Group #72243561 — subgroups

Subgroups — D₉×#6894 #72243561

Order 4374.

841 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 841 conjugacy classes of subgroups — too many to draw. Only its 156 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	C₉×#6894	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	D₃×#6894	—	3	1	no	maximal
3	C₃×D₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₉×D₉	C₃	1	1	yes	maximal, characteristic
5	D₉×C₉⋊C₉	C₃	1	6	yes	maximal, complemented
6	D₉×C₉⋊C₉	C₃	1	3	yes	maximal, complemented
7	D₉×C₃²⋊C₉	C₃	1	2	yes	maximal
8	C₃×#6894	D₃	1	1	yes	characteristic
9	C₃×C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic
10	C₃²×C₉²	C₂×C₃	1	1	yes	characteristic
11	#10624561	—	2	3	no	—
12	#10624559	—	2	6	no	—
13	#10624558	—	2	1	no	—
14	#10624556	—	2	2	no	—
15	#10624548	—	2	1	no	—
16	C₉×C₉⋊C₉	C₂×C₃	1	6	yes	complemented
17	C₉×C₉⋊C₉	C₂×C₃	1	3	yes	complemented
18	C₉×C₃²⋊C₉	C₂×C₃	1	2	yes	—
19	C₃×D₃×3₋¹⁺²	—	3	1	no	—
20	C₃²×D₃×C₉	—	3	1	no	—
21	C₃³×D₉	C₃²	1	1	yes	characteristic
22	C₂×#6894	—	9	1	no	—
23	D₉×3₋¹⁺²	—	3	3	no	—
24	D₃×C₉⋊C₉	—	3	3	no	—
25	D₃×C₉⋊C₉	—	3	6	no	—
26	D₃×C₃²⋊C₉	—	3	2	no	—
27	C₃×C₉×D₉	—	3	3	no	—
28	C₃×C₉×D₉	C₃²	1	3	yes	—
29	C₃×C₉×D₉	C₃²	1	6	yes	—
30	C₃×C₉×D₉	C₃²	1	2	yes	—
31	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
32	C₃²×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
33	C₃³×C₉	—	2	1	no	—
34	C₃³×C₉	C₃×D₃	1	1	yes	characteristic
35	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
36	#6894	—	2	1	no	—
37	#6894	—	2	1	no	—
38	#6894	—	2	6	no	—
39	#6894	—	2	3	no	—
40	#6894	—	2	2	no	—
41	#6894	D₉	1	1	yes	characteristic, direct product factor
42	C₉×3₋¹⁺²	—	3	3	no	—
43	C₉×3₋¹⁺²	—	6	3	no	—
44	C₃×C₉⋊C₉	—	2	3	no	—
45	C₃×C₉⋊C₉	—	2	6	no	—
46	C₃×C₉⋊C₉	—	2	3	no	—
47	C₃×C₉⋊C₉	C₃×D₃	1	6	yes	—
48	C₃×C₉⋊C₉	C₃×D₃	1	3	yes	—
49	C₃×C₃²⋊C₉	—	2	2	no	—
50	C₃×C₃²⋊C₉	—	2	1	no	—
51	C₃×C₃²⋊C₉	C₃×D₃	1	2	yes	—
