Group #13141542 — subgroups

Subgroups — #10588395⋊C₃ #13141542

Order 1728.

320 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 92 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	#63437⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#63431⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	3₋¹⁺²×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	#63380⋊C₃	C₂	1	2	yes	maximal
5	#63376⋊C₃	C₂	1	2	yes	maximal, complemented
6	C₃×#4714	—	3	1	no	maximal
7	#10588395	C₃	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
9	C₂×3₋¹⁺²⋊Q₈	—	2	1	no	—
10	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₈×3₋¹⁺²	C₂²	1	2	yes	—
12	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
13	(C₂×AGL(1,ℤ/9))⋊C₄	—	2	1	no	—
14	(C₂×AGL(1,ℤ/9))⋊C₄	—	2	1	no	—
15	C₄⋊(3₋¹⁺²⋊C₄)	—	2	1	no	—
16	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	2	yes	—
17	C₃×#875	—	3	1	no	—
18	C₃×#869	—	3	1	no	—
19	C₃²×#97	D₃	1	1	yes	characteristic
20	C₃×#821	—	3	2	no	—
21	C₃×#816	—	3	2	no	—
22	#63437	C₂×C₃	1	1	yes	characteristic
23	#63431	C₂×C₃	1	1	yes	characteristic, complemented
24	C₉×#97	—	2	1	no	—
25	C₉×#97	C₂×C₃	1	1	yes	characteristic, complemented
26	#63380	C₂×C₃	1	2	yes	—
27	#63376	C₂×C₃	1	2	yes	complemented
28	C₂²×AGL(1,ℤ/9)	—	2	1	no	—
29	C₂×C₄×3₋¹⁺²	D₄	1	1	yes	characteristic
30	C₂×C₄×3₋¹⁺²	D₄	1	1	yes	characteristic
31	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
32	C₂×3₋¹⁺²⋊C₄	—	2	2	no	—
33	C₂×3₋¹⁺²⋊C₄	—	2	1	no	—
34	C₄⋊AGL(1,ℤ/9)	—	2	2	no	—
35	3₋¹⁺²⋊Q₈	—	2	2	no	—
36	3₋¹⁺²⋊Q₈	—	4	2	no	—
37	C₈×3₋¹⁺²	—	2	2	no	—
38	C₃×#489	—	9	1	no	—
39	#4714	—	3	1	no	—
40	C₂×C₃×D₁₂	—	3	1	no	—
41	C₂×C₃×Dic₆	—	3	1	no	—
42	C₂×C₃×Dic₆	—	6	1	no	—
43	C₂×C₃²×C₈	C₂×D₃	1	2	yes	—
44	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
45	C₃×(C₂×D₃)⋊C₄	—	6	1	no	—
46	C₃×(C₂×D₃)⋊C₄	—	6	1	no	—
47	C₃×C₄⋊Dic₃	—	3	2	no	—
48	C₃×C₄⋊Dic₃	—	6	1	no	—
49	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
50	C₂×Dic₁₈	—	2	1	no	—
51	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
52	C₂×C₈×C₉	—	2	2	no	—
53	C₂×C₈×C₉	C₂²×C₃	1	2	yes	—
54	C₄²×C₉	—	2	1	no	—
55	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
56	(C₂×D₉)⋊C₄	—	2	1	no	—
57	(C₂×D₉)⋊C₄	—	2	1	no	—
58	C₄⋊Dic₉	—	2	1	no	—
59	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
60	C₂²×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
61	C₂×AGL(1,ℤ/9)	—	4	1	no	—
62	C₂×AGL(1,ℤ/9)	—	4	1	no	—
63	C₂×AGL(1,ℤ/9)	—	4	1	no	—
64	C₄×3₋¹⁺²	—	2	1	no	—
65	C₄×3₋¹⁺²	—	2	1	no	—
66	C₄×3₋¹⁺²	#41	1	2	yes	—
67	3₋¹⁺²⋊C₄	—	4	1	no	—
68	3₋¹⁺²⋊C₄	—	4	2	no	—
69	C₃×C₄⋊Q₈	—	9	1	no	—
