Subgroups — #72243703

Order 4374.

850 conjugacy classes of subgroups.

The subgroup lattice has 745 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14552244	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	D₃×#6896	—	3	1	no	maximal
3	C₃×#92262	C₃	1	1	yes	maximal, characteristic
4	C₃×#92262	C₃	1	1	yes	maximal, characteristic
5	C₃⋊D₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
6	((C₃⋊D₃)⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
7	((C₃⋊D₃)⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
8	((C₃⋊D₃)⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
9	((C₃⋊D₃)⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
10	((C₃⋊D₃)⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
11	((C₃⋊D₃)⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
12	((C₃⋊D₃)⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
13	(C₃×(C₃⋊D₃)⋊C₃)⋊C₉	C₃	1	1	yes	maximal, characteristic
14	(C₃×(C₃⋊D₃)⋊C₃)⋊C₉	C₃	1	1	yes	maximal, characteristic
15	C₉×(C₃⋊D₃)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
16	C₃×#6896	—	2	1	no	—
17	C₃×#6896	D₃	1	1	yes	characteristic, complemented
18	C₃×C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
19	C₃×C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
20	C₃²×C₉⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
21	#10624566	—	2	1	no	—
22	#10624566	—	2	1	no	—
23	#10624566	—	2	1	no	—
24	#10624565	—	2	1	no	—
25	#10624565	—	2	1	no	—
26	#10624565	—	2	1	no	—
27	#10624565	—	2	1	no	—
28	#10624565	—	2	1	no	—
29	#10624565	—	2	1	no	—
30	#10624557	—	2	1	no	—
31	#10624557	—	2	1	no	—
32	#10624557	—	2	1	no	—
33	#10624556	C₂×C₃	1	1	yes	characteristic, complemented
34	#10624556	C₂×C₃	1	1	yes	characteristic, complemented
35	#10624556	C₂×C₃	1	1	yes	characteristic, complemented
36	#10624556	C₂×C₃	1	1	yes	characteristic, complemented
37	#10624556	C₂×C₃	1	1	yes	characteristic, complemented
38	#10624556	C₂×C₃	1	1	yes	characteristic, complemented
39	#10624556	C₂×C₃	1	1	yes	characteristic, complemented
40	#10624555	C₂×C₃	1	1	yes	characteristic
41	#10624555	C₂×C₃	1	1	yes	characteristic
42	C₉×C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
43	C₃×C₉×C₃⋊D₃	C₃²	1	1	yes	characteristic
44	C₃×C₉×C₃⋊D₃	C₃²	1	1	yes	characteristic
45	C₃×C₉×C₃⋊D₃	C₃²	1	1	yes	characteristic
46	C₃×C₉×C₃⋊D₃	C₃²	1	1	yes	characteristic
47	C₃×D₃×3₋¹⁺²	—	3	1	no	—
48	C₃×D₃×3₋¹⁺²	—	3	1	no	—
49	C₃²×(C₃⋊D₃)⋊C₃	C₃²	1	1	yes	characteristic
50	C₂×#6896	—	9	1	no	—
51	#92262	—	3	1	no	—
52	#92262	—	3	2	no	—
53	#92262	—	3	1	no	—
54	#92262	—	3	2	no	—
55	D₃×C₉⋊C₉	—	3	1	no	—
56	D₃×C₉⋊C₉	—	3	1	no	—
57	D₃×C₉⋊C₉	—	3	1	no	—
58	D₃×C₉⋊C₉	—	3	1	no	—
59	D₃×C₉⋊C₉	—	3	1	no	—
60	D₃×C₉⋊C₉	—	3	1	no	—
61	D₃×C₉⋊C₉	—	3	1	no	—
62	D₃×C₉⋊C₉	—	3	1	no	—
63	D₃×C₉⋊C₉	—	9	1	no	—
