Subgroups — C₉×#3490 #11768211

Order 1152.

1992 conjugacy classes of subgroups.

The subgroup lattice has 429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#551	C₂	1	8	yes	maximal, complemented
2	C₉×#546	C₂	1	8	yes	maximal, complemented
3	C₉×#543	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#538	C₂	1	4	yes	maximal, complemented
5	C₉×#534	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#525	C₂	1	4	yes	maximal, complemented
7	C₂×C₉×#120	C₂	1	2	yes	maximal, complemented
8	C₉×#518	C₂	1	2	yes	maximal, complemented
9	C₂²×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3490	C₃	1	1	yes	maximal, characteristic
11	C₂⁵×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₉×#41	C₂²	1	4	yes	complemented
13	C₂²×D₄×C₉	C₂²	1	2	yes	—
14	C₂²×D₄×C₉	C₂²	1	4	yes	complemented
15	C₂³×C₄×C₉	C₂²	1	2	yes	complemented
16	C₉×#126	C₂²	1	8	yes	complemented
17	C₉×#124	C₂²	1	8	yes	complemented
18	C₉×#123	C₂²	1	8	yes	complemented
19	C₉×#123	C₂²	1	8	yes	complemented
20	C₉×#123	C₂²	1	4	yes	complemented
21	C₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
22	C₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
23	C₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
24	C₉×#121	C₂²	1	8	yes	complemented
25	C₉×#121	C₂²	1	4	yes	complemented
26	C₉×#121	C₂²	1	4	yes	complemented
27	C₉×#120	C₂²	1	8	yes	—
28	C₉×#120	C₂²	1	4	yes	complemented
29	C₉×#120	C₂²	1	4	yes	complemented
30	C₉×#120	C₂²	1	4	yes	complemented
31	C₄×D₄×C₉	C₂²	1	8	yes	complemented
32	C₄×D₄×C₉	C₂²	1	8	yes	complemented
33	C₄×D₄×C₉	C₂²	1	8	yes	complemented
34	C₉×#117	C₂²	1	4	yes	complemented
35	C₉×#117	C₂²	1	4	yes	complemented
36	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
40	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
41	C₂×C₉×C₂²⋊C₄	C₂²	1	8	yes	complemented
42	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
43	C₃×#551	C₂×C₃	1	8	yes	—
44	C₃×#546	C₂×C₃	1	8	yes	—
45	C₃×#543	C₂×C₃	1	1	yes	characteristic
46	C₃×#538	C₂×C₃	1	4	yes	—
47	C₃×#534	C₂×C₃	1	1	yes	characteristic
48	C₃×#525	C₂×C₃	1	4	yes	—
49	C₂×C₃×#120	C₂×C₃	1	2	yes	—
50	C₃×#518	C₂×C₃	1	2	yes	—
51	C₂²×C₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
52	C₂⁴×C₉	—	2	4	no	—
53	C₂⁴×C₉	—	4	4	no	—
54	C₂⁴×C₉	C₂³	1	1	yes	characteristic
55	C₂⁴×C₉	C₂³	1	4	yes	—
56	C₂⁴×C₉	C₂³	1	1	yes	characteristic
57	C₂⁴×C₉	C₂³	1	2	yes	—
58	C₂⁴×C₉	C₂³	1	1	yes	characteristic
59	C₉×#41	—	4	8	no	—
60	C₂×Q₈×C₉	C₂³	1	4	yes	complemented
61	C₂×D₄×C₉	—	2	8	no	—
62	C₂×D₄×C₉	—	4	8	no	—
63	C₂×D₄×C₉	C₂³	1	4	yes	—
64	C₂×D₄×C₉	C₂³	1	4	yes	—
65	C₂×D₄×C₉	C₂³	1	8	yes	—
66	C₂×D₄×C₉	C₂³	1	8	yes	—
67	C₂×D₄×C₉	C₂³	1	4	yes	complemented
68	C₂²×C₄×C₉	—	4	4	no	—
69	C₂²×C₄×C₉	C₂³	1	2	yes	—
70	C₂²×C₄×C₉	C₂³	1	4	yes	—
71	C₂²×C₄×C₉	C₂³	1	2	yes	—
72	C₂²×C₄×C₉	C₂³	1	4	yes	—
73	C₂²×C₄×C₉	C₂³	1	2	yes	—
74	C₂²×C₄×C₉	C₂³	1	4	yes	—
75	C₂²×C₄×C₉	C₂³	1	8	yes	complemented
76	C₉×C₄⋊C₄	C₂³	1	8	yes	complemented
77	C₉×C₄⋊C₄	C₂³	1	4	yes	complemented
78	C₉×C₄⋊C₄	C₂³	1	4	yes	complemented
79	C₉×C₄⋊C₄	C₂³	1	8	yes	complemented
