Subgroups — C₉×#5627 #13152926

Order 1728.

1064 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#239	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#895	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#894	C₂	1	2	yes	maximal, complemented
8	C₉×#893	C₂	1	2	yes	maximal, complemented
9	C₉×#892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#882	C₂	1	2	yes	maximal, complemented
11	C₉×#67⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₃×#5627	C₃	1	1	yes	maximal, characteristic
13	C₉×#525	—	3	1	no	maximal
14	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₉×#67	C₂²	1	2	yes	—
18	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
19	C₉×#239	—	2	4	no	—
20	C₂×C₉×D₁₂	C₂²	1	2	yes	—
21	C₂×C₉×D₁₂	C₂²	1	2	yes	—
22	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₄×D₃×C₉	—	2	4	no	—
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	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₃×C₉	C₂²	1	2	yes	complemented
29	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
31	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
33	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
34	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
35	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
36	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
37	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
38	C₄×C₉×Dic₃	C₂²	1	2	yes	complemented
39	C₂×C₃×#239	C₂×C₃	1	1	yes	characteristic
40	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
41	C₃²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
42	C₃×#946	C₂×C₃	1	1	yes	characteristic
43	C₃×#930	C₂×C₃	1	1	yes	characteristic
44	C₃×#895	C₂×C₃	1	1	yes	characteristic
45	C₃×#894	C₂×C₃	1	2	yes	—
46	C₃×#893	C₂×C₃	1	2	yes	—
47	C₃×#892	C₂×C₃	1	1	yes	characteristic
48	C₃×#882	C₂×C₃	1	2	yes	—
49	C₃×#67⋊C₄	C₂×C₃	1	2	yes	—
50	C₂×C₉×#41	—	3	1	no	—
51	C₂³×C₄×C₉	—	3	1	no	—
52	C₉×#123	—	3	2	no	—
53	C₉×C₂²⋊Q₈	—	2	1	no	—
54	C₉×C₂²⋊Q₈	—	3	1	no	—
55	C₉×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
56	C₉×#121	—	3	1	no	—
57	C₉×#121	—	3	1	no	—
58	C₉×#120	—	3	2	no	—
59	C₄×D₄×C₉	—	3	2	no	—
60	C₄×D₄×C₉	—	3	2	no	—
61	C₉×#117	—	3	1	no	—
62	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
63	C₂²×D₃×C₉	—	2	2	no	—
64	C₂²×D₃×C₉	—	2	2	no	—
65	C₂²×D₃×C₉	—	2	2	no	—
66	C₂²×D₃×C₉	C₂³	1	2	yes	—
67	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
68	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
69	C₃×Q₈×C₉	—	2	2	no	—
70	C₂×C₃×C₄×C₉	—	2	2	no	—
71	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
73	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
74	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
75	C₉×#67	—	2	4	no	—
76	C₂×C₉×Dic₃	—	2	2	no	—
77	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
78	C₂×C₉×Dic₃	C₂³	1	2	yes	—
79	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
80	C₉×D₁₂	—	2	4	no	—
81	C₉×D₁₂	—	2	4	no	—
82	C₉×D₁₂	—	2	2	no	—
83	C₄×D₃×C₉	—	2	2	no	—
84	C₄×D₃×C₉	—	2	2	no	—
85	C₄×D₃×C₉	—	2	2	no	—
86	C₄×D₃×C₉	—	2	4	no	—
87	C₄×D₃×C₉	D₄	1	4	yes	complemented
88	C₃×#525	—	3	1	no	—
