Subgroups — C₉×#5690 #13153165

Order 1728.

740 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#897	C₂	1	2	yes	maximal, complemented
3	C₉×#896	C₂	1	2	yes	maximal, complemented
4	C₉×#896	C₂	1	2	yes	maximal, complemented
5	C₉×#893	C₂	1	1	yes	maximal, characteristic
6	C₉×#893	C₂	1	1	yes	maximal, characteristic
7	D₃×C₉×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₉×#890	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#888	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic
11	C₄×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5690	C₃	1	1	yes	maximal, characteristic
13	C₉×#554	—	3	1	no	maximal
14	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
16	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
17	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
18	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
19	C₂×C₉×Dic₆	C₂²	1	2	yes	—
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
23	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
24	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
25	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
26	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
29	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
30	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
31	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
32	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
33	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
35	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
36	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
37	C₃²×#125	C₂×C₃	1	1	yes	characteristic
38	C₃×#897	C₂×C₃	1	2	yes	—
39	C₃×#896	C₂×C₃	1	2	yes	—
40	C₃×#896	C₂×C₃	1	2	yes	—
41	C₃×#893	C₂×C₃	1	1	yes	characteristic
42	C₃×#893	C₂×C₃	1	1	yes	characteristic
43	C₃×D₃×C₄⋊C₄	C₂×C₃	1	2	yes	—
44	C₃×#890	C₂×C₃	1	1	yes	characteristic
45	C₃×#888	C₂×C₃	1	1	yes	characteristic
46	C₃×C₄×D₁₂	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×#125	—	2	1	no	—
50	C₉×#125	—	3	1	no	—
51	C₉×#125	D₃	1	1	yes	characteristic, complemented
52	C₉×C₂²⋊Q₈	—	3	2	no	—
53	C₉×C₂²⋊Q₈	—	3	2	no	—
54	C₉×C₂²⋊Q₈	—	3	2	no	—
55	C₄×Q₈×C₉	—	3	1	no	—
56	C₄×D₄×C₉	—	3	1	no	—
57	C₄×D₄×C₉	—	3	1	no	—
58	C₄×D₄×C₉	—	3	1	no	—
59	C₂×C₉×C₄⋊C₄	—	3	2	no	—
60	C₂²×D₃×C₉	C₂³	1	2	yes	—
61	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
62	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
65	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
67	C₂×C₉×Dic₃	C₂³	1	2	yes	—
68	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
69	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
71	C₉×D₁₂	Q₈	1	4	yes	complemented
72	C₄×D₃×C₉	—	2	4	no	—
73	C₄×D₃×C₉	—	4	2	no	—
74	C₄×D₃×C₉	—	4	2	no	—
75	C₉×Dic₆	—	2	2	no	—
76	C₉×Dic₆	—	4	2	no	—
77	C₃×#554	—	3	1	no	—
78	#5690	C₉	1	1	yes	characteristic, direct product factor
79	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
81	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
82	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
83	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
85	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
88	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
89	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
90	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
91	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
