Subgroups — C₉×#5578 #13152699

Order 1728.

736 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#946	C₂	1	1	yes	maximal, characteristic
3	C₉×#944	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#897	C₂	1	1	yes	maximal, characteristic
5	C₉×#896	C₂	1	2	yes	maximal
6	C₉×#889	C₂	1	2	yes	maximal, complemented
7	C₉×#888	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#872	C₂	1	2	yes	maximal
9	C₄²×D₃×C₉	C₂	1	1	yes	maximal, characteristic
10	C₄×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₉×Dic₆	C₂	1	2	yes	maximal, complemented
12	C₃×#5578	C₃	1	1	yes	maximal, characteristic
13	C₉×#533	—	3	1	no	maximal
14	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
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	2	yes	—
22	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
23	C₃×C₄²×C₉	C₂²	1	2	yes	—
24	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
25	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
26	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
27	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
28	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
29	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
30	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
35	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
36	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
37	C₃²×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
38	C₃×#946	C₂×C₃	1	1	yes	characteristic
39	C₃×#944	C₂×C₃	1	1	yes	characteristic
40	C₃×#897	C₂×C₃	1	1	yes	characteristic
41	C₃×#896	C₂×C₃	1	2	yes	—
42	C₃×#889	C₂×C₃	1	2	yes	—
43	C₃×#888	C₂×C₃	1	1	yes	characteristic
44	C₃×#872	C₂×C₃	1	2	yes	—
45	C₃×C₄²×D₃	C₂×C₃	1	1	yes	characteristic
46	C₃×C₄×Dic₆	C₂×C₃	1	2	yes	—
47	C₃×C₄×Dic₆	C₂×C₃	1	1	yes	characteristic
48	C₉×C₄⋊Q₈	—	3	1	no	—
49	C₉×C₄⋊Q₈	—	3	1	no	—
50	C₉×#125	—	3	2	no	—
51	C₉×C₂²⋊Q₈	—	3	1	no	—
52	C₉×C₂²⋊Q₈	—	3	2	no	—
53	C₉×C₂²⋊Q₈	—	3	1	no	—
54	C₄×Q₈×C₉	—	2	1	no	—
55	C₄×Q₈×C₉	—	3	2	no	—
56	C₄×Q₈×C₉	—	3	1	no	—
57	C₄×Q₈×C₉	D₃	1	1	yes	characteristic, complemented
58	C₉×#117	—	3	2	no	—
59	C₂×C₄²×C₉	—	3	1	no	—
60	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
61	C₃×Q₈×C₉	—	2	2	no	—
62	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
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×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₉×Dic₃	C₂³	1	2	yes	—
68	C₂×C₉×Dic₃	C₂³	1	2	yes	—
69	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
72	C₄×D₃×C₉	—	2	2	no	—
73	C₄×D₃×C₉	—	2	2	no	—
74	C₄×D₃×C₉	Q₈	1	4	yes	complemented
75	C₉×Dic₆	—	2	2	no	—
76	C₉×Dic₆	—	2	4	no	—
77	C₃×#533	—	3	1	no	—
78	#5578	C₉	1	1	yes	characteristic, direct product factor
79	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
84	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
85	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
87	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
88	C₃²×C₄²	C₂²×C₃	1	2	yes	—
89	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
90	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
91	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
