Subgroups — C₉×#2564 #11767285

Order 1152.

876 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic
3	C₉×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#399	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#395	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#393	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#387	C₂	1	2	yes	maximal, complemented
8	C₉×#386	C₂	1	2	yes	maximal
9	C₉×#385	C₂	1	2	yes	maximal, complemented
10	C₉×#380	C₂	1	2	yes	maximal, complemented
11	C₂×C₉×#95	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2564	C₃	1	1	yes	maximal, characteristic
13	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₉	C₂²	1	2	yes	—
16	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
18	C₉×C₂²⋊Q₈	—	2	4	no	—
19	C₄×D₄×C₉	—	2	4	no	—
20	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
31	C₉×#95	C₂²	1	2	yes	—
32	C₉×#95	C₂²	1	1	yes	characteristic
33	C₉×#95	C₂²	1	1	yes	characteristic
34	C₉×#95	C₂²	1	2	yes	—
35	C₉×#95	C₂²	1	2	yes	—
36	C₉×#95	C₂²	1	2	yes	—
37	C₉×#95	C₂²	1	2	yes	—
38	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
39	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
40	C₃×#400	C₂×C₃	1	1	yes	characteristic
41	C₃×#399	C₂×C₃	1	1	yes	characteristic
42	C₃×#395	C₂×C₃	1	1	yes	characteristic
43	C₃×#393	C₂×C₃	1	1	yes	characteristic
44	C₃×#387	C₂×C₃	1	2	yes	—
45	C₃×#386	C₂×C₃	1	2	yes	—
46	C₃×#385	C₂×C₃	1	2	yes	—
47	C₃×#380	C₂×C₃	1	2	yes	—
48	C₂×C₃×#95	C₂×C₃	1	1	yes	characteristic
49	C₂⁴×C₉	C₂³	1	1	yes	characteristic
50	C₂⁴×C₉	C₂³	1	1	yes	characteristic
51	C₂×Q₈×C₉	—	2	2	no	—
52	C₂×Q₈×C₉	—	4	2	no	—
53	C₂×D₄×C₉	—	2	2	no	—
54	C₂×D₄×C₉	—	2	2	no	—
55	C₂×D₄×C₉	Q₈	1	4	yes	complemented
56	C₂²×C₄×C₉	—	2	4	no	—
57	C₂²×C₄×C₉	—	2	2	no	—
58	C₂²×C₄×C₉	—	2	4	no	—
59	C₂²×C₄×C₉	—	4	2	no	—
60	C₂²×C₄×C₉	—	4	2	no	—
61	C₂²×C₄×C₉	—	4	2	no	—
62	C₂²×C₄×C₉	D₄	1	4	yes	—
63	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₉	C₂³	1	2	yes	—
65	C₂²×C₄×C₉	C₂³	1	2	yes	—
66	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₉	C₂³	1	2	yes	—
68	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₉	C₂³	1	2	yes	—
72	C₉×C₄⋊C₄	—	2	2	no	—
73	C₉×C₄⋊C₄	—	2	2	no	—
74	C₉×C₄⋊C₄	—	2	4	no	—
75	C₉×C₄⋊C₄	—	2	4	no	—
76	C₉×C₄⋊C₄	—	4	2	no	—
77	C₉×C₂²⋊C₄	—	2	2	no	—
78	C₉×C₂²⋊C₄	—	2	4	no	—
79	C₉×C₂²⋊C₄	—	2	2	no	—
80	C₉×C₂²⋊C₄	—	2	4	no	—
81	C₉×C₂²⋊C₄	—	4	2	no	—
82	C₄²×C₉	—	2	2	no	—
83	#2564	C₉	1	1	yes	characteristic, direct product factor, Sylow
84	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
85	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
86	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
87	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
88	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
89	C₃×C₂²⋊Q₈	—	2	4	no	—
90	C₃×C₄×D₄	—	2	4	no	—
91	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
92	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
98	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
99	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
101	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
102	C₃×#95	C₂²×C₃	1	2	yes	—
103	C₃×#95	C₂²×C₃	1	1	yes	characteristic
104	C₃×#95	C₂²×C₃	1	1	yes	characteristic
