Subgroups — C₉×#5671 #13153084

Order 1728.

712 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#124	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#944	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#936	C₂	1	1	yes	maximal, characteristic
5	D₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic
6	C₉×#879	C₂	1	2	yes	maximal, complemented
7	C₉×#879	C₂	1	2	yes	maximal, complemented
8	C₉×#878	C₂	1	2	yes	maximal, complemented
9	C₉×#877	C₂	1	2	yes	maximal, complemented
10	C₄×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5671	C₃	1	1	yes	maximal, characteristic
13	C₉×#556	—	3	1	no	maximal
14	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
16	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
17	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
18	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
19	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
22	C₉×#217	C₂²	1	2	yes	—
23	C₉×#217	C₂²	1	2	yes	—
24	C₉×#217	C₂²	1	2	yes	—
25	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
26	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
27	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
28	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
29	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
30	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
31	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
32	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
33	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
34	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
35	C₄×C₉×Dic₃	C₂²	1	2	yes	—
36	C₄×C₉×Dic₃	C₂²	1	2	yes	—
37	C₃²×#124	C₂×C₃	1	1	yes	characteristic
38	C₃×Q₈×Dic₃	C₂×C₃	1	1	yes	characteristic
39	C₃×#944	C₂×C₃	1	1	yes	characteristic
40	C₃×#936	C₂×C₃	1	1	yes	characteristic
41	C₃×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic
42	C₃×#879	C₂×C₃	1	2	yes	—
43	C₃×#879	C₂×C₃	1	2	yes	—
44	C₃×#878	C₂×C₃	1	2	yes	—
45	C₃×#877	C₂×C₃	1	2	yes	—
46	C₃×C₄×Dic₆	C₂×C₃	1	1	yes	characteristic
47	C₃×C₄×Dic₆	C₂×C₃	1	1	yes	characteristic
48	C₉×C₄⋊Q₈	—	3	1	no	—
49	C₉×#126	—	3	2	no	—
50	C₉×#126	—	3	2	no	—
51	C₉×#124	—	2	1	no	—
52	C₉×#124	—	3	1	no	—
53	C₉×#124	D₃	1	1	yes	characteristic
54	C₉×C₂²⋊Q₈	—	3	2	no	—
55	C₄×Q₈×C₉	—	3	1	no	—
56	C₄×Q₈×C₉	—	3	1	no	—
57	C₄×Q₈×C₉	—	3	1	no	—
58	C₄×D₄×C₉	—	3	1	no	—
59	C₉×#117	—	3	2	no	—
60	C₂³×C₃×C₉	C₂³	1	2	yes	—
61	C₃×Q₈×C₉	—	2	2	no	—
62	C₃×D₄×C₉	—	2	2	no	—
63	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
66	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₉×Dic₃	—	2	4	no	—
68	C₂×C₉×Dic₃	C₂³	1	2	yes	—
69	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₉×Dic₃	C₂³	1	2	yes	—
71	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
72	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
73	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
74	C₉×Dic₆	—	2	2	no	—
75	C₉×Dic₆	—	2	2	no	—
76	C₃×#556	—	3	1	no	—
77	#5671	C₉	1	1	yes	characteristic, direct product factor
78	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
80	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
81	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
83	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
84	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
85	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
86	C₃×#217	C₂²×C₃	1	2	yes	—