92	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
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	2	yes	—
97	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
98	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
99	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
100	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
101	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
102	C₂×Q₈×C₉	—	2	1	no	—
103	C₂×Q₈×C₉	—	3	2	no	—
104	C₂×Q₈×C₉	—	3	1	no	—
105	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
106	C₂²×C₄×C₉	—	3	1	no	—
107	C₂²×C₄×C₉	—	3	1	no	—
108	C₂²×C₄×C₉	—	3	1	no	—
109	C₉×C₄⋊C₄	—	2	2	no	—
110	C₉×C₄⋊C₄	—	2	1	no	—
111	C₉×C₄⋊C₄	—	3	2	no	—
112	C₉×C₄⋊C₄	—	3	2	no	—
113	C₉×C₄⋊C₄	—	3	2	no	—
114	C₉×C₄⋊C₄	—	3	2	no	—
115	C₉×C₄⋊C₄	—	3	2	no	—
116	C₉×C₄⋊C₄	—	3	2	no	—
117	C₉×C₄⋊C₄	—	3	1	no	—
118	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
119	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
120	C₉×C₂²⋊C₄	—	3	2	no	—
121	C₉×C₂²⋊C₄	—	3	2	no	—
122	C₄²×C₉	—	2	1	no	—
123	C₄²×C₉	—	2	2	no	—
124	C₄²×C₉	—	3	1	no	—
125	C₄²×C₉	—	3	1	no	—
126	C₄²×C₉	—	3	1	no	—
127	C₄²×C₉	—	3	2	no	—
128	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
129	C₄²×C₉	C₂×D₃	1	2	yes	—
130	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
131	C₂×D₃×C₉	—	2	1	no	—
132	C₂×D₃×C₉	—	2	1	no	—
133	C₂×D₃×C₉	C₂×Q₈	1	2	yes	—
134	C₃×C₄×C₉	—	2	2	no	—
135	C₃×C₄×C₉	—	2	2	no	—
136	C₃×C₄×C₉	—	2	1	no	—
137	C₃×C₄×C₉	C₂×Q₈	1	2	yes	—
138	C₃×C₄×C₉	#41	1	2	yes	—
139	C₉×Dic₃	—	2	2	no	—
140	C₉×Dic₃	—	2	2	no	—
141	C₉×Dic₃	—	2	1	no	—
142	C₉×Dic₃	C₂×Q₈	1	2	yes	—
143	C₉×Dic₃	#41	1	2	yes	—
144	C₃×C₄⋊Q₈	—	3	1	no	—
145	C₃×C₄⋊Q₈	—	3	1	no	—
146	C₃×#125	—	3	2	no	—
147	C₃×C₂²⋊Q₈	—	3	1	no	—
148	C₃×C₂²⋊Q₈	—	3	2	no	—
149	C₃×C₂²⋊Q₈	—	3	1	no	—
150	C₃×C₄×Q₈	—	2	1	no	—
151	C₃×C₄×Q₈	—	3	2	no	—
152	C₃×C₄×Q₈	—	3	1	no	—
153	C₃×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
154	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
155	C₃×#117	—	3	2	no	—
156	C₂×C₃×C₄²	—	3	1	no	—
157	#946	C₂×C₉	1	1	yes	characteristic
158	#944	C₂×C₉	1	1	yes	characteristic, complemented
159	#897	C₂×C₉	1	1	yes	characteristic
160	#896	C₂×C₉	1	2	yes	—
161	#889	C₂×C₉	1	2	yes	complemented
162	#888	C₂×C₉	1	1	yes	characteristic, complemented
163	#872	C₂×C₉	1	2	yes	—
164	C₄²×D₃	C₂×C₉	1	1	yes	characteristic
165	C₄×Dic₆	C₂×C₉	1	2	yes	complemented
166	C₄×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
167	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
168	C₃²×Q₈	—	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	2	yes	—
172	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
173	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
177	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
178	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
179	C₃×C₄×D₃	—	2	2	no	—
180	C₃×C₄×D₃	—	2	2	no	—
181	C₃×C₄×D₃	C₃×Q₈	1	4	yes	—
182	C₃×Dic₆	—	2	2	no	—
183	C₃×Dic₆	—	2	4	no	—
184	C₂³×C₉	—	3	1	no	—
185	Q₈×C₉	—	2	4	no	—
186	Q₈×C₉	—	2	2	no	—
187	Q₈×C₉	—	6	4	no	—
188	Q₈×C₉	—	6	2	no	—
189	C₂×C₄×C₉	—	2	1	no	—
190	C₂×C₄×C₉	—	2	2	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	4	no	—
