Subgroups — C₉×#5636 #13152932

Order 1728.

758 conjugacy classes of subgroups.

The subgroup lattice has 676 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×#944	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₉×#67	C₂	1	1	yes	maximal, characteristic
5	C₂×C₉×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#896	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#896	C₂	1	1	yes	maximal, characteristic, complemented
8	D₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#889	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#889	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#887	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#67⋊C₄	C₂	1	1	yes	maximal, characteristic
13	C₉×#67⋊C₄	C₂	1	1	yes	maximal, characteristic
14	C₉×#878	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#878	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5636	C₃	1	1	yes	maximal, characteristic
17	C₉×#554	—	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	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
22	C₂²×C₉×Dic₃	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×C₉×Dic₆	C₂²	1	1	yes	characteristic
27	C₂×C₉×Dic₆	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×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×C₉×C₂²⋊C₄	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×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
38	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
39	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
40	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
41	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
42	C₉×Dic₃⋊C₄	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	C₄×C₉×Dic₃	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×#944	C₂×C₃	1	1	yes	characteristic
56	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
57	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic
58	C₃×#896	C₂×C₃	1	1	yes	characteristic
59	C₃×#896	C₂×C₃	1	1	yes	characteristic
60	C₃×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
61	C₃×#889	C₂×C₃	1	1	yes	characteristic
62	C₃×#889	C₂×C₃	1	1	yes	characteristic
63	C₃×#887	C₂×C₃	1	1	yes	characteristic
64	C₃×#67⋊C₄	C₂×C₃	1	1	yes	characteristic
65	C₃×#67⋊C₄	C₂×C₃	1	1	yes	characteristic
66	C₃×#878	C₂×C₃	1	1	yes	characteristic
67	C₃×#878	C₂×C₃	1	1	yes	characteristic
68	C₉×C₄⋊Q₈	—	3	1	no	—
69	C₉×#125	—	3	1	no	—
70	C₉×#125	—	3	1	no	—
71	C₉×C₂²⋊Q₈	—	2	1	no	—
72	C₉×C₂²⋊Q₈	—	3	1	no	—
73	C₉×C₂²⋊Q₈	—	3	1	no	—
74	C₉×C₂²⋊Q₈	—	3	1	no	—
75	C₉×C₂²⋊Q₈	—	3	1	no	—
76	C₉×C₂²⋊Q₈	—	3	1	no	—
77	C₉×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
78	C₄×Q₈×C₉	—	3	1	no	—
79	C₄×D₄×C₉	—	3	1	no	—
80	C₄×D₄×C₉	—	3	1	no	—
81	C₄×D₄×C₉	—	3	1	no	—
82	C₂×C₉×C₄⋊C₄	—	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	C₃×Q₈×C₉	—	4	1	no	—
87	C₂×C₃×C₄×C₉	—	4	1	no	—
88	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
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	C₉×#67	Q₈	1	4	yes	complemented
95	C₂×C₉×Dic₃	—	2	2	no	—
96	C₂×C₉×Dic₃	—	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	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
104	C₄×D₃×C₉	—	2	2	no	—
