Group #13142930 — subgroups

Subgroups — #10588734⋊C₃ #13142930

Order 1728.

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

normal subgroups only

This group has 338 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	3₋¹⁺²×#124	C₂	1	1	yes	maximal, characteristic
2	#63431⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#63395⋊C₃	C₂	1	2	yes	maximal, complemented
4	#63392⋊C₃	C₂	1	2	yes	maximal
5	#63362⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5055	—	3	1	no	maximal
7	#10588734	C₃	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×3₋¹⁺²	C₂²	1	1	yes	characteristic
9	C₂×D₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
10	C₂×3₋¹⁺²⋊Q₈	—	2	1	no	—
11	C₂²⋊C₄×3₋¹⁺²	—	2	1	no	—
12	C₂²⋊C₄×3₋¹⁺²	—	2	1	no	—
13	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
14	C₄⋊(3₋¹⁺²⋊C₄)	—	2	1	no	—
15	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	2	yes	—
16	C₂×3₋¹⁺²⋊C₈	C₂²	1	2	yes	—
17	C₃²×#124	D₃	1	1	yes	characteristic
18	C₃×#869	—	3	1	no	—
19	C₃×#835	—	3	2	no	—
20	C₃×#832	—	3	2	no	—
21	C₃×#803	—	3	1	no	—
22	C₉×#124	—	2	1	no	—
23	C₉×#124	C₂×C₃	1	1	yes	characteristic
24	#63431	C₂×C₃	1	1	yes	characteristic, complemented
25	#63395	C₂×C₃	1	2	yes	complemented
26	#63392	C₂×C₃	1	2	yes	—
27	#63362	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂³×3₋¹⁺²	—	2	1	no	—
29	Q₈×3₋¹⁺²	—	2	2	no	—
30	D₄×3₋¹⁺²	—	2	2	no	—
31	C₂×C₄×3₋¹⁺²	—	2	1	no	—
32	C₂×C₄×3₋¹⁺²	D₄	1	1	yes	characteristic
33	C₂×C₄×3₋¹⁺²	D₄	1	1	yes	characteristic
34	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
35	C₂×3₋¹⁺²⋊C₄	—	2	2	no	—
36	3₋¹⁺²⋊Q₈	—	4	2	no	—
37	3₋¹⁺²⋊C₈	—	2	2	no	—
38	C₃×#489	—	9	1	no	—
39	#5055	—	3	1	no	—
40	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
41	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
42	C₂×C₃×Dic₆	—	6	1	no	—
43	C₃²×C₂²⋊C₄	—	2	1	no	—
44	C₃²×C₂²⋊C₄	—	2	1	no	—
45	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
46	C₃×C₄⋊Dic₃	—	3	2	no	—
47	C₃×C₄⋊Dic₃	—	6	1	no	—
48	C₂×C₃×C₃⋊C₈	—	3	2	no	—
49	C₂×Q₈×C₉	—	2	1	no	—
50	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
51	C₂×D₄×C₉	—	2	1	no	—
52	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
53	C₂×Dic₁₈	—	2	1	no	—
54	C₉×C₂²⋊C₄	—	2	2	no	—
55	C₉×C₂²⋊C₄	—	2	2	no	—
56	C₉×C₂²⋊C₄	—	2	1	no	—
57	C₉×C₂²⋊C₄	—	2	1	no	—
58	C₄²×C₉	—	2	1	no	—
59	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
60	C₄⋊Dic₉	—	2	1	no	—
61	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
62	C₂×C₉⋊C₈	C₂²×C₃	1	2	yes	—
63	C₂²×3₋¹⁺²	—	4	1	no	—
64	C₂²×3₋¹⁺²	—	4	1	no	—
65	C₂²×3₋¹⁺²	—	4	1	no	—
66	C₂²×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
67	C₄×3₋¹⁺²	—	2	1	no	—
68	C₄×3₋¹⁺²	—	2	1	no	—
69	C₄×3₋¹⁺²	—	4	1	no	—
70	C₄×3₋¹⁺²	#41	1	2	yes	—
