Subgroups — #72243834

Order 4374.

949 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14552204	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×#6894⋊C₂	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#6894⋊C₂	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×#6894⋊C₂	C₃	1	1	yes	maximal, characteristic, complemented
5	D₃×C₉⋊H(3,𝔽₃)	—	3	1	no	maximal
6	C₃×D₉×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
7	C₃²×D₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
8	#13090623	C₃	1	1	yes	maximal, characteristic, complemented
9	#13090623	C₃	1	1	yes	maximal, characteristic, complemented
10	#13090623	C₃	1	1	yes	maximal, characteristic, complemented
11	#13090623	C₃	1	1	yes	maximal, characteristic, complemented
12	#13090623	C₃	1	1	yes	maximal, characteristic, complemented
13	#13090623	C₃	1	1	yes	maximal, characteristic, complemented
14	#13090623	C₃	1	1	yes	maximal, characteristic, complemented
15	#13090623	C₃	1	1	yes	maximal, characteristic, complemented
16	C₃×#6894	C₂×C₃	1	1	yes	characteristic, complemented
17	C₃×#6894	C₂×C₃	1	1	yes	characteristic, complemented
18	C₃×#6894	C₂×C₃	1	1	yes	characteristic, complemented
19	C₃×C₉⋊H(3,𝔽₃)	D₃	1	1	yes	characteristic
20	C₃×C₉×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
21	C₃²×C₉⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
22	#10624566	—	2	1	no	—
23	#10624566	—	2	1	no	—
24	#10624566	—	2	1	no	—
25	#10624566	—	2	1	no	—
26	#10624566	—	2	1	no	—
27	#10624566	—	2	1	no	—
28	#10624565	—	2	1	no	—
29	#10624565	—	2	1	no	—
30	#10624565	—	2	1	no	—
31	#10624556	—	2	1	no	—
32	#10624556	—	2	1	no	—
33	#10624555	—	2	1	no	—
34	#10624548	—	2	1	no	—
35	#10624548	C₂×C₃	1	1	yes	characteristic, complemented
36	#10624548	C₂×C₃	1	1	yes	characteristic, complemented
37	#10624548	C₂×C₃	1	1	yes	characteristic, complemented
38	#10624548	C₂×C₃	1	1	yes	characteristic, complemented
39	#10624548	C₂×C₃	1	1	yes	characteristic, complemented
40	#10624548	C₂×C₃	1	1	yes	characteristic, complemented
41	#10624548	C₂×C₃	1	1	yes	characteristic, complemented
42	#10624548	C₂×C₃	1	1	yes	characteristic, complemented
43	C₃×D₃×3₋¹⁺²	—	3	1	no	—
44	C₃×D₃×3₋¹⁺²	—	3	1	no	—
45	C₃×D₃×3₋¹⁺²	—	3	1	no	—
46	C₃×D₃×H(3,𝔽₃)	—	3	1	no	—
47	C₃²×D₃×C₉	—	3	1	no	—
48	C₃³×D₉	C₃²	1	1	yes	characteristic
49	C₃³×D₉	C₃²	1	1	yes	characteristic
50	C₃³×D₉	C₃²	1	1	yes	characteristic
51	C₃³×D₉	C₃²	1	1	yes	characteristic
52	C₂×C₉⋊H(3,𝔽₃)	—	9	1	no	—
53	#6894⋊C₂	—	3	1	no	—
54	#6894⋊C₂	—	3	1	no	—
55	#6894⋊C₂	—	3	1	no	—
56	#6894⋊C₂	—	3	1	no	—
57	#6894⋊C₂	—	3	1	no	—
58	#6894⋊C₂	—	3	1	no	—
59	#6894⋊C₂	—	3	1	no	—
60	#6894⋊C₂	—	3	1	no	—
61	#6894⋊C₂	—	3	1	no	—
62	D₉×H(3,𝔽₃)	—	3	3	no	—
63	C₃×D₉⋊C₉	—	3	1	no	—
64	C₃×D₉⋊C₉	—	3	1	no	—
65	C₃×D₉⋊C₉	—	3	1	no	—
66	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
67	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
68	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
69	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
70	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