70	C₃×#124	—	9	1	no	—
71	#875	—	3	1	no	—
72	#869	—	3	1	no	—
73	C₃×#103	—	9	2	no	—
74	C₃×#102	—	9	2	no	—
75	C₃×#97	—	3	1	no	—
76	C₃×#97	C₃×D₃	1	1	yes	characteristic
77	#821	—	3	2	no	—
78	#816	—	3	2	no	—
79	C₂²×C₃×D₃	—	6	1	no	—
80	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
81	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
82	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
83	C₂×C₃×Dic₃	—	6	2	no	—
84	C₂×C₃×Dic₃	—	6	1	no	—
85	C₃×D₁₂	—	6	2	no	—
86	C₃×Dic₆	—	6	2	no	—
87	C₃×Dic₆	—	12	2	no	—
88	C₂²×D₉	—	2	1	no	—
89	C₃²×C₈	—	2	2	no	—
90	C₂×C₄×C₉	—	2	1	no	—
91	C₂×C₄×C₉	—	2	1	no	—
92	C₂×C₄×C₉	—	2	1	no	—
93	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
94	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
95	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
96	C₂×Dic₉	—	2	2	no	—
97	C₂×Dic₉	—	2	1	no	—
98	D₃₆	—	2	2	no	—
99	Dic₁₈	—	2	2	no	—
100	Dic₁₈	—	4	2	no	—
101	C₈×C₉	—	2	4	no	—
102	C₈×C₉	—	2	2	no	—
103	#489	—	9	1	no	Sylow
104	C₂×3₋¹⁺²	#124	1	1	yes	characteristic
105	C₂×3₋¹⁺²	AGL(1,ℤ/8)	1	1	yes	characteristic
106	C₂×3₋¹⁺²	#137	1	1	yes	characteristic
107	AGL(1,ℤ/9)	—	8	1	no	—
108	C₂×C₃×Q₈	—	9	1	no	—
109	C₂×C₃×Q₈	—	18	1	no	—
110	C₂×C₃×D₄	—	9	1	no	—
111	C₂×D₁₂	—	3	1	no	—
112	C₂×Dic₆	—	3	1	no	—
113	C₂×Dic₆	—	6	1	no	—
114	C₂×C₃×C₈	—	3	2	no	—
115	C₂×C₃×C₈	C₂×C₃×D₃	1	2	yes	—
116	C₃×C₄⋊C₄	—	9	2	no	—
117	C₃×C₄⋊C₄	—	18	1	no	—
118	C₃×C₂²⋊C₄	—	18	1	no	—
119	C₃×C₂²⋊C₄	—	18	1	no	—
120	C₃×C₄²	—	3	1	no	—
121	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
122	(C₂×D₃)⋊C₄	—	6	1	no	—
123	(C₂×D₃)⋊C₄	—	6	1	no	—
124	C₄⋊Dic₃	—	3	2	no	—
125	C₄⋊Dic₃	—	6	1	no	—
126	C₂²×C₃²	C₂×D₁₂	1	1	yes	characteristic
127	C₂×C₃×D₃	—	12	1	no	—
128	C₂×C₃×D₃	—	12	1	no	—
129	C₂×C₃×D₃	—	12	1	no	—
130	C₃²×C₄	—	2	1	no	—
131	C₃²×C₄	—	2	1	no	—
132	C₃²×C₄	#235	1	2	yes	—
133	C₃×Dic₃	—	12	1	no	—
134	C₃×Dic₃	—	12	2	no	—
135	C₂²×C₉	—	2	1	no	—
136	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
137	C₂×D₉	—	4	1	no	—
138	C₂×D₉	—	4	1	no	—
139	C₂×D₉	—	4	1	no	—
140	C₄×C₉	—	2	1	no	—
141	C₄×C₉	—	2	1	no	—
142	C₄×C₉	—	2	2	no	—
143	C₄×C₉	—	4	1	no	—
144	C₄×C₉	—	4	1	no	—
145	C₄×C₉	C₃×#41	1	2	yes	—
146	Dic₉	—	4	1	no	—
147	Dic₉	—	4	2	no	—
148	C₄⋊Q₈	—	9	1	no	—
149	#124	—	9	1	no	—
150	#103	—	9	2	no	—
151	#102	—	9	2	no	—
152	#97	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
153	3₋¹⁺²	#489	1	1	yes	characteristic, complemented, Sylow
154	C₂³×C₃	—	18	1	no	—
155	C₂²×D₃	—	6	1	no	—
156	C₃×Q₈	—	18	2	no	—
157	C₃×Q₈	—	36	2	no	—
158	C₃×D₄	—	18	2	no	—
159	C₂×C₃×C₄	—	3	1	no	—
160	C₂×C₃×C₄	—	3	1	no	—
161	C₂×C₃×C₄	—	3	1	no	—