71	3₋¹⁺²⋊C₄	—	4	2	no	—
72	C₃×C₄⋊Q₈	—	9	1	no	—
73	C₃×#124	—	3	1	no	—
74	C₃×#124	C₃×D₃	1	1	yes	characteristic
75	#869	—	3	1	no	—
76	C₃×#103	—	9	2	no	—
77	C₃×#102	—	9	2	no	—
78	C₃×#97	—	9	1	no	—
79	#835	—	3	2	no	—
80	#832	—	3	2	no	—
81	#803	—	3	1	no	—
82	C₂³×C₃²	—	2	1	no	—
83	C₃²×Q₈	—	2	2	no	—
84	C₃²×D₄	—	2	2	no	—
85	C₂×C₃²×C₄	—	2	1	no	—
86	C₂×C₃²×C₄	#67	1	1	yes	characteristic
87	C₂×C₃²×C₄	#67	1	1	yes	characteristic
88	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
89	C₂×C₃×Dic₃	—	6	2	no	—
90	C₃×Dic₆	—	12	2	no	—
91	C₂³×C₉	—	2	2	no	—
92	C₂³×C₉	—	2	1	no	—
93	C₃×C₃⋊C₈	—	6	2	no	—
94	Q₈×C₉	—	2	2	no	—
95	Q₈×C₉	—	4	2	no	—
96	D₄×C₉	—	2	2	no	—
97	D₄×C₉	—	4	2	no	—
98	C₂×C₄×C₉	—	2	2	no	—
99	C₂×C₄×C₉	—	2	1	no	—
100	C₂×C₄×C₉	—	2	1	no	—
101	C₂×C₄×C₉	—	2	1	no	—
102	C₂×C₄×C₉	—	2	1	no	—
103	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
104	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
105	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
106	C₂×Dic₉	—	2	2	no	—
107	Dic₁₈	—	4	2	no	—
108	C₉⋊C₈	—	2	2	no	—
109	#489	—	9	1	no	Sylow
110	C₂×3₋¹⁺²	—	8	1	no	—
111	C₂×3₋¹⁺²	#124	1	1	yes	characteristic
112	C₂×3₋¹⁺²	AGL(1,ℤ/8)	1	1	yes	characteristic
113	C₂×3₋¹⁺²	#137	1	1	yes	characteristic
114	C₂×C₃×Q₈	—	3	1	no	—
115	C₂×C₃×Q₈	—	18	1	no	—
116	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
117	C₂×C₃×D₄	—	3	1	no	—
118	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
119	C₂×Dic₆	—	6	1	no	—
120	C₂×C₃×C₈	—	9	2	no	—
121	C₃×C₄⋊C₄	—	9	2	no	—
122	C₃×C₄⋊C₄	—	18	1	no	—
123	C₃×C₂²⋊C₄	—	2	1	no	—
124	C₃×C₂²⋊C₄	—	2	1	no	—
125	C₃×C₂²⋊C₄	—	6	1	no	—
126	C₃×C₂²⋊C₄	—	6	1	no	—
127	C₃×C₄²	—	3	1	no	—
128	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
129	C₄⋊Dic₃	—	3	2	no	—
130	C₄⋊Dic₃	—	6	1	no	—
131	C₂×C₃⋊C₈	—	3	2	no	—
132	C₂²×C₃²	—	4	1	no	—
133	C₂²×C₃²	—	4	1	no	—
134	C₂²×C₃²	—	4	1	no	—
135	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
136	C₃²×C₄	—	2	1	no	—
137	C₃²×C₄	—	2	1	no	—
138	C₃²×C₄	—	4	1	no	—
139	C₃²×C₄	#237	1	2	yes	—
140	C₃×Dic₃	—	12	2	no	—
141	C₂²×C₉	—	2	1	no	—
142	C₂²×C₉	—	4	2	no	—
143	C₂²×C₉	—	4	2	no	—
144	C₂²×C₉	—	4	2	no	—
145	C₂²×C₉	—	4	1	no	—
146	C₂²×C₉	—	4	1	no	—
147	C₂²×C₉	—	4	1	no	—
148	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
149	C₄×C₉	—	2	1	no	—
150	C₄×C₉	—	2	1	no	—
151	C₄×C₉	—	2	2	no	—
152	C₄×C₉	—	4	1	no	—
153	C₄×C₉	—	4	1	no	—
154	C₄×C₉	—	4	2	no	—
155	C₄×C₉	—	4	1	no	—
156	C₄×C₉	C₃×#41	1	2	yes	—
157	Dic₉	—	4	2	no	—
158	C₄⋊Q₈	—	9	1	no	—
159	#124	AGL(1,ℤ/9)	1	1	yes	characteristic
160	#103	—	9	2	no	—
161	#102	—	9	2	no	—
162	#97	—	9	1	no	—
163	3₋¹⁺²	#489	1	1	yes	characteristic, complemented, Sylow
164	C₂³×C₃	—	2	1	no	—
165	C₂³×C₃	—	6	1	no	—
166	C₃×Q₈	—	2	2	no	—
167	C₃×Q₈	—	6	2	no	—
