	C₂²×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₉	C₃×C₄⋊C₄	1	1	yes	characteristic
112	C₄×C₉	—	2	2	no	—
113	C₄×C₉	—	2	2	no	—
114	C₄×C₉	—	4	4	no	—
115	C₄×C₉	—	4	2	no	—
116	C₄×C₉	C₃×C₂²⋊C₄	1	2	yes	—
117	C₄×C₉	C₃×C₄⋊C₄	1	2	yes	—
118	C₂×M₁₆	—	9	2	no	—
119	C₂×C₄⋊C₄	AGL(1,ℤ/9)	1	1	yes	characteristic
120	3₋¹⁺²	#343	1	1	yes	characteristic, complemented, Sylow
121	C₂³×C₃	—	3	1	no	—
122	C₂³×C₃	C₂×C₃×Dic₃	1	1	yes	characteristic
123	C₂×C₃×C₄	—	2	2	no	—
124	C₂×C₃×C₄	—	3	1	no	—
125	C₂×C₃×C₄	—	3	2	no	—
126	C₂×C₃×C₄	—	3	1	no	—
127	C₂×C₃×C₄	—	3	2	no	—
128	C₂×C₃×C₄	—	4	2	no	—
129	C₂×C₃×C₄	—	6	2	no	—
130	C₂×C₃×C₄	—	12	2	no	—
131	C₂×C₃×C₄	C₃×Dic₆	1	1	yes	characteristic
132	C₂×C₃×C₄	C₃×C₄×D₃	1	2	yes	—
133	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
134	C₂×C₃×C₄	C₃×#67	1	2	yes	—
135	C₃×C₈	—	18	4	no	—
136	C₃⋊C₈	—	6	4	no	—
137	C₂×C₃²	—	2	1	no	—
138	C₂×C₃²	—	2	1	no	—
139	C₂×C₃²	C₃⋊#95	1	1	yes	characteristic
140	C₂×C₃²	#833	1	1	yes	characteristic
141	C₂×C₃²	#836	1	1	yes	characteristic
142	C₂×C₉	—	2	2	no	—
143	C₂×C₉	—	2	2	no	—
144	C₂×C₉	—	2	1	no	—
145	C₂×C₉	—	2	1	no	—
146	C₂×C₉	—	2	1	no	—
147	C₂×C₉	—	2	1	no	—
148	C₂×C₉	—	2	1	no	—
149	C₂×C₉	C₃×#95	1	1	yes	characteristic
150	C₂×C₉	C₃×#100	1	1	yes	characteristic
151	C₂×C₉	C₃×#101	1	1	yes	characteristic
152	C₂²×C₄	3₋¹⁺²⋊C₄	1	2	yes	—
153	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
154	M₁₆	—	9	4	no	—
155	M₁₆	—	18	2	no	—
156	C₂×C₈	—	18	2	no	—
157	C₄⋊C₄	—	2	2	no	—
158	C₂²×C₃	—	2	1	no	—
159	C₂²×C₃	—	2	1	no	—
160	C₂²×C₃	—	3	1	no	—
161	C₂²×C₃	—	3	1	no	—
162	C₂²×C₃	—	3	1	no	—
163	C₂²×C₃	—	6	1	no	—
164	C₂²×C₃	—	6	1	no	—
165	C₂²×C₃	C₃×C₄×Dic₃	1	1	yes	characteristic
166	C₂²×C₃	C₃×C₄⋊Dic₃	1	1	yes	characteristic
167	C₂²×C₃	C₃×#217	1	1	yes	characteristic
168	C₃×C₄	—	3	2	no	—
169	C₃×C₄	—	3	2	no	—
170	C₃×C₄	—	4	2	no	—
171	C₃×C₄	—	12	2	no	—
172	C₃×C₄	C₃×Dic₃⋊C₄	1	2	yes	—
173	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
174	C₃²	#4530	1	1	yes	characteristic
175	C₉	—	2	1	no	—
176	C₉	C₃×#343	1	1	yes	characteristic, complemented
177	C₂³	C₂×3₋¹⁺²⋊C₄	1	1	yes	characteristic
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	4	2	no	—
180	C₂×C₄	3₋¹⁺²⋊Q₈	1	1	yes	characteristic
181	C₂×C₄	C₄×AGL(1,ℤ/9)	1	2	yes	—
182	C₂×C₄	C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
183	C₂×C₄	#611⋊C₃	1	2	yes	—
184	C₈	—	18	4	no	—
185	C₂×C₃	—	2	1	no	—
186	C₂×C₃	—	2	1	no	—
187	C₂×C₃	—	3	1	no	—
188	C₂×C₃	—	3	1	no	—
189	C₂×C₃	—	3	1	no	—
190	C₂×C₃	—	6	1	no	—
191	C₂×C₃	—	6	1	no	—
192	C₂×C₃	C₃×C₃⋊#95	1	1	yes	characteristic
193	C₂×C₃	C₃×#833	1	1	yes	characteristic
194	C₂×C₃	C₃×#836	1	1	yes	characteristic
195	C₂²	—	2	1	no	—
196	C₂²	—	2	1	no	—
197	C₂²	C₄×3₋¹⁺²⋊C₄	1	1	yes	characteristic
198	C₂²	C₄⋊(3₋¹⁺²⋊C₄)	1	1	yes	characteristic
199	C₂²	#3676⋊C₃	1	1	yes	characteristic
200	C₄	—	4	2	no	—
201	C₄	(3₋¹⁺²⋊C₄)⋊C₄	1	2	yes	—
202	C₄	(C₂×AGL(1,ℤ/9))⋊C₄	1	2	yes	—
203	C₃	—	3	1	no	—
204	C₃	C₃×#4530	1	1	yes	characteristic
205	C₂	—	2	1	no	—
206	C₂	—	2	1	no	—
207	C₂	3₋¹⁺²⋊#95	1	1	yes	characteristic
208	C₂	#63391⋊C₃	1	1	yes	characteristic
209	C₂	#63394⋊C₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊C₄×3₋¹⁺²