197	C₂×C₄×C₉	—	3	1	no	—
198	C₂×C₄×C₉	—	3	2	no	—
199	C₂×C₄×C₉	—	3	2	no	—
200	C₂×C₄×C₉	—	6	2	no	—
201	C₂×C₄×C₉	—	6	2	no	—
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	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
207	#533	—	3	1	no	Sylow
208	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
209	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
210	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
211	D₃×C₉	—	2	2	no	—
212	C₂×C₃×Q₈	—	2	1	no	—
213	C₂×C₃×Q₈	—	3	2	no	—
214	C₂×C₃×Q₈	—	3	1	no	—
215	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
216	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
217	C₂²×C₃×C₄	—	3	1	no	—
218	C₂²×C₃×C₄	—	3	1	no	—
219	C₂²×C₃×C₄	—	3	1	no	—
220	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
221	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
222	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
223	C₂×Dic₆	C₂²×C₉	1	2	yes	—
224	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
225	C₃×C₄⋊C₄	—	2	2	no	—
226	C₃×C₄⋊C₄	—	2	1	no	—
227	C₃×C₄⋊C₄	—	3	2	no	—
228	C₃×C₄⋊C₄	—	3	2	no	—
229	C₃×C₄⋊C₄	—	3	2	no	—
230	C₃×C₄⋊C₄	—	3	2	no	—
231	C₃×C₄⋊C₄	—	3	2	no	—
232	C₃×C₄⋊C₄	—	3	2	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	2	yes	—
236	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
237	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
238	C₃×C₂²⋊C₄	—	3	2	no	—
239	C₃×C₂²⋊C₄	—	3	2	no	—
240	C₃×C₄²	—	2	1	no	—
241	C₃×C₄²	—	2	2	no	—
242	C₃×C₄²	—	3	1	no	—
243	C₃×C₄²	—	3	1	no	—
244	C₃×C₄²	—	3	1	no	—
245	C₃×C₄²	—	3	2	no	—
246	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
247	C₃×C₄²	C₂²×C₉	1	2	yes	—
248	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
249	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
250	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
251	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
252	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
253	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
254	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
255	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
256	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
257	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
258	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
259	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
260	C₄×Dic₃	C₂²×C₉	1	2	yes	—
261	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
262	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
263	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
264	C₂×C₃×D₃	—	2	1	no	—
265	C₂×C₃×D₃	—	2	1	no	—
266	C₂×C₃×D₃	C₂×C₃×Q₈	1	2	yes	—
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	C₃²×C₄	C₃×#41	1	2	yes	—
272	C₃×Dic₃	—	2	2	no	—
273	C₃×Dic₃	—	2	2	no	—
274	C₃×Dic₃	—	2	1	no	—
275	C₃×Dic₃	C₂×C₃×Q₈	1	2	yes	—
276	C₃×Dic₃	C₃×#41	1	2	yes	—
277	C₂²×C₉	—	2	1	no	—
278	C₂²×C₉	—	3	2	no	—
279	C₂²×C₉	—	6	1	no	—
280	C₂²×C₉	—	6	1	no	—
281	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
282	C₄×C₉	—	2	4	no	—
283	C₄×C₉	—	2	2	no	—
284	C₄×C₉	—	2	1	no	—
285	C₄×C₉	—	2	2	no	—
