Subgroups — C₉×#2408 #11767129

Order 1152.

1848 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#121	C₂	1	2	yes	maximal, complemented
3	C₂×C₉×#120	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#394	C₂	1	2	yes	maximal, complemented
6	C₉×#392	C₂	1	2	yes	maximal, complemented
7	C₉×#390	C₂	1	2	yes	maximal, complemented
8	C₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#379	C₂	1	2	yes	maximal, complemented
10	C₃×#2408	C₃	1	1	yes	maximal, characteristic
11	C₂⁵×C₉	C₂²	1	2	yes	—
12	C₂²×D₄×C₉	—	2	8	no	—
13	C₂²×D₄×C₉	—	2	4	no	—
14	C₂²×D₄×C₉	C₂²	1	2	yes	—
15	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
16	C₂²×D₄×C₉	C₂²	1	2	yes	—
17	C₂²×D₄×C₉	C₂²	1	4	yes	complemented
18	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
20	C₉×#121	—	2	8	no	—
21	C₉×#120	—	2	8	no	—
22	C₄×D₄×C₉	—	2	4	no	—
23	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
24	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
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	4	yes	complemented
28	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
29	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
31	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
32	C₉×#95	C₂²	1	2	yes	complemented
33	C₂³×C₃×D₄	C₂×C₃	1	1	yes	characteristic
34	C₂×C₃×#121	C₂×C₃	1	2	yes	—
35	C₂×C₃×#120	C₂×C₃	1	2	yes	—
36	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
37	C₃×#394	C₂×C₃	1	2	yes	—
38	C₃×#392	C₂×C₃	1	2	yes	—
39	C₃×#390	C₂×C₃	1	2	yes	—
40	C₃×#380	C₂×C₃	1	1	yes	characteristic
41	C₃×#379	C₂×C₃	1	2	yes	—
42	C₂⁴×C₉	—	2	8	no	—
43	C₂⁴×C₉	—	2	4	no	—
44	C₂⁴×C₉	—	2	4	no	—
45	C₂⁴×C₉	—	2	4	no	—
46	C₂⁴×C₉	—	4	4	no	—
47	C₂⁴×C₉	C₂³	1	4	yes	—
48	C₂⁴×C₉	C₂³	1	1	yes	characteristic
49	C₂⁴×C₉	C₂³	1	1	yes	characteristic
50	C₂×D₄×C₉	—	2	32	no	—
51	C₂×D₄×C₉	—	2	2	no	—
52	C₂×D₄×C₉	—	2	8	no	—
53	C₂×D₄×C₉	—	2	2	no	—
54	C₂×D₄×C₉	—	2	8	no	—
55	C₂×D₄×C₉	—	2	8	no	—
56	C₂×D₄×C₉	—	2	4	no	—
57	C₂×D₄×C₉	—	2	4	no	—
58	C₂×D₄×C₉	—	2	4	no	—
59	C₂×D₄×C₉	—	4	4	no	—
60	C₂×D₄×C₉	D₄	1	8	yes	complemented
61	C₂×D₄×C₉	D₄	1	4	yes	complemented
62	C₂²×C₄×C₉	—	2	4	no	—
63	C₂²×C₄×C₉	—	2	2	no	—
64	C₂²×C₄×C₉	—	2	4	no	—
65	C₂²×C₄×C₉	D₄	1	4	yes	complemented
66	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₉	C₂³	1	4	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	C₉×C₄⋊C₄	—	2	2	no	—
73	C₉×C₄⋊C₄	—	2	4	no	—
74	C₉×C₂²⋊C₄	—	2	2	no	—
75	C₉×C₂²⋊C₄	—	2	4	no	—
76	C₉×C₂²⋊C₄	—	2	8	no	—
77	C₉×C₂²⋊C₄	—	2	2	no	—
78	C₉×C₂²⋊C₄	—	2	8	no	—
79	C₉×C₂²⋊C₄	—	4	4	no	—
80	C₄²×C₉	—	2	2	no	—
81	#2408	C₉	1	1	yes	characteristic, direct product factor, Sylow
82	C₂⁵×C₃	C₂²×C₃	1	2	yes	—
83	C₂²×C₃×D₄	—	2	8	no	—
84	C₂²×C₃×D₄	—	2	4	no	—
85	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
86	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
87	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
88	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
89	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
91	C₃×#121	—	2	8	no	—
92	C₃×#120	—	2	8	no	—
93	C₃×C₄×D₄	—	2	4	no	—
94	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
95	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	4	yes	—
