Subgroups — C₉×#5638 #13152935

Order 1728.

728 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#946	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#946	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#929	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#898	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#894	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#893	C₂	1	1	yes	maximal, characteristic, complemented
9	D₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#889	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#889	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#884	C₂	1	1	yes	maximal, characteristic
13	C₉×#883	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#883	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#879	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5638	C₃	1	1	yes	maximal, characteristic
17	C₉×#539	—	3	1	no	maximal
18	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₉×#67	C₂²	1	1	yes	characteristic
21	C₂×C₉×#67	C₂²	1	1	yes	characteristic
22	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
27	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₉×#217	C₂²	1	1	yes	characteristic
33	C₉×#217	C₂²	1	1	yes	characteristic
34	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
35	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
36	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
38	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
39	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
40	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
41	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
42	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
43	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
44	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
45	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
46	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
47	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
48	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
49	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
50	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
52	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
53	C₃²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
54	C₃×#946	C₂×C₃	1	1	yes	characteristic
55	C₃×#946	C₂×C₃	1	1	yes	characteristic
56	C₃×#929	C₂×C₃	1	1	yes	characteristic
57	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
58	C₃×#898	C₂×C₃	1	1	yes	characteristic
59	C₃×#894	C₂×C₃	1	1	yes	characteristic
60	C₃×#893	C₂×C₃	1	1	yes	characteristic
61	C₃×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
62	C₃×#889	C₂×C₃	1	1	yes	characteristic
63	C₃×#889	C₂×C₃	1	1	yes	characteristic
64	C₃×#884	C₂×C₃	1	1	yes	characteristic
65	C₃×#883	C₂×C₃	1	1	yes	characteristic
66	C₃×#883	C₂×C₃	1	1	yes	characteristic
67	C₃×#879	C₂×C₃	1	1	yes	characteristic
68	C₉×#126	—	3	1	no	—
69	C₉×#126	—	3	1	no	—
70	C₉×#125	—	3	1	no	—
71	C₉×#125	—	3	1	no	—
72	C₉×#123	—	3	1	no	—
73	C₉×#123	—	3	1	no	—
74	C₉×#123	—	3	1	no	—
75	C₉×#123	—	3	1	no	—
76	C₉×C₂²⋊Q₈	—	2	1	no	—
77	C₉×C₂²⋊Q₈	—	3	1	no	—
78	C₉×C₂²⋊Q₈	—	3	1	no	—
79	C₉×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
80	C₉×#121	—	3	1	no	—
81	C₄×D₄×C₉	—	3	1	no	—
82	C₄×D₄×C₉	—	3	1	no	—
83	C₂×C₉×C₄⋊C₄	—	3	1	no	—
84	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
85	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