71	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
72	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
73	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
74	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
75	D₃×C₃²⋊C₉	—	3	1	no	—
76	D₃×C₃²⋊C₉	—	3	1	no	—
77	D₃×C₃²⋊C₉	—	3	1	no	—
78	D₃×C₃²⋊C₉	—	3	1	no	—
79	D₃×C₃²⋊C₉	—	3	1	no	—
80	D₃×C₃²⋊C₉	—	3	1	no	—
81	D₃×C₃²⋊C₉	—	3	1	no	—
82	D₃×C₃²⋊C₉	—	3	1	no	—
83	C₃²×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
84	C₃²×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
85	C₃²×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
86	C₃²×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
87	C₃³×C₉	—	2	1	no	—
88	C₃³×C₉	C₃×D₃	1	1	yes	characteristic
89	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
90	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
91	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
92	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
93	#6894	—	3	1	no	—
94	#6894	—	3	1	no	—
95	#6894	—	3	1	no	—
96	#6894	—	3	1	no	—
97	#6894	—	3	1	no	—
98	#6894	—	3	1	no	—
99	#6894	—	3	1	no	—
100	#6894	—	3	1	no	—
101	#6894	—	3	1	no	—
102	#6894	—	6	1	no	—
103	#6894	—	6	1	no	—
104	#6894	—	6	1	no	—
105	#6894	—	6	1	no	—
106	#6894	—	6	1	no	—
107	#6894	—	6	1	no	—
108	#6894	—	6	1	no	—
109	#6894	—	6	1	no	—
110	#6894	—	6	1	no	—
111	C₉⋊H(3,𝔽₃)	—	6	1	no	—
112	C₉⋊H(3,𝔽₃)	—	6	1	no	—
113	C₉⋊H(3,𝔽₃)	—	6	1	no	—
114	C₉⋊H(3,𝔽₃)	—	6	1	no	—
115	C₉⋊H(3,𝔽₃)	—	6	1	no	—
116	C₉×H(3,𝔽₃)	—	3	3	no	—
117	C₉×H(3,𝔽₃)	—	6	3	no	—
118	C₃×C₉⋊C₉	—	2	1	no	—
119	C₃×C₉⋊C₉	—	2	1	no	—
120	C₃×C₉⋊C₉	—	2	1	no	—
121	C₃×C₉⋊C₉	—	2	1	no	—
122	C₃×C₉⋊C₉	—	2	1	no	—
123	C₃×C₉⋊C₉	—	2	1	no	—
124	C₃×C₉⋊C₉	—	2	1	no	—
125	C₃×C₉⋊C₉	—	2	1	no	—
126	C₃×C₉⋊C₉	—	2	1	no	—
127	C₃×C₉⋊C₉	—	2	1	no	—
128	C₃×C₉⋊C₉	—	2	1	no	—
129	C₃×C₉⋊C₉	—	2	1	no	—
130	C₃×C₉⋊C₉	—	3	1	no	—
131	C₃×C₉⋊C₉	—	3	1	no	—
132	C₃×C₉⋊C₉	—	3	1	no	—
133	C₃×C₉⋊C₉	—	6	1	no	—
134	C₃×C₉⋊C₉	—	6	1	no	—
135	C₃×C₉⋊C₉	—	6	1	no	—
136	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
137	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
138	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
139	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
140	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
141	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
142	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
143	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
144	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
145	C₃×C₃²⋊C₉	—	2	1	no	—
146	C₃×C₃²⋊C₉	—	2	1	no	—
147	C₃×C₃²⋊C₉	—	2	1	no	—
148	C₃×C₃²⋊C₉	—	2	1	no	—
149	C₃×C₃²⋊C₉	—	2	1	no	—
150	C₃×C₃²⋊C₉	—	2	1	no	—
151	C₃×C₃²⋊C₉	—	2	1	no	—
152	C₃×C₃²⋊C₉	—	2	1	no	—
153	C₃×C₃²⋊C₉	—	2	1	no	—
154	C₃×C₃²⋊C₉	—	2	1	no	—
155	C₃×C₃²⋊C₉	—	2	1	no	—
156	C₃×C₃²⋊C₉	—	2	1	no	—
157	C₃×C₃²⋊C₉	—	2	1	no	—
158	C₃×C₃²⋊C₉	—	2	1	no	—
159	C₃×C₃²⋊C₉	—	2	1	no	—
160	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
161	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
162	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