52	C₃×C₉²	—	2	2	no	—
53	C₃×C₉²	—	2	1	no	—
54	C₃×C₉²	—	3	3	no	—
55	C₃×C₉²	—	6	3	no	—
56	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
57	C₃×C₉²	C₂×C₃²	1	6	yes	—
58	C₃×C₉²	C₂×C₃²	1	2	yes	—
59	C₃×C₉²	C₂×C₃²	1	3	yes	—
60	#6855	—	2	6	no	—
61	#6855	—	2	6	no	—
62	#6855	—	2	6	no	—
63	#6855	—	2	6	no	—
64	#6855	—	2	3	no	—
65	#6855	—	2	6	no	—
66	C₃³×D₃	—	3	1	no	—
67	C₂×C₃×3₋¹⁺²	—	9	1	no	—
68	C₂×C₃²×C₉	—	9	1	no	—
69	D₃×3₋¹⁺²	—	9	3	no	—
70	C₃×D₃×C₉	—	3	1	no	—
71	C₃×D₃×C₉	—	3	6	no	—
72	C₃×D₃×C₉	—	3	2	no	—
73	C₃×D₃×C₉	—	3	3	no	—
74	C₃×D₃×C₉	—	9	3	no	—
75	C₃²×D₉	—	3	1	no	—
76	C₃²×D₉	—	3	2	no	—
77	C₃²×D₉	3₋¹⁺²	1	3	yes	—
78	C₃²×D₉	C₃³	1	1	yes	characteristic
79	C₂×C₉⋊C₉	—	9	3	no	—
80	C₂×C₉⋊C₉	—	9	6	no	—
81	C₂×C₃²⋊C₉	—	9	2	no	—
82	C₉×D₉	—	3	2	no	—
83	C₉×D₉	—	3	3	no	—
84	C₉×D₉	—	3	6	no	—
85	C₉×D₉	3₋¹⁺²	1	3	yes	complemented
86	C₃⁴	C₃²×D₃	1	1	yes	characteristic
87	C₃×3₋¹⁺²	—	2	1	no	—
88	C₃×3₋¹⁺²	—	2	3	no	—
89	C₃×3₋¹⁺²	—	3	3	no	—
90	C₃×3₋¹⁺²	—	6	3	no	—
91	C₃×3₋¹⁺²	C₃×D₉	1	1	yes	characteristic
92	C₃²×C₉	—	2	1	no	—
93	C₃²×C₉	—	2	3	no	—
94	C₃²×C₉	—	2	1	no	—
95	C₃²×C₉	—	2	2	no	—
96	C₃²×C₉	—	2	1	no	—
97	C₃²×C₉	—	2	2	no	—
98	C₃²×C₉	—	2	1	no	—
99	C₃²×C₉	—	2	6	no	—
100	C₃²×C₉	—	2	3	no	—
101	C₃²×C₉	—	3	3	no	—
102	C₃²×C₉	—	3	1	no	—
103	C₃²×C₉	—	3	2	no	—
104	C₃²×C₉	—	6	3	no	—
105	C₃²×C₉	—	6	3	no	—
106	C₃²×C₉	—	6	6	no	—
107	C₃²×C₉	—	6	2	no	—
108	C₃²×C₉	—	6	1	no	—
109	C₃²×C₉	—	6	3	no	—
110	C₃²×C₉	C₃×D₉	1	1	yes	characteristic
111	C₃²×C₉	C₂×3₋¹⁺²	1	3	yes	—
112	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
113	C₃²×C₉	C₃²×D₃	1	2	yes	—
114	C₃²×C₉	C₃²×D₃	1	3	yes	—
115	C₃²×C₉	C₃²×D₃	1	6	yes	—
116	C₃²×C₉	C₂×C₃³	1	1	yes	characteristic
117	C₉⋊C₉	—	2	3	no	—
118	C₉⋊C₉	—	2	6	no	—
119	C₉⋊C₉	—	2	6	no	—
120	C₉⋊C₉	—	2	6	no	—
121	C₉⋊C₉	—	2	3	no	—
122	C₉⋊C₉	—	2	12	no	—
123	C₉⋊C₉	—	6	9	no	—
124	C₉⋊C₉	—	6	9	no	—
125	C₉⋊C₉	—	6	18	no	—
126	C₉⋊C₉	C₃×D₉	1	6	yes	complemented