168	C₃×Q₈	—	36	2	no	—
169	C₃×D₄	—	2	2	no	—
170	C₃×D₄	—	6	2	no	—
171	C₂×C₃×C₄	—	2	1	no	—
172	C₂×C₃×C₄	—	3	1	no	—
173	C₂×C₃×C₄	—	3	1	no	—
174	C₂×C₃×C₄	—	3	1	no	—
175	C₂×C₃×C₄	—	6	1	no	—
176	C₂×C₃×C₄	—	18	2	no	—
177	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
178	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
179	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
180	C₂×Dic₃	—	6	2	no	—
181	Dic₆	—	12	2	no	—
182	C₃×C₈	—	18	2	no	—
183	C₃⋊C₈	—	6	2	no	—
184	C₂×C₃²	—	8	1	no	—
185	C₂×C₃²	#936	1	1	yes	characteristic
186	C₂×C₃²	#949	1	1	yes	characteristic
187	C₂×C₃²	#951	1	1	yes	characteristic
188	C₂×C₉	—	2	1	no	—
189	C₂×C₉	—	2	1	no	—
190	C₂×C₉	—	2	1	no	—
191	C₂×C₉	—	8	2	no	—
192	C₂×C₉	—	8	1	no	—
193	C₂×C₉	C₃×#124	1	1	yes	characteristic
194	C₂×C₉	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂×C₉	C₃×#137	1	1	yes	characteristic
196	C₂×Q₈	—	18	1	no	—
197	C₂×Q₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
198	C₂×D₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
199	C₂×C₈	—	9	2	no	—
200	C₄⋊C₄	—	9	2	no	—
201	C₄⋊C₄	—	18	1	no	—
202	C₂²⋊C₄	—	2	1	no	—
203	C₂²⋊C₄	—	2	1	no	—
204	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
205	C₂²×C₃	—	3	1	no	—
206	C₂²×C₃	—	4	1	no	—
207	C₂²×C₃	—	4	1	no	—
208	C₂²×C₃	—	4	1	no	—
209	C₂²×C₃	—	12	1	no	—
210	C₂²×C₃	—	12	1	no	—
211	C₂²×C₃	—	12	1	no	—
212	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
213	C₃×C₄	—	2	1	no	—
214	C₃×C₄	—	2	1	no	—
215	C₃×C₄	—	3	2	no	—
216	C₃×C₄	—	4	1	no	—
217	C₃×C₄	—	6	1	no	—
218	C₃×C₄	—	6	1	no	—
219	C₃×C₄	—	12	1	no	—
220	C₃×C₄	—	36	2	no	—
221	C₃×C₄	C₃×#237	1	2	yes	—
222	Dic₃	—	12	2	no	—
223	C₃²	#5055	1	1	yes	characteristic
224	C₉	—	2	1	no	—
225	C₉	C₃×#489	1	1	yes	characteristic, complemented
226	C₂³	—	2	1	no	—
227	Q₈	—	2	2	no	—
228	Q₈	—	36	2	no	—
229	D₄	—	2	2	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	18	2	no	—
232	C₂×C₄	#611⋊C₃	1	1	yes	characteristic
233	C₂×C₄	#611⋊C₃	1	1	yes	characteristic
234	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
235	C₈	—	18	2	no	—
236	C₂×C₃	—	3	1	no	—
237	C₂×C₃	—	3	1	no	—
238	C₂×C₃	—	3	1	no	—
239	C₂×C₃	—	8	1	no	—
240	C₂×C₃	—	24	1	no	—
241	C₂×C₃	C₃×#936	1	1	yes	characteristic
242	C₂×C₃	C₃×#949	1	1	yes	characteristic
243	C₂×C₃	C₃×#951	1	1	yes	characteristic
244	C₂²	—	4	1	no	—
245	C₂²	—	4	1	no	—
246	C₂²	—	4	1	no	—
247	C₂²	C₂×#611⋊C₃	1	1	yes	characteristic
248	C₄	—	2	1	no	—
249	C₄	—	2	1	no	—
250	C₄	—	4	1	no	—
251	C₄	—	36	2	no	—
252	C₄	#3699⋊C₃	1	2	yes	—
253	C₃	—	3	1	no	—
254	C₃	C₃×#5055	1	1	yes	characteristic
255	C₂	—	8	1	no	—
256	C₂	#63498⋊C₃	1	1	yes	characteristic
257	C₂	#63511⋊C₃	1	1	yes	characteristic
258	C₂	#63512⋊C₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