86	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
87	C₃×Q₈×C₉	—	4	1	no	—
88	C₂×C₃×C₄×C₉	—	4	1	no	—
89	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
95	C₉×#67	—	2	2	no	—
96	C₉×#67	—	4	1	no	—
97	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
98	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
99	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
100	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
101	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
102	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
103	C₉×D₁₂	—	2	2	no	—
104	C₄×D₃×C₉	—	2	2	no	—
105	C₄×D₃×C₉	—	4	1	no	—
106	C₄×D₃×C₉	—	4	1	no	—
107	C₄×D₃×C₉	—	4	1	no	—
108	C₃×#539	—	3	1	no	—
109	#5638	C₉	1	1	yes	characteristic, direct product factor
110	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
111	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
119	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₃×#217	C₂²×C₃	1	1	yes	characteristic
125	C₃×#217	C₂²×C₃	1	1	yes	characteristic
126	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
133	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
134	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
135	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
136	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
141	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
142	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
143	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
144	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
145	C₂×Q₈×C₉	—	2	1	no	—
146	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
147	C₂×D₄×C₉	—	3	1	no	—
148	C₂×D₄×C₉	—	3	1	no	—
149	C₂×D₄×C₉	—	3	1	no	—
150	C₂²×C₄×C₉	—	2	1	no	—
151	C₂²×C₄×C₉	—	3	1	no	—
152	C₂²×C₄×C₉	—	3	1	no	—
153	C₂²×C₄×C₉	—	3	1	no	—
154	C₂²×C₄×C₉	—	3	1	no	—
155	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
156	C₉×C₄⋊C₄	—	2	1	no	—
157	C₉×C₄⋊C₄	—	2	1	no	—
158	C₉×C₄⋊C₄	—	2	1	no	—
159	C₉×C₄⋊C₄	—	3	1	no	—
160	C₉×C₄⋊C₄	—	3	1	no	—
161	C₉×C₄⋊C₄	—	3	1	no	—
162	C₉×C₄⋊C₄	—	3	1	no	—
163	C₉×C₄⋊C₄	—	3	1	no	—
164	C₉×C₄⋊C₄	—	3	1	no	—
165	C₉×C₄⋊C₄	—	3	1	no	—
166	C₉×C₄⋊C₄	—	3	1	no	—
167	C₉×C₄⋊C₄	—	3	1	no	—
168	C₉×C₄⋊C₄	—	3	1	no	—
169	C₉×C₄⋊C₄	—	3	1	no	—
170	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
171	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
172	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
173	C₉×C₂²⋊C₄	—	2	1	no	—
174	C₉×C₂²⋊C₄	—	2	1	no	—
175	C₉×C₂²⋊C₄	—	3	1	no	—
176	C₉×C₂²⋊C₄	—	3	1	no	—
177	C₉×C₂²⋊C₄	—	3	1	no	—
178	C₉×C₂²⋊C₄	—	3	1	no	—
179	C₉×C₂²⋊C₄	—	3	1	no	—
180	C₉×C₂²⋊C₄	—	3	1	no	—
181	C₉×C₂²⋊C₄	—	3	1	no	—
182	C₉×C₂²⋊C₄	—	3	1	no	—
183	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
184	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
185	C₄²×C₉	—	3	1	no	—
186	C₄²×C₉	—	3	1	no	—
187	C₂²×C₃×C₉	—	2	1	no	—
188	C₂²×C₃×C₉	—	2	1	no	—
189	C₂²×C₃×C₉	—	2	1	no	—
190	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
191	C₂×D₃×C₉	—	2	1	no	—
192	C₂×D₃×C₉	—	2	1	no	—
193	C₂×D₃×C₉	—	2	1	no	—
194	C₂×D₃×C₉	—	2	1	no	—
195	C₂×D₃×C₉	—	2	1	no	—
196	C₂×D₃×C₉	#41	1	2	yes	—
197	C₃×C₄×C₉	—	2	1	no	—
198	C₃×C₄×C₉	—	2	1	no	—
199	C₃×C₄×C₉	—	2	1	no	—
200	C₃×C₄×C₉	—	2	1	no	—
201	C₃×C₄×C₉	—	2	1	no	—
202	C₃×C₄×C₉	—	2	1	no	—
203	C₉×Dic₃	—	2	1	no	—
204	C₉×Dic₃	—	2	1	no	—
205	C₉×Dic₃	—	2	1	no	—
206	C₉×Dic₃	—	2	1	no	—
207	C₉×Dic₃	—	2	1	no	—
