Subgroups — C₉×#3244 #11767965

Order 1152.

480 conjugacy classes of subgroups.

The subgroup lattice has 480 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, complemented
2	C₉×#542	C₂	1	1	yes	maximal, characteristic
3	C₉×#501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#498	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#489	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#488	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#485	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#483	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#482	C₂	1	1	yes	maximal, characteristic
10	C₉×#481	C₂	1	1	yes	maximal, characteristic
11	C₉×#479	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#478	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#476	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, complemented
16	C₃×#3244	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×#125	—	2	1	no	—
23	C₉×#125	C₂²	1	1	yes	characteristic
24	C₉×#125	C₂²	1	1	yes	characteristic
25	C₉×#124	—	2	1	no	—
26	C₉×#124	C₂²	1	1	yes	characteristic
27	C₉×#123	—	2	1	no	—
28	C₉×C₂²⋊Q₈	—	2	1	no	—
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×#121	C₂²	1	1	yes	characteristic
33	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
34	C₄×D₄×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×#106	C₂²	1	1	yes	characteristic
41	C₉×#106	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×#102	C₂²	1	1	yes	characteristic
53	C₉×#102	C₂²	1	1	yes	characteristic
54	C₉×#102	C₂²	1	1	yes	characteristic
55	C₉×#102	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×#542	C₂×C₃	1	1	yes	characteristic
62	C₃×#501	C₂×C₃	1	1	yes	characteristic
63	C₃×#498	C₂×C₃	1	1	yes	characteristic
64	C₃×#489	C₂×C₃	1	1	yes	characteristic
65	C₃×#488	C₂×C₃	1	1	yes	characteristic
66	C₃×#485	C₂×C₃	1	1	yes	characteristic
67	C₃×#483	C₂×C₃	1	1	yes	characteristic
68	C₃×#482	C₂×C₃	1	1	yes	characteristic
69	C₃×#481	C₂×C₃	1	1	yes	characteristic
70	C₃×#479	C₂×C₃	1	1	yes	characteristic
71	C₃×#478	C₂×C₃	1	1	yes	characteristic
72	C₃×#476	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	—	2	1	no	—
78	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
79	C₂×D₄×C₉	—	2	1	no	—
80	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₉	—	2	1	no	—
82	C₂²×C₄×C₉	—	2	1	no	—
83	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
84	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
86	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
87	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
99	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
100	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₉×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
107	C₉×C₂²⋊C₄	—	2	1	no	—
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	—	2	1	no	—
112	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
113	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
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	#3244	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×#125	—	2	1	no	—
125	C₃×#125	C₂²×C₃	1	1	yes	characteristic
126	C₃×#125	C₂²×C₃	1	1	yes	characteristic
127	C₃×#124	—	2	1	no	—
128	C₃×#124	C₂²×C₃	1	1	yes	characteristic
129	C₃×#123	—	2	1	no	—
130	C₃×C₂²⋊Q₈	—	2	1	no	—
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×#121	C₂²×C₃	1	1	yes	characteristic
135	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
136	C₃×C₄×D₄	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×#106	C₂²×C₃	1	1	yes	characteristic
143	C₃×#106	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×#102	C₂²×C₃	1	1	yes	characteristic
155	C₃×#102	C₂²×C₃	1	1	yes	characteristic
156	C₃×#102	C₂²×C₃	1	1	yes	characteristic
157	C₃×#102	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	—	2	1	no	—
163	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
164	Q₈×C₉	—	2	1	no	—
165	Q₈×C₉	—	2	1	no	—
166	Q₈×C₉	—	8	1	no	—
167	Q₈×C₉	—	8	1	no	—
168	Q₈×C₉	—	8	1	no	—
169	D₄×C₉	—	2	1	no	—
170	D₄×C₉	—	2	1	no	—
171	D₄×C₉	—	8	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	—	2	1	no	—
180	C₂×C₄×C₉	—	2	1	no	—
181	C₂×C₄×C₉	—	8	1	no	—
182	C₂×C₄×C₉	—	8	1	no	—
183	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
184	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
185	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
186	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
187	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
188	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
189	C₈×C₉	—	2	1	no	—
190	C₈×C₉	—	2	1	no	—
191	C₈×C₉	—	2	1	no	—