89	#5627	C₉	1	1	yes	characteristic, direct product factor
90	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
92	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
94	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
95	C₃×#239	—	2	4	no	—
96	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
97	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
98	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃×C₄×D₃	—	2	4	no	—
100	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
104	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
105	C₂⁴×C₉	—	3	1	no	—
106	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
108	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
109	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
110	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
111	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
112	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
113	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
114	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
115	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
116	C₉×#41	—	6	4	no	—
117	C₂×Q₈×C₉	—	2	1	no	—
118	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
119	C₂×D₄×C₉	—	3	2	no	—
120	C₂×D₄×C₉	—	3	2	no	—
121	C₂×D₄×C₉	—	3	2	no	—
122	C₂×D₄×C₉	—	3	1	no	—
123	C₂²×C₄×C₉	—	2	1	no	—
124	C₂²×C₄×C₉	—	3	1	no	—
125	C₂²×C₄×C₉	—	3	1	no	—
126	C₂²×C₄×C₉	—	3	1	no	—
127	C₂²×C₄×C₉	—	3	2	no	—
128	C₂²×C₄×C₉	—	3	1	no	—
129	C₂²×C₄×C₉	—	3	1	no	—
130	C₂²×C₄×C₉	—	6	4	no	—
131	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
132	C₉×C₄⋊C₄	—	2	1	no	—
133	C₉×C₄⋊C₄	—	2	2	no	—
134	C₉×C₄⋊C₄	—	3	1	no	—
135	C₉×C₄⋊C₄	—	3	2	no	—
136	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
137	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
138	C₉×C₂²⋊C₄	—	2	2	no	—
139	C₉×C₂²⋊C₄	—	3	2	no	—
140	C₉×C₂²⋊C₄	—	3	2	no	—
141	C₉×C₂²⋊C₄	—	3	2	no	—
142	C₉×C₂²⋊C₄	—	3	2	no	—
143	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
144	C₄²×C₉	—	3	2	no	—
145	C₂²×C₃×C₉	—	2	1	no	—
146	C₂²×C₃×C₉	—	2	1	no	—
147	C₂²×C₃×C₉	#41	1	2	yes	complemented
148	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
149	C₂×D₃×C₉	—	2	8	no	—
150	C₂×D₃×C₉	—	2	1	no	—
151	C₂×D₃×C₉	—	2	1	no	—
152	C₂×D₃×C₉	—	2	1	no	—
153	C₂×D₃×C₉	—	2	1	no	—
154	C₂×D₃×C₉	—	2	2	no	—
155	C₂×D₃×C₉	—	2	2	no	—
156	C₂×D₃×C₉	—	2	2	no	—
157	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
158	C₂×D₃×C₉	#41	1	2	yes	complemented
159	C₃×C₄×C₉	—	2	1	no	—
160	C₃×C₄×C₉	—	2	2	no	—
161	C₃×C₄×C₉	—	2	2	no	—
162	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
163	C₉×Dic₃	—	2	1	no	—
164	C₉×Dic₃	—	2	2	no	—
165	C₉×Dic₃	C₂×D₄	1	2	yes	—
166	C₂×C₃×#41	—	3	1	no	—
167	C₂³×C₃×C₄	—	3	1	no	—
168	C₂×#239	C₂×C₉	1	1	yes	characteristic, complemented
169	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic, complemented
170	C₃×#123	—	3	2	no	—
171	C₃×C₂²⋊Q₈	—	2	1	no	—
172	C₃×C₂²⋊Q₈	—	3	1	no	—
173	C₃×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
174	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
175	C₃×#121	—	3	1	no	—
176	C₃×#121	—	3	1	no	—
177	C₃×#120	—	3	2	no	—