99	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
100	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
102	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
103	C₃×#95	C₂²×C₃	1	2	yes	—
104	C₂³×C₉	—	2	2	no	—
105	C₂³×C₉	—	2	2	no	—
106	C₂³×C₉	—	2	16	no	—
107	C₂³×C₉	—	2	1	no	—
108	C₂³×C₉	—	2	4	no	—
109	C₂³×C₉	—	2	2	no	—
110	C₂³×C₉	—	2	4	no	—
111	C₂³×C₉	—	2	4	no	—
112	C₂³×C₉	—	2	1	no	—
113	C₂³×C₉	—	2	4	no	—
114	C₂³×C₉	—	2	4	no	—
115	C₂³×C₉	—	2	2	no	—
116	C₂³×C₉	—	2	4	no	—
117	C₂³×C₉	—	4	16	no	—
118	C₂³×C₉	—	4	16	no	—
119	C₂³×C₉	—	4	8	no	—
120	C₂³×C₉	—	4	8	no	—
121	C₂³×C₉	C₂×D₄	1	8	yes	—
122	C₂³×C₉	C₂×D₄	1	2	yes	—
123	C₂³×C₉	C₂×D₄	1	2	yes	—
124	C₂³×C₉	C₂×D₄	1	2	yes	complemented
125	C₂³×C₉	#41	1	2	yes	—
126	C₂³×C₉	C₂⁴	1	1	yes	characteristic
127	D₄×C₉	—	2	16	no	—
128	D₄×C₉	—	2	8	no	—
129	D₄×C₉	—	2	16	no	—
130	D₄×C₉	—	4	16	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	2	2	no	—
133	C₂×C₄×C₉	—	2	1	no	—
134	C₂×C₄×C₉	—	2	8	no	—
135	C₂×C₄×C₉	—	2	1	no	—
136	C₂×C₄×C₉	—	2	2	no	—
137	C₂×C₄×C₉	—	2	4	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	—	2	4	no	—
140	C₂×C₄×C₉	—	2	2	no	—
141	C₂×C₄×C₉	—	2	4	no	—
142	C₂×C₄×C₉	—	4	4	no	—
143	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
144	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
145	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
146	C₂×C₄×C₉	C₂×D₄	1	2	yes	complemented
147	C₂³×D₄	C₂×C₉	1	1	yes	characteristic, complemented
148	C₂×#121	C₂×C₉	1	2	yes	complemented
149	C₂×#120	C₂×C₉	1	2	yes	complemented
150	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
151	#394	C₂×C₉	1	2	yes	complemented
152	#392	C₂×C₉	1	2	yes	complemented
153	#390	C₂×C₉	1	2	yes	complemented
154	#380	C₂×C₉	1	1	yes	characteristic, complemented
155	#379	C₂×C₉	1	2	yes	complemented
156	C₂⁴×C₃	—	2	8	no	—
157	C₂⁴×C₃	—	2	4	no	—
158	C₂⁴×C₃	—	2	4	no	—
159	C₂⁴×C₃	—	2	4	no	—
160	C₂⁴×C₃	—	4	4	no	—
161	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
162	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
163	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
164	C₂×C₃×D₄	—	2	32	no	—
165	C₂×C₃×D₄	—	2	2	no	—
166	C₂×C₃×D₄	—	2	8	no	—
167	C₂×C₃×D₄	—	2	2	no	—
168	C₂×C₃×D₄	—	2	8	no	—
169	C₂×C₃×D₄	—	2	8	no	—
170	C₂×C₃×D₄	—	2	4	no	—
171	C₂×C₃×D₄	—	2	4	no	—
172	C₂×C₃×D₄	—	2	4	no	—
173	C₂×C₃×D₄	—	4	4	no	—
174	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
175	C₂×C₃×D₄	C₃×D₄	1	8	yes	—
176	C₂²×C₃×C₄	—	2	4	no	—
177	C₂²×C₃×C₄	—	2	2	no	—
178	C₂²×C₃×C₄	—	2	4	no	—
179	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
180	C₂²×C₃×C₄	C₂³×C₃	1	4	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	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
186	C₃×C₄⋊C₄	—	2	2	no	—
187	C₃×C₄⋊C₄	—	2	4	no	—
188	C₃×C₂²⋊C₄	—	2	2	no	—
189	C₃×C₂²⋊C₄	—	2	4	no	—
190	C₃×C₂²⋊C₄	—	2	8	no	—
191	C₃×C₂²⋊C₄	—	2	2	no	—
192	C₃×C₂²⋊C₄	—	2	8	no	—
193	C₃×C₂²⋊C₄	—	4	4	no	—
194	C₃×C₄²	—	2	2	no	—
195	C₂²×C₉	—	2	2	no	—
196	C₂²×C₉	—	2	2	no	—
197	C₂²×C₉	—	2	4	no	—
198	C₂²×C₉	—	2	4	no	—
199	C₂²×C₉	—	2	8	no	—
200	C₂²×C₉	—	2	2	no	—
201	C₂²×C₉	—	2	4	no	—
