Subgroups — C₉×#3488 #11768209

Order 1152.

2487 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#550	C₂	1	2	yes	maximal, complemented
4	C₉×#548	C₂	1	2	yes	maximal, complemented
5	C₉×#546	C₂	1	6	yes	maximal, complemented
6	D₄²×C₉	C₂	1	6	yes	maximal, complemented
7	C₉×#537	C₂	1	3	yes	maximal, complemented
8	C₉×#535	C₂	1	3	yes	maximal, complemented
9	C₉×#525	C₂	1	3	yes	maximal, complemented
10	C₂×C₉×#121	C₂	1	3	yes	maximal, complemented
11	C₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3488	C₃	1	1	yes	maximal, characteristic
13	C₉×H(5,𝔽₂)	—	2	8	no	—
14	C₂×C₉×#41	—	2	8	no	—
15	C₂×C₉×#41	C₂²	1	1	yes	characteristic
16	C₂×C₉×#41	C₂²	1	3	yes	complemented
17	C₂×C₉×#41	C₂²	1	3	yes	complemented
18	C₂×C₉×#41	C₂²	1	3	yes	complemented
19	C₂×C₉×#41	C₂²	1	2	yes	complemented
20	C₂×C₉×#41	C₂²	1	1	yes	characteristic, complemented
21	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₄×C₉	C₂²	1	3	yes	complemented
23	C₂²×D₄×C₉	C₂²	1	3	yes	complemented
24	C₂²×D₄×C₉	C₂²	1	6	yes	complemented
25	C₂²×D₄×C₉	C₂²	1	6	yes	complemented
26	C₂³×C₄×C₉	C₂²	1	3	yes	complemented
27	C₉×#127	C₂²	1	6	yes	complemented
28	C₉×#124	C₂²	1	6	yes	complemented
29	C₉×#123	C₂²	1	6	yes	complemented
30	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₉×C₂²⋊Q₈	C₂²	1	3	yes	complemented
32	C₉×C₂²⋊Q₈	C₂²	1	6	yes	complemented
33	C₉×#121	C₂²	1	3	yes	complemented
34	C₉×#121	C₂²	1	6	yes	complemented
35	C₉×#121	C₂²	1	6	yes	complemented
36	C₉×#121	C₂²	1	6	yes	complemented
37	C₉×#121	C₂²	1	3	yes	complemented
38	C₉×#121	C₂²	1	12	yes	complemented
39	C₉×#121	C₂²	1	6	yes	complemented
40	C₉×#120	C₂²	1	6	yes	complemented
41	C₉×#120	C₂²	1	12	yes	complemented
42	C₄×Q₈×C₉	C₂²	1	2	yes	complemented
43	C₄×D₄×C₉	C₂²	1	6	yes	complemented
44	C₄×D₄×C₉	C₂²	1	6	yes	complemented
45	C₄×D₄×C₉	C₂²	1	6	yes	complemented
46	C₉×#117	C₂²	1	3	yes	complemented
47	C₂×C₉×C₄⋊C₄	C₂²	1	3	yes	complemented
48	C₂×C₉×C₂²⋊C₄	C₂²	1	6	yes	complemented
49	C₂×C₃×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic
50	C₂²×C₃×#41	C₂×C₃	1	1	yes	characteristic
51	C₃×#550	C₂×C₃	1	2	yes	—
52	C₃×#548	C₂×C₃	1	2	yes	—
53	C₃×#546	C₂×C₃	1	6	yes	—
54	C₃×D₄²	C₂×C₃	1	6	yes	—
55	C₃×#537	C₂×C₃	1	3	yes	—
56	C₃×#535	C₂×C₃	1	3	yes	—
57	C₃×#525	C₂×C₃	1	3	yes	—
58	C₂×C₃×#121	C₂×C₃	1	3	yes	—
59	C₃×#520	C₂×C₃	1	1	yes	characteristic
60	C₂⁴×C₉	C₂³	1	3	yes	—
61	C₂⁴×C₉	C₂³	1	6	yes	—
62	C₉×#41	—	2	4	no	—
63	C₉×#41	—	2	8	no	—