80	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
81	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
82	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
83	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
84	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
85	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
87	C₉×C₂²⋊C₄	C₂³	1	8	yes	complemented
88	C₉×C₂²⋊C₄	C₂³	1	8	yes	complemented
89	C₄²×C₉	C₂³	1	8	yes	complemented
90	#3490	C₉	1	1	yes	characteristic, direct product factor, Sylow
91	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
93	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
94	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
95	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
96	C₃×#126	C₂²×C₃	1	8	yes	—
97	C₃×#124	C₂²×C₃	1	8	yes	—
98	C₃×#123	C₂²×C₃	1	8	yes	—
99	C₃×#123	C₂²×C₃	1	4	yes	—
100	C₃×#123	C₂²×C₃	1	8	yes	—
101	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
102	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
103	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
104	C₃×#121	C₂²×C₃	1	4	yes	—
105	C₃×#121	C₂²×C₃	1	4	yes	—
106	C₃×#121	C₂²×C₃	1	8	yes	—
107	C₃×#120	C₂²×C₃	1	8	yes	—
108	C₃×#120	C₂²×C₃	1	4	yes	—
109	C₃×#120	C₂²×C₃	1	4	yes	—
110	C₃×#120	C₂²×C₃	1	4	yes	—
111	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
112	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
113	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
114	C₃×#117	C₂²×C₃	1	4	yes	—
115	C₃×#117	C₂²×C₃	1	4	yes	—
116	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
119	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
120	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
121	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
122	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
123	C₂³×C₉	—	2	2	no	—
124	C₂³×C₉	—	2	4	no	—
125	C₂³×C₉	—	2	8	no	—
126	C₂³×C₉	—	2	2	no	—
127	C₂³×C₉	—	2	8	no	—
128	C₂³×C₉	—	2	4	no	—
129	C₂³×C₉	—	4	2	no	—
130	C₂³×C₉	—	4	4	no	—
131	C₂³×C₉	—	4	2	no	—
132	C₂³×C₉	—	4	4	no	—
133	C₂³×C₉	—	4	16	no	—
134	C₂³×C₉	#41	1	4	yes	complemented
135	C₂³×C₉	C₂⁴	1	2	yes	—
136	C₂³×C₉	C₂⁴	1	4	yes	—
137	C₂³×C₉	C₂⁴	1	2	yes	—
138	C₂³×C₉	C₂⁴	1	1	yes	characteristic
139	C₂³×C₉	C₂⁴	1	2	yes	—
140	Q₈×C₉	—	4	4	no	—
141	D₄×C₉	—	2	8	no	—
142	D₄×C₉	—	2	8	no	—
143	D₄×C₉	—	2	16	no	—
144	D₄×C₉	—	4	8	no	—
145	D₄×C₉	—	4	4	no	—
146	C₂×C₄×C₉	—	2	4	no	—
147	C₂×C₄×C₉	—	2	8	no	—
148	C₂×C₄×C₉	—	4	2	no	—
149	C₂×C₄×C₉	—	4	4	no	—
150	C₂×C₄×C₉	—	4	2	no	—
151	C₂×C₄×C₉	—	4	4	no	—
152	C₂×C₄×C₉	—	4	8	no	—
153	C₂×C₄×C₉	C₂⁴	1	4	yes	—
154	C₂×C₄×C₉	C₂⁴	1	4	yes	—
155	C₂×C₄×C₉	C₂⁴	1	8	yes	—
156	C₂×C₄×C₉	C₂⁴	1	4	yes	—
157	#551	C₂×C₉	1	8	yes	complemented
158	#546	C₂×C₉	1	8	yes	complemented
159	#543	C₂×C₉	1	1	yes	characteristic, complemented
160	#538	C₂×C₉	1	4	yes	complemented
161	#534	C₂×C₉	1	1	yes	characteristic, complemented
162	#525	C₂×C₉	1	4	yes	complemented
163	C₂×#120	C₂×C₉	1	2	yes	complemented
164	#518	C₂×C₉	1	2	yes	complemented
165	C₂²×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