208	C₉×Dic₃	—	2	1	no	—
209	C₃×#126	—	3	1	no	—
210	C₃×#126	—	3	1	no	—
211	C₃×#125	—	3	1	no	—
212	C₃×#125	—	3	1	no	—
213	C₃×#123	—	3	1	no	—
214	C₃×#123	—	3	1	no	—
215	C₃×#123	—	3	1	no	—
216	C₃×#123	—	3	1	no	—
217	C₃×C₂²⋊Q₈	—	2	1	no	—
218	C₃×C₂²⋊Q₈	—	3	1	no	—
219	C₃×C₂²⋊Q₈	—	3	1	no	—
220	C₃×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
221	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
222	C₃×#121	—	3	1	no	—
223	C₃×C₄×D₄	—	3	1	no	—
224	C₃×C₄×D₄	—	3	1	no	—
225	C₂×C₃×C₄⋊C₄	—	3	1	no	—
226	#946	C₂×C₉	1	1	yes	characteristic, complemented
227	#946	C₂×C₉	1	1	yes	characteristic, complemented
228	#929	C₂×C₉	1	1	yes	characteristic, complemented
229	C₄×#67	C₂×C₉	1	1	yes	characteristic, complemented
230	#898	C₂×C₉	1	1	yes	characteristic, complemented
231	#894	C₂×C₉	1	1	yes	characteristic, complemented
232	#893	C₂×C₉	1	1	yes	characteristic, complemented
233	D₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
234	#889	C₂×C₉	1	1	yes	characteristic, complemented
235	#889	C₂×C₉	1	1	yes	characteristic, complemented
236	#884	C₂×C₉	1	1	yes	characteristic
237	#883	C₂×C₉	1	1	yes	characteristic, complemented
238	#883	C₂×C₉	1	1	yes	characteristic, complemented
239	#879	C₂×C₉	1	1	yes	characteristic, complemented
240	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
241	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
242	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
243	C₃²×Q₈	—	4	1	no	—
244	C₂×C₃²×C₄	—	4	1	no	—
245	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
246	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
247	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
248	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
249	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
250	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
251	C₃×#67	—	2	2	no	—
252	C₃×#67	—	4	1	no	—
253	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
254	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
255	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
256	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
257	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
258	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
259	C₃×D₁₂	—	2	2	no	—
260	C₃×C₄×D₃	—	2	2	no	—
261	C₃×C₄×D₃	—	4	1	no	—
262	C₃×C₄×D₃	—	4	1	no	—
263	C₃×C₄×D₃	—	4	1	no	—
264	C₂³×C₉	—	2	1	no	—
265	C₂³×C₉	—	3	1	no	—
266	C₂³×C₉	—	3	1	no	—
267	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
268	Q₈×C₉	—	4	1	no	—
269	Q₈×C₉	—	4	2	no	—
270	D₄×C₉	—	6	2	no	—
271	D₄×C₉	—	6	2	no	—
272	D₄×C₉	—	12	1	no	—
273	C₂×C₄×C₉	—	2	1	no	—
274	C₂×C₄×C₉	—	2	1	no	—
275	C₂×C₄×C₉	—	2	1	no	—
276	C₂×C₄×C₉	—	2	1	no	—
277	C₂×C₄×C₉	—	2	1	no	—
278	C₂×C₄×C₉	—	2	1	no	—
279	C₂×C₄×C₉	—	3	1	no	—
280	C₂×C₄×C₉	—	3	1	no	—
281	C₂×C₄×C₉	—	3	1	no	—
282	C₂×C₄×C₉	—	3	1	no	—
283	C₂×C₄×C₉	—	3	1	no	—
284	C₂×C₄×C₉	—	3	1	no	—
285	C₂×C₄×C₉	—	4	1	no	—
286	C₂×C₄×C₉	—	4	2	no	—
287	C₂×C₄×C₉	—	6	2	no	—
288	C₂×C₄×C₉	—	12	1	no	—
289	C₂×C₄×C₉	—	12	1	no	—
290	C₂×C₄×C₉	—	12	1	no	—
291	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
292	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
293	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
294	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
295	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
296	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
297	#539	—	3	1	no	Sylow