64	C₉×#41	—	2	12	no	—
65	C₉×#41	—	2	12	no	—
66	C₉×#41	—	2	12	no	—
67	C₉×#41	D₄	1	8	yes	complemented
68	C₂×Q₈×C₉	—	2	4	no	—
69	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
70	C₂×Q₈×C₉	C₂³	1	3	yes	—
71	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
72	C₂×D₄×C₉	—	2	12	no	—
73	C₂×D₄×C₉	—	2	24	no	—
74	C₂×D₄×C₉	—	2	12	no	—
75	C₂×D₄×C₉	—	4	12	no	—
76	C₂×D₄×C₉	C₂³	1	6	yes	—
77	C₂×D₄×C₉	C₂³	1	6	yes	—
78	C₂×D₄×C₉	C₂³	1	6	yes	—
79	C₂×D₄×C₉	C₂³	1	3	yes	—
80	C₂×D₄×C₉	C₂³	1	6	yes	—
81	C₂×D₄×C₉	C₂³	1	3	yes	—
82	C₂×D₄×C₉	C₂³	1	6	yes	—
83	C₂×D₄×C₉	C₂³	1	12	yes	—
84	C₂×D₄×C₉	C₂³	1	3	yes	—
85	C₂²×C₄×C₉	—	2	12	no	—
86	C₂²×C₄×C₉	C₂³	1	3	yes	—
87	C₂²×C₄×C₉	C₂³	1	3	yes	—
88	C₂²×C₄×C₉	C₂³	1	3	yes	—
89	C₂²×C₄×C₉	C₂³	1	6	yes	—
90	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₉	C₂³	1	3	yes	—
92	C₂²×C₄×C₉	C₂³	1	6	yes	—
93	C₂²×C₄×C₉	C₂³	1	3	yes	—
94	C₉×C₄⋊C₄	C₂³	1	3	yes	—
95	C₉×C₄⋊C₄	C₂³	1	6	yes	—
96	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₉×C₄⋊C₄	C₂³	1	2	yes	—
98	C₉×C₄⋊C₄	C₂³	1	6	yes	—
99	C₉×C₂²⋊C₄	C₂³	1	6	yes	—
100	C₉×C₂²⋊C₄	C₂³	1	12	yes	—
101	C₉×C₂²⋊C₄	C₂³	1	6	yes	—
102	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
103	C₉×C₂²⋊C₄	C₂³	1	6	yes	—
104	C₉×C₂²⋊C₄	C₂³	1	6	yes	—
105	C₄²×C₉	C₂³	1	6	yes	—
106	#3488	C₉	1	1	yes	characteristic, direct product factor, Sylow
107	C₃×H(5,𝔽₂)	—	2	8	no	—
108	C₂×C₃×#41	—	2	8	no	—
109	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₃×#41	C₂²×C₃	1	3	yes	—
111	C₂×C₃×#41	C₂²×C₃	1	3	yes	—
112	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₃×#41	C₂²×C₃	1	3	yes	—
114	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
115	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
116	C₂²×C₃×D₄	C₂²×C₃	1	3	yes	—
117	C₂²×C₃×D₄	C₂²×C₃	1	3	yes	—
118	C₂²×C₃×D₄	C₂²×C₃	1	6	yes	—
119	C₂²×C₃×D₄	C₂²×C₃	1	6	yes	—
120	C₂³×C₃×C₄	C₂²×C₃	1	3	yes	—
121	C₃×#127	C₂²×C₃	1	6	yes	—
122	C₃×#124	C₂²×C₃	1	6	yes	—
123	C₃×#123	C₂²×C₃	1	6	yes	—
124	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
125	C₃×C₂²⋊Q₈	C₂²×C₃	1	3	yes	—
126	C₃×C₂²⋊Q₈	C₂²×C₃	1	6	yes	—
127	C₃×#121	C₂²×C₃	1	3	yes	—
128	C₃×#121	C₂²×C₃	1	6	yes	—
129	C₃×#121	C₂²×C₃	1	6	yes	—
130	C₃×#121	C₂²×C₃	1	6	yes	—
131	C₃×#121	C₂²×C₃	1	3	yes	—
132	C₃×#121	C₂²×C₃	1	12	yes	—
133	C₃×#121	C₂²×C₃	1	6	yes	—
134	C₃×#120	C₂²×C₃	1	6	yes	—
135	C₃×#120	C₂²×C₃	1	12	yes	—
136	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