105	C₄×D₃×C₉	—	4	1	no	—
106	C₄×D₃×C₉	—	4	1	no	—
107	C₉×Dic₆	—	2	2	no	—
108	C₉×Dic₆	—	4	1	no	—
109	C₃×#554	—	3	1	no	—
110	#5636	C₉	1	1	yes	characteristic, direct product factor
111	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
112	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
114	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
115	C₂²×C₃×Dic₃	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	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
121	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	C₃×#217	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×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
131	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
132	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₃×Dic₃⋊C₄	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	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
146	C₂×Q₈×C₉	—	2	1	no	—
147	C₂×Q₈×C₉	—	3	1	no	—
148	C₂×Q₈×C₉	—	3	1	no	—
149	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
150	C₂×D₄×C₉	—	3	1	no	—
151	C₂²×C₄×C₉	—	2	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	—	3	1	no	—
156	C₂²×C₄×C₉	—	3	1	no	—
157	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
158	C₉×C₄⋊C₄	—	2	1	no	—
159	C₉×C₄⋊C₄	—	2	1	no	—
160	C₉×C₄⋊C₄	—	2	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	—	3	1	no	—
171	C₉×C₄⋊C₄	—	3	1	no	—
172	C₉×C₄⋊C₄	—	3	1	no	—
173	C₉×C₄⋊C₄	—	3	1	no	—
174	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
175	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
176	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
177	C₉×C₂²⋊C₄	—	2	1	no	—
178	C₉×C₂²⋊C₄	—	2	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	C₄²×C₉	—	3	1	no	—
188	C₂²×C₃×C₉	—	2	1	no	—
189	C₂²×C₃×C₉	—	2	1	no	—
190	C₂²×C₃×C₉	C₂×Q₈	1	2	yes	—
191	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
192	C₂×D₃×C₉	—	2	1	no	—
193	C₂×D₃×C₉	—	2	1	no	—
194	C₂×D₃×C₉	C₂×Q₈	1	2	yes	—
195	C₃×C₄×C₉	—	2	1	no	—
196	C₃×C₄×C₉	—	2	1	no	—
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	C₉×Dic₃	—	2	1	no	—
202	C₉×Dic₃	—	2	1	no	—
203	C₉×Dic₃	—	2	1	no	—
204	C₉×Dic₃	—	2	1	no	—
205	C₉×Dic₃	—	2	1	no	—
206	C₉×Dic₃	C₂×Q₈	1	2	yes	—
207	C₉×Dic₃	#41	1	2	yes	—
208	C₃×C₄⋊Q₈	—	3	1	no	—
209	C₃×#125	—	3	1	no	—
210	C₃×#125	—	3	1	no	—
211	C₃×C₂²⋊Q₈	—	2	1	no	—
212	C₃×C₂²⋊Q₈	—	3	1	no	—
213	C₃×C₂²⋊Q₈	—	3	1	no	—
214	C₃×C₂²⋊Q₈	—	3	1	no	—
215	C₃×C₂²⋊Q₈	—	3	1	no	—
216	C₃×C₂²⋊Q₈	—	3	1	no	—
217	C₃×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
218	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
219	C₃×C₄×Q₈	—	3	1	no	—
220	C₃×C₄×D₄	—	3	1	no	—
221	C₃×C₄×D₄	—	3	1	no	—
222	C₃×C₄×D₄	—	3	1	no	—
223	C₂×C₃×C₄⋊C₄	—	3	1	no	—
224	C₂×C₃×C₄⋊C₄	—	3	1	no	—
225	#946	C₂×C₉	1	1	yes	characteristic, complemented
226	#944	C₂×C₉	1	1	yes	characteristic, complemented
227	C₄×#67	C₂×C₉	1	1	yes	characteristic
228	C₂×Dic₃⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
229	#896	C₂×C₉	1	1	yes	characteristic, complemented
230	#896	C₂×C₉	1	1	yes	characteristic, complemented
231	D₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
232	#889	C₂×C₉	1	1	yes	characteristic, complemented
233	#889	C₂×C₉	1	1	yes	characteristic, complemented