298	C₂×C₃×C₉	—	4	1	no	—
299	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
300	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
301	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
302	D₃×C₉	—	2	2	no	—
303	D₃×C₉	—	4	1	no	—
304	C₂×C₃×Q₈	—	2	1	no	—
305	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
306	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
307	C₂×C₃×D₄	—	3	1	no	—
308	C₂×C₃×D₄	—	3	1	no	—
309	C₂×C₃×D₄	—	3	1	no	—
310	C₂²×C₃×C₄	—	2	1	no	—
311	C₂²×C₃×C₄	—	3	1	no	—
312	C₂²×C₃×C₄	—	3	1	no	—
313	C₂²×C₃×C₄	—	3	1	no	—
314	C₂²×C₃×C₄	—	3	1	no	—
315	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
316	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
317	C₂×#67	C₂²×C₉	1	1	yes	characteristic
318	C₂×#67	C₂²×C₉	1	1	yes	characteristic
319	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
320	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
321	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
322	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
323	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
324	C₃×C₄⋊C₄	—	2	1	no	—
325	C₃×C₄⋊C₄	—	2	1	no	—
326	C₃×C₄⋊C₄	—	2	1	no	—
327	C₃×C₄⋊C₄	—	3	1	no	—
328	C₃×C₄⋊C₄	—	3	1	no	—
329	C₃×C₄⋊C₄	—	3	1	no	—
330	C₃×C₄⋊C₄	—	3	1	no	—
331	C₃×C₄⋊C₄	—	3	1	no	—
332	C₃×C₄⋊C₄	—	3	1	no	—
333	C₃×C₄⋊C₄	—	3	1	no	—
334	C₃×C₄⋊C₄	—	3	1	no	—
335	C₃×C₄⋊C₄	—	3	1	no	—
336	C₃×C₄⋊C₄	—	3	1	no	—
337	C₃×C₄⋊C₄	—	3	1	no	—
338	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
339	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
340	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
341	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
342	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
343	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
344	C₃×C₂²⋊C₄	—	2	1	no	—
345	C₃×C₂²⋊C₄	—	2	1	no	—
346	C₃×C₂²⋊C₄	—	3	1	no	—
347	C₃×C₂²⋊C₄	—	3	1	no	—
348	C₃×C₂²⋊C₄	—	3	1	no	—
349	C₃×C₂²⋊C₄	—	3	1	no	—
350	C₃×C₂²⋊C₄	—	3	1	no	—
351	C₃×C₂²⋊C₄	—	3	1	no	—
352	C₃×C₂²⋊C₄	—	3	1	no	—
353	C₃×C₂²⋊C₄	—	3	1	no	—
354	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
355	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
356	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
357	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
358	C₃×C₄²	—	3	1	no	—
359	C₃×C₄²	—	3	1	no	—
360	#217	C₂²×C₉	1	1	yes	characteristic
361	#217	C₂²×C₉	1	1	yes	characteristic
362	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
363	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
364	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
365	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
366	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
367	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
368	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
369	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
370	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
371	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
372	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
373	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
374	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
375	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
376	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
377	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
378	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
