Subgroups — C₂×C₉×#482 #11767808

Order 1152.

702 conjugacy classes of subgroups.

The subgroup lattice has 345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#482	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#482	C₃	1	1	yes	maximal, characteristic
10	C₂²×D₄×C₉	—	2	1	no	—
11	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
12	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
15	C₉×#121	—	2	2	no	—
16	C₉×#121	C₂²	1	4	yes	—
17	C₉×#117	—	2	2	no	—
18	C₉×#117	C₂²	1	4	yes	complemented
19	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
23	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
24	C₂×C₄²×C₉	—	2	1	no	—
25	C₉×#107	C₂²	1	4	yes	complemented
26	C₉×#106	C₂²	1	4	yes	complemented
27	C₉×#102	C₂²	1	4	yes	complemented
28	C₉×#102	C₂²	1	4	yes	complemented
29	C₉×C₂²⋊C₈	C₂²	1	4	yes	complemented
30	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
31	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
32	C₃×#482	C₂×C₃	1	8	yes	—
33	C₂×C₃×#107	C₂×C₃	1	1	yes	characteristic
34	C₂×C₃×#106	C₂×C₃	1	1	yes	characteristic
35	C₂×C₃×#102	C₂×C₃	1	1	yes	characteristic
36	C₂×C₃×#102	C₂×C₃	1	1	yes	characteristic
37	C₂×C₃×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
38	C₂⁴×C₉	—	2	1	no	—
39	C₂⁴×C₉	D₄	1	1	yes	characteristic
40	C₂×D₄×C₉	—	2	4	no	—
41	C₂×D₄×C₉	—	2	1	no	—
42	C₂×D₄×C₉	—	2	2	no	—
43	C₂×D₄×C₉	—	2	2	no	—
44	C₂×D₄×C₉	—	4	4	no	—
45	C₂×D₄×C₉	C₂³	1	2	yes	—
46	C₂²×C₄×C₉	—	2	2	no	—
47	C₂²×C₄×C₉	—	2	2	no	—
48	C₂²×C₄×C₉	—	2	1	no	—
49	C₂²×C₄×C₉	—	2	1	no	—
50	C₂²×C₄×C₉	—	2	1	no	—
51	C₂²×C₄×C₉	D₄	1	2	yes	—
52	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
53	C₂²×C₄×C₉	C₂³	1	2	yes	—
54	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
55	C₂×C₈×C₉	—	2	2	no	—
56	C₂×C₈×C₉	—	2	2	no	—
57	C₂×C₈×C₉	C₂³	1	2	yes	—
58	C₂×C₈×C₉	C₂³	1	2	yes	—
59	C₉×C₄⋊C₄	—	2	1	no	—
60	C₉×C₄⋊C₄	—	2	1	no	—
61	C₉×C₄⋊C₄	—	2	1	no	—
62	C₉×C₄⋊C₄	C₂³	1	2	yes	—
63	C₉×C₄⋊C₄	C₂³	1	2	yes	—
64	C₉×C₄⋊C₄	C₂³	1	2	yes	—
65	C₉×C₂²⋊C₄	—	2	4	no	—
66	C₉×C₂²⋊C₄	—	2	4	no	—
67	C₄²×C₉	—	2	4	no	—
68	C₂×#482	C₉	1	1	yes	characteristic, direct product factor, Sylow
69	C₂²×C₃×D₄	—	2	1	no	—
70	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
71	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
74	C₃×#121	—	2	2	no	—
75	C₃×#121	C₂²×C₃	1	4	yes	—
76	C₃×#117	—	2	2	no	—
77	C₃×#117	C₂²×C₃	1	4	yes	—
78	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
82	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
83	C₂×C₃×C₄²	—	2	1	no	—
84	C₃×#107	C₂²×C₃	1	4	yes	—
85	C₃×#106	C₂²×C₃	1	4	yes	—
86	C₃×#102	C₂²×C₃	1	4	yes	—
87	C₃×#102	C₂²×C₃	1	4	yes	—
88	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
89	C₂³×C₉	—	2	2	no	—
90	C₂³×C₉	—	2	2	no	—
91	C₂³×C₉	—	2	2	no	—
92	C₂³×C₉	—	2	2	no	—
93	C₂³×C₉	—	4	2	no	—
94	C₂³×C₉	—	4	2	no	—
95	C₂³×C₉	—	4	2	no	—
96	C₂³×C₉	C₂×D₄	1	2	yes	—
97	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
98	D₄×C₉	—	2	2	no	—
99	D₄×C₉	—	2	2	no	—
100	D₄×C₉	—	4	8	no	—
