Subgroups — C₂×C₉×#483 #11767807

Order 1152.

690 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₉×#483	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₉×#106	C₂	1	2	yes	maximal, complemented
5	C₂×C₉×#103	C₂	1	2	yes	maximal, complemented
6	C₂×C₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₂×C₃×#483	C₃	1	1	yes	maximal, characteristic
8	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
9	C₂³×C₄×C₉	—	2	1	no	—
10	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₉	C₂²	1	2	yes	—
12	C₉×C₂²⋊Q₈	—	2	2	no	—
13	C₉×C₂²⋊Q₈	C₂²	1	4	yes	—
14	C₂×C₉×C₄⋊C₄	—	2	1	no	—
15	C₂×C₉×C₄⋊C₄	—	2	2	no	—
16	C₂×C₉×C₄⋊C₄	—	2	1	no	—
17	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
20	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
21	C₉×#106	C₂²	1	8	yes	complemented
22	C₉×#103	C₂²	1	8	yes	complemented
23	C₉×C₂²⋊C₈	C₂²	1	4	yes	—
24	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
25	C₂²×C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
26	C₃×#483	C₂×C₃	1	8	yes	—
27	C₂×C₃×#106	C₂×C₃	1	2	yes	—
28	C₂×C₃×#103	C₂×C₃	1	2	yes	—
29	C₂×C₃×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
30	C₂⁴×C₉	D₄	1	1	yes	characteristic
31	C₂×Q₈×C₉	—	2	1	no	—
32	C₂×Q₈×C₉	—	2	4	no	—
33	C₂×Q₈×C₉	C₂³	1	2	yes	—
34	C₂²×C₄×C₉	—	2	4	no	—
35	C₂²×C₄×C₉	—	2	4	no	—
36	C₂²×C₄×C₉	—	2	1	no	—
37	C₂²×C₄×C₉	—	2	1	no	—
38	C₂²×C₄×C₉	—	2	2	no	—
39	C₂²×C₄×C₉	—	4	4	no	—
40	C₂²×C₄×C₉	D₄	1	2	yes	—
41	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
42	C₂²×C₄×C₉	C₂³	1	2	yes	—
43	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
44	C₂×C₈×C₉	—	2	4	no	—
45	C₂×C₈×C₉	C₂³	1	4	yes	—
46	C₉×C₄⋊C₄	—	2	4	no	—
47	C₉×C₄⋊C₄	—	2	2	no	—
48	C₉×C₄⋊C₄	—	2	4	no	—
49	C₉×C₄⋊C₄	—	2	1	no	—
50	C₉×C₄⋊C₄	C₂³	1	4	yes	—
51	C₉×C₄⋊C₄	C₂³	1	2	yes	—
52	C₉×C₂²⋊C₄	—	2	4	no	—
53	C₂×#483	C₉	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
55	C₂³×C₃×C₄	—	2	1	no	—
56	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
57	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
58	C₃×C₂²⋊Q₈	—	2	2	no	—
59	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
60	C₂×C₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
64	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
66	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
67	C₃×#106	C₂²×C₃	1	8	yes	—
68	C₃×#103	C₂²×C₃	1	8	yes	—
69	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
70	C₂³×C₉	—	2	2	no	—
71	C₂³×C₉	—	2	2	no	—
72	C₂³×C₉	SD₁₆	1	4	yes	—
73	C₂³×C₉	C₂×D₄	1	2	yes	—
74	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
75	Q₈×C₉	—	2	4	no	—
76	Q₈×C₉	—	4	2	no	—
77	C₂×C₄×C₉	—	2	2	no	—
78	C₂×C₄×C₉	—	2	4	no	—
79	C₂×C₄×C₉	—	2	4	no	—
80	C₂×C₄×C₉	—	2	2	no	—
81	C₂×C₄×C₉	—	2	2	no	—
82	C₂×C₄×C₉	—	2	4	no	—
83	C₂×C₄×C₉	—	4	2	no	—
84	C₂×C₄×C₉	—	4	8	no	—
85	C₂×C₄×C₉	—	4	4	no	—
86	C₂×C₄×C₉	—	4	2	no	—
87	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
88	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×C₉	#41	1	4	yes	—
90	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
91	C₈×C₉	—	2	4	no	—
92	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic
