Subgroups — C₂×C₉×#443 #11767674

Order 1152.

708 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#131	C₂	1	2	yes	maximal, complemented
3	C₉×#443	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₉×#108	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×#104	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#443	C₃	1	1	yes	maximal, characteristic
8	C₂×C₉×#41	C₂²	1	2	yes	—
9	C₉×#135	C₄	1	4	yes	complemented
10	C₉×#135	C₂²	1	4	yes	—
11	C₂×C₉×Q₁₆	C₄	1	1	yes	characteristic, complemented
12	C₂×C₉×SD₁₆	C₄	1	2	yes	complemented
13	C₂×C₉×D₈	C₄	1	1	yes	characteristic, complemented
14	C₉×#131	—	2	4	no	—
15	C₉×#131	C₂²	1	8	yes	complemented
16	C₂×C₉×M₁₆	—	2	2	no	—
17	C₂×C₉×M₁₆	C₂²	1	2	yes	—
18	C₂²×C₈×C₉	—	2	2	no	—
19	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
20	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
21	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
22	C₉×#108	C₂²	1	4	yes	complemented
23	C₉×#104	C₂²	1	8	yes	complemented
24	C₄×C₈×C₉	C₂²	1	4	yes	complemented
25	C₂×C₃×#135	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃×#131	C₂×C₃	1	2	yes	—
27	C₃×#443	C₂×C₃	1	8	yes	—
28	C₂×C₃×#108	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃×#104	C₂×C₃	1	2	yes	—
30	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic
31	C₉×#41	—	2	2	no	—
32	C₉×#41	—	2	2	no	—
33	C₉×#41	C₂×C₄	1	4	yes	—
34	C₉×#41	C₂³	1	4	yes	—
35	C₂×Q₈×C₉	C₂×C₄	1	2	yes	—
36	C₂×D₄×C₉	—	2	2	no	—
37	C₂×D₄×C₉	C₂×C₄	1	2	yes	—
38	C₂²×C₄×C₉	—	2	1	no	—
39	C₂²×C₄×C₉	—	2	2	no	—
40	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
41	C₉×Q₁₆	C₂×C₄	1	4	yes	complemented
42	C₉×SD₁₆	C₂×C₄	1	8	yes	complemented
43	C₉×D₈	C₂×C₄	1	4	yes	complemented
44	C₉×M₁₆	—	2	2	no	—
45	C₉×M₁₆	—	2	8	no	—
46	C₉×M₁₆	C₂³	1	4	yes	—
47	C₂×C₈×C₉	—	2	2	no	—
48	C₂×C₈×C₉	—	2	8	no	—
49	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×C₉	C₂×C₄	1	2	yes	—
52	C₂×C₈×C₉	D₄	1	1	yes	characteristic
53	C₂×C₈×C₉	D₄	1	2	yes	—
54	C₂×C₈×C₉	D₄	1	1	yes	characteristic
55	C₂×C₈×C₉	C₂³	1	2	yes	—
56	C₂×C₈×C₉	C₂³	1	2	yes	—
57	C₄²×C₉	—	2	1	no	—
58	C₄²×C₉	C₂³	1	2	yes	—
59	C₂×#443	C₉	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
61	C₃×#135	C₃×C₄	1	4	yes	—
62	C₃×#135	C₂²×C₃	1	4	yes	—
63	C₂×C₃×Q₁₆	C₃×C₄	1	1	yes	characteristic
64	C₂×C₃×SD₁₆	C₃×C₄	1	2	yes	—
65	C₂×C₃×D₈	C₃×C₄	1	1	yes	characteristic
66	C₃×#131	—	2	4	no	—
67	C₃×#131	C₂²×C₃	1	8	yes	—
68	C₂×C₃×M₁₆	—	2	2	no	—
69	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
70	C₂²×C₃×C₈	—	2	2	no	—
71	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
74	C₃×#108	C₂²×C₃	1	4	yes	—
75	C₃×#104	C₂²×C₃	1	8	yes	—
76	C₃×C₄×C₈	C₂²×C₃	1	4	yes	—
77	C₂³×C₉	—	2	2	no	—
78	C₂³×C₉	#41	1	1	yes	characteristic
79	Q₈×C₉	—	2	2	no	—
80	Q₈×C₉	C₂²×C₄	1	4	yes	—
81	D₄×C₉	—	2	4	no	—
82	D₄×C₉	—	2	4	no	—
83	D₄×C₉	—	2	2	no	—
84	D₄×C₉	C₂²×C₄	1	4	yes	—