162	C₂×C₃×C₄	—	18	1	no	—
163	C₂×C₃×C₄	—	18	2	no	—
164	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
165	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
166	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
167	C₂×Dic₃	—	6	2	no	—
168	C₂×Dic₃	—	6	1	no	—
169	D₁₂	—	6	2	no	—
170	Dic₆	—	6	2	no	—
171	Dic₆	—	12	2	no	—
172	C₃×C₈	—	2	2	no	—
173	C₃×C₈	—	6	2	no	—
174	C₂×C₃²	#875	1	1	yes	characteristic
175	C₂×C₃²	#908	1	1	yes	characteristic
176	C₂×C₃²	#909	1	1	yes	characteristic
177	C₃×D₃	—	24	1	no	—
178	C₂×C₉	—	2	1	no	—
179	C₂×C₉	—	2	1	no	—
180	C₂×C₉	—	2	1	no	—
181	C₂×C₉	C₃×#124	1	1	yes	characteristic
182	C₂×C₉	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂×C₉	C₃×#137	1	1	yes	characteristic
184	D₉	—	8	1	no	—
185	C₂×Q₈	—	9	1	no	—
186	C₂×Q₈	—	18	1	no	—
187	C₂×D₄	—	9	1	no	—
188	C₂×C₈	C₂×AGL(1,ℤ/9)	1	2	yes	—
189	C₄⋊C₄	—	9	2	no	—
190	C₄⋊C₄	—	18	1	no	—
191	C₂²⋊C₄	—	18	1	no	—
192	C₂²⋊C₄	—	18	1	no	—
193	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
194	C₂²×C₃	—	3	1	no	—
195	C₂²×C₃	—	36	1	no	—
196	C₂²×C₃	—	36	1	no	—
197	C₂²×C₃	—	36	1	no	—
198	C₂²×C₃	C₂×C₃×D₁₂	1	1	yes	characteristic
199	C₂×D₃	—	12	1	no	—
200	C₂×D₃	—	12	1	no	—
201	C₂×D₃	—	12	1	no	—
202	C₃×C₄	—	2	1	no	—
203	C₃×C₄	—	2	1	no	—
204	C₃×C₄	—	3	2	no	—
205	C₃×C₄	—	6	1	no	—
206	C₃×C₄	—	6	1	no	—
207	C₃×C₄	—	36	1	no	—
208	C₃×C₄	—	36	2	no	—
209	C₃×C₄	C₃×#235	1	2	yes	—
210	Dic₃	—	12	2	no	—
211	Dic₃	—	12	1	no	—
212	C₃²	#4714	1	1	yes	characteristic
213	C₉	—	2	1	no	—
214	C₉	C₃×#489	1	1	yes	characteristic, complemented
215	C₂³	—	18	1	no	—
216	Q₈	—	18	2	no	—
217	Q₈	—	36	2	no	—
218	D₄	—	18	2	no	—
219	C₂×C₄	—	18	1	no	—
220	C₂×C₄	—	18	2	no	—
221	C₂×C₄	C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
222	C₂×C₄	C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
223	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
224	C₈	—	2	2	no	—
225	C₂×C₃	—	3	1	no	—
226	C₂×C₃	—	3	1	no	—
227	C₂×C₃	—	3	1	no	—
228	C₂×C₃	—	72	1	no	—
229	C₂×C₃	C₃×#875	1	1	yes	characteristic
230	C₂×C₃	C₃×#908	1	1	yes	characteristic
231	C₂×C₃	C₃×#909	1	1	yes	characteristic
232	D₃	—	24	1	no	—
233	C₂²	—	36	1	no	—
234	C₂²	—	36	1	no	—
235	C₂²	—	36	1	no	—
236	C₂²	C₂×C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
237	C₄	—	2	1	no	—
238	C₄	—	2	1	no	—
239	C₄	—	36	2	no	—
240	C₄	—	36	1	no	—
241	C₄	#3697⋊C₃	1	2	yes	—
242	C₃	—	3	1	no	—
243	C₃	C₃×#4714	1	1	yes	characteristic
244	C₂	—	72	1	no	—
245	C₂	#63437⋊C₃	1	1	yes	characteristic
246	C₂	#63470⋊C₃	1	1	yes	characteristic
247	C₂	#63471⋊C₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#63437⋊C₃