93	C₂²×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
94	#483	C₂×C₉	1	8	yes	direct product factor
95	C₂×#106	C₂×C₉	1	2	yes	complemented
96	C₂×#103	C₂×C₉	1	2	yes	complemented
97	C₂×C₂²⋊C₈	C₂×C₉	1	1	yes	characteristic
98	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
99	C₂×C₃×Q₈	—	2	1	no	—
100	C₂×C₃×Q₈	—	2	4	no	—
101	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
102	C₂²×C₃×C₄	—	2	4	no	—
103	C₂²×C₃×C₄	—	2	1	no	—
104	C₂²×C₃×C₄	—	2	1	no	—
105	C₂²×C₃×C₄	—	2	4	no	—
106	C₂²×C₃×C₄	—	2	2	no	—
107	C₂²×C₃×C₄	—	4	4	no	—
108	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
109	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
110	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
111	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
112	C₂×C₃×C₈	—	2	4	no	—
113	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
114	C₃×C₄⋊C₄	—	2	4	no	—
115	C₃×C₄⋊C₄	—	2	2	no	—
116	C₃×C₄⋊C₄	—	2	4	no	—
117	C₃×C₄⋊C₄	—	2	1	no	—
118	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
119	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
120	C₃×C₂²⋊C₄	—	2	4	no	—
121	C₂²×C₉	—	2	2	no	—
122	C₂²×C₉	—	2	2	no	—
123	C₂²×C₉	—	2	8	no	—
124	C₂²×C₉	#123	1	2	yes	—
125	C₂²×C₉	C₂×SD₁₆	1	4	yes	—
126	C₂²×C₉	C₂×SD₁₆	1	2	yes	—
127	C₂²×C₉	#137	1	2	yes	—
128	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
129	C₄×C₉	—	2	2	no	—
130	C₄×C₉	—	4	2	no	—
131	C₄×C₉	—	4	4	no	—
132	C₄×C₉	—	4	2	no	—
133	C₄×C₉	#123	1	2	yes	—
134	C₄×C₉	C₂×#41	1	2	yes	—
135	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
136	C₂³×C₄	—	2	1	no	—
137	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
138	C₂²×C₈	C₂²×C₉	1	2	yes	—
139	C₂²⋊Q₈	—	2	2	no	—
140	C₂²⋊Q₈	C₂²×C₉	1	4	yes	—
141	C₂×C₄⋊C₄	—	2	1	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	—	2	1	no	—
144	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
145	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
146	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
147	C₂×C₂²⋊C₄	—	2	1	no	—
148	#106	C₂²×C₉	1	8	yes	complemented
149	#103	C₂²×C₉	1	8	yes	complemented
150	C₂²⋊C₈	C₂²×C₉	1	4	yes	—
151	C₂³×C₃	—	2	2	no	—
152	C₂³×C₃	—	2	2	no	—
153	C₂³×C₃	C₃×SD₁₆	1	4	yes	—
154	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
155	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
156	C₃×Q₈	—	2	4	no	—
157	C₃×Q₈	—	4	2	no	—
158	C₂×C₃×C₄	—	2	2	no	—
159	C₂×C₃×C₄	—	2	4	no	—
160	C₂×C₃×C₄	—	2	4	no	—
161	C₂×C₃×C₄	—	2	2	no	—
162	C₂×C₃×C₄	—	2	2	no	—
163	C₂×C₃×C₄	—	2	4	no	—
164	C₂×C₃×C₄	—	4	2	no	—
165	C₂×C₃×C₄	—	4	8	no	—
166	C₂×C₃×C₄	—	4	4	no	—
167	C₂×C₃×C₄	—	4	2	no	—
168	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
169	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
170	C₂×C₃×C₄	C₃×#41	1	4	yes	—
171	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
172	C₃×C₈	—	2	4	no	—
173	C₂×C₉	—	2	4	no	—
174	C₂×C₉	#483	1	4	yes	direct product factor
175	C₂×C₉	C₂×#123	1	1	yes	characteristic
176	C₂×C₉	C₂²×SD₁₆	1	1	yes	characteristic
177	C₂×C₉	C₂×#137	1	1	yes	characteristic
178	C₂⁴	D₄×C₉	1	1	yes	characteristic
179	C₂×Q₈	—	2	1	no	—
180	C₂×Q₈	—	2	4	no	—
181	C₂×Q₈	C₂³×C₉	1	2	yes	—
182	C₂²×C₄	—	2	4	no	—