92	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
93	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
94	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
95	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
96	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
97	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
98	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
99	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
100	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
101	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
102	C₂×Q₈×C₉	—	3	1	no	—
103	C₂×Q₈×C₉	—	3	2	no	—
104	C₂×D₄×C₉	—	3	1	no	—
105	C₂²×C₄×C₉	—	3	2	no	—
106	C₂²×C₄×C₉	—	3	2	no	—
107	C₂²×C₄×C₉	—	3	2	no	—
108	C₉×C₄⋊C₄	—	2	1	no	—
109	C₉×C₄⋊C₄	—	2	1	no	—
110	C₉×C₄⋊C₄	—	2	2	no	—
111	C₉×C₄⋊C₄	—	2	2	no	—
112	C₉×C₄⋊C₄	—	3	1	no	—
113	C₉×C₄⋊C₄	—	3	2	no	—
114	C₉×C₄⋊C₄	—	3	2	no	—
115	C₉×C₄⋊C₄	—	3	1	no	—
116	C₉×C₄⋊C₄	—	3	1	no	—
117	C₉×C₄⋊C₄	—	3	1	no	—
118	C₉×C₄⋊C₄	—	3	2	no	—
119	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
120	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
121	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
122	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
123	C₉×C₂²⋊C₄	—	3	2	no	—
124	C₉×C₂²⋊C₄	—	3	2	no	—
125	C₉×C₂²⋊C₄	—	3	2	no	—
126	C₄²×C₉	—	2	1	no	—
127	C₄²×C₉	—	3	1	no	—
128	C₄²×C₉	—	3	1	no	—
129	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
130	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
131	C₂×D₃×C₉	—	2	2	no	—
132	C₂×D₃×C₉	—	2	2	no	—
133	C₂×D₃×C₉	C₂×Q₈	1	4	yes	—
134	C₃×C₄×C₉	—	2	1	no	—
135	C₃×C₄×C₉	—	2	2	no	—
136	C₃×C₄×C₉	—	2	2	no	—
137	C₃×C₄×C₉	—	2	1	no	—
138	C₃×C₄×C₉	C₂×Q₈	1	2	yes	—
139	C₉×Dic₃	—	2	1	no	—
140	C₉×Dic₃	—	2	1	no	—
141	C₉×Dic₃	—	2	2	no	—
142	C₉×Dic₃	—	2	1	no	—
143	C₉×Dic₃	#41	1	2	yes	—
144	C₃×C₄⋊Q₈	—	3	1	no	—
145	C₃×#125	—	2	1	no	—
146	C₃×#125	—	3	1	no	—
147	C₃×#125	C₂×C₉	1	1	yes	characteristic, complemented
148	C₃×#125	C₃×D₃	1	1	yes	characteristic
149	C₃×C₂²⋊Q₈	—	3	2	no	—
150	C₃×C₂²⋊Q₈	—	3	2	no	—
151	C₃×C₂²⋊Q₈	—	3	2	no	—
152	C₃×C₄×Q₈	—	3	1	no	—
153	C₃×C₄×D₄	—	3	1	no	—
154	C₃×C₄×D₄	—	3	1	no	—
155	C₃×C₄×D₄	—	3	1	no	—
156	C₂×C₃×C₄⋊C₄	—	3	2	no	—
157	#897	C₂×C₉	1	2	yes	complemented
158	#896	C₂×C₉	1	2	yes	complemented
159	#896	C₂×C₉	1	2	yes	complemented
160	#893	C₂×C₉	1	1	yes	characteristic
161	#893	C₂×C₉	1	1	yes	characteristic
162	D₃×C₄⋊C₄	C₂×C₉	1	2	yes	complemented
163	#890	C₂×C₉	1	1	yes	characteristic, complemented
164	#888	C₂×C₉	1	1	yes	characteristic, complemented
165	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic
166	C₄×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
167	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
168	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
169	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
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	C₂³×C₃	1	1	yes	characteristic
174	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
175	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
176	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
177	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
178	C₃×D₁₂	C₃×Q₈	1	4	yes	—
179	C₃×C₄×D₃	—	2	4	no	—
180	C₃×C₄×D₃	—	4	2	no	—
181	C₃×C₄×D₃	—	4	2	no	—
182	C₃×Dic₆	—	2	2	no	—
183	C₃×Dic₆	—	4	2	no	—
184	C₂³×C₉	—	3	2	no	—
185	Q₈×C₉	—	6	2	no	—