64	D₃×C₃²⋊C₉	—	3	1	no	—
65	D₃×C₃²⋊C₉	—	3	1	no	—
66	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
67	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
68	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
69	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
70	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
71	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
72	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
73	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
74	D₃×C₉²	—	3	1	no	—
75	C₃²×3₋¹⁺²	—	2	1	no	—
76	C₃²×3₋¹⁺²	—	2	1	no	—
77	C₃²×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
78	C₃²×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
79	C₃²×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
80	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
81	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
82	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
83	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
84	#6896	—	6	1	no	—
85	#6896	—	6	1	no	—
86	#6896	—	6	1	no	—
87	#6896	—	6	1	no	—
88	#6896	—	6	2	no	—
89	#6896	—	6	2	no	—
90	#6896	—	6	2	no	—
91	#6896	—	6	2	no	—
92	#6896	—	6	1	no	—
93	#6896	—	6	1	no	—
94	C₉⋊H(3,𝔽₃)	—	3	1	no	—
95	C₉⋊H(3,𝔽₃)	—	3	2	no	—
96	C₉⋊H(3,𝔽₃)	—	3	1	no	—
97	C₉⋊H(3,𝔽₃)	—	3	2	no	—
98	C₉⋊H(3,𝔽₃)	—	6	1	no	—
99	C₉⋊H(3,𝔽₃)	—	6	2	no	—
100	C₉⋊H(3,𝔽₃)	—	6	1	no	—
101	C₉⋊H(3,𝔽₃)	—	6	2	no	—
102	C₃×C₉⋊C₉	—	2	1	no	—
103	C₃×C₉⋊C₉	—	2	1	no	—
104	C₃×C₉⋊C₉	—	2	1	no	—
105	C₃×C₉⋊C₉	—	2	1	no	—
106	C₃×C₉⋊C₉	—	2	1	no	—
107	C₃×C₉⋊C₉	—	2	1	no	—
108	C₃×C₉⋊C₉	—	2	1	no	—
109	C₃×C₉⋊C₉	—	2	1	no	—
110	C₃×C₉⋊C₉	—	2	1	no	—
111	C₃×C₉⋊C₉	—	2	1	no	—
112	C₃×C₉⋊C₉	—	2	1	no	—
113	C₃×C₉⋊C₉	—	3	1	no	—
114	C₃×C₉⋊C₉	—	6	1	no	—
115	C₃×C₉⋊C₉	—	6	1	no	—
116	C₃×C₉⋊C₉	—	6	1	no	—
117	C₃×C₉⋊C₉	—	6	1	no	—
118	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
119	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
120	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
121	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
122	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
123	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
124	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
125	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
126	C₃×C₃²⋊C₉	—	2	1	no	—
127	C₃×C₃²⋊C₉	—	2	1	no	—
128	C₃×C₃²⋊C₉	—	2	1	no	—
129	C₃×C₃²⋊C₉	—	2	1	no	—
130	C₃×C₃²⋊C₉	—	2	1	no	—
131	C₃×C₃²⋊C₉	—	2	1	no	—
132	C₃×C₃²⋊C₉	—	2	1	no	—
133	C₃×C₃²⋊C₉	—	2	1	no	—
134	C₃×C₃²⋊C₉	—	2	1	no	—
135	C₃×C₃²⋊C₉	—	2	1	no	—
136	C₃×C₃²⋊C₉	—	2	1	no	—
137	C₃×C₃²⋊C₉	—	2	1	no	—
138	C₃×C₃²⋊C₉	—	2	1	no	—
139	C₃×C₃²⋊C₉	—	2	1	no	—
140	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
141	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