137	C₃×C₄×D₄	C₂²×C₃	1	6	yes	—
138	C₃×C₄×D₄	C₂²×C₃	1	6	yes	—
139	C₃×C₄×D₄	C₂²×C₃	1	6	yes	—
140	C₃×#117	C₂²×C₃	1	3	yes	—
141	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	3	yes	—
142	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
143	C₂³×C₉	—	2	6	no	—
144	C₂³×C₉	—	2	6	no	—
145	C₂³×C₉	—	2	12	no	—
146	C₂³×C₉	—	4	3	no	—
147	C₂³×C₉	—	4	6	no	—
148	C₂³×C₉	—	4	6	no	—
149	C₂³×C₉	C₂⁴	1	6	yes	—
150	C₂³×C₉	C₂⁴	1	3	yes	—
151	C₂³×C₉	C₂⁴	1	3	yes	—
152	C₂³×C₉	C₂⁴	1	1	yes	characteristic
153	Q₈×C₉	—	2	6	no	—
154	Q₈×C₉	—	2	2	no	—
155	Q₈×C₉	C₂×D₄	1	4	yes	complemented
156	D₄×C₉	—	2	12	no	—
157	D₄×C₉	—	2	12	no	—
158	D₄×C₉	—	2	12	no	—
159	D₄×C₉	—	2	6	no	—
160	D₄×C₉	—	2	12	no	—
161	D₄×C₉	—	2	6	no	—
162	D₄×C₉	—	4	12	no	—
163	D₄×C₉	—	4	6	no	—
164	D₄×C₉	C₂×D₄	1	12	yes	complemented
165	C₂×C₄×C₉	—	2	6	no	—
166	C₂×C₄×C₉	—	2	2	no	—
167	C₂×C₄×C₉	—	2	6	no	—
168	C₂×C₄×C₉	—	2	6	no	—
169	C₂×C₄×C₉	—	2	6	no	—
170	C₂×C₄×C₉	—	2	12	no	—
171	C₂×C₄×C₉	—	4	6	no	—
172	C₂×C₄×C₉	C₂×D₄	1	12	yes	complemented
173	C₂×C₄×C₉	C₂⁴	1	2	yes	—
174	C₂×C₄×C₉	C₂⁴	1	6	yes	—
175	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₉	C₂⁴	1	3	yes	—
177	C₂×C₄×C₉	C₂⁴	1	2	yes	—
178	C₂×C₄×C₉	C₂⁴	1	3	yes	—
179	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
180	C₂×H(5,𝔽₂)	C₂×C₉	1	1	yes	characteristic, complemented
181	C₂²×#41	C₂×C₉	1	1	yes	characteristic, complemented
182	#550	C₂×C₉	1	2	yes	complemented
183	#548	C₂×C₉	1	2	yes	complemented
184	#546	C₂×C₉	1	6	yes	complemented
185	D₄²	C₂×C₉	1	6	yes	complemented
186	#537	C₂×C₉	1	3	yes	complemented
187	#535	C₂×C₉	1	3	yes	complemented
188	#525	C₂×C₉	1	3	yes	complemented
189	C₂×#121	C₂×C₉	1	3	yes	complemented
190	#520	C₂×C₉	1	1	yes	characteristic, complemented
191	C₂⁴×C₃	C₂³×C₃	1	3	yes	—
192	C₂⁴×C₃	C₂³×C₃	1	6	yes	—
193	C₃×#41	—	2	4	no	—
194	C₃×#41	—	2	8	no	—
195	C₃×#41	—	2	12	no	—
196	C₃×#41	—	2	12	no	—
197	C₃×#41	—	2	12	no	—
198	C₃×#41	C₃×D₄	1	8	yes	—
199	C₂×C₃×Q₈	—	2	4	no	—
200	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₃×Q₈	C₂³×C₃	1	3	yes	—
202	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
203	C₂×C₃×D₄	—	2	12	no	—
204	C₂×C₃×D₄	—	2	24	no	—
205	C₂×C₃×D₄	—	2	12	no	—
206	C₂×C₃×D₄	—	4	12	no	—
207	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
208	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
209	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
210	C₂×C₃×D₄	C₂³×C₃	1	3	yes	—
