Subgroups — C₉×#1805 #11766526

Order 1152.

438 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉×#103	C₂	1	2	yes	maximal
4	C₉×#382	C₂	1	1	yes	maximal, characteristic
5	C₉×#340	C₂	1	2	yes	maximal
6	C₃×#1805	C₃	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₉	C₂²	1	2	yes	—
9	C₄×Q₈×C₉	—	2	2	no	—
10	C₄×Q₈×C₉	C₄	1	4	yes	complemented
11	C₂×C₉×C₄⋊C₄	—	2	1	no	—
12	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₉	—	2	1	no	—
15	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
16	C₉×C₄⋊C₈	—	2	2	no	—
17	C₉×#103	—	2	4	no	—
18	C₉×#95	—	2	1	no	—
19	C₉×#95	—	2	1	no	—
20	C₂×C₃×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
21	C₂×C₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
22	C₂×C₃×#103	C₂×C₃	1	2	yes	—
23	C₃×#382	C₂×C₃	1	1	yes	characteristic
24	C₃×#340	C₂×C₃	1	2	yes	—
25	C₂×Q₈×C₉	—	2	1	no	—
26	C₂×Q₈×C₉	—	2	1	no	—
27	C₂×Q₈×C₉	—	2	1	no	—
28	C₂×Q₈×C₉	C₂×C₄	1	2	yes	—
29	C₂×Q₈×C₉	D₄	1	2	yes	—
30	C₂×Q₈×C₉	Q₈	1	2	yes	—
31	C₂²×C₄×C₉	—	2	1	no	—
32	C₂²×C₄×C₉	—	2	1	no	—
33	C₂²×C₄×C₉	—	2	2	no	—
34	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
35	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
36	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
37	C₂×C₈×C₉	—	2	2	no	—
38	C₂×C₈×C₉	—	2	2	no	—
39	C₂×C₈×C₉	—	2	2	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	—	2	2	no	—
44	C₉×C₄⋊C₄	C₂×C₄	1	2	yes	—
45	C₄²×C₉	—	2	4	no	—
46	C₄²×C₉	C₂×C₄	1	2	yes	—
47	C₄²×C₉	D₄	1	2	yes	—
48	#1805	C₉	1	1	yes	characteristic, direct product factor, Sylow
49	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
50	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
51	C₃×C₄×Q₈	—	2	2	no	—
52	C₃×C₄×Q₈	C₃×C₄	1	4	yes	—
53	C₂×C₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
55	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
56	C₂×C₃×C₄²	—	2	1	no	—
57	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
58	C₃×C₄⋊C₈	—	2	2	no	—
59	C₃×#103	—	2	4	no	—
60	C₃×#95	—	2	1	no	—
61	C₃×#95	—	2	1	no	—
62	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
63	Q₈×C₉	—	2	2	no	—
64	Q₈×C₉	—	2	2	no	—
65	Q₈×C₉	—	2	2	no	—
66	Q₈×C₉	C₄⋊C₄	1	4	yes	—
67	C₂×C₄×C₉	—	2	2	no	—
68	C₂×C₄×C₉	—	2	2	no	—
69	C₂×C₄×C₉	—	2	2	no	—
70	C₂×C₄×C₉	—	2	2	no	—
71	C₂×C₄×C₉	—	2	2	no	—
72	C₂×C₄×C₉	—	2	2	no	—
73	C₂×C₄×C₉	—	4	2	no	—
74	C₂×C₄×C₉	—	4	2	no	—
75	C₂×C₄×C₉	—	4	2	no	—
76	C₂×C₄×C₉	—	4	2	no	—
77	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
78	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
79	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₉	C₂×Q₈	1	1	yes	characteristic
83	C₂×C₄×C₉	#41	1	1	yes	characteristic
84	C₂×C₄×C₉	#41	1	1	yes	characteristic
85	C₈×C₉	—	4	2	no	—
86	C₂×C₄×Q₈	C₂×C₉	1	1	yes	characteristic
87	C₂×C₄⋊C₈	C₂×C₉	1	1	yes	characteristic
88	C₂×#103	C₂×C₉	1	2	yes	—
89	#382	C₂×C₉	1	1	yes	characteristic