C₂

yes

maximal, characteristic

C₂×#3667⋊C₃

C₂

yes

—

C₃

yes

maximal, characteristic, complemented

C₂²×C₄×3₋¹⁺²

C₄

yes

—

C₂²×C₄×3₋¹⁺²

C₂²

yes

characteristic

C₄⋊C₄×3₋¹⁺²

—

#3667⋊C₃

—

#3667⋊C₃

C₄

yes

complemented

C₂×3₋¹⁺²⋊C₈

—

C₂×C₃²×C₄⋊C₄

D₃

yes

characteristic

C₂×C₃×#208

—

C₂×C₉×C₄⋊C₄

—

C₂×C₉×C₄⋊C₄

C₂×C₃

yes

characteristic

C₂×#3667

C₂×C₃

yes

—

C₂³×3₋¹⁺²

C₂×C₄

yes

characteristic

C₂×C₄×3₋¹⁺²

—

C₂×C₄×3₋¹⁺²

—

C₂×C₄×3₋¹⁺²

C₂×C₄

yes

—

C₂×C₄×3₋¹⁺²

D₄

yes

characteristic

C₂×C₄×3₋¹⁺²

D₄

yes

—

C₂×C₄×3₋¹⁺²

Q₈

yes

characteristic

3₋¹⁺²⋊C₈

—

C₃×#343

—

#4530

—

C₂²×C₃²×C₄

Dic₃

yes

—

C₂²×C₃²×C₄

C₂×D₃

yes

characteristic

C₃²×C₄⋊C₄

—

C₃×#208

—

C₃×#208

—

C₂×C₃×C₃⋊C₈

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

C₃×C₄

yes

—

C₂²×C₄×C₉

C₂²×C₃

yes

characteristic

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

—

#3667

—

#3667

C₃×C₄

yes

complemented

C₂×C₉⋊C₈

—

C₂²×3₋¹⁺²

—

C₂²×3₋¹⁺²

—

C₂²×3₋¹⁺²

C₄²

yes

characteristic

C₂²×3₋¹⁺²

C₂²⋊C₄

yes

characteristic

C₂²×3₋¹⁺²

C₄⋊C₄

yes

characteristic

C₄×3₋¹⁺²

—

C₄×3₋¹⁺²

C₂²⋊C₄

yes

—

C₄×3₋¹⁺²

C₄⋊C₄

yes

—

C₂×C₃×M₁₆

—

C₂×C₃×C₄⋊C₄

—

C₂×C₃×C₄⋊C₄

C₃×D₃

yes

characteristic

C₂×#208

—

C₂³×C₃²

C₂×Dic₃

yes

characteristic

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

Dic₆

yes

characteristic

C₂×C₃²×C₄

C₄×D₃

yes

—

C₂×C₃²×C₄

D₁₂

yes

characteristic

C₂×C₃²×C₄

#67

yes

—

C₂³×C₉

—

C₂³×C₉

C₂×C₃×C₄

yes

characteristic

C₃×C₃⋊C₈

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂×C₃×C₄

yes

—

C₂×C₄×C₉

C₃×D₄

yes

characteristic

C₂×C₄×C₉

C₃×D₄

yes

—

C₂×C₄×C₉

C₃×Q₈

yes

characteristic

C₉⋊C₈

—

#343

—

Sylow

C₂×3₋¹⁺²

—

C₂×3₋¹⁺²

—

C₂×3₋¹⁺²

yes

C₂×3₋¹⁺²

yes