127	C₉⋊C₉	C₃×D₉	1	3	yes	complemented
128	C₃²⋊C₉	—	2	2	no	—
129	C₃²⋊C₉	—	2	6	no	—
130	C₃²⋊C₉	—	6	6	no	—
131	C₃²⋊C₉	—	6	3	no	—
132	C₃²⋊C₉	C₃×D₉	1	2	yes	—
133	C₉²	—	2	3	no	—
134	C₉²	—	3	2	no	—
135	C₉²	—	3	3	no	—
136	C₉²	—	3	6	no	—
137	C₉²	—	6	2	no	—
138	C₉²	—	6	6	no	—
139	C₉²	—	6	3	no	—
140	C₉²	—	6	6	no	—
141	C₉²	—	6	3	no	—
142	C₉²	C₂×3₋¹⁺²	1	3	yes	complemented
143	C₂×C₃³	—	9	1	no	—
144	C₃²×D₃	—	3	1	no	—
145	C₃²×D₃	—	3	3	no	—
146	C₃²×D₃	—	9	1	no	—
147	C₃²×D₃	—	9	2	no	—
148	C₂×3₋¹⁺²	—	27	3	no	—
149	C₂×C₃×C₉	—	9	1	no	—
150	C₂×C₃×C₉	—	9	6	no	—
151	C₂×C₃×C₉	—	9	2	no	—
152	C₂×C₃×C₉	—	9	3	no	—
153	C₂×C₃×C₉	—	27	3	no	—
154	D₃×C₉	—	3	3	no	—
155	D₃×C₉	—	9	6	no	—
156	D₃×C₉	—	9	2	no	—
157	D₃×C₉	—	9	3	no	—
158	C₃×D₉	—	3	3	no	—
159	C₃×D₉	C₃×3₋¹⁺²	1	1	yes	characteristic
160	C₃×D₉	C₃×3₋¹⁺²	1	1	yes	characteristic
161	C₃×D₉	#737	1	2	yes	—
162	C₃³	—	2	3	no	—
163	C₃³	—	2	1	no	—
164	C₃³	—	3	1	no	—
165	C₃³	—	3	2	no	—
166	C₃³	—	6	1	no	—
167	C₃³	—	6	2	no	—
168	C₃³	C₃²×D₉	1	1	yes	characteristic
169	C₃³	D₃×3₋¹⁺²	1	3	yes	—
170	C₃³	C₃³×D₃	1	1	yes	characteristic
171	3₋¹⁺²	—	3	3	no	—
172	3₋¹⁺²	—	6	9	no	—
173	3₋¹⁺²	—	6	3	no	—
174	C₃×C₉	—	2	1	no	—
175	C₃×C₉	—	2	1	no	—
176	C₃×C₉	—	2	1	no	—
177	C₃×C₉	—	2	2	no	—
178	C₃×C₉	—	2	3	no	—
179	C₃×C₉	—	2	6	no	—
180	C₃×C₉	—	2	6	no	—
181	C₃×C₉	—	2	2	no	—
182	C₃×C₉	—	2	3	no	—
183	C₃×C₉	—	2	3	no	—
184	C₃×C₉	—	2	3	no	—
185	C₃×C₉	—	3	3	no	—
186	C₃×C₉	—	3	2	no	—
187	C₃×C₉	—	3	3	no	—
188	C₃×C₉	—	3	6	no	—
189	C₃×C₉	—	3	3	no	—
190	C₃×C₉	—	6	6	no	—
191	C₃×C₉	—	6	3	no	—
192	C₃×C₉	—	6	3	no	—
193	C₃×C₉	—	6	6	no	—
194	C₃×C₉	—	6	3	no	—
195	C₃×C₉	—	6	6	no	—
196	C₃×C₉	—	6	2	no	—
197	C₃×C₉	—	6	3	no	—
198	C₃×C₉	—	6	1	no	—
199	C₃×C₉	—	6	2	no	—
200	C₃×C₉	—	6	2	no	—
201	C₃×C₉	—	6	2	no	—
202	C₃×C₉	—	6	27	no	—
203	C₃×C₉	—	6	2	no	—
204	C₃×C₉	—	6	1	no	—
205	C₃×C₉	—	6	2	no	—
206	C₃×C₉	—	6	3	no	—
207	C₃×C₉	—	6	6	no	—
208	C₃×C₉	—	6	6	no	—