379	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
380	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
381	C₂²×C₃²	—	2	1	no	—
382	C₂²×C₃²	—	2	1	no	—
383	C₂²×C₃²	—	2	1	no	—
384	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
385	C₂×C₃×D₃	—	2	1	no	—
386	C₂×C₃×D₃	—	2	1	no	—
387	C₂×C₃×D₃	—	2	1	no	—
388	C₂×C₃×D₃	—	2	1	no	—
389	C₂×C₃×D₃	—	2	1	no	—
390	C₂×C₃×D₃	C₃×#41	1	2	yes	—
391	C₃²×C₄	—	2	1	no	—
392	C₃²×C₄	—	2	1	no	—
393	C₃²×C₄	—	2	1	no	—
394	C₃²×C₄	—	2	1	no	—
395	C₃²×C₄	—	2	1	no	—
396	C₃²×C₄	—	2	1	no	—
397	C₃×Dic₃	—	2	1	no	—
398	C₃×Dic₃	—	2	1	no	—
399	C₃×Dic₃	—	2	1	no	—
400	C₃×Dic₃	—	2	1	no	—
401	C₃×Dic₃	—	2	1	no	—
402	C₃×Dic₃	—	2	1	no	—
403	C₂²×C₉	—	2	2	no	—
404	C₂²×C₉	—	2	1	no	—
405	C₂²×C₉	—	2	1	no	—
406	C₂²×C₉	—	2	1	no	—
407	C₂²×C₉	—	2	1	no	—
408	C₂²×C₉	—	3	2	no	—
409	C₂²×C₉	—	4	1	no	—
410	C₂²×C₉	—	4	1	no	—
411	C₂²×C₉	—	6	1	no	—
412	C₂²×C₉	—	6	1	no	—
413	C₂²×C₉	—	6	1	no	—
414	C₂²×C₉	—	6	1	no	—
415	C₂²×C₉	—	6	1	no	—
416	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
417	C₄×C₉	—	2	2	no	—
418	C₄×C₉	—	2	1	no	—
419	C₄×C₉	—	2	1	no	—
420	C₄×C₉	—	2	1	no	—
421	C₄×C₉	—	2	1	no	—
422	C₄×C₉	—	2	1	no	—
423	C₄×C₉	—	2	1	no	—
424	C₄×C₉	—	4	1	no	—
425	C₄×C₉	—	4	1	no	—
426	C₄×C₉	—	4	1	no	—
427	C₄×C₉	—	4	1	no	—
428	C₄×C₉	—	4	1	no	—
429	C₄×C₉	—	6	1	no	—
430	C₄×C₉	—	6	1	no	—
431	C₄×C₉	—	6	1	no	—
432	C₄×C₉	—	6	1	no	—
433	C₄×C₉	—	6	1	no	—
434	C₄×C₉	—	6	1	no	—
435	#126	—	3	1	no	—
436	#126	—	3	1	no	—
437	#125	—	3	1	no	—
438	#125	—	3	1	no	—
439	#123	—	3	1	no	—
440	#123	—	3	1	no	—
441	#123	—	3	1	no	—
442	#123	—	3	1	no	—
443	C₂²⋊Q₈	—	3	1	no	—
444	C₂²⋊Q₈	—	3	1	no	—
445	C₂²⋊Q₈	D₃×C₉	1	1	yes	characteristic, complemented
446	#121	—	3	1	no	—
447	C₄×D₄	—	3	1	no	—
448	C₄×D₄	—	3	1	no	—
449	C₂×C₄⋊C₄	—	3	1	no	—
450	C₃×C₉	#539	1	1	yes	characteristic, complemented, Sylow
451	C₂³×C₃	—	2	1	no	—
452	C₂³×C₃	—	3	1	no	—
453	C₂³×C₃	—	3	1	no	—
454	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
455	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
456	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
457	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
458	C₃×Q₈	—	4	1	no	—
459	C₃×Q₈	—	4	1	no	—
460	C₃×Q₈	—	4	2	no	—
461	C₃×D₄	—	6	2	no	—
462	C₃×D₄	—	6	2	no	—
463	C₃×D₄	—	12	1	no	—
464	C₂×C₃×C₄	—	2	1	no	—
465	C₂×C₃×C₄	—	2	1	no	—
466	C₂×C₃×C₄	—	2	1	no	—
467	C₂×C₃×C₄	—	2	1	no	—
468	C₂×C₃×C₄	—	2	1	no	—
469	C₂×C₃×C₄	—	2	1	no	—
470	C₂×C₃×C₄	—	3	1	no	—
471	C₂×C₃×C₄	—	3	1	no	—
472	C₂×C₃×C₄	—	3	1	no	—
473	C₂×C₃×C₄	—	3	1	no	—
474	C₂×C₃×C₄	—	3	1	no	—
475	C₂×C₃×C₄	—	3	1	no	—
476	C₂×C₃×C₄	—	4	1	no	—
477	C₂×C₃×C₄	—	4	1	no	—
478	C₂×C₃×C₄	—	4	2	no	—
479	C₂×C₃×C₄	—	6	2	no	—
480	C₂×C₃×C₄	—	12	1	no	—
481	C₂×C₃×C₄	—	12	1	no	—
482	C₂×C₃×C₄	—	12	1	no	—
483	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
484	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
485	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
486	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
487	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
488	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
489	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
490	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
491	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
492	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
493	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
494	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
