Subgroups — C₉×#2324 #11767045

Order 1152.

1002 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#390	C₂	1	2	yes	maximal, complemented
6	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#388	C₂	1	2	yes	maximal, complemented
8	C₉×#386	C₂	1	2	yes	maximal, complemented
9	C₉×#385	C₂	1	2	yes	maximal, complemented
10	C₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2324	C₃	1	1	yes	maximal, characteristic
13	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₉	C₂²	1	2	yes	—
15	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₉	C₂²	1	2	yes	—
17	C₉×#121	C₄	1	8	yes	complemented
18	C₄×D₄×C₉	—	2	4	no	—
19	C₉×#117	—	2	4	no	—
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	1	yes	characteristic
23	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
34	C₂×C₄²×C₉	C₂²	1	2	yes	—
35	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
36	C₉×#95	C₂²	1	2	yes	—
37	C₉×#95	C₂²	1	2	yes	—
38	C₉×#95	C₂²	1	2	yes	—
39	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
41	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
42	C₃×#390	C₂×C₃	1	1	yes	characteristic
43	C₃×#390	C₂×C₃	1	2	yes	—
44	C₃×#389	C₂×C₃	1	1	yes	characteristic
45	C₃×#388	C₂×C₃	1	2	yes	—
46	C₃×#386	C₂×C₃	1	2	yes	—
47	C₃×#385	C₂×C₃	1	2	yes	—
48	C₃×#380	C₂×C₃	1	1	yes	characteristic
49	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
50	C₂⁴×C₉	C₂³	1	1	yes	characteristic
51	C₂⁴×C₉	C₂³	1	2	yes	—
52	C₂×D₄×C₉	—	2	2	no	—
53	C₂×D₄×C₉	—	2	2	no	—
54	C₂×D₄×C₉	—	4	2	no	—
55	C₂×D₄×C₉	—	4	2	no	—
56	C₂×D₄×C₉	C₂×C₄	1	4	yes	—
57	C₂×D₄×C₉	C₂×C₄	1	8	yes	complemented
58	C₂²×C₄×C₉	—	2	2	no	—
59	C₂²×C₄×C₉	—	2	2	no	—
60	C₂²×C₄×C₉	—	2	4	no	—
61	C₂²×C₄×C₉	—	4	2	no	—
62	C₂²×C₄×C₉	—	4	2	no	—
63	C₂²×C₄×C₉	C₂×C₄	1	4	yes	complemented
64	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₉	C₂³	1	2	yes	—
67	C₂²×C₄×C₉	C₂³	1	2	yes	—
68	C₂²×C₄×C₉	C₂³	1	2	yes	—
69	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
73	C₉×C₄⋊C₄	—	2	2	no	—
74	C₉×C₄⋊C₄	—	2	2	no	—
75	C₉×C₄⋊C₄	—	2	2	no	—
76	C₉×C₄⋊C₄	—	2	2	no	—
77	C₉×C₄⋊C₄	—	4	2	no	—
78	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
79	C₉×C₂²⋊C₄	—	2	2	no	—
80	C₉×C₂²⋊C₄	—	2	2	no	—
81	C₉×C₂²⋊C₄	—	2	4	no	—
82	C₉×C₂²⋊C₄	—	4	2	no	—
83	C₉×C₂²⋊C₄	—	4	2	no	—
84	C₉×C₂²⋊C₄	—	4	2	no	—
85	C₉×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
86	C₄²×C₉	—	2	2	no	—
87	C₄²×C₉	—	4	2	no	—
88	C₄²×C₉	D₄	1	4	yes	complemented
89	#2324	C₉	1	1	yes	characteristic, direct product factor, Sylow
90	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
92	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
93	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
94	C₃×#121	C₃×C₄	1	8	yes	—
95	C₃×C₄×D₄	—	2	4	no	—
96	C₃×#117	—	2	4	no	—
97	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
102	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
105	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
107	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
108	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
109	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
110	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
112	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
113	C₃×#95	C₂²×C₃	1	2	yes	—
114	C₃×#95	C₂²×C₃	1	2	yes	—
115	C₃×#95	C₂²×C₃	1	2	yes	—
116	C₂³×C₉	—	2	1	no	—
117	C₂³×C₉	—	2	2	no	—
118	C₂³×C₉	—	2	1	no	—
119	C₂³×C₉	—	2	2	no	—
120	C₂³×C₉	—	2	1	no	—
121	C₂³×C₉	—	2	2	no	—
122	C₂³×C₉	—	2	2	no	—
123	C₂³×C₉	—	2	2	no	—
124	C₂³×C₉	—	2	1	no	—
125	C₂³×C₉	—	2	1	no	—
126	C₂³×C₉	—	2	1	no	—
127	C₂³×C₉	—	2	2	no	—
128	C₂³×C₉	C₂²×C₄	1	4	yes	—
129	C₂³×C₉	C₂²×C₄	1	2	yes	—
130	C₂³×C₉	C₂⁴	1	1	yes	characteristic
131	D₄×C₉	—	2	8	no	—