C₂

yes

maximal, characteristic

#63431⋊C₃

C₂

yes

maximal, characteristic, complemented

3₋¹⁺²×#97

C₂

yes

maximal, characteristic, complemented

#63380⋊C₃

C₂

yes

maximal

#63376⋊C₃

C₂

yes

maximal, complemented

C₃×#4714

—

maximal

#10588395

C₃

yes

maximal, characteristic, complemented

C₂×C₄⋊AGL(1,ℤ/9)

C₂²

yes

characteristic

C₂×3₋¹⁺²⋊Q₈

—

C₂×3₋¹⁺²⋊Q₈

C₂²

yes

characteristic

C₂×C₈×3₋¹⁺²

C₂²

yes

—

C₄²×3₋¹⁺²

C₂²

yes

characteristic

(C₂×AGL(1,ℤ/9))⋊C₄

—

(C₂×AGL(1,ℤ/9))⋊C₄

—

C₄⋊(3₋¹⁺²⋊C₄)

—

C₄⋊(3₋¹⁺²⋊C₄)

C₂²

yes

—

C₃×#875

—

C₃×#869

—

C₃²×#97

D₃

yes

—

—

C₂×C₃

yes

characteristic

#63431

C₂×C₃

yes

characteristic, complemented

C₉×#97

—

C₉×#97

C₂×C₃

yes

characteristic, complemented

#63380

C₂×C₃

yes

—

#63376

C₂×C₃

yes

complemented

C₂²×AGL(1,ℤ/9)

—

C₂×C₄×3₋¹⁺²

D₄

yes

characteristic

C₂×C₄×3₋¹⁺²

D₄

yes

characteristic

C₂×C₄×3₋¹⁺²

C₂³

yes

characteristic

C₂×3₋¹⁺²⋊C₄

—

C₂×3₋¹⁺²⋊C₄

—

C₄⋊AGL(1,ℤ/9)

