Subgroups — C₉×#3481 #11768202

Order 1152.

1863 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#554	C₂	1	2	yes	maximal, complemented
3	C₉×#553	C₂	1	4	yes	maximal, complemented
4	C₉×#551	C₂	1	4	yes	maximal, complemented
5	C₉×#546	C₂	1	4	yes	maximal, complemented
6	D₄²×C₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#529	C₂	1	4	yes	maximal, complemented
9	C₉×#525	C₂	1	4	yes	maximal, complemented
10	C₄×C₉×#41	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×D₄×C₉	C₂	1	4	yes	maximal, complemented
12	C₃×#3481	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	2	yes	—
14	C₂×C₉×#41	C₂²	1	2	yes	complemented
15	C₂²×D₄×C₉	C₂²	1	4	yes	—
16	C₂³×C₄×C₉	C₂²	1	4	yes	complemented
17	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₉×#127	C₂²	1	1	yes	characteristic
19	C₉×#126	C₂²	1	8	yes	complemented
20	C₉×#125	C₂²	1	4	yes	complemented
21	C₉×#124	C₂²	1	4	yes	complemented
22	C₉×#124	C₂²	1	2	yes	complemented
23	C₉×#123	C₂²	1	4	yes	complemented
24	C₉×#123	C₂²	1	4	yes	complemented
25	C₉×#123	C₂²	1	8	yes	complemented
26	C₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
27	C₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
28	C₉×#121	C₂²	1	4	yes	—
29	C₉×#121	C₂²	1	8	yes	complemented
30	C₉×#121	C₂²	1	4	yes	complemented
31	C₉×#120	C₂²	1	4	yes	—
32	C₉×#120	C₂²	1	4	yes	complemented
33	C₄×Q₈×C₉	C₂²	1	2	yes	complemented
34	C₄×Q₈×C₉	C₂²	1	2	yes	complemented
35	C₄×D₄×C₉	C₂²	1	2	yes	—
36	C₄×D₄×C₉	C₂²	1	4	yes	—
37	C₄×D₄×C₉	C₂²	1	2	yes	—
38	C₄×D₄×C₉	C₂²	1	4	yes	complemented
39	C₄×D₄×C₉	C₂²	1	8	yes	complemented
40	C₄×D₄×C₉	C₂²	1	4	yes	complemented
41	C₄×D₄×C₉	C₂²	1	4	yes	complemented
42	C₄×D₄×C₉	C₂²	1	8	yes	complemented
43	C₄×D₄×C₉	C₂²	1	4	yes	complemented
44	C₉×#117	C₂²	1	4	yes	complemented
45	C₉×#117	C₂²	1	4	yes	complemented
46	C₉×#117	C₂²	1	2	yes	complemented
47	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	complemented
48	C₂×C₉×C₂²⋊C₄	C₂²	1	8	yes	complemented
49	C₂×C₄²×C₉	C₂²	1	4	yes	complemented
50	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
51	C₃×#559	C₂×C₃	1	1	yes	characteristic
52	C₃×#554	C₂×C₃	1	2	yes	—
53	C₃×#553	C₂×C₃	1	4	yes	—
54	C₃×#551	C₂×C₃	1	4	yes	—
55	C₃×#546	C₂×C₃	1	4	yes	—
56	C₃×D₄²	C₂×C₃	1	1	yes	characteristic
57	C₃×#532	C₂×C₃	1	1	yes	characteristic
58	C₃×#529	C₂×C₃	1	4	yes	—
59	C₃×#525	C₂×C₃	1	4	yes	—
60	C₃×C₄×#41	C₂×C₃	1	2	yes	—
61	C₂×C₃×C₄×D₄	C₂×C₃	1	4	yes	—
62	C₂⁴×C₉	C₂³	1	4	yes	—
63	C₉×#41	—	2	8	no	—
64	C₉×#41	—	4	4	no	—
65	C₂×Q₈×C₉	C₂³	1	2	yes	—
66	C₂×Q₈×C₉	C₂³	1	2	yes	—
67	C₂×D₄×C₉	—	2	16	no	—
68	C₂×D₄×C₉	C₂³	1	8	yes	—
69	C₂×D₄×C₉	C₂³	1	4	yes	—
70	C₂×D₄×C₉	C₂³	1	4	yes	—
71	C₂×D₄×C₉	C₂³	1	2	yes	—
72	C₂×D₄×C₉	C₂³	1	4	yes	—
73	C₂×D₄×C₉	C₂³	1	2	yes	—
74	C₂²×C₄×C₉	—	4	8	no	—
75	C₂²×C₄×C₉	C₂³	1	4	yes	—
76	C₂²×C₄×C₉	C₂³	1	4	yes	—
77	C₂²×C₄×C₉	C₂³	1	2	yes	—
78	C₂²×C₄×C₉	C₂³	1	4	yes	—
79	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₉	C₂³	1	4	yes	—
81	C₂²×C₄×C₉	C₂³	1	8	yes	—
82	C₂²×C₄×C₉	C₂³	1	4	yes	—
83	C₉×C₄⋊C₄	C₂³	1	2	yes	—
84	C₉×C₄⋊C₄	C₂³	1	4	yes	—
85	C₉×C₄⋊C₄	C₂³	1	8	yes	—
