Group #13142991 — subgroups

Subgroups — #10588750⋊C₃ #13142991

Order 1728.

408 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 112 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	3₋¹⁺²×#127	C₂	1	1	yes	maximal, characteristic
2	#63431⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#63392⋊C₃	C₂	1	4	yes	maximal, complemented
4	C₄×3₋¹⁺²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5070	—	3	1	no	maximal
6	#10588750	C₃	1	1	yes	maximal, characteristic, complemented
7	C₂×D₄×3₋¹⁺²	—	2	1	no	—
8	C₂×D₄×3₋¹⁺²	—	2	1	no	—
9	C₂×D₄×3₋¹⁺²	C₂²	1	2	yes	—
10	C₂×3₋¹⁺²⋊Q₈	—	2	1	no	—
11	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
12	C₄⋊(3₋¹⁺²⋊C₄)	—	2	1	no	—
13	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	2	yes	—
14	C₂×3₋¹⁺²⋊C₈	C₂²	1	2	yes	—
15	C₃²×#127	D₃	1	1	yes	characteristic
16	C₃×#869	—	3	1	no	—
17	C₃×#832	—	3	4	no	—
18	C₃×C₄×C₃⋊C₈	—	3	1	no	—
19	C₉×#127	—	2	1	no	—
20	C₉×#127	C₂×C₃	1	1	yes	characteristic
21	#63431	C₂×C₃	1	1	yes	characteristic, complemented
22	#63392	C₂×C₃	1	4	yes	complemented
23	C₄×C₉⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂³×3₋¹⁺²	—	2	2	no	—
25	D₄×3₋¹⁺²	—	2	4	no	—
26	D₄×3₋¹⁺²	—	4	2	no	—
27	D₄×3₋¹⁺²	—	4	2	no	—
28	C₂×C₄×3₋¹⁺²	D₄	1	1	yes	characteristic
29	C₂×C₄×3₋¹⁺²	D₄	1	1	yes	characteristic
30	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
31	C₂×3₋¹⁺²⋊C₄	—	2	2	no	—
32	3₋¹⁺²⋊Q₈	—	4	2	no	—
33	3₋¹⁺²⋊C₈	—	2	2	no	—
34	C₃×#486	—	9	1	no	—
35	#5070	—	3	1	no	—
36	C₂×C₃²×D₄	—	2	1	no	—
37	C₂×C₃²×D₄	—	2	1	no	—
38	C₂×C₃²×D₄	C₂×D₃	1	2	yes	—
39	C₂×C₃×Dic₆	—	6	1	no	—
40	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
41	C₃×C₄⋊Dic₃	—	3	2	no	—
42	C₃×C₄⋊Dic₃	—	6	1	no	—
43	C₂×C₃×C₃⋊C₈	—	3	2	no	—
44	C₂×D₄×C₉	—	2	2	no	—
45	C₂×D₄×C₉	—	2	2	no	—
46	C₂×D₄×C₉	—	2	2	no	—
47	C₂×D₄×C₉	—	2	1	no	—
48	C₂×D₄×C₉	—	2	1	no	—
49	C₂×D₄×C₉	C₂²×C₃	1	2	yes	—
50	C₂×Dic₁₈	—	2	1	no	—
51	C₄²×C₉	—	2	1	no	—
52	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
53	C₄⋊Dic₉	—	2	1	no	—
54	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
55	C₂×C₉⋊C₈	C₂²×C₃	1	2	yes	—
56	C₂²×3₋¹⁺²	—	4	2	no	—
57	C₂²×3₋¹⁺²	—	4	2	no	—
58	C₂²×3₋¹⁺²	—	4	2	no	—
59	C₂²×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
60	C₄×3₋¹⁺²	D₈	1	2	yes	—
61	C₄×3₋¹⁺²	SD₁₆	1	2	yes	—
62	C₄×3₋¹⁺²	#41	1	2	yes	—
63	3₋¹⁺²⋊C₄	—	4	2	no	—
64	C₃×C₄⋊Q₈	—	9	1	no	—
65	C₃×#127	—	3	1	no	—
66	C₃×#127	C₃×D₃	1	1	yes	characteristic