178	C₃×C₄×D₄	—	3	2	no	—
179	C₃×C₄×D₄	—	3	2	no	—
180	C₃×#117	—	3	1	no	—
181	#946	C₂×C₉	1	1	yes	characteristic, complemented
182	#930	C₂×C₉	1	1	yes	characteristic, complemented
183	#895	C₂×C₉	1	1	yes	characteristic, complemented
184	#894	C₂×C₉	1	2	yes	complemented
185	#893	C₂×C₉	1	2	yes	complemented
186	#892	C₂×C₉	1	1	yes	characteristic, complemented
187	#882	C₂×C₉	1	2	yes	complemented
188	#67⋊C₄	C₂×C₉	1	2	yes	complemented
189	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
190	C₂²×C₃×D₃	—	2	2	no	—
191	C₂²×C₃×D₃	—	2	2	no	—
192	C₂²×C₃×D₃	—	2	2	no	—
193	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
194	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
195	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
196	C₃²×Q₈	—	2	2	no	—
197	C₂×C₃²×C₄	—	2	2	no	—
198	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
199	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
200	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
202	C₃×#67	—	2	4	no	—
203	C₂×C₃×Dic₃	—	2	2	no	—
204	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
205	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
206	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
207	C₃×D₁₂	—	2	4	no	—
208	C₃×D₁₂	—	2	4	no	—
209	C₃×D₁₂	—	2	2	no	—
210	C₃×C₄×D₃	—	2	2	no	—
211	C₃×C₄×D₃	—	2	2	no	—
212	C₃×C₄×D₃	—	2	2	no	—
213	C₃×C₄×D₃	—	2	4	no	—
214	C₃×C₄×D₃	C₃×D₄	1	4	yes	—
215	C₂³×C₉	—	2	1	no	—
216	C₂³×C₉	—	3	1	no	—
217	C₂³×C₉	—	3	1	no	—
218	C₂³×C₉	—	3	2	no	—
219	C₂³×C₉	—	6	2	no	—
220	C₂³×C₉	—	6	2	no	—
221	C₂³×C₉	—	6	2	no	—
222	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
223	Q₈×C₉	—	2	2	no	—
224	Q₈×C₉	—	4	2	no	—
225	D₄×C₉	—	6	4	no	—
226	D₄×C₉	—	6	4	no	—
227	D₄×C₉	—	6	4	no	—
228	D₄×C₉	—	6	2	no	—
229	C₂×C₄×C₉	—	2	2	no	—
230	C₂×C₄×C₉	—	2	1	no	—
231	C₂×C₄×C₉	—	2	2	no	—
232	C₂×C₄×C₉	—	2	2	no	—
233	C₂×C₄×C₉	—	2	1	no	—
234	C₂×C₄×C₉	—	3	1	no	—
235	C₂×C₄×C₉	—	3	4	no	—
236	C₂×C₄×C₉	—	3	2	no	—
237	C₂×C₄×C₉	—	3	1	no	—
238	C₂×C₄×C₉	—	4	2	no	—
239	C₂×C₄×C₉	—	6	2	no	—
240	C₂×C₄×C₉	—	6	4	no	—
241	C₂×C₄×C₉	—	6	2	no	—
242	C₂×C₄×C₉	—	6	2	no	—
243	C₂×C₄×C₉	—	6	2	no	—
244	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
245	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
246	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
247	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
248	#525	—	3	1	no	Sylow
249	C₂×C₃×C₉	—	2	2	no	—
250	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
252	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
253	D₃×C₉	—	2	2	no	—
254	D₃×C₉	—	2	2	no	—
255	D₃×C₉	—	4	2	no	—
256	C₂⁴×C₃	—	3	1	no	—
257	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
258	C₃×#41	—	6	4	no	—
259	C₂×C₃×Q₈	—	2	1	no	—
260	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
261	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
262	C₂×C₃×D₄	—	3	2	no	—
263	C₂×C₃×D₄	—	3	2	no	—
264	C₂×C₃×D₄	—	3	2	no	—
265	C₂×C₃×D₄	—	3	1	no	—
266	C₂²×C₃×C₄	—	2	1	no	—
267	C₂²×C₃×C₄	—	3	1	no	—
268	C₂²×C₃×C₄	—	3	1	no	—
269	C₂²×C₃×C₄	—	3	1	no	—
270	C₂²×C₃×C₄	—	3	2	no	—
271	C₂²×C₃×C₄	—	3	1	no	—
272	C₂²×C₃×C₄	—	3	1	no	—
