Subgroups — C₉×#3242 #11767963

Order 1152.

462 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#544	C₂	1	1	yes	maximal, characteristic
2	C₉×#541	C₂	1	1	yes	maximal, characteristic
3	C₉×#501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#499	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#491	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#485	C₂	1	1	yes	maximal, characteristic
8	C₉×#485	C₂	1	1	yes	maximal, characteristic
9	C₉×#484	C₂	1	1	yes	maximal, characteristic
10	C₉×#483	C₂	1	1	yes	maximal, characteristic
11	C₉×#479	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#479	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#477	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#433	C₂	1	1	yes	maximal, characteristic
16	C₃×#3242	C₃	1	1	yes	maximal, characteristic
17	C₉×C₄⋊Q₈	—	2	1	no	—
18	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₉×#126	—	2	1	no	—
22	C₉×#126	—	2	1	no	—
23	C₉×#125	—	2	1	no	—
24	C₉×#125	—	2	1	no	—
25	C₉×#125	—	2	1	no	—
26	C₉×#125	C₂²	1	1	yes	characteristic
27	C₉×#125	C₂²	1	1	yes	characteristic
28	C₉×#125	C₂²	1	1	yes	characteristic
29	C₉×C₂²⋊Q₈	—	2	1	no	—
30	C₉×C₂²⋊Q₈	—	2	1	no	—
31	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
34	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
35	C₉×#117	C₂²	1	1	yes	characteristic
36	C₉×#117	C₂²	1	1	yes	characteristic
37	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₉×#107	C₂²	1	1	yes	characteristic
39	C₉×#107	C₂²	1	1	yes	characteristic
40	C₉×#107	C₂²	1	1	yes	characteristic
41	C₉×#107	C₂²	1	1	yes	characteristic
42	C₉×#106	C₂²	1	1	yes	characteristic
43	C₉×#106	C₂²	1	1	yes	characteristic
44	C₉×#106	C₂²	1	1	yes	characteristic
45	C₉×#106	C₂²	1	1	yes	characteristic
46	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₉×#103	C₂²	1	1	yes	characteristic
49	C₉×#103	C₂²	1	1	yes	characteristic
50	C₉×#103	C₂²	1	1	yes	characteristic
51	C₉×#103	C₂²	1	1	yes	characteristic
52	C₉×#103	C₂²	1	1	yes	characteristic
53	C₉×#103	C₂²	1	1	yes	characteristic
54	C₉×#103	C₂²	1	1	yes	characteristic
55	C₉×#103	C₂²	1	1	yes	characteristic
56	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₉×#97	C₂²	1	1	yes	characteristic
59	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
60	C₃×#544	C₂×C₃	1	1	yes	characteristic
61	C₃×#541	C₂×C₃	1	1	yes	characteristic
62	C₃×#501	C₂×C₃	1	1	yes	characteristic
63	C₃×#499	C₂×C₃	1	1	yes	characteristic
64	C₃×#491	C₂×C₃	1	1	yes	characteristic
65	C₃×#487	C₂×C₃	1	1	yes	characteristic
66	C₃×#485	C₂×C₃	1	1	yes	characteristic
67	C₃×#485	C₂×C₃	1	1	yes	characteristic
68	C₃×#484	C₂×C₃	1	1	yes	characteristic
69	C₃×#483	C₂×C₃	1	1	yes	characteristic
70	C₃×#479	C₂×C₃	1	1	yes	characteristic
71	C₃×#479	C₂×C₃	1	1	yes	characteristic
72	C₃×#477	C₂×C₃	1	1	yes	characteristic
73	C₃×#475	C₂×C₃	1	1	yes	characteristic
74	C₃×#433	C₂×C₃	1	1	yes	characteristic
75	C₂×Q₈×C₉	—	2	1	no	—
76	C₂×Q₈×C₉	—	2	1	no	—
77	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
78	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₉	—	2	1	no	—
80	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
81	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
82	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