166	C₂⁴×C₃	—	2	4	no	—
167	C₂⁴×C₃	—	4	4	no	—
168	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
169	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
170	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
171	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
172	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
173	C₃×#41	—	4	8	no	—
174	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
175	C₂×C₃×D₄	—	2	8	no	—
176	C₂×C₃×D₄	—	4	8	no	—
177	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
178	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
179	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
180	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
181	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
182	C₂²×C₃×C₄	—	4	4	no	—
183	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
184	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
185	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
186	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
187	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
188	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
189	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
190	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
191	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
192	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
193	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
194	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
195	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
196	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
197	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
198	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
199	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
200	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
201	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
202	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
203	C₃×C₄²	C₂³×C₃	1	8	yes	—
204	C₂²×C₉	—	2	8	no	—
205	C₂²×C₉	—	2	2	no	—
206	C₂²×C₉	—	2	2	no	—
207	C₂²×C₉	—	2	2	no	—
208	C₂²×C₉	—	2	4	no	—
209	C₂²×C₉	—	2	4	no	—
210	C₂²×C₉	—	2	2	no	—
211	C₂²×C₉	—	2	8	no	—
212	C₂²×C₉	—	2	4	no	—
213	C₂²×C₉	—	4	4	no	—
214	C₂²×C₉	—	4	16	no	—
215	C₂²×C₉	—	4	4	no	—
216	C₂²×C₉	—	8	4	no	—
217	C₂²×C₉	C₂×#41	1	4	yes	—
218	C₂²×C₉	C₂×#41	1	2	yes	—
219	C₂²×C₉	H(5,𝔽₂)	1	4	yes	—
220	C₂²×C₉	C₂⁵	1	1	yes	characteristic
221	C₄×C₉	—	2	4	no	—
222	C₄×C₉	—	2	4	no	—
223	C₄×C₉	—	2	4	no	—
224	C₄×C₉	—	2	8	no	—
225	C₂⁵	C₂²×C₉	1	1	yes	characteristic
226	C₂×#41	C₂²×C₉	1	4	yes	complemented
227	C₂²×D₄	C₂²×C₉	1	2	yes	—
228	C₂²×D₄	C₂²×C₉	1	4	yes	complemented
229	C₂³×C₄	C₂²×C₉	1	2	yes	complemented
230	#126	C₂²×C₉	1	8	yes	complemented
231	#124	C₂²×C₉	1	8	yes	complemented
232	#123	C₂²×C₉	1	8	yes	complemented
233	#123	C₂²×C₉	1	8	yes	complemented
234	#123	C₂²×C₉	1	4	yes	complemented
235	C₂²⋊Q₈	C₂²×C₉	1	4	yes	complemented
236	C₂²⋊Q₈	C₂²×C₉	1	4	yes	complemented
237	C₂²⋊Q₈	C₂²×C₉	1	8	yes	complemented