86	C₉×C₄⋊C₄	C₂³	1	2	yes	—
87	C₉×C₄⋊C₄	C₂³	1	4	yes	—
88	C₉×C₄⋊C₄	C₂³	1	4	yes	—
89	C₉×C₄⋊C₄	C₂³	1	8	yes	—
90	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
91	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
92	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
93	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
94	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
98	C₄²×C₉	C₂³	1	1	yes	characteristic
99	C₄²×C₉	C₂³	1	4	yes	—
100	C₄²×C₉	C₂³	1	1	yes	characteristic
101	C₄²×C₉	C₂³	1	4	yes	—
102	C₄²×C₉	C₂³	1	2	yes	—
103	C₄²×C₉	C₂³	1	4	yes	—
104	#3481	C₉	1	1	yes	characteristic, direct product factor, Sylow
105	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
106	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
107	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
108	C₂³×C₃×C₄	C₂²×C₃	1	4	yes	—
109	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
110	C₃×#127	C₂²×C₃	1	1	yes	characteristic
111	C₃×#126	C₂²×C₃	1	8	yes	—
112	C₃×#125	C₂²×C₃	1	4	yes	—
113	C₃×#124	C₂²×C₃	1	4	yes	—
114	C₃×#124	C₂²×C₃	1	2	yes	—
115	C₃×#123	C₂²×C₃	1	4	yes	—
116	C₃×#123	C₂²×C₃	1	4	yes	—
117	C₃×#123	C₂²×C₃	1	8	yes	—
118	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
119	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
120	C₃×#121	C₂²×C₃	1	4	yes	—
121	C₃×#121	C₂²×C₃	1	8	yes	—
122	C₃×#121	C₂²×C₃	1	4	yes	—
123	C₃×#120	C₂²×C₃	1	4	yes	—
124	C₃×#120	C₂²×C₃	1	4	yes	—
125	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
126	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
127	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
128	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
129	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
130	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
131	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
132	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
133	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
134	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
135	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
136	C₃×#117	C₂²×C₃	1	4	yes	—
137	C₃×#117	C₂²×C₃	1	2	yes	—
138	C₃×#117	C₂²×C₃	1	4	yes	—
139	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
140	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
141	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
142	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
143	C₂³×C₉	—	2	16	no	—
144	C₂³×C₉	—	4	4	no	—
145	C₂³×C₉	C₂⁴	1	4	yes	—
146	C₂³×C₉	C₂⁴	1	1	yes	characteristic
147	C₂³×C₉	C₂⁴	1	4	yes	—
148	Q₈×C₉	—	2	4	no	—
149	Q₈×C₉	—	4	2	no	—
150	D₄×C₉	—	2	16	no	—
151	D₄×C₉	—	2	8	no	—
152	D₄×C₉	—	2	8	no	—
153	D₄×C₉	—	4	4	no	—
154	D₄×C₉	—	4	2	no	—
155	D₄×C₉	#41	1	8	yes	complemented
156	C₂×C₄×C₉	—	2	8	no	—
157	C₂×C₄×C₉	—	2	8	no	—
158	C₂×C₄×C₉	—	2	4	no	—
159	C₂×C₄×C₉	—	2	8	no	—
160	C₂×C₄×C₉	—	2	8	no	—
161	C₂×C₄×C₉	—	2	2	no	—
162	C₂×C₄×C₉	—	4	4	no	—
163	C₂×C₄×C₉	—	4	8	no	—
164	C₂×C₄×C₉	C₂⁴	1	2	yes	—
165	C₂×C₄×C₉	C₂⁴	1	4	yes	—
166	C₂×C₄×C₉	C₂⁴	1	4	yes	—
167	C₂×C₄×C₉	C₂⁴	1	4	yes	—
