Subgroups — C₉×#2482 #11767203

Order 1152.

1008 conjugacy classes of subgroups.

The subgroup lattice has 327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₉×#399	C₂	1	2	yes	maximal, complemented
4	C₉×#397	C₂	1	2	yes	maximal, complemented
5	C₉×#388	C₂	1	4	yes	maximal, complemented
6	C₉×#385	C₂	1	2	yes	maximal, complemented
7	C₉×#381	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#379	C₂	1	2	yes	maximal
9	C₃×#2482	C₃	1	1	yes	maximal, characteristic
10	C₂⁵×C₉	C₂²	1	1	yes	characteristic
11	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₉×#117	—	2	4	no	—
14	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	complemented
17	C₂×C₉×C₂²⋊C₄	—	2	4	no	—
18	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	—
21	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	—
24	C₂×C₄²×C₉	C₂²	1	2	yes	complemented
25	C₉×#95	C₂²	1	2	yes	complemented
26	C₉×#95	C₂²	1	2	yes	complemented
27	C₉×#95	C₂²	1	4	yes	complemented
28	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
29	C₂²×C₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
30	C₃×#399	C₂×C₃	1	2	yes	—
31	C₃×#397	C₂×C₃	1	2	yes	—
32	C₃×#388	C₂×C₃	1	4	yes	—
33	C₃×#385	C₂×C₃	1	2	yes	—
34	C₃×#381	C₂×C₃	1	1	yes	characteristic
35	C₃×#379	C₂×C₃	1	2	yes	—
36	C₂⁴×C₉	—	2	2	no	—
37	C₂⁴×C₉	—	2	4	no	—
38	C₂⁴×C₉	—	2	4	no	—
39	C₂⁴×C₉	—	4	2	no	—
40	C₂⁴×C₉	C₂³	1	2	yes	—
41	C₂⁴×C₉	C₂³	1	1	yes	characteristic
42	C₂²×C₄×C₉	—	2	4	no	—
43	C₂²×C₄×C₉	—	2	2	no	—
44	C₂²×C₄×C₉	—	4	2	no	—
45	C₂²×C₄×C₉	D₄	1	4	yes	—
46	C₂²×C₄×C₉	C₂³	1	2	yes	—
47	C₂²×C₄×C₉	C₂³	1	2	yes	—
48	C₂²×C₄×C₉	C₂³	1	4	yes	—
49	C₂²×C₄×C₉	C₂³	1	2	yes	—
50	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
52	C₉×C₄⋊C₄	—	2	2	no	—
53	C₉×C₄⋊C₄	—	2	2	no	—
54	C₉×C₄⋊C₄	—	4	4	no	—
55	C₉×C₂²⋊C₄	—	2	4	no	—
56	C₉×C₂²⋊C₄	—	2	8	no	—
57	C₉×C₂²⋊C₄	—	2	4	no	—
58	C₉×C₂²⋊C₄	—	2	4	no	—
59	C₉×C₂²⋊C₄	—	2	4	no	—
60	C₉×C₂²⋊C₄	—	4	4	no	—
61	C₄²×C₉	—	2	4	no	—
62	#2482	C₉	1	1	yes	characteristic, direct product factor, Sylow
63	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
64	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
65	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
66	C₃×#117	—	2	4	no	—
67	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
70	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
71	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
72	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
73	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
74	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
75	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
76	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
77	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
78	C₃×#95	C₂²×C₃	1	2	yes	—
79	C₃×#95	C₂²×C₃	1	2	yes	—
80	C₃×#95	C₂²×C₃	1	4	yes	—
81	C₂³×C₉	—	2	2	no	—