67	#869	—	3	1	no	—
68	C₃×#102	—	9	4	no	—
69	C₃×C₄×C₈	—	9	1	no	—
70	#832	—	3	4	no	—
71	C₄×C₃⋊C₈	—	3	1	no	—
72	C₂³×C₃²	—	2	2	no	—
73	C₃²×D₄	—	2	4	no	—
74	C₃²×D₄	—	4	2	no	—
75	C₃²×D₄	—	4	2	no	—
76	C₂×C₃²×C₄	#67	1	1	yes	characteristic
77	C₂×C₃²×C₄	#67	1	1	yes	characteristic
78	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
79	C₂×C₃×Dic₃	—	6	2	no	—
80	C₃×Dic₆	—	12	2	no	—
81	C₂³×C₉	—	2	4	no	—
82	C₂³×C₉	—	2	2	no	—
83	C₃×C₃⋊C₈	—	6	2	no	—
84	D₄×C₉	—	2	4	no	—
85	D₄×C₉	—	4	4	no	—
86	D₄×C₉	—	4	4	no	—
87	D₄×C₉	—	4	4	no	—
88	D₄×C₉	—	4	2	no	—
89	D₄×C₉	—	4	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	Dic₁₈	—	4	2	no	—
98	C₉⋊C₈	—	2	2	no	—
99	#486	—	9	1	no	Sylow
100	C₂×3₋¹⁺²	—	8	2	no	—
101	C₂×3₋¹⁺²	#124	1	1	yes	characteristic
102	C₂×3₋¹⁺²	C₂×D₈	1	1	yes	characteristic
103	C₂×3₋¹⁺²	C₂×SD₁₆	1	1	yes	characteristic
104	C₂×C₃×Q₈	—	18	1	no	—
105	C₂×C₃×D₄	—	2	1	no	—
106	C₂×C₃×D₄	—	2	1	no	—
107	C₂×C₃×D₄	—	3	2	no	—
108	C₂×C₃×D₄	—	6	1	no	—
109	C₂×C₃×D₄	—	6	1	no	—
110	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
111	C₂×Dic₆	—	6	1	no	—
112	C₂×C₃×C₈	—	9	2	no	—
113	C₃×C₄⋊C₄	—	9	2	no	—
114	C₃×C₄⋊C₄	—	18	1	no	—
115	C₃×C₄²	—	3	1	no	—
116	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
117	C₄⋊Dic₃	—	3	2	no	—
118	C₄⋊Dic₃	—	6	1	no	—
119	C₂×C₃⋊C₈	—	3	2	no	—
120	C₂²×C₃²	—	4	2	no	—
121	C₂²×C₃²	—	4	2	no	—
122	C₂²×C₃²	—	4	2	no	—
123	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
124	C₃²×C₄	#213	1	2	yes	—
125	C₃²×C₄	#214	1	2	yes	—
126	C₃²×C₄	#237	1	2	yes	—
127	C₃×Dic₃	—	12	2	no	—
128	C₂²×C₉	—	2	1	no	—
129	C₂²×C₉	—	4	4	no	—
130	C₂²×C₉	—	4	4	no	—
131	C₂²×C₉	—	4	4	no	—
132	C₂²×C₉	—	4	2	no	—
133	C₂²×C₉	—	4	2	no	—
134	C₂²×C₉	—	4	2	no	—
135	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
136	C₄×C₉	—	2	2	no	—
137	C₄×C₉	—	2	2	no	—
138	C₄×C₉	—	2	2	no	—
139	C₄×C₉	C₃×D₈	1	2	yes	—
140	C₄×C₉	C₃×SD₁₆	1	2	yes	—
141	C₄×C₉	C₃×#41	1	2	yes	—
142	Dic₉	—	4	2	no	—
143	C₄⋊Q₈	—	9	1	no	—
144	#127	AGL(1,ℤ/9)	1	1	yes	characteristic
145	#102	—	9	4	no	—
146	C₄×C₈	—	9	1	no	—
147	3₋¹⁺²	#486	1	1	yes	characteristic, complemented, Sylow
148	C₂³×C₃	—	2	2	no	—
149	C₂³×C₃	—	6	2	no	—
150	C₃×Q₈	—	36	2	no	—
151	C₃×D₄	—	2	4	no	—
152	C₃×D₄	—	4	2	no	—
153	C₃×D₄	—	4	2	no	—
154	C₃×D₄	—	6	4	no	—
155	C₃×D₄	—	12	2	no	—
156	C₃×D₄	—	12	2	no	—
157	C₂×C₃×C₄	—	3	1	no	—
158	C₂×C₃×C₄	—	3	1	no	—
159	C₂×C₃×C₄	—	3	1	no	—
