Subgroups — C₉×#2043 #11766764

Order 1152.

447 conjugacy classes of subgroups.

The subgroup lattice has 261 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#103	C₂	1	2	yes	maximal
3	C₂×C₉×#103	C₂	1	2	yes	maximal
4	C₉×#389	C₂	1	1	yes	maximal, characteristic
5	C₉×#336	C₂	1	1	yes	maximal, characteristic
6	C₃×#2043	C₃	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₉	C₂²	1	2	yes	—
8	C₂²×C₈×C₉	C₂²	1	2	yes	—
9	C₉×C₄⋊Q₈	—	2	4	no	—
10	C₂×C₉×C₄⋊C₄	—	2	1	no	—
11	C₂×C₉×C₄⋊C₄	—	2	1	no	—
12	C₂×C₉×C₄⋊C₄	—	2	1	no	—
13	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
16	C₉×#103	—	2	4	no	—
17	C₉×#103	—	2	4	no	—
18	C₉×#95	—	2	1	no	—
19	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
20	C₂×C₃×#103	C₂×C₃	1	2	yes	—
21	C₂×C₃×#103	C₂×C₃	1	2	yes	—
22	C₃×#389	C₂×C₃	1	1	yes	characteristic
23	C₃×#336	C₂×C₃	1	1	yes	characteristic
24	C₂×Q₈×C₉	—	2	2	no	—
25	C₂×Q₈×C₉	—	2	2	no	—
26	C₂×Q₈×C₉	—	2	2	no	—
27	C₂×Q₈×C₉	—	2	2	no	—
28	C₂×Q₈×C₉	—	2	2	no	—
29	C₂×Q₈×C₉	D₄	1	4	yes	—
30	C₂²×C₄×C₉	—	2	2	no	—
31	C₂²×C₄×C₉	—	2	1	no	—
32	C₂²×C₄×C₉	—	2	1	no	—
33	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
34	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
35	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
36	C₂×C₈×C₉	—	2	2	no	—
37	C₂×C₈×C₉	—	2	2	no	—
38	C₂×C₈×C₉	—	2	2	no	—
39	C₉×C₄⋊C₄	—	2	4	no	—
40	C₉×C₄⋊C₄	—	2	4	no	—
41	C₉×C₄⋊C₄	—	2	1	no	—
42	C₉×C₄⋊C₄	—	2	2	no	—
43	C₉×C₄⋊C₄	—	4	2	no	—
44	C₉×C₄⋊C₄	D₄	1	2	yes	—
45	C₄²×C₉	—	2	2	no	—
46	#2043	C₉	1	1	yes	characteristic, direct product factor, Sylow
47	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
48	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
49	C₃×C₄⋊Q₈	—	2	4	no	—
50	C₂×C₃×C₄⋊C₄	—	2	1	no	—
51	C₂×C₃×C₄⋊C₄	—	2	1	no	—
52	C₂×C₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
54	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
55	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
56	C₃×#103	—	2	4	no	—
57	C₃×#103	—	2	4	no	—
58	C₃×#95	—	2	1	no	—
59	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
60	Q₈×C₉	—	2	4	no	—
61	Q₈×C₉	—	2	4	no	—
62	Q₈×C₉	—	4	2	no	—
63	Q₈×C₉	—	4	2	no	—
64	C₂×C₄×C₉	—	2	1	no	—
65	C₂×C₄×C₉	—	2	1	no	—
66	C₂×C₄×C₉	—	2	1	no	—
67	C₂×C₄×C₉	—	2	1	no	—
68	C₂×C₄×C₉	—	2	4	no	—
69	C₂×C₄×C₉	—	2	2	no	—
70	C₂×C₄×C₉	—	4	2	no	—
71	C₂×C₄×C₉	—	4	2	no	—
72	C₂×C₄×C₉	—	4	1	no	—
73	C₂×C₄×C₉	—	4	1	no	—
74	C₂×C₄×C₉	—	4	1	no	—
75	C₂×C₄×C₉	—	4	1	no	—
76	C₂×C₄×C₉	—	4	1	no	—
77	C₂×C₄×C₉	SD₁₆	1	2	yes	—
78	C₂×C₄×C₉	Q₁₆	1	2	yes	—
79	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
81	C₂×C₄×C₉	#41	1	2	yes	—
82	C₂×C₄×C₉	#41	1	1	yes	characteristic
83	C₈×C₉	—	4	2	no	—
84	C₂×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic
85	C₂×#103	C₂×C₉	1	2	yes	—
86	C₂×#103	C₂×C₉	1	2	yes	—
87	#389	C₂×C₉	1	1	yes	characteristic
88	#336	C₂×C₉	1	1	yes	characteristic
