Subgroups — C₉×#3455 #11768176

Order 1152.

1560 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#542	C₂	1	4	yes	maximal, complemented
2	C₉×#541	C₂	1	2	yes	maximal, complemented
3	C₉×#540	C₂	1	2	yes	maximal, complemented
4	C₉×#539	C₂	1	4	yes	maximal, complemented
5	C₉×#538	C₂	1	4	yes	maximal, complemented
6	C₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#529	C₂	1	8	yes	maximal, complemented
9	C₉×#525	C₂	1	2	yes	maximal, complemented
10	C₄×C₉×#41	C₂	1	2	yes	maximal, complemented
11	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3455	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	2	yes	—
14	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
17	C₉×#127	C₂²	1	1	yes	characteristic, complemented
18	C₉×#126	C₂²	1	8	yes	—
19	C₉×#126	C₂²	1	8	yes	complemented
20	C₉×#125	C₂²	1	8	yes	complemented
21	C₉×#125	C₂²	1	2	yes	complemented
22	C₉×#124	C₂²	1	8	yes	—
23	C₉×#124	C₂²	1	2	yes	complemented
24	C₉×#123	C₂²	1	4	yes	—
25	C₉×#123	C₂²	1	8	yes	—
26	C₉×#123	C₂²	1	8	yes	complemented
27	C₉×C₂²⋊Q₈	C₂²	1	4	yes	—
28	C₉×C₂²⋊Q₈	C₂²	1	4	yes	—
29	C₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
30	C₉×#121	C₂²	1	4	yes	—
31	C₉×#121	C₂²	1	8	yes	—
32	C₉×#121	C₂²	1	4	yes	—
33	C₉×#120	C₂²	1	4	yes	—
34	C₄×Q₈×C₉	C₂²	1	4	yes	complemented
35	C₄×Q₈×C₉	C₂²	1	4	yes	complemented
36	C₄×D₄×C₉	C₂²	1	8	yes	—
37	C₄×D₄×C₉	C₂²	1	8	yes	—
38	C₄×D₄×C₉	C₂²	1	4	yes	complemented
39	C₄×D₄×C₉	C₂²	1	4	yes	complemented
40	C₉×#117	C₂²	1	2	yes	—
41	C₉×#117	C₂²	1	4	yes	—
42	C₉×#117	C₂²	1	2	yes	—
43	C₉×#117	C₂²	1	2	yes	—
44	C₉×#117	C₂²	1	4	yes	complemented
45	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
46	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
47	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
48	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
49	C₂×C₄²×C₉	C₂²	1	4	yes	complemented
50	C₃×#542	C₂×C₃	1	4	yes	—
51	C₃×#541	C₂×C₃	1	2	yes	—
52	C₃×#540	C₂×C₃	1	2	yes	—
53	C₃×#539	C₂×C₃	1	4	yes	—
54	C₃×#538	C₂×C₃	1	4	yes	—
55	C₃×#533	C₂×C₃	1	1	yes	characteristic
56	C₃×#532	C₂×C₃	1	1	yes	characteristic
57	C₃×#529	C₂×C₃	1	8	yes	—
58	C₃×#525	C₂×C₃	1	2	yes	—
59	C₃×C₄×#41	C₂×C₃	1	2	yes	—
60	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
61	C₂⁴×C₉	C₂³	1	1	yes	characteristic
62	C₉×#41	—	2	8	no	—
63	C₂×Q₈×C₉	C₂³	1	2	yes	—
64	C₂×Q₈×C₉	C₂³	1	4	yes	—
65	C₂×D₄×C₉	C₂³	1	4	yes	—
66	C₂×D₄×C₉	C₂³	1	2	yes	—
67	C₂×D₄×C₉	C₂³	1	8	yes	—
68	C₂×D₄×C₉	C₂³	1	4	yes	—
69	C₂²×C₄×C₉	—	2	4	no	—
70	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₉	C₂³	1	2	yes	—
72	C₂²×C₄×C₉	C₂³	1	4	yes	—
73	C₂²×C₄×C₉	C₂³	1	2	yes	—
74	C₂²×C₄×C₉	C₂³	1	2	yes	—
75	C₂²×C₄×C₉	C₂³	1	2	yes	—
76	C₂²×C₄×C₉	C₂³	1	8	yes	—
77	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
78	C₉×C₄⋊C₄	C₂³	1	4	yes	—
79	C₉×C₄⋊C₄	C₂³	1	4	yes	—
80	C₉×C₄⋊C₄	C₂³	1	4	yes	—
81	C₉×C₄⋊C₄	C₂³	1	8	yes	—
82	C₉×C₄⋊C₄	C₂³	1	8	yes	—
83	C₉×C₄⋊C₄	C₂³	1	4	yes	—
84	C₉×C₄⋊C₄	C₂³	1	8	yes	—
85	C₉×C₄⋊C₄	C₂³	1	4	yes	—
86	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
87	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
88	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
89	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
90	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
91	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