163	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
164	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
165	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
166	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
167	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
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	#6855	—	2	1	no	—
177	#6855	—	2	1	no	—
178	#6855	—	2	1	no	—
179	#6855	—	2	1	no	—
180	#6855	—	2	1	no	—
181	#6855	—	2	1	no	—
182	#6855	—	2	1	no	—
183	#6855	—	2	1	no	—
184	#6855	—	2	1	no	—
185	#6855	—	2	1	no	—
186	#6855	—	2	1	no	—
187	#6855	—	2	1	no	—
188	#6855	—	2	1	no	—
189	#6855	—	2	1	no	—
190	#6855	—	2	1	no	—
191	#6855	—	2	1	no	—
192	C₃³×D₃	—	3	1	no	—
193	C₃³×D₃	—	3	1	no	—
194	C₃³×D₃	—	3	1	no	—
195	C₃³×D₃	—	3	1	no	—
196	C₂×C₃×3₋¹⁺²	—	9	1	no	—
197	C₂×C₃×3₋¹⁺²	—	9	1	no	—
198	C₂×C₃×3₋¹⁺²	—	9	1	no	—
199	C₂×C₃×H(3,𝔽₃)	—	9	1	no	—
200	C₂×C₃²×C₉	—	9	1	no	—
201	D₃×3₋¹⁺²	—	9	1	no	—
202	D₃×3₋¹⁺²	—	9	1	no	—
203	D₃×3₋¹⁺²	—	9	1	no	—
204	D₃×3₋¹⁺²	—	9	1	no	—
205	D₃×3₋¹⁺²	—	9	1	no	—
206	D₃×3₋¹⁺²	—	9	1	no	—
207	D₃×3₋¹⁺²	—	9	1	no	—
208	D₃×3₋¹⁺²	—	9	1	no	—
209	D₃×3₋¹⁺²	—	9	1	no	—
210	D₃×H(3,𝔽₃)	—	9	3	no	—
211	C₃×D₃×C₉	—	3	1	no	—
212	C₃×D₃×C₉	—	3	1	no	—
213	C₃×D₃×C₉	—	3	1	no	—
214	C₃×D₃×C₉	—	3	1	no	—
215	C₃×D₃×C₉	—	3	1	no	—
216	C₃×D₃×C₉	—	3	1	no	—
217	C₃×D₃×C₉	—	3	1	no	—
218	C₃×D₃×C₉	—	3	1	no	—
219	C₃×D₃×C₉	—	3	1	no	—
220	C₃×D₃×C₉	—	9	1	no	—
221	C₃×D₃×C₉	—	9	1	no	—
222	C₃×D₃×C₉	—	9	1	no	—
223	C₃²×D₉	—	3	1	no	—
224	C₃²×D₉	—	3	1	no	—
225	C₃²×D₉	—	3	1	no	—
226	C₃²×D₉	—	3	1	no	—
227	C₃²×D₉	—	3	1	no	—
228	C₃²×D₉	—	3	1	no	—
229	C₃²×D₉	—	3	1	no	—
230	C₃²×D₉	—	3	1	no	—
231	C₃²×D₉	—	3	1	no	—
232	C₃²×D₉	—	3	1	no	—
233	C₃²×D₉	—	3	1	no	—
234	C₃²×D₉	—	3	1	no	—
235	C₃²×D₉	—	3	1	no	—
236	C₃²×D₉	—	3	1	no	—
237	C₃²×D₉	—	3	1	no	—
238	C₃²×D₉	3₋¹⁺²	1	3	yes	complemented
239	C₃²×D₉	C₃³	1	1	yes	characteristic
240	C₂×C₃²⋊C₉	—	9	1	no	—
241	C₂×C₃²⋊C₉	—	9	1	no	—
242	C₂×C₃²⋊C₉	—	9	1	no	—
243	C₂×C₃²⋊C₉	—	9	1	no	—
244	C₂×C₃²⋊C₉	—	9	1	no	—
245	C₂×C₃²⋊C₉	—	9	1	no	—
246	C₂×C₃²⋊C₉	—	9	1	no	—
247	C₂×C₃²⋊C₉	—	9	1	no	—
248	D₉⋊C₉	—	3	1	no	—
249	D₉⋊C₉	—	3	1	no	—
250	D₉⋊C₉	—	3	1	no	—
251	D₉⋊C₉	—	3	1	no	—
252	D₉⋊C₉	—	3	1	no	—
253	D₉⋊C₉	—	3	1	no	—
254	D₉⋊C₉	—	3	1	no	—
255	D₉⋊C₉	—	3	1	no	—
256	D₉⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic, complemented
257	D₉⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic, complemented
258	D₉⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic, complemented
259	C₃⁴	C₃²×D₃	1	1	yes	characteristic
260	C₃⁴	C₃²×D₃	1	1	yes	characteristic
261	C₃⁴	C₃²×D₃	1	1	yes	characteristic
262	C₃⁴	C₃²×D₃	1	1	yes	characteristic
263	C₃×3₋¹⁺²	—	3	1	no	—
264	C₃×3₋¹⁺²	—	3	1	no	—
265	C₃×3₋¹⁺²	—	3	1	no	—
266	C₃×3₋¹⁺²	—	3	1	no	—
267	C₃×3₋¹⁺²	—	3	1	no	—
268	C₃×3₋¹⁺²	—	3	1	no	—
269	C₃×3₋¹⁺²	—	3	1	no	—
270	C₃×3₋¹⁺²	—	3	1	no	—
271	C₃×3₋¹⁺²	—	3	1	no	—
272	C₃×3₋¹⁺²	—	3	1	no	—
273	C₃×3₋¹⁺²	—	3	1	no	—
274	C₃×3₋¹⁺²	—	6	1	no	—
275	C₃×3₋¹⁺²	—	6	1	no	—
276	C₃×3₋¹⁺²	—	6	1	no	—
277	C₃×3₋¹⁺²	—	6	1	no	—
278	C₃×3₋¹⁺²	—	18	1	no	—