82	C₂³×C₉	—	2	2	no	—
83	C₂³×C₉	—	2	8	no	—
84	C₂³×C₉	—	2	2	no	—
85	C₂³×C₉	—	2	2	no	—
86	C₂³×C₉	—	2	4	no	—
87	C₂³×C₉	—	2	4	no	—
88	C₂³×C₉	—	4	16	no	—
89	C₂³×C₉	—	4	4	no	—
90	C₂³×C₉	—	4	4	no	—
91	C₂³×C₉	C₂×D₄	1	2	yes	—
92	C₂³×C₉	#41	1	4	yes	—
93	C₂³×C₉	#41	1	4	yes	—
94	C₂³×C₉	C₂⁴	1	1	yes	characteristic
95	C₂×C₄×C₉	—	2	8	no	—
96	C₂×C₄×C₉	—	2	2	no	—
97	C₂×C₄×C₉	—	2	2	no	—
98	C₂×C₄×C₉	—	2	2	no	—
99	C₂×C₄×C₉	—	2	2	no	—
100	C₂×C₄×C₉	—	2	2	no	—
101	C₂×C₄×C₉	—	2	4	no	—
102	C₂×C₄×C₉	—	2	4	no	—
103	C₂×C₄×C₉	—	2	4	no	—
104	C₂×C₄×C₉	—	2	4	no	—
105	C₂×C₄×C₉	—	2	4	no	—
106	C₂×C₄×C₉	—	2	4	no	—
107	C₂×C₄×C₉	—	4	4	no	—
108	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
109	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
110	C₂×#117	C₂×C₉	1	1	yes	characteristic, complemented
111	C₂²×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic
112	#399	C₂×C₉	1	2	yes	complemented
113	#397	C₂×C₉	1	2	yes	complemented
114	#388	C₂×C₉	1	4	yes	complemented
115	#385	C₂×C₉	1	2	yes	complemented
116	#381	C₂×C₉	1	1	yes	characteristic, complemented
117	#379	C₂×C₉	1	2	yes	—
118	C₂⁴×C₃	—	2	2	no	—
119	C₂⁴×C₃	—	2	4	no	—
120	C₂⁴×C₃	—	2	4	no	—
121	C₂⁴×C₃	—	4	2	no	—
122	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
123	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
124	C₂²×C₃×C₄	—	2	4	no	—
125	C₂²×C₃×C₄	—	2	2	no	—
126	C₂²×C₃×C₄	—	4	2	no	—
127	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
128	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
129	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
130	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
131	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
132	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
133	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
134	C₃×C₄⋊C₄	—	2	2	no	—
135	C₃×C₄⋊C₄	—	2	2	no	—
136	C₃×C₄⋊C₄	—	4	4	no	—
137	C₃×C₂²⋊C₄	—	2	4	no	—
138	C₃×C₂²⋊C₄	—	2	8	no	—
139	C₃×C₂²⋊C₄	—	2	4	no	—
140	C₃×C₂²⋊C₄	—	2	4	no	—
141	C₃×C₂²⋊C₄	—	2	4	no	—
142	C₃×C₂²⋊C₄	—	4	4	no	—
143	C₃×C₄²	—	2	4	no	—
144	C₂²×C₉	—	2	2	no	—
145	C₂²×C₉	—	2	2	no	—
146	C₂²×C₉	—	2	8	no	—
147	C₂²×C₉	—	2	4	no	—
148	C₂²×C₉	—	2	8	no	—
149	C₂²×C₉	—	4	16	no	—
150	C₂²×C₉	—	4	2	no	—
151	C₂²×C₉	—	4	2	no	—
152	C₂²×C₉	—	4	4	no	—
153	C₂²×C₉	#123	1	4	yes	—
154	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
155	C₂²×C₉	C₂×#41	1	2	yes	—
156	C₂²×C₉	C₂×#41	1	2	yes	—
157	C₂²×C₉	H(5,𝔽₂)	1	2	yes	—
158	C₄×C₉	—	2	2	no	—
159	C₄×C₉	—	2	2	no	—
160	C₄×C₉	—	4	2	no	—
161	C₄×C₉	—	4	2	no	—
162	C₄×C₉	—	4	2	no	—
163	C₄×C₉	—	4	4	no	—
164	C₂⁵	C₂²×C₉	1	1	yes	characteristic
165	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
166	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
167	#117	—	2	4	no	—
168	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