3₋¹⁺²×#124

C₂

yes

maximal, characteristic

#63431⋊C₃

C₂

yes

maximal, characteristic, complemented

#63395⋊C₃

C₂

yes

maximal, complemented

#63392⋊C₃

C₂

yes

maximal

#63362⋊C₃

C₂

yes

maximal, characteristic, complemented

C₃×#5055

—

maximal

#10588734

C₃

yes

maximal, characteristic, complemented

C₂×Q₈×3₋¹⁺²

C₂²

yes

characteristic

C₂×D₄×3₋¹⁺²

C₂²

yes

characteristic

C₂×3₋¹⁺²⋊Q₈

—

C₂²⋊C₄×3₋¹⁺²

—

C₂²⋊C₄×3₋¹⁺²

—

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×#124

D₃

yes

—

—

—

—

—

C₂×C₃

yes

characteristic

#63431

C₂×C₃

yes

characteristic, complemented

#63395

C₂×C₃

yes

complemented

#63392

C₂×C₃

yes

—

#63362

C₂×C₃

yes

characteristic, complemented

C₂³×3₋¹⁺²

—

Q₈×3₋¹⁺²

—

D₄×3₋¹⁺²

—

C₂×C₄×3₋¹⁺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×#489

—

#5055

—

C₂×C₃²×Q₈

C₂×D₃

yes

characteristic

C₂×C₃²×D₄

C₂×D₃

yes

characteristic

C₂×C₃×Dic₆

—

C₃²×C₂²⋊C₄

—

C₃²×C₂²⋊C₄

—

C₃²×C₄²

C₂×D₃

yes

characteristic

C₃×C₄⋊Dic₃

—

C₃×C₄⋊Dic₃

—

C₂×C₃×C₃⋊C₈

—

C₂×Q₈×C₉

—

C₂×Q₈×C₉

C₂²×C₃

yes

characteristic

C₂×D₄×C₉

—

C₂×D₄×C₉

C₂²×C₃

yes

characteristic

C₂×Dic₁₈

—

C₉×C₂²⋊C₄

—

C₉×C₂²⋊C₄

—

C₉×C₂²⋊C₄

—

C₉×C₂²⋊C₄

—

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

—

C₄×3₋¹⁺²

—

C₄×3₋¹⁺²

—

C₄×3₋¹⁺²

#41

yes

—

3₋¹⁺²⋊C₄

—

C₃×C₄⋊Q₈

—

C₃×#124

—

C₃×#124

C₃×D₃

yes

—

—

—

C₃×#97

—

#835

—

#832

—

#803

—

C₂³×C₃²

—

C₃²×Q₈

—

C₃²×D₄

—

C₂×C₃²×C₄

—

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

—

Q₈×C₉

—

Q₈×C₉

—

D₄×C₉

—

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

100

C₂×C₄×C₉

—

101

C₂×C₄×C₉

—

102

C₂×C₄×C₉

—

103

C₂×C₄×C₉

C₃×D₄

yes

characteristic

104

C₂×C₄×C₉

C₃×D₄

yes

characteristic

105

C₂×C₄×C₉

C₂³×C₃

yes

characteristic

106

C₂×Dic₉

—

107

Dic₁₈

—

108

C₉⋊C₈

—

109

#489

