Subgroups — C₉×#2367 #11767088

Order 1152.

948 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#124	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic
4	C₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#390	C₂	1	1	yes	maximal, characteristic
6	C₉×#388	C₂	1	2	yes	maximal, complemented
7	C₉×#388	C₂	1	2	yes	maximal, complemented
8	C₉×#385	C₂	1	2	yes	maximal, complemented
9	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₃×#2367	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	C₉×#124	C₄	1	8	yes	complemented
17	C₄×Q₈×C₉	—	2	4	no	—
18	C₄×D₄×C₉	—	2	4	no	—
19	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₄²×C₉	C₂²	1	2	yes	—
30	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
31	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
32	C₂×C₄²×C₉	C₂²	1	2	yes	—
33	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
34	C₉×#95	C₂²	1	1	yes	characteristic
35	C₉×#95	C₂²	1	2	yes	—
36	C₉×#95	C₂²	1	2	yes	—
37	C₉×#95	C₂²	1	1	yes	characteristic
38	C₉×#95	C₂²	1	2	yes	—
39	C₂×C₃×#124	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
41	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
42	C₃×#391	C₂×C₃	1	1	yes	characteristic
43	C₃×#390	C₂×C₃	1	1	yes	characteristic
44	C₃×#388	C₂×C₃	1	2	yes	—
45	C₃×#388	C₂×C₃	1	2	yes	—
46	C₃×#385	C₂×C₃	1	2	yes	—
47	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
48	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
49	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	2	yes	—
50	C₂⁴×C₉	C₂³	1	2	yes	—
51	C₂×Q₈×C₉	—	2	2	no	—
52	C₂×Q₈×C₉	—	2	2	no	—
53	C₂×Q₈×C₉	C₂×C₄	1	4	yes	complemented
54	C₂×D₄×C₉	—	2	2	no	—
55	C₂×D₄×C₉	—	2	2	no	—
56	C₂×D₄×C₉	C₂×C₄	1	4	yes	—
57	C₂²×C₄×C₉	—	2	4	no	—
58	C₂²×C₄×C₉	—	2	4	no	—
59	C₂²×C₄×C₉	—	4	2	no	—
60	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₉	C₂³	1	2	yes	—
63	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₉	C₂³	1	2	yes	—
66	C₂²×C₄×C₉	C₂³	1	2	yes	—
67	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₉×C₄⋊C₄	—	2	4	no	—
71	C₉×C₄⋊C₄	—	2	2	no	—
72	C₉×C₄⋊C₄	—	2	2	no	—
73	C₉×C₄⋊C₄	—	2	2	no	—
74	C₉×C₄⋊C₄	D₄	1	4	yes	—
75	C₉×C₂²⋊C₄	—	2	4	no	—
76	C₉×C₂²⋊C₄	—	2	4	no	—
77	C₉×C₂²⋊C₄	—	4	2	no	—
78	C₉×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
79	C₉×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
80	C₄²×C₉	—	2	2	no	—
81	C₄²×C₉	—	2	4	no	—
82	C₄²×C₉	—	2	2	no	—
83	C₄²×C₉	—	4	2	no	—
84	C₄²×C₉	C₂×C₄	1	4	yes	complemented
85	#2367	C₉	1	1	yes	characteristic, direct product factor, Sylow
86	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
87	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
88	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
89	C₃×#124	C₃×C₄	1	8	yes	—
90	C₃×C₄×Q₈	—	2	4	no	—
91	C₃×C₄×D₄	—	2	4	no	—
92	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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×C₄⋊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	2	yes	—
100	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
101	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
102	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
103	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
106	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
107	C₃×#95	C₂²×C₃	1	1	yes	characteristic
108	C₃×#95	C₂²×C₃	1	2	yes	—
109	C₃×#95	C₂²×C₃	1	2	yes	—
110	C₃×#95	C₂²×C₃	1	1	yes	characteristic
111	C₃×#95	C₂²×C₃	1	2	yes	—
112	C₂³×C₉	—	2	2	no	—
113	C₂³×C₉	—	2	2	no	—
114	C₂³×C₉	—	2	2	no	—