85	C₂×C₄×C₉	—	2	4	no	—
86	C₂×C₄×C₉	—	2	2	no	—
87	C₂×C₄×C₉	—	2	2	no	—
88	C₂×C₄×C₉	—	2	4	no	—
89	C₂×C₄×C₉	—	2	4	no	—
90	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
93	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
94	C₂×C₄×C₉	#41	1	1	yes	characteristic
95	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
96	C₈×C₉	—	2	4	no	—
97	C₈×C₉	C₂²×C₄	1	2	yes	—
98	C₈×C₉	C₂²×C₄	1	2	yes	—
99	C₈×C₉	C₂×D₄	1	2	yes	—
100	C₈×C₉	C₂×D₄	1	2	yes	—
101	C₂×#135	C₂×C₉	1	1	yes	characteristic
102	C₂×#131	C₂×C₉	1	2	yes	complemented
103	#443	C₂×C₉	1	8	yes	direct product factor
104	C₂×#108	C₂×C₉	1	1	yes	characteristic, complemented
105	C₂×#104	C₂×C₉	1	2	yes	complemented
106	C₂×C₄×C₈	C₂×C₉	1	1	yes	characteristic, complemented
107	C₃×#41	—	2	2	no	—
108	C₃×#41	—	2	2	no	—
109	C₃×#41	C₂×C₃×C₄	1	4	yes	—
110	C₃×#41	C₂³×C₃	1	4	yes	—
111	C₂×C₃×Q₈	C₂×C₃×C₄	1	2	yes	—
112	C₂×C₃×D₄	—	2	2	no	—
113	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
114	C₂²×C₃×C₄	—	2	1	no	—
115	C₂²×C₃×C₄	—	2	2	no	—
116	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
117	C₃×Q₁₆	C₂×C₃×C₄	1	4	yes	—
118	C₃×SD₁₆	C₂×C₃×C₄	1	8	yes	—
119	C₃×D₈	C₂×C₃×C₄	1	4	yes	—
120	C₃×M₁₆	—	2	2	no	—
121	C₃×M₁₆	—	2	8	no	—
122	C₃×M₁₆	C₂³×C₃	1	4	yes	—
123	C₂×C₃×C₈	—	2	2	no	—
124	C₂×C₃×C₈	—	2	8	no	—
125	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
126	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
127	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
128	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
129	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
130	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
131	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
132	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
133	C₃×C₄²	—	2	1	no	—
134	C₃×C₄²	C₂³×C₃	1	2	yes	—
135	C₂²×C₉	—	2	2	no	—
136	C₂²×C₉	—	2	4	no	—
137	C₂²×C₉	—	4	4	no	—
138	C₂²×C₉	C₄×D₄	1	1	yes	characteristic
139	C₂²×C₉	C₄×D₄	1	1	yes	characteristic
140	C₂²×C₉	C₂×#41	1	1	yes	characteristic
141	C₄×C₉	—	2	4	no	—
142	C₄×C₉	—	2	4	no	—
143	C₄×C₉	C₄×D₄	1	1	yes	characteristic
144	C₄×C₉	C₄×D₄	1	1	yes	characteristic
145	C₄×C₉	C₂³×C₄	1	1	yes	characteristic
146	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
147	C₂×#41	C₂²×C₉	1	2	yes	—
148	#135	C₄×C₉	1	4	yes	complemented
149	#135	C₂²×C₉	1	4	yes	—
150	C₂×Q₁₆	C₄×C₉	1	1	yes	characteristic, complemented
151	C₂×SD₁₆	C₄×C₉	1	2	yes	complemented
152	C₂×D₈	C₄×C₉	1	1	yes	characteristic, complemented
153	#131	—	2	4	no	—
154	#131	C₂²×C₉	1	8	yes	complemented
155	C₂×M₁₆	—	2	2	no	—
156	C₂×M₁₆	C₂²×C₉	1	2	yes	—
157	C₂²×C₈	—	2	2	no	—
158	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
159	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
160	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
161	#108	C₂²×C₉	1	4	yes	complemented