142	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
143	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
144	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
145	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
146	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
147	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
148	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
149	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
150	C₃×C₉²	—	2	1	no	—
151	C₃×C₉²	C₃×D₃	1	1	yes	characteristic
152	#6855	—	2	1	no	—
153	#6855	—	2	1	no	—
154	#6855	—	2	1	no	—
155	#6855	—	2	1	no	—
156	#6855	—	2	1	no	—
157	#6855	—	2	1	no	—
158	#6855	—	2	1	no	—
159	#6855	—	2	1	no	—
160	#6855	—	2	1	no	—
161	#6855	—	2	1	no	—
162	#6855	—	2	1	no	—
163	#6855	—	2	1	no	—
164	#6855	—	2	1	no	—
165	#6855	—	2	1	no	—
166	#6855	—	2	1	no	—
167	#6855	—	2	1	no	—
168	#6855	—	2	1	no	—
169	#6855	—	2	1	no	—
170	#6855	—	2	1	no	—
171	#6855	—	2	1	no	—
172	#6855	—	2	1	no	—
173	#6855	—	2	1	no	—
174	#6855	—	2	1	no	—
175	#6855	—	2	1	no	—
176	C₃²×C₃⋊D₃	C₃³	1	1	yes	characteristic
177	C₃³×D₃	—	3	1	no	—
178	C₂×C₃×3₋¹⁺²	—	9	1	no	—
179	C₂×C₃×3₋¹⁺²	—	9	1	no	—
180	C₉×C₃⋊D₃	—	3	1	no	—
181	C₉×C₃⋊D₃	—	3	1	no	—
182	C₉×C₃⋊D₃	—	3	1	no	—
183	C₉×C₃⋊D₃	—	3	1	no	—
184	D₃×3₋¹⁺²	—	9	1	no	—
185	D₃×3₋¹⁺²	—	9	2	no	—
186	D₃×3₋¹⁺²	—	9	1	no	—
187	D₃×3₋¹⁺²	—	9	2	no	—
188	C₃×(C₃⋊D₃)⋊C₃	—	3	1	no	—
189	C₃×(C₃⋊D₃)⋊C₃	—	3	1	no	—
190	C₃×(C₃⋊D₃)⋊C₃	—	3	1	no	—
191	C₃×(C₃⋊D₃)⋊C₃	—	3	1	no	—
192	C₃×D₃×C₉	—	3	1	no	—
193	C₃×D₃×C₉	—	3	1	no	—
194	C₃×D₃×C₉	—	3	1	no	—
195	C₃×D₃×C₉	—	3	1	no	—
196	C₃×D₃×C₉	—	3	1	no	—
197	C₃×D₃×C₉	—	3	1	no	—
198	C₃×D₃×C₉	—	3	1	no	—
199	C₃×D₃×C₉	—	3	1	no	—
200	C₃×D₃×C₉	—	3	1	no	—
201	C₃×D₃×C₉	—	3	1	no	—
202	C₃×D₃×C₉	—	3	1	no	—
203	C₃×D₃×C₉	—	3	1	no	—
204	C₃×D₃×C₉	—	9	1	no	—
205	C₃×D₃×C₉	—	9	1	no	—
206	C₃×D₃×C₉	—	9	1	no	—
207	C₃×D₃×C₉	—	9	1	no	—
208	C₂×C₉⋊C₉	—	9	1	no	—
209	C₂×C₉⋊C₉	—	9	1	no	—
210	C₂×C₉⋊C₉	—	9	1	no	—
211	C₂×C₉⋊C₉	—	9	1	no	—
212	C₂×C₉⋊C₉	—	9	1	no	—
213	C₂×C₉⋊C₉	—	9	1	no	—
214	C₂×C₉⋊C₉	—	9	1	no	—
215	C₂×C₉⋊C₉	—	9	1	no	—
216	C₂×C₃²⋊C₉	—	9	1	no	—
217	C₂×C₃²⋊C₉	—	9	1	no	—
218	C₂×C₉²	—	9	1	no	—
219	(C₃⋊D₃)⋊C₉	—	3	1	no	—
220	(C₃⋊D₃)⋊C₉	—	3	1	no	—
221	(C₃⋊D₃)⋊C₉	—	3	1	no	—
222	(C₃⋊D₃)⋊C₉	—	3	1	no	—
223	(C₃⋊D₃)⋊C₉	—	3	1	no	—
224	(C₃⋊D₃)⋊C₉	—	3	1	no	—
225	(C₃⋊D₃)⋊C₉	3₋¹⁺²	1	1	yes	characteristic, complemented
226	(C₃⋊D₃)⋊C₉	3₋¹⁺²	1	1	yes	characteristic, complemented
227	(C₃⋊D₃)⋊C₉	3₋¹⁺²	1	2	yes	complemented
228	(C₃⋊D₃)⋊C₉	3₋¹⁺²	1	2	yes	complemented
229	C₃⁴	—	2	1	no	—
230	C₃⁴	C₃²×D₃	1	1	yes	characteristic
231	C₃⁴	C₂×C₃³	1	1	yes	characteristic
232	C₃×3₋¹⁺²	—	3	1	no	—
233	C₃×3₋¹⁺²	—	3	2	no	—
234	C₃×3₋¹⁺²	—	3	1	no	—
235	C₃×3₋¹⁺²	—	3	2	no	—
236	C₃×3₋¹⁺²	—	3	1	no	—
237	C₃×3₋¹⁺²	—	6	2	no	—