115	C₂³×C₉	—	2	2	no	—
116	C₂³×C₉	—	2	2	no	—
117	C₂³×C₉	—	2	2	no	—
118	C₂³×C₉	C₂²×C₄	1	4	yes	—
119	C₂³×C₉	C₂⁴	1	1	yes	characteristic
120	Q₈×C₉	—	2	8	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	1	no	—
126	C₂×C₄×C₉	—	2	1	no	—
127	C₂×C₄×C₉	—	2	2	no	—
128	C₂×C₄×C₉	—	2	2	no	—
129	C₂×C₄×C₉	—	2	1	no	—
130	C₂×C₄×C₉	—	2	2	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	2	1	no	—
133	C₂×C₄×C₉	—	2	1	no	—
134	C₂×C₄×C₉	—	2	1	no	—
135	C₂×C₄×C₉	—	2	1	no	—
136	C₂×C₄×C₉	—	2	2	no	—
137	C₂×C₄×C₉	—	2	1	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	—	2	2	no	—
140	C₂×C₄×C₉	—	2	2	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	4	8	no	—
144	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
145	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
146	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
147	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
148	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
149	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
150	C₂×C₄×C₉	#41	1	2	yes	—
151	C₂×C₄×C₉	#41	1	2	yes	—
152	C₂×C₄×C₉	#41	1	2	yes	—
153	C₂×#124	C₂×C₉	1	1	yes	characteristic
154	C₂×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
155	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic
156	#391	C₂×C₉	1	1	yes	characteristic, complemented
157	#390	C₂×C₉	1	1	yes	characteristic
158	#388	C₂×C₉	1	2	yes	complemented
159	#388	C₂×C₉	1	2	yes	complemented
160	#385	C₂×C₉	1	2	yes	complemented
161	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
162	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
163	C₄×C₂²⋊C₄	C₂×C₉	1	2	yes	complemented
164	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
165	C₂×C₃×Q₈	—	2	2	no	—
166	C₂×C₃×Q₈	—	2	2	no	—
167	C₂×C₃×Q₈	C₂×C₃×C₄	1	4	yes	—
168	C₂×C₃×D₄	—	2	2	no	—
169	C₂×C₃×D₄	—	2	2	no	—
170	C₂×C₃×D₄	C₂×C₃×C₄	1	4	yes	—
171	C₂²×C₃×C₄	—	2	4	no	—
172	C₂²×C₃×C₄	—	2	4	no	—
173	C₂²×C₃×C₄	—	4	2	no	—
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	1	yes	characteristic
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	2	yes	—
180	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
181	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
184	C₃×C₄⋊C₄	—	2	4	no	—
185	C₃×C₄⋊C₄	—	2	2	no	—
186	C₃×C₄⋊C₄	—	2	2	no	—
187	C₃×C₄⋊C₄	—	2	2	no	—
188	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
189	C₃×C₂²⋊C₄	—	2	4	no	—
190	C₃×C₂²⋊C₄	—	2	4	no	—
191	C₃×C₂²⋊C₄	—	4	2	no	—
192	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
193	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
194	C₃×C₄²	—	2	2	no	—
195	C₃×C₄²	—	2	4	no	—
196	C₃×C₄²	—	2	2	no	—
197	C₃×C₄²	—	4	2	no	—
198	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
199	C₂²×C₉	—	2	4	no	—
200	C₂²×C₉	—	2	4	no	—
201	C₂²×C₉	—	2	4	no	—
202	C₂²×C₉	—	4	2	no	—
203	C₂²×C₉	—	4	2	no	—
204	C₂²×C₉	—	4	2	no	—
205	C₂²×C₉	—	4	2	no	—
206	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
207	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
208	C₂²×C₉	C₂×#41	1	1	yes	characteristic
209	C₂²×C₉	C₂×#41	1	1	yes	characteristic
210	C₂²×C₉	C₂×#41	1	1	yes	characteristic
211	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
213	C₄×C₉	—	2	4	no	—
214	C₄×C₉	—	2	2	no	—
215	C₄×C₉	—	2	2	no	—
216	C₄×C₉	—	2	2	no	—
217	C₄×C₉	—	2	4	no	—
218	C₄×C₉	—	2	2	no	—
219	C₄×C₉	—	4	1	no	—
220	C₄×C₉	—	4	1	no	—
221	C₄×C₉	—	4	2	no	—
222	C₄×C₉	C₄×D₄	1	4	yes	—
223	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
224	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