92	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
93	C₄²×C₉	C₂³	1	2	yes	—
94	C₄²×C₉	C₂³	1	1	yes	characteristic
95	C₄²×C₉	C₂³	1	1	yes	characteristic
96	C₄²×C₉	C₂³	1	8	yes	—
97	C₄²×C₉	C₂³	1	2	yes	—
98	C₄²×C₉	C₂³	1	2	yes	—
99	C₄²×C₉	C₂³	1	4	yes	—
100	#3455	C₉	1	1	yes	characteristic, direct product factor, Sylow
101	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
102	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
103	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
104	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
105	C₃×#127	C₂²×C₃	1	1	yes	characteristic
106	C₃×#126	C₂²×C₃	1	8	yes	—
107	C₃×#126	C₂²×C₃	1	8	yes	—
108	C₃×#125	C₂²×C₃	1	8	yes	—
109	C₃×#125	C₂²×C₃	1	2	yes	—
110	C₃×#124	C₂²×C₃	1	8	yes	—
111	C₃×#124	C₂²×C₃	1	2	yes	—
112	C₃×#123	C₂²×C₃	1	4	yes	—
113	C₃×#123	C₂²×C₃	1	8	yes	—
114	C₃×#123	C₂²×C₃	1	8	yes	—
115	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
116	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
117	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
118	C₃×#121	C₂²×C₃	1	4	yes	—
119	C₃×#121	C₂²×C₃	1	8	yes	—
120	C₃×#121	C₂²×C₃	1	4	yes	—
121	C₃×#120	C₂²×C₃	1	4	yes	—
122	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
123	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
124	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
125	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
126	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
127	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
128	C₃×#117	C₂²×C₃	1	4	yes	—
129	C₃×#117	C₂²×C₃	1	2	yes	—
130	C₃×#117	C₂²×C₃	1	2	yes	—
131	C₃×#117	C₂²×C₃	1	2	yes	—
132	C₃×#117	C₂²×C₃	1	4	yes	—
133	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
134	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
135	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
138	C₂³×C₉	—	2	2	no	—
139	C₂³×C₉	—	4	2	no	—
140	C₂³×C₉	C₂⁴	1	2	yes	—
141	C₂³×C₉	C₂⁴	1	4	yes	—
142	C₂³×C₉	C₂⁴	1	1	yes	characteristic
143	Q₈×C₉	—	2	4	no	—
144	Q₈×C₉	—	4	4	no	—
145	D₄×C₉	—	2	8	no	—
146	D₄×C₉	—	2	4	no	—
147	D₄×C₉	—	4	4	no	—
148	D₄×C₉	—	4	8	no	—
149	C₂×C₄×C₉	—	2	2	no	—
150	C₂×C₄×C₉	—	2	4	no	—
151	C₂×C₄×C₉	—	2	4	no	—
152	C₂×C₄×C₉	—	2	8	no	—
153	C₂×C₄×C₉	—	4	2	no	—
154	C₂×C₄×C₉	—	4	8	no	—
155	C₂×C₄×C₉	—	4	2	no	—
156	C₂×C₄×C₉	#41	1	4	yes	—
157	C₂×C₄×C₉	C₂⁴	1	4	yes	—
158	C₂×C₄×C₉	C₂⁴	1	2	yes	—
159	C₂×C₄×C₉	C₂⁴	1	4	yes	—
160	C₂×C₄×C₉	C₂⁴	1	8	yes	—
161	C₂×C₄×C₉	C₂⁴	1	2	yes	—
162	C₂×C₄×C₉	C₂⁴	1	2	yes	—
163	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
165	#542	C₂×C₉	1	4	yes	complemented
166	#541	C₂×C₉	1	2	yes	complemented
167	#540	C₂×C₉	1	2	yes	complemented
168	#539	C₂×C₉	1	4	yes	complemented
169	#538	C₂×C₉	1	4	yes	complemented
170	#533	C₂×C₉	1	1	yes	characteristic, complemented
171	#532	C₂×C₉	1	1	yes	characteristic, complemented
172	#529	C₂×C₉	1	8	yes	complemented
173	#525	C₂×C₉	1	2	yes	complemented
174	C₄×#41	C₂×C₉	1	2	yes	complemented
175	C₂×#117	C₂×C₉	1	1	yes	characteristic, complemented
176	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
177	C₃×#41	—	2	8	no	—
178	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
179	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
180	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
181	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