238	#121	C₂²×C₉	1	8	yes	complemented
239	#121	C₂²×C₉	1	4	yes	complemented
240	#121	C₂²×C₉	1	4	yes	complemented
241	#120	C₂²×C₉	1	8	yes	—
242	#120	C₂²×C₉	1	4	yes	complemented
243	#120	C₂²×C₉	1	4	yes	complemented
244	#120	C₂²×C₉	1	4	yes	complemented
245	C₄×D₄	C₂²×C₉	1	8	yes	complemented
246	C₄×D₄	C₂²×C₉	1	8	yes	complemented
247	C₄×D₄	C₂²×C₉	1	8	yes	complemented
248	#117	C₂²×C₉	1	4	yes	complemented
249	#117	C₂²×C₉	1	4	yes	complemented
250	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
253	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
254	C₂×C₂²⋊C₄	C₂²×C₉	1	8	yes	complemented
255	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	complemented
256	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	complemented
257	C₂³×C₃	—	2	2	no	—
258	C₂³×C₃	—	2	4	no	—
259	C₂³×C₃	—	2	8	no	—
260	C₂³×C₃	—	2	2	no	—
261	C₂³×C₃	—	2	8	no	—
262	C₂³×C₃	—	2	4	no	—
263	C₂³×C₃	—	4	2	no	—
264	C₂³×C₃	—	4	4	no	—
265	C₂³×C₃	—	4	2	no	—
266	C₂³×C₃	—	4	4	no	—
267	C₂³×C₃	—	4	16	no	—
268	C₂³×C₃	C₃×#41	1	4	yes	—
269	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
270	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
271	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
272	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
273	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
274	C₃×Q₈	—	4	4	no	—
275	C₃×D₄	—	2	8	no	—
276	C₃×D₄	—	2	8	no	—
277	C₃×D₄	—	2	16	no	—
278	C₃×D₄	—	4	8	no	—
279	C₃×D₄	—	4	4	no	—
280	C₂×C₃×C₄	—	2	4	no	—
281	C₂×C₃×C₄	—	2	8	no	—
282	C₂×C₃×C₄	—	4	2	no	—
283	C₂×C₃×C₄	—	4	4	no	—
284	C₂×C₃×C₄	—	4	2	no	—
285	C₂×C₃×C₄	—	4	4	no	—
286	C₂×C₃×C₄	—	4	8	no	—
287	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
288	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
289	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
290	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
291	C₂×C₉	—	2	2	no	—
292	C₂×C₉	—	2	4	no	—
293	C₂×C₉	—	2	4	no	—
294	C₂×C₉	—	4	2	no	—
295	C₂×C₉	—	4	4	no	—
296	C₂×C₉	C₂²×#41	1	1	yes	characteristic
297	C₂×C₉	C₂×H(5,𝔽₂)	1	2	yes	—
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	4	4	no	—
300	C₂⁴	C₂³×C₉	1	1	yes	characteristic
301	C₂⁴	C₂³×C₉	1	4	yes	—
302	C₂⁴	C₂³×C₉	1	1	yes	characteristic
303	C₂⁴	C₂³×C₉	1	2	yes	—
304	C₂⁴	C₂³×C₉	1	1	yes	characteristic
305	#41	—	4	8	no	—
306	C₂×Q₈	C₂³×C₉	1	4	yes	complemented
307	C₂×D₄	—	2	8	no	—
308	C₂×D₄	—	4	8	no	—
309	C₂×D₄	C₂³×C₉	1	4	yes	—
310	C₂×D₄	C₂³×C₉	1	4	yes	—
311	C₂×D₄	C₂³×C₉	1	8	yes	—
312	C₂×D₄	C₂³×C₉	1	8	yes	—
313	C₂×D₄	C₂³×C₉	1	4	yes	complemented
314	C₂²×C₄	—	4	4	no	—
315	C₂²×C₄	C₂³×C₉	1	2	yes	—
316	C₂²×C₄	C₂³×C₉	1	4	yes	—
317	C₂²×C₄	C₂³×C₉	1	2	yes	—
318	C₂²×C₄	C₂³×C₉	1	4	yes	—
319	C₂²×C₄	C₂³×C₉	1	2	yes	—
320	C₂²×C₄	C₂³×C₉	1	4	yes	—
321	C₂²×C₄	C₂³×C₉	1	8	yes	complemented
322	C₄⋊C₄	C₂³×C₉	1	8	yes	complemented
323	C₄⋊C₄	C₂³×C₉	1	4	yes	complemented
324	C₄⋊C₄	C₂³×C₉	1	4	yes	complemented
325	C₄⋊C₄	C₂³×C₉	1	8	yes	complemented
326	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
327	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