225	C₂³×C₄	C₂²×C₉	1	2	yes	—
226	#124	C₄×C₉	1	8	yes	complemented
227	C₄×Q₈	—	2	4	no	—
228	C₄×D₄	—	2	4	no	—
229	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
230	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
234	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
235	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
236	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
237	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
238	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
239	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
240	C₂×C₄²	C₂²×C₉	1	2	yes	—
241	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
242	C₂×C₄²	C₂²×C₉	1	2	yes	—
243	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
244	#95	C₂²×C₉	1	1	yes	characteristic
245	#95	C₂²×C₉	1	2	yes	—
246	#95	C₂²×C₉	1	2	yes	—
247	#95	C₂²×C₉	1	1	yes	characteristic
248	#95	C₂²×C₉	1	2	yes	—
249	C₂³×C₃	—	2	2	no	—
250	C₂³×C₃	—	2	2	no	—
251	C₂³×C₃	—	2	2	no	—
252	C₂³×C₃	—	2	2	no	—
253	C₂³×C₃	—	2	2	no	—
254	C₂³×C₃	—	2	2	no	—
255	C₂³×C₃	C₂²×C₃×C₄	1	4	yes	—
256	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
257	C₃×Q₈	—	2	8	no	—
258	C₃×D₄	—	2	8	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	1	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	1	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	2	1	no	—
280	C₂×C₃×C₄	—	4	8	no	—
281	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
282	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
283	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
284	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
285	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
286	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
287	C₂×C₃×C₄	C₃×#41	1	2	yes	—
288	C₂×C₃×C₄	C₃×#41	1	2	yes	—
289	C₂×C₃×C₄	C₃×#41	1	2	yes	—
290	C₂×C₉	—	4	4	no	—
291	C₂×C₉	C₂×C₄×D₄	1	1	yes	characteristic
292	C₂×C₉	C₄×#41	1	1	yes	characteristic
293	C₂×C₉	#520	1	1	yes	characteristic
294	C₂×C₉	#546	1	1	yes	characteristic
295	C₂×C₉	#548	1	1	yes	characteristic
296	C₂×C₉	#556	1	1	yes	characteristic
297	C₂×C₉	#559	1	1	yes	characteristic
298	C₂⁴	C₂³×C₉	1	2	yes	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	C₂×C₄×C₉	1	4	yes	complemented
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	C₂×C₄×C₉	1	4	yes	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
309	C₂²×C₄	C₂³×C₉	1	2	yes	—
310	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
311	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
312	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
313	C₂²×C₄	C₂³×C₉	1	2	yes	—
314	C₂²×C₄	C₂³×C₉	1	2	yes	—
315	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
316	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
317	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	D₄×C₉	1	4	yes	—
323	C₂²⋊C₄	—	2	4	no	—
324	C₂²⋊C₄	—	2	4	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	C₂×C₄×C₉	1	8	yes	complemented
327	C₂²⋊C₄	C₂×C₄×C₉	1	8	yes	complemented
328	C₄²	—	2	2	no	—
329	C₄²	—	2	4	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	4	2	no	—
332	C₄²	C₂×C₄×C₉	1	4	yes	complemented
333	C₂²×C₃	—	2	4	no	—
334	C₂²×C₃	—	2	4	no	—
335	C₂²×C₃	—	2	4	no	—
336	C₂²×C₃	—	4	2	no	—
337	C₂²×C₃	—	4	2	no	—
338	C₂²×C₃	—	4	2	no	—
339	C₂²×C₃	—	4	2	no	—
340	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
341	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
342	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