160	C₂×C₃×C₄	—	18	2	no	—
161	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
162	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
163	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
164	C₂×Dic₃	—	6	2	no	—
165	Dic₆	—	12	2	no	—
166	C₃×C₈	—	18	2	no	—
167	C₃⋊C₈	—	6	2	no	—
168	C₂×C₃²	—	8	2	no	—
169	C₂×C₃²	C₂×#213	1	1	yes	characteristic
170	C₂×C₃²	C₂×#214	1	1	yes	characteristic
171	C₂×C₃²	#936	1	1	yes	characteristic
172	C₂×C₉	—	2	1	no	—
173	C₂×C₉	—	2	1	no	—
174	C₂×C₉	—	2	1	no	—
175	C₂×C₉	—	8	4	no	—
176	C₂×C₉	—	8	2	no	—
177	C₂×C₉	C₃×#124	1	1	yes	characteristic
178	C₂×C₉	C₂×C₃×D₈	1	1	yes	characteristic
179	C₂×C₉	C₂×C₃×SD₁₆	1	1	yes	characteristic
180	C₂×Q₈	—	18	1	no	—
181	C₂×D₄	—	2	1	no	—
182	C₂×D₄	—	2	1	no	—
183	C₂×D₄	C₂×AGL(1,ℤ/9)	1	2	yes	—
184	C₂×C₈	—	9	2	no	—
185	C₄⋊C₄	—	9	2	no	—
186	C₄⋊C₄	—	18	1	no	—
187	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
188	C₂²×C₃	—	3	1	no	—
189	C₂²×C₃	—	4	2	no	—
190	C₂²×C₃	—	4	2	no	—
191	C₂²×C₃	—	4	2	no	—
192	C₂²×C₃	—	12	2	no	—
193	C₂²×C₃	—	12	2	no	—
194	C₂²×C₃	—	12	2	no	—
195	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
196	C₃×C₄	—	3	2	no	—
197	C₃×C₄	—	3	2	no	—
198	C₃×C₄	—	3	2	no	—
199	C₃×C₄	—	36	2	no	—
200	C₃×C₄	C₃×#213	1	2	yes	—
201	C₃×C₄	C₃×#214	1	2	yes	—
202	C₃×C₄	C₃×#237	1	2	yes	—
203	Dic₃	—	12	2	no	—
204	C₃²	#5070	1	1	yes	characteristic
205	C₉	—	2	1	no	—
206	C₉	C₃×#486	1	1	yes	characteristic, complemented
207	C₂³	—	2	2	no	—
208	Q₈	—	36	2	no	—
209	D₄	—	2	4	no	—
210	D₄	—	4	2	no	—
211	D₄	—	4	2	no	—
212	C₂×C₄	—	18	2	no	—
213	C₂×C₄	#611⋊C₃	1	1	yes	characteristic
214	C₂×C₄	#611⋊C₃	1	1	yes	characteristic
215	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
216	C₈	—	18	2	no	—
217	C₂×C₃	—	3	1	no	—
218	C₂×C₃	—	3	1	no	—
219	C₂×C₃	—	3	1	no	—
220	C₂×C₃	—	8	2	no	—
221	C₂×C₃	—	24	2	no	—
222	C₂×C₃	C₂×C₃×#213	1	1	yes	characteristic
223	C₂×C₃	C₂×C₃×#214	1	1	yes	characteristic
224	C₂×C₃	C₃×#936	1	1	yes	characteristic
225	C₂²	—	4	2	no	—
226	C₂²	—	4	2	no	—
227	C₂²	—	4	2	no	—
228	C₂²	C₂×#611⋊C₃	1	1	yes	characteristic
229	C₄	—	36	2	no	—
230	C₄	#3672⋊C₃	1	2	yes	—
231	C₄	#3673⋊C₃	1	2	yes	—
232	C₄	#3699⋊C₃	1	2	yes	—
233	C₃	—	3	1	no	—
234	C₃	C₃×#5070	1	1	yes	characteristic
235	C₂	—	8	2	no	—
236	C₂	C₂×#3672⋊C₃	1	1	yes	characteristic
237	C₂	C₂×#3673⋊C₃	1	1	yes	characteristic
238	C₂	#63498⋊C₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