182	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
183	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
184	C₂²×C₃×C₄	—	2	4	no	—
185	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
186	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
187	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
188	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
189	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
190	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
191	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
192	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
193	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
194	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
195	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
196	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
197	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
198	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
199	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
200	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
201	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
202	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
203	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
204	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
205	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
206	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
207	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
208	C₃×C₄²	C₂³×C₃	1	2	yes	—
209	C₃×C₄²	C₂³×C₃	1	2	yes	—
210	C₃×C₄²	C₂³×C₃	1	2	yes	—
211	C₃×C₄²	C₂³×C₃	1	4	yes	—
212	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
213	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
214	C₃×C₄²	C₂³×C₃	1	8	yes	—
215	C₂²×C₉	—	2	2	no	—
216	C₂²×C₉	—	2	2	no	—
217	C₂²×C₉	—	2	4	no	—
218	C₂²×C₉	—	2	8	no	—
219	C₂²×C₉	—	2	4	no	—
220	C₂²×C₉	—	4	4	no	—
221	C₂²×C₉	C₂×#41	1	2	yes	—
222	C₂²×C₉	C₂⁵	1	1	yes	characteristic
223	C₄×C₉	—	2	2	no	—
224	C₄×C₉	—	2	4	no	—
225	C₄×C₉	—	2	4	no	—
226	C₄×C₉	—	2	2	no	—
227	C₄×C₉	—	2	8	no	—
228	C₄×C₉	—	2	2	no	—
229	C₄×C₉	C₂×#41	1	2	yes	—
230	C₄×C₉	C₂×#41	1	2	yes	—
231	C₂×#41	C₂²×C₉	1	2	yes	—
232	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
233	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
234	C₄⋊Q₈	C₂²×C₉	1	2	yes	complemented
235	#127	C₂²×C₉	1	1	yes	characteristic, complemented
236	#126	C₂²×C₉	1	8	yes	—
237	#126	C₂²×C₉	1	8	yes	complemented
238	#125	C₂²×C₉	1	8	yes	complemented
239	#125	C₂²×C₉	1	2	yes	complemented
240	#124	C₂²×C₉	1	8	yes	—
241	#124	C₂²×C₉	1	2	yes	complemented
242	#123	C₂²×C₉	1	4	yes	—
243	#123	C₂²×C₉	1	8	yes	—
244	#123	C₂²×C₉	1	8	yes	complemented
245	C₂²⋊Q₈	C₂²×C₉	1	4	yes	—
246	C₂²⋊Q₈	C₂²×C₉	1	4	yes	—
247	C₂²⋊Q₈	C₂²×C₉	1	8	yes	complemented
248	#121	C₂²×C₉	1	4	yes	—
249	#121	C₂²×C₉	1	8	yes	—
250	#121	C₂²×C₉	1	4	yes	—
251	#120	C₂²×C₉	1	4	yes	—
252	C₄×Q₈	C₂²×C₉	1	4	yes	complemented
253	C₄×Q₈	C₂²×C₉	1	4	yes	complemented
254	C₄×D₄	C₂²×C₉	1	8	yes	—
255	C₄×D₄	C₂²×C₉	1	8	yes	—
256	C₄×D₄	C₂²×C₉	1	4	yes	complemented
257	C₄×D₄	C₂²×C₉	1	4	yes	complemented
258	#117	C₂²×C₉	1	4	yes	—
259	#117	C₂²×C₉	1	2	yes	—
260	#117	C₂²×C₉	1	2	yes	—
261	#117	C₂²×C₉	1	2	yes	—
262	#117	C₂²×C₉	1	4	yes	complemented