132	D₄×C₉	—	4	8	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	2	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	—	2	1	no	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	2	8	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	1	no	—
144	C₂×C₄×C₉	—	2	2	no	—
145	C₂×C₄×C₉	—	2	2	no	—
146	C₂×C₄×C₉	—	2	2	no	—
147	C₂×C₄×C₉	—	2	1	no	—
148	C₂×C₄×C₉	—	2	1	no	—
149	C₂×C₄×C₉	—	2	2	no	—
150	C₂×C₄×C₉	—	2	2	no	—
151	C₂×C₄×C₉	—	2	1	no	—
152	C₂×C₄×C₉	—	2	2	no	—
153	C₂×C₄×C₉	—	2	1	no	—
154	C₂×C₄×C₉	—	4	8	no	—
155	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
156	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
157	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
158	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
159	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
160	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
161	C₂×C₄×C₉	#41	1	2	yes	—
162	C₂×#121	C₂×C₉	1	1	yes	characteristic
163	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
164	C₂×#117	C₂×C₉	1	1	yes	characteristic, complemented
165	#390	C₂×C₉	1	1	yes	characteristic, complemented
166	#390	C₂×C₉	1	2	yes	complemented
167	#389	C₂×C₉	1	1	yes	characteristic, complemented
168	#388	C₂×C₉	1	2	yes	complemented
169	#386	C₂×C₉	1	2	yes	complemented
170	#385	C₂×C₉	1	2	yes	complemented
171	#380	C₂×C₉	1	1	yes	characteristic, complemented
172	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
173	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
174	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
175	C₂×C₃×D₄	—	2	2	no	—
176	C₂×C₃×D₄	—	2	2	no	—
177	C₂×C₃×D₄	—	4	2	no	—
178	C₂×C₃×D₄	—	4	2	no	—
179	C₂×C₃×D₄	C₂×C₃×C₄	1	4	yes	—
180	C₂×C₃×D₄	C₂×C₃×C₄	1	8	yes	—
181	C₂²×C₃×C₄	—	2	2	no	—
182	C₂²×C₃×C₄	—	2	2	no	—
183	C₂²×C₃×C₄	—	2	4	no	—
184	C₂²×C₃×C₄	—	4	2	no	—
185	C₂²×C₃×C₄	—	4	2	no	—
186	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
187	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
191	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
192	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
195	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
196	C₃×C₄⋊C₄	—	2	2	no	—
197	C₃×C₄⋊C₄	—	2	2	no	—
198	C₃×C₄⋊C₄	—	2	2	no	—
199	C₃×C₄⋊C₄	—	2	2	no	—
200	C₃×C₄⋊C₄	—	4	2	no	—
201	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
202	C₃×C₂²⋊C₄	—	2	2	no	—
203	C₃×C₂²⋊C₄	—	2	2	no	—
204	C₃×C₂²⋊C₄	—	2	4	no	—
205	C₃×C₂²⋊C₄	—	4	2	no	—
206	C₃×C₂²⋊C₄	—	4	2	no	—
207	C₃×C₂²⋊C₄	—	4	2	no	—
208	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
209	C₃×C₄²	—	2	2	no	—
210	C₃×C₄²	—	4	2	no	—
211	C₃×C₄²	C₃×D₄	1	4	yes	—
212	C₂²×C₉	—	2	2	no	—
213	C₂²×C₉	—	2	4	no	—
214	C₂²×C₉	—	2	2	no	—
215	C₂²×C₉	—	2	4	no	—
216	C₂²×C₉	—	2	2	no	—
217	C₂²×C₉	—	2	4	no	—
218	C₂²×C₉	—	4	2	no	—
219	C₂²×C₉	—	4	1	no	—
220	C₂²×C₉	—	4	1	no	—
221	C₂²×C₉	—	4	2	no	—
222	C₂²×C₉	—	4	1	no	—
223	C₂²×C₉	—	4	2	no	—
224	C₂²×C₉	—	4	1	no	—
225	C₂²×C₉	—	4	2	no	—
226	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
227	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
228	C₂²×C₉	C₂×#41	1	1	yes	characteristic
229	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
230	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
231	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
233	C₄×C₉	—	2	2	no	—
234	C₄×C₉	—	2	4	no	—
235	C₄×C₉	—	2	2	no	—
236	C₄×C₉	—	2	2	no	—
237	C₄×C₉	—	4	1	no	—
238	C₄×C₉	—	4	2	no	—
239	C₄×C₉	—	4	1	no	—
240	C₄×C₉	—	4	2	no	—
241	C₄×C₉	C₄×D₄	1	4	yes	—
242	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
243	C₂²×D₄	C₂²×C₉	1	2	yes	—
244	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
245	C₂³×C₄	C₂²×C₉	1	2	yes	—
246	#121	C₄×C₉	1	8	yes	complemented
247	C₄×D₄	—	2	4	no	—
248	#117	—	2	4	no	—