192	C₈×C₉	—	2	1	no	—
193	#544	C₂×C₉	1	1	yes	characteristic, complemented
194	#542	C₂×C₉	1	1	yes	characteristic
195	#501	C₂×C₉	1	1	yes	characteristic, complemented
196	#498	C₂×C₉	1	1	yes	characteristic, complemented
197	#489	C₂×C₉	1	1	yes	characteristic, complemented
198	#488	C₂×C₉	1	1	yes	characteristic, complemented
199	#485	C₂×C₉	1	1	yes	characteristic, complemented
200	#483	C₂×C₉	1	1	yes	characteristic, complemented
201	#482	C₂×C₉	1	1	yes	characteristic
202	#481	C₂×C₉	1	1	yes	characteristic
203	#479	C₂×C₉	1	1	yes	characteristic, complemented
204	#478	C₂×C₉	1	1	yes	characteristic, complemented
205	#476	C₂×C₉	1	1	yes	characteristic, complemented
206	#475	C₂×C₉	1	1	yes	characteristic, complemented
207	#433	C₂×C₉	1	1	yes	characteristic, complemented
208	C₂×C₃×Q₈	—	2	1	no	—
209	C₂×C₃×Q₈	—	2	1	no	—
210	C₂×C₃×Q₈	—	2	1	no	—
211	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
212	C₂×C₃×D₄	—	2	1	no	—
213	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
214	C₂²×C₃×C₄	—	2	1	no	—
215	C₂²×C₃×C₄	—	2	1	no	—
216	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
218	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
219	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
220	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
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	—	2	1	no	—
231	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
232	C₃×C₄⋊C₄	C₃×D₄	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×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
239	C₃×C₂²⋊C₄	—	2	1	no	—
240	C₃×C₂²⋊C₄	—	2	1	no	—
241	C₃×C₂²⋊C₄	—	2	1	no	—
242	C₃×C₂²⋊C₄	—	2	1	no	—
243	C₃×C₂²⋊C₄	—	2	1	no	—
244	C₃×C₂²⋊C₄	—	2	1	no	—
245	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
246	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
247	C₃×C₄²	—	2	1	no	—
248	C₃×C₄²	—	2	1	no	—
249	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
250	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
251	C₂²×C₉	—	2	1	no	—
252	C₂²×C₉	—	2	1	no	—
253	C₂²×C₉	—	2	1	no	—
254	C₂²×C₉	—	4	1	no	—
255	C₂²×C₉	—	4	1	no	—
256	C₂²×C₉	—	4	1	no	—
257	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
258	C₄×C₉	—	2	1	no	—
259	C₄×C₉	—	2	1	no	—
260	C₄×C₉	—	2	1	no	—
261	C₄×C₉	—	2	1	no	—
262	C₄×C₉	—	2	1	no	—
263	C₄×C₉	—	4	1	no	—
264	C₄×C₉	—	4	1	no	—
265	C₄×C₉	—	4	1	no	—
266	C₄×C₉	—	4	1	no	—
267	C₄×C₉	—	4	1	no	—
268	C₄×C₉	—	4	1	no	—
269	C₄×C₉	—	4	1	no	—
270	C₄×C₉	2₋¹⁺⁴	1	1	yes	characteristic
271	C₄×C₉	2₋¹⁺⁴	1	1	yes	characteristic
272	C₄⋊Q₈	—	2	1	no	—
273	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
274	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
275	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
276	#126	—	2	1	no	—
277	#125	—	2	1	no	—
278	#125	C₂²×C₉	1	1	yes	characteristic
279	#125	C₂²×C₉	1	1	yes	characteristic
280	#124	—	2	1	no	—
281	#124	C₂²×C₉	1	1	yes	characteristic
282	#123	—	2	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	C₂²⋊Q₈	—	2	1	no	—
285	C₂²⋊Q₈	—	2	1	no	—
286	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
287	#121	C₂²×C₉	1	1	yes	characteristic
288	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
289	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
290	#117	C₂²×C₉	1	1	yes	characteristic
291	#117	C₂²×C₉	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
293	#107	C₂²×C₉	1	1	yes	characteristic
294	#107	C₂²×C₉	1	1	yes	characteristic
295	#106	C₂²×C₉	1	1	yes	characteristic
296	#106	C₂²×C₉	1	1	yes	characteristic
297	#106	C₂²×C₉	1	1	yes	characteristic
298	#106	C₂²×C₉	1	1	yes	characteristic
299	#106	C₂²×C₉	1	1	yes	characteristic
300	#106	C₂²×C₉	1	1	yes	characteristic
301	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
302	C₄⋊C₈	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	#103	C₂²×C₉	1	1	yes	characteristic
307	#102	C₂²×C₉	1	1	yes	characteristic
308	#102	C₂²×C₉	1	1	yes	characteristic
309	#102	C₂²×C₉	1	1	yes	characteristic
310	#102	C₂²×C₉	1	1	yes	characteristic
311	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
312	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
313	#97	C₂²×C₉	1	1	yes	characteristic
314	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
315	C₂³×C₃	—	2	1	no	—
316	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
317	C₃×Q₈	—	2	1	no	—
318	C₃×Q₈	—	2	1	no	—
319	C₃×Q₈	—	8	1	no	—
320	C₃×Q₈	—	8	1	no	—
321	C₃×Q₈	—	8	1	no	—
322	C₃×D₄	—	2	1	no	—
323	C₃×D₄	—	2	1	no	—
324	C₃×D₄	—	8	1	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	2	1	no	—
328	C₂×C₃×C₄	—	2	1	no	—
329	C₂×C₃×C₄	—	2	1	no	—
330	C₂×C₃×C₄	—	2	1	no	—
331	C₂×C₃×C₄	—	2	1	no	—
332	C₂×C₃×C₄	—	2	1	no	—