186	Q₈×C₉	—	12	2	no	—
187	D₄×C₉	—	3	4	no	—
188	C₂×C₄×C₉	—	2	1	no	—
189	C₂×C₄×C₉	—	2	1	no	—
190	C₂×C₄×C₉	—	2	1	no	—
191	C₂×C₄×C₉	—	2	2	no	—
192	C₂×C₄×C₉	—	2	2	no	—
193	C₂×C₄×C₉	—	3	1	no	—
194	C₂×C₄×C₉	—	3	1	no	—
195	C₂×C₄×C₉	—	3	1	no	—
196	C₂×C₄×C₉	—	3	1	no	—
197	C₂×C₄×C₉	—	3	2	no	—
198	C₂×C₄×C₉	—	6	4	no	—
199	C₂×C₄×C₉	—	12	2	no	—
200	C₂×C₄×C₉	—	12	2	no	—
201	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
202	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
203	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
204	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
205	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
206	#554	—	3	1	no	Sylow
207	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
208	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
209	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
210	D₃×C₉	—	2	4	no	—
211	C₂×C₃×Q₈	—	3	1	no	—
212	C₂×C₃×Q₈	—	3	2	no	—
213	C₂×C₃×D₄	—	3	1	no	—
214	C₂²×C₃×C₄	—	3	2	no	—
215	C₂²×C₃×C₄	—	3	2	no	—
216	C₂²×C₃×C₄	—	3	2	no	—
217	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
218	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
219	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
220	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
221	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
222	C₂×Dic₆	C₂²×C₉	1	2	yes	—
223	C₃×C₄⋊C₄	—	2	2	no	—
224	C₃×C₄⋊C₄	—	2	1	no	—
225	C₃×C₄⋊C₄	—	2	1	no	—
226	C₃×C₄⋊C₄	—	2	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×C₄⋊C₄	—	3	2	no	—
231	C₃×C₄⋊C₄	—	3	2	no	—
232	C₃×C₄⋊C₄	—	3	1	no	—
233	C₃×C₄⋊C₄	—	3	1	no	—
234	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
235	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
236	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
237	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
238	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
239	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
240	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
241	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
242	C₃×C₂²⋊C₄	—	3	2	no	—
243	C₃×C₂²⋊C₄	—	3	2	no	—
244	C₃×C₂²⋊C₄	—	3	2	no	—
245	C₃×C₄²	—	2	1	no	—
246	C₃×C₄²	—	3	1	no	—
247	C₃×C₄²	—	3	1	no	—
248	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
249	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
250	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
251	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
252	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
253	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
254	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
255	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
256	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
257	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
258	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
259	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
260	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
261	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
262	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
263	C₂×C₃×D₃	—	2	2	no	—
264	C₂×C₃×D₃	—	2	2	no	—
265	C₂×C₃×D₃	C₂×C₃×Q₈	1	4	yes	—
266	C₃²×C₄	—	2	1	no	—
267	C₃²×C₄	—	2	2	no	—
268	C₃²×C₄	—	2	2	no	—
269	C₃²×C₄	—	2	1	no	—
270	C₃²×C₄	C₂×C₃×Q₈	1	2	yes	—
271	C₃×Dic₃	—	2	1	no	—
272	C₃×Dic₃	—	2	1	no	—