202	C₂²×C₉	—	2	8	no	—
203	C₂²×C₉	—	2	8	no	—
204	C₂²×C₉	—	4	32	no	—
205	C₂²×C₉	—	4	1	no	—
206	C₂²×C₉	—	4	4	no	—
207	C₂²×C₉	—	4	1	no	—
208	C₂²×C₉	—	4	4	no	—
209	C₂²×C₉	—	4	4	no	—
210	C₂²×C₉	—	4	2	no	—
211	C₂²×C₉	—	4	4	no	—
212	C₂²×C₉	#121	1	4	yes	complemented
213	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
214	C₂²×C₉	C₂²×D₄	1	2	yes	—
215	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
216	C₂²×C₉	C₂×#41	1	1	yes	characteristic
217	C₂²×C₉	H(5,𝔽₂)	1	2	yes	—
218	C₄×C₉	—	2	2	no	—
219	C₄×C₉	—	2	2	no	—
220	C₄×C₉	—	4	1	no	—
221	C₄×C₉	—	4	1	no	—
222	C₄×C₉	—	4	4	no	—
223	C₄×C₉	#120	1	4	yes	complemented
224	C₂⁵	C₂²×C₉	1	2	yes	—
225	C₂²×D₄	—	2	8	no	—
226	C₂²×D₄	—	2	4	no	—
227	C₂²×D₄	C₂²×C₉	1	2	yes	—
228	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
229	C₂²×D₄	C₂²×C₉	1	2	yes	—
230	C₂²×D₄	C₂²×C₉	1	4	yes	complemented
231	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
232	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
233	#121	—	2	8	no	—
234	#120	—	2	8	no	—
235	C₄×D₄	—	2	4	no	—
236	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
237	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
238	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
240	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
241	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	complemented
242	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	complemented
243	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	complemented
244	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic, complemented
245	#95	C₂²×C₉	1	2	yes	complemented
246	C₂³×C₃	—	2	2	no	—
247	C₂³×C₃	—	2	2	no	—
248	C₂³×C₃	—	2	16	no	—
249	C₂³×C₃	—	2	1	no	—
250	C₂³×C₃	—	2	4	no	—
251	C₂³×C₃	—	2	2	no	—
252	C₂³×C₃	—	2	4	no	—
253	C₂³×C₃	—	2	4	no	—
254	C₂³×C₃	—	2	1	no	—
255	C₂³×C₃	—	2	4	no	—
256	C₂³×C₃	—	2	4	no	—
257	C₂³×C₃	—	2	2	no	—
258	C₂³×C₃	—	2	4	no	—
259	C₂³×C₃	—	4	16	no	—
260	C₂³×C₃	—	4	16	no	—
261	C₂³×C₃	—	4	8	no	—
262	C₂³×C₃	—	4	8	no	—
263	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
264	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
265	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
266	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
267	C₂³×C₃	C₃×#41	1	2	yes	—
268	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
269	C₃×D₄	—	2	16	no	—
270	C₃×D₄	—	2	8	no	—
271	C₃×D₄	—	2	16	no	—
272	C₃×D₄	—	4	16	no	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	8	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	4	no	—
280	C₂×C₃×C₄	—	2	1	no	—
281	C₂×C₃×C₄	—	2	4	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	—	2	4	no	—
284	C₂×C₃×C₄	—	4	4	no	—
285	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
286	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
287	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
288	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
289	C₂×C₉	—	2	4	no	—
290	C₂×C₉	—	4	2	no	—
291	C₂×C₉	—	4	8	no	—
292	C₂×C₉	C₂×#120	1	1	yes	characteristic
293	C₂×C₉	C₂×#121	1	1	yes	characteristic
294	C₂×C₉	#535	1	1	yes	characteristic
295	C₂×C₉	D₄²	1	2	yes	—
296	C₂×C₉	#546	1	2	yes	—