234	#887	C₂×C₉	1	1	yes	characteristic, complemented
235	#67⋊C₄	C₂×C₉	1	1	yes	characteristic
236	#67⋊C₄	C₂×C₉	1	1	yes	characteristic
237	#878	C₂×C₉	1	1	yes	characteristic, complemented
238	#878	C₂×C₉	1	1	yes	characteristic, complemented
239	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
240	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
241	C₃²×Q₈	—	4	1	no	—
242	C₂×C₃²×C₄	—	4	1	no	—
243	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
244	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
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	C₃×#67	C₃×Q₈	1	4	yes	—
250	C₂×C₃×Dic₃	—	2	2	no	—
251	C₂×C₃×Dic₃	—	4	1	no	—
252	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
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×C₄×D₃	—	2	2	no	—
260	C₃×C₄×D₃	—	4	1	no	—
261	C₃×C₄×D₃	—	4	1	no	—
262	C₃×Dic₆	—	2	2	no	—
263	C₃×Dic₆	—	4	1	no	—
264	C₂³×C₉	—	2	1	no	—
265	C₂³×C₉	—	3	1	no	—
266	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
267	Q₈×C₉	—	4	1	no	—
268	Q₈×C₉	—	4	2	no	—
269	Q₈×C₉	—	6	2	no	—
270	Q₈×C₉	—	12	1	no	—
271	D₄×C₉	—	3	4	no	—
272	C₂×C₄×C₉	—	2	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	—	3	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	—	6	2	no	—
289	C₂×C₄×C₉	—	12	1	no	—
290	C₂×C₄×C₉	—	12	1	no	—
291	C₂×C₄×C₉	—	12	1	no	—
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	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
298	#554	—	3	1	no	Sylow
299	C₂×C₃×C₉	—	2	2	no	—
300	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
301	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
302	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
303	D₃×C₉	—	2	2	no	—
304	C₂×C₃×Q₈	—	2	1	no	—
305	C₂×C₃×Q₈	—	3	1	no	—
306	C₂×C₃×Q₈	—	3	1	no	—
307	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
308	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
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	—	3	1	no	—
316	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
317	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
318	C₂×#67	C₂²×C₉	1	1	yes	characteristic
319	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
320	C₂²×Dic₃	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	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
325	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
326	C₃×C₄⋊C₄	—	2	1	no	—
327	C₃×C₄⋊C₄	—	2	1	no	—
328	C₃×C₄⋊C₄	—	2	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	—	3	1	no	—
339	C₃×C₄⋊C₄	—	3	1	no	—
340	C₃×C₄⋊C₄	—	3	1	no	—
341	C₃×C₄⋊C₄	—	3	1	no	—
342	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
343	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
344	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
345	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
346	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
347	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
348	C₃×C₂²⋊C₄	—	2	1	no	—
349	C₃×C₂²⋊C₄	—	2	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	C₃×C₄²	—	3	1	no	—
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	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
366	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