211	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
212	C₂×C₃×D₄	C₂³×C₃	1	3	yes	—
213	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
214	C₂×C₃×D₄	C₂³×C₃	1	12	yes	—
215	C₂×C₃×D₄	C₂³×C₃	1	3	yes	—
216	C₂²×C₃×C₄	—	2	12	no	—
217	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
218	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
219	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
220	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
221	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
223	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
224	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
225	C₃×C₄⋊C₄	C₂³×C₃	1	3	yes	—
226	C₃×C₄⋊C₄	C₂³×C₃	1	6	yes	—
227	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
228	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
229	C₃×C₄⋊C₄	C₂³×C₃	1	6	yes	—
230	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
231	C₃×C₂²⋊C₄	C₂³×C₃	1	12	yes	—
232	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
233	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
234	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
235	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
236	C₃×C₄²	C₂³×C₃	1	6	yes	—
237	C₂²×C₉	—	2	1	no	—
238	C₂²×C₉	—	2	3	no	—
239	C₂²×C₉	—	2	1	no	—
240	C₂²×C₉	—	2	3	no	—
241	C₂²×C₉	—	2	3	no	—
242	C₂²×C₉	—	2	6	no	—
243	C₂²×C₉	—	2	6	no	—
244	C₂²×C₉	—	2	3	no	—
245	C₂²×C₉	—	2	3	no	—
246	C₂²×C₉	—	2	6	no	—
247	C₂²×C₉	—	4	12	no	—
248	C₂²×C₉	—	8	12	no	—
249	C₂²×C₉	C₂²×D₄	1	6	yes	—
250	C₂²×C₉	H(5,𝔽₂)	1	2	yes	complemented
251	C₂²×C₉	C₂⁵	1	1	yes	characteristic
252	C₄×C₉	—	2	1	no	—
253	C₄×C₉	—	2	2	no	—
254	C₄×C₉	—	2	3	no	—
255	C₄×C₉	—	2	6	no	—
256	C₄×C₉	—	2	2	no	—
257	C₄×C₉	C₂²×D₄	1	2	yes	—
258	C₄×C₉	C₂²×D₄	1	6	yes	—
259	H(5,𝔽₂)	—	2	8	no	—
260	C₂×#41	—	2	8	no	—
261	C₂×#41	C₂²×C₉	1	1	yes	characteristic
262	C₂×#41	C₂²×C₉	1	3	yes	complemented
263	C₂×#41	C₂²×C₉	1	3	yes	complemented
264	C₂×#41	C₂²×C₉	1	3	yes	complemented
265	C₂×#41	C₂²×C₉	1	2	yes	complemented
266	C₂×#41	C₂²×C₉	1	1	yes	characteristic, complemented
267	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
268	C₂²×D₄	C₂²×C₉	1	3	yes	complemented
269	C₂²×D₄	C₂²×C₉	1	3	yes	complemented
270	C₂²×D₄	C₂²×C₉	1	6	yes	complemented
271	C₂²×D₄	C₂²×C₉	1	6	yes	complemented
272	C₂³×C₄	C₂²×C₉	1	3	yes	complemented
273	#127	C₂²×C₉	1	6	yes	complemented
274	#124	C₂²×C₉	1	6	yes	complemented