—

Sylow

110

C₂×3₋¹⁺²

—

111

C₂×3₋¹⁺²

#124

yes

characteristic

112

C₂×3₋¹⁺²

AGL(1,ℤ/8)

yes

characteristic

113

C₂×3₋¹⁺²

#137

yes

characteristic

114

C₂×C₃×Q₈

—

115

C₂×C₃×Q₈

—

116

C₂×C₃×Q₈

C₂×C₃×D₃

yes

characteristic

117

C₂×C₃×D₄

—

118

C₂×C₃×D₄

C₂×C₃×D₃

yes

characteristic

119

C₂×Dic₆

—

120

C₂×C₃×C₈

—

121

C₃×C₄⋊C₄

—

122

C₃×C₄⋊C₄

—

123

C₃×C₂²⋊C₄

—

124

C₃×C₂²⋊C₄

—

125

C₃×C₂²⋊C₄

—

126

C₃×C₂²⋊C₄

—

127

C₃×C₄²

—

128

C₃×C₄²

C₂×C₃×D₃

yes

characteristic

129

C₄⋊Dic₃

—

130

C₄⋊Dic₃

—

131

C₂×C₃⋊C₈

—

132

C₂²×C₃²

—

133

C₂²×C₃²

—

134

C₂²×C₃²

—

135

C₂²×C₃²

C₂×#67

yes

characteristic

136

C₃²×C₄

—

137

C₃²×C₄

—

138

C₃²×C₄

—

139

C₃²×C₄

#237

yes

—

140

C₃×Dic₃

—

141

C₂²×C₉

—

142

C₂²×C₉

—

143

C₂²×C₉

—

144

C₂²×C₉

—

145

C₂²×C₉

—

146

C₂²×C₉

—

147

C₂²×C₉

—

148

C₂²×C₉

C₂×C₃×D₄

yes

characteristic

149

C₄×C₉

—

150

C₄×C₉

—

151

C₄×C₉

—

152

C₄×C₉

—

153

C₄×C₉

—

154

C₄×C₉

—

155

C₄×C₉

—

156

C₄×C₉

C₃×#41

yes

—

157

Dic₉

—

158

C₄⋊Q₈

—

159

yes

160

—

161

#102

—

162

#97

—

163

3₋¹⁺²

#489

yes

characteristic, complemented, Sylow

164

C₂³×C₃

—

165

C₂³×C₃

—

166

C₃×Q₈

—

167

C₃×Q₈

—

168

C₃×Q₈

—

169

C₃×D₄

—

170

C₃×D₄

—

171

C₂×C₃×C₄

—

172

C₂×C₃×C₄

—

173

C₂×C₃×C₄

—

174

C₂×C₃×C₄

—

175

C₂×C₃×C₄

—

176

C₂×C₃×C₄

—

177

C₂×C₃×C₄

C₃×#67

yes

characteristic

178

C₂×C₃×C₄

C₃×#67

yes

characteristic

179

C₂×C₃×C₄

C₂²×C₃×D₃

yes

characteristic

180

C₂×Dic₃

—

181

Dic₆

—

182

C₃×C₈

—

183

C₃⋊C₈

—

184

C₂×C₃²

—

185

C₂×C₃²

#936

yes

characteristic

186

C₂×C₃²

#949

yes

characteristic

187

C₂×C₃²

#951

yes

characteristic

188

C₂×C₉

—

189

C₂×C₉

—

190

C₂×C₉

—

191

C₂×C₉

—

192

C₂×C₉

—

193

C₂×C₉

C₃×#124

yes

characteristic

194

C₂×C₉

C₃×AGL(1,ℤ/8)