105	C₃×#95	C₂²×C₃	1	2	yes	—
106	C₃×#95	C₂²×C₃	1	2	yes	—
107	C₃×#95	C₂²×C₃	1	2	yes	—
108	C₃×#95	C₂²×C₃	1	2	yes	—
109	C₂³×C₉	—	2	2	no	—
110	C₂³×C₉	—	2	2	no	—
111	C₂³×C₉	—	2	1	no	—
112	C₂³×C₉	—	2	2	no	—
113	C₂³×C₉	—	2	1	no	—
114	C₂³×C₉	—	2	2	no	—
115	C₂³×C₉	C₂×D₄	1	2	yes	—
116	C₂³×C₉	C₂×Q₈	1	2	yes	—
117	C₂³×C₉	C₂×Q₈	1	2	yes	—
118	C₂³×C₉	#41	1	2	yes	—
119	C₂³×C₉	C₂⁴	1	1	yes	characteristic
120	Q₈×C₉	—	4	4	no	—
121	D₄×C₉	—	2	8	no	—
122	C₂×C₄×C₉	—	2	1	no	—
123	C₂×C₄×C₉	—	2	2	no	—
124	C₂×C₄×C₉	—	2	1	no	—
125	C₂×C₄×C₉	—	2	2	no	—
126	C₂×C₄×C₉	—	2	2	no	—
127	C₂×C₄×C₉	—	2	2	no	—
128	C₂×C₄×C₉	—	2	1	no	—
129	C₂×C₄×C₉	—	2	2	no	—
130	C₂×C₄×C₉	—	2	1	no	—
131	C₂×C₄×C₉	—	2	2	no	—
132	C₂×C₄×C₉	—	2	2	no	—
133	C₂×C₄×C₉	—	2	2	no	—
134	C₂×C₄×C₉	—	2	2	no	—
135	C₂×C₄×C₉	—	2	2	no	—
136	C₂×C₄×C₉	—	2	2	no	—
137	C₂×C₄×C₉	—	2	2	no	—
138	C₂×C₄×C₉	—	2	2	no	—
139	C₂×C₄×C₉	—	2	2	no	—
140	C₂×C₄×C₉	—	2	2	no	—
141	C₂×C₄×C₉	—	4	4	no	—
142	C₂×C₄×C₉	—	4	8	no	—
143	C₂×C₄×C₉	—	4	4	no	—
144	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
145	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
146	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
147	C₂×C₄×C₉	#41	1	4	yes	—
148	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
149	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic
150	#400	C₂×C₉	1	1	yes	characteristic, complemented
151	#399	C₂×C₉	1	1	yes	characteristic, complemented
152	#395	C₂×C₉	1	1	yes	characteristic, complemented
153	#393	C₂×C₉	1	1	yes	characteristic, complemented
154	#387	C₂×C₉	1	2	yes	complemented
155	#386	C₂×C₉	1	2	yes	—
156	#385	C₂×C₉	1	2	yes	complemented
157	#380	C₂×C₉	1	2	yes	complemented
158	C₂×#95	C₂×C₉	1	1	yes	characteristic, complemented
159	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
160	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
161	C₂×C₃×Q₈	—	2	2	no	—
162	C₂×C₃×Q₈	—	4	2	no	—
163	C₂×C₃×D₄	—	2	2	no	—
164	C₂×C₃×D₄	—	2	2	no	—
165	C₂×C₃×D₄	C₃×Q₈	1	4	yes	—
166	C₂²×C₃×C₄	—	2	4	no	—
167	C₂²×C₃×C₄	—	2	2	no	—
168	C₂²×C₃×C₄	—	2	4	no	—
169	C₂²×C₃×C₄	—	4	2	no	—
170	C₂²×C₃×C₄	—	4	2	no	—
171	C₂²×C₃×C₄	—	4	2	no	—
172	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
173	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
174	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
176	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
177	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
181	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
182	C₃×C₄⋊C₄	—	2	2	no	—
183	C₃×C₄⋊C₄	—	2	2	no	—
184	C₃×C₄⋊C₄	—	2	4	no	—
185	C₃×C₄⋊C₄	—	2	4	no	—
186	C₃×C₄⋊C₄	—	4	2	no	—
187	C₃×C₂²⋊C₄	—	2	2	no	—
188	C₃×C₂²⋊C₄	—	2	4	no	—
189	C₃×C₂²⋊C₄	—	2	2	no	—
190	C₃×C₂²⋊C₄	—	2	4	no	—
191	C₃×C₂²⋊C₄	—	4	2	no	—
192	C₃×C₄²	—	2	2	no	—
193	C₂²×C₉	—	2	2	no	—
194	C₂²×C₉	—	2	2	no	—
195	C₂²×C₉	—	2	4	no	—
196	C₂²×C₉	—	2	4	no	—
197	C₂²×C₉	—	2	2	no	—
198	C₂²×C₉	—	2	4	no	—
199	C₂²×C₉	—	4	1	no	—
200	C₂²×C₉	—	4	1	no	—
201	C₂²×C₉	—	4	2	no	—
202	C₂²×C₉	C₂²⋊Q₈	1	4	yes	—
203	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
204	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
205	C₂²×C₉	C₂×#41	1	1	yes	characteristic
206	C₂²×C₉	C₂×#41	1	2	yes	—