—

3₋¹⁺²⋊Q₈

—

3₋¹⁺²⋊Q₈

—

C₈×3₋¹⁺²

—

C₃×#489

—

#4714

—

C₂×C₃×D₁₂

—

C₂×C₃×Dic₆

—

C₂×C₃×Dic₆

—

C₂×C₃²×C₈

C₂×D₃

yes

—

C₃²×C₄²

C₂×D₃

yes

characteristic

C₃×(C₂×D₃)⋊C₄

—

C₃×(C₂×D₃)⋊C₄

—

C₃×C₄⋊Dic₃

—

C₃×C₄⋊Dic₃

—

C₂×D₃₆

C₂²×C₃

yes

characteristic

C₂×Dic₁₈

—

C₂×Dic₁₈

C₂²×C₃

yes

characteristic

C₂×C₈×C₉

—

C₂×C₈×C₉

C₂²×C₃

yes

—

C₄²×C₉

—

C₄²×C₉

C₂²×C₃

yes

characteristic

(C₂×D₉)⋊C₄

—

(C₂×D₉)⋊C₄

—

C₄⋊Dic₉

—

C₄⋊Dic₉

C₂²×C₃

yes

—

C₂²×3₋¹⁺²

C₂×D₄

yes

—

—

—

C₄×3₋¹⁺²

—

C₄×3₋¹⁺²

—

C₄×3₋¹⁺²

#41

yes

—

3₋¹⁺²⋊C₄

—

3₋¹⁺²⋊C₄

—

C₃×C₄⋊Q₈

—

—

—

—

—

—

C₃×#97

—

C₃×#97

C₃×D₃

yes

characteristic

#821

—

#816

—

C₂²×C₃×D₃

—

C₂×C₃²×C₄

D₁₂

yes

characteristic

C₂×C₃²×C₄

D₁₂

yes

characteristic

C₂×C₃²×C₄

C₂²×D₃

yes

characteristic

C₂×C₃×Dic₃

—

C₂×C₃×Dic₃

—

C₃×D₁₂

—

C₃×Dic₆

—

C₃×Dic₆

—

C₂²×D₉

—

C₃²×C₈

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₃×D₄

yes

characteristic

C₂×C₄×C₉

C₃×D₄

yes

characteristic

C₂×C₄×C₉

C₂³×C₃

yes

characteristic

C₂×Dic₉

—

C₂×Dic₉

—

D₃₆

—

Dic₁₈

—

100

Dic₁₈

—

101

C₈×C₉

—

102

C₈×C₉

—

103

#489

—

Sylow

104

C₂×3₋¹⁺²

#124

yes

characteristic

105

C₂×3₋¹⁺²

AGL(1,ℤ/8)

yes

characteristic

106

C₂×3₋¹⁺²

#137

yes

characteristic

107

AGL(1,ℤ/9)

—

108

C₂×C₃×Q₈

—

109

C₂×C₃×Q₈

—

110

C₂×C₃×D₄

—

111

C₂×D₁₂

—

112

C₂×Dic₆

—

113

C₂×Dic₆

—

114

C₂×C₃×C₈

—

115

C₂×C₃×C₈

C₂×C₃×D₃

yes

—

116

C₃×C₄⋊C₄

—

117

C₃×C₄⋊C₄

—

118

C₃×C₂²⋊C₄

—

119

C₃×C₂²⋊C₄

—

120

C₃×C₄²

—

121

C₃×C₄²

C₂×C₃×D₃

yes

characteristic

122

(C₂×D₃)⋊C₄

—

123

(C₂×D₃)⋊C₄

—

124

C₄⋊Dic₃

—

125

C₄⋊Dic₃

—

126

C₂²×C₃²

C₂×D₁₂

yes

characteristic

127

C₂×C₃×D₃

—

128

C₂×C₃×D₃

—

129

C₂×C₃×D₃

—

130

C₃²×C₄

—

131

C₃²×C₄

—

132

C₃²×C₄

#235

yes

—

133

C₃×Dic₃

—

134

C₃×Dic₃

—

135

C₂²×C₉

—

136

C₂²×C₉

C₂×C₃×D₄

yes

characteristic

137

C₂×D₉

—

138

C₂×D₉

—

139

C₂×D₉

—

140

C₄×C₉

—

141

C₄×C₉

—

142

C₄×C₉

—

143

C₄×C₉

—

144

C₄×C₉

—

145

C₄×C₉

C₃×#41

yes

—

146

Dic₉

—

147

Dic₉

—

148

C₄⋊Q₈

—

149

#124

—

150

#103

—

151

#102

—

152

#97

AGL(1,ℤ/9)

yes

characteristic, complemented

153

3₋¹⁺²

#489

yes

characteristic, complemented, Sylow

154

C₂³×C₃

—

155

C₂²×D₃

—

156

C₃×Q₈

—

157

C₃×Q₈

—

158

C₃×D₄

—

159

C₂×C₃×C₄

—

160

C₂×C₃×C₄

—

161

C₂×C₃×C₄

—

162

C₂×C₃×C₄

—

163

C₂×C₃×C₄

—

164

C₂×C₃×C₄

C₃×D₁₂

yes

characteristic

165

C₂×C₃×C₄

C₃×D₁₂

yes

characteristic

166

C₂×C₃×C₄

C₂²×C₃×D₃

yes

characteristic

167

C₂×Dic₃

—

168

C₂×Dic₃

—

169

D₁₂

—

170

Dic₆

—

171

Dic₆

—

172

C₃×C₈

—

173

C₃×C₈

—

174

C₂×C₃²

#875

yes

characteristic

175

C₂×C₃²

#908

yes

characteristic

176

C₂×C₃²

#909

yes

characteristic

177

C₃×D₃

—

178

C₂×C₉

—

179

C₂×C₉

—

180

C₂×C₉

—

181

C₂×C₉

C₃×#124

yes

characteristic

182

C₂×C₉

C₃×AGL(1,ℤ/8)

yes

characteristic

183

C₂×C₉

C₃×#137

yes

characteristic

184

D₉

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×D₄

—

188

C₂×C₈

C₂×AGL(1,ℤ/9)