168	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₉	C₂⁴	1	4	yes	—
170	C₂×C₄×C₉	C₂⁴	1	2	yes	—
171	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
172	#559	C₂×C₉	1	1	yes	characteristic, complemented
173	#554	C₂×C₉	1	2	yes	complemented
174	#553	C₂×C₉	1	4	yes	complemented
175	#551	C₂×C₉	1	4	yes	complemented
176	#546	C₂×C₉	1	4	yes	complemented
177	D₄²	C₂×C₉	1	1	yes	characteristic, complemented
178	#532	C₂×C₉	1	1	yes	characteristic, complemented
179	#529	C₂×C₉	1	4	yes	complemented
180	#525	C₂×C₉	1	4	yes	complemented
181	C₄×#41	C₂×C₉	1	2	yes	complemented
182	C₂×C₄×D₄	C₂×C₉	1	4	yes	complemented
183	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
184	C₃×#41	—	2	8	no	—
185	C₃×#41	—	4	4	no	—
186	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
187	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
188	C₂×C₃×D₄	—	2	16	no	—
189	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
190	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
191	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
192	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
193	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
194	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
195	C₂²×C₃×C₄	—	4	8	no	—
196	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
197	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
198	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
199	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
200	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
202	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
203	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
204	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
205	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
206	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
207	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
208	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
209	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
210	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
211	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
212	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
213	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
214	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
215	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
216	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
217	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
218	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
219	C₃×C₄²	C₂³×C₃	1	2	yes	—
220	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
221	C₃×C₄²	C₂³×C₃	1	4	yes	—
222	C₃×C₄²	C₂³×C₃	1	4	yes	—
223	C₃×C₄²	C₂³×C₃	1	4	yes	—
224	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
225	C₂²×C₉	—	2	4	no	—
226	C₂²×C₉	—	2	4	no	—
227	C₂²×C₉	—	2	2	no	—
228	C₂²×C₉	—	2	8	no	—
229	C₂²×C₉	—	2	4	no	—
230	C₂²×C₉	—	2	1	no	—
231	C₂²×C₉	—	4	16	no	—
232	C₂²×C₉	C₂×#41	1	8	yes	—
233	C₂²×C₉	C₂⁵	1	1	yes	characteristic
234	C₄×C₉	—	2	2	no	—
235	C₄×C₉	—	2	4	no	—