286	C₄×C₉	—	2	2	no	—
287	C₄×C₉	—	2	2	no	—
288	C₄×C₉	—	3	2	no	—
289	C₄×C₉	—	3	2	no	—
290	C₄×C₉	—	4	1	no	—
291	C₄×C₉	—	4	2	no	—
292	C₄×C₉	—	6	1	no	—
293	C₄×C₉	—	6	2	no	—
294	C₄×C₉	—	6	2	no	—
295	C₄×C₉	#235	1	2	yes	—
296	C₄×C₉	D₃×Q₈	1	2	yes	—
297	C₄⋊Q₈	—	3	1	no	—
298	C₄⋊Q₈	—	3	1	no	—
299	#125	—	3	2	no	—
300	C₂²⋊Q₈	—	3	1	no	—
301	C₂²⋊Q₈	—	3	2	no	—
302	C₂²⋊Q₈	—	3	1	no	—
303	C₄×Q₈	—	3	2	no	—
304	C₄×Q₈	—	3	1	no	—
305	C₄×Q₈	D₃×C₉	1	1	yes	characteristic, complemented
306	#117	—	3	2	no	—
307	C₂×C₄²	—	3	1	no	—
308	C₃×C₉	#533	1	1	yes	characteristic, complemented, Sylow
309	C₂³×C₃	—	3	1	no	—
310	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
311	C₃×Q₈	—	2	4	no	—
312	C₃×Q₈	—	2	2	no	—
313	C₃×Q₈	—	2	2	no	—
314	C₃×Q₈	—	6	4	no	—
315	C₃×Q₈	—	6	2	no	—
316	C₂×C₃×C₄	—	2	1	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	1	no	—
319	C₂×C₃×C₄	—	2	1	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	3	1	no	—
322	C₂×C₃×C₄	—	3	1	no	—
323	C₂×C₃×C₄	—	3	4	no	—
324	C₂×C₃×C₄	—	3	1	no	—
325	C₂×C₃×C₄	—	3	2	no	—
326	C₂×C₃×C₄	—	3	2	no	—
327	C₂×C₃×C₄	—	6	2	no	—
328	C₂×C₃×C₄	—	6	2	no	—
329	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
331	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
332	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
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	C₂³×C₉	1	1	yes	characteristic
340	C₂×Dic₃	C₂³×C₉	1	2	yes	—
341	C₂×Dic₃	C₂³×C₉	1	2	yes	—
342	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
343	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
344	C₄×D₃	—	2	2	no	—
345	C₄×D₃	—	2	2	no	—
346	C₄×D₃	Q₈×C₉	1	4	yes	complemented
347	Dic₆	—	2	2	no	—
348	Dic₆	—	2	4	no	—
349	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
350	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
351	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
352	C₃×D₃	—	2	2	no	—
353	C₂×C₉	—	2	1	no	—
354	C₂×C₉	—	2	1	no	—
355	C₂×C₉	—	2	1	no	—
356	C₂×C₉	—	6	2	no	—
357	C₂×C₉	C₂×#235	1	1	yes	characteristic
358	C₂×C₉	C₂×D₃×Q₈	1	1	yes	characteristic
359	C₂×C₉	D₃×#41	1	1	yes	characteristic
360	C₂×Q₈	—	3	2	no	—
361	C₂×Q₈	—	3	1	no	—
362	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
363	C₂²×C₄	—	3	1	no	—
364	C₂²×C₄	—	3	1	no	—
365	C₂²×C₄	—	3	1	no	—
366	C₄⋊C₄	—	3	2	no	—
367	C₄⋊C₄	—	3	2	no	—
368	C₄⋊C₄	—	3	2	no	—
369	C₄⋊C₄	—	3	2	no	—
370	C₄⋊C₄	—	3	2	no	—
371	C₄⋊C₄	—	3	2	no	—
372	C₄⋊C₄	—	3	1	no	—
373	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
374	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
375	C₂²⋊C₄	—	3	2	no	—
376	C₂²⋊C₄	—	3	2	no	—
377	C₄²	—	3	1	no	—
378	C₄²	—	3	1	no	—
379	C₄²	—	3	1	no	—
380	C₄²	—	3	2	no	—
381	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
382	C₄²	C₂×D₃×C₉	1	2	yes	—
383	C₂²×C₃	—	2	1	no	—
384	C₂²×C₃	—	3	2	no	—
385	C₂²×C₃	—	6	1	no	—
386	C₂²×C₃	—	6	1	no	—
387	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
388	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
389	C₂×D₃	—	2	1	no	—
390	C₂×D₃	—	2	1	no	—
391	C₂×D₃	C₂×Q₈×C₉	1	2	yes	—
392	C₃×C₄	—	2	4	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	—	2	2	no	—
400	C₃×C₄	—	2	2	no	—