162	#104	C₂²×C₉	1	8	yes	complemented
163	C₄×C₈	C₂²×C₉	1	4	yes	complemented
164	C₂³×C₃	—	2	2	no	—
165	C₂³×C₃	C₃×#41	1	1	yes	characteristic
166	C₃×Q₈	—	2	2	no	—
167	C₃×Q₈	C₂²×C₃×C₄	1	4	yes	—
168	C₃×D₄	—	2	4	no	—
169	C₃×D₄	—	2	4	no	—
170	C₃×D₄	—	2	2	no	—
171	C₃×D₄	C₂²×C₃×C₄	1	4	yes	—
172	C₂×C₃×C₄	—	2	4	no	—
173	C₂×C₃×C₄	—	2	2	no	—
174	C₂×C₃×C₄	—	2	2	no	—
175	C₂×C₃×C₄	—	2	4	no	—
176	C₂×C₃×C₄	—	2	4	no	—
177	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
178	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
179	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
180	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
181	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
182	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
183	C₃×C₈	—	2	4	no	—
184	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
185	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
186	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
187	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
188	C₂×C₉	—	2	1	no	—
189	C₂×C₉	—	2	1	no	—
190	C₂×C₉	—	4	4	no	—
191	C₂×C₉	#443	1	2	yes	direct product factor
192	C₂×C₉	C₂×C₄×D₄	1	1	yes	characteristic
193	#41	—	2	2	no	—
194	#41	—	2	2	no	—
195	#41	C₂×C₄×C₉	1	4	yes	—
196	#41	C₂³×C₉	1	4	yes	—
197	C₂×Q₈	C₂×C₄×C₉	1	2	yes	—
198	C₂×D₄	—	2	2	no	—
199	C₂×D₄	C₂×C₄×C₉	1	2	yes	—
200	C₂²×C₄	—	2	1	no	—
201	C₂²×C₄	—	2	2	no	—
202	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
203	Q₁₆	C₂×C₄×C₉	1	4	yes	complemented
204	SD₁₆	C₂×C₄×C₉	1	8	yes	complemented
205	D₈	C₂×C₄×C₉	1	4	yes	complemented
206	M₁₆	—	2	2	no	—
207	M₁₆	—	2	8	no	—
208	M₁₆	C₂³×C₉	1	4	yes	—
209	C₂×C₈	—	2	2	no	—
210	C₂×C₈	—	2	8	no	—
211	C₂×C₈	C₂×C₄×C₉	1	1	yes	characteristic
212	C₂×C₈	C₂×C₄×C₉	1	1	yes	characteristic
213	C₂×C₈	C₂×C₄×C₉	1	2	yes	—
214	C₂×C₈	D₄×C₉	1	1	yes	characteristic
215	C₂×C₈	D₄×C₉	1	1	yes	characteristic
216	C₂×C₈	D₄×C₉	1	2	yes	—
217	C₂×C₈	C₂³×C₉	1	2	yes	—
218	C₂×C₈	C₂³×C₉	1	2	yes	—
219	C₄²	—	2	1	no	—
220	C₄²	C₂³×C₉	1	2	yes	—
221	C₂²×C₃	—	2	2	no	—
222	C₂²×C₃	—	2	4	no	—
223	C₂²×C₃	—	4	4	no	—
224	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
225	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
226	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
227	C₃×C₄	—	2	4	no	—
228	C₃×C₄	—	2	4	no	—
229	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
230	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
231	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
232	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
233	C₉	C₂×#443	1	1	yes	characteristic, direct product factor, Sylow
234	C₂³	—	2	2	no	—
235	C₂³	C₉×#41	1	1	yes	characteristic
236	Q₈	—	2	2	no	—
237	Q₈	C₂²×C₄×C₉	1	4	yes	—
238	D₄	—	2	4	no	—
239	D₄	—	2	4	no	—
240	D₄	—	2	2	no	—
241	D₄	C₂²×C₄×C₉	1	4	yes	—