275	#123	C₂²×C₉	1	6	yes	complemented
276	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
277	C₂²⋊Q₈	C₂²×C₉	1	3	yes	complemented
278	C₂²⋊Q₈	C₂²×C₉	1	6	yes	complemented
279	#121	C₂²×C₉	1	3	yes	complemented
280	#121	C₂²×C₉	1	6	yes	complemented
281	#121	C₂²×C₉	1	6	yes	complemented
282	#121	C₂²×C₉	1	6	yes	complemented
283	#121	C₂²×C₉	1	3	yes	complemented
284	#121	C₂²×C₉	1	12	yes	complemented
285	#121	C₂²×C₉	1	6	yes	complemented
286	#120	C₂²×C₉	1	6	yes	complemented
287	#120	C₂²×C₉	1	12	yes	complemented
288	C₄×Q₈	C₂²×C₉	1	2	yes	complemented
289	C₄×D₄	C₂²×C₉	1	6	yes	complemented
290	C₄×D₄	C₂²×C₉	1	6	yes	complemented
291	C₄×D₄	C₂²×C₉	1	6	yes	complemented
292	#117	C₂²×C₉	1	3	yes	complemented
293	C₂×C₄⋊C₄	C₂²×C₉	1	3	yes	complemented
294	C₂×C₂²⋊C₄	C₂²×C₉	1	6	yes	complemented
295	C₂³×C₃	—	2	6	no	—
296	C₂³×C₃	—	2	6	no	—
297	C₂³×C₃	—	2	12	no	—
298	C₂³×C₃	—	4	3	no	—
299	C₂³×C₃	—	4	6	no	—
300	C₂³×C₃	—	4	6	no	—
301	C₂³×C₃	C₂⁴×C₃	1	6	yes	—
302	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
303	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
304	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
305	C₃×Q₈	—	2	6	no	—
306	C₃×Q₈	—	2	2	no	—
307	C₃×Q₈	C₂×C₃×D₄	1	4	yes	—
308	C₃×D₄	—	2	12	no	—
309	C₃×D₄	—	2	12	no	—
310	C₃×D₄	—	2	12	no	—
311	C₃×D₄	—	2	6	no	—
312	C₃×D₄	—	2	12	no	—
313	C₃×D₄	—	2	6	no	—
314	C₃×D₄	—	4	12	no	—
315	C₃×D₄	—	4	6	no	—
316	C₃×D₄	C₂×C₃×D₄	1	12	yes	—
317	C₂×C₃×C₄	—	2	6	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	2	6	no	—
320	C₂×C₃×C₄	—	2	6	no	—
321	C₂×C₃×C₄	—	2	6	no	—
322	C₂×C₃×C₄	—	2	12	no	—
323	C₂×C₃×C₄	—	4	6	no	—
324	C₂×C₃×C₄	C₂×C₃×D₄	1	12	yes	—
325	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
326	C₂×C₃×C₄	C₂⁴×C₃	1	6	yes	—
327	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
329	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
330	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
331	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
332	C₂×C₉	—	2	2	no	—
333	C₂×C₉	—	2	6	no	—
334	C₂×C₉	—	4	3	no	—
335	C₂×C₉	—	4	6	no	—
336	C₂×C₉	C₂³×D₄	1	1	yes	characteristic
337	C₂×C₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₉	#585	1	1	yes	characteristic
339	C₂⁴	C₂³×C₉	1	3	yes	—
340	C₂⁴	C₂³×C₉	1	6	yes	—
341	#41	—	2	4	no	—
342	#41	—	2	8	no	—
343	#41	—	2	12	no	—
344	#41	—	2	12	no	—
345	#41	—	2	12	no	—
346	#41	D₄×C₉	1	8	yes	complemented
347	C₂×Q₈	—	2	4	no	—