279	C₃×3₋¹⁺²	—	18	1	no	—
280	C₃×3₋¹⁺²	—	18	1	no	—
281	C₃×H(3,𝔽₃)	—	2	1	no	—
282	C₃×H(3,𝔽₃)	—	2	1	no	—
283	C₃×H(3,𝔽₃)	—	2	1	no	—
284	C₃×H(3,𝔽₃)	—	2	1	no	—
285	C₃×H(3,𝔽₃)	—	3	3	no	—
286	C₃×H(3,𝔽₃)	—	6	3	no	—
287	C₃×H(3,𝔽₃)	AGL(1,ℤ/9)	1	1	yes	characteristic
288	C₃²×C₉	—	2	3	no	—
289	C₃²×C₉	—	2	1	no	—
290	C₃²×C₉	—	2	1	no	—
291	C₃²×C₉	—	2	1	no	—
292	C₃²×C₉	—	2	1	no	—
293	C₃²×C₉	—	2	1	no	—
294	C₃²×C₉	—	2	1	no	—
295	C₃²×C₉	—	2	1	no	—
296	C₃²×C₉	—	2	1	no	—
297	C₃²×C₉	—	2	1	no	—
298	C₃²×C₉	—	2	1	no	—
299	C₃²×C₉	—	2	1	no	—
300	C₃²×C₉	—	2	1	no	—
301	C₃²×C₉	—	2	1	no	—
302	C₃²×C₉	—	3	1	no	—
303	C₃²×C₉	—	3	1	no	—
304	C₃²×C₉	—	3	1	no	—
305	C₃²×C₉	—	3	1	no	—
306	C₃²×C₉	—	3	1	no	—
307	C₃²×C₉	—	3	1	no	—
308	C₃²×C₉	—	3	1	no	—
309	C₃²×C₉	—	3	1	no	—
310	C₃²×C₉	—	3	1	no	—
311	C₃²×C₉	—	3	1	no	—
312	C₃²×C₉	—	3	1	no	—
313	C₃²×C₉	—	3	1	no	—
314	C₃²×C₉	—	3	1	no	—
315	C₃²×C₉	—	3	1	no	—
316	C₃²×C₉	—	3	1	no	—
317	C₃²×C₉	—	3	1	no	—
318	C₃²×C₉	—	3	1	no	—
319	C₃²×C₉	—	3	1	no	—
320	C₃²×C₉	—	3	1	no	—
321	C₃²×C₉	—	6	1	no	—
322	C₃²×C₉	—	6	1	no	—
323	C₃²×C₉	—	6	1	no	—
324	C₃²×C₉	—	6	1	no	—
325	C₃²×C₉	—	6	1	no	—
326	C₃²×C₉	—	6	1	no	—
327	C₃²×C₉	—	6	1	no	—
328	C₃²×C₉	—	6	1	no	—
329	C₃²×C₉	—	6	1	no	—
330	C₃²×C₉	—	6	1	no	—
331	C₃²×C₉	—	6	1	no	—
332	C₃²×C₉	—	6	1	no	—
333	C₃²×C₉	—	6	1	no	—
334	C₃²×C₉	—	6	1	no	—
335	C₃²×C₉	—	6	1	no	—
336	C₃²×C₉	—	6	1	no	—
337	C₃²×C₉	—	6	1	no	—
338	C₃²×C₉	—	6	1	no	—
339	C₃²×C₉	—	6	1	no	—
340	C₃²×C₉	—	6	3	no	—
341	C₃²×C₉	—	18	1	no	—
342	C₃²×C₉	—	18	1	no	—
343	C₃²×C₉	—	18	1	no	—
344	C₃²×C₉	C₂×3₋¹⁺²	1	3	yes	complemented
345	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
346	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
347	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
348	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
349	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
350	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
351	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
352	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
353	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
354	C₃²×C₉	C₂×C₃³	1	1	yes	characteristic
355	C₉⋊C₉	—	2	1	no	—
356	C₉⋊C₉	—	2	1	no	—
357	C₉⋊C₉	—	2	1	no	—
358	C₉⋊C₉	—	3	1	no	—
359	C₉⋊C₉	—	3	1	no	—
360	C₉⋊C₉	—	3	1	no	—
361	C₉⋊C₉	—	3	1	no	—
362	C₉⋊C₉	—	3	1	no	—
363	C₉⋊C₉	—	3	1	no	—
364	C₉⋊C₉	—	3	1	no	—
365	C₉⋊C₉	—	3	1	no	—
366	C₉⋊C₉	—	6	1	no	—
367	C₉⋊C₉	—	6	1	no	—
368	C₉⋊C₉	—	6	1	no	—
369	C₉⋊C₉	—	6	1	no	—
370	C₉⋊C₉	—	6	1	no	—
371	C₉⋊C₉	—	6	1	no	—
372	C₉⋊C₉	—	6	1	no	—
373	C₉⋊C₉	—	6	1	no	—
374	C₉⋊C₉	—	6	1	no	—
375	C₉⋊C₉	—	6	1	no	—
376	C₉⋊C₉	—	6	1	no	—
377	C₉⋊C₉	—	6	1	no	—
378	C₉⋊C₉	—	6	1	no	—
379	C₉⋊C₉	—	6	1	no	—
380	C₉⋊C₉	—	6	1	no	—
381	C₉⋊C₉	—	6	1	no	—
382	C₉⋊C₉	—	6	1	no	—
383	C₉⋊C₉	—	6	1	no	—
384	C₉⋊C₉	—	6	1	no	—
385	C₉⋊C₉	—	6	1	no	—
386	C₉⋊C₉	—	6	1	no	—
387	C₉⋊C₉	—	6	1	no	—
388	C₉⋊C₉	—	6	1	no	—
389	C₉⋊C₉	—	6	1	no	—
390	C₉⋊C₉	—	6	1	no	—
391	C₉⋊C₉	—	6	1	no	—
392	C₉⋊C₉	—	6	1	no	—
393	C₉⋊C₉	—	6	1	no	—
394	C₉⋊C₉	—	6	1	no	—
395	C₉⋊C₉	—	6	1	no	—
396	C₉⋊C₉	—	6	1	no	—
397	C₉⋊C₉	—	6	1	no	—