238	C₃×3₋¹⁺²	—	6	1	no	—
239	C₃×3₋¹⁺²	—	6	2	no	—
240	C₃×3₋¹⁺²	—	6	1	no	—
241	C₃×3₋¹⁺²	—	6	1	no	—
242	C₃×3₋¹⁺²	—	6	2	no	—
243	C₃×3₋¹⁺²	—	6	2	no	—
244	C₃×3₋¹⁺²	—	6	1	no	—
245	C₃×3₋¹⁺²	—	6	1	no	—
246	C₃×3₋¹⁺²	—	6	1	no	—
247	C₃×3₋¹⁺²	—	6	1	no	—
248	C₃×3₋¹⁺²	—	18	1	no	—
249	C₃×3₋¹⁺²	—	18	1	no	—
250	C₃×3₋¹⁺²	—	18	1	no	—
251	C₃×3₋¹⁺²	—	18	1	no	—
252	C₃×3₋¹⁺²	—	18	1	no	—
253	C₃×3₋¹⁺²	—	18	1	no	—
254	C₃×H(3,𝔽₃)	—	3	1	no	—
255	C₃×H(3,𝔽₃)	—	3	1	no	—
256	C₃×H(3,𝔽₃)	—	3	1	no	—
257	C₃×H(3,𝔽₃)	—	3	1	no	—
258	C₃×H(3,𝔽₃)	—	6	1	no	—
259	C₃×H(3,𝔽₃)	—	6	1	no	—
260	C₃×H(3,𝔽₃)	—	6	1	no	—
261	C₃×H(3,𝔽₃)	—	6	1	no	—
262	C₃²×C₉	—	2	1	no	—
263	C₃²×C₉	—	2	1	no	—
264	C₃²×C₉	—	2	1	no	—
265	C₃²×C₉	—	2	1	no	—
266	C₃²×C₉	—	2	1	no	—
267	C₃²×C₉	—	2	1	no	—
268	C₃²×C₉	—	2	1	no	—
269	C₃²×C₉	—	2	1	no	—
270	C₃²×C₉	—	2	1	no	—
271	C₃²×C₉	—	2	1	no	—
272	C₃²×C₉	—	2	1	no	—
273	C₃²×C₉	—	2	1	no	—
274	C₃²×C₉	—	3	1	no	—
275	C₃²×C₉	—	3	1	no	—
276	C₃²×C₉	—	3	1	no	—
277	C₃²×C₉	—	3	1	no	—
278	C₃²×C₉	—	3	1	no	—
279	C₃²×C₉	—	3	1	no	—
280	C₃²×C₉	—	3	1	no	—
281	C₃²×C₉	—	3	1	no	—
282	C₃²×C₉	—	6	3	no	—
283	C₃²×C₉	—	6	1	no	—
284	C₃²×C₉	—	6	1	no	—
285	C₃²×C₉	—	6	1	no	—
286	C₃²×C₉	—	6	1	no	—
287	C₃²×C₉	—	6	1	no	—
288	C₃²×C₉	—	6	1	no	—
289	C₃²×C₉	—	6	1	no	—
290	C₃²×C₉	—	6	1	no	—
291	C₃²×C₉	—	18	1	no	—
292	C₃²×C₉	—	18	1	no	—
293	C₃²×C₉	—	18	1	no	—
294	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
295	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
296	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
297	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
298	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
299	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
300	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
301	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
302	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
303	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
304	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
305	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
306	C₉⋊C₉	—	2	1	no	—
307	C₉⋊C₉	—	2	1	no	—
308	C₉⋊C₉	—	2	1	no	—
309	C₉⋊C₉	—	2	1	no	—
310	C₉⋊C₉	—	3	1	no	—
311	C₉⋊C₉	—	6	1	no	—
312	C₉⋊C₉	—	6	1	no	—
313	C₉⋊C₉	—	6	1	no	—
314	C₉⋊C₉	—	6	1	no	—
315	C₉⋊C₉	—	6	1	no	—
316	C₉⋊C₉	—	6	1	no	—
317	C₉⋊C₉	—	6	1	no	—
318	C₉⋊C₉	—	6	2	no	—
319	C₉⋊C₉	—	6	2	no	—
320	C₉⋊C₉	—	6	2	no	—
321	C₉⋊C₉	—	6	2	no	—
322	C₉⋊C₉	—	6	2	no	—
323	C₉⋊C₉	—	6	2	no	—
324	C₉⋊C₉	—	6	2	no	—
325	C₉⋊C₉	—	6	2	no	—
326	C₉⋊C₉	—	6	2	no	—
327	C₉⋊C₉	—	6	2	no	—
328	C₉⋊C₉	—	6	2	no	—
329	C₉⋊C₉	—	6	1	no	—
330	C₉⋊C₉	—	6	1	no	—
331	C₉⋊C₉	—	6	1	no	—
332	C₉⋊C₉	—	6	1	no	—
333	C₉⋊C₉	—	6	1	no	—
334	C₉⋊C₉	—	6	1	no	—
335	C₉⋊C₉	—	6	1	no	—
336	C₉⋊C₉	—	6	1	no	—
337	C₉⋊C₉	—	6	1	no	—
338	C₉⋊C₉	—	6	1	no	—
339	C₉⋊C₉	—	6	1	no	—