328	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
329	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
330	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
331	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
332	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
333	C₂²⋊C₄	C₂³×C₉	1	8	yes	complemented
334	C₂²⋊C₄	C₂³×C₉	1	8	yes	complemented
335	C₄²	C₂³×C₉	1	8	yes	complemented
336	C₂²×C₃	—	2	8	no	—
337	C₂²×C₃	—	2	2	no	—
338	C₂²×C₃	—	2	2	no	—
339	C₂²×C₃	—	2	2	no	—
340	C₂²×C₃	—	2	4	no	—
341	C₂²×C₃	—	2	4	no	—
342	C₂²×C₃	—	2	2	no	—
343	C₂²×C₃	—	2	8	no	—
344	C₂²×C₃	—	2	4	no	—
345	C₂²×C₃	—	4	4	no	—
346	C₂²×C₃	—	4	16	no	—
347	C₂²×C₃	—	4	4	no	—
348	C₂²×C₃	—	8	4	no	—
349	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
350	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
351	C₂²×C₃	C₃×H(5,𝔽₂)	1	4	yes	—
352	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
353	C₃×C₄	—	2	4	no	—
354	C₃×C₄	—	2	4	no	—
355	C₃×C₄	—	2	4	no	—
356	C₃×C₄	—	2	8	no	—
357	C₉	#3490	1	1	yes	characteristic, direct product factor, Sylow
358	C₂³	—	2	2	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	8	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	8	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	4	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	4	no	—
368	C₂³	—	4	16	no	—
369	C₂³	C₉×#41	1	4	yes	complemented
370	C₂³	C₂⁴×C₉	1	2	yes	—
371	C₂³	C₂⁴×C₉	1	4	yes	—
372	C₂³	C₂⁴×C₉	1	2	yes	—
373	C₂³	C₂⁴×C₉	1	1	yes	characteristic
374	C₂³	C₂⁴×C₉	1	2	yes	—
375	Q₈	—	4	4	no	—
376	D₄	—	2	8	no	—
377	D₄	—	2	8	no	—
378	D₄	—	2	16	no	—
379	D₄	—	4	8	no	—
380	D₄	—	4	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	8	no	—
388	C₂×C₄	C₂⁴×C₉	1	4	yes	—
389	C₂×C₄	C₂⁴×C₉	1	4	yes	—
390	C₂×C₄	C₂⁴×C₉	1	8	yes	—
391	C₂×C₄	C₂⁴×C₉	1	4	yes	—
392	C₂×C₃	—	2	2	no	—
393	C₂×C₃	—	2	4	no	—
394	C₂×C₃	—	2	4	no	—
395	C₂×C₃	—	4	2	no	—
396	C₂×C₃	—	4	4	no	—
397	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
398	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
399	C₂²	—	2	8	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	8	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	16	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	8	4	no	—
412	C₂²	C₂×C₉×#41	1	4	yes	—
413	C₂²	C₂×C₉×#41	1	2	yes	—
414	C₂²	C₉×H(5,𝔽₂)	1	4	yes	—
415	C₂²	C₂⁵×C₉	1	1	yes	characteristic
416	C₄	—	2	4	no	—
417	C₄	—	2	4	no	—
418	C₄	—	2	4	no	—
419	C₄	—	2	8	no	—
420	C₃	C₃×#3490	1	1	yes	characteristic
421	C₂	—	2	2	no	—
422	C₂	—	2	4	no	—
423	C₂	—	2	4	no	—
424	C₂	—	4	2	no	—
425	C₂	—	4	4	no	—
426	C₂	C₂²×C₉×#41	1	1	yes	characteristic
427	C₂	C₂×C₉×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂⁵
commutator	C₂²	C₂⁵×C₉
Frattini, socle, cosocle	C₂²×C₃	C₂⁵×C₃
prime radical	C₃×#3490	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. C₉×#551	C₂	semidirect
2. C₉×#546	C₂	semidirect
3. C₉×#543	C₂	semidirect
4. C₉×#538	C₂	semidirect
5. C₉×#534	C₂	semidirect
6. C₉×#525	C₂	semidirect
7. C₂×C₉×#120	C₂	semidirect
8. C₉×#518	C₂	semidirect