343	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
344	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
345	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
347	C₃×C₄	—	2	4	no	—
348	C₃×C₄	—	2	2	no	—
349	C₃×C₄	—	2	2	no	—
350	C₃×C₄	—	2	2	no	—
351	C₃×C₄	—	2	4	no	—
352	C₃×C₄	—	2	2	no	—
353	C₃×C₄	—	4	2	no	—
354	C₃×C₄	—	4	1	no	—
355	C₃×C₄	—	4	1	no	—
356	C₃×C₄	C₃×C₄×D₄	1	4	yes	—
357	C₉	#2367	1	1	yes	characteristic, direct product factor, Sylow
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	2	no	—
364	C₂³	C₂²×C₄×C₉	1	4	yes	—
365	C₂³	C₂⁴×C₉	1	1	yes	characteristic
366	Q₈	—	2	8	no	—
367	D₄	—	2	8	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
391	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
392	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
393	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
394	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
395	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
396	C₂×C₄	C₉×#41	1	2	yes	—
397	C₂×C₄	C₉×#41	1	2	yes	—
398	C₂×C₄	C₉×#41	1	2	yes	—
399	C₂×C₃	—	4	4	no	—
400	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
401	C₂×C₃	C₃×C₄×#41	1	1	yes	characteristic
402	C₂×C₃	C₃×#520	1	1	yes	characteristic
403	C₂×C₃	C₃×#546	1	1	yes	characteristic
404	C₂×C₃	C₃×#548	1	1	yes	characteristic
405	C₂×C₃	C₃×#556	1	1	yes	characteristic
406	C₂×C₃	C₃×#559	1	1	yes	characteristic
407	C₂²	—	2	4	no	—
408	C₂²	—	2	4	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
415	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
416	C₂²	C₂×C₉×#41	1	1	yes	characteristic
417	C₂²	C₂×C₉×#41	1	1	yes	characteristic
418	C₂²	C₂×C₉×#41	1	1	yes	characteristic
419	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
420	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	4	no	—
426	C₄	—	2	2	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	1	no	—
429	C₄	—	4	2	no	—
430	C₄	C₄×D₄×C₉	1	4	yes	—
431	C₃	C₃×#2367	1	1	yes	characteristic
432	C₂	—	4	4	no	—
433	C₂	C₂×C₄×D₄×C₉	1	1	yes	characteristic
434	C₂	C₄×C₉×#41	1	1	yes	characteristic
435	C₂	C₉×#520	1	1	yes	characteristic
436	C₂	C₉×#546	1	1	yes	characteristic
437	C₂	C₉×#548	1	1	yes	characteristic
438	C₂	C₉×#556	1	1	yes	characteristic
439	C₂	C₉×#559	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂²×C₃×D₄	C₂²×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₈×C₉	C₂	semidirect
4. C₉×#391	C₂	semidirect
6. C₉×#388	C₂	semidirect
7. C₉×#388	C₂	semidirect
8. C₉×#385	C₂	semidirect
9. C₄×C₉×C₄⋊C₄	C₂	semidirect
10. C₄×C₉×C₄⋊C₄	C₂	semidirect
11. C₄×C₉×C₂²⋊C₄	C₂	semidirect
16. C₉×#124	C₄	semidirect
53. C₂×Q₈×C₉	C₂×C₄	semidirect
78. C₉×C₂²⋊C₄	C₂×C₄	semidirect
79. C₉×C₂²⋊C₄	C₂×C₄	semidirect
84. C₄²×C₉	C₂×C₄	semidirect
85. #2367	C₉	direct (N × H)
154. C₂×C₄×Q₈	C₂×C₉	semidirect
156. #391	C₂×C₉	semidirect
158. #388	C₂×C₉	semidirect
159. #388	C₂×C₉	semidirect
160. #385	C₂×C₉	semidirect
161. C₄×C₄⋊C₄	C₂×C₉	semidirect
162. C₄×C₄⋊C₄	C₂×C₉	semidirect
163. C₄×C₂²⋊C₄	C₂×C₉	semidirect
226. #124	C₄×C₉	semidirect
301. C₂×Q₈	C₂×C₄×C₉	semidirect
326. C₂²⋊C₄	C₂×C₄×C₉	semidirect
327. C₂²⋊C₄	C₂×C₄×C₉	semidirect
332. C₄²	C₂×C₄×C₉	semidirect
357. C₉	#2367	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×#124	2
C₂×C₄×Q₈×C₉	2
C₂×C₄×D₄×C₉	2
C₉×#391	2
C₉×#390	2
C₉×#388	2
C₉×#385	2
C₄×C₉×C₄⋊C₄	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2367	3

Subgroups — C9×#2367 #11767088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2367 #11767088