101	D₄×C₉	—	4	2	no	—
102	C₂×C₄×C₉	—	2	2	no	—
103	C₂×C₄×C₉	—	2	4	no	—
104	C₂×C₄×C₉	—	2	2	no	—
105	C₂×C₄×C₉	—	2	2	no	—
106	C₂×C₄×C₉	—	2	2	no	—
107	C₂×C₄×C₉	—	2	2	no	—
108	C₂×C₄×C₉	—	2	2	no	—
109	C₂×C₄×C₉	—	4	2	no	—
110	C₂×C₄×C₉	—	4	2	no	—
111	C₂×C₄×C₉	—	4	2	no	—
112	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
113	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×C₉	#41	1	2	yes	—
115	C₂×C₄×C₉	#41	1	2	yes	—
116	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
117	C₈×C₉	—	2	2	no	—
118	C₈×C₉	—	2	2	no	—
119	C₂×#121	C₂×C₉	1	1	yes	characteristic
120	C₂×#117	C₂×C₉	1	1	yes	characteristic, complemented
121	#482	C₂×C₉	1	8	yes	direct product factor
122	C₂×#107	C₂×C₉	1	1	yes	characteristic, complemented
123	C₂×#106	C₂×C₉	1	1	yes	characteristic, complemented
124	C₂×#102	C₂×C₉	1	1	yes	characteristic, complemented
125	C₂×#102	C₂×C₉	1	1	yes	characteristic, complemented
126	C₂×C₂²⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
127	C₂⁴×C₃	—	2	1	no	—
128	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
129	C₂×C₃×D₄	—	2	4	no	—
130	C₂×C₃×D₄	—	2	1	no	—
131	C₂×C₃×D₄	—	2	2	no	—
132	C₂×C₃×D₄	—	2	2	no	—
133	C₂×C₃×D₄	—	4	4	no	—
134	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
135	C₂²×C₃×C₄	—	2	2	no	—
136	C₂²×C₃×C₄	—	2	2	no	—
137	C₂²×C₃×C₄	—	2	1	no	—
138	C₂²×C₃×C₄	—	2	1	no	—
139	C₂²×C₃×C₄	—	2	1	no	—
140	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
141	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
142	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
143	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
144	C₂×C₃×C₈	—	2	2	no	—
145	C₂×C₃×C₈	—	2	2	no	—
146	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
147	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
148	C₃×C₄⋊C₄	—	2	1	no	—
149	C₃×C₄⋊C₄	—	2	1	no	—
150	C₃×C₄⋊C₄	—	2	1	no	—
151	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
152	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
153	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
154	C₃×C₂²⋊C₄	—	2	4	no	—
155	C₃×C₂²⋊C₄	—	2	4	no	—
156	C₃×C₄²	—	2	4	no	—
157	C₂²×C₉	—	2	2	no	—
158	C₂²×C₉	—	2	2	no	—
159	C₂²×C₉	—	2	2	no	—
160	C₂²×C₉	—	4	4	no	—
161	C₂²×C₉	—	4	2	no	—
162	C₂²×C₉	—	4	2	no	—
163	C₂²×C₉	—	4	2	no	—
164	C₂²×C₉	—	8	4	no	—
165	C₂²×C₉	#123	1	2	yes	—
166	C₂²×C₉	#135	1	2	yes	—
167	C₂²×C₉	AGL(1,ℤ/8)	1	2	yes	—
168	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
169	C₄×C₉	—	2	2	no	—
170	C₄×C₉	—	4	2	no	—
171	C₄×C₉	—	4	2	no	—
172	C₄×C₉	—	4	2	no	—
173	C₄×C₉	#123	1	2	yes	—
174	C₄×C₉	C₂×#41	1	1	yes	characteristic
175	C₄×C₉	C₂×#41	1	1	yes	characteristic
176	C₂²×D₄	—	2	1	no	—
177	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
178	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
179	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
180	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
181	#121	—	2	2	no	—
182	#121	C₂²×C₉	1	4	yes	—
183	#117	—	2	2	no	—
184	#117	C₂²×C₉	1	4	yes	complemented