83	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
84	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
85	C₉×C₄⋊C₄	—	2	1	no	—
86	C₉×C₄⋊C₄	—	2	1	no	—
87	C₉×C₄⋊C₄	—	2	1	no	—
88	C₉×C₄⋊C₄	—	2	1	no	—
89	C₉×C₄⋊C₄	—	2	1	no	—
90	C₉×C₄⋊C₄	—	2	1	no	—
91	C₉×C₄⋊C₄	—	2	1	no	—
92	C₉×C₄⋊C₄	—	2	1	no	—
93	C₉×C₄⋊C₄	—	2	1	no	—
94	C₉×C₄⋊C₄	—	2	1	no	—
95	C₉×C₄⋊C₄	—	2	1	no	—
96	C₉×C₄⋊C₄	—	2	1	no	—
97	C₉×C₄⋊C₄	—	2	1	no	—
98	C₉×C₄⋊C₄	—	2	1	no	—
99	C₉×C₄⋊C₄	—	2	1	no	—
100	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
101	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
102	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₉×C₂²⋊C₄	—	2	1	no	—
109	C₉×C₂²⋊C₄	—	2	1	no	—
110	C₉×C₂²⋊C₄	—	2	1	no	—
111	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
112	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
113	C₄²×C₉	—	2	1	no	—
114	C₄²×C₉	—	2	1	no	—
115	C₄²×C₉	—	2	1	no	—
116	C₄²×C₉	C₂³	1	1	yes	characteristic
117	C₄²×C₉	C₂³	1	1	yes	characteristic
118	#3242	C₉	1	1	yes	characteristic, direct product factor, Sylow
119	C₃×C₄⋊Q₈	—	2	1	no	—
120	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
121	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
122	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
123	C₃×#126	—	2	1	no	—
124	C₃×#126	—	2	1	no	—
125	C₃×#125	—	2	1	no	—
126	C₃×#125	—	2	1	no	—
127	C₃×#125	—	2	1	no	—
128	C₃×#125	C₂²×C₃	1	1	yes	characteristic
129	C₃×#125	C₂²×C₃	1	1	yes	characteristic
130	C₃×#125	C₂²×C₃	1	1	yes	characteristic
131	C₃×C₂²⋊Q₈	—	2	1	no	—
132	C₃×C₂²⋊Q₈	—	2	1	no	—
133	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
134	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
135	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
136	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
137	C₃×#117	C₂²×C₃	1	1	yes	characteristic
138	C₃×#117	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	C₃×#107	C₂²×C₃	1	1	yes	characteristic
141	C₃×#107	C₂²×C₃	1	1	yes	characteristic
142	C₃×#107	C₂²×C₃	1	1	yes	characteristic
143	C₃×#107	C₂²×C₃	1	1	yes	characteristic
144	C₃×#106	C₂²×C₃	1	1	yes	characteristic
145	C₃×#106	C₂²×C₃	1	1	yes	characteristic
146	C₃×#106	C₂²×C₃	1	1	yes	characteristic
147	C₃×#106	C₂²×C₃	1	1	yes	characteristic
148	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
149	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
150	C₃×#103	C₂²×C₃	1	1	yes	characteristic
151	C₃×#103	C₂²×C₃	1	1	yes	characteristic
152	C₃×#103	C₂²×C₃	1	1	yes	characteristic
153	C₃×#103	C₂²×C₃	1	1	yes	characteristic
154	C₃×#103	C₂²×C₃	1	1	yes	characteristic
155	C₃×#103	C₂²×C₃	1	1	yes	characteristic
156	C₃×#103	C₂²×C₃	1	1	yes	characteristic
157	C₃×#103	C₂²×C₃	1	1	yes	characteristic
158	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
159	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
160	C₃×#97	C₂²×C₃	1	1	yes	characteristic
161	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
162	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
163	Q₈×C₉	—	2	1	no	—
164	Q₈×C₉	—	2	1	no	—
165	Q₈×C₉	—	2	1	no	—
166	Q₈×C₉	—	2	1	no	—
167	Q₈×C₉	—	8	1	no	—
168	Q₈×C₉	—	8	1	no	—
169	C₂×C₄×C₉	—	2	1	no	—
170	C₂×C₄×C₉	—	2	1	no	—
171	C₂×C₄×C₉	—	2	1	no	—
172	C₂×C₄×C₉	—	2	1	no	—
173	C₂×C₄×C₉	—	2	1	no	—
174	C₂×C₄×C₉	—	2	1	no	—