236	C₄×C₉	—	2	4	no	—
237	C₄×C₉	—	2	4	no	—
238	C₄×C₉	—	2	4	no	—
239	C₄×C₉	—	2	1	no	—
240	C₄×C₉	C₂×#41	1	4	yes	—
241	C₄×C₉	H(5,𝔽₂)	1	2	yes	—
242	C₂×#41	C₂²×C₉	1	2	yes	—
243	C₂×#41	C₂²×C₉	1	2	yes	complemented
244	C₂²×D₄	C₂²×C₉	1	4	yes	—
245	C₂³×C₄	C₂²×C₉	1	4	yes	complemented
246	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
247	#127	C₂²×C₉	1	1	yes	characteristic
248	#126	C₂²×C₉	1	8	yes	complemented
249	#125	C₂²×C₉	1	4	yes	complemented
250	#124	C₂²×C₉	1	4	yes	complemented
251	#124	C₂²×C₉	1	2	yes	complemented
252	#123	C₂²×C₉	1	4	yes	complemented
253	#123	C₂²×C₉	1	4	yes	complemented
254	#123	C₂²×C₉	1	8	yes	complemented
255	C₂²⋊Q₈	C₂²×C₉	1	8	yes	complemented
256	C₂²⋊Q₈	C₂²×C₉	1	4	yes	complemented
257	#121	C₂²×C₉	1	4	yes	—
258	#121	C₂²×C₉	1	8	yes	complemented
259	#121	C₂²×C₉	1	4	yes	complemented
260	#120	C₂²×C₉	1	4	yes	—
261	#120	C₂²×C₉	1	4	yes	complemented
262	C₄×Q₈	C₂²×C₉	1	2	yes	complemented
263	C₄×Q₈	C₂²×C₉	1	2	yes	complemented
264	C₄×D₄	C₂²×C₉	1	2	yes	—
265	C₄×D₄	C₂²×C₉	1	4	yes	—
266	C₄×D₄	C₂²×C₉	1	2	yes	—
267	C₄×D₄	C₂²×C₉	1	8	yes	complemented
268	C₄×D₄	C₂²×C₉	1	4	yes	complemented
269	C₄×D₄	C₂²×C₉	1	8	yes	complemented
270	C₄×D₄	C₂²×C₉	1	4	yes	complemented
271	C₄×D₄	C₂²×C₉	1	4	yes	complemented
272	C₄×D₄	C₂²×C₉	1	4	yes	complemented
273	#117	C₂²×C₉	1	4	yes	complemented
274	#117	C₂²×C₉	1	2	yes	complemented
275	#117	C₂²×C₉	1	4	yes	complemented
276	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	complemented
277	C₂×C₂²⋊C₄	C₂²×C₉	1	8	yes	complemented
278	C₂×C₄²	C₂²×C₉	1	4	yes	complemented
279	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic, complemented
280	C₂³×C₃	—	2	16	no	—
281	C₂³×C₃	—	4	4	no	—
282	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
283	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
284	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
285	C₃×Q₈	—	2	4	no	—
286	C₃×Q₈	—	4	2	no	—
287	C₃×D₄	—	2	16	no	—
288	C₃×D₄	—	2	8	no	—
289	C₃×D₄	—	2	8	no	—
290	C₃×D₄	—	4	4	no	—
291	C₃×D₄	—	4	2	no	—
292	C₃×D₄	C₃×#41	1	8	yes	—
293	C₂×C₃×C₄	—	2	8	no	—
294	C₂×C₃×C₄	—	2	8	no	—
295	C₂×C₃×C₄	—	2	4	no	—
296	C₂×C₃×C₄	—	2	8	no	—
297	C₂×C₃×C₄	—	2	8	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	4	4	no	—
300	C₂×C₃×C₄	—	4	8	no	—
301	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
302	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
303	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
304	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
305	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
306	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
307	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
308	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
309	C₂×C₉	—	2	8	no	—
310	C₂×C₉	—	4	1	no	—
311	C₂×C₉	—	4	4	no	—
312	C₂×C₉	C₂²×#41	1	2	yes	—
313	C₂×C₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
314	C₂⁴	C₂³×C₉	1	4	yes	—
315	#41	—	2	8	no	—
316	#41	—	4	4	no	—
317	C₂×Q₈	C₂³×C₉	1	2	yes	—
318	C₂×Q₈	C₂³×C₉	1	2	yes	—
319	C₂×D₄	—	2	16	no	—
320	C₂×D₄	C₂³×C₉	1	8	yes	—