273	C₂²×C₃×C₄	—	6	4	no	—
274	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
275	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
276	C₂×#67	C₂²×C₉	1	2	yes	—
277	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
278	#239	—	2	4	no	—
279	C₂×D₁₂	C₂²×C₉	1	2	yes	—
280	C₂×D₁₂	C₂²×C₉	1	2	yes	—
281	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
282	C₂×C₄×D₃	—	2	4	no	—
283	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
284	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
285	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
286	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
287	C₂×C₄×D₃	C₂²×C₉	1	2	yes	complemented
288	C₃×C₄⋊C₄	—	2	1	no	—
289	C₃×C₄⋊C₄	—	2	2	no	—
290	C₃×C₄⋊C₄	—	3	2	no	—
291	C₃×C₄⋊C₄	—	3	1	no	—
292	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
293	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
294	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
295	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
296	C₃×C₂²⋊C₄	—	2	2	no	—
297	C₃×C₂²⋊C₄	—	3	2	no	—
298	C₃×C₂²⋊C₄	—	3	2	no	—
299	C₃×C₂²⋊C₄	—	3	2	no	—
300	C₃×C₂²⋊C₄	—	3	2	no	—
301	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
302	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
303	C₃×C₄²	—	3	2	no	—
304	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
305	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
306	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
307	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
308	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
309	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
310	C₄×Dic₃	C₂²×C₉	1	2	yes	complemented
311	C₂²×C₃²	—	2	1	no	—
312	C₂²×C₃²	—	2	1	no	—
313	C₂²×C₃²	C₃×#41	1	2	yes	—
314	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
315	C₂×C₃×D₃	—	2	8	no	—
316	C₂×C₃×D₃	—	2	1	no	—
317	C₂×C₃×D₃	—	2	1	no	—
318	C₂×C₃×D₃	—	2	1	no	—
319	C₂×C₃×D₃	—	2	1	no	—
320	C₂×C₃×D₃	—	2	2	no	—
321	C₂×C₃×D₃	—	2	2	no	—
322	C₂×C₃×D₃	—	2	2	no	—
323	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
324	C₂×C₃×D₃	C₃×#41	1	2	yes	—
325	C₃²×C₄	—	2	1	no	—
326	C₃²×C₄	—	2	2	no	—
327	C₃²×C₄	—	2	2	no	—
328	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
329	C₃×Dic₃	—	2	1	no	—
330	C₃×Dic₃	—	2	2	no	—
331	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
332	C₂²×C₉	—	2	1	no	—
333	C₂²×C₉	—	2	1	no	—
334	C₂²×C₉	—	2	1	no	—
335	C₂²×C₉	—	2	2	no	—
336	C₂²×C₉	—	3	2	no	—
337	C₂²×C₉	—	3	2	no	—
338	C₂²×C₉	—	4	1	no	—
339	C₂²×C₉	—	4	1	no	—
340	C₂²×C₉	—	6	8	no	—
341	C₂²×C₉	—	6	1	no	—
342	C₂²×C₉	—	6	1	no	—
343	C₂²×C₉	—	6	1	no	—
344	C₂²×C₉	—	6	1	no	—
345	C₂²×C₉	—	6	2	no	—
346	C₂²×C₉	—	6	2	no	—
347	C₂²×C₉	—	6	2	no	—
348	C₂²×C₉	#239	1	2	yes	complemented
349	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
350	C₄×C₉	—	2	1	no	—
351	C₄×C₉	—	2	2	no	—
352	C₄×C₉	—	2	2	no	—
353	C₄×C₉	—	2	2	no	—
354	C₄×C₉	—	3	2	no	—
355	C₄×C₉	—	4	2	no	—
356	C₄×C₉	—	4	1	no	—
357	C₄×C₉	—	4	2	no	—
358	C₄×C₉	—	6	1	no	—
359	C₄×C₉	—	6	2	no	—
360	C₄×C₉	D₃×D₄	1	2	yes	—
361	C₂×#41	—	3	1	no	—
362	C₂³×C₄	—	3	1	no	—
363	#123	—	3	2	no	—