249	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
254	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
258	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
259	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
260	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
261	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
262	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
263	C₂×C₄²	C₂²×C₉	1	2	yes	—
264	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
265	#95	C₂²×C₉	1	2	yes	—
266	#95	C₂²×C₉	1	2	yes	—
267	#95	C₂²×C₉	1	2	yes	—
268	C₂³×C₃	—	2	1	no	—
269	C₂³×C₃	—	2	2	no	—
270	C₂³×C₃	—	2	1	no	—
271	C₂³×C₃	—	2	2	no	—
272	C₂³×C₃	—	2	1	no	—
273	C₂³×C₃	—	2	2	no	—
274	C₂³×C₃	—	2	2	no	—
275	C₂³×C₃	—	2	2	no	—
276	C₂³×C₃	—	2	1	no	—
277	C₂³×C₃	—	2	1	no	—
278	C₂³×C₃	—	2	1	no	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	C₂²×C₃×C₄	1	4	yes	—
281	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
282	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
283	C₃×D₄	—	2	8	no	—
284	C₃×D₄	—	4	8	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	2	1	no	—
292	C₂×C₃×C₄	—	2	1	no	—
293	C₂×C₃×C₄	—	2	8	no	—
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	1	no	—
300	C₂×C₃×C₄	—	2	1	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	1	no	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	—	2	1	no	—
306	C₂×C₃×C₄	—	4	8	no	—
307	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
308	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
309	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
310	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
311	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
312	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
313	C₂×C₃×C₄	C₃×#41	1	2	yes	—
314	C₂×C₉	—	4	2	no	—
315	C₂×C₉	—	4	4	no	—
316	C₂×C₉	C₂×C₄×D₄	1	1	yes	characteristic
317	C₂×C₉	#518	1	1	yes	characteristic
318	C₂×C₉	#520	1	1	yes	characteristic
319	C₂×C₉	#535	1	1	yes	characteristic
320	C₂×C₉	#537	1	1	yes	characteristic
321	C₂×C₉	#540	1	1	yes	characteristic
322	C₂×C₉	#542	1	1	yes	characteristic
323	C₂⁴	C₂³×C₉	1	1	yes	characteristic
324	C₂⁴	C₂³×C₉	1	2	yes	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	C₂×C₄×C₉	1	4	yes	—
330	C₂×D₄	C₂×C₄×C₉	1	8	yes	complemented
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	C₂×C₄×C₉	1	4	yes	complemented
337	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
338	C₂²×C₄	C₂³×C₉	1	2	yes	—
339	C₂²×C₄	C₂³×C₉	1	2	yes	—
340	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
341	C₂²×C₄	C₂³×C₉	1	2	yes	—
342	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
343	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
344	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
345	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	complemented
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	4	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₂²⋊C₄	C₂×C₄×C₉	1	8	yes	complemented
359	C₄²	—	2	2	no	—
360	C₄²	—	4	2	no	—
361	C₄²	D₄×C₉	1	4	yes	complemented
362	C₂²×C₃	—	2	2	no	—
363	C₂²×C₃	—	2	4	no	—
364	C₂²×C₃	—	2	2	no	—
365	C₂²×C₃	—	2	4	no	—
366	C₂²×C₃	—	2	2	no	—
367	C₂²×C₃	—	2	4	no	—
368	C₂²×C₃	—	4	2	no	—
369	C₂²×C₃	—	4	1	no	—
370	C₂²×C₃	—	4	1	no	—
371	C₂²×C₃	—	4	2	no	—
372	C₂²×C₃	—	4	1	no	—
373	C₂²×C₃	—	4	2	no	—
374	C₂²×C₃	—	4	1	no	—
375	C₂²×C₃	—	4	2	no	—
376	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
377	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
378	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
379	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
380	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