209	C₃×C₉	—	6	3	no	—
210	C₃×C₉	—	6	6	no	—
211	C₃×C₉	—	6	6	no	—
212	C₃×C₉	—	6	3	no	—
213	C₃×C₉	—	6	6	no	—
214	C₃×C₉	C₃²×D₉	1	6	yes	—
215	C₃×C₉	C₃²×D₉	1	2	yes	—
216	C₃×C₉	C₃²×D₉	1	3	yes	—
217	C₃×C₉	C₃²×D₉	1	1	yes	characteristic
218	C₃×C₉	D₃×3₋¹⁺²	1	3	yes	—
219	C₃×C₉	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
220	C₃×C₉	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
221	C₃×C₉	C₂×#737	1	2	yes	—
222	C₂×C₃²	—	9	1	no	—
223	C₂×C₃²	—	9	3	no	—
224	C₂×C₃²	—	27	1	no	—
225	C₂×C₃²	—	27	2	no	—
226	C₃×D₃	—	3	1	no	—
227	C₃×D₃	—	3	1	no	—
228	C₃×D₃	—	3	2	no	—
229	C₃×D₃	—	9	3	no	—
230	C₂×C₉	—	9	3	no	—
231	C₂×C₉	—	27	6	no	—
232	C₂×C₉	—	27	2	no	—
233	C₂×C₉	—	27	3	no	—
234	D₉	#6894	1	1	yes	characteristic, direct product factor
235	C₃²	—	2	1	no	—
236	C₃²	—	2	1	no	—
237	C₃²	—	2	2	no	—
238	C₃²	—	2	3	no	—
239	C₃²	—	3	1	no	—
240	C₃²	—	3	2	no	—
241	C₃²	—	3	3	no	—
242	C₃²	—	6	3	no	—
243	C₃²	—	6	3	no	—
244	C₃²	—	6	6	no	—
245	C₃²	—	6	1	no	—
246	C₃²	—	6	2	no	—
247	C₃²	D₉×3₋¹⁺²	1	3	yes	—
248	C₃²	C₃³×D₉	1	1	yes	characteristic
249	C₃²	C₃×D₃×3₋¹⁺²	1	1	yes	characteristic
250	C₃²	C₃×D₃×3₋¹⁺²	1	1	yes	characteristic
251	C₃²	D₃×#737	1	2	yes	—
252	C₉	—	2	3	no	—
253	C₉	—	2	1	no	—
254	C₉	—	2	1	no	—
255	C₉	—	2	2	no	—
256	C₉	—	3	2	no	—
257	C₉	—	3	3	no	—
258	C₉	—	3	6	no	—
259	C₉	—	6	6	no	—
260	C₉	—	6	3	no	—
261	C₉	—	6	2	no	—
262	C₉	—	6	3	no	—
263	C₉	—	6	6	no	—
264	C₉	—	6	3	no	—
265	C₉	—	18	3	no	—
266	C₉	—	18	6	no	—
267	C₉	D₉×3₋¹⁺²	1	3	yes	complemented
268	C₉	C₂×#6894	1	1	yes	characteristic, complemented
269	C₂×C₃	—	9	1	no	—
270	C₂×C₃	—	9	1	no	—
271	C₂×C₃	—	9	2	no	—
272	C₂×C₃	—	27	3	no	—
273	D₃	—	3	1	no	—
274	C₃	—	2	1	no	—
275	C₃	—	2	1	no	—
276	C₃	—	2	2	no	—
277	C₃	—	3	3	no	—
278	C₃	—	6	3	no	—
279	C₃	C₃×D₉×3₋¹⁺²	1	1	yes	characteristic
280	C₃	C₃×D₉×3₋¹⁺²	1	1	yes	characteristic
281	C₃	D₉×#737	1	2	yes	—
282	C₃	D₃×#6894	1	1	yes	characteristic
283	C₂	—	9	1	no	Sylow