398	C₉⋊C₉	—	6	1	no	—
399	C₉⋊C₉	—	6	1	no	—
400	C₉⋊C₉	—	6	1	no	—
401	C₉⋊C₉	—	6	1	no	—
402	C₉⋊C₉	—	6	1	no	—
403	C₉⋊C₉	—	6	1	no	—
404	C₉⋊C₉	—	6	1	no	—
405	C₉⋊C₉	—	6	1	no	—
406	C₉⋊C₉	—	6	1	no	—
407	C₉⋊C₉	—	6	1	no	—
408	C₉⋊C₉	—	6	1	no	—
409	C₉⋊C₉	—	6	1	no	—
410	C₉⋊C₉	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
411	C₉⋊C₉	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
412	C₉⋊C₉	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
413	C₃²⋊C₉	—	6	3	no	—
414	C₃²⋊C₉	—	6	3	no	—
415	C₃²⋊C₉	—	6	3	no	—
416	C₃²⋊C₉	—	6	1	no	—
417	C₃²⋊C₉	—	6	1	no	—
418	C₃²⋊C₉	—	6	1	no	—
419	C₃²⋊C₉	—	6	1	no	—
420	C₃²⋊C₉	—	6	1	no	—
421	C₃²⋊C₉	—	6	1	no	—
422	C₃²⋊C₉	—	6	1	no	—
423	C₃²⋊C₉	—	6	1	no	—
424	C₃²⋊C₉	—	6	1	no	—
425	C₃²⋊C₉	—	6	1	no	—
426	C₃²⋊C₉	—	6	1	no	—
427	C₃²⋊C₉	—	6	1	no	—
428	C₃²⋊C₉	—	6	1	no	—
429	C₃²⋊C₉	—	6	1	no	—
430	C₃²⋊C₉	—	6	1	no	—
431	C₃²⋊C₉	—	6	1	no	—
432	C₃²⋊C₉	—	6	1	no	—
433	C₃²⋊C₉	—	6	1	no	—
434	C₃²⋊C₉	—	6	1	no	—
435	C₃²⋊C₉	—	6	1	no	—
436	C₃²⋊C₉	—	6	1	no	—
437	C₃²⋊C₉	—	6	3	no	—
438	C₃²⋊C₉	—	6	3	no	—
439	C₃²⋊C₉	—	6	1	no	—
440	C₃²⋊C₉	—	6	1	no	—
441	C₃²⋊C₉	—	6	1	no	—
442	C₃²⋊C₉	—	6	1	no	—
443	C₃²⋊C₉	—	6	3	no	—
444	C₃²⋊C₉	—	18	1	no	—
445	C₃²⋊C₉	—	18	1	no	—
446	C₃²⋊C₉	—	18	1	no	—
447	C₃²⋊C₉	—	18	1	no	—
448	C₃²⋊C₉	—	18	1	no	—
449	C₃²⋊C₉	—	18	1	no	—
450	C₂×C₃³	—	9	1	no	—
451	C₂×C₃³	—	9	1	no	—
452	C₂×C₃³	—	9	1	no	—
453	C₂×C₃³	—	9	1	no	—
454	C₃²×D₃	—	3	1	no	—
455	C₃²×D₃	—	3	3	no	—
456	C₃²×D₃	—	9	1	no	—
457	C₃²×D₃	—	9	1	no	—
458	C₃²×D₃	—	9	1	no	—
459	C₃²×D₃	—	9	1	no	—
460	C₃²×D₃	—	9	1	no	—
461	C₃²×D₃	—	9	1	no	—
462	C₃²×D₃	—	9	1	no	—
463	C₃²×D₃	—	9	1	no	—
464	C₃²×D₃	—	9	1	no	—
465	C₃²×D₃	—	9	1	no	—
466	C₃²×D₃	—	9	1	no	—
467	C₃²×D₃	—	9	1	no	—
468	C₃²×D₃	—	9	1	no	—
469	C₃²×D₃	—	9	1	no	—
470	C₃²×D₃	—	9	1	no	—
471	C₂×3₋¹⁺²	—	27	1	no	—
472	C₂×3₋¹⁺²	—	27	1	no	—
473	C₂×3₋¹⁺²	—	27	1	no	—
474	C₂×3₋¹⁺²	—	27	1	no	—
475	C₂×3₋¹⁺²	—	27	1	no	—
476	C₂×3₋¹⁺²	—	27	1	no	—
477	C₂×3₋¹⁺²	—	27	1	no	—
478	C₂×3₋¹⁺²	—	27	1	no	—
479	C₂×3₋¹⁺²	—	27	1	no	—
480	C₂×H(3,𝔽₃)	—	27	3	no	—
481	C₂×C₃×C₉	—	9	1	no	—
482	C₂×C₃×C₉	—	9	1	no	—
483	C₂×C₃×C₉	—	9	1	no	—
484	C₂×C₃×C₉	—	9	1	no	—
485	C₂×C₃×C₉	—	9	1	no	—
486	C₂×C₃×C₉	—	9	1	no	—
487	C₂×C₃×C₉	—	9	1	no	—
488	C₂×C₃×C₉	—	9	1	no	—
489	C₂×C₃×C₉	—	9	1	no	—
490	C₂×C₃×C₉	—	27	1	no	—
491	C₂×C₃×C₉	—	27	1	no	—
492	C₂×C₃×C₉	—	27	1	no	—
493	D₃×C₉	—	3	1	no	—
494	D₃×C₉	—	3	1	no	—
495	D₃×C₉	—	3	1	no	—
496	D₃×C₉	—	9	1	no	—
497	D₃×C₉	—	9	1	no	—
498	D₃×C₉	—	9	1	no	—
499	D₃×C₉	—	9	1	no	—
500	D₃×C₉	—	9	1	no	—
501	D₃×C₉	—	9	1	no	—
502	D₃×C₉	—	9	1	no	—
503	D₃×C₉	—	9	1	no	—
504	C₃×D₉	—	3	3	no	—
505	C₃×D₉	—	9	1	no	—
506	C₃×D₉	—	9	1	no	—
507	C₃×D₉	—	9	1	no	—
508	C₃×D₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
509	C₃×D₉	C₃×3₋¹⁺²	1	1	yes	characteristic
510	C₃×D₉	#737	1	1	yes	characteristic
511	C₃×D₉	#737	1	1	yes	characteristic
512	C₃³	—	2	3	no	—
513	C₃³	—	2	1	no	—
514	C₃³	—	2	1	no	—
515	C₃³	—	2	1	no	—
516	C₃³	—	2	1	no	—
517	C₃³	—	3	1	no	—
518	C₃³	—	3	1	no	—
519	C₃³	—	3	1	no	—
520	C₃³	—	3	1	no	—
521	C₃³	—	3	1	no	—
522	C₃³	—	3	1	no	—