273	C₃×Dic₃	—	2	2	no	—
274	C₃×Dic₃	—	2	1	no	—
275	C₃×Dic₃	C₃×#41	1	2	yes	—
276	C₂²×C₉	—	2	1	no	—
277	C₂²×C₉	—	3	4	no	—
278	C₂²×C₉	—	6	2	no	—
279	C₂²×C₉	—	6	2	no	—
280	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
281	C₄×C₉	—	2	2	no	—
282	C₄×C₉	—	2	1	no	—
283	C₄×C₉	—	2	1	no	—
284	C₄×C₉	—	2	2	no	—
285	C₄×C₉	—	2	2	no	—
286	C₄×C₉	—	3	2	no	—
287	C₄×C₉	—	4	2	no	—
288	C₄×C₉	—	4	1	no	—
289	C₄×C₉	—	4	1	no	—
290	C₄×C₉	—	4	2	no	—
291	C₄×C₉	—	6	1	no	—
292	C₄×C₉	—	6	1	no	—
293	C₄×C₉	—	6	2	no	—
294	C₄×C₉	—	6	1	no	—
295	C₄×C₉	D₃×Q₈	1	2	yes	—
296	C₄⋊Q₈	—	3	1	no	—
297	#125	—	3	1	no	—
298	#125	D₃×C₉	1	1	yes	characteristic, complemented
299	C₂²⋊Q₈	—	3	2	no	—
300	C₂²⋊Q₈	—	3	2	no	—
301	C₂²⋊Q₈	—	3	2	no	—
302	C₄×Q₈	—	3	1	no	—
303	C₄×D₄	—	3	1	no	—
304	C₄×D₄	—	3	1	no	—
305	C₄×D₄	—	3	1	no	—
306	C₂×C₄⋊C₄	—	3	2	no	—
307	C₃×C₉	#554	1	1	yes	characteristic, complemented, Sylow
308	C₂³×C₃	—	3	2	no	—
309	C₂²×D₃	C₂³×C₉	1	2	yes	—
310	C₃×Q₈	—	6	2	no	—
311	C₃×Q₈	—	12	2	no	—
312	C₃×D₄	—	3	4	no	—
313	C₂×C₃×C₄	—	2	1	no	—
314	C₂×C₃×C₄	—	2	1	no	—
315	C₂×C₃×C₄	—	2	1	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	3	1	no	—
319	C₂×C₃×C₄	—	3	1	no	—
320	C₂×C₃×C₄	—	3	1	no	—
321	C₂×C₃×C₄	—	3	1	no	—
322	C₂×C₃×C₄	—	3	2	no	—
323	C₂×C₃×C₄	—	6	4	no	—
324	C₂×C₃×C₄	—	12	2	no	—
325	C₂×C₃×C₄	—	12	2	no	—
326	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
328	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
329	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
331	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
334	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
335	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
336	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
337	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
338	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
339	C₂×Dic₃	C₂³×C₉	1	2	yes	—
340	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
341	D₁₂	Q₈×C₉	1	4	yes	complemented
342	C₄×D₃	—	2	4	no	—
343	C₄×D₃	—	4	2	no	—
344	C₄×D₃	—	4	2	no	—
345	Dic₆	—	2	2	no	—
346	Dic₆	—	4	2	no	—
347	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
348	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
349	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
350	C₃×D₃	—	2	4	no	—
351	C₂×C₉	—	2	1	no	—
352	C₂×C₉	—	2	1	no	—
353	C₂×C₉	—	2	1	no	—
354	C₂×C₉	—	6	4	no	—
355	C₂×C₉	C₂×D₃×Q₈	1	1	yes	characteristic
356	C₂×C₉	D₃×#41	1	1	yes	characteristic
357	C₂×C₉	#1009	1	1	yes	characteristic
358	C₂×Q₈	—	3	1	no	—
359	C₂×Q₈	—	3	2	no	—
360	C₂×D₄	—	3	1	no	—
361	C₂²×C₄	—	3	2	no	—
362	C₂²×C₄	—	3	2	no	—
363	C₂²×C₄	—	3	2	no	—
364	C₄⋊C₄	—	3	1	no	—
365	C₄⋊C₄	—	3	2	no	—
366	C₄⋊C₄	—	3	2	no	—
367	C₄⋊C₄	—	3	1	no	—
368	C₄⋊C₄	—	3	1	no	—
369	C₄⋊C₄	—	3	1	no	—
370	C₄⋊C₄	—	3	2	no	—
371	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
372	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
373	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
374	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
375	C₂²⋊C₄	—	3	2	no	—
376	C₂²⋊C₄	—	3	2	no	—
377	C₂²⋊C₄	—	3	2	no	—
378	C₄²	—	3	1	no	—
379	C₄²	—	3	1	no	—
380	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
381	C₂²×C₃	—	2	1	no	—
382	C₂²×C₃	—	3	4	no	—
383	C₂²×C₃	—	6	2	no	—
384	C₂²×C₃	—	6	2	no	—
385	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
386	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