364	C₂²⋊Q₈	—	3	1	no	—
365	C₂²⋊Q₈	D₃×C₉	1	1	yes	characteristic, complemented
366	#121	—	3	1	no	—
367	#121	—	3	1	no	—
368	#120	—	3	2	no	—
369	C₄×D₄	—	3	2	no	—
370	C₄×D₄	—	3	2	no	—
371	#117	—	3	1	no	—
372	C₃×C₉	#525	1	1	yes	characteristic, complemented, Sylow
373	C₂³×C₃	—	2	1	no	—
374	C₂³×C₃	—	3	1	no	—
375	C₂³×C₃	—	3	1	no	—
376	C₂³×C₃	—	3	2	no	—
377	C₂³×C₃	—	6	2	no	—
378	C₂³×C₃	—	6	2	no	—
379	C₂³×C₃	—	6	2	no	—
380	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
381	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
382	C₂²×D₃	—	2	2	no	—
383	C₂²×D₃	—	2	2	no	—
384	C₂²×D₃	—	2	2	no	—
385	C₂²×D₃	C₂³×C₉	1	2	yes	—
386	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
387	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
388	C₃×Q₈	—	2	2	no	—
389	C₃×Q₈	—	2	2	no	—
390	C₃×Q₈	—	4	2	no	—
391	C₃×D₄	—	6	4	no	—
392	C₃×D₄	—	6	4	no	—
393	C₃×D₄	—	6	4	no	—
394	C₃×D₄	—	6	2	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	2	2	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	2	no	—
399	C₂×C₃×C₄	—	2	2	no	—
400	C₂×C₃×C₄	—	2	1	no	—
401	C₂×C₃×C₄	—	3	1	no	—
402	C₂×C₃×C₄	—	3	4	no	—
403	C₂×C₃×C₄	—	3	2	no	—
404	C₂×C₃×C₄	—	3	1	no	—
405	C₂×C₃×C₄	—	4	2	no	—
406	C₂×C₃×C₄	—	6	2	no	—
407	C₂×C₃×C₄	—	6	4	no	—
408	C₂×C₃×C₄	—	6	2	no	—
409	C₂×C₃×C₄	—	6	2	no	—
410	C₂×C₃×C₄	—	6	2	no	—
411	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
412	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
413	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
414	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
415	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
416	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
417	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
418	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
419	#67	—	2	4	no	—
420	C₂×Dic₃	—	2	2	no	—
421	C₂×Dic₃	C₂³×C₉	1	2	yes	—
422	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
423	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
424	D₁₂	—	2	4	no	—
425	D₁₂	—	2	4	no	—
426	D₁₂	—	2	2	no	—
427	C₄×D₃	—	2	2	no	—
428	C₄×D₃	—	2	2	no	—
429	C₄×D₃	—	2	2	no	—
430	C₄×D₃	—	2	4	no	—
431	C₄×D₃	D₄×C₉	1	4	yes	complemented
432	C₂×C₃²	—	2	2	no	—
433	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
434	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
435	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
436	C₃×D₃	—	2	2	no	—
437	C₃×D₃	—	2	2	no	—
438	C₃×D₃	—	4	2	no	—
439	C₂×C₉	—	2	2	no	—
440	C₂×C₉	—	2	1	no	—
441	C₂×C₉	—	2	1	no	—
442	C₂×C₉	—	2	1	no	—
443	C₂×C₉	—	4	2	no	—
444	C₂×C₉	—	6	2	no	—
445	C₂×C₉	—	6	2	no	—
446	C₂×C₉	—	12	2	no	—
447	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
448	C₂×C₉	C₂×#239	1	1	yes	characteristic
449	C₂×C₉	D₃×#41	1	1	yes	characteristic
450	C₂⁴	—	3	1	no	—
451	#41	—	6	4	no	—
452	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
453	C₂×D₄	—	3	2	no	—
454	C₂×D₄	—	3	2	no	—
455	C₂×D₄	—	3	2	no	—
456	C₂×D₄	—	3	1	no	—
457	C₂²×C₄	—	3	1	no	—
458	C₂²×C₄	—	3	1	no	—
459	C₂²×C₄	—	3	1	no	—
460	C₂²×C₄	—	3	2	no	—
461	C₂²×C₄	—	3	1	no	—
462	C₂²×C₄	—	3	1	no	—
463	C₂²×C₄	—	6	4	no	—