340	C₉⋊C₉	—	6	1	no	—
341	C₉⋊C₉	—	6	1	no	—
342	C₉⋊C₉	—	6	1	no	—
343	C₉⋊C₉	—	6	1	no	—
344	C₉⋊C₉	—	6	1	no	—
345	C₉⋊C₉	—	6	1	no	—
346	C₉⋊C₉	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, complemented
347	C₃²⋊C₉	—	2	1	no	—
348	C₃²⋊C₉	—	2	1	no	—
349	C₃²⋊C₉	—	2	2	no	—
350	C₃²⋊C₉	—	2	2	no	—
351	C₃²⋊C₉	—	3	1	no	—
352	C₃²⋊C₉	—	3	1	no	—
353	C₃²⋊C₉	—	3	1	no	—
354	C₃²⋊C₉	—	3	1	no	—
355	C₃²⋊C₉	—	3	1	no	—
356	C₃²⋊C₉	—	3	1	no	—
357	C₃²⋊C₉	—	3	1	no	—
358	C₃²⋊C₉	—	6	1	no	—
359	C₃²⋊C₉	—	6	2	no	—
360	C₃²⋊C₉	—	6	1	no	—
361	C₃²⋊C₉	—	6	2	no	—
362	C₃²⋊C₉	—	6	1	no	—
363	C₃²⋊C₉	—	6	1	no	—
364	C₃²⋊C₉	—	6	2	no	—
365	C₃²⋊C₉	—	6	1	no	—
366	C₃²⋊C₉	—	6	2	no	—
367	C₃²⋊C₉	—	6	1	no	—
368	C₃²⋊C₉	—	6	3	no	—
369	C₃²⋊C₉	—	6	3	no	—
370	C₃²⋊C₉	—	6	3	no	—
371	C₃²⋊C₉	—	6	2	no	—
372	C₃²⋊C₉	—	6	2	no	—
373	C₃²⋊C₉	—	6	1	no	—
374	C₃²⋊C₉	—	6	1	no	—
375	C₃²⋊C₉	—	6	1	no	—
376	C₃²⋊C₉	—	6	1	no	—
377	C₃²⋊C₉	—	6	1	no	—
378	C₃²⋊C₉	—	6	1	no	—
379	C₃²⋊C₉	—	6	1	no	—
380	C₃²⋊C₉	—	6	1	no	—
381	C₃²⋊C₉	—	6	1	no	—
382	C₃²⋊C₉	—	6	1	no	—
383	C₃²⋊C₉	—	6	1	no	—
384	C₃²⋊C₉	—	6	2	no	—
385	C₃²⋊C₉	—	6	2	no	—
386	C₃²⋊C₉	—	18	1	no	—
387	C₃²⋊C₉	—	18	1	no	—
388	C₃²⋊C₉	—	18	1	no	—
389	C₃²⋊C₉	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
390	C₃²⋊C₉	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
391	C₃²⋊C₉	C₂×3₋¹⁺²	1	2	yes	complemented
392	C₃²⋊C₉	C₂×3₋¹⁺²	1	2	yes	complemented
393	C₉²	—	6	1	no	—
394	C₉²	—	6	2	no	—
395	C₉²	—	6	1	no	—
396	C₉²	—	6	1	no	—
397	C₂×C₃³	—	9	1	no	—
398	C₃×C₃⋊D₃	C₃×3₋¹⁺²	1	1	yes	characteristic
399	C₃×C₃⋊D₃	C₃×3₋¹⁺²	1	1	yes	characteristic
400	C₃×C₃⋊D₃	#737	1	1	yes	characteristic
401	C₃×C₃⋊D₃	#737	1	1	yes	characteristic
402	C₃²×D₃	—	3	1	no	—
403	C₃²×D₃	—	9	1	no	—
404	C₃²×D₃	—	9	1	no	—
405	C₃²×D₃	—	9	1	no	—
406	C₃²×D₃	—	9	1	no	—
407	C₃²×D₃	—	9	1	no	—
408	C₂×3₋¹⁺²	—	27	1	no	—
409	C₂×3₋¹⁺²	—	27	2	no	—
410	C₂×3₋¹⁺²	—	27	1	no	—
411	C₂×3₋¹⁺²	—	27	2	no	—
412	C₂×C₃×C₉	—	9	1	no	—
413	C₂×C₃×C₉	—	9	1	no	—
414	C₂×C₃×C₉	—	9	1	no	—
415	C₂×C₃×C₉	—	9	1	no	—
416	C₂×C₃×C₉	—	9	1	no	—
417	C₂×C₃×C₉	—	9	1	no	—
418	C₂×C₃×C₉	—	9	1	no	—
419	C₂×C₃×C₉	—	9	1	no	—
420	C₂×C₃×C₉	—	9	1	no	—
421	C₂×C₃×C₉	—	9	1	no	—
422	C₂×C₃×C₉	—	9	1	no	—
423	C₂×C₃×C₉	—	9	1	no	—
424	(C₃⋊D₃)⋊C₃	—	9	1	no	—
425	D₃×C₉	—	3	1	no	—
426	D₃×C₉	—	3	1	no	—
427	D₃×C₉	—	3	2	no	—
428	D₃×C₉	—	3	2	no	—
429	D₃×C₉	—	9	1	no	—
430	D₃×C₉	—	9	1	no	—
431	D₃×C₉	—	9	1	no	—
432	D₃×C₉	—	9	1	no	—
433	D₃×C₉	—	9	1	no	—
434	D₃×C₉	—	9	1	no	—
435	D₃×C₉	—	9	1	no	—
436	D₃×C₉	—	9	1	no	—
437	D₃×C₉	—	9	1	no	—
438	D₃×C₉	—	9	1	no	—
439	D₃×C₉	—	9	3	no	—
440	D₃×C₉	—	27	1	no	—
441	D₃×C₉	—	27	1	no	—
442	D₃×C₉	—	27	1	no	—
443	C₃³	—	2	1	no	—
444	C₃³	—	2	1	no	—
445	C₃³	—	2	1	no	—
446	C₃³	—	2	1	no	—
447	C₃³	—	3	1	no	—
448	C₃³	—	3	1	no	—
449	C₃³	—	3	1	no	—
450	C₃³	—	3	1	no	—