yes

characteristic

195

C₂×C₉

C₃×#137

yes

characteristic

196

C₂×Q₈

—

197

C₂×Q₈

C₂×AGL(1,ℤ/9)

yes

characteristic

198

C₂×D₄

C₂×AGL(1,ℤ/9)

yes

characteristic

199

C₂×C₈

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₂²⋊C₄

—

203

C₂²⋊C₄

—

204

C₄²

C₂×AGL(1,ℤ/9)

yes

characteristic

205

C₂²×C₃

—

206

C₂²×C₃

—

207

C₂²×C₃

—

208

C₂²×C₃

—

209

C₂²×C₃

—

210

C₂²×C₃

—

211

C₂²×C₃

—

212

C₂²×C₃

C₂×C₃×#67

yes

characteristic

213

C₃×C₄

—

214

C₃×C₄

—

215

C₃×C₄

—

216

C₃×C₄

—

217

C₃×C₄

—

218

C₃×C₄

—

219

C₃×C₄

—

220

C₃×C₄

—

221

C₃×C₄

C₃×#237

yes

—

222

Dic₃

—

223

C₃²

#5055

yes

characteristic

224

C₉

—

225

C₉

C₃×#489

yes

characteristic, complemented

226

C₂³

—

227

Q₈

—

228

Q₈

—

229

D₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

#611⋊C₃

yes

characteristic

233

C₂×C₄

#611⋊C₃

yes

characteristic

234

C₂×C₄

C₂²×AGL(1,ℤ/9)

yes

characteristic

235

C₈

—

236

C₂×C₃

—

237

C₂×C₃

—

238

C₂×C₃

—

239

C₂×C₃

—

240

C₂×C₃

—

241

C₂×C₃

C₃×#936

yes

characteristic

242

C₂×C₃

C₃×#949

yes

characteristic

243

C₂×C₃

C₃×#951

yes

characteristic

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

C₂×#611⋊C₃

yes

characteristic

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

#3699⋊C₃

yes

—

253

C₃

—

254

C₃

C₃×#5055

yes

characteristic

255

C₂

—

256

C₂

#63498⋊C₃

yes

characteristic

257

C₂

#63511⋊C₃

yes

characteristic

258

C₂

#63512⋊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×#124	C₂
socle	C₂²×C₃	C₂×C₃×#67
prime radical	C₂×C₃²×D₄	C₂×D₃
hypercenter	#124	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#489
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #124

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×#124

C₂

socle

C₂²×C₃

C₂×C₃×#67

prime radical

C₂×C₃²×D₄

C₂×D₃

C₉

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #124

N	H ≅ G/N	type
2. #63431⋊C₃	C₂	semidirect
3. #63395⋊C₃	C₂	semidirect
5. #63362⋊C₃	C₂	semidirect
7. #10588734	C₃	semidirect
24. #63431	C₂×C₃	semidirect
25. #63395	C₂×C₃	semidirect
27. #63362	C₂×C₃	semidirect
163. 3₋¹⁺²	#489	semidirect
225. C₉	C₃×#489	semidirect

H ≅ G/N

type

2. #63431⋊C₃

C₂

semidirect

3. #63395⋊C₃

C₂

semidirect

5. #63362⋊C₃

C₂

semidirect

7. #10588734

C₃

semidirect

24. #63431

C₂×C₃

semidirect

25. #63395

C₂×C₃

semidirect

27. #63362

C₂×C₃

semidirect

163. 3₋¹⁺²

#489

semidirect

225. C₉

C₃×#489

semidirect

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

subgroup	index
3₋¹⁺²×#124	2
#63431⋊C₃	2
#63395⋊C₃	2
#63392⋊C₃	2
#63362⋊C₃	2
C₃×#5055	3
#10588734	3

subgroup

index

3₋¹⁺²×#124

Subgroups — #10588734⋊C₃ #13142930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10588734⋊C3 #13142930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10588734⋊C₃ #13142930