175	C₂×C₄×C₉	—	2	1	no	—
176	C₂×C₄×C₉	—	2	1	no	—
177	C₂×C₄×C₉	—	2	1	no	—
178	C₂×C₄×C₉	—	2	1	no	—
179	C₂×C₄×C₉	—	8	1	no	—
180	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
181	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
182	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
183	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
184	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
185	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
186	C₈×C₉	—	2	1	no	—
187	C₈×C₉	—	2	1	no	—
188	C₈×C₉	—	2	1	no	—
189	C₈×C₉	—	2	1	no	—
190	#544	C₂×C₉	1	1	yes	characteristic
191	#541	C₂×C₉	1	1	yes	characteristic
192	#501	C₂×C₉	1	1	yes	characteristic, complemented
193	#499	C₂×C₉	1	1	yes	characteristic, complemented
194	#491	C₂×C₉	1	1	yes	characteristic, complemented
195	#487	C₂×C₉	1	1	yes	characteristic, complemented
196	#485	C₂×C₉	1	1	yes	characteristic
197	#485	C₂×C₉	1	1	yes	characteristic
198	#484	C₂×C₉	1	1	yes	characteristic
199	#483	C₂×C₉	1	1	yes	characteristic
200	#479	C₂×C₉	1	1	yes	characteristic, complemented
201	#479	C₂×C₉	1	1	yes	characteristic, complemented
202	#477	C₂×C₉	1	1	yes	characteristic, complemented
203	#475	C₂×C₉	1	1	yes	characteristic, complemented
204	#433	C₂×C₉	1	1	yes	characteristic
205	C₂×C₃×Q₈	—	2	1	no	—
206	C₂×C₃×Q₈	—	2	1	no	—
207	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
208	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
209	C₂²×C₃×C₄	—	2	1	no	—
210	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
211	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
212	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
213	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
214	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
215	C₃×C₄⋊C₄	—	2	1	no	—
216	C₃×C₄⋊C₄	—	2	1	no	—
217	C₃×C₄⋊C₄	—	2	1	no	—
218	C₃×C₄⋊C₄	—	2	1	no	—
219	C₃×C₄⋊C₄	—	2	1	no	—
220	C₃×C₄⋊C₄	—	2	1	no	—
221	C₃×C₄⋊C₄	—	2	1	no	—
222	C₃×C₄⋊C₄	—	2	1	no	—
223	C₃×C₄⋊C₄	—	2	1	no	—
224	C₃×C₄⋊C₄	—	2	1	no	—
225	C₃×C₄⋊C₄	—	2	1	no	—
226	C₃×C₄⋊C₄	—	2	1	no	—
227	C₃×C₄⋊C₄	—	2	1	no	—
228	C₃×C₄⋊C₄	—	2	1	no	—
229	C₃×C₄⋊C₄	—	2	1	no	—
230	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
231	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
232	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
233	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
234	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
235	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
236	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
237	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
238	C₃×C₂²⋊C₄	—	2	1	no	—
239	C₃×C₂²⋊C₄	—	2	1	no	—
240	C₃×C₂²⋊C₄	—	2	1	no	—
241	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
242	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
243	C₃×C₄²	—	2	1	no	—
244	C₃×C₄²	—	2	1	no	—
245	C₃×C₄²	—	2	1	no	—
246	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
247	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
248	C₂²×C₉	—	2	1	no	—
249	C₂²×C₉	—	2	1	no	—
250	C₂²×C₉	—	2	1	no	—
251	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
252	C₄×C₉	—	2	1	no	—
253	C₄×C₉	—	2	1	no	—
254	C₄×C₉	—	2	1	no	—
255	C₄×C₉	—	2	1	no	—
256	C₄×C₉	—	2	1	no	—
257	C₄×C₉	—	4	1	no	—