381	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
383	C₃×C₄	—	2	2	no	—
384	C₃×C₄	—	2	4	no	—
385	C₃×C₄	—	2	2	no	—
386	C₃×C₄	—	2	2	no	—
387	C₃×C₄	—	4	2	no	—
388	C₃×C₄	—	4	1	no	—
389	C₃×C₄	—	4	1	no	—
390	C₃×C₄	—	4	2	no	—
391	C₃×C₄	C₃×C₄×D₄	1	4	yes	—
392	C₉	#2324	1	1	yes	characteristic, direct product factor, Sylow
393	C₂³	—	2	1	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	1	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	2	2	no	—
405	C₂³	C₂²×C₄×C₉	1	4	yes	—
406	C₂³	C₂²×C₄×C₉	1	2	yes	—
407	C₂³	C₂⁴×C₉	1	1	yes	characteristic
408	D₄	—	2	8	no	—
409	D₄	—	4	8	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	8	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	4	8	no	—
432	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
433	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
434	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
435	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
436	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
437	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
438	C₂×C₄	C₉×#41	1	2	yes	—
439	C₂×C₃	—	4	2	no	—
440	C₂×C₃	—	4	4	no	—
441	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
442	C₂×C₃	C₃×#518	1	1	yes	characteristic
443	C₂×C₃	C₃×#520	1	1	yes	characteristic
444	C₂×C₃	C₃×#535	1	1	yes	characteristic
445	C₂×C₃	C₃×#537	1	1	yes	characteristic
446	C₂×C₃	C₃×#540	1	1	yes	characteristic
447	C₂×C₃	C₃×#542	1	1	yes	characteristic
448	C₂²	—	2	2	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	4	2	no	—
462	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
463	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
464	C₂²	C₂×C₉×#41	1	1	yes	characteristic
465	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
466	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
467	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
468	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	4	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	2	no	—
477	C₄	C₄×D₄×C₉	1	4	yes	—
478	C₃	C₃×#2324	1	1	yes	characteristic
479	C₂	—	4	2	no	—
480	C₂	—	4	4	no	—
481	C₂	C₂×C₄×D₄×C₉	1	1	yes	characteristic
482	C₂	C₉×#518	1	1	yes	characteristic
483	C₂	C₉×#520	1	1	yes	characteristic
484	C₂	C₉×#535	1	1	yes	characteristic
485	C₂	C₉×#537	1	1	yes	characteristic
486	C₂	C₉×#540	1	1	yes	characteristic
487	C₂	C₉×#542	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	C₂×C₃×#121	C₂×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×D₄×C₉	C₂	semidirect
3. C₂×C₉×#117	C₂	semidirect
4. C₉×#390	C₂	semidirect
5. C₉×#390	C₂	semidirect
6. C₉×#389	C₂	semidirect
7. C₉×#388	C₂	semidirect
8. C₉×#386	C₂	semidirect
9. C₉×#385	C₂	semidirect
10. C₉×#380	C₂	semidirect
11. C₄×C₉×C₄⋊C₄	C₂	semidirect
17. C₉×#121	C₄	semidirect
57. C₂×D₄×C₉	C₂×C₄	semidirect
63. C₂²×C₄×C₉	C₂×C₄	semidirect
78. C₉×C₄⋊C₄	C₂×C₄	semidirect
85. C₉×C₂²⋊C₄	C₂×C₄	semidirect
88. C₄²×C₉	D₄	semidirect
89. #2324	C₉	direct (N × H)
163. C₂×C₄×D₄	C₂×C₉	semidirect
164. C₂×#117	C₂×C₉	semidirect
165. #390	C₂×C₉	semidirect
166. #390	C₂×C₉	semidirect
167. #389	C₂×C₉	semidirect
168. #388	C₂×C₉	semidirect
169. #386	C₂×C₉	semidirect
170. #385	C₂×C₉	semidirect
171. #380	C₂×C₉	semidirect
172. C₄×C₄⋊C₄	C₂×C₉	semidirect
246. #121	C₄×C₉	semidirect
330. C₂×D₄	C₂×C₄×C₉	semidirect
336. C₂²×C₄	C₂×C₄×C₉	semidirect
351. C₄⋊C₄	C₂×C₄×C₉	semidirect
358. C₂²⋊C₄	C₂×C₄×C₉	semidirect
361. C₄²	D₄×C₉	semidirect
392. C₉	#2324	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×#121	2
C₂×C₄×D₄×C₉	2
C₂×C₉×#117	2
C₉×#390	2
C₉×#389	2
C₉×#388	2
C₉×#386	2
C₉×#385	2
C₉×#380	2
C₄×C₉×C₄⋊C₄	2
C₃×#2324	3

Subgroups — C9×#2324 #11767045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2324 #11767045