87	C₃×#217	C₂²×C₃	1	2	yes	—
88	C₃×#217	C₂²×C₃	1	2	yes	—
89	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
90	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
91	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
92	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
93	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
94	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
95	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
96	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
98	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
99	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
100	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
101	C₂×Q₈×C₉	—	2	1	no	—
102	C₂×Q₈×C₉	—	3	1	no	—
103	C₂×Q₈×C₉	—	3	1	no	—
104	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
105	C₂×D₄×C₉	—	2	1	no	—
106	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
107	C₂²×C₄×C₉	—	3	2	no	—
108	C₉×C₄⋊C₄	—	3	1	no	—
109	C₉×C₄⋊C₄	—	3	2	no	—
110	C₉×C₄⋊C₄	—	3	1	no	—
111	C₉×C₄⋊C₄	—	3	2	no	—
112	C₉×C₄⋊C₄	—	3	2	no	—
113	C₉×C₄⋊C₄	—	3	1	no	—
114	C₉×C₄⋊C₄	—	3	1	no	—
115	C₉×C₄⋊C₄	—	3	2	no	—
116	C₉×C₂²⋊C₄	—	2	2	no	—
117	C₉×C₂²⋊C₄	—	2	2	no	—
118	C₉×C₂²⋊C₄	—	3	2	no	—
119	C₉×C₂²⋊C₄	—	3	2	no	—
120	C₉×C₂²⋊C₄	—	3	2	no	—
121	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
122	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
123	C₄²×C₉	—	2	1	no	—
124	C₄²×C₉	—	3	2	no	—
125	C₄²×C₉	—	3	2	no	—
126	C₄²×C₉	—	3	1	no	—
127	C₄²×C₉	—	3	1	no	—
128	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
129	C₂²×C₃×C₉	—	2	2	no	—
130	C₂²×C₃×C₉	—	2	2	no	—
131	C₂²×C₃×C₉	—	2	2	no	—
132	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
133	C₃×C₄×C₉	—	2	1	no	—
134	C₃×C₄×C₉	—	2	2	no	—
135	C₃×C₄×C₉	—	2	1	no	—
136	C₃×C₄×C₉	#41	1	2	yes	—
137	C₉×Dic₃	—	2	2	no	—
138	C₉×Dic₃	—	2	1	no	—
139	C₉×Dic₃	—	2	2	no	—
140	C₉×Dic₃	—	2	1	no	—
141	C₉×Dic₃	—	2	1	no	—
142	C₉×Dic₃	#41	1	2	yes	—
143	C₃×C₄⋊Q₈	—	3	1	no	—
144	C₃×#126	—	3	2	no	—
145	C₃×#126	—	3	2	no	—
146	C₃×#124	—	2	1	no	—
147	C₃×#124	—	3	1	no	—
148	C₃×#124	C₂×C₉	1	1	yes	characteristic
149	C₃×#124	C₃×D₃	1	1	yes	characteristic
150	C₃×C₂²⋊Q₈	—	3	2	no	—
151	C₃×C₄×Q₈	—	3	1	no	—
152	C₃×C₄×Q₈	—	3	1	no	—
153	C₃×C₄×Q₈	—	3	1	no	—
154	C₃×C₄×D₄	—	3	1	no	—
155	C₃×#117	—	3	2	no	—
156	Q₈×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
157	#944	C₂×C₉	1	1	yes	characteristic, complemented
158	#936	C₂×C₉	1	1	yes	characteristic
159	D₄×Dic₃	C₂×C₉	1	1	yes	characteristic
160	#879	C₂×C₉	1	2	yes	complemented
161	#879	C₂×C₉	1	2	yes	complemented
162	#878	C₂×C₉	1	2	yes	complemented
163	#877	C₂×C₉	1	2	yes	complemented
164	C₄×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
165	C₄×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
166	C₂³×C₃²	C₂³×C₃	1	2	yes	—
167	C₃²×Q₈	—	2	2	no	—
168	C₃²×D₄	—	2	2	no	—
169	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
170	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
171	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
172	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
173	C₂×C₃×Dic₃	—	2	4	no	—
174	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
175	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
176	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
177	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
178	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