C₂×3₋¹⁺²

yes

C₂²×C₃×C₄

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₃×Dic₃

yes

—

C₂²×C₃×C₄

C₂×C₃×D₃

yes

characteristic

C₃×M₁₆

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

#208

—

#208

—

C₂×C₃⋊C₈

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

C₄×Dic₃

yes

characteristic

C₂²×C₃²

C₄⋊Dic₃

yes

characteristic

C₂²×C₃²

#217

yes

characteristic

C₃²×C₄

—

100

C₃²×C₄

Dic₃⋊C₄

yes

—

101

C₃²×C₄

(C₂×D₃)⋊C₄

yes

—

102

C₂²×C₉

—

103

C₂²×C₉

—

104

C₂²×C₉

—

105

C₂²×C₉

—

106

C₂²×C₉

—

107

C₂²×C₉

—

108

C₂²×C₉

—

109

C₂²×C₉

C₃×C₄²

yes

characteristic

110

C₂²×C₉

C₃×C₂²⋊C₄

yes

characteristic

111

C₂²×C₉

C₃×C₄⋊C₄

yes

characteristic

112

C₄×C₉

—

113

C₄×C₉

—

114

C₄×C₉

—

115

C₄×C₉

—

116

C₄×C₉

C₃×C₂²⋊C₄

yes

—

117

C₄×C₉

C₃×C₄⋊C₄

yes

—

118

C₂×M₁₆

—

119

C₂×C₄⋊C₄

AGL(1,ℤ/9)

yes

characteristic

120

3₋¹⁺²

#343

yes

characteristic, complemented, Sylow

121

C₂³×C₃

—

122

C₂³×C₃

C₂×C₃×Dic₃

yes

characteristic

123

C₂×C₃×C₄

—

124

C₂×C₃×C₄

—

125

C₂×C₃×C₄

—

126

C₂×C₃×C₄

—

127

C₂×C₃×C₄

—

128

C₂×C₃×C₄

—

129

C₂×C₃×C₄

—

130

C₂×C₃×C₄

—

131

C₂×C₃×C₄

C₃×Dic₆

yes

characteristic

132

C₂×C₃×C₄

C₃×C₄×D₃

yes

—

133

C₂×C₃×C₄

C₃×D₁₂

yes

characteristic

134

C₂×C₃×C₄

C₃×#67

yes

—

135

C₃×C₈

—

136

C₃⋊C₈

—

137

C₂×C₃²

—

138

C₂×C₃²

—

139

C₂×C₃²

C₃⋊#95

yes

characteristic

140

C₂×C₃²

#833

yes

characteristic

141

C₂×C₃²

#836

yes

characteristic

142

C₂×C₉

—

143

C₂×C₉

—

144

C₂×C₉

—

145

C₂×C₉

—

146

C₂×C₉

—

147

C₂×C₉

—

148

C₂×C₉

—

149

C₂×C₉

C₃×#95

yes

characteristic

150

C₂×C₉

C₃×#100

yes

characteristic

151

C₂×C₉

C₃×#101

yes

characteristic

152

C₂²×C₄

3₋¹⁺²⋊C₄

yes

—

153

C₂²×C₄

C₂×AGL(1,ℤ/9)