367	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
368	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
369	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
370	Dic₃⋊C₄	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	C₄×Dic₃	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	C₂×C₃×Q₈	1	2	yes	—
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	C₂×C₃×Q₈	1	2	yes	—
388	C₃²×C₄	—	2	1	no	—
389	C₃²×C₄	—	2	1	no	—
390	C₃²×C₄	—	2	1	no	—
391	C₃²×C₄	—	2	1	no	—
392	C₃²×C₄	—	2	1	no	—
393	C₃²×C₄	—	2	1	no	—
394	C₃×Dic₃	—	2	1	no	—
395	C₃×Dic₃	—	2	1	no	—
396	C₃×Dic₃	—	2	1	no	—
397	C₃×Dic₃	—	2	1	no	—
398	C₃×Dic₃	—	2	1	no	—
399	C₃×Dic₃	C₂×C₃×Q₈	1	2	yes	—
400	C₃×Dic₃	C₃×#41	1	2	yes	—
401	C₂²×C₉	—	2	1	no	—
402	C₂²×C₉	—	2	1	no	—
403	C₂²×C₉	—	2	1	no	—
404	C₂²×C₉	—	2	2	no	—
405	C₂²×C₉	—	3	2	no	—
406	C₂²×C₉	—	4	1	no	—
407	C₂²×C₉	—	4	1	no	—
408	C₂²×C₉	—	6	1	no	—
409	C₂²×C₉	—	6	1	no	—
410	C₂²×C₉	D₃×Q₈	1	2	yes	—
411	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
412	C₄×C₉	—	2	2	no	—
413	C₄×C₉	—	2	1	no	—
414	C₄×C₉	—	2	1	no	—
415	C₄×C₉	—	2	1	no	—
416	C₄×C₉	—	2	1	no	—
417	C₄×C₉	—	2	1	no	—
418	C₄×C₉	—	2	1	no	—
419	C₄×C₉	—	3	2	no	—
420	C₄×C₉	—	3	2	no	—
421	C₄×C₉	—	4	1	no	—
422	C₄×C₉	—	4	1	no	—
423	C₄×C₉	—	4	1	no	—
424	C₄×C₉	—	4	1	no	—
425	C₄×C₉	—	4	1	no	—
426	C₄×C₉	—	6	1	no	—
427	C₄×C₉	—	6	1	no	—
428	C₄×C₉	—	6	1	no	—
429	C₄×C₉	—	6	1	no	—
430	C₄×C₉	—	6	1	no	—
431	C₄⋊Q₈	—	3	1	no	—
432	#125	—	3	1	no	—
433	#125	—	3	1	no	—
434	C₂²⋊Q₈	—	3	1	no	—
435	C₂²⋊Q₈	—	3	1	no	—
436	C₂²⋊Q₈	—	3	1	no	—
437	C₂²⋊Q₈	—	3	1	no	—
438	C₂²⋊Q₈	—	3	1	no	—
439	C₂²⋊Q₈	D₃×C₉	1	1	yes	characteristic, complemented
440	C₄×Q₈	—	3	1	no	—
441	C₄×D₄	—	3	1	no	—
442	C₄×D₄	—	3	1	no	—
443	C₄×D₄	—	3	1	no	—
444	C₂×C₄⋊C₄	—	3	1	no	—
445	C₂×C₄⋊C₄	—	3	1	no	—
446	C₃×C₉	#554	1	1	yes	characteristic, complemented, Sylow
447	C₂³×C₃	—	2	1	no	—
448	C₂³×C₃	—	3	1	no	—
449	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
450	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
451	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
452	C₃×Q₈	—	4	1	no	—
453	C₃×Q₈	—	4	1	no	—
454	C₃×Q₈	—	4	2	no	—
455	C₃×Q₈	—	6	2	no	—
456	C₃×Q₈	—	12	1	no	—
457	C₃×D₄	—	3	4	no	—
458	C₂×C₃×C₄	—	2	1	no	—
459	C₂×C₃×C₄	—	2	1	no	—
460	C₂×C₃×C₄	—	2	1	no	—
461	C₂×C₃×C₄	—	2	1	no	—
462	C₂×C₃×C₄	—	2	1	no	—
463	C₂×C₃×C₄	—	2	1	no	—
464	C₂×C₃×C₄	—	3	1	no	—
465	C₂×C₃×C₄	—	3	1	no	—
466	C₂×C₃×C₄	—	3	1	no	—
467	C₂×C₃×C₄	—	3	1	no	—
468	C₂×C₃×C₄	—	3	1	no	—
469	C₂×C₃×C₄	—	3	1	no	—
470	C₂×C₃×C₄	—	3	1	no	—
471	C₂×C₃×C₄	—	4	1	no	—
472	C₂×C₃×C₄	—	4	1	no	—
473	C₂×C₃×C₄	—	4	2	no	—
474	C₂×C₃×C₄	—	6	2	no	—
475	C₂×C₃×C₄	—	6	2	no	—
476	C₂×C₃×C₄	—	12	1	no	—
477	C₂×C₃×C₄	—	12	1	no	—
478	C₂×C₃×C₄	—	12	1	no	—
479	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
480	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
481	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
482	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
483	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
484	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
485	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
486	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