179	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
180	C₃×Dic₆	—	2	2	no	—
181	C₃×Dic₆	—	2	2	no	—
182	C₂³×C₉	—	2	2	no	—
183	C₂³×C₉	C₂²×D₃	1	2	yes	—
184	Q₈×C₉	—	2	2	no	—
185	Q₈×C₉	—	4	2	no	—
186	Q₈×C₉	—	6	2	no	—
187	Q₈×C₉	—	6	2	no	—
188	D₄×C₉	—	2	2	no	—
189	D₄×C₉	—	4	2	no	—
190	C₂×C₄×C₉	—	2	1	no	—
191	C₂×C₄×C₉	—	2	1	no	—
192	C₂×C₄×C₉	—	2	1	no	—
193	C₂×C₄×C₉	—	2	2	no	—
194	C₂×C₄×C₉	—	3	1	no	—
195	C₂×C₄×C₉	—	3	1	no	—
196	C₂×C₄×C₉	—	3	2	no	—
197	C₂×C₄×C₉	—	3	1	no	—
198	C₂×C₄×C₉	—	3	2	no	—
199	C₂×C₄×C₉	—	3	1	no	—
200	C₂×C₄×C₉	—	6	4	no	—
201	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
202	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
203	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
204	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
205	#556	—	3	1	no	Sylow
206	C₂×C₃×C₉	—	4	2	no	—
207	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
208	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
209	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
210	C₂×C₃×Q₈	—	2	1	no	—
211	C₂×C₃×Q₈	—	3	1	no	—
212	C₂×C₃×Q₈	—	3	1	no	—
213	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
214	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
215	C₂×C₃×D₄	—	2	1	no	—
216	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
217	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
218	C₂²×C₃×C₄	—	3	2	no	—
219	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
220	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
221	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
222	C₃×C₄⋊C₄	—	3	1	no	—
223	C₃×C₄⋊C₄	—	3	2	no	—
224	C₃×C₄⋊C₄	—	3	2	no	—
225	C₃×C₄⋊C₄	—	3	1	no	—
226	C₃×C₄⋊C₄	—	3	2	no	—
227	C₃×C₄⋊C₄	—	3	1	no	—
228	C₃×C₄⋊C₄	—	3	2	no	—
229	C₃×C₄⋊C₄	—	3	1	no	—
230	C₃×C₂²⋊C₄	—	2	2	no	—
231	C₃×C₂²⋊C₄	—	2	2	no	—
232	C₃×C₂²⋊C₄	—	3	2	no	—
233	C₃×C₂²⋊C₄	—	3	2	no	—
234	C₃×C₂²⋊C₄	—	3	2	no	—
235	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
236	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
237	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
238	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
239	C₃×C₄²	—	2	1	no	—
240	C₃×C₄²	—	3	2	no	—
241	C₃×C₄²	—	3	2	no	—
242	C₃×C₄²	—	3	1	no	—
243	C₃×C₄²	—	3	1	no	—
244	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
245	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
246	#217	C₂²×C₉	1	2	yes	—
247	#217	C₂²×C₉	1	2	yes	—
248	#217	C₂²×C₉	1	2	yes	—
249	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
250	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
251	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
252	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
253	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
254	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
255	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
256	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
257	C₄×Dic₃	C₂²×C₉	1	2	yes	—
258	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
259	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
260	C₄×Dic₃	C₂²×C₉	1	2	yes	—
261	C₂²×C₃²	—	2	2	no	—
262	C₂²×C₃²	—	2	2	no	—
263	C₂²×C₃²	—	2	2	no	—
264	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
265	C₃²×C₄	—	2	1	no	—
266	C₃²×C₄	—	2	2	no	—
267	C₃²×C₄	—	2	1	no	—
268	C₃²×C₄	C₃×#41	1	2	yes	—
269	C₃×Dic₃	—	2	2	no	—
270	C₃×Dic₃	—	2	1	no	—