333	C₂×C₃×C₄	—	2	1	no	—
334	C₂×C₃×C₄	—	8	1	no	—
335	C₂×C₃×C₄	—	8	1	no	—
336	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
337	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
338	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
341	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
342	C₃×C₈	—	2	1	no	—
343	C₃×C₈	—	2	1	no	—
344	C₃×C₈	—	2	1	no	—
345	C₃×C₈	—	2	1	no	—
346	C₂×C₉	—	4	1	no	—
347	C₂×C₉	—	8	1	no	—
348	C₂×C₉	#536	1	1	yes	characteristic
349	C₂×C₉	#577	1	1	yes	characteristic
350	C₂×C₉	#577	1	1	yes	characteristic
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
360	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
361	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
362	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
363	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
375	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
376	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
377	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
378	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
379	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
380	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
381	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₂²⋊C₄	—	2	1	no	—
388	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
389	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
390	C₄²	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	C₂³×C₉	1	1	yes	characteristic
393	C₄²	C₂³×C₉	1	1	yes	characteristic
394	C₂²×C₃	—	2	1	no	—
395	C₂²×C₃	—	2	1	no	—
396	C₂²×C₃	—	2	1	no	—
397	C₂²×C₃	—	4	1	no	—
398	C₂²×C₃	—	4	1	no	—
399	C₂²×C₃	—	4	1	no	—
400	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
401	C₃×C₄	—	2	1	no	—
402	C₃×C₄	—	2	1	no	—
403	C₃×C₄	—	2	1	no	—
404	C₃×C₄	—	2	1	no	—
405	C₃×C₄	—	2	1	no	—
406	C₃×C₄	—	4	1	no	—
407	C₃×C₄	—	4	1	no	—
408	C₃×C₄	—	4	1	no	—
409	C₃×C₄	—	4	1	no	—
410	C₃×C₄	—	4	1	no	—
411	C₃×C₄	—	4	1	no	—
412	C₃×C₄	—	4	1	no	—
413	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
414	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
415	C₉	#3244	1	1	yes	characteristic, direct product factor, Sylow
416	C₂³	—	2	1	no	—
417	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
418	Q₈	—	2	1	no	—
419	Q₈	—	2	1	no	—
420	Q₈	—	8	1	no	—
421	Q₈	—	8	1	no	—
422	Q₈	—	8	1	no	—
423	D₄	—	2	1	no	—
424	D₄	—	2	1	no	—
425	D₄	—	8	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	8	1	no	—
436	C₂×C₄	—	8	1	no	—
437	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
438	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
439	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
440	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
441	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
442	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
443	C₈	—	2	1	no	—
444	C₈	—	2	1	no	—
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₂×C₃	—	4	1	no	—
448	C₂×C₃	—	8	1	no	—
449	C₂×C₃	C₃×#536	1	1	yes	characteristic
450	C₂×C₃	C₃×#577	1	1	yes	characteristic
451	C₂×C₃	C₃×#577	1	1	yes	characteristic
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	1	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	1	no	—
470	C₄	—	4	1	no	—
471	C₄	C₉×2₋¹⁺⁴	1	1	yes	characteristic
472	C₄	C₉×2₋¹⁺⁴	1	1	yes	characteristic
473	C₃	C₃×#3244	1	1	yes	characteristic
474	C₂	—	4	1	no	—
475	C₂	—	8	1	no	—
476	C₂	C₉×#536	1	1	yes	characteristic
477	C₂	C₉×#577	1	1	yes	characteristic
478	C₂	C₉×#577	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	C₃×#121	C₂²×C₃
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
1. C₉×#544	C₂	semidirect
3. C₉×#501	C₂	semidirect
4. C₉×#498	C₂	semidirect
5. C₉×#489	C₂	semidirect
6. C₉×#488	C₂	semidirect
7. C₉×#485	C₂	semidirect
8. C₉×#483	C₂	semidirect
11. C₉×#479	C₂	semidirect
12. C₉×#478	C₂	semidirect
13. C₉×#476	C₂	semidirect
14. C₉×#475	C₂	semidirect
15. C₉×#433	C₂	semidirect
118. #3244	C₉	direct (N × H)
193. #544	C₂×C₉	semidirect
195. #501	C₂×C₉	semidirect
196. #498	C₂×C₉	semidirect
197. #489	C₂×C₉	semidirect
198. #488	C₂×C₉	semidirect
199. #485	C₂×C₉	semidirect
200. #483	C₂×C₉	semidirect
203. #479	C₂×C₉	semidirect
204. #478	C₂×C₉	semidirect
205. #476	C₂×C₉	semidirect
206. #475	C₂×C₉	semidirect
207. #433	C₂×C₉	semidirect
415. C₉	#3244	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×#542	2
C₉×#501	2
C₉×#498	2
C₉×#489	2
C₉×#488	2
C₉×#485	2
C₉×#483	2
C₉×#482	2
C₉×#481	2
C₉×#479	2
C₉×#478	2
C₉×#476	2
C₉×#475	2
C₉×#433	2
C₃×#3244	3

Subgroups — C9×#3244 #11767965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3244 #11767965