523	C₃³	—	3	1	no	—
524	C₃³	—	3	1	no	—
525	C₃³	—	3	1	no	—
526	C₃³	—	3	1	no	—
527	C₃³	—	3	1	no	—
528	C₃³	—	3	1	no	—
529	C₃³	—	3	1	no	—
530	C₃³	—	3	1	no	—
531	C₃³	—	3	1	no	—
532	C₃³	—	6	1	no	—
533	C₃³	—	6	1	no	—
534	C₃³	—	6	1	no	—
535	C₃³	—	6	1	no	—
536	C₃³	—	6	1	no	—
537	C₃³	—	6	1	no	—
538	C₃³	—	6	1	no	—
539	C₃³	—	6	1	no	—
540	C₃³	—	6	1	no	—
541	C₃³	—	6	1	no	—
542	C₃³	—	6	1	no	—
543	C₃³	—	6	1	no	—
544	C₃³	—	6	1	no	—
545	C₃³	—	6	1	no	—
546	C₃³	—	6	1	no	—
547	C₃³	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
548	C₃³	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
549	C₃³	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
550	C₃³	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
551	C₃³	D₃×3₋¹⁺²	1	3	yes	—
552	C₃³	C₃³×D₃	1	1	yes	characteristic
553	3₋¹⁺²	—	9	1	no	—
554	3₋¹⁺²	—	9	1	no	—
555	3₋¹⁺²	—	9	1	no	—
556	3₋¹⁺²	—	18	1	no	—
557	3₋¹⁺²	—	18	1	no	—
558	3₋¹⁺²	—	18	1	no	—
559	3₋¹⁺²	—	18	1	no	—
560	3₋¹⁺²	—	18	1	no	—
561	3₋¹⁺²	—	18	1	no	—
562	3₋¹⁺²	—	18	1	no	—
563	3₋¹⁺²	—	18	1	no	—
564	3₋¹⁺²	—	18	1	no	—
565	3₋¹⁺²	—	18	1	no	—
566	3₋¹⁺²	—	18	1	no	—
567	3₋¹⁺²	—	18	1	no	—
568	3₋¹⁺²	—	18	1	no	—
569	3₋¹⁺²	—	18	1	no	—
570	3₋¹⁺²	—	18	1	no	—
571	H(3,𝔽₃)	—	3	3	no	—
572	H(3,𝔽₃)	—	6	3	no	—
573	H(3,𝔽₃)	—	6	3	no	—
574	H(3,𝔽₃)	—	6	3	no	—
575	H(3,𝔽₃)	—	6	3	no	—
576	C₃×C₉	—	2	1	no	—
577	C₃×C₉	—	2	1	no	—
578	C₃×C₉	—	2	1	no	—
579	C₃×C₉	—	2	1	no	—
580	C₃×C₉	—	2	1	no	—
581	C₃×C₉	—	2	1	no	—
582	C₃×C₉	—	2	1	no	—
583	C₃×C₉	—	2	3	no	—
584	C₃×C₉	—	3	1	no	—
585	C₃×C₉	—	3	3	no	—
586	C₃×C₉	—	3	1	no	—
587	C₃×C₉	—	3	1	no	—
588	C₃×C₉	—	3	1	no	—
589	C₃×C₉	—	3	1	no	—
590	C₃×C₉	—	3	1	no	—
591	C₃×C₉	—	3	1	no	—
592	C₃×C₉	—	3	1	no	—
593	C₃×C₉	—	3	1	no	—
594	C₃×C₉	—	3	1	no	—
595	C₃×C₉	—	3	1	no	—
596	C₃×C₉	—	3	1	no	—
597	C₃×C₉	—	6	3	no	—
598	C₃×C₉	—	6	3	no	—
599	C₃×C₉	—	6	3	no	—
600	C₃×C₉	—	6	3	no	—
601	C₃×C₉	—	6	1	no	—
602	C₃×C₉	—	6	1	no	—
603	C₃×C₉	—	6	1	no	—
604	C₃×C₉	—	6	1	no	—
605	C₃×C₉	—	6	1	no	—
606	C₃×C₉	—	6	1	no	—
607	C₃×C₉	—	6	1	no	—
608	C₃×C₉	—	6	1	no	—
609	C₃×C₉	—	6	1	no	—
610	C₃×C₉	—	6	1	no	—
611	C₃×C₉	—	6	1	no	—
612	C₃×C₉	—	6	1	no	—
613	C₃×C₉	—	6	1	no	—
614	C₃×C₉	—	6	1	no	—
615	C₃×C₉	—	6	1	no	—
616	C₃×C₉	—	6	1	no	—
617	C₃×C₉	—	6	1	no	—
618	C₃×C₉	—	6	1	no	—
619	C₃×C₉	—	6	1	no	—
620	C₃×C₉	—	6	1	no	—
621	C₃×C₉	—	6	1	no	—
622	C₃×C₉	—	6	1	no	—
623	C₃×C₉	—	6	1	no	—
624	C₃×C₉	—	6	1	no	—
625	C₃×C₉	—	6	1	no	—
626	C₃×C₉	—	6	1	no	—
627	C₃×C₉	—	6	1	no	—
628	C₃×C₉	—	6	1	no	—
629	C₃×C₉	—	6	1	no	—
630	C₃×C₉	—	6	1	no	—
631	C₃×C₉	—	6	1	no	—
632	C₃×C₉	—	6	1	no	—
633	C₃×C₉	—	6	1	no	—
634	C₃×C₉	—	6	1	no	—
635	C₃×C₉	—	6	1	no	—
636	C₃×C₉	—	6	1	no	—
637	C₃×C₉	—	6	1	no	—
638	C₃×C₉	—	6	1	no	—
639	C₃×C₉	—	6	1	no	—
640	C₃×C₉	—	6	1	no	—
641	C₃×C₉	—	6	1	no	—
642	C₃×C₉	—	6	1	no	—
643	C₃×C₉	—	6	1	no	—
644	C₃×C₉	—	6	1	no	—
645	C₃×C₉	—	6	1	no	—
646	C₃×C₉	—	6	1	no	—
647	C₃×C₉	—	6	1	no	—
648	C₃×C₉	—	6	1	no	—
649	C₃×C₉	—	6	1	no	—
650	C₃×C₉	—	6	1	no	—
651	C₃×C₉	—	6	1	no	—
652	C₃×C₉	—	6	1	no	—
653	C₃×C₉	—	6	1	no	—
654	C₃×C₉	—	6	1	no	—
655	C₃×C₉	—	6	1	no	—
656	C₃×C₉	—	6	1	no	—
657	C₃×C₉	—	6	1	no	—