495	#67	—	2	2	no	—
496	#67	—	4	1	no	—
497	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
498	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
499	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
500	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
501	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
502	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
503	D₁₂	—	2	2	no	—
504	C₄×D₃	—	2	2	no	—
505	C₄×D₃	—	4	1	no	—
506	C₄×D₃	—	4	1	no	—
507	C₄×D₃	—	4	1	no	—
508	C₂×C₃²	—	4	1	no	—
509	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
510	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
511	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
512	C₃×D₃	—	2	2	no	—
513	C₃×D₃	—	4	1	no	—
514	C₂×C₉	—	2	1	no	—
515	C₂×C₉	—	2	1	no	—
516	C₂×C₉	—	2	1	no	—
517	C₂×C₉	—	4	2	no	—
518	C₂×C₉	—	4	1	no	—
519	C₂×C₉	—	6	2	no	—
520	C₂×C₉	—	12	1	no	—
521	C₂×C₉	#1004	1	1	yes	characteristic
522	C₂×C₉	#1007	1	1	yes	characteristic
523	C₂×C₉	D₃×#41	1	1	yes	characteristic
524	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
525	C₂×D₄	—	3	1	no	—
526	C₂×D₄	—	3	1	no	—
527	C₂×D₄	—	3	1	no	—
528	C₂²×C₄	—	3	1	no	—
529	C₂²×C₄	—	3	1	no	—
530	C₂²×C₄	—	3	1	no	—
531	C₂²×C₄	—	3	1	no	—
532	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
533	C₄⋊C₄	—	3	1	no	—
534	C₄⋊C₄	—	3	1	no	—
535	C₄⋊C₄	—	3	1	no	—
536	C₄⋊C₄	—	3	1	no	—
537	C₄⋊C₄	—	3	1	no	—
538	C₄⋊C₄	—	3	1	no	—
539	C₄⋊C₄	—	3	1	no	—
540	C₄⋊C₄	—	3	1	no	—
541	C₄⋊C₄	—	3	1	no	—
542	C₄⋊C₄	—	3	1	no	—
543	C₄⋊C₄	—	3	1	no	—
544	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
545	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
546	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
547	C₂²⋊C₄	—	3	1	no	—
548	C₂²⋊C₄	—	3	1	no	—
549	C₂²⋊C₄	—	3	1	no	—
550	C₂²⋊C₄	—	3	1	no	—
551	C₂²⋊C₄	—	3	1	no	—
552	C₂²⋊C₄	—	3	1	no	—
553	C₂²⋊C₄	—	3	1	no	—
554	C₂²⋊C₄	—	3	1	no	—
555	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
556	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
557	C₄²	—	3	1	no	—
558	C₄²	—	3	1	no	—
559	C₂²×C₃	—	2	2	no	—
560	C₂²×C₃	—	2	1	no	—
561	C₂²×C₃	—	2	1	no	—
562	C₂²×C₃	—	2	1	no	—
563	C₂²×C₃	—	2	1	no	—
564	C₂²×C₃	—	2	1	no	—
565	C₂²×C₃	—	2	1	no	—
566	C₂²×C₃	—	2	1	no	—
567	C₂²×C₃	—	3	2	no	—
568	C₂²×C₃	—	4	1	no	—
569	C₂²×C₃	—	4	1	no	—
570	C₂²×C₃	—	6	1	no	—
571	C₂²×C₃	—	6	1	no	—
572	C₂²×C₃	—	6	1	no	—
573	C₂²×C₃	—	6	1	no	—
574	C₂²×C₃	—	6	1	no	—
575	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
576	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
577	C₂×D₃	—	2	1	no	—
578	C₂×D₃	—	2	1	no	—
579	C₂×D₃	—	2	1	no	—
580	C₂×D₃	—	2	1	no	—
581	C₂×D₃	—	2	1	no	—
582	C₂×D₃	C₉×#41	1	2	yes	—
583	C₃×C₄	—	2	2	no	—
584	C₃×C₄	—	2	1	no	—
585	C₃×C₄	—	2	1	no	—
586	C₃×C₄	—	2	1	no	—
587	C₃×C₄	—	2	1	no	—
588	C₃×C₄	—	2	1	no	—
589	C₃×C₄	—	2	1	no	—
590	C₃×C₄	—	2	1	no	—
591	C₃×C₄	—	2	1	no	—
592	C₃×C₄	—	2	1	no	—
593	C₃×C₄	—	2	1	no	—
594	C₃×C₄	—	2	1	no	—
595	C₃×C₄	—	2	1	no	—
596	C₃×C₄	—	4	1	no	—
597	C₃×C₄	—	4	1	no	—
598	C₃×C₄	—	4	1	no	—
599	C₃×C₄	—	4	1	no	—
600	C₃×C₄	—	4	1	no	—
601	C₃×C₄	—	6	1	no	—
602	C₃×C₄	—	6	1	no	—
603	C₃×C₄	—	6	1	no	—
604	C₃×C₄	—	6	1	no	—
605	C₃×C₄	—	6	1	no	—
606	C₃×C₄	—	6	1	no	—
607	Dic₃	—	2	1	no	—
608	Dic₃	—	2	1	no	—
609	Dic₃	—	2	1	no	—
610	Dic₃	—	2	1	no	—
611	Dic₃	—	2	1	no	—
612	Dic₃	—	2	1	no	—
613	C₃²	C₃×#539	1	1	yes	characteristic
614	C₉	—	2	1	no	—
615	C₉	#5638	1	1	yes	characteristic, direct product factor