451	C₃³	—	3	1	no	—
452	C₃³	—	6	1	no	—
453	C₃³	—	6	1	no	—
454	C₃³	—	6	1	no	—
455	C₃³	—	6	1	no	—
456	C₃³	—	6	1	no	—
457	C₃³	—	6	1	no	—
458	C₃³	—	6	1	no	—
459	C₃³	—	6	1	no	—
460	C₃³	—	6	1	no	—
461	C₃³	—	6	1	no	—
462	C₃³	—	6	1	no	—
463	C₃³	—	6	1	no	—
464	C₃³	—	6	1	no	—
465	C₃³	—	6	1	no	—
466	C₃³	—	6	1	no	—
467	C₃³	—	6	1	no	—
468	C₃³	—	6	1	no	—
469	C₃³	—	6	1	no	—
470	C₃³	—	6	1	no	—
471	C₃³	—	6	1	no	—
472	C₃³	—	6	1	no	—
473	C₃³	—	6	1	no	—
474	C₃³	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
475	C₃³	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
476	C₃³	C₂×#737	1	1	yes	characteristic
477	C₃³	C₂×#737	1	1	yes	characteristic
478	C₃³	C₃³×D₃	1	1	yes	characteristic
479	3₋¹⁺²	—	9	1	no	—
480	3₋¹⁺²	—	9	2	no	—
481	3₋¹⁺²	—	18	1	no	—
482	3₋¹⁺²	—	18	1	no	—
483	3₋¹⁺²	—	18	2	no	—
484	3₋¹⁺²	—	18	1	no	—
485	3₋¹⁺²	—	18	2	no	—
486	3₋¹⁺²	—	18	1	no	—
487	3₋¹⁺²	—	18	2	no	—
488	3₋¹⁺²	—	18	1	no	—
489	3₋¹⁺²	—	18	2	no	—
490	3₋¹⁺²	—	18	2	no	—
491	3₋¹⁺²	—	18	4	no	—
492	3₋¹⁺²	—	18	2	no	—
493	3₋¹⁺²	—	18	4	no	—
494	3₋¹⁺²	—	18	2	no	—
495	H(3,𝔽₃)	—	9	1	no	—
496	H(3,𝔽₃)	—	18	1	no	—
497	H(3,𝔽₃)	—	18	1	no	—
498	H(3,𝔽₃)	—	18	1	no	—
499	H(3,𝔽₃)	—	18	1	no	—
500	C₃×C₉	—	2	3	no	—
501	C₃×C₉	—	2	1	no	—
502	C₃×C₉	—	2	1	no	—
503	C₃×C₉	—	2	1	no	—
504	C₃×C₉	—	2	1	no	—
505	C₃×C₉	—	2	2	no	—
506	C₃×C₉	—	2	1	no	—
507	C₃×C₉	—	2	2	no	—
508	C₃×C₉	—	2	1	no	—
509	C₃×C₉	—	3	3	no	—
510	C₃×C₉	—	3	1	no	—
511	C₃×C₉	—	3	1	no	—
512	C₃×C₉	—	3	1	no	—
513	C₃×C₉	—	3	1	no	—
514	C₃×C₉	—	3	1	no	—
515	C₃×C₉	—	3	1	no	—
516	C₃×C₉	—	3	1	no	—
517	C₃×C₉	—	3	1	no	—
518	C₃×C₉	—	3	1	no	—
519	C₃×C₉	—	3	1	no	—
520	C₃×C₉	—	3	1	no	—
521	C₃×C₉	—	3	1	no	—
522	C₃×C₉	—	3	1	no	—
523	C₃×C₉	—	3	1	no	—
524	C₃×C₉	—	6	1	no	—
525	C₃×C₉	—	6	1	no	—
526	C₃×C₉	—	6	3	no	—
527	C₃×C₉	—	6	1	no	—
528	C₃×C₉	—	6	1	no	—
529	C₃×C₉	—	6	1	no	—
530	C₃×C₉	—	6	1	no	—
531	C₃×C₉	—	6	1	no	—
532	C₃×C₉	—	6	1	no	—
533	C₃×C₉	—	6	1	no	—
534	C₃×C₉	—	6	1	no	—
535	C₃×C₉	—	6	1	no	—
536	C₃×C₉	—	6	1	no	—
537	C₃×C₉	—	6	1	no	—
538	C₃×C₉	—	6	3	no	—
539	C₃×C₉	—	6	3	no	—
540	C₃×C₉	—	6	1	no	—
541	C₃×C₉	—	6	1	no	—
542	C₃×C₉	—	6	1	no	—
543	C₃×C₉	—	6	1	no	—
544	C₃×C₉	—	6	3	no	—
545	C₃×C₉	—	6	1	no	—
546	C₃×C₉	—	6	1	no	—
547	C₃×C₉	—	6	1	no	—
548	C₃×C₉	—	6	1	no	—
549	C₃×C₉	—	6	1	no	—
550	C₃×C₉	—	6	1	no	—
551	C₃×C₉	—	6	1	no	—
552	C₃×C₉	—	6	1	no	—
553	C₃×C₉	—	6	1	no	—
554	C₃×C₉	—	6	1	no	—
555	C₃×C₉	—	6	1	no	—
556	C₃×C₉	—	6	1	no	—
557	C₃×C₉	—	6	1	no	—
558	C₃×C₉	—	6	1	no	—
559	C₃×C₉	—	6	1	no	—
560	C₃×C₉	—	6	1	no	—
561	C₃×C₉	—	6	2	no	—
562	C₃×C₉	—	6	2	no	—
563	C₃×C₉	—	6	1	no	—
564	C₃×C₉	—	6	1	no	—
565	C₃×C₉	—	6	1	no	—
566	C₃×C₉	—	6	1	no	—
567	C₃×C₉	—	6	1	no	—
568	C₃×C₉	—	6	1	no	—
569	C₃×C₉	—	6	1	no	—
570	C₃×C₉	—	6	1	no	—
571	C₃×C₉	—	6	1	no	—
572	C₃×C₉	—	6	1	no	—
573	C₃×C₉	—	6	1	no	—
574	C₃×C₉	—	6	1	no	—