464	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
465	C₄⋊C₄	—	3	1	no	—
466	C₄⋊C₄	—	3	2	no	—
467	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
468	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
469	C₂²⋊C₄	—	3	2	no	—
470	C₂²⋊C₄	—	3	2	no	—
471	C₂²⋊C₄	—	3	2	no	—
472	C₂²⋊C₄	—	3	2	no	—
473	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
474	C₄²	—	3	2	no	—
475	C₂²×C₃	—	2	1	no	—
476	C₂²×C₃	—	2	1	no	—
477	C₂²×C₃	—	2	1	no	—
478	C₂²×C₃	—	2	1	no	—
479	C₂²×C₃	—	2	1	no	—
480	C₂²×C₃	—	2	2	no	—
481	C₂²×C₃	—	3	2	no	—
482	C₂²×C₃	—	3	2	no	—
483	C₂²×C₃	—	4	1	no	—
484	C₂²×C₃	—	4	1	no	—
485	C₂²×C₃	—	6	8	no	—
486	C₂²×C₃	—	6	1	no	—
487	C₂²×C₃	—	6	1	no	—
488	C₂²×C₃	—	6	1	no	—
489	C₂²×C₃	—	6	1	no	—
490	C₂²×C₃	—	6	2	no	—
491	C₂²×C₃	—	6	2	no	—
492	C₂²×C₃	—	6	2	no	—
493	C₂²×C₃	C₉×#41	1	2	yes	complemented
494	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
495	C₂²×C₃	C₃×#239	1	2	yes	—
496	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
497	C₂×D₃	—	2	8	no	—
498	C₂×D₃	—	2	1	no	—
499	C₂×D₃	—	2	1	no	—
500	C₂×D₃	—	2	1	no	—
501	C₂×D₃	—	2	1	no	—
502	C₂×D₃	—	2	2	no	—
503	C₂×D₃	—	2	2	no	—
504	C₂×D₃	—	2	2	no	—
505	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
506	C₂×D₃	C₉×#41	1	2	yes	complemented
507	C₃×C₄	—	2	1	no	—
508	C₃×C₄	—	2	2	no	—
509	C₃×C₄	—	2	2	no	—
510	C₃×C₄	—	2	1	no	—
511	C₃×C₄	—	2	2	no	—
512	C₃×C₄	—	2	2	no	—
513	C₃×C₄	—	2	2	no	—
514	C₃×C₄	—	3	2	no	—
515	C₃×C₄	—	4	1	no	—
516	C₃×C₄	—	4	2	no	—
517	C₃×C₄	—	4	2	no	—
518	C₃×C₄	—	6	1	no	—
519	C₃×C₄	—	6	2	no	—
520	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
521	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
522	Dic₃	—	2	1	no	—
523	Dic₃	—	2	2	no	—
524	Dic₃	C₂×D₄×C₉	1	2	yes	—
525	C₃²	C₃×#525	1	1	yes	characteristic
526	C₉	—	2	1	no	—
527	C₉	#5627	1	1	yes	characteristic, direct product factor
528	C₂³	—	3	1	no	—
529	C₂³	—	3	1	no	—
530	C₂³	—	3	2	no	—
531	C₂³	—	6	2	no	—
532	C₂³	—	6	2	no	—
533	C₂³	—	6	2	no	—
534	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
535	Q₈	—	2	2	no	—
536	D₄	—	6	4	no	—
537	D₄	—	6	4	no	—
538	D₄	—	6	4	no	—
539	D₄	—	6	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	3	1	no	—
542	C₂×C₄	—	3	4	no	—
543	C₂×C₄	—	3	2	no	—
544	C₂×C₄	—	3	1	no	—
545	C₂×C₄	—	6	2	no	—
546	C₂×C₄	—	6	4	no	—
547	C₂×C₄	—	6	2	no	—
548	C₂×C₄	—	6	2	no	—
549	C₂×C₄	—	6	2	no	—
550	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
551	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
553	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
554	C₂×C₃	—	2	2	no	—
555	C₂×C₃	—	2	2	no	—
556	C₂×C₃	—	2	1	no	—
557	C₂×C₃	—	2	1	no	—
558	C₂×C₃	—	2	1	no	—
559	C₂×C₃	—	4	2	no	—
560	C₂×C₃	—	6	2	no	—
561	C₂×C₃	—	6	2	no	—
562	C₂×C₃	—	12	2	no	—
563	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
564	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
565	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
566	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
567	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
568	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
569	D₃	—	2	2	no	—
570	D₃	—	2	2	no	—