183	C₂²×C₄	—	2	1	no	—
184	C₂²×C₄	—	2	1	no	—
185	C₂²×C₄	—	2	4	no	—
186	C₂²×C₄	—	2	2	no	—
187	C₂²×C₄	—	4	4	no	—
188	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
189	C₂²×C₄	D₄×C₉	1	2	yes	—
190	C₂²×C₄	C₂³×C₉	1	2	yes	—
191	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
192	C₂×C₈	—	2	4	no	—
193	C₂×C₈	C₂³×C₉	1	4	yes	—
194	C₄⋊C₄	—	2	4	no	—
195	C₄⋊C₄	—	2	2	no	—
196	C₄⋊C₄	—	2	4	no	—
197	C₄⋊C₄	—	2	1	no	—
198	C₄⋊C₄	C₂³×C₉	1	4	yes	—
199	C₄⋊C₄	C₂³×C₉	1	2	yes	—
200	C₂²⋊C₄	—	2	4	no	—
201	C₂²×C₃	—	2	2	no	—
202	C₂²×C₃	—	2	2	no	—
203	C₂²×C₃	—	2	8	no	—
204	C₂²×C₃	C₃×#123	1	2	yes	—
205	C₂²×C₃	C₂×C₃×SD₁₆	1	4	yes	—
206	C₂²×C₃	C₂×C₃×SD₁₆	1	2	yes	—
207	C₂²×C₃	C₃×#137	1	2	yes	—
208	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
209	C₃×C₄	—	2	2	no	—
210	C₃×C₄	—	4	4	no	—
211	C₃×C₄	—	4	2	no	—
212	C₃×C₄	—	4	2	no	—
213	C₃×C₄	C₃×#123	1	2	yes	—
214	C₃×C₄	C₂×C₃×#41	1	2	yes	—
215	C₉	C₂×#483	1	1	yes	characteristic, direct product factor, Sylow
216	C₂³	—	2	2	no	—
217	C₂³	—	2	2	no	—
218	C₂³	C₉×SD₁₆	1	4	yes	—
219	C₂³	C₂×D₄×C₉	1	2	yes	—
220	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
221	Q₈	—	2	4	no	—
222	Q₈	—	4	2	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	4	no	—
225	C₂×C₄	—	2	4	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	4	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	8	no	—
231	C₂×C₄	—	4	4	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
234	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
235	C₂×C₄	C₉×#41	1	4	yes	—
236	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
237	C₈	—	2	4	no	—
238	C₂×C₃	—	2	4	no	—
239	C₂×C₃	C₃×#483	1	4	yes	—
240	C₂×C₃	C₂×C₃×#123	1	1	yes	characteristic
241	C₂×C₃	C₂²×C₃×SD₁₆	1	1	yes	characteristic
242	C₂×C₃	C₂×C₃×#137	1	1	yes	characteristic
243	C₂²	—	2	2	no	—
244	C₂²	—	2	2	no	—
245	C₂²	—	2	8	no	—
246	C₂²	C₉×#123	1	2	yes	—
247	C₂²	C₂×C₉×SD₁₆	1	4	yes	—
248	C₂²	C₂×C₉×SD₁₆	1	2	yes	—
249	C₂²	C₉×#137	1	2	yes	—
250	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
251	C₄	—	2	2	no	—
252	C₄	—	4	2	no	—
253	C₄	—	4	4	no	—
254	C₄	—	4	2	no	—
255	C₄	C₉×#123	1	2	yes	—
256	C₄	C₂×C₉×#41	1	2	yes	—
257	C₃	C₂×C₃×#483	1	1	yes	characteristic
258	C₂	—	2	4	no	—
259	C₂	C₉×#483	1	4	yes	direct product factor
260	C₂	C₂×C₉×#123	1	1	yes	characteristic
261	C₂	C₂²×C₉×SD₁₆	1	1	yes	characteristic
262	C₂	C₂×C₉×#137	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	C₂⁴×C₃	C₃×D₄
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
3. C₉×#483	C₂	direct (N × H)
4. C₂×C₉×#106	C₂	semidirect
5. C₂×C₉×#103	C₂	semidirect
21. C₉×#106	C₂²	semidirect
22. C₉×#103	C₂²	semidirect
53. C₂×#483	C₉	direct (N × H)
94. #483	C₂×C₉	direct (N × H)
95. C₂×#106	C₂×C₉	semidirect
96. C₂×#103	C₂×C₉	semidirect
148. #106	C₂²×C₉	semidirect
149. #103	C₂²×C₉	semidirect
174. C₂×C₉	#483	direct (N × H)
215. C₉	C₂×#483	direct (N × H)
259. C₂	C₉×#483	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×C₂²⋊Q₈	2
C₂²×C₉×C₄⋊C₄	2
C₉×#483	2
C₂×C₉×#106	2
C₂×C₉×#103	2
C₂×C₉×C₂²⋊C₈	2
C₂×C₃×#483	3

Subgroups — C2×C9×#483 #11767807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#483 #11767807