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#6894

C₂

yes

maximal, characteristic, complemented, Sylow

D₃×#6894

—

maximal

C₃×D₉×3₋¹⁺²

C₃

yes

maximal, characteristic

C₃²×C₉×D₉

C₃

yes

maximal, characteristic

D₉×C₉⋊C₉

C₃

yes

maximal, complemented

D₉×C₉⋊C₉

C₃

yes

maximal, complemented

D₉×C₃²⋊C₉

C₃

yes

maximal

C₃×#6894

D₃

yes

characteristic

C₃×C₉×3₋¹⁺²

C₂×C₃

yes

characteristic

C₃²×C₉²

C₂×C₃

yes

—

—

—

—

—

C₉×C₉⋊C₉

C₂×C₃

yes

complemented

C₉×C₉⋊C₉

C₂×C₃

yes

complemented

C₉×C₃²⋊C₉

C₂×C₃

yes

—

C₃×D₃×3₋¹⁺²

—

C₃²×D₃×C₉

—

C₃³×D₉

C₃²

yes

characteristic

C₂×#6894

—

D₉×3₋¹⁺²

—

D₃×C₉⋊C₉

—

D₃×C₉⋊C₉

—

D₃×C₃²⋊C₉

—

C₃×C₉×D₉

—

C₃×C₉×D₉

C₃²

yes

—

C₃×C₉×D₉

C₃²

yes

—

C₃×C₉×D₉

C₃²

yes

—

C₃×C₉×D₉

C₃²

yes

characteristic

C₃²×3₋¹⁺²

C₃×D₃

yes

characteristic

C₃³×C₉

—

C₃³×C₉

C₃×D₃

yes

characteristic

C₃³×C₉

C₂×C₃²

yes

—

—

—

—

—

D₉

yes

characteristic, direct product factor

C₉×3₋¹⁺²

—

C₉×3₋¹⁺²

—

C₃×C₉⋊C₉

—

C₃×C₉⋊C₉

—

C₃×C₉⋊C₉

—

C₃×C₉⋊C₉

C₃×D₃

yes

—

C₃×C₉⋊C₉

C₃×D₃

yes

—

C₃×C₃²⋊C₉

—

C₃×C₃²⋊C₉

—

C₃×C₃²⋊C₉

C₃×D₃

yes

—

C₃×C₉²

—

C₃×C₉²

—

C₃×C₉²

—

C₃×C₉²

—

C₃×C₉²

C₂×C₃²

yes

characteristic

C₃×C₉²

C₂×C₃²

yes

—

C₃×C₉²

C₂×C₃²

yes

—

C₃×C₉²

C₂×C₃²

yes

—

—

—

—

—

—

—

C₃³×D₃

—

C₂×C₃×3₋¹⁺²

—

C₂×C₃²×C₉

—

D₃×3₋¹⁺²

—

C₃×D₃×C₉

—

C₃×D₃×C₉

—

C₃×D₃×C₉

—

C₃×D₃×C₉

—

C₃×D₃×C₉

—

C₃²×D₉

—

C₃²×D₉

—

C₃²×D₉

3₋¹⁺²

yes

—

C₃²×D₉

C₃³

yes

characteristic

C₂×C₉⋊C₉

—

C₂×C₉⋊C₉

—

C₂×C₃²⋊C₉

—

C₉×D₉

—

C₉×D₉

—

C₉×D₉

—

C₉×D₉

3₋¹⁺²

yes

complemented

C₃⁴

C₃²×D₃

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

C₃×D₉

yes

characteristic

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

100

C₃²×C₉

—

101

C₃²×C₉

—

102

C₃²×C₉

—

103

C₃²×C₉

—

104

C₃²×C₉

—

105

C₃²×C₉

—

106

C₃²×C₉

—

107

C₃²×C₉

—

108

C₃²×C₉

—

109

C₃²×C₉

—

110

C₃²×C₉

C₃×D₉

yes

characteristic

111

C₃²×C₉

C₂×3₋¹⁺²

yes

—

112

C₃²×C₉

C₃²×D₃

yes

characteristic

113

C₃²×C₉

C₃²×D₃

yes

—

114

C₃²×C₉

C₃²×D₃

yes

—

115

C₃²×C₉

C₃²×D₃

yes

—

116

C₃²×C₉

C₂×C₃³

yes

characteristic

117

C₉⋊C₉

—

118

C₉⋊C₉

—

119

C₉⋊C₉

—

120

C₉⋊C₉

—

121

C₉⋊C₉

—

122

C₉⋊C₉

—

123

C₉⋊C₉

—

124

C₉⋊C₉

—

125