yes

characteristic

154

M₁₆

—

155

M₁₆

—

156

C₂×C₈

—

157

C₄⋊C₄

—

158

C₂²×C₃

—

159

C₂²×C₃

—

160

C₂²×C₃

—

161

C₂²×C₃

—

162

C₂²×C₃

—

163

C₂²×C₃

—

164

C₂²×C₃

—

165

C₂²×C₃

C₃×C₄×Dic₃

yes

characteristic

166

C₂²×C₃

C₃×C₄⋊Dic₃

yes

characteristic

167

C₂²×C₃

C₃×#217

yes

characteristic

168

C₃×C₄

—

169

C₃×C₄

—

170

C₃×C₄

—

171

C₃×C₄

—

172

C₃×C₄

C₃×Dic₃⋊C₄

yes

—

173

C₃×C₄

C₃×(C₂×D₃)⋊C₄

yes

—

174

C₃²

#4530

yes

characteristic

175

C₉

—

176

C₉

C₃×#343

yes

characteristic, complemented

177

C₂³

C₂×3₋¹⁺²⋊C₄

yes

characteristic

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

3₋¹⁺²⋊Q₈

yes

characteristic

181

C₂×C₄

C₄×AGL(1,ℤ/9)

yes

—

182

C₂×C₄

C₄⋊AGL(1,ℤ/9)

yes

characteristic

183

C₂×C₄

#611⋊C₃

yes

—

184

C₈

—

185

C₂×C₃

—

186

C₂×C₃

—

187

C₂×C₃

—

188

C₂×C₃

—

189

C₂×C₃

—

190

C₂×C₃

—

191

C₂×C₃

—

192

C₂×C₃

C₃×C₃⋊#95

yes

characteristic

193

C₂×C₃

C₃×#833

yes

characteristic

194

C₂×C₃

C₃×#836

yes

characteristic

195

C₂²

—

196

C₂²

—

197

C₂²

C₄×3₋¹⁺²⋊C₄

yes

characteristic

198

C₂²

C₄⋊(3₋¹⁺²⋊C₄)

yes

characteristic

199

C₂²

#3676⋊C₃

yes

characteristic

200

C₄

—

201

C₄

(3₋¹⁺²⋊C₄)⋊C₄

yes

—

202

C₄

(C₂×AGL(1,ℤ/9))⋊C₄

yes

—

203

C₃

—

204

C₃

C₃×#4530

yes

characteristic

205

C₂

—

206

C₂

—

207

C₂

3₋¹⁺²⋊#95

yes

characteristic

208

C₂

#63391⋊C₃

yes

characteristic

209

C₂

#63394⋊C₃

yes

characteristic

	subgroup	G/H
center	C₂²	#3676⋊C₃
commutator	C₂²×C₉	C₃×C₄²
Frattini	C₂²×C₃×C₄	C₂×C₃×D₃
Fitting	C₂×C₄⋊C₄×3₋¹⁺²	C₂
socle	C₂²×C₃	C₃×#217
prime radical	C₂³×C₃²	C₂×Dic₃
cosocle	C₂²×C₄×C₉	C₂²×C₃
hypercenter	C₂×C₄⋊C₄	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#343
LCS	G ▷ C₂²×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

subgroup

G/H

center

C₂²

#3676⋊C₃

commutator

C₂²×C₉

C₃×C₄²

Frattini

C₂²×C₃×C₄

C₂×C₃×D₃

Fitting

C₂×C₄⋊C₄×3₋¹⁺²

C₂

socle

C₂²×C₃

C₃×#217

prime radical

C₂³×C₃²

C₂×Dic₃

cosocle

C₂²×C₄×C₉

C₂²×C₃

C₂×C₄⋊C₄

C₉

G ▷ C₂²×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
4. #10588207	C₃	semidirect
9. #3667⋊C₃	C₄	semidirect
39. #3667	C₃×C₄	semidirect
120. 3₋¹⁺²	#343	semidirect
176. C₉	C₃×#343	semidirect

H ≅ G/N

type

4. #10588207

C₃

semidirect

9. #3667⋊C₃

C₄

semidirect

39. #3667

C₃×C₄

semidirect

120. 3₋¹⁺²

#343

semidirect

176. C₉

C₃×#343

semidirect

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

subgroup	index
C₂×C₄⋊C₄×3₋¹⁺²	2
C₂×#3667⋊C₃	2
C₃×#4530	3
#10588207	3

subgroup

index

C₂×C₄⋊C₄×3₋¹⁺²

C₂×#3667⋊C₃

C₃×#4530

#10588207

Subgroups — #10588207⋊C₃ #13135570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10588207⋊C3 #13135570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10588207⋊C₃ #13135570