575	C₃×C₉	—	6	1	no	—
576	C₃×C₉	—	6	1	no	—
577	C₃×C₉	—	6	1	no	—
578	C₃×C₉	—	6	1	no	—
579	C₃×C₉	—	6	1	no	—
580	C₃×C₉	—	6	1	no	—
581	C₃×C₉	—	6	1	no	—
582	C₃×C₉	—	6	1	no	—
583	C₃×C₉	—	6	1	no	—
584	C₃×C₉	—	6	1	no	—
585	C₃×C₉	—	6	1	no	—
586	C₃×C₉	—	6	1	no	—
587	C₃×C₉	—	9	1	no	—
588	C₃×C₉	—	9	1	no	—
589	C₃×C₉	—	9	1	no	—
590	C₃×C₉	—	18	1	no	—
591	C₃×C₉	—	18	1	no	—
592	C₃×C₉	—	18	1	no	—
593	C₃×C₉	—	18	1	no	—
594	C₃×C₉	—	18	1	no	—
595	C₃×C₉	—	18	1	no	—
596	C₃×C₉	—	18	2	no	—
597	C₃×C₉	—	18	2	no	—
598	C₃×C₉	—	18	2	no	—
599	C₃×C₉	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
600	C₃×C₉	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
601	C₃×C₉	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
602	C₃×C₉	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
603	C₃×C₉	D₃×3₋¹⁺²	1	1	yes	characteristic
604	C₃×C₉	D₃×3₋¹⁺²	1	1	yes	characteristic
605	C₃×C₉	D₃×3₋¹⁺²	1	2	yes	—
606	C₃×C₉	D₃×3₋¹⁺²	1	2	yes	—
607	C₂×C₃²	—	9	1	no	—
608	C₂×C₃²	—	27	1	no	—
609	C₂×C₃²	—	27	1	no	—
610	C₂×C₃²	—	27	1	no	—
611	C₂×C₃²	—	27	1	no	—
612	C₃⋊D₃	#6896	1	1	yes	characteristic, complemented
613	C₃×D₃	—	3	1	no	—
614	C₃×D₃	—	3	1	no	—
615	C₃×D₃	—	3	1	no	—
616	C₃×D₃	—	3	1	no	—
617	C₃×D₃	—	9	1	no	—
618	C₃×D₃	—	9	1	no	—
619	C₃×D₃	—	9	1	no	—
620	C₃×D₃	—	9	1	no	—
621	C₃×D₃	—	27	1	no	—
622	C₂×C₉	—	9	1	no	—
623	C₂×C₉	—	9	1	no	—
624	C₂×C₉	—	9	2	no	—
625	C₂×C₉	—	9	2	no	—
626	C₂×C₉	—	27	1	no	—
627	C₂×C₉	—	27	1	no	—
628	C₂×C₉	—	27	1	no	—
629	C₂×C₉	—	27	1	no	—
630	C₂×C₉	—	27	1	no	—
631	C₂×C₉	—	27	1	no	—
632	C₂×C₉	—	27	1	no	—
633	C₂×C₉	—	27	1	no	—
634	C₂×C₉	—	27	1	no	—
635	C₂×C₉	—	27	1	no	—
636	C₃²	—	2	1	no	—
637	C₃²	—	2	1	no	—
638	C₃²	—	2	1	no	—
639	C₃²	—	2	1	no	—
640	C₃²	—	2	1	no	—
641	C₃²	—	2	1	no	—
642	C₃²	—	2	1	no	—
643	C₃²	—	2	1	no	—
644	C₃²	—	3	1	no	—
645	C₃²	—	3	1	no	—
646	C₃²	—	3	1	no	—
647	C₃²	—	3	1	no	—
648	C₃²	—	6	1	no	—
649	C₃²	—	6	1	no	—
650	C₃²	—	6	1	no	—
651	C₃²	—	6	1	no	—
652	C₃²	—	6	2	no	—
653	C₃²	—	6	2	no	—
654	C₃²	—	6	2	no	—
655	C₃²	—	6	2	no	—
656	C₃²	—	6	1	no	—
657	C₃²	—	6	1	no	—
658	C₃²	—	6	1	no	—
659	C₃²	—	6	1	no	—
660	C₃²	—	9	1	no	—
661	C₃²	—	9	1	no	—
662	C₃²	—	9	1	no	—
663	C₃²	—	18	1	no	—
664	C₃²	—	18	1	no	—
665	C₃²	—	18	1	no	—
666	C₃²	—	18	1	no	—
667	C₃²	—	18	1	no	—
668	C₃²	—	18	1	no	—
669	C₃²	—	18	1	no	—
670	C₃²	—	18	1	no	—
671	C₃²	—	18	1	no	—
672	C₃²	—	18	1	no	—
673	C₃²	—	18	1	no	—
674	C₃²	—	18	1	no	—
675	C₃²	—	18	1	no	—
676	C₃²	—	18	1	no	—
677	C₃²	—	18	1	no	—
678	C₃²	—	18	1	no	—
679	C₃²	—	18	1	no	—
680	C₃²	—	18	1	no	—
681	C₃²	—	18	1	no	—
682	C₃²	C₂×#6896	1	1	yes	characteristic, complemented
683	C₃²	C₃²×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
684	C₃²	C₃×D₃×3₋¹⁺²	1	1	yes	characteristic
685	C₃²	C₃×D₃×3₋¹⁺²	1	1	yes	characteristic
686	C₃²	D₃×#737	1	1	yes	characteristic