487	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
488	C₂×C₃×C₄	C₂²×C₃×D₃	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	#67	Q₈×C₉	1	4	yes	complemented
492	C₂×Dic₃	—	2	2	no	—
493	C₂×Dic₃	—	4	1	no	—
494	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
495	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
496	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
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	C₄×D₃	—	2	2	no	—
502	C₄×D₃	—	4	1	no	—
503	C₄×D₃	—	4	1	no	—
504	Dic₆	—	2	2	no	—
505	Dic₆	—	4	1	no	—
506	C₂×C₃²	—	2	2	no	—
507	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
508	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
509	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
510	C₃×D₃	—	2	2	no	—
511	C₂×C₉	—	2	2	no	—
512	C₂×C₉	—	2	1	no	—
513	C₂×C₉	—	2	1	no	—
514	C₂×C₉	—	2	1	no	—
515	C₂×C₉	—	4	2	no	—
516	C₂×C₉	—	6	2	no	—
517	C₂×C₉	#1004	1	1	yes	characteristic
518	C₂×C₉	C₂×D₃×Q₈	1	1	yes	characteristic
519	C₂×C₉	D₃×#41	1	1	yes	characteristic
520	C₂×Q₈	—	3	1	no	—
521	C₂×Q₈	—	3	1	no	—
522	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
523	C₂×D₄	—	3	1	no	—
524	C₂²×C₄	—	3	1	no	—
525	C₂²×C₄	—	3	1	no	—
526	C₂²×C₄	—	3	1	no	—
527	C₂²×C₄	—	3	1	no	—
528	C₂²×C₄	—	3	1	no	—
529	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
530	C₄⋊C₄	—	3	1	no	—
531	C₄⋊C₄	—	3	1	no	—
532	C₄⋊C₄	—	3	1	no	—
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	C₂×D₃×C₉	1	1	yes	characteristic
544	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
545	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
546	C₂²⋊C₄	—	3	1	no	—
547	C₂²⋊C₄	—	3	1	no	—
548	C₂²⋊C₄	—	3	1	no	—
549	C₂²⋊C₄	—	3	1	no	—
550	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
551	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
552	C₄²	—	3	1	no	—
553	C₄²	—	3	1	no	—
554	C₄²	—	3	1	no	—
555	C₂²×C₃	—	2	1	no	—
556	C₂²×C₃	—	2	1	no	—
557	C₂²×C₃	—	2	1	no	—
558	C₂²×C₃	—	2	1	no	—
559	C₂²×C₃	—	2	1	no	—
560	C₂²×C₃	—	2	2	no	—
561	C₂²×C₃	—	3	2	no	—
562	C₂²×C₃	—	4	1	no	—
563	C₂²×C₃	—	4	1	no	—
564	C₂²×C₃	—	6	1	no	—
565	C₂²×C₃	—	6	1	no	—
566	C₂²×C₃	C₂×Q₈×C₉	1	2	yes	—
567	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
568	C₂²×C₃	C₃×D₃×Q₈	1	2	yes	—
569	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
570	C₂×D₃	—	2	1	no	—
571	C₂×D₃	—	2	1	no	—
572	C₂×D₃	C₂×Q₈×C₉	1	2	yes	—
573	C₃×C₄	—	2	2	no	—
574	C₃×C₄	—	2	1	no	—
575	C₃×C₄	—	2	1	no	—
576	C₃×C₄	—	2	1	no	—
577	C₃×C₄	—	2	1	no	—
578	C₃×C₄	—	2	1	no	—
579	C₃×C₄	—	2	1	no	—
580	C₃×C₄	—	2	1	no	—
581	C₃×C₄	—	2	1	no	—
582	C₃×C₄	—	2	1	no	—
583	C₃×C₄	—	2	1	no	—
584	C₃×C₄	—	2	1	no	—
585	C₃×C₄	—	2	1	no	—
586	C₃×C₄	—	3	2	no	—
587	C₃×C₄	—	3	2	no	—
588	C₃×C₄	—	4	1	no	—
589	C₃×C₄	—	4	1	no	—
590	C₃×C₄	—	4	1	no	—
591	C₃×C₄	—	4	1	no	—
592	C₃×C₄	—	4	1	no	—
593	C₃×C₄	—	6	1	no	—
594	C₃×C₄	—	6	1	no	—
595	C₃×C₄	—	6	1	no	—
596	C₃×C₄	—	6	1	no	—
597	C₃×C₄	—	6	1	no	—
598	Dic₃	—	2	1	no	—
599	Dic₃	—	2	1	no	—
600	Dic₃	—	2	1	no	—
601	Dic₃	—	2	1	no	—
602	Dic₃	—	2	1	no	—
603	Dic₃	C₂×Q₈×C₉	1	2	yes	—
604	Dic₃	C₉×#41	1	2	yes	—
605	C₃²	C₃×#554	1	1	yes	characteristic
606	C₉	—	2	1	no	—
607	C₉	#5636	1	1	yes	characteristic, direct product factor