242	C₂×C₄	—	2	4	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	2	4	no	—
246	C₂×C₄	—	2	4	no	—
247	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
248	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
249	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
250	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
251	C₂×C₄	C₉×#41	1	1	yes	characteristic
252	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
253	C₈	—	2	4	no	—
254	C₈	C₂²×C₄×C₉	1	2	yes	—
255	C₈	C₂²×C₄×C₉	1	2	yes	—
256	C₈	C₂×D₄×C₉	1	2	yes	—
257	C₈	C₂×D₄×C₉	1	2	yes	—
258	C₂×C₃	—	2	1	no	—
259	C₂×C₃	—	2	1	no	—
260	C₂×C₃	—	4	4	no	—
261	C₂×C₃	C₃×#443	1	2	yes	—
262	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
263	C₂²	—	2	2	no	—
264	C₂²	—	2	4	no	—
265	C₂²	—	4	4	no	—
266	C₂²	C₄×D₄×C₉	1	1	yes	characteristic
267	C₂²	C₄×D₄×C₉	1	1	yes	characteristic
268	C₂²	C₂×C₉×#41	1	1	yes	characteristic
269	C₄	—	2	4	no	—
270	C₄	—	2	4	no	—
271	C₄	C₄×D₄×C₉	1	1	yes	characteristic
272	C₄	C₄×D₄×C₉	1	1	yes	characteristic
273	C₄	C₂³×C₄×C₉	1	1	yes	characteristic
274	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
275	C₃	C₂×C₃×#443	1	1	yes	characteristic
276	C₂	—	2	1	no	—
277	C₂	—	2	1	no	—
278	C₂	—	4	4	no	—
279	C₂	C₉×#443	1	2	yes	direct product factor
280	C₂	C₂×C₄×D₄×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₉	D₄
commutator	C₄	C₂³×C₄×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₃×C₄×D₄
prime radical	C₂×C₃×#135	C₂×C₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₉ ◁ C₂²×C₈×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₉×#131	C₂	semidirect
3. C₉×#443	C₂	direct (N × H)
4. C₂×C₉×#108	C₂	semidirect
5. C₂×C₉×#104	C₂	semidirect
6. C₂×C₄×C₈×C₉	C₂	semidirect
9. C₉×#135	C₄	semidirect
11. C₂×C₉×Q₁₆	C₄	semidirect
12. C₂×C₉×SD₁₆	C₄	semidirect
13. C₂×C₉×D₈	C₄	semidirect
15. C₉×#131	C₂²	semidirect
22. C₉×#108	C₂²	semidirect
23. C₉×#104	C₂²	semidirect
24. C₄×C₈×C₉	C₂²	semidirect
41. C₉×Q₁₆	C₂×C₄	semidirect
42. C₉×SD₁₆	C₂×C₄	semidirect
43. C₉×D₈	C₂×C₄	semidirect
59. C₂×#443	C₉	direct (N × H)
102. C₂×#131	C₂×C₉	semidirect
103. #443	C₂×C₉	direct (N × H)
104. C₂×#108	C₂×C₉	semidirect
105. C₂×#104	C₂×C₉	semidirect
106. C₂×C₄×C₈	C₂×C₉	semidirect
148. #135	C₄×C₉	semidirect
150. C₂×Q₁₆	C₄×C₉	semidirect
151. C₂×SD₁₆	C₄×C₉	semidirect
152. C₂×D₈	C₄×C₉	semidirect
154. #131	C₂²×C₉	semidirect
161. #108	C₂²×C₉	semidirect
162. #104	C₂²×C₉	semidirect
163. C₄×C₈	C₂²×C₉	semidirect
191. C₂×C₉	#443	direct (N × H)
203. Q₁₆	C₂×C₄×C₉	semidirect
204. SD₁₆	C₂×C₄×C₉	semidirect
205. D₈	C₂×C₄×C₉	semidirect
233. C₉	C₂×#443	direct (N × H)
279. C₂	C₉×#443	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×#135	2
C₂×C₉×#131	2
C₉×#443	2
C₂×C₉×#108	2
C₂×C₉×#104	2
C₂×C₄×C₈×C₉	2
C₂×C₃×#443	3

Subgroups — C2×C9×#443 #11767674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#443 #11767674