387	C₂×D₃	—	2	2	no	—
388	C₂×D₃	—	2	2	no	—
389	C₂×D₃	C₂×Q₈×C₉	1	4	yes	—
390	C₃×C₄	—	2	2	no	—
391	C₃×C₄	—	2	1	no	—
392	C₃×C₄	—	2	1	no	—
393	C₃×C₄	—	2	2	no	—
394	C₃×C₄	—	2	1	no	—
395	C₃×C₄	—	2	2	no	—
396	C₃×C₄	—	2	2	no	—
397	C₃×C₄	—	2	1	no	—
398	C₃×C₄	—	2	2	no	—
399	C₃×C₄	—	3	2	no	—
400	C₃×C₄	—	4	2	no	—
401	C₃×C₄	—	4	1	no	—
402	C₃×C₄	—	4	1	no	—
403	C₃×C₄	—	4	2	no	—
404	C₃×C₄	—	6	1	no	—
405	C₃×C₄	—	6	1	no	—
406	C₃×C₄	—	6	2	no	—
407	C₃×C₄	—	6	1	no	—
408	C₃×C₄	C₂×Q₈×C₉	1	2	yes	—
409	C₃×C₄	C₃×D₃×Q₈	1	2	yes	—
410	Dic₃	—	2	1	no	—
411	Dic₃	—	2	1	no	—
412	Dic₃	—	2	2	no	—
413	Dic₃	—	2	1	no	—
414	Dic₃	C₉×#41	1	2	yes	—
415	C₃²	C₃×#554	1	1	yes	characteristic
416	C₉	—	2	1	no	—
417	C₉	#5690	1	1	yes	characteristic, direct product factor
418	C₂³	—	3	2	no	—
419	Q₈	—	6	2	no	—
420	Q₈	—	12	2	no	—
421	D₄	—	3	4	no	—
422	C₂×C₄	—	3	1	no	—
423	C₂×C₄	—	3	1	no	—
424	C₂×C₄	—	3	1	no	—
425	C₂×C₄	—	3	1	no	—
426	C₂×C₄	—	3	2	no	—
427	C₂×C₄	—	6	4	no	—
428	C₂×C₄	—	12	2	no	—
429	C₂×C₄	—	12	2	no	—
430	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
433	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
434	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
435	C₂×C₃	—	2	1	no	—
436	C₂×C₃	—	2	1	no	—
437	C₂×C₃	—	2	1	no	—
438	C₂×C₃	—	6	4	no	—
439	C₂×C₃	C₂²×Q₈×C₉	1	1	yes	characteristic
440	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
441	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
442	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
443	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
444	C₂×C₃	C₃×#1009	1	1	yes	characteristic
445	D₃	—	2	4	no	—
446	C₂²	—	3	4	no	—
447	C₂²	—	6	2	no	—
448	C₂²	—	6	2	no	—
449	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
450	C₄	—	2	2	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	2	no	—
454	C₄	—	3	2	no	—
455	C₄	—	6	1	no	—
456	C₄	—	6	1	no	—
457	C₄	—	6	2	no	—
458	C₄	—	6	1	no	—
459	C₄	D₃×Q₈×C₉	1	2	yes	—
460	C₃	—	2	1	no	—
461	C₃	C₉×#554	1	1	yes	characteristic, complemented
462	C₃	C₃×#5690	1	1	yes	characteristic
463	C₂	—	6	4	no	—
464	C₂	C₂×D₃×Q₈×C₉	1	1	yes	characteristic
465	C₂	D₃×C₉×#41	1	1	yes	characteristic
466	C₂	C₉×#1009	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×#125	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×D₁₂	C₂²×C₃
hypercenter	C₉×#125	D₃
hypocenter	C₃	C₉×#554
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#125

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#125	C₂	semidirect
2. C₉×#897	C₂	semidirect
3. C₉×#896	C₂	semidirect
4. C₉×#896	C₂	semidirect
7. D₃×C₉×C₄⋊C₄	C₂	semidirect
8. C₉×#890	C₂	semidirect
9. C₉×#888	C₂	semidirect
11. C₄×C₉×Dic₆	C₂	semidirect
51. C₉×#125	D₃	semidirect
71. C₉×D₁₂	Q₈	semidirect
78. #5690	C₉	direct (N × H)
147. C₃×#125	C₂×C₉	semidirect
157. #897	C₂×C₉	semidirect
158. #896	C₂×C₉	semidirect
159. #896	C₂×C₉	semidirect
162. D₃×C₄⋊C₄	C₂×C₉	semidirect
163. #890	C₂×C₉	semidirect
164. #888	C₂×C₉	semidirect
166. C₄×Dic₆	C₂×C₉	semidirect
298. #125	D₃×C₉	semidirect
307. C₃×C₉	#554	semidirect
341. D₁₂	Q₈×C₉	semidirect
417. C₉	#5690	direct (N × H)
461. C₃	C₉×#554	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#125	2
C₉×#897	2
C₉×#896	2
C₉×#893	2
D₃×C₉×C₄⋊C₄	2
C₉×#890	2
C₉×#888	2
C₄×C₉×D₁₂	2
C₄×C₉×Dic₆	2
C₃×#5690	3
C₉×#554	3

Subgroups — C9×#5690 #13153165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5690 #13153165