608	C₂³	—	3	1	no	—
609	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
610	Q₈	—	4	1	no	—
611	Q₈	—	6	2	no	—
612	Q₈	—	12	1	no	—
613	D₄	—	3	4	no	—
614	C₂×C₄	—	3	1	no	—
615	C₂×C₄	—	3	1	no	—
616	C₂×C₄	—	3	1	no	—
617	C₂×C₄	—	3	1	no	—
618	C₂×C₄	—	3	1	no	—
619	C₂×C₄	—	3	1	no	—
620	C₂×C₄	—	3	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	6	2	no	—
623	C₂×C₄	—	6	2	no	—
624	C₂×C₄	—	12	1	no	—
625	C₂×C₄	—	12	1	no	—
626	C₂×C₄	—	12	1	no	—
627	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
628	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
629	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
630	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
631	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
632	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
633	C₂×C₃	—	2	2	no	—
634	C₂×C₃	—	2	2	no	—
635	C₂×C₃	—	2	1	no	—
636	C₂×C₃	—	2	1	no	—
637	C₂×C₃	—	2	1	no	—
638	C₂×C₃	—	4	2	no	—
639	C₂×C₃	—	6	2	no	—
640	C₂×C₃	C₂²×Q₈×C₉	1	1	yes	characteristic
641	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
642	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
643	C₂×C₃	C₃×#1004	1	1	yes	characteristic
644	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
645	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
646	D₃	—	2	2	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	3	2	no	—
650	C₂²	—	6	1	no	—
651	C₂²	—	6	1	no	—
652	C₂²	D₃×Q₈×C₉	1	2	yes	—
653	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	3	2	no	—
661	C₄	—	3	2	no	—
662	C₄	—	6	1	no	—
663	C₄	—	6	1	no	—
664	C₄	—	6	1	no	—
665	C₄	—	6	1	no	—
666	C₄	—	6	1	no	—
667	C₃	—	2	1	no	—
668	C₃	C₉×#554	1	1	yes	characteristic, complemented
669	C₃	C₃×#5636	1	1	yes	characteristic
670	C₂	—	2	2	no	—
671	C₂	—	6	2	no	—
672	C₂	C₉×#1004	1	1	yes	characteristic
673	C₂	C₂×D₃×Q₈×C₉	1	1	yes	characteristic
674	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	C₂×C₃×#67	C₂²×C₃
hypercenter	C₉×C₂²⋊Q₈	D₃
hypocenter	C₃	C₉×#554
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×#944	C₂	semidirect
5. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
6. C₉×#896	C₂	semidirect
7. C₉×#896	C₂	semidirect
8. D₃×C₉×C₄⋊C₄	C₂	semidirect
9. C₉×#889	C₂	semidirect
10. C₉×#889	C₂	semidirect
11. C₉×#887	C₂	semidirect
14. C₉×#878	C₂	semidirect
15. C₉×#878	C₂	semidirect
77. C₉×C₂²⋊Q₈	D₃	semidirect
94. C₉×#67	Q₈	semidirect
110. #5636	C₉	direct (N × H)
217. C₃×C₂²⋊Q₈	C₂×C₉	semidirect
225. #946	C₂×C₉	semidirect
226. #944	C₂×C₉	semidirect
228. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
229. #896	C₂×C₉	semidirect
230. #896	C₂×C₉	semidirect
231. D₃×C₄⋊C₄	C₂×C₉	semidirect
232. #889	C₂×C₉	semidirect
233. #889	C₂×C₉	semidirect
234. #887	C₂×C₉	semidirect
237. #878	C₂×C₉	semidirect
238. #878	C₂×C₉	semidirect
439. C₂²⋊Q₈	D₃×C₉	semidirect
446. C₃×C₉	#554	semidirect
491. #67	Q₈×C₉	semidirect
607. C₉	#5636	direct (N × H)
668. 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×C₂²⋊Q₈	2
C₉×#946	2
C₉×#944	2
C₄×C₉×#67	2
C₂×C₉×Dic₃⋊C₄	2
C₉×#896	2
D₃×C₉×C₄⋊C₄	2
C₉×#889	2
C₉×#887	2
C₉×#67⋊C₄	2
C₉×#878	2
C₃×#5636	3
C₉×#554	3

Subgroups — C9×#5636 #13152932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5636 #13152932