348	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
349	C₂×Q₈	C₂³×C₉	1	3	yes	—
350	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
351	C₂×D₄	—	2	12	no	—
352	C₂×D₄	—	2	24	no	—
353	C₂×D₄	—	2	12	no	—
354	C₂×D₄	—	4	12	no	—
355	C₂×D₄	C₂³×C₉	1	6	yes	—
356	C₂×D₄	C₂³×C₉	1	6	yes	—
357	C₂×D₄	C₂³×C₉	1	6	yes	—
358	C₂×D₄	C₂³×C₉	1	3	yes	—
359	C₂×D₄	C₂³×C₉	1	6	yes	—
360	C₂×D₄	C₂³×C₉	1	3	yes	—
361	C₂×D₄	C₂³×C₉	1	6	yes	—
362	C₂×D₄	C₂³×C₉	1	12	yes	—
363	C₂×D₄	C₂³×C₉	1	3	yes	—
364	C₂²×C₄	—	2	12	no	—
365	C₂²×C₄	C₂³×C₉	1	3	yes	—
366	C₂²×C₄	C₂³×C₉	1	3	yes	—
367	C₂²×C₄	C₂³×C₉	1	3	yes	—
368	C₂²×C₄	C₂³×C₉	1	6	yes	—
369	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
370	C₂²×C₄	C₂³×C₉	1	3	yes	—
371	C₂²×C₄	C₂³×C₉	1	6	yes	—
372	C₂²×C₄	C₂³×C₉	1	3	yes	—
373	C₄⋊C₄	C₂³×C₉	1	3	yes	—
374	C₄⋊C₄	C₂³×C₉	1	6	yes	—
375	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
376	C₄⋊C₄	C₂³×C₉	1	2	yes	—
377	C₄⋊C₄	C₂³×C₉	1	6	yes	—
378	C₂²⋊C₄	C₂³×C₉	1	6	yes	—
379	C₂²⋊C₄	C₂³×C₉	1	12	yes	—
380	C₂²⋊C₄	C₂³×C₉	1	6	yes	—
381	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
382	C₂²⋊C₄	C₂³×C₉	1	6	yes	—
383	C₂²⋊C₄	C₂³×C₉	1	6	yes	—
384	C₄²	C₂³×C₉	1	6	yes	—
385	C₂²×C₃	—	2	1	no	—
386	C₂²×C₃	—	2	3	no	—
387	C₂²×C₃	—	2	1	no	—
388	C₂²×C₃	—	2	3	no	—
389	C₂²×C₃	—	2	3	no	—
390	C₂²×C₃	—	2	6	no	—
391	C₂²×C₃	—	2	6	no	—
392	C₂²×C₃	—	2	3	no	—
393	C₂²×C₃	—	2	3	no	—
394	C₂²×C₃	—	2	6	no	—
395	C₂²×C₃	—	4	12	no	—
396	C₂²×C₃	—	8	12	no	—
397	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
398	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
399	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
400	C₃×C₄	—	2	1	no	—
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	2	3	no	—
403	C₃×C₄	—	2	6	no	—
404	C₃×C₄	—	2	2	no	—
405	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
406	C₃×C₄	C₂²×C₃×D₄	1	6	yes	—
407	C₉	#3488	1	1	yes	characteristic, direct product factor, Sylow
408	C₂³	—	2	6	no	—
409	C₂³	—	2	6	no	—
410	C₂³	—	2	12	no	—
411	C₂³	—	4	3	no	—
412	C₂³	—	4	6	no	—
413	C₂³	—	4	6	no	—
414	C₂³	C₂⁴×C₉	1	6	yes	—
415	C₂³	C₂⁴×C₉	1	3	yes	—
416	C₂³	C₂⁴×C₉	1	3	yes	—
417	C₂³	C₂⁴×C₉	1	1	yes	characteristic
418	Q₈	—	2	6	no	—
419	Q₈	—	2	2	no	—
420	Q₈	C₂×D₄×C₉	1	4	yes	complemented
421	D₄	—	2	12	no	—
422	D₄	—	2	12	no	—
423	D₄	—	2	12	no	—
424	D₄	—	2	6	no	—
425	D₄	—	2	12	no	—
426	D₄	—	2	6	no	—
427	D₄	—	4	12	no	—
428	D₄	—	4	6	no	—
429	D₄	C₂×D₄×C₉	1	12	yes	complemented