yes

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₂²⋊C₄

—

192

C₂²⋊C₄

—

193

C₄²

C₂×AGL(1,ℤ/9)

yes

characteristic

194

C₂²×C₃

—

195

C₂²×C₃

—

196

C₂²×C₃

—

197

C₂²×C₃

—

198

C₂²×C₃

C₂×C₃×D₁₂

yes

characteristic

199

C₂×D₃

—

200

C₂×D₃

—

201

C₂×D₃

—

202

C₃×C₄

—

203

C₃×C₄

—

204

C₃×C₄

—

205

C₃×C₄

—

206

C₃×C₄

—

207

C₃×C₄

—

208

C₃×C₄

—

209

C₃×C₄

C₃×#235

yes

—

210

Dic₃

—

211

Dic₃

—

212

C₃²

#4714

yes

characteristic

213

C₉

—

214

C₉

C₃×#489

yes

characteristic, complemented

215

C₂³

—

216

Q₈

—

217

Q₈

—

218

D₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

C₄⋊AGL(1,ℤ/9)

yes

characteristic

222

C₂×C₄

C₄⋊AGL(1,ℤ/9)

yes

characteristic

223

C₂×C₄

C₂²×AGL(1,ℤ/9)

yes

characteristic

224

C₈

—

225

C₂×C₃

—

226

C₂×C₃

—

227

C₂×C₃

—

228

C₂×C₃

—

229

C₂×C₃

C₃×#875

yes

characteristic

230

C₂×C₃

C₃×#908

yes

characteristic

231

C₂×C₃

C₃×#909

yes

characteristic

232

D₃

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

C₂×C₄⋊AGL(1,ℤ/9)

yes

characteristic

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

241

C₄

#3697⋊C₃

yes

—

242

C₃

—

243

C₃

C₃×#4714

yes

characteristic

244

C₂

—

245

C₂

#63437⋊C₃

yes

characteristic

246

C₂

#63470⋊C₃

yes

characteristic

247

C₂

#63471⋊C₃

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊AGL(1,ℤ/9)
commutator, cosocle	C₂×C₄×C₉	C₂³×C₃
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	3₋¹⁺²×#97	C₂
socle	C₂²×C₃	C₂×C₃×D₁₂
prime radical	C₂×C₄⋊AGL(1,ℤ/9)	C₂²
hypercenter	#97	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#489
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊AGL(1,ℤ/9)

commutator, cosocle

C₂×C₄×C₉

C₂³×C₃

Frattini

C₂×C₃×C₄

C₂²×C₃×D₃

Fitting

3₋¹⁺²×#97

C₂

socle

C₂²×C₃

C₂×C₃×D₁₂

C₂²

C₉

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
2. #63431⋊C₃	C₂	semidirect
3. 3₋¹⁺²×#97	C₂	semidirect
5. #63376⋊C₃	C₂	semidirect
7. #10588395	C₃	semidirect
23. #63431	C₂×C₃	semidirect
25. C₉×#97	C₂×C₃	semidirect
27. #63376	C₂×C₃	semidirect
152. #97	AGL(1,ℤ/9)	semidirect
153. 3₋¹⁺²	#489	semidirect
214. C₉	C₃×#489	semidirect

H ≅ G/N

type

2. #63431⋊C₃

C₂

semidirect

3. 3₋¹⁺²×#97

C₂

semidirect

5. #63376⋊C₃

C₂

semidirect

7. #10588395

C₃

semidirect

23. #63431

C₂×C₃

semidirect

25. C₉×#97

C₂×C₃

semidirect

27. #63376

C₂×C₃

semidirect

152. #97

AGL(1,ℤ/9)

semidirect

153. 3₋¹⁺²

#489

semidirect

214. C₉

C₃×#489

semidirect

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

subgroup	index
#63437⋊C₃	2
#63431⋊C₃	2
3₋¹⁺²×#97	2
#63380⋊C₃	2
#63376⋊C₃	2
C₃×#4714	3
#10588395	3

subgroup

index

3₋¹⁺²×#97

Subgroups — #10588395⋊C₃ #13141542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10588395⋊C3 #13141542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10588395⋊C₃ #13141542