C₉⋊C₉

—

126

C₉⋊C₉

C₃×D₉

yes

complemented

127

C₉⋊C₉

C₃×D₉

yes

complemented

128

C₃²⋊C₉

—

129

C₃²⋊C₉

—

130

C₃²⋊C₉

—

131

C₃²⋊C₉

—

132

C₃²⋊C₉

C₃×D₉

yes

—

133

C₉²

—

134

C₉²

—

135

C₉²

—

136

C₉²

—

137

C₉²

—

138

C₉²

—

139

C₉²

—

140

C₉²

—

141

C₉²

—

142

C₉²

C₂×3₋¹⁺²

yes

complemented

143

C₂×C₃³

—

144

C₃²×D₃

—

145

C₃²×D₃

—

146

C₃²×D₃

—

147

C₃²×D₃

—

148

C₂×3₋¹⁺²

—

149

C₂×C₃×C₉

—

150

C₂×C₃×C₉

—

151

C₂×C₃×C₉

—

152

C₂×C₃×C₉

—

153

C₂×C₃×C₉

—

154

D₃×C₉

—

155

D₃×C₉

—

156

D₃×C₉

—

157

D₃×C₉

—

158

C₃×D₉

—

159

C₃×D₉

C₃×3₋¹⁺²

yes

characteristic

160

C₃×D₉

C₃×3₋¹⁺²

yes

characteristic

161

C₃×D₉

#737

yes

—

162

C₃³

—

163

C₃³

—

164

C₃³

—

165

C₃³

—

166

C₃³

—

167

C₃³

—

168

C₃³

C₃²×D₉

yes

characteristic

169

C₃³

D₃×3₋¹⁺²

yes

—

170

C₃³

C₃³×D₃

yes

characteristic

171

3₋¹⁺²

—

172

3₋¹⁺²

—

173

3₋¹⁺²

—

174

C₃×C₉

—

175

C₃×C₉

—

176

C₃×C₉

—

177

C₃×C₉

—

178

C₃×C₉

—

179

C₃×C₉

—

180

C₃×C₉

—

181

C₃×C₉

—

182

C₃×C₉

—

183

C₃×C₉

—

184

C₃×C₉

—

185

C₃×C₉

—

186

C₃×C₉

—

187

C₃×C₉

—

188

C₃×C₉

—

189

C₃×C₉

—

190

C₃×C₉

—

191

C₃×C₉

—

192

C₃×C₉

—

193

C₃×C₉

—

194

C₃×C₉

—

195

C₃×C₉

—

196

C₃×C₉

—

197

C₃×C₉

—

198

C₃×C₉

—

199

C₃×C₉

—

200

C₃×C₉

—

201

C₃×C₉

—

202

C₃×C₉

—

203

C₃×C₉

—

204

C₃×C₉

—

205

C₃×C₉

—

206

C₃×C₉

—

207

C₃×C₉

—

208

C₃×C₉

—

209

C₃×C₉

—

210

C₃×C₉

—

211

C₃×C₉

—

212

C₃×C₉

—

213

C₃×C₉

—

214

C₃×C₉

C₃²×D₉

yes

—

215

C₃×C₉

C₃²×D₉

yes

—

216

C₃×C₉

C₃²×D₉

yes

—

217

C₃×C₉

C₃²×D₉

yes

characteristic

218

C₃×C₉

D₃×3₋¹⁺²

yes

—

219

C₃×C₉

C₂×C₃×3₋¹⁺²

yes

characteristic

220

C₃×C₉

C₂×C₃×3₋¹⁺²

yes

characteristic

221

C₃×C₉

C₂×#737

yes

—

222

C₂×C₃²

—

223

C₂×C₃²

—

224

C₂×C₃²

—

225

C₂×C₃²

—

226

C₃×D₃

—

227

C₃×D₃

—

228

C₃×D₃

—

229

C₃×D₃

—

230

C₂×C₉

—

231

C₂×C₉

—

232

C₂×C₉

—

233

C₂×C₉

—

234

D₉

#6894

yes

characteristic, direct product factor

235

C₃²

—

236

C₃²

—

237

C₃²

—

238

C₃²

—

239

C₃²

—

240

C₃²

—

241

C₃²

—

242

C₃²

—

243

C₃²

—

244

C₃²

—

245

C₃²

—

246

C₃²

—

247

C₃²

D₉×3₋¹⁺²

yes

—

248

C₃²

C₃³×D₉

yes

characteristic

249

C₃²