430	C₂×C₄	—	2	6	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	6	no	—
433	C₂×C₄	—	2	6	no	—
434	C₂×C₄	—	2	6	no	—
435	C₂×C₄	—	2	12	no	—
436	C₂×C₄	—	4	6	no	—
437	C₂×C₄	C₂×D₄×C₉	1	12	yes	complemented
438	C₂×C₄	C₂⁴×C₉	1	2	yes	—
439	C₂×C₄	C₂⁴×C₉	1	6	yes	—
440	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
441	C₂×C₄	C₂⁴×C₉	1	3	yes	—
442	C₂×C₄	C₂⁴×C₉	1	2	yes	—
443	C₂×C₄	C₂⁴×C₉	1	3	yes	—
444	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
445	C₂×C₃	—	2	2	no	—
446	C₂×C₃	—	2	6	no	—
447	C₂×C₃	—	4	3	no	—
448	C₂×C₃	—	4	6	no	—
449	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
450	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂×C₃	C₃×#585	1	1	yes	characteristic
452	C₂²	—	2	1	no	—
453	C₂²	—	2	3	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	3	no	—
456	C₂²	—	2	3	no	—
457	C₂²	—	2	6	no	—
458	C₂²	—	2	6	no	—
459	C₂²	—	2	3	no	—
460	C₂²	—	2	3	no	—
461	C₂²	—	2	6	no	—
462	C₂²	—	4	12	no	—
463	C₂²	—	8	12	no	—
464	C₂²	C₂²×D₄×C₉	1	6	yes	—
465	C₂²	C₉×H(5,𝔽₂)	1	2	yes	complemented
466	C₂²	C₂⁵×C₉	1	1	yes	characteristic
467	C₄	—	2	1	no	—
468	C₄	—	2	2	no	—
469	C₄	—	2	3	no	—
470	C₄	—	2	6	no	—
471	C₄	—	2	2	no	—
472	C₄	C₂²×D₄×C₉	1	2	yes	—
473	C₄	C₂²×D₄×C₉	1	6	yes	—
474	C₃	C₃×#3488	1	1	yes	characteristic
475	C₂	—	2	2	no	—
476	C₂	—	2	6	no	—
477	C₂	—	4	3	no	—
478	C₂	—	4	6	no	—
479	C₂	C₂³×D₄×C₉	1	1	yes	characteristic
480	C₂	C₂×C₉×H(5,𝔽₂)	1	1	yes	characteristic
481	C₂	C₉×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂⁵
commutator	C₂²	C₂⁵×C₉
Frattini, socle, cosocle	C₂²×C₃	C₂⁵×C₃
prime radical	C₃×#3488	C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×H(5,𝔽₂)	C₂	semidirect
2. C₂²×C₉×#41	C₂	semidirect
3. C₉×#550	C₂	semidirect
4. C₉×#548	C₂	semidirect
5. C₉×#546	C₂	semidirect
6. D₄²×C₉	C₂	semidirect
7. C₉×#537	C₂	semidirect
8. C₉×#535	C₂	semidirect
9. C₉×#525	C₂	semidirect
10. C₂×C₉×#121	C₂	semidirect
11. C₉×#520	C₂	semidirect
16. C₂×C₉×#41	C₂²	semidirect
17. C₂×C₉×#41	C₂²	semidirect
18. C₂×C₉×#41	C₂²	semidirect
19. C₂×C₉×#41	C₂²	semidirect
20. C₂×C₉×#41	C₂²	semidirect
21. C₂²×Q₈×C₉	C₂²	semidirect
22. C₂²×D₄×C₉	C₂²	semidirect
23. C₂²×D₄×C₉	C₂²	semidirect
24. C₂²×D₄×C₉	C₂²	semidirect
25. C₂²×D₄×C₉	C₂²	semidirect
26. C₂³×C₄×C₉	C₂²	semidirect
27. C₉×#127	C₂²	semidirect
28. C₉×#124	C₂²	semidirect
29. C₉×#123	C₂²	semidirect
30. C₉×C₂²⋊Q₈	C₂²	semidirect
31. C₉×C₂²⋊Q₈	C₂²	semidirect
32. C₉×C₂²⋊Q₈	C₂²	semidirect
33. C₉×#121	C₂²	semidirect