297	C₂⁴	—	2	8	no	—
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	2	4	no	—
300	C₂⁴	—	2	4	no	—
301	C₂⁴	—	4	4	no	—
302	C₂⁴	C₂³×C₉	1	4	yes	—
303	C₂⁴	C₂³×C₉	1	1	yes	characteristic
304	C₂⁴	C₂³×C₉	1	1	yes	characteristic
305	C₂×D₄	—	2	32	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	8	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	8	no	—
310	C₂×D₄	—	2	8	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	4	4	no	—
315	C₂×D₄	D₄×C₉	1	8	yes	complemented
316	C₂×D₄	D₄×C₉	1	4	yes	complemented
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	D₄×C₉	1	4	yes	complemented
321	C₂²×C₄	C₂³×C₉	1	4	yes	—
322	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
323	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
324	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
325	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
326	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₂²⋊C₄	—	2	8	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₂²⋊C₄	—	2	8	no	—
334	C₂²⋊C₄	—	4	4	no	—
335	C₄²	—	2	2	no	—
336	C₂²×C₃	—	2	2	no	—
337	C₂²×C₃	—	2	2	no	—
338	C₂²×C₃	—	2	4	no	—
339	C₂²×C₃	—	2	4	no	—
340	C₂²×C₃	—	2	8	no	—
341	C₂²×C₃	—	2	2	no	—
342	C₂²×C₃	—	2	4	no	—
343	C₂²×C₃	—	2	8	no	—
344	C₂²×C₃	—	2	8	no	—
345	C₂²×C₃	—	4	32	no	—
346	C₂²×C₃	—	4	1	no	—
347	C₂²×C₃	—	4	4	no	—
348	C₂²×C₃	—	4	4	no	—
349	C₂²×C₃	—	4	1	no	—
350	C₂²×C₃	—	4	4	no	—
351	C₂²×C₃	—	4	4	no	—
352	C₂²×C₃	—	4	2	no	—
353	C₂²×C₃	C₃×#121	1	4	yes	—
354	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
355	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
356	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
357	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
358	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
359	C₃×C₄	—	2	2	no	—
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	4	1	no	—
362	C₃×C₄	—	4	1	no	—
363	C₃×C₄	—	4	4	no	—
364	C₃×C₄	C₃×#120	1	4	yes	—
365	C₉	#2408	1	1	yes	characteristic, direct product factor, Sylow
366	C₂³	—	2	2	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	16	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	4	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	4	no	—
373	C₂³	—	2	4	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	2	4	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	4	16	no	—
380	C₂³	—	4	16	no	—
381	C₂³	—	4	8	no	—
382	C₂³	—	4	8	no	—
383	C₂³	C₂×D₄×C₉	1	8	yes	—
384	C₂³	C₂×D₄×C₉	1	2	yes	—
385	C₂³	C₂×D₄×C₉	1	2	yes	—
386	C₂³	C₂×D₄×C₉	1	2	yes	complemented
387	C₂³	C₉×#41	1	2	yes	—
388	C₂³	C₂⁴×C₉	1	1	yes	characteristic
389	D₄	—	2	16	no	—
390	D₄	—	2	8	no	—
391	D₄	—	2	16	no	—
392	D₄	—	4	16	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
406	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
407	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
408	C₂×C₄	C₂×D₄×C₉	1	2	yes	complemented
409	C₂×C₃	—	2	4	no	—
410	C₂×C₃	—	4	8	no	—
411	C₂×C₃	—	4	2	no	—
412	C₂×C₃	C₂×C₃×#120	1	1	yes	characteristic
413	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
414	C₂×C₃	C₃×#535	1	1	yes	characteristic
415	C₂×C₃	C₃×D₄²	1	2	yes	—