C₃×D₃×3₋¹⁺²

yes

characteristic

250

C₃²

C₃×D₃×3₋¹⁺²

yes

characteristic

251

C₃²

D₃×#737

yes

—

252

C₉

—

253

C₉

—

254

C₉

—

255

C₉

—

256

C₉

—

257

C₉

—

258

C₉

—

259

C₉

—

260

C₉

—

261

C₉

—

262

C₉

—

263

C₉

—

264

C₉

—

265

C₉

—

266

C₉

—

267

C₉

D₉×3₋¹⁺²

yes

complemented

268

C₉

C₂×#6894

yes

characteristic, complemented

269

C₂×C₃

—

270

C₂×C₃

—

271

C₂×C₃

—

272

C₂×C₃

—

273

D₃

—

274

C₃

—

275

C₃

—

276

C₃

—

277

C₃

—

278

C₃

—

279

C₃

C₃×D₉×3₋¹⁺²

yes

characteristic

280

C₃

C₃×D₉×3₋¹⁺²

yes

characteristic

281

C₃

D₉×#737

yes

—

282

C₃

D₃×#6894

yes

characteristic

283

C₂

—

Sylow

	subgroup	G/H
center	C₃²	C₃³×D₉
commutator, cosocle	C₃²×C₉	C₂×C₃³
Frattini, socle	C₃³	C₃³×D₃
Fitting	C₉×#6894	C₂
prime radical	C₃³×D₉	C₃²
hypercenter	#6894	D₉
hypocenter	C₉	C₂×#6894
LCS	G ▷ C₃²×C₉ ▷ C₉
UCS	C₁ ◁ C₃² ◁ #6894

subgroup

G/H

center

C₃²

C₃³×D₉

commutator, cosocle

C₃²×C₉

C₂×C₃³

Frattini, socle

C₃³

C₃³×D₃

Fitting

C₉×#6894

C₂

prime radical

C₃³×D₉

C₃²

D₉

C₉

G ▷ C₃²×C₉ ▷ C₉

C₁ ◁ C₃² ◁ #6894

N	H ≅ G/N	type
1. C₉×#6894	C₂	semidirect
5. D₉×C₉⋊C₉	C₃	semidirect
6. D₉×C₉⋊C₉	C₃	semidirect
16. C₉×C₉⋊C₉	C₂×C₃	semidirect
17. C₉×C₉⋊C₉	C₂×C₃	semidirect
41. #6894	D₉	direct (N × H)
85. C₉×D₉	3₋¹⁺²	semidirect
126. C₉⋊C₉	C₃×D₉	semidirect
127. C₉⋊C₉	C₃×D₉	semidirect
142. C₉²	C₂×3₋¹⁺²	semidirect
234. D₉	#6894	direct (N × H)
267. C₉	D₉×3₋¹⁺²	semidirect
268. C₉	C₂×#6894	semidirect

H ≅ G/N

type

1. C₉×#6894

C₂

semidirect

5. D₉×C₉⋊C₉

C₃

semidirect

6. D₉×C₉⋊C₉

C₃

semidirect

16. C₉×C₉⋊C₉

C₂×C₃

semidirect

17. C₉×C₉⋊C₉

C₂×C₃

semidirect

41. #6894

D₉

direct (N × H)

85. C₉×D₉

3₋¹⁺²

semidirect

126. C₉⋊C₉

C₃×D₉

semidirect

127. C₉⋊C₉

C₃×D₉

semidirect

142. C₉²

C₂×3₋¹⁺²

semidirect

234. D₉

#6894

direct (N × H)

267. C₉

D₉×3₋¹⁺²

semidirect

268. C₉

C₂×#6894

semidirect

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

subgroup	index
C₉×#6894	2
D₃×#6894	3
C₃×D₉×3₋¹⁺²	3
C₃²×C₉×D₉	3
D₉×C₉⋊C₉	3
D₉×C₃²⋊C₉	3

subgroup

index

C₉×#6894

D₃×#6894

C₃×D₉×3₋¹⁺²

C₃²×C₉×D₉

D₉×C₉⋊C₉

D₉×C₃²⋊C₉

Subgroups — D₉×#6894 #72243561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D9×#6894 #72243561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×#6894 #72243561