263	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
264	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
265	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
266	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
267	C₂×C₄²	C₂²×C₉	1	4	yes	complemented
268	C₂³×C₃	—	2	2	no	—
269	C₂³×C₃	—	4	2	no	—
270	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
271	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
272	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
273	C₃×Q₈	—	2	4	no	—
274	C₃×Q₈	—	4	4	no	—
275	C₃×D₄	—	2	8	no	—
276	C₃×D₄	—	2	4	no	—
277	C₃×D₄	—	4	4	no	—
278	C₃×D₄	—	4	8	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	4	no	—
281	C₂×C₃×C₄	—	2	4	no	—
282	C₂×C₃×C₄	—	2	8	no	—
283	C₂×C₃×C₄	—	4	2	no	—
284	C₂×C₃×C₄	—	4	8	no	—
285	C₂×C₃×C₄	—	4	2	no	—
286	C₂×C₃×C₄	C₃×#41	1	4	yes	—
287	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
288	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
289	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
290	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
291	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
292	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
293	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
295	C₂×C₉	—	2	2	no	—
296	C₂×C₉	—	4	4	no	—
297	C₂×C₉	—	4	2	no	—
298	C₂×C₉	C₂²×#41	1	1	yes	characteristic
299	C₂×C₉	#585	1	2	yes	—
300	C₂⁴	C₂³×C₉	1	1	yes	characteristic
301	#41	—	2	8	no	—
302	C₂×Q₈	C₂³×C₉	1	2	yes	—
303	C₂×Q₈	C₂³×C₉	1	4	yes	—
304	C₂×D₄	C₂³×C₉	1	4	yes	—
305	C₂×D₄	C₂³×C₉	1	2	yes	—
306	C₂×D₄	C₂³×C₉	1	8	yes	—
307	C₂×D₄	C₂³×C₉	1	4	yes	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	C₂³×C₉	1	4	yes	—
310	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
311	C₂²×C₄	C₂³×C₉	1	2	yes	—
312	C₂²×C₄	C₂³×C₉	1	2	yes	—
313	C₂²×C₄	C₂³×C₉	1	2	yes	—
314	C₂²×C₄	C₂³×C₉	1	2	yes	—
315	C₂²×C₄	C₂³×C₉	1	8	yes	—
316	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
317	C₄⋊C₄	C₂³×C₉	1	4	yes	—
318	C₄⋊C₄	C₂³×C₉	1	4	yes	—
319	C₄⋊C₄	C₂³×C₉	1	4	yes	—
320	C₄⋊C₄	C₂³×C₉	1	8	yes	—
321	C₄⋊C₄	C₂³×C₉	1	8	yes	—
322	C₄⋊C₄	C₂³×C₉	1	4	yes	—
323	C₄⋊C₄	C₂³×C₉	1	8	yes	—
324	C₄⋊C₄	C₂³×C₉	1	4	yes	—
325	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
326	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
327	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
328	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
329	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
330	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
331	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
332	C₄²	C₂³×C₉	1	2	yes	—
333	C₄²	C₂³×C₉	1	2	yes	—
334	C₄²	C₂³×C₉	1	2	yes	—
335	C₄²	C₂³×C₉	1	1	yes	characteristic
336	C₄²	C₂³×C₉	1	1	yes	characteristic
337	C₄²	C₂³×C₉	1	4	yes	—
338	C₄²	C₂³×C₉	1	8	yes	—
339	C₂²×C₃	—	2	2	no	—
340	C₂²×C₃	—	2	2	no	—
341	C₂²×C₃	—	2	4	no	—
342	C₂²×C₃	—	2	8	no	—
343	C₂²×C₃	—	2	4	no	—
344	C₂²×C₃	—	4	4	no	—
345	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
346	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
347	C₃×C₄	—	2	2	no	—
348	C₃×C₄	—	2	4	no	—
349	C₃×C₄	—	2	4	no	—
350	C₃×C₄	—	2	2	no	—
351	C₃×C₄	—	2	8	no	—
352	C₃×C₄	—	2	2	no	—
353	C₃×C₄	C₂×C₃×#41	1	2	yes	—
354	C₃×C₄	C₂×C₃×#41	1	2	yes	—
355	C₉	#3455	1	1	yes	characteristic, direct product factor, Sylow