321	C₂×D₄	C₂³×C₉	1	4	yes	—
322	C₂×D₄	C₂³×C₉	1	4	yes	—
323	C₂×D₄	C₂³×C₉	1	2	yes	—
324	C₂×D₄	C₂³×C₉	1	4	yes	—
325	C₂×D₄	C₂³×C₉	1	2	yes	—
326	C₂²×C₄	—	4	8	no	—
327	C₂²×C₄	C₂³×C₉	1	4	yes	—
328	C₂²×C₄	C₂³×C₉	1	4	yes	—
329	C₂²×C₄	C₂³×C₉	1	2	yes	—
330	C₂²×C₄	C₂³×C₉	1	4	yes	—
331	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
332	C₂²×C₄	C₂³×C₉	1	4	yes	—
333	C₂²×C₄	C₂³×C₉	1	8	yes	—
334	C₂²×C₄	C₂³×C₉	1	4	yes	—
335	C₄⋊C₄	C₂³×C₉	1	2	yes	—
336	C₄⋊C₄	C₂³×C₉	1	4	yes	—
337	C₄⋊C₄	C₂³×C₉	1	8	yes	—
338	C₄⋊C₄	C₂³×C₉	1	2	yes	—
339	C₄⋊C₄	C₂³×C₉	1	4	yes	—
340	C₄⋊C₄	C₂³×C₉	1	4	yes	—
341	C₄⋊C₄	C₂³×C₉	1	8	yes	—
342	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
343	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
344	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
345	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
346	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
347	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
348	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
349	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
350	C₄²	C₂³×C₉	1	2	yes	—
351	C₄²	C₂³×C₉	1	1	yes	characteristic
352	C₄²	C₂³×C₉	1	4	yes	—
353	C₄²	C₂³×C₉	1	4	yes	—
354	C₄²	C₂³×C₉	1	1	yes	characteristic
355	C₄²	C₂³×C₉	1	4	yes	—
356	C₂²×C₃	—	2	4	no	—
357	C₂²×C₃	—	2	4	no	—
358	C₂²×C₃	—	2	2	no	—
359	C₂²×C₃	—	2	8	no	—
360	C₂²×C₃	—	2	4	no	—
361	C₂²×C₃	—	2	1	no	—
362	C₂²×C₃	—	4	16	no	—
363	C₂²×C₃	C₂×C₃×#41	1	8	yes	—
364	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
365	C₃×C₄	—	2	2	no	—
366	C₃×C₄	—	2	4	no	—
367	C₃×C₄	—	2	4	no	—
368	C₃×C₄	—	2	4	no	—
369	C₃×C₄	—	2	4	no	—
370	C₃×C₄	—	2	1	no	—
371	C₃×C₄	C₂×C₃×#41	1	4	yes	—
372	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
373	C₉	#3481	1	1	yes	characteristic, direct product factor, Sylow
374	C₂³	—	2	16	no	—
375	C₂³	—	4	4	no	—
376	C₂³	C₂⁴×C₉	1	4	yes	—
377	C₂³	C₂⁴×C₉	1	1	yes	characteristic
378	C₂³	C₂⁴×C₉	1	4	yes	—
379	Q₈	—	2	4	no	—
380	Q₈	—	4	2	no	—
381	D₄	—	2	16	no	—
382	D₄	—	2	8	no	—
383	D₄	—	2	8	no	—
384	D₄	—	4	4	no	—
385	D₄	—	4	2	no	—
386	D₄	C₉×#41	1	8	yes	complemented
387	C₂×C₄	—	2	8	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	8	no	—
395	C₂×C₄	C₂⁴×C₉	1	2	yes	—
396	C₂×C₄	C₂⁴×C₉	1	4	yes	—
397	C₂×C₄	C₂⁴×C₉	1	4	yes	—
398	C₂×C₄	C₂⁴×C₉	1	4	yes	—
399	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
400	C₂×C₄	C₂⁴×C₉	1	4	yes	—
401	C₂×C₄	C₂⁴×C₉	1	2	yes	—
402	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
403	C₂×C₃	—	2	8	no	—
404	C₂×C₃	—	4	4	no	—
405	C₂×C₃	—	4	1	no	—
406	C₂×C₃	C₂²×C₃×#41	1	2	yes	—
407	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
408	C₂²	—	2	4	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	8	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	4	16	no	—
415	C₂²	C₂×C₉×#41	1	8	yes	—
416	C₂²	C₂⁵×C₉	1	1	yes	characteristic
417	C₄	—	2	2	no	—
418	C₄	—	2	4	no	—
419	C₄	—	2	4	no	—
420	C₄	—	2	4	no	—
421	C₄	—	2	4	no	—
422	C₄	—	2	1	no	—
423	C₄	C₂×C₉×#41	1	4	yes	—
424	C₄	C₉×H(5,𝔽₂)	1	2	yes	—
425	C₃	C₃×#3481	1	1	yes	characteristic
426	C₂	—	2	8	no	—