9. C₂²×C₉×C₂²⋊C₄	C₂	semidirect
12. C₂×C₉×#41	C₂²	semidirect
14. C₂²×D₄×C₉	C₂²	semidirect
15. C₂³×C₄×C₉	C₂²	semidirect
16. C₉×#126	C₂²	semidirect
17. C₉×#124	C₂²	semidirect
18. C₉×#123	C₂²	semidirect
19. C₉×#123	C₂²	semidirect
20. C₉×#123	C₂²	semidirect
21. C₉×C₂²⋊Q₈	C₂²	semidirect
22. C₉×C₂²⋊Q₈	C₂²	semidirect
23. C₉×C₂²⋊Q₈	C₂²	semidirect
24. C₉×#121	C₂²	semidirect
25. C₉×#121	C₂²	semidirect
26. C₉×#121	C₂²	semidirect
28. C₉×#120	C₂²	semidirect
29. C₉×#120	C₂²	semidirect
30. C₉×#120	C₂²	semidirect
31. C₄×D₄×C₉	C₂²	semidirect
32. C₄×D₄×C₉	C₂²	semidirect
33. C₄×D₄×C₉	C₂²	semidirect
34. C₉×#117	C₂²	semidirect
35. C₉×#117	C₂²	semidirect
39. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
40. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
41. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
42. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
60. C₂×Q₈×C₉	C₂³	semidirect
67. C₂×D₄×C₉	C₂³	semidirect
75. C₂²×C₄×C₉	C₂³	semidirect
76. C₉×C₄⋊C₄	C₂³	semidirect
77. C₉×C₄⋊C₄	C₂³	semidirect
78. C₉×C₄⋊C₄	C₂³	semidirect
79. C₉×C₄⋊C₄	C₂³	semidirect
87. C₉×C₂²⋊C₄	C₂³	semidirect
88. C₉×C₂²⋊C₄	C₂³	semidirect
89. C₄²×C₉	C₂³	semidirect
90. #3490	C₉	direct (N × H)
134. C₂³×C₉	#41	semidirect
157. #551	C₂×C₉	semidirect
158. #546	C₂×C₉	semidirect
159. #543	C₂×C₉	semidirect
160. #538	C₂×C₉	semidirect
161. #534	C₂×C₉	semidirect
162. #525	C₂×C₉	semidirect
163. C₂×#120	C₂×C₉	semidirect
164. #518	C₂×C₉	semidirect
165. C₂²×C₂²⋊C₄	C₂×C₉	semidirect
226. C₂×#41	C₂²×C₉	semidirect
228. C₂²×D₄	C₂²×C₉	semidirect
229. C₂³×C₄	C₂²×C₉	semidirect
230. #126	C₂²×C₉	semidirect
231. #124	C₂²×C₉	semidirect
232. #123	C₂²×C₉	semidirect
233. #123	C₂²×C₉	semidirect
234. #123	C₂²×C₉	semidirect
235. C₂²⋊Q₈	C₂²×C₉	semidirect
236. C₂²⋊Q₈	C₂²×C₉	semidirect
237. C₂²⋊Q₈	C₂²×C₉	semidirect
238. #121	C₂²×C₉	semidirect
239. #121	C₂²×C₉	semidirect
240. #121	C₂²×C₉	semidirect
242. #120	C₂²×C₉	semidirect
243. #120	C₂²×C₉	semidirect
244. #120	C₂²×C₉	semidirect
245. C₄×D₄	C₂²×C₉	semidirect
246. C₄×D₄	C₂²×C₉	semidirect
247. C₄×D₄	C₂²×C₉	semidirect
248. #117	C₂²×C₉	semidirect
249. #117	C₂²×C₉	semidirect
253. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
254. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
255. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
256. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
306. C₂×Q₈	C₂³×C₉	semidirect
313. C₂×D₄	C₂³×C₉	semidirect
321. C₂²×C₄	C₂³×C₉	semidirect
322. C₄⋊C₄	C₂³×C₉	semidirect
323. C₄⋊C₄	C₂³×C₉	semidirect
324. C₄⋊C₄	C₂³×C₉	semidirect
325. C₄⋊C₄	C₂³×C₉	semidirect
333. C₂²⋊C₄	C₂³×C₉	semidirect
334. C₂²⋊C₄	C₂³×C₉	semidirect
335. C₄²	C₂³×C₉	semidirect
357. C₉	#3490	direct (N × H)
369. C₂³	C₉×#41	semidirect

Maximal subgroups

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

subgroup	index
C₉×#551	2
C₉×#546	2
C₉×#543	2
C₉×#538	2
C₉×#534	2
C₉×#525	2
C₂×C₉×#120	2
C₉×#518	2
C₂²×C₉×C₂²⋊C₄	2
C₃×#3490	3

Subgroups — C9×#3490 #11768211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3490 #11768211