658	C₃×C₉	—	6	1	no	—
659	C₃×C₉	—	6	1	no	—
660	C₃×C₉	—	6	1	no	—
661	C₃×C₉	—	6	1	no	—
662	C₃×C₉	—	6	1	no	—
663	C₃×C₉	—	6	1	no	—
664	C₃×C₉	—	6	1	no	—
665	C₃×C₉	—	9	1	no	—
666	C₃×C₉	—	9	1	no	—
667	C₃×C₉	—	9	1	no	—
668	C₃×C₉	—	18	1	no	—
669	C₃×C₉	—	18	1	no	—
670	C₃×C₉	—	18	1	no	—
671	C₃×C₉	—	18	1	no	—
672	C₃×C₉	—	18	1	no	—
673	C₃×C₉	—	18	1	no	—
674	C₃×C₉	—	18	1	no	—
675	C₃×C₉	—	18	1	no	—
676	C₃×C₉	—	18	1	no	—
677	C₃×C₉	—	18	1	no	—
678	C₃×C₉	—	18	1	no	—
679	C₃×C₉	—	18	1	no	—
680	C₃×C₉	—	18	1	no	—
681	C₃×C₉	—	18	1	no	—
682	C₃×C₉	—	18	1	no	—
683	C₃×C₉	—	18	1	no	—
684	C₃×C₉	—	18	1	no	—
685	C₃×C₉	—	18	1	no	—
686	C₃×C₉	—	18	3	no	—
687	C₃×C₉	—	18	3	no	—
688	C₃×C₉	—	18	3	no	—
689	C₃×C₉	D₃×H(3,𝔽₃)	1	1	yes	characteristic
690	C₃×C₉	D₃×H(3,𝔽₃)	1	1	yes	characteristic
691	C₃×C₉	D₃×H(3,𝔽₃)	1	1	yes	characteristic
692	C₃×C₉	C₂×C₃×H(3,𝔽₃)	1	1	yes	characteristic
693	C₃×C₉	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
694	C₃×C₉	C₂×#737	1	1	yes	characteristic
695	C₃×C₉	C₂×#737	1	1	yes	characteristic
696	C₂×C₃²	—	9	1	no	—
697	C₂×C₃²	—	9	3	no	—
698	C₂×C₃²	—	27	1	no	—
699	C₂×C₃²	—	27	1	no	—
700	C₂×C₃²	—	27	1	no	—
701	C₂×C₃²	—	27	1	no	—
702	C₂×C₃²	—	27	1	no	—
703	C₂×C₃²	—	27	1	no	—
704	C₂×C₃²	—	27	1	no	—
705	C₂×C₃²	—	27	1	no	—
706	C₂×C₃²	—	27	1	no	—
707	C₂×C₃²	—	27	1	no	—
708	C₂×C₃²	—	27	1	no	—
709	C₂×C₃²	—	27	1	no	—
710	C₂×C₃²	—	27	1	no	—
711	C₂×C₃²	—	27	1	no	—
712	C₂×C₃²	—	27	1	no	—
713	C₃×D₃	—	3	1	no	—
714	C₃×D₃	—	3	1	no	—
715	C₃×D₃	—	3	1	no	—
716	C₃×D₃	—	3	1	no	—
717	C₃×D₃	—	9	3	no	—
718	C₃×D₃	—	27	1	no	—
719	C₃×D₃	—	27	1	no	—
720	C₃×D₃	—	27	1	no	—
721	C₂×C₉	—	9	1	no	—
722	C₂×C₉	—	9	1	no	—
723	C₂×C₉	—	9	1	no	—
724	C₂×C₉	—	27	1	no	—
725	C₂×C₉	—	27	1	no	—
726	C₂×C₉	—	27	1	no	—
727	C₂×C₉	—	27	1	no	—
728	C₂×C₉	—	27	1	no	—
729	C₂×C₉	—	27	1	no	—
730	C₂×C₉	—	27	1	no	—
731	C₂×C₉	—	27	1	no	—
732	D₉	C₉⋊H(3,𝔽₃)	1	1	yes	characteristic, complemented
733	C₃²	—	2	1	no	—
734	C₃²	—	2	1	no	—
735	C₃²	—	2	1	no	—
736	C₃²	—	2	1	no	—
737	C₃²	—	2	3	no	—
738	C₃²	—	3	1	no	—
739	C₃²	—	3	1	no	—
740	C₃²	—	3	1	no	—
741	C₃²	—	3	3	no	—
742	C₃²	—	3	1	no	—
743	C₃²	—	3	1	no	—
744	C₃²	—	3	1	no	—
745	C₃²	—	3	1	no	—
746	C₃²	—	3	1	no	—
747	C₃²	—	3	1	no	—
748	C₃²	—	3	1	no	—
749	C₃²	—	3	1	no	—
750	C₃²	—	3	1	no	—
751	C₃²	—	3	1	no	—
752	C₃²	—	3	1	no	—
753	C₃²	—	3	1	no	—
754	C₃²	—	6	3	no	—
755	C₃²	—	6	3	no	—
756	C₃²	—	6	3	no	—
757	C₃²	—	6	3	no	—
758	C₃²	—	6	1	no	—
759	C₃²	—	6	1	no	—
760	C₃²	—	6	1	no	—
761	C₃²	—	6	1	no	—
762	C₃²	—	6	1	no	—
763	C₃²	—	6	1	no	—
764	C₃²	—	6	1	no	—
765	C₃²	—	6	1	no	—
766	C₃²	—	6	1	no	—
767	C₃²	—	6	1	no	—
768	C₃²	—	6	1	no	—
769	C₃²	—	6	1	no	—
770	C₃²	—	6	1	no	—
771	C₃²	—	6	1	no	—
772	C₃²	—	6	1	no	—
773	C₃²	—	9	1	no	—
774	C₃²	—	9	1	no	—
775	C₃²	—	9	1	no	—
776	C₃²	—	18	1	no	—
777	C₃²	—	18	1	no	—
778	C₃²	—	18	1	no	—
779	C₃²	—	18	1	no	—
780	C₃²	—	18	1	no	—
781	C₃²	—	18	1	no	—
782	C₃²	—	18	1	no	—
783	C₃²	—	18	1	no	—
784	C₃²	—	18	1	no	—
785	C₃²	—	18	1	no	—
786	C₃²	—	18	1	no	—
787	C₃²	—	18	1	no	—
788	C₃²	#6894⋊C₂	1	3	yes	complemented
789	C₃²	C₃×D₃×H(3,𝔽₃)	1	1	yes	characteristic