207	C₂²×C₉	H(5,𝔽₂)	1	2	yes	—
208	C₄×C₉	—	2	2	no	—
209	C₄×C₉	—	2	2	no	—
210	C₄×C₉	—	2	2	no	—
211	C₄×C₉	—	2	4	no	—
212	C₄×C₉	—	4	1	no	—
213	C₄×C₉	—	4	2	no	—
214	C₄×C₉	—	4	1	no	—
215	C₄×C₉	—	4	2	no	—
216	C₄×C₉	—	4	2	no	—
217	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
218	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
219	C₂³×C₄	C₂²×C₉	1	2	yes	—
220	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
221	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
222	C₂²⋊Q₈	—	2	4	no	—
223	C₄×D₄	—	2	4	no	—
224	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
226	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
228	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
229	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
230	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
231	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
232	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
233	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
234	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
235	#95	C₂²×C₉	1	2	yes	—
236	#95	C₂²×C₉	1	1	yes	characteristic
237	#95	C₂²×C₉	1	1	yes	characteristic
238	#95	C₂²×C₉	1	2	yes	—
239	#95	C₂²×C₉	1	2	yes	—
240	#95	C₂²×C₉	1	2	yes	—
241	#95	C₂²×C₉	1	2	yes	—
242	C₂³×C₃	—	2	2	no	—
243	C₂³×C₃	—	2	2	no	—
244	C₂³×C₃	—	2	1	no	—
245	C₂³×C₃	—	2	2	no	—
246	C₂³×C₃	—	2	1	no	—
247	C₂³×C₃	—	2	2	no	—
248	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
249	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
250	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
251	C₂³×C₃	C₃×#41	1	2	yes	—
252	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
253	C₃×Q₈	—	4	4	no	—
254	C₃×D₄	—	2	8	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	4	4	no	—
275	C₂×C₃×C₄	—	4	8	no	—
276	C₂×C₃×C₄	—	4	4	no	—
277	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
278	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
279	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
280	C₂×C₃×C₄	C₃×#41	1	4	yes	—
281	C₂×C₉	—	2	4	no	—
282	C₂×C₉	—	4	2	no	—
283	C₂×C₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
284	C₂×C₉	#532	1	1	yes	characteristic
285	C₂×C₉	#534	1	1	yes	characteristic
286	C₂×C₉	#551	1	2	yes	—
287	C₂×C₉	#554	1	2	yes	—
288	C₂⁴	C₂³×C₉	1	1	yes	characteristic
289	C₂⁴	C₂³×C₉	1	1	yes	characteristic
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	4	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	Q₈×C₉	1	4	yes	complemented
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	D₄×C₉	1	4	yes	—
302	C₂²×C₄	C₂³×C₉	1	2	yes	—
303	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
304	C₂²×C₄	C₂³×C₉	1	2	yes	—
305	C₂²×C₄	C₂³×C₉	1	2	yes	—
306	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
307	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
308	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
309	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
310	C₂²×C₄	C₂³×C₉	1	2	yes	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	4	no	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	2	4	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₄²	—	2	2	no	—