3₋¹⁺²×#127

C₂

yes

maximal, characteristic

#63431⋊C₃

C₂

yes

maximal, characteristic, complemented

#63392⋊C₃

C₂

yes

maximal, complemented

C₄×3₋¹⁺²⋊C₈

C₂

yes

maximal, characteristic, complemented

C₃×#5070

—

maximal

#10588750

C₃

yes

maximal, characteristic, complemented

C₂×D₄×3₋¹⁺²

—

C₂×D₄×3₋¹⁺²

—

C₂×D₄×3₋¹⁺²

C₂²

yes

—

C₂×3₋¹⁺²⋊Q₈

—

C₄²×3₋¹⁺²

C₂²

yes

characteristic

C₄⋊(3₋¹⁺²⋊C₄)

—

C₄⋊(3₋¹⁺²⋊C₄)

C₂²

yes

—

C₂×3₋¹⁺²⋊C₈

C₂²

yes

—

C₃²×#127

D₃

yes

characteristic

C₃×#869

—

C₃×#832

—

C₃×C₄×C₃⋊C₈

—

C₉×#127

—

C₉×#127

C₂×C₃

yes

characteristic

#63431

C₂×C₃

yes

characteristic, complemented

#63392

C₂×C₃

yes

complemented

C₄×C₉⋊C₈

C₂×C₃

yes

characteristic, complemented

C₂³×3₋¹⁺²

—

D₄×3₋¹⁺²

—

D₄×3₋¹⁺²

—

D₄×3₋¹⁺²

—

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

—

3₋¹⁺²⋊Q₈

—

3₋¹⁺²⋊C₈

—

C₃×#486

—

#5070

—

C₂×C₃²×D₄

—

C₂×C₃²×D₄

—

C₂×C₃²×D₄

C₂×D₃

yes

—

C₂×C₃×Dic₆

—

C₃²×C₄²

C₂×D₃

yes

characteristic

C₃×C₄⋊Dic₃

—

C₃×C₄⋊Dic₃

—

C₂×C₃×C₃⋊C₈

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

C₂²×C₃

yes

—

C₂×Dic₁₈

—

C₄²×C₉

—

C₄²×C₉

C₂²×C₃

yes

characteristic

C₄⋊Dic₉

—

C₄⋊Dic₉

C₂²×C₃

yes

—

C₂×C₉⋊C₈

C₂²×C₃

yes

—

C₂²×3₋¹⁺²

—

C₂²×3₋¹⁺²

—

C₂²×3₋¹⁺²

—

C₂²×3₋¹⁺²

C₂×D₄

yes

characteristic

C₄×3₋¹⁺²

D₈

yes

—

C₄×3₋¹⁺²

SD₁₆

yes

—

C₄×3₋¹⁺²

#41

yes

—

3₋¹⁺²⋊C₄

—

C₃×C₄⋊Q₈

—

C₃×#127

—

C₃×#127

C₃×D₃

yes

characteristic

#869

—

C₃×#102

—

C₃×C₄×C₈

—

#832

—

C₄×C₃⋊C₈

—

C₂³×C₃²

—

C₃²×D₄

—

C₃²×D₄

—

C₃²×D₄

—

C₂×C₃²×C₄

yes

C₂×C₃²×C₄

yes

C₂×C₃²×C₄

C₂²×D₃

yes

characteristic

C₂×C₃×Dic₃

—

C₃×Dic₆

—

C₂³×C₉

—

C₂³×C₉

—

C₃×C₃⋊C₈

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

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

—

Dic₁₈

—

C₉⋊C₈

—

#486

—

Sylow

100

C₂×3₋¹⁺²

—

101

C₂×3₋¹⁺²

#124

yes

characteristic

102

C₂×3₋¹⁺²