571	D₃	—	4	2	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	3	2	no	—
575	C₂²	—	3	2	no	—
576	C₂²	—	6	8	no	—
577	C₂²	—	6	1	no	—
578	C₂²	—	6	1	no	—
579	C₂²	—	6	1	no	—
580	C₂²	—	6	1	no	—
581	C₂²	—	6	2	no	—
582	C₂²	—	6	2	no	—
583	C₂²	—	6	2	no	—
584	C₂²	C₉×#239	1	2	yes	complemented
585	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
586	C₄	—	2	1	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	3	2	no	—
590	C₄	—	6	1	no	—
591	C₄	—	6	2	no	—
592	C₄	D₃×D₄×C₉	1	2	yes	—
593	C₃	—	2	1	no	—
594	C₃	C₉×#525	1	1	yes	characteristic, complemented
595	C₃	C₃×#5627	1	1	yes	characteristic
596	C₂	—	2	2	no	—
597	C₂	—	6	2	no	—
598	C₂	—	6	2	no	—
599	C₂	—	12	2	no	—
600	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
601	C₂	C₂×C₉×#239	1	1	yes	characteristic
602	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×#5627	C₃
hypercenter	C₉×C₂²⋊Q₈	D₃
hypocenter	C₃	C₉×#525
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. C₂×C₉×#239	C₂	semidirect
2. C₂²×C₄×D₃×C₉	C₂	semidirect
3. C₃×C₉×C₂²⋊Q₈	C₂	semidirect
4. C₉×#946	C₂	semidirect
5. C₉×#930	C₂	semidirect
6. C₉×#895	C₂	semidirect
7. C₉×#894	C₂	semidirect
8. C₉×#893	C₂	semidirect
9. C₉×#892	C₂	semidirect
10. C₉×#882	C₂	semidirect
11. C₉×#67⋊C₄	C₂	semidirect
15. C₂×C₃×Q₈×C₉	C₂²	semidirect
22. C₂×C₉×D₁₂	C₂²	semidirect
28. C₂×C₄×D₃×C₉	C₂²	semidirect
29. C₃×C₉×C₄⋊C₄	C₂²	semidirect
30. C₃×C₉×C₄⋊C₄	C₂²	semidirect
34. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₉×C₄⋊Dic₃	C₂²	semidirect
37. C₉×Dic₃⋊C₄	C₂²	semidirect
38. C₄×C₉×Dic₃	C₂²	semidirect
55. C₉×C₂²⋊Q₈	D₃	semidirect
87. C₄×D₃×C₉	D₄	semidirect
89. #5627	C₉	direct (N × H)
118. C₂×Q₈×C₉	C₂×D₃	semidirect
136. C₉×C₄⋊C₄	C₂×D₃	semidirect
137. C₉×C₄⋊C₄	C₂×D₃	semidirect
147. C₂²×C₃×C₉	#41	semidirect
158. C₂×D₃×C₉	#41	semidirect
168. C₂×#239	C₂×C₉	semidirect
169. C₂²×C₄×D₃	C₂×C₉	semidirect
173. C₃×C₂²⋊Q₈	C₂×C₉	semidirect
181. #946	C₂×C₉	semidirect
182. #930	C₂×C₉	semidirect
183. #895	C₂×C₉	semidirect
184. #894	C₂×C₉	semidirect
185. #893	C₂×C₉	semidirect
186. #892	C₂×C₉	semidirect
187. #882	C₂×C₉	semidirect
188. #67⋊C₄	C₂×C₉	semidirect
260. C₂×C₃×Q₈	C₂²×C₉	semidirect
281. C₂×D₁₂	C₂²×C₉	semidirect
287. C₂×C₄×D₃	C₂²×C₉	semidirect
292. C₃×C₄⋊C₄	C₂²×C₉	semidirect
293. C₃×C₄⋊C₄	C₂²×C₉	semidirect
306. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
307. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
308. C₄⋊Dic₃	C₂²×C₉	semidirect
309. Dic₃⋊C₄	C₂²×C₉	semidirect
310. C₄×Dic₃	C₂²×C₉	semidirect
348. C₂²×C₉	#239	semidirect
365. C₂²⋊Q₈	D₃×C₉	semidirect
372. C₃×C₉	#525	semidirect
431. C₄×D₃	D₄×C₉	semidirect
452. C₂×Q₈	C₂×D₃×C₉	semidirect
467. C₄⋊C₄	C₂×D₃×C₉	semidirect
468. C₄⋊C₄	C₂×D₃×C₉	semidirect
493. C₂²×C₃	C₉×#41	semidirect
506. C₂×D₃	C₉×#41	semidirect
527. C₉	#5627	direct (N × H)
584. C₂²	C₉×#239	semidirect
594. C₃	C₉×#525	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#239	2
C₂²×C₄×D₃×C₉	2
C₃×C₉×C₂²⋊Q₈	2
C₉×#946	2
C₉×#930	2
C₉×#895	2
C₉×#894	2
C₉×#893	2
C₉×#892	2
C₉×#882	2
C₉×#67⋊C₄	2
C₃×#5627	3
C₉×#525	3

Subgroups — C9×#5627 #13152926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5627 #13152926