271	C₃×Dic₃	—	2	2	no	—
272	C₃×Dic₃	—	2	1	no	—
273	C₃×Dic₃	—	2	1	no	—
274	C₃×Dic₃	C₃×#41	1	2	yes	—
275	C₂²×C₉	—	2	2	no	—
276	C₂²×C₉	—	2	2	no	—
277	C₂²×C₉	—	2	2	no	—
278	C₂²×C₉	—	2	1	no	—
279	C₂²×C₉	—	4	2	no	—
280	C₂²×C₉	—	4	2	no	—
281	C₂²×C₉	—	4	2	no	—
282	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
283	C₄×C₉	—	2	2	no	—
284	C₄×C₉	—	2	1	no	—
285	C₄×C₉	—	2	1	no	—
286	C₄×C₉	—	2	2	no	—
287	C₄×C₉	—	3	2	no	—
288	C₄×C₉	—	4	1	no	—
289	C₄×C₉	—	4	1	no	—
290	C₄×C₉	—	4	2	no	—
291	C₄×C₉	—	6	2	no	—
292	C₄×C₉	—	6	2	no	—
293	C₄×C₉	—	6	1	no	—
294	C₄×C₉	—	6	1	no	—
295	C₄×C₉	—	6	1	no	—
296	C₄×C₉	#237	1	2	yes	—
297	C₄⋊Q₈	—	3	1	no	—
298	#126	—	3	2	no	—
299	#126	—	3	2	no	—
300	#124	—	3	1	no	—
301	#124	D₃×C₉	1	1	yes	characteristic
302	C₂²⋊Q₈	—	3	2	no	—
303	C₄×Q₈	—	3	1	no	—
304	C₄×Q₈	—	3	1	no	—
305	C₄×Q₈	—	3	1	no	—
306	C₄×D₄	—	3	1	no	—
307	#117	—	3	2	no	—
308	C₃×C₉	#556	1	1	yes	characteristic, complemented, Sylow
309	C₂³×C₃	—	2	2	no	—
310	C₂³×C₃	C₂³×C₉	1	2	yes	—
311	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
312	C₃×Q₈	—	2	2	no	—
313	C₃×Q₈	—	2	2	no	—
314	C₃×Q₈	—	4	2	no	—
315	C₃×Q₈	—	6	2	no	—
316	C₃×Q₈	—	6	2	no	—
317	C₃×D₄	—	2	2	no	—
318	C₃×D₄	—	2	2	no	—
319	C₃×D₄	—	4	2	no	—
320	C₂×C₃×C₄	—	2	1	no	—
321	C₂×C₃×C₄	—	2	1	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	2	2	no	—
324	C₂×C₃×C₄	—	3	1	no	—
325	C₂×C₃×C₄	—	3	1	no	—
326	C₂×C₃×C₄	—	3	2	no	—
327	C₂×C₃×C₄	—	3	1	no	—
328	C₂×C₃×C₄	—	3	2	no	—
329	C₂×C₃×C₄	—	3	1	no	—
330	C₂×C₃×C₄	—	6	4	no	—
331	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
333	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
336	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
337	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
338	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
339	C₂×Dic₃	—	2	4	no	—
340	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
341	C₂×Dic₃	C₂³×C₉	1	2	yes	—
342	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
343	C₂×Dic₃	C₂³×C₉	1	2	yes	—
344	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
345	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
346	Dic₆	—	2	2	no	—
347	Dic₆	—	2	2	no	—
348	C₂×C₃²	—	4	2	no	—
349	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
350	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
351	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
352	C₂×C₉	—	2	1	no	—
353	C₂×C₉	—	2	1	no	—
354	C₂×C₉	—	2	1	no	—
355	C₂×C₉	—	4	2	no	—
356	C₂×C₉	—	8	2	no	—
357	C₂×C₉	C₂×#237	1	1	yes	characteristic
358	C₂×C₉	D₃×#41	1	1	yes	characteristic
359	C₂×C₉	#1010	1	1	yes	characteristic
360	C₂×Q₈	—	3	1	no	—
361	C₂×Q₈	—	3	1	no	—
362	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
363	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
364	C₂²×C₄	—	3	2	no	—
365	C₄⋊C₄	—	3	1	no	—
366	C₄⋊C₄	—	3	2	no	—
367	C₄⋊C₄	—	3	1	no	—
368	C₄⋊C₄	—	3	2	no	—
369	C₄⋊C₄	—	3	2	no	—
370	C₄⋊C₄	—	3	1	no	—
371	C₄⋊C₄	—	3	1	no	—
372	C₄⋊C₄	—	3	2	no	—
373	C₂²⋊C₄	—	3	2	no	—
374	C₂²⋊C₄	—	3	2	no	—
375	C₂²⋊C₄	—	3	2	no	—
376	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
377	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
378	C₄²	—	3	2	no	—
379	C₄²	—	3	2	no	—
380	C₄²	—	3	1	no	—
381	C₄²	—	3	1	no	—
382	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
383	C₂²×C₃	—	2	2	no	—
384	C₂²×C₃	—	2	2	no	—
385	C₂²×C₃	—	2	2	no	—
386	C₂²×C₃	—	2	2	no	—