34. C₉×#121	C₂²	semidirect
35. C₉×#121	C₂²	semidirect
36. C₉×#121	C₂²	semidirect
37. C₉×#121	C₂²	semidirect
38. C₉×#121	C₂²	semidirect
39. C₉×#121	C₂²	semidirect
40. C₉×#120	C₂²	semidirect
41. C₉×#120	C₂²	semidirect
42. C₄×Q₈×C₉	C₂²	semidirect
43. C₄×D₄×C₉	C₂²	semidirect
44. C₄×D₄×C₉	C₂²	semidirect
45. C₄×D₄×C₉	C₂²	semidirect
46. C₉×#117	C₂²	semidirect
47. C₂×C₉×C₄⋊C₄	C₂²	semidirect
48. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
67. C₉×#41	D₄	semidirect
106. #3488	C₉	direct (N × H)
155. Q₈×C₉	C₂×D₄	semidirect
164. D₄×C₉	C₂×D₄	semidirect
172. C₂×C₄×C₉	C₂×D₄	semidirect
180. C₂×H(5,𝔽₂)	C₂×C₉	semidirect
181. C₂²×#41	C₂×C₉	semidirect
182. #550	C₂×C₉	semidirect
183. #548	C₂×C₉	semidirect
184. #546	C₂×C₉	semidirect
185. D₄²	C₂×C₉	semidirect
186. #537	C₂×C₉	semidirect
187. #535	C₂×C₉	semidirect
188. #525	C₂×C₉	semidirect
189. C₂×#121	C₂×C₉	semidirect
190. #520	C₂×C₉	semidirect
250. C₂²×C₉	H(5,𝔽₂)	semidirect
262. C₂×#41	C₂²×C₉	semidirect
263. C₂×#41	C₂²×C₉	semidirect
264. C₂×#41	C₂²×C₉	semidirect
265. C₂×#41	C₂²×C₉	semidirect
266. C₂×#41	C₂²×C₉	semidirect
267. C₂²×Q₈	C₂²×C₉	semidirect
268. C₂²×D₄	C₂²×C₉	semidirect
269. C₂²×D₄	C₂²×C₉	semidirect
270. C₂²×D₄	C₂²×C₉	semidirect
271. C₂²×D₄	C₂²×C₉	semidirect
272. C₂³×C₄	C₂²×C₉	semidirect
273. #127	C₂²×C₉	semidirect
274. #124	C₂²×C₉	semidirect
275. #123	C₂²×C₉	semidirect
276. C₂²⋊Q₈	C₂²×C₉	semidirect
277. C₂²⋊Q₈	C₂²×C₉	semidirect
278. C₂²⋊Q₈	C₂²×C₉	semidirect
279. #121	C₂²×C₉	semidirect
280. #121	C₂²×C₉	semidirect
281. #121	C₂²×C₉	semidirect
282. #121	C₂²×C₉	semidirect
283. #121	C₂²×C₉	semidirect
284. #121	C₂²×C₉	semidirect
285. #121	C₂²×C₉	semidirect
286. #120	C₂²×C₉	semidirect
287. #120	C₂²×C₉	semidirect
288. C₄×Q₈	C₂²×C₉	semidirect
289. C₄×D₄	C₂²×C₉	semidirect
290. C₄×D₄	C₂²×C₉	semidirect
291. C₄×D₄	C₂²×C₉	semidirect
292. #117	C₂²×C₉	semidirect
293. C₂×C₄⋊C₄	C₂²×C₉	semidirect
294. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
346. #41	D₄×C₉	semidirect
407. C₉	#3488	direct (N × H)
420. Q₈	C₂×D₄×C₉	semidirect
429. D₄	C₂×D₄×C₉	semidirect
437. C₂×C₄	C₂×D₄×C₉	semidirect
465. C₂²	C₉×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×H(5,𝔽₂)	2
C₂²×C₉×#41	2
C₉×#550	2
C₉×#548	2
C₉×#546	2
D₄²×C₉	2
C₉×#537	2
C₉×#535	2
C₉×#525	2
C₂×C₉×#121	2
C₉×#520	2
C₃×#3488	3

Subgroups — C9×#3488 #11768209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3488 #11768209