89	C₂×C₃×Q₈	—	2	2	no	—
90	C₂×C₃×Q₈	—	2	2	no	—
91	C₂×C₃×Q₈	—	2	2	no	—
92	C₂×C₃×Q₈	—	2	2	no	—
93	C₂×C₃×Q₈	—	2	2	no	—
94	C₂×C₃×Q₈	C₃×D₄	1	4	yes	—
95	C₂²×C₃×C₄	—	2	1	no	—
96	C₂²×C₃×C₄	—	2	2	no	—
97	C₂²×C₃×C₄	—	2	1	no	—
98	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
99	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
100	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
101	C₂×C₃×C₈	—	2	2	no	—
102	C₂×C₃×C₈	—	2	2	no	—
103	C₂×C₃×C₈	—	2	2	no	—
104	C₃×C₄⋊C₄	—	2	4	no	—
105	C₃×C₄⋊C₄	—	2	4	no	—
106	C₃×C₄⋊C₄	—	2	1	no	—
107	C₃×C₄⋊C₄	—	2	2	no	—
108	C₃×C₄⋊C₄	—	4	2	no	—
109	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
110	C₃×C₄²	—	2	2	no	—
111	C₂²×C₉	#120	1	1	yes	characteristic
112	C₂²×C₉	#121	1	1	yes	characteristic
113	C₂²×C₉	#124	1	1	yes	characteristic
114	C₂²×C₉	C₂×SD₁₆	1	1	yes	characteristic
115	C₂²×C₉	C₂×Q₁₆	1	1	yes	characteristic
116	C₂²×C₉	#137	1	1	yes	characteristic
117	C₂²×C₉	#137	1	1	yes	characteristic
118	C₄×C₉	—	2	2	no	—
119	C₄×C₉	—	2	2	no	—
120	C₄×C₉	—	4	4	no	—
121	C₄×C₉	—	4	2	no	—
122	C₄×C₉	—	8	1	no	—
123	C₄×C₉	#121	1	2	yes	—
124	C₄×C₉	#123	1	2	yes	—
125	C₂²×Q₈	C₂²×C₉	1	2	yes	—
126	C₂²×C₈	C₂²×C₉	1	2	yes	—
127	C₄⋊Q₈	—	2	4	no	—
128	C₂×C₄⋊C₄	—	2	1	no	—
129	C₂×C₄⋊C₄	—	2	1	no	—
130	C₂×C₄⋊C₄	—	2	1	no	—
131	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
132	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
133	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
134	#103	—	2	4	no	—
135	#103	—	2	4	no	—
136	#95	—	2	1	no	—
137	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
138	C₃×Q₈	—	2	4	no	—
139	C₃×Q₈	—	2	4	no	—
140	C₃×Q₈	—	4	2	no	—
141	C₃×Q₈	—	4	2	no	—
142	C₂×C₃×C₄	—	2	1	no	—
143	C₂×C₃×C₄	—	2	1	no	—
144	C₂×C₃×C₄	—	2	1	no	—
145	C₂×C₃×C₄	—	2	1	no	—
146	C₂×C₃×C₄	—	2	4	no	—
147	C₂×C₃×C₄	—	2	2	no	—
148	C₂×C₃×C₄	—	4	2	no	—
149	C₂×C₃×C₄	—	4	2	no	—
150	C₂×C₃×C₄	—	4	1	no	—
151	C₂×C₃×C₄	—	4	1	no	—
152	C₂×C₃×C₄	—	4	1	no	—
153	C₂×C₃×C₄	—	4	1	no	—
154	C₂×C₃×C₄	—	4	1	no	—
155	C₂×C₃×C₄	C₃×SD₁₆	1	2	yes	—
156	C₂×C₃×C₄	C₃×Q₁₆	1	2	yes	—
157	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
158	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
159	C₂×C₃×C₄	C₃×#41	1	2	yes	—
160	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
161	C₃×C₈	—	4	2	no	—
162	C₂×C₉	#394	1	1	yes	characteristic
163	C₂×C₉	#448	1	1	yes	characteristic
164	C₂×C₉	#451	1	1	yes	characteristic
165	C₂×C₉	#461	1	1	yes	characteristic
166	C₂×C₉	#462	1	1	yes	characteristic
167	C₂×C₉	#487	1	1	yes	characteristic
168	C₂×C₉	#491	1	1	yes	characteristic
169	C₂×Q₈	—	2	2	no	—
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	—	2	2	no	—
172	C₂×Q₈	—	2	2	no	—
173	C₂×Q₈	—	2	2	no	—
174	C₂×Q₈	D₄×C₉	1	4	yes	—
175	C₂²×C₄	—	2	1	no	—
176	C₂²×C₄	—	2	2	no	—
177	C₂²×C₄	—	2	1	no	—
178	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