356	C₂³	—	2	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	C₂⁴×C₉	1	2	yes	—
359	C₂³	C₂⁴×C₉	1	4	yes	—
360	C₂³	C₂⁴×C₉	1	1	yes	characteristic
361	Q₈	—	2	4	no	—
362	Q₈	—	4	4	no	—
363	D₄	—	2	8	no	—
364	D₄	—	2	4	no	—
365	D₄	—	4	4	no	—
366	D₄	—	4	8	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	8	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	C₉×#41	1	4	yes	—
375	C₂×C₄	C₂⁴×C₉	1	4	yes	—
376	C₂×C₄	C₂⁴×C₉	1	2	yes	—
377	C₂×C₄	C₂⁴×C₉	1	4	yes	—
378	C₂×C₄	C₂⁴×C₉	1	8	yes	—
379	C₂×C₄	C₂⁴×C₉	1	2	yes	—
380	C₂×C₄	C₂⁴×C₉	1	2	yes	—
381	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
382	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
383	C₂×C₃	—	2	2	no	—
384	C₂×C₃	—	4	2	no	—
385	C₂×C₃	—	4	4	no	—
386	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
387	C₂×C₃	C₃×#585	1	2	yes	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	8	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	C₂×C₉×#41	1	2	yes	—
395	C₂²	C₂⁵×C₉	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	4	no	—
398	C₄	—	2	4	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	8	no	—
401	C₄	—	2	2	no	—
402	C₄	C₂×C₉×#41	1	2	yes	—
403	C₄	C₂×C₉×#41	1	2	yes	—
404	C₃	C₃×#3455	1	1	yes	characteristic
405	C₂	—	2	2	no	—
406	C₂	—	4	2	no	—
407	C₂	—	4	4	no	—
408	C₂	C₂²×C₉×#41	1	1	yes	characteristic
409	C₂	C₉×#585	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₉	C₂⁴
commutator	C₂²	C₂⁵×C₉
Frattini, socle, cosocle	C₂²×C₃	C₂⁵×C₃
prime radical	C₃×#3455	C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#542	C₂	semidirect
2. C₉×#541	C₂	semidirect
3. C₉×#540	C₂	semidirect
4. C₉×#539	C₂	semidirect
5. C₉×#538	C₂	semidirect
6. C₉×#533	C₂	semidirect
7. C₉×#532	C₂	semidirect
8. C₉×#529	C₂	semidirect
9. C₉×#525	C₂	semidirect
10. C₄×C₉×#41	C₂	semidirect
11. C₂×C₉×#117	C₂	semidirect
15. C₉×C₄⋊Q₈	C₂²	semidirect
16. C₉×C₄⋊Q₈	C₂²	semidirect
17. C₉×#127	C₂²	semidirect
19. C₉×#126	C₂²	semidirect
20. C₉×#125	C₂²	semidirect
21. C₉×#125	C₂²	semidirect
23. C₉×#124	C₂²	semidirect
26. C₉×#123	C₂²	semidirect
29. C₉×C₂²⋊Q₈	C₂²	semidirect
34. C₄×Q₈×C₉	C₂²	semidirect
35. C₄×Q₈×C₉	C₂²	semidirect
38. C₄×D₄×C₉	C₂²	semidirect
39. C₄×D₄×C₉	C₂²	semidirect
44. C₉×#117	C₂²	semidirect
49. C₂×C₄²×C₉	C₂²	semidirect
100. #3455	C₉	direct (N × H)
165. #542	C₂×C₉	semidirect
166. #541	C₂×C₉	semidirect
167. #540	C₂×C₉	semidirect
168. #539	C₂×C₉	semidirect
169. #538	C₂×C₉	semidirect
170. #533	C₂×C₉	semidirect
171. #532	C₂×C₉	semidirect
172. #529	C₂×C₉	semidirect
173. #525	C₂×C₉	semidirect
174. C₄×#41	C₂×C₉	semidirect
175. C₂×#117	C₂×C₉	semidirect
233. C₄⋊Q₈	C₂²×C₉	semidirect
234. C₄⋊Q₈	C₂²×C₉	semidirect
235. #127	C₂²×C₉	semidirect
237. #126	C₂²×C₉	semidirect
238. #125	C₂²×C₉	semidirect
239. #125	C₂²×C₉	semidirect
241. #124	C₂²×C₉	semidirect
244. #123	C₂²×C₉	semidirect
247. C₂²⋊Q₈	C₂²×C₉	semidirect
252. C₄×Q₈	C₂²×C₉	semidirect
253. C₄×Q₈	C₂²×C₉	semidirect
256. C₄×D₄	C₂²×C₉	semidirect
257. C₄×D₄	C₂²×C₉	semidirect
262. #117	C₂²×C₉	semidirect
267. C₂×C₄²	C₂²×C₉	semidirect
355. C₉	#3455	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#542	2
C₉×#541	2
C₉×#540	2
C₉×#539	2
C₉×#538	2
C₉×#533	2
C₉×#532	2
C₉×#529	2
C₉×#525	2
C₄×C₉×#41	2
C₂×C₉×#117	2
C₃×#3455	3

Subgroups — C9×#3455 #11768176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3455 #11768176