169	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
170	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	complemented
171	C₂×C₂²⋊C₄	—	2	4	no	—
172	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
173	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
174	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
175	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
176	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	—
177	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	—
178	C₂×C₄²	C₂²×C₉	1	2	yes	complemented
179	#95	C₂²×C₉	1	2	yes	complemented
180	#95	C₂²×C₉	1	2	yes	complemented
181	#95	C₂²×C₉	1	4	yes	complemented
182	C₂³×C₃	—	2	2	no	—
183	C₂³×C₃	—	2	2	no	—
184	C₂³×C₃	—	2	8	no	—
185	C₂³×C₃	—	2	2	no	—
186	C₂³×C₃	—	2	2	no	—
187	C₂³×C₃	—	2	4	no	—
188	C₂³×C₃	—	2	4	no	—
189	C₂³×C₃	—	4	16	no	—
190	C₂³×C₃	—	4	4	no	—
191	C₂³×C₃	—	4	4	no	—
192	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
193	C₂³×C₃	C₃×#41	1	4	yes	—
194	C₂³×C₃	C₃×#41	1	4	yes	—
195	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
196	C₂×C₃×C₄	—	2	8	no	—
197	C₂×C₃×C₄	—	2	2	no	—
198	C₂×C₃×C₄	—	2	2	no	—
199	C₂×C₃×C₄	—	2	2	no	—
200	C₂×C₃×C₄	—	2	2	no	—
201	C₂×C₃×C₄	—	2	2	no	—
202	C₂×C₃×C₄	—	2	4	no	—
203	C₂×C₃×C₄	—	2	4	no	—
204	C₂×C₃×C₄	—	2	4	no	—
205	C₂×C₃×C₄	—	2	4	no	—
206	C₂×C₃×C₄	—	2	4	no	—
207	C₂×C₃×C₄	—	2	4	no	—
208	C₂×C₃×C₄	—	4	4	no	—
209	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
210	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
211	C₂×C₉	—	2	4	no	—
212	C₂×C₉	—	4	4	no	—
213	C₂×C₉	C₂×#123	1	1	yes	characteristic
214	C₂×C₉	#525	1	1	yes	characteristic
215	C₂×C₉	#535	1	1	yes	characteristic
216	C₂×C₉	#551	1	4	yes	—
217	C₂⁴	—	2	2	no	—
218	C₂⁴	—	2	4	no	—
219	C₂⁴	—	2	4	no	—
220	C₂⁴	—	4	2	no	—
221	C₂⁴	C₂³×C₉	1	2	yes	—
222	C₂⁴	C₂³×C₉	1	1	yes	characteristic
223	C₂²×C₄	—	2	4	no	—
224	C₂²×C₄	—	2	2	no	—
225	C₂²×C₄	—	4	2	no	—
226	C₂²×C₄	D₄×C₉	1	4	yes	—
227	C₂²×C₄	C₂³×C₉	1	4	yes	—
228	C₂²×C₄	C₂³×C₉	1	2	yes	—
229	C₂²×C₄	C₂³×C₉	1	2	yes	—
230	C₂²×C₄	C₂³×C₉	1	2	yes	—
231	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
232	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
233	C₄⋊C₄	—	2	2	no	—
234	C₄⋊C₄	—	2	2	no	—
235	C₄⋊C₄	—	4	4	no	—
236	C₂²⋊C₄	—	2	4	no	—
237	C₂²⋊C₄	—	2	8	no	—
238	C₂²⋊C₄	—	2	4	no	—
239	C₂²⋊C₄	—	2	4	no	—
240	C₂²⋊C₄	—	2	4	no	—
241	C₂²⋊C₄	—	4	4	no	—
242	C₄²	—	2	4	no	—
243	C₂²×C₃	—	2	2	no	—
244	C₂²×C₃	—	2	2	no	—
245	C₂²×C₃	—	2	8	no	—
246	C₂²×C₃	—	2	4	no	—
247	C₂²×C₃	—	2	8	no	—
248	C₂²×C₃	—	4	16	no	—
249	C₂²×C₃	—	4	2	no	—
250	C₂²×C₃	—	4	2	no	—
251	C₂²×C₃	—	4	4	no	—
252	C₂²×C₃	C₃×#123	1	4	yes	—
253	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
254	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
255	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
256	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