416	C₂×C₃	C₃×#546	1	2	yes	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	8	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	4	no	—
424	C₂²	—	2	8	no	—
425	C₂²	—	2	8	no	—
426	C₂²	—	4	32	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	2	no	—
434	C₂²	C₉×#121	1	4	yes	complemented
435	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
436	C₂²	C₂²×D₄×C₉	1	2	yes	—
437	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
438	C₂²	C₂×C₉×#41	1	1	yes	characteristic
439	C₂²	C₉×H(5,𝔽₂)	1	2	yes	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	1	no	—
443	C₄	—	4	1	no	—
444	C₄	—	4	4	no	—
445	C₄	C₉×#120	1	4	yes	complemented
446	C₃	C₃×#2408	1	1	yes	characteristic
447	C₂	—	2	4	no	—
448	C₂	—	4	8	no	—
449	C₂	—	4	2	no	—
450	C₂	C₂×C₉×#120	1	1	yes	characteristic
451	C₂	C₂×C₉×#121	1	1	yes	characteristic
452	C₂	C₉×#535	1	1	yes	characteristic
453	C₂	D₄²×C₉	1	2	yes	—
454	C₂	C₉×#546	1	2	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₃×#2408	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. C₂³×D₄×C₉	C₂	semidirect
2. C₂×C₉×#121	C₂	semidirect
3. C₂×C₉×#120	C₂	semidirect
4. C₂×C₄×D₄×C₉	C₂	semidirect
5. C₉×#394	C₂	semidirect
6. C₉×#392	C₂	semidirect
7. C₉×#390	C₂	semidirect
8. C₉×#380	C₂	semidirect
9. C₉×#379	C₂	semidirect
17. C₂²×D₄×C₉	C₂²	semidirect
19. C₂³×C₄×C₉	C₂²	semidirect
23. C₂×C₉×C₄⋊C₄	C₂²	semidirect
24. C₂×C₉×C₄⋊C₄	C₂²	semidirect
27. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
28. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
29. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
30. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
31. C₂×C₄²×C₉	C₂²	semidirect
32. C₉×#95	C₂²	semidirect
60. C₂×D₄×C₉	D₄	semidirect
61. C₂×D₄×C₉	D₄	semidirect
65. C₂²×C₄×C₉	D₄	semidirect
81. #2408	C₉	direct (N × H)
124. C₂³×C₉	C₂×D₄	semidirect
146. C₂×C₄×C₉	C₂×D₄	semidirect
147. C₂³×D₄	C₂×C₉	semidirect
148. C₂×#121	C₂×C₉	semidirect
149. C₂×#120	C₂×C₉	semidirect
150. C₂×C₄×D₄	C₂×C₉	semidirect
151. #394	C₂×C₉	semidirect
152. #392	C₂×C₉	semidirect
153. #390	C₂×C₉	semidirect
154. #380	C₂×C₉	semidirect
155. #379	C₂×C₉	semidirect
212. C₂²×C₉	#121	semidirect
223. C₄×C₉	#120	semidirect
230. C₂²×D₄	C₂²×C₉	semidirect
232. C₂³×C₄	C₂²×C₉	semidirect
236. C₂×C₄⋊C₄	C₂²×C₉	semidirect
237. C₂×C₄⋊C₄	C₂²×C₉	semidirect
240. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
241. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
242. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
243. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
244. C₂×C₄²	C₂²×C₉	semidirect
245. #95	C₂²×C₉	semidirect
315. C₂×D₄	D₄×C₉	semidirect
316. C₂×D₄	D₄×C₉	semidirect
320. C₂²×C₄	D₄×C₉	semidirect
365. C₉	#2408	direct (N × H)
386. C₂³	C₂×D₄×C₉	semidirect
408. C₂×C₄	C₂×D₄×C₉	semidirect
434. C₂²	C₉×#121	semidirect
445. C₄	C₉×#120	semidirect

Maximal subgroups

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

subgroup	index
C₂³×D₄×C₉	2
C₂×C₉×#121	2
C₂×C₉×#120	2
C₂×C₄×D₄×C₉	2
C₉×#394	2
C₉×#392	2
C₉×#390	2
C₉×#380	2
C₉×#379	2
C₃×#2408	3

Subgroups — C9×#2408 #11767129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2408 #11767129