179	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
180	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	2	4	no	—
186	C₄⋊C₄	—	2	1	no	—
187	C₄⋊C₄	—	2	2	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	D₄×C₉	1	2	yes	—
190	C₄²	—	2	2	no	—
191	C₂²×C₃	C₃×#120	1	1	yes	characteristic
192	C₂²×C₃	C₃×#121	1	1	yes	characteristic
193	C₂²×C₃	C₃×#124	1	1	yes	characteristic
194	C₂²×C₃	C₂×C₃×SD₁₆	1	1	yes	characteristic
195	C₂²×C₃	C₂×C₃×Q₁₆	1	1	yes	characteristic
196	C₂²×C₃	C₃×#137	1	1	yes	characteristic
197	C₂²×C₃	C₃×#137	1	1	yes	characteristic
198	C₃×C₄	—	2	2	no	—
199	C₃×C₄	—	2	2	no	—
200	C₃×C₄	—	4	4	no	—
201	C₃×C₄	—	4	2	no	—
202	C₃×C₄	—	8	1	no	—
203	C₃×C₄	C₃×#121	1	2	yes	—
204	C₃×C₄	C₃×#123	1	2	yes	—
205	C₉	#2043	1	1	yes	characteristic, direct product factor, Sylow
206	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
207	Q₈	—	2	4	no	—
208	Q₈	—	2	4	no	—
209	Q₈	—	4	2	no	—
210	Q₈	—	4	2	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	1	no	—
220	C₂×C₄	—	4	1	no	—
221	C₂×C₄	—	4	1	no	—
222	C₂×C₄	—	4	1	no	—
223	C₂×C₄	—	4	1	no	—
224	C₂×C₄	C₉×SD₁₆	1	2	yes	—
225	C₂×C₄	C₉×Q₁₆	1	2	yes	—
226	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
227	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
228	C₂×C₄	C₉×#41	1	2	yes	—
229	C₂×C₄	C₉×#41	1	1	yes	characteristic
230	C₈	—	4	2	no	—
231	C₂×C₃	C₃×#394	1	1	yes	characteristic
232	C₂×C₃	C₃×#448	1	1	yes	characteristic
233	C₂×C₃	C₃×#451	1	1	yes	characteristic
234	C₂×C₃	C₃×#461	1	1	yes	characteristic
235	C₂×C₃	C₃×#462	1	1	yes	characteristic
236	C₂×C₃	C₃×#487	1	1	yes	characteristic
237	C₂×C₃	C₃×#491	1	1	yes	characteristic
238	C₂²	C₉×#120	1	1	yes	characteristic
239	C₂²	C₉×#121	1	1	yes	characteristic
240	C₂²	C₉×#124	1	1	yes	characteristic
241	C₂²	C₂×C₉×SD₁₆	1	1	yes	characteristic
242	C₂²	C₂×C₉×Q₁₆	1	1	yes	characteristic
243	C₂²	C₉×#137	1	1	yes	characteristic
244	C₂²	C₉×#137	1	1	yes	characteristic
245	C₄	—	2	2	no	—
246	C₄	—	2	2	no	—
247	C₄	—	4	4	no	—
248	C₄	—	4	2	no	—
249	C₄	—	8	1	no	—
250	C₄	C₉×#121	1	2	yes	—
251	C₄	C₉×#123	1	2	yes	—
252	C₃	C₃×#2043	1	1	yes	characteristic
253	C₂	C₉×#394	1	1	yes	characteristic
254	C₂	C₉×#448	1	1	yes	characteristic
255	C₂	C₉×#451	1	1	yes	characteristic
256	C₂	C₉×#461	1	1	yes	characteristic
257	C₂	C₉×#462	1	1	yes	characteristic
258	C₂	C₉×#487	1	1	yes	characteristic
259	C₂	C₉×#491	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂×D₄
commutator	C₂²×C₄	C₂³×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle, prime radical	C₂³×C₃	C₂×C₃×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
46. #2043	C₉	direct (N × H)
205. C₉	#2043	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×C₄⋊Q₈	2
C₂×C₉×#103	2
C₉×#389	2
C₉×#336	2
C₃×#2043	3

Subgroups — C9×#2043 #11766764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2043 #11766764