257	C₃×C₄	—	2	2	no	—
258	C₃×C₄	—	2	2	no	—
259	C₃×C₄	—	4	2	no	—
260	C₃×C₄	—	4	2	no	—
261	C₃×C₄	—	4	2	no	—
262	C₃×C₄	—	4	4	no	—
263	C₉	#2482	1	1	yes	characteristic, direct product factor, Sylow
264	C₂³	—	2	2	no	—
265	C₂³	—	2	2	no	—
266	C₂³	—	2	8	no	—
267	C₂³	—	2	2	no	—
268	C₂³	—	2	2	no	—
269	C₂³	—	2	4	no	—
270	C₂³	—	2	4	no	—
271	C₂³	—	4	16	no	—
272	C₂³	—	4	4	no	—
273	C₂³	—	4	4	no	—
274	C₂³	C₂×D₄×C₉	1	2	yes	—
275	C₂³	C₉×#41	1	4	yes	—
276	C₂³	C₉×#41	1	4	yes	—
277	C₂³	C₂⁴×C₉	1	1	yes	characteristic
278	C₂×C₄	—	2	8	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	4	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	4	4	no	—
291	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
292	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
293	C₂×C₃	—	2	4	no	—
294	C₂×C₃	—	4	4	no	—
295	C₂×C₃	C₂×C₃×#123	1	1	yes	characteristic
296	C₂×C₃	C₃×#525	1	1	yes	characteristic
297	C₂×C₃	C₃×#535	1	1	yes	characteristic
298	C₂×C₃	C₃×#551	1	4	yes	—
299	C₂²	—	2	2	no	—
300	C₂²	—	2	2	no	—
301	C₂²	—	2	8	no	—
302	C₂²	—	2	4	no	—
303	C₂²	—	2	8	no	—
304	C₂²	—	4	16	no	—
305	C₂²	—	4	2	no	—
306	C₂²	—	4	2	no	—
307	C₂²	—	4	4	no	—
308	C₂²	C₉×#123	1	4	yes	—
309	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
310	C₂²	C₂×C₉×#41	1	2	yes	—
311	C₂²	C₂×C₉×#41	1	2	yes	—
312	C₂²	C₉×H(5,𝔽₂)	1	2	yes	—
313	C₄	—	2	2	no	—
314	C₄	—	2	2	no	—
315	C₄	—	4	2	no	—
316	C₄	—	4	2	no	—
317	C₄	—	4	2	no	—
318	C₄	—	4	4	no	—
319	C₃	C₃×#2482	1	1	yes	characteristic
320	C₂	—	2	4	no	—
321	C₂	—	4	4	no	—
322	C₂	C₂×C₉×#123	1	1	yes	characteristic
323	C₂	C₉×#525	1	1	yes	characteristic
324	C₂	C₉×#535	1	1	yes	characteristic
325	C₂	C₉×#551	1	4	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂⁵×C₃	C₂²×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#117	C₂	semidirect
3. C₉×#399	C₂	semidirect
4. C₉×#397	C₂	semidirect
5. C₉×#388	C₂	semidirect
6. C₉×#385	C₂	semidirect
7. C₉×#381	C₂	semidirect
14. C₂×C₉×C₄⋊C₄	C₂²	semidirect
15. C₂×C₉×C₄⋊C₄	C₂²	semidirect
16. C₂×C₉×C₄⋊C₄	C₂²	semidirect
24. C₂×C₄²×C₉	C₂²	semidirect
25. C₉×#95	C₂²	semidirect
26. C₉×#95	C₂²	semidirect
27. C₉×#95	C₂²	semidirect
62. #2482	C₉	direct (N × H)
110. C₂×#117	C₂×C₉	semidirect
112. #399	C₂×C₉	semidirect
113. #397	C₂×C₉	semidirect
114. #388	C₂×C₉	semidirect
115. #385	C₂×C₉	semidirect
116. #381	C₂×C₉	semidirect
168. C₂×C₄⋊C₄	C₂²×C₉	semidirect
169. C₂×C₄⋊C₄	C₂²×C₉	semidirect
170. C₂×C₄⋊C₄	C₂²×C₉	semidirect
178. C₂×C₄²	C₂²×C₉	semidirect
179. #95	C₂²×C₉	semidirect
180. #95	C₂²×C₉	semidirect
181. #95	C₂²×C₉	semidirect
263. C₉	#2482	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×#117	2
C₂²×C₉×C₂²⋊C₄	2
C₉×#399	2
C₉×#397	2
C₉×#388	2
C₉×#385	2
C₉×#381	2
C₉×#379	2
C₃×#2482	3

Subgroups — C9×#2482 #11767203

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2482 #11767203