687	C₃²	D₃×#737	1	1	yes	characteristic
688	C₉	—	3	1	no	—
689	C₉	—	3	1	no	—
690	C₉	—	3	1	no	—
691	C₉	—	3	1	no	—
692	C₉	—	3	1	no	—
693	C₉	—	3	1	no	—
694	C₉	—	6	3	no	—
695	C₉	—	6	1	no	—
696	C₉	—	6	2	no	—
697	C₉	—	6	2	no	—
698	C₉	—	6	1	no	—
699	C₉	—	6	1	no	—
700	C₉	—	6	2	no	—
701	C₉	—	6	1	no	—
702	C₉	—	6	2	no	—
703	C₉	—	6	1	no	—
704	C₉	—	6	1	no	—
705	C₉	—	9	1	no	—
706	C₉	—	9	1	no	—
707	C₉	—	9	1	no	—
708	C₉	—	18	1	no	—
709	C₉	—	18	1	no	—
710	C₉	—	18	1	no	—
711	C₉	—	18	1	no	—
712	C₉	—	18	1	no	—
713	C₉	—	18	1	no	—
714	C₉	—	18	1	no	—
715	C₉	—	18	1	no	—
716	C₉	—	18	1	no	—
717	C₉	—	18	1	no	—
718	C₉	—	18	1	no	—
719	C₉	—	18	1	no	—
720	C₂×C₃	—	9	1	no	—
721	C₂×C₃	—	9	1	no	—
722	C₂×C₃	—	9	1	no	—
723	C₂×C₃	—	9	1	no	—
724	C₂×C₃	—	81	1	no	—
725	D₃	—	3	1	no	—
726	D₃	—	9	1	no	—
727	C₃	—	2	1	no	—
728	C₃	—	2	1	no	—
729	C₃	—	2	1	no	—
730	C₃	—	2	1	no	—
731	C₃	—	3	1	no	—
732	C₃	—	6	1	no	—
733	C₃	—	6	1	no	—
734	C₃	—	6	1	no	—
735	C₃	—	6	1	no	—
736	C₃	—	54	1	no	—
737	C₃	—	54	1	no	—
738	C₃	#13091420	1	1	yes	characteristic
739	C₃	D₃×#6896	1	1	yes	characteristic
740	C₃	3₋¹⁺²×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
741	C₃	3₋¹⁺²×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
742	C₃	#13091514	1	1	yes	characteristic
743	C₂	—	9	1	no	Sylow

	subgroup	G/H
center	C₃²	C₃²×(C₃⋊D₃)⋊C₃
commutator, cosocle	C₃⁴	C₂×C₃³
Frattini, socle	C₃³	C₃³×D₃
Fitting	#14552244	C₂
prime radical	C₃²×(C₃⋊D₃)⋊C₃	C₃²
hypercenter	C₉⋊C₉	(C₃⋊D₃)⋊C₃
hypocenter	C₃²	C₂×#6896
LCS	G ▷ C₃⁴ ▷ C₃²
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #14552244	C₂	semidirect
5. C₃⋊D₃×C₉⋊C₉	C₃	semidirect
6. ((C₃⋊D₃)⋊C₉)⋊C₉	C₃	semidirect
7. ((C₃⋊D₃)⋊C₉)⋊C₉	C₃	semidirect
8. ((C₃⋊D₃)⋊C₉)⋊C₉	C₃	semidirect
9. ((C₃⋊D₃)⋊C₉)⋊C₉	C₃	semidirect
10. ((C₃⋊D₃)⋊C₉)⋊C₉	C₃	semidirect
11. ((C₃⋊D₃)⋊C₉)⋊C₉	C₃	semidirect
12. ((C₃⋊D₃)⋊C₉)⋊C₉	C₃	semidirect
15. C₉×(C₃⋊D₃)⋊C₉	C₃	semidirect
17. C₃×#6896	D₃	semidirect
20. C₃²×C₉⋊C₉	C₂×C₃	semidirect
33. #10624556	C₂×C₃	semidirect
34. #10624556	C₂×C₃	semidirect
35. #10624556	C₂×C₃	semidirect
36. #10624556	C₂×C₃	semidirect
37. #10624556	C₂×C₃	semidirect
38. #10624556	C₂×C₃	semidirect
39. #10624556	C₂×C₃	semidirect
42. C₉×C₃²⋊C₉	C₂×C₃	semidirect
225. (C₃⋊D₃)⋊C₉	3₋¹⁺²	semidirect
226. (C₃⋊D₃)⋊C₉	3₋¹⁺²	semidirect
227. (C₃⋊D₃)⋊C₉	3₋¹⁺²	semidirect
228. (C₃⋊D₃)⋊C₉	3₋¹⁺²	semidirect
346. C₉⋊C₉	(C₃⋊D₃)⋊C₃	semidirect
389. C₃²⋊C₉	C₂×3₋¹⁺²	semidirect
390. C₃²⋊C₉	C₂×3₋¹⁺²	semidirect
391. C₃²⋊C₉	C₂×3₋¹⁺²	semidirect
392. C₃²⋊C₉	C₂×3₋¹⁺²	semidirect
612. C₃⋊D₃	#6896	semidirect
682. C₃²	C₂×#6896	semidirect

Maximal subgroups

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

subgroup	index
#14552244	2
D₃×#6896	3
C₃×#92262	3
C₃⋊D₃×C₉⋊C₉	3
((C₃⋊D₃)⋊C₉)⋊C₉	3
(C₃×(C₃⋊D₃)⋊C₃)⋊C₉	3
C₉×(C₃⋊D₃)⋊C₉	3