427	C₂	—	4	4	no	—
428	C₂	—	4	1	no	—
429	C₂	C₂²×C₉×#41	1	2	yes	—
430	C₂	C₂×C₉×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂⁴
commutator	C₂²	C₂⁵×C₉
Frattini, socle, cosocle	C₂²×C₃	C₂⁵×C₃
prime radical	C₃×#3481	C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#559	C₂	semidirect
2. C₉×#554	C₂	semidirect
3. C₉×#553	C₂	semidirect
4. C₉×#551	C₂	semidirect
5. C₉×#546	C₂	semidirect
6. D₄²×C₉	C₂	semidirect
7. C₉×#532	C₂	semidirect
8. C₉×#529	C₂	semidirect
9. C₉×#525	C₂	semidirect
10. C₄×C₉×#41	C₂	semidirect
11. C₂×C₄×D₄×C₉	C₂	semidirect
14. C₂×C₉×#41	C₂²	semidirect
16. C₂³×C₄×C₉	C₂²	semidirect
17. C₉×C₄⋊Q₈	C₂²	semidirect
19. C₉×#126	C₂²	semidirect
20. C₉×#125	C₂²	semidirect
21. C₉×#124	C₂²	semidirect
22. C₉×#124	C₂²	semidirect
23. C₉×#123	C₂²	semidirect
24. C₉×#123	C₂²	semidirect
25. C₉×#123	C₂²	semidirect
26. C₉×C₂²⋊Q₈	C₂²	semidirect
27. C₉×C₂²⋊Q₈	C₂²	semidirect
29. C₉×#121	C₂²	semidirect
30. C₉×#121	C₂²	semidirect
32. C₉×#120	C₂²	semidirect
33. C₄×Q₈×C₉	C₂²	semidirect
34. C₄×Q₈×C₉	C₂²	semidirect
38. C₄×D₄×C₉	C₂²	semidirect
39. C₄×D₄×C₉	C₂²	semidirect
40. C₄×D₄×C₉	C₂²	semidirect
41. C₄×D₄×C₉	C₂²	semidirect
42. C₄×D₄×C₉	C₂²	semidirect
43. C₄×D₄×C₉	C₂²	semidirect
44. C₉×#117	C₂²	semidirect
45. C₉×#117	C₂²	semidirect
46. C₉×#117	C₂²	semidirect
47. C₂×C₉×C₄⋊C₄	C₂²	semidirect
48. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
49. C₂×C₄²×C₉	C₂²	semidirect
50. C₂×C₄²×C₉	C₂²	semidirect
104. #3481	C₉	direct (N × H)
155. D₄×C₉	#41	semidirect
172. #559	C₂×C₉	semidirect
173. #554	C₂×C₉	semidirect
174. #553	C₂×C₉	semidirect
175. #551	C₂×C₉	semidirect
176. #546	C₂×C₉	semidirect
177. D₄²	C₂×C₉	semidirect
178. #532	C₂×C₉	semidirect
179. #529	C₂×C₉	semidirect
180. #525	C₂×C₉	semidirect
181. C₄×#41	C₂×C₉	semidirect
182. C₂×C₄×D₄	C₂×C₉	semidirect
243. C₂×#41	C₂²×C₉	semidirect
245. C₂³×C₄	C₂²×C₉	semidirect
246. C₄⋊Q₈	C₂²×C₉	semidirect
248. #126	C₂²×C₉	semidirect
249. #125	C₂²×C₉	semidirect
250. #124	C₂²×C₉	semidirect
251. #124	C₂²×C₉	semidirect
252. #123	C₂²×C₉	semidirect
253. #123	C₂²×C₉	semidirect
254. #123	C₂²×C₉	semidirect
255. C₂²⋊Q₈	C₂²×C₉	semidirect
256. C₂²⋊Q₈	C₂²×C₉	semidirect
258. #121	C₂²×C₉	semidirect
259. #121	C₂²×C₉	semidirect
261. #120	C₂²×C₉	semidirect
262. C₄×Q₈	C₂²×C₉	semidirect
263. C₄×Q₈	C₂²×C₉	semidirect
267. C₄×D₄	C₂²×C₉	semidirect
268. C₄×D₄	C₂²×C₉	semidirect
269. C₄×D₄	C₂²×C₉	semidirect
270. C₄×D₄	C₂²×C₉	semidirect
271. C₄×D₄	C₂²×C₉	semidirect
272. C₄×D₄	C₂²×C₉	semidirect
273. #117	C₂²×C₉	semidirect
274. #117	C₂²×C₉	semidirect
275. #117	C₂²×C₉	semidirect
276. C₂×C₄⋊C₄	C₂²×C₉	semidirect
277. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
278. C₂×C₄²	C₂²×C₉	semidirect
279. C₂×C₄²	C₂²×C₉	semidirect
373. C₉	#3481	direct (N × H)
386. D₄	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×#559	2
C₉×#554	2
C₉×#553	2
C₉×#551	2
C₉×#546	2
D₄²×C₉	2
C₉×#532	2
C₉×#529	2
C₉×#525	2
C₄×C₉×#41	2
C₂×C₄×D₄×C₉	2
C₃×#3481	3

Subgroups — C9×#3481 #11768202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3481 #11768202