258	C₄×C₉	—	4	1	no	—
259	C₄×C₉	—	4	1	no	—
260	C₄×C₉	—	4	1	no	—
261	C₄×C₉	—	4	1	no	—
262	C₄×C₉	—	4	1	no	—
263	C₄×C₉	—	4	1	no	—
264	C₄×C₉	—	4	1	no	—
265	C₄×C₉	2₋¹⁺⁴	1	1	yes	characteristic
266	C₄×C₉	2₋¹⁺⁴	1	1	yes	characteristic
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
269	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
270	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
271	#126	—	2	1	no	—
272	#126	—	2	1	no	—
273	#125	—	2	1	no	—
274	#125	—	2	1	no	—
275	#125	—	2	1	no	—
276	#125	C₂²×C₉	1	1	yes	characteristic
277	#125	C₂²×C₉	1	1	yes	characteristic
278	#125	C₂²×C₉	1	1	yes	characteristic
279	C₂²⋊Q₈	—	2	1	no	—
280	C₂²⋊Q₈	—	2	1	no	—
281	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
282	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
283	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
284	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
285	#117	C₂²×C₉	1	1	yes	characteristic
286	#117	C₂²×C₉	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
288	#107	C₂²×C₉	1	1	yes	characteristic
289	#107	C₂²×C₉	1	1	yes	characteristic
290	#107	C₂²×C₉	1	1	yes	characteristic
291	#107	C₂²×C₉	1	1	yes	characteristic
292	#106	C₂²×C₉	1	1	yes	characteristic
293	#106	C₂²×C₉	1	1	yes	characteristic
294	#106	C₂²×C₉	1	1	yes	characteristic
295	#106	C₂²×C₉	1	1	yes	characteristic
296	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
297	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
298	#103	C₂²×C₉	1	1	yes	characteristic
299	#103	C₂²×C₉	1	1	yes	characteristic
300	#103	C₂²×C₉	1	1	yes	characteristic
301	#103	C₂²×C₉	1	1	yes	characteristic
302	#103	C₂²×C₉	1	1	yes	characteristic
303	#103	C₂²×C₉	1	1	yes	characteristic
304	#103	C₂²×C₉	1	1	yes	characteristic
305	#103	C₂²×C₉	1	1	yes	characteristic
306	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
307	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
308	#97	C₂²×C₉	1	1	yes	characteristic
309	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
310	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
311	C₃×Q₈	—	2	1	no	—
312	C₃×Q₈	—	2	1	no	—
313	C₃×Q₈	—	2	1	no	—
314	C₃×Q₈	—	2	1	no	—
315	C₃×Q₈	—	8	1	no	—
316	C₃×Q₈	—	8	1	no	—
317	C₂×C₃×C₄	—	2	1	no	—
318	C₂×C₃×C₄	—	2	1	no	—
319	C₂×C₃×C₄	—	2	1	no	—
320	C₂×C₃×C₄	—	2	1	no	—
321	C₂×C₃×C₄	—	2	1	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	2	1	no	—
324	C₂×C₃×C₄	—	2	1	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	8	1	no	—
328	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
331	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
334	C₃×C₈	—	2	1	no	—
335	C₃×C₈	—	2	1	no	—
336	C₃×C₈	—	2	1	no	—
337	C₃×C₈	—	2	1	no	—
338	C₂×C₉	—	4	1	no	—
339	C₂×C₉	#536	1	1	yes	characteristic
340	C₂×C₉	#577	1	1	yes	characteristic
341	C₂×C₉	#578	1	1	yes	characteristic
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
345	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
348	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
349	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
350	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
351	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
368	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
369	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