790	C₃²	C₃²×AGL(1,ℤ/9)	1	1	yes	characteristic
791	C₃²	C₃×D₃×3₋¹⁺²	1	1	yes	characteristic
792	C₃²	D₃×#737	1	1	yes	characteristic
793	C₃²	D₃×#737	1	1	yes	characteristic
794	C₉	—	2	1	no	—
795	C₉	—	2	1	no	—
796	C₉	—	2	1	no	—
797	C₉	—	2	1	no	—
798	C₉	—	3	1	no	—
799	C₉	—	6	1	no	—
800	C₉	—	6	1	no	—
801	C₉	—	6	1	no	—
802	C₉	—	6	3	no	—
803	C₉	—	6	1	no	—
804	C₉	—	6	1	no	—
805	C₉	—	9	1	no	—
806	C₉	—	9	1	no	—
807	C₉	—	9	1	no	—
808	C₉	—	9	1	no	—
809	C₉	—	18	1	no	—
810	C₉	—	18	1	no	—
811	C₉	—	18	1	no	—
812	C₉	—	18	1	no	—
813	C₉	—	18	1	no	—
814	C₉	—	18	1	no	—
815	C₉	—	18	1	no	—
816	C₉	—	18	1	no	—
817	C₉	—	18	1	no	—
818	C₉	—	18	1	no	—
819	C₉	—	18	1	no	—
820	C₉	—	18	1	no	—
821	C₉	—	18	1	no	—
822	C₉	—	18	1	no	—
823	C₉	—	18	1	no	—
824	C₉	C₂×C₉⋊H(3,𝔽₃)	1	1	yes	characteristic, complemented
825	C₂×C₃	—	9	1	no	—
826	C₂×C₃	—	9	1	no	—
827	C₂×C₃	—	9	1	no	—
828	C₂×C₃	—	9	1	no	—
829	C₂×C₃	—	27	3	no	—
830	C₂×C₃	—	81	1	no	—
831	C₂×C₃	—	81	1	no	—
832	C₂×C₃	—	81	1	no	—
833	D₃	—	3	1	no	—
834	C₃	—	2	1	no	—
835	C₃	—	2	1	no	—
836	C₃	—	2	1	no	—
837	C₃	—	2	1	no	—
838	C₃	—	3	3	no	—
839	C₃	—	6	3	no	—
840	C₃	—	9	1	no	—
841	C₃	—	9	1	no	—
842	C₃	—	9	1	no	—
843	C₃	—	18	1	no	—
844	C₃	—	18	1	no	—
845	C₃	—	18	1	no	—
846	C₃	D₃×C₉⋊H(3,𝔽₃)	1	1	yes	characteristic
847	C₃	C₃×#6894⋊C₂	1	1	yes	characteristic
848	C₃	H(3,𝔽₃)×AGL(1,ℤ/9)	1	1	yes	characteristic
849	C₃	#13091525	1	1	yes	characteristic
850	C₃	#13091525	1	1	yes	characteristic
851	C₂	—	9	1	no	Sylow

	subgroup	G/H
center	C₃²	C₃²×AGL(1,ℤ/9)
commutator, cosocle	C₃²×C₉	C₂×C₃³
Frattini, socle	C₃³	C₃³×D₃
Fitting	#14552204	C₂
prime radical	C₃×D₉×H(3,𝔽₃)	C₃
hypercenter	C₃×H(3,𝔽₃)	AGL(1,ℤ/9)
hypocenter	C₉	C₂×C₉⋊H(3,𝔽₃)
LCS	G ▷ C₃²×C₉ ▷ C₉
UCS	C₁ ◁ C₃² ◁ C₃×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. #14552204	C₂	semidirect
2. C₃×#6894⋊C₂	C₃	semidirect
3. C₃×#6894⋊C₂	C₃	semidirect
4. C₃×#6894⋊C₂	C₃	semidirect
7. C₃²×D₉⋊C₉	C₃	semidirect
8. #13090623	C₃	semidirect
9. #13090623	C₃	semidirect
10. #13090623	C₃	semidirect
11. #13090623	C₃	semidirect
12. #13090623	C₃	semidirect
13. #13090623	C₃	semidirect
14. #13090623	C₃	semidirect
15. #13090623	C₃	semidirect
16. C₃×#6894	C₂×C₃	semidirect
17. C₃×#6894	C₂×C₃	semidirect
18. C₃×#6894	C₂×C₃	semidirect
21. C₃²×C₉⋊C₉	C₂×C₃	semidirect
35. #10624548	C₂×C₃	semidirect
36. #10624548	C₂×C₃	semidirect
37. #10624548	C₂×C₃	semidirect
38. #10624548	C₂×C₃	semidirect
39. #10624548	C₂×C₃	semidirect
40. #10624548	C₂×C₃	semidirect
41. #10624548	C₂×C₃	semidirect
42. #10624548	C₂×C₃	semidirect
238. C₃²×D₉	3₋¹⁺²	semidirect
256. D₉⋊C₉	H(3,𝔽₃)	semidirect
257. D₉⋊C₉	H(3,𝔽₃)	semidirect
258. D₉⋊C₉	H(3,𝔽₃)	semidirect
344. C₃²×C₉	C₂×3₋¹⁺²	semidirect
410. C₉⋊C₉	C₂×H(3,𝔽₃)	semidirect
411. C₉⋊C₉	C₂×H(3,𝔽₃)	semidirect
412. C₉⋊C₉	C₂×H(3,𝔽₃)	semidirect
732. D₉	C₉⋊H(3,𝔽₃)	semidirect
788. C₃²	#6894⋊C₂	semidirect
824. C₉	C₂×C₉⋊H(3,𝔽₃)	semidirect

Maximal subgroups

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

subgroup	index
#14552204	2
C₃×#6894⋊C₂	3
D₃×C₉⋊H(3,𝔽₃)	3
C₃×D₉×H(3,𝔽₃)	3
C₃²×D₉⋊C₉	3
#13090623	3