322	C₂²×C₃	—	2	2	no	—
323	C₂²×C₃	—	2	2	no	—
324	C₂²×C₃	—	2	4	no	—
325	C₂²×C₃	—	2	4	no	—
326	C₂²×C₃	—	2	2	no	—
327	C₂²×C₃	—	2	4	no	—
328	C₂²×C₃	—	4	1	no	—
329	C₂²×C₃	—	4	1	no	—
330	C₂²×C₃	—	4	2	no	—
331	C₂²×C₃	C₃×C₂²⋊Q₈	1	4	yes	—
332	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
333	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
334	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
335	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
336	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	—	2	2	no	—
339	C₃×C₄	—	2	2	no	—
340	C₃×C₄	—	2	4	no	—
341	C₃×C₄	—	4	1	no	—
342	C₃×C₄	—	4	2	no	—
343	C₃×C₄	—	4	1	no	—
344	C₃×C₄	—	4	2	no	—
345	C₃×C₄	—	4	2	no	—
346	C₉	#2564	1	1	yes	characteristic, direct product factor, Sylow
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	2	no	—
353	C₂³	C₂×D₄×C₉	1	2	yes	—
354	C₂³	C₂×Q₈×C₉	1	2	yes	—
355	C₂³	C₂×Q₈×C₉	1	2	yes	—
356	C₂³	C₉×#41	1	2	yes	—
357	C₂³	C₂⁴×C₉	1	1	yes	characteristic
358	Q₈	—	4	4	no	—
359	D₄	—	2	8	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	8	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
383	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
384	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
385	C₂×C₄	C₉×#41	1	4	yes	—
386	C₂×C₃	—	2	4	no	—
387	C₂×C₃	—	4	2	no	—
388	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
389	C₂×C₃	C₃×#532	1	1	yes	characteristic
390	C₂×C₃	C₃×#534	1	1	yes	characteristic
391	C₂×C₃	C₃×#551	1	2	yes	—
392	C₂×C₃	C₃×#554	1	2	yes	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	2	no	—
402	C₂²	C₉×C₂²⋊Q₈	1	4	yes	—
403	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
404	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
405	C₂²	C₂×C₉×#41	1	1	yes	characteristic
406	C₂²	C₂×C₉×#41	1	2	yes	—
407	C₂²	C₉×H(5,𝔽₂)	1	2	yes	—
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	2	2	no	—
411	C₄	—	2	4	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₃	C₃×#2564	1	1	yes	characteristic
418	C₂	—	2	4	no	—
419	C₂	—	4	2	no	—
420	C₂	C₂×C₉×C₂²⋊Q₈	1	1	yes	characteristic
421	C₂	C₉×#532	1	1	yes	characteristic
422	C₂	C₉×#534	1	1	yes	characteristic
423	C₂	C₉×#551	1	2	yes	—
424	C₂	C₉×#554	1	2	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂²×C₃×D₄	C₂²×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
3. C₉×#400	C₂	semidirect
4. C₉×#399	C₂	semidirect
5. C₉×#395	C₂	semidirect
6. C₉×#393	C₂	semidirect
7. C₉×#387	C₂	semidirect
9. C₉×#385	C₂	semidirect
10. C₉×#380	C₂	semidirect
11. C₂×C₉×#95	C₂	semidirect
55. C₂×D₄×C₉	Q₈	semidirect
83. #2564	C₉	direct (N × H)
148. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
150. #400	C₂×C₉	semidirect
151. #399	C₂×C₉	semidirect
152. #395	C₂×C₉	semidirect
153. #393	C₂×C₉	semidirect
154. #387	C₂×C₉	semidirect
156. #385	C₂×C₉	semidirect
157. #380	C₂×C₉	semidirect
158. C₂×#95	C₂×C₉	semidirect
294. C₂×D₄	Q₈×C₉	semidirect
346. C₉	#2564	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×C₂²⋊Q₈	2
C₂×C₄×D₄×C₉	2
C₉×#400	2
C₉×#399	2
C₉×#395	2
C₉×#393	2
C₉×#387	2
C₉×#386	2
C₉×#385	2
C₉×#380	2
C₂×C₉×#95	2
C₃×#2564	3

Subgroups — C9×#2564 #11767285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2564 #11767285