185	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
186	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
187	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
188	C₂×C₂²⋊C₄	—	2	1	no	—
189	C₂×C₂²⋊C₄	—	2	1	no	—
190	C₂×C₄²	—	2	1	no	—
191	#107	C₂²×C₉	1	4	yes	complemented
192	#106	C₂²×C₉	1	4	yes	complemented
193	#102	C₂²×C₉	1	4	yes	complemented
194	#102	C₂²×C₉	1	4	yes	complemented
195	C₂²⋊C₈	C₂²×C₉	1	4	yes	complemented
196	C₂³×C₃	—	2	2	no	—
197	C₂³×C₃	—	2	2	no	—
198	C₂³×C₃	—	2	2	no	—
199	C₂³×C₃	—	2	2	no	—
200	C₂³×C₃	—	4	2	no	—
201	C₂³×C₃	—	4	2	no	—
202	C₂³×C₃	—	4	2	no	—
203	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
204	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
205	C₃×D₄	—	2	2	no	—
206	C₃×D₄	—	2	2	no	—
207	C₃×D₄	—	4	8	no	—
208	C₃×D₄	—	4	2	no	—
209	C₂×C₃×C₄	—	2	2	no	—
210	C₂×C₃×C₄	—	2	4	no	—
211	C₂×C₃×C₄	—	2	2	no	—
212	C₂×C₃×C₄	—	2	2	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	2	no	—
216	C₂×C₃×C₄	—	4	2	no	—
217	C₂×C₃×C₄	—	4	2	no	—
218	C₂×C₃×C₄	—	4	2	no	—
219	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
220	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
221	C₂×C₃×C₄	C₃×#41	1	2	yes	—
222	C₂×C₃×C₄	C₃×#41	1	2	yes	—
223	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
224	C₃×C₈	—	2	2	no	—
225	C₃×C₈	—	2	2	no	—
226	C₂×C₉	—	4	2	no	—
227	C₂×C₉	—	8	2	no	—
228	C₂×C₉	#482	1	4	yes	direct product factor
229	C₂×C₉	C₂×#123	1	1	yes	characteristic
230	C₂×C₉	C₂×#135	1	1	yes	characteristic
231	C₂×C₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
232	C₂⁴	—	2	1	no	—
233	C₂⁴	D₄×C₉	1	1	yes	characteristic
234	C₂×D₄	—	2	4	no	—
235	C₂×D₄	—	2	1	no	—
236	C₂×D₄	—	2	2	no	—
237	C₂×D₄	—	2	2	no	—
238	C₂×D₄	—	4	4	no	—
239	C₂×D₄	C₂³×C₉	1	2	yes	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	1	no	—
243	C₂²×C₄	—	2	1	no	—
244	C₂²×C₄	—	2	1	no	—
245	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
246	C₂²×C₄	D₄×C₉	1	2	yes	—
247	C₂²×C₄	C₂³×C₉	1	2	yes	—
248	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
249	C₂×C₈	—	2	2	no	—
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	C₂³×C₉	1	2	yes	—
252	C₂×C₈	C₂³×C₉	1	2	yes	—
253	C₄⋊C₄	—	2	1	no	—
254	C₄⋊C₄	—	2	1	no	—
255	C₄⋊C₄	—	2	1	no	—
256	C₄⋊C₄	C₂³×C₉	1	2	yes	—
257	C₄⋊C₄	C₂³×C₉	1	2	yes	—
258	C₄⋊C₄	C₂³×C₉	1	2	yes	—
259	C₂²⋊C₄	—	2	4	no	—
260	C₂²⋊C₄	—	2	4	no	—
261	C₄²	—	2	4	no	—
262	C₂²×C₃	—	2	2	no	—
263	C₂²×C₃	—	2	2	no	—
264	C₂²×C₃	—	2	2	no	—
265	C₂²×C₃	—	4	4	no	—
266	C₂²×C₃	—	4	2	no	—
267	C₂²×C₃	—	4	2	no	—
268	C₂²×C₃	—	4	2	no	—
269	C₂²×C₃	—	8	4	no	—
270	C₂²×C₃	C₃×#123	1	2	yes	—
271	C₂²×C₃	C₃×#135	1	2	yes	—
272	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	2	yes	—
273	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
274	C₃×C₄	—	2	2	no	—
275	C₃×C₄	—	4	2	no	—
276	C₃×C₄	—	4	2	no	—
277	C₃×C₄	—	4	2	no	—
278	C₃×C₄	C₃×#123	1	2	yes	—
279	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
280	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