C₂×D₈

yes

characteristic

103

C₂×3₋¹⁺²

C₂×SD₁₆

yes

characteristic

104

C₂×C₃×Q₈

—

105

C₂×C₃×D₄

—

106

C₂×C₃×D₄

—

107

C₂×C₃×D₄

—

108

C₂×C₃×D₄

—

109

C₂×C₃×D₄

—

110

C₂×C₃×D₄

C₂×C₃×D₃

yes

—

111

C₂×Dic₆

—

112

C₂×C₃×C₈

—

113

C₃×C₄⋊C₄

—

114

C₃×C₄⋊C₄

—

115

C₃×C₄²

—

116

C₃×C₄²

C₂×C₃×D₃

yes

characteristic

117

C₄⋊Dic₃

—

118

C₄⋊Dic₃

—

119

C₂×C₃⋊C₈

—

120

C₂²×C₃²

—

121

C₂²×C₃²

—

122

C₂²×C₃²

—

123

C₂²×C₃²

C₂×#67

yes

characteristic

124

C₃²×C₄

#213

yes

—

125

C₃²×C₄

#214

yes

—

126

C₃²×C₄

#237

yes

—

127

C₃×Dic₃

—

128

C₂²×C₉

—

129

C₂²×C₉

—

130

C₂²×C₉

—

131

C₂²×C₉

—

132

C₂²×C₉

—

133

C₂²×C₉

—

134

C₂²×C₉

—

135

C₂²×C₉

C₂×C₃×D₄

yes

characteristic

136

C₄×C₉

—

137

C₄×C₉

—

138

C₄×C₉

—

139

C₄×C₉

C₃×D₈

yes

—

140

C₄×C₉

C₃×SD₁₆

yes

—

141

C₄×C₉

C₃×#41

yes

—

142

Dic₉

—

143

C₄⋊Q₈

—

144

yes

145

—

146

C₄×C₈

—

147

3₋¹⁺²

#486

yes

characteristic, complemented, Sylow

148

C₂³×C₃

—

149

C₂³×C₃

—

150

C₃×Q₈

—

151

C₃×D₄

—

152

C₃×D₄

—

153

C₃×D₄

—

154

C₃×D₄

—

155

C₃×D₄

—

156

C₃×D₄

—

157

C₂×C₃×C₄

—

158

C₂×C₃×C₄

—

159

C₂×C₃×C₄

—

160

C₂×C₃×C₄

—

161

C₂×C₃×C₄

C₃×#67

yes

characteristic

162

C₂×C₃×C₄

C₃×#67

yes

characteristic

163

C₂×C₃×C₄

C₂²×C₃×D₃

yes

characteristic

164

C₂×Dic₃

—

165

Dic₆

—

166

C₃×C₈

—

167

C₃⋊C₈

—

168

C₂×C₃²

—

169

C₂×C₃²

C₂×#213

yes

characteristic

170

C₂×C₃²

C₂×#214

yes

characteristic

171

C₂×C₃²

#936

yes

characteristic

172

C₂×C₉

—

173

C₂×C₉

—

174

C₂×C₉

—

175

C₂×C₉

—

176

C₂×C₉

—

177

C₂×C₉

C₃×#124

yes

characteristic

178

C₂×C₉

C₂×C₃×D₈

yes

characteristic

179

C₂×C₉

C₂×C₃×SD₁₆

yes

characteristic

180

C₂×Q₈

—

181

C₂×D₄

—

182

C₂×D₄

—

183

C₂×D₄

C₂×AGL(1,ℤ/9)

yes

—

184

C₂×C₈

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄²

C₂×AGL(1,ℤ/9)