616	C₂³	—	3	1	no	—
617	C₂³	—	3	1	no	—
618	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
619	Q₈	—	4	1	no	—
620	D₄	—	6	2	no	—
621	D₄	—	6	2	no	—
622	D₄	—	12	1	no	—
623	C₂×C₄	—	3	1	no	—
624	C₂×C₄	—	3	1	no	—
625	C₂×C₄	—	3	1	no	—
626	C₂×C₄	—	3	1	no	—
627	C₂×C₄	—	3	1	no	—
628	C₂×C₄	—	3	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	6	2	no	—
631	C₂×C₄	—	12	1	no	—
632	C₂×C₄	—	12	1	no	—
633	C₂×C₄	—	12	1	no	—
634	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
635	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
636	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
637	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
638	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
639	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
640	C₂×C₃	—	2	1	no	—
641	C₂×C₃	—	2	1	no	—
642	C₂×C₃	—	2	1	no	—
643	C₂×C₃	—	4	2	no	—
644	C₂×C₃	—	4	1	no	—
645	C₂×C₃	—	4	1	no	—
646	C₂×C₃	—	6	2	no	—
647	C₂×C₃	—	12	1	no	—
648	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
649	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
650	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
651	C₂×C₃	C₃×#1004	1	1	yes	characteristic
652	C₂×C₃	C₃×#1007	1	1	yes	characteristic
653	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
654	D₃	—	2	2	no	—
655	D₃	—	4	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	3	2	no	—
660	C₂²	—	6	1	no	—
661	C₂²	—	6	1	no	—
662	C₂²	—	6	1	no	—
663	C₂²	—	6	1	no	—
664	C₂²	—	6	1	no	—
665	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	1	no	—
670	C₄	—	2	1	no	—
671	C₄	—	2	1	no	—
672	C₄	—	6	1	no	—
673	C₄	—	6	1	no	—
674	C₄	—	6	1	no	—
675	C₄	—	6	1	no	—
676	C₄	—	6	1	no	—
677	C₄	—	6	1	no	—
678	C₃	—	2	1	no	—
679	C₃	C₉×#539	1	1	yes	characteristic, complemented
680	C₃	C₃×#5638	1	1	yes	characteristic
681	C₂	—	4	1	no	—
682	C₂	—	6	2	no	—
683	C₂	—	12	1	no	—
684	C₂	C₉×#1004	1	1	yes	characteristic
685	C₂	C₉×#1007	1	1	yes	characteristic
686	C₂	D₃×C₉×#41	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×C₂²⋊Q₈	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#884	C₂×C₃
hypercenter	C₉×C₂²⋊Q₈	D₃
hypocenter	C₃	C₉×#539
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×C₂²⋊Q₈	C₂	semidirect
2. C₉×#946	C₂	semidirect
3. C₉×#946	C₂	semidirect
4. C₉×#929	C₂	semidirect
5. C₄×C₉×#67	C₂	semidirect
6. C₉×#898	C₂	semidirect
7. C₉×#894	C₂	semidirect
8. C₉×#893	C₂	semidirect
9. D₃×C₉×C₄⋊C₄	C₂	semidirect
10. C₉×#889	C₂	semidirect
11. C₉×#889	C₂	semidirect
13. C₉×#883	C₂	semidirect
14. C₉×#883	C₂	semidirect
15. C₉×#879	C₂	semidirect
79. C₉×C₂²⋊Q₈	D₃	semidirect
109. #5638	C₉	direct (N × H)
220. C₃×C₂²⋊Q₈	C₂×C₉	semidirect
226. #946	C₂×C₉	semidirect
227. #946	C₂×C₉	semidirect
228. #929	C₂×C₉	semidirect
229. C₄×#67	C₂×C₉	semidirect
230. #898	C₂×C₉	semidirect
231. #894	C₂×C₉	semidirect
232. #893	C₂×C₉	semidirect
233. D₃×C₄⋊C₄	C₂×C₉	semidirect
234. #889	C₂×C₉	semidirect
235. #889	C₂×C₉	semidirect
237. #883	C₂×C₉	semidirect
238. #883	C₂×C₉	semidirect
239. #879	C₂×C₉	semidirect
445. C₂²⋊Q₈	D₃×C₉	semidirect
450. C₃×C₉	#539	semidirect
615. C₉	#5638	direct (N × H)
679. C₃	C₉×#539	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×C₂²⋊Q₈	2
C₉×#946	2
C₉×#929	2
C₄×C₉×#67	2
C₉×#898	2
C₉×#894	2
C₉×#893	2
D₃×C₉×C₄⋊C₄	2
C₉×#889	2
C₉×#884	2
C₉×#883	2
C₉×#879	2
C₃×#5638	3
C₉×#539	3

Subgroups — C9×#5638 #13152935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5638 #13152935