370	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
371	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
372	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
373	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
374	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	2	1	no	—
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
379	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	C₂³×C₉	1	1	yes	characteristic
384	C₄²	C₂³×C₉	1	1	yes	characteristic
385	C₂²×C₃	—	2	1	no	—
386	C₂²×C₃	—	2	1	no	—
387	C₂²×C₃	—	2	1	no	—
388	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
389	C₃×C₄	—	2	1	no	—
390	C₃×C₄	—	2	1	no	—
391	C₃×C₄	—	2	1	no	—
392	C₃×C₄	—	2	1	no	—
393	C₃×C₄	—	2	1	no	—
394	C₃×C₄	—	4	1	no	—
395	C₃×C₄	—	4	1	no	—
396	C₃×C₄	—	4	1	no	—
397	C₃×C₄	—	4	1	no	—
398	C₃×C₄	—	4	1	no	—
399	C₃×C₄	—	4	1	no	—
400	C₃×C₄	—	4	1	no	—
401	C₃×C₄	—	4	1	no	—
402	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
403	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
404	C₉	#3242	1	1	yes	characteristic, direct product factor, Sylow
405	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
406	Q₈	—	2	1	no	—
407	Q₈	—	2	1	no	—
408	Q₈	—	2	1	no	—
409	Q₈	—	2	1	no	—
410	Q₈	—	8	1	no	—
411	Q₈	—	8	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	8	1	no	—
423	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
424	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
425	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
426	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
427	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
428	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
429	C₈	—	2	1	no	—
430	C₈	—	2	1	no	—
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₂×C₃	—	4	1	no	—
434	C₂×C₃	C₃×#536	1	1	yes	characteristic
435	C₂×C₃	C₃×#577	1	1	yes	characteristic
436	C₂×C₃	C₃×#578	1	1	yes	characteristic
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	1	no	—
448	C₄	—	4	1	no	—
449	C₄	—	4	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	C₉×2₋¹⁺⁴	1	1	yes	characteristic
455	C₄	C₉×2₋¹⁺⁴	1	1	yes	characteristic
456	C₃	C₃×#3242	1	1	yes	characteristic
457	C₂	—	4	1	no	—
458	C₂	C₉×#536	1	1	yes	characteristic
459	C₂	C₉×#577	1	1	yes	characteristic
460	C₂	C₉×#578	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂²×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₂³×C₃	C₂×C₃×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉×#501	C₂	semidirect
4. C₉×#499	C₂	semidirect
5. C₉×#491	C₂	semidirect
6. C₉×#487	C₂	semidirect
11. C₉×#479	C₂	semidirect
12. C₉×#479	C₂	semidirect
13. C₉×#477	C₂	semidirect
14. C₉×#475	C₂	semidirect
118. #3242	C₉	direct (N × H)
192. #501	C₂×C₉	semidirect
193. #499	C₂×C₉	semidirect
194. #491	C₂×C₉	semidirect
195. #487	C₂×C₉	semidirect
200. #479	C₂×C₉	semidirect
201. #479	C₂×C₉	semidirect
202. #477	C₂×C₉	semidirect
203. #475	C₂×C₉	semidirect
404. C₉	#3242	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#544	2
C₉×#541	2
C₉×#501	2
C₉×#499	2
C₉×#491	2
C₉×#487	2
C₉×#485	2
C₉×#484	2
C₉×#483	2
C₉×#479	2
C₉×#477	2
C₉×#475	2
C₉×#433	2
C₃×#3242	3

Subgroups — C9×#3242 #11767963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3242 #11767963