yes

characteristic

188

C₂²×C₃

—

189

C₂²×C₃

—

190

C₂²×C₃

—

191

C₂²×C₃

—

192

C₂²×C₃

—

193

C₂²×C₃

—

194

C₂²×C₃

—

195

C₂²×C₃

C₂×C₃×#67

yes

characteristic

196

C₃×C₄

—

197

C₃×C₄

—

198

C₃×C₄

—

199

C₃×C₄

—

200

C₃×C₄

C₃×#213

yes

—

201

C₃×C₄

C₃×#214

yes

—

202

C₃×C₄

C₃×#237

yes

—

203

Dic₃

—

204

C₃²

#5070

yes

characteristic

205

C₉

—

206

C₉

C₃×#486

yes

characteristic, complemented

207

C₂³

—

208

Q₈

—

209

D₄

—

210

D₄

—

211

D₄

—

212

C₂×C₄

—

213

C₂×C₄

#611⋊C₃

yes

characteristic

214

C₂×C₄

#611⋊C₃

yes

characteristic

215

C₂×C₄

C₂²×AGL(1,ℤ/9)

yes

characteristic

216

C₈

—

217

C₂×C₃

—

218

C₂×C₃

—

219

C₂×C₃

—

220

C₂×C₃

—

221

C₂×C₃

—

222

C₂×C₃

C₂×C₃×#213

yes

characteristic

223

C₂×C₃

C₂×C₃×#214

yes

characteristic

224

C₂×C₃

C₃×#936

yes

characteristic

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

C₂×#611⋊C₃

yes

characteristic

229

C₄

—

230

C₄

#3672⋊C₃

yes

—

231

C₄

#3673⋊C₃

yes

—

232

C₄

#3699⋊C₃

yes

—

233

C₃

—

234

C₃

C₃×#5070

yes

characteristic

235

C₂

—

236

C₂

C₂×#3672⋊C₃

yes

characteristic

237

C₂

C₂×#3673⋊C₃

yes

characteristic

238

C₂

#63498⋊C₃

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#611⋊C₃
commutator, cosocle	C₂×C₄×C₉	C₂³×C₃
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	3₋¹⁺²×#127	C₂
socle	C₂²×C₃	C₂×C₃×#67
prime radical	C₃²×#127	D₃
hypercenter	#127	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#486
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

subgroup

G/H

center

C₂²

C₂×#611⋊C₃

commutator, cosocle

C₂×C₄×C₉

C₂³×C₃

Frattini

C₂×C₃×C₄

C₂²×C₃×D₃

Fitting

3₋¹⁺²×#127

C₂

socle

C₂²×C₃

C₂×C₃×#67

prime radical

C₃²×#127

D₃

C₉

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #127

N	H ≅ G/N	type
2. #63431⋊C₃	C₂	semidirect
3. #63392⋊C₃	C₂	semidirect
4. C₄×3₋¹⁺²⋊C₈	C₂	semidirect
6. #10588750	C₃	semidirect
21. #63431	C₂×C₃	semidirect
22. #63392	C₂×C₃	semidirect
23. C₄×C₉⋊C₈	C₂×C₃	semidirect
147. 3₋¹⁺²	#486	semidirect
206. C₉	C₃×#486	semidirect

H ≅ G/N

type

2. #63431⋊C₃

C₂

semidirect

3. #63392⋊C₃

C₂

semidirect

4. C₄×3₋¹⁺²⋊C₈

C₂

semidirect

6. #10588750

C₃

semidirect

21. #63431

C₂×C₃

semidirect

22. #63392

C₂×C₃

semidirect

23. C₄×C₉⋊C₈

C₂×C₃

semidirect

147. 3₋¹⁺²

#486

semidirect

206. C₉

C₃×#486

semidirect

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

subgroup	index
3₋¹⁺²×#127	2
#63431⋊C₃	2
#63392⋊C₃	2
C₄×3₋¹⁺²⋊C₈	2
C₃×#5070	3
#10588750	3

subgroup

index

3₋¹⁺²×#127

C₄×3₋¹⁺²⋊C₈

Subgroups — #10588750⋊C₃ #13142991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10588750⋊C3 #13142991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10588750⋊C₃ #13142991