401	C₃×C₄	—	3	2	no	—
402	C₃×C₄	—	3	2	no	—
403	C₃×C₄	—	4	1	no	—
404	C₃×C₄	—	4	2	no	—
405	C₃×C₄	—	6	1	no	—
406	C₃×C₄	—	6	2	no	—
407	C₃×C₄	—	6	2	no	—
408	C₃×C₄	C₂×Q₈×C₉	1	2	yes	—
409	C₃×C₄	C₉×#41	1	2	yes	—
410	C₃×C₄	C₃×#235	1	2	yes	—
411	C₃×C₄	C₃×D₃×Q₈	1	2	yes	—
412	Dic₃	—	2	2	no	—
413	Dic₃	—	2	2	no	—
414	Dic₃	—	2	1	no	—
415	Dic₃	C₂×Q₈×C₉	1	2	yes	—
416	Dic₃	C₉×#41	1	2	yes	—
417	C₃²	C₃×#533	1	1	yes	characteristic
418	C₉	—	2	1	no	—
419	C₉	#5578	1	1	yes	characteristic, direct product factor
420	C₂³	—	3	1	no	—
421	Q₈	—	2	2	no	—
422	Q₈	—	6	4	no	—
423	Q₈	—	6	2	no	—
424	C₂×C₄	—	3	1	no	—
425	C₂×C₄	—	3	1	no	—
426	C₂×C₄	—	3	4	no	—
427	C₂×C₄	—	3	1	no	—
428	C₂×C₄	—	3	2	no	—
429	C₂×C₄	—	3	2	no	—
430	C₂×C₄	—	6	2	no	—
431	C₂×C₄	—	6	2	no	—
432	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
433	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
434	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
435	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
436	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
437	C₂×C₃	—	2	1	no	—
438	C₂×C₃	—	2	1	no	—
439	C₂×C₃	—	2	1	no	—
440	C₂×C₃	—	6	2	no	—
441	C₂×C₃	C₂²×Q₈×C₉	1	1	yes	characteristic
442	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
443	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
444	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
445	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
446	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
447	D₃	—	2	2	no	—
448	C₂²	—	3	2	no	—
449	C₂²	—	6	1	no	—
450	C₂²	—	6	1	no	—
451	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	2	no	—
455	C₄	—	3	2	no	—
456	C₄	—	3	2	no	—
457	C₄	—	6	1	no	—
458	C₄	—	6	2	no	—
459	C₄	—	6	2	no	—
460	C₄	C₉×#235	1	2	yes	—
461	C₄	D₃×Q₈×C₉	1	2	yes	—
462	C₃	—	2	1	no	—
463	C₃	C₉×#533	1	1	yes	characteristic, complemented
464	C₃	C₃×#5578	1	1	yes	characteristic
465	C₂	—	6	2	no	—
466	C₂	C₂×C₉×#235	1	1	yes	characteristic
467	C₂	C₂×D₃×Q₈×C₉	1	1	yes	characteristic
468	C₂	D₃×C₉×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₄×Q₈×C₉	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂²×C₃×D₃	C₂³×C₃
hypercenter	C₄×Q₈×C₉	D₃
hypocenter	C₃	C₉×#533
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₄×Q₈×C₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×Q₈×C₉	C₂	semidirect
3. C₉×#944	C₂	semidirect
6. C₉×#889	C₂	semidirect
7. C₉×#888	C₂	semidirect
10. C₄×C₉×Dic₆	C₂	semidirect
11. C₄×C₉×Dic₆	C₂	semidirect
57. C₄×Q₈×C₉	D₃	semidirect
74. C₄×D₃×C₉	Q₈	semidirect
78. #5578	C₉	direct (N × H)
153. C₃×C₄×Q₈	C₂×C₉	semidirect
158. #944	C₂×C₉	semidirect
161. #889	C₂×C₉	semidirect
162. #888	C₂×C₉	semidirect
165. C₄×Dic₆	C₂×C₉	semidirect
166. C₄×Dic₆	C₂×C₉	semidirect
305. C₄×Q₈	D₃×C₉	semidirect
308. C₃×C₉	#533	semidirect
346. C₄×D₃	Q₈×C₉	semidirect
419. C₉	#5578	direct (N × H)
463. C₃	C₉×#533	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×Q₈×C₉	2
C₉×#946	2
C₉×#944	2
C₉×#897	2
C₉×#896	2
C₉×#889	2
C₉×#888	2
C₉×#872	2
C₄²×D₃×C₉	2
C₄×C₉×Dic₆	2
C₃×#5578	3
C₉×#533	3

Subgroups — C9×#5578 #13152699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5578 #13152699