387	C₂²×C₃	—	2	2	no	—
388	C₂²×C₃	—	2	2	no	—
389	C₂²×C₃	—	2	1	no	—
390	C₂²×C₃	—	4	2	no	—
391	C₂²×C₃	—	4	2	no	—
392	C₂²×C₃	—	4	2	no	—
393	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
394	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
395	C₃×C₄	—	2	2	no	—
396	C₃×C₄	—	2	1	no	—
397	C₃×C₄	—	2	1	no	—
398	C₃×C₄	—	2	1	no	—
399	C₃×C₄	—	2	2	no	—
400	C₃×C₄	—	2	1	no	—
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	3	2	no	—
403	C₃×C₄	—	4	2	no	—
404	C₃×C₄	—	4	1	no	—
405	C₃×C₄	—	4	1	no	—
406	C₃×C₄	—	6	2	no	—
407	C₃×C₄	—	6	2	no	—
408	C₃×C₄	—	6	1	no	—
409	C₃×C₄	—	6	1	no	—
410	C₃×C₄	—	6	1	no	—
411	C₃×C₄	C₉×#41	1	2	yes	—
412	C₃×C₄	C₃×#237	1	2	yes	—
413	Dic₃	—	2	2	no	—
414	Dic₃	—	2	1	no	—
415	Dic₃	—	2	2	no	—
416	Dic₃	—	2	1	no	—
417	Dic₃	—	2	1	no	—
418	Dic₃	C₉×#41	1	2	yes	—
419	C₃²	C₃×#556	1	1	yes	characteristic
420	C₉	—	2	1	no	—
421	C₉	#5671	1	1	yes	characteristic, direct product factor
422	C₂³	C₂²×D₃×C₉	1	2	yes	—
423	Q₈	—	2	2	no	—
424	Q₈	—	6	2	no	—
425	Q₈	—	6	2	no	—
426	D₄	—	2	2	no	—
427	C₂×C₄	—	3	1	no	—
428	C₂×C₄	—	3	1	no	—
429	C₂×C₄	—	3	2	no	—
430	C₂×C₄	—	3	1	no	—
431	C₂×C₄	—	3	2	no	—
432	C₂×C₄	—	3	1	no	—
433	C₂×C₄	—	6	4	no	—
434	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
436	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
437	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
438	C₂×C₃	—	2	1	no	—
439	C₂×C₃	—	2	1	no	—
440	C₂×C₃	—	2	1	no	—
441	C₂×C₃	—	4	2	no	—
442	C₂×C₃	—	4	2	no	—
443	C₂×C₃	—	8	2	no	—
444	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
445	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
446	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
447	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
448	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
449	C₂×C₃	C₃×#1010	1	1	yes	characteristic
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	3	2	no	—
458	C₄	—	6	2	no	—
459	C₄	—	6	2	no	—
460	C₄	—	6	1	no	—
461	C₄	—	6	1	no	—
462	C₄	—	6	1	no	—
463	C₄	C₉×#237	1	2	yes	—
464	C₃	—	2	1	no	—
465	C₃	C₉×#556	1	1	yes	characteristic, complemented
466	C₃	C₃×#5671	1	1	yes	characteristic
467	C₂	—	4	2	no	—
468	C₂	C₂×C₉×#237	1	1	yes	characteristic
469	C₂	D₃×C₉×#41	1	1	yes	characteristic
470	C₂	C₉×#1010	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#124	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃²×D₄	C₂²×C₃
hypercenter	C₉×#124	D₃
hypocenter	C₃	C₉×#556
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#124

Complements

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

N	H ≅ G/N	type
2. Q₈×C₉×Dic₃	C₂	semidirect
3. C₉×#944	C₂	semidirect
6. C₉×#879	C₂	semidirect
7. C₉×#879	C₂	semidirect
8. C₉×#878	C₂	semidirect
9. C₉×#877	C₂	semidirect
10. C₄×C₉×Dic₆	C₂	semidirect
11. C₄×C₉×Dic₆	C₂	semidirect
77. #5671	C₉	direct (N × H)
156. Q₈×Dic₃	C₂×C₉	semidirect
157. #944	C₂×C₉	semidirect
160. #879	C₂×C₉	semidirect
161. #879	C₂×C₉	semidirect
162. #878	C₂×C₉	semidirect
163. #877	C₂×C₉	semidirect
164. C₄×Dic₆	C₂×C₉	semidirect
165. C₄×Dic₆	C₂×C₉	semidirect
308. C₃×C₉	#556	semidirect
421. C₉	#5671	direct (N × H)
465. C₃	C₉×#556	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#124	2
Q₈×C₉×Dic₃	2
C₉×#944	2
C₉×#936	2
D₄×C₉×Dic₃	2
C₉×#879	2
C₉×#878	2
C₉×#877	2
C₄×C₉×Dic₆	2
C₃×#5671	3
C₉×#556	3

Subgroups — C9×#5671 #13153084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5671 #13153084