281	C₉	C₂×#482	1	1	yes	characteristic, direct product factor, Sylow
282	C₂³	—	2	2	no	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	4	2	no	—
287	C₂³	—	4	2	no	—
288	C₂³	—	4	2	no	—
289	C₂³	C₂×D₄×C₉	1	2	yes	—
290	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
291	D₄	—	2	2	no	—
292	D₄	—	2	2	no	—
293	D₄	—	4	8	no	—
294	D₄	—	4	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	4	2	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
306	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
307	C₂×C₄	C₉×#41	1	2	yes	—
308	C₂×C₄	C₉×#41	1	2	yes	—
309	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
310	C₈	—	2	2	no	—
311	C₈	—	2	2	no	—
312	C₂×C₃	—	4	2	no	—
313	C₂×C₃	—	8	2	no	—
314	C₂×C₃	C₃×#482	1	4	yes	—
315	C₂×C₃	C₂×C₃×#123	1	1	yes	characteristic
316	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
317	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
318	C₂²	—	2	2	no	—
319	C₂²	—	2	2	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	4	4	no	—
322	C₂²	—	4	2	no	—
323	C₂²	—	4	2	no	—
324	C₂²	—	4	2	no	—
325	C₂²	—	8	4	no	—
326	C₂²	C₉×#123	1	2	yes	—
327	C₂²	C₉×#135	1	2	yes	—
328	C₂²	C₉×AGL(1,ℤ/8)	1	2	yes	—
329	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
330	C₄	—	2	2	no	—
331	C₄	—	4	2	no	—
332	C₄	—	4	2	no	—
333	C₄	—	4	2	no	—
334	C₄	C₉×#123	1	2	yes	—
335	C₄	C₂×C₉×#41	1	1	yes	characteristic
336	C₄	C₂×C₉×#41	1	1	yes	characteristic
337	C₃	C₂×C₃×#482	1	1	yes	characteristic
338	C₂	—	4	2	no	—
339	C₂	—	8	2	no	—
340	C₂	C₉×#482	1	4	yes	direct product factor
341	C₂	C₂×C₉×#123	1	1	yes	characteristic
342	C₂	C₂×C₉×#135	1	1	yes	characteristic
343	C₂	C₂×C₉×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂³×C₃	C₂×C₃×D₄
prime radical	C₂×C₃×#121	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ C₂³×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₉×#117	C₂	semidirect
3. C₉×#482	C₂	direct (N × H)
4. C₂×C₉×#107	C₂	semidirect
5. C₂×C₉×#106	C₂	semidirect
6. C₂×C₉×#102	C₂	semidirect
7. C₂×C₉×#102	C₂	semidirect
8. C₂×C₉×C₂²⋊C₈	C₂	semidirect
18. C₉×#117	C₂²	semidirect
25. C₉×#107	C₂²	semidirect
26. C₉×#106	C₂²	semidirect
27. C₉×#102	C₂²	semidirect
28. C₉×#102	C₂²	semidirect
29. C₉×C₂²⋊C₈	C₂²	semidirect
68. C₂×#482	C₉	direct (N × H)
120. C₂×#117	C₂×C₉	semidirect
121. #482	C₂×C₉	direct (N × H)
122. C₂×#107	C₂×C₉	semidirect
123. C₂×#106	C₂×C₉	semidirect
124. C₂×#102	C₂×C₉	semidirect
125. C₂×#102	C₂×C₉	semidirect
126. C₂×C₂²⋊C₈	C₂×C₉	semidirect
184. #117	C₂²×C₉	semidirect
191. #107	C₂²×C₉	semidirect
192. #106	C₂²×C₉	semidirect
193. #102	C₂²×C₉	semidirect
194. #102	C₂²×C₉	semidirect
195. C₂²⋊C₈	C₂²×C₉	semidirect
228. C₂×C₉	#482	direct (N × H)
281. C₉	C₂×#482	direct (N × H)
340. C₂	C₉×#482	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×#121	2
C₂×C₉×#117	2
C₉×#482	2
C₂×C₉×#107	2
C₂×C₉×#106	2
C₂×C₉×#102	2
C₂×C₉×C₂²⋊C₈	2
C₂×C₃×#482	3

Subgroups — C2×C9×#482 #11767808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#482 #11767808