90	#340	C₂×C₉	1	2	yes	—
91	C₂×C₃×Q₈	—	2	1	no	—
92	C₂×C₃×Q₈	—	2	1	no	—
93	C₂×C₃×Q₈	—	2	1	no	—
94	C₂×C₃×Q₈	C₂×C₃×C₄	1	2	yes	—
95	C₂×C₃×Q₈	C₃×D₄	1	2	yes	—
96	C₂×C₃×Q₈	C₃×Q₈	1	2	yes	—
97	C₂²×C₃×C₄	—	2	1	no	—
98	C₂²×C₃×C₄	—	2	1	no	—
99	C₂²×C₃×C₄	—	2	2	no	—
100	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
101	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
102	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
103	C₂×C₃×C₈	—	2	2	no	—
104	C₂×C₃×C₈	—	2	2	no	—
105	C₂×C₃×C₈	—	2	2	no	—
106	C₃×C₄⋊C₄	—	2	4	no	—
107	C₃×C₄⋊C₄	—	2	1	no	—
108	C₃×C₄⋊C₄	—	2	2	no	—
109	C₃×C₄⋊C₄	—	2	2	no	—
110	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
111	C₃×C₄²	—	2	4	no	—
112	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
113	C₃×C₄²	C₃×D₄	1	2	yes	—
114	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×C₉	#121	1	1	yes	characteristic
116	C₂²×C₉	C₂²⋊Q₈	1	1	yes	characteristic
117	C₂²×C₉	#135	1	2	yes	—
118	C₂²×C₉	#137	1	2	yes	—
119	C₄×C₉	—	2	4	no	—
120	C₄×C₉	—	2	2	no	—
121	C₄×C₉	—	2	2	no	—
122	C₄×C₉	—	4	2	no	—
123	C₄×C₉	—	8	2	no	—
124	C₄×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₄×C₉	#117	1	1	yes	characteristic
126	C₄×C₉	#121	1	1	yes	characteristic
127	C₄×C₉	C₂²⋊Q₈	1	1	yes	characteristic
128	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
129	C₂²×C₈	C₂²×C₉	1	2	yes	—
130	C₄×Q₈	—	2	2	no	—
131	C₄×Q₈	C₄×C₉	1	4	yes	complemented
132	C₂×C₄⋊C₄	—	2	1	no	—
133	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
134	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
135	C₂×C₄²	—	2	1	no	—
136	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
137	C₄⋊C₈	—	2	2	no	—
138	#103	—	2	4	no	—
139	#95	—	2	1	no	—
140	#95	—	2	1	no	—
141	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
142	C₃×Q₈	—	2	2	no	—
143	C₃×Q₈	—	2	2	no	—
144	C₃×Q₈	—	2	2	no	—
145	C₃×Q₈	C₃×C₄⋊C₄	1	4	yes	—
146	C₂×C₃×C₄	—	2	2	no	—
147	C₂×C₃×C₄	—	2	2	no	—
148	C₂×C₃×C₄	—	2	2	no	—
149	C₂×C₃×C₄	—	2	2	no	—
150	C₂×C₃×C₄	—	2	2	no	—
151	C₂×C₃×C₄	—	2	2	no	—
152	C₂×C₃×C₄	—	4	2	no	—
153	C₂×C₃×C₄	—	4	2	no	—
154	C₂×C₃×C₄	—	4	2	no	—
155	C₂×C₃×C₄	—	4	2	no	—
156	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
157	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
158	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
159	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
161	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
162	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
163	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
164	C₃×C₈	—	4	2	no	—
165	C₂×C₉	#380	1	1	yes	characteristic
166	C₂×C₉	#416	1	1	yes	characteristic
167	C₂×C₉	#419	1	1	yes	characteristic
168	C₂×C₉	#464	1	2	yes	—
169	C₂×C₉	#479	1	2	yes	—
170	C₂×Q₈	—	2	1	no	—
171	C₂×Q₈	—	2	1	no	—
172	C₂×Q₈	—	2	1	no	—
173	C₂×Q₈	C₂×C₄×C₉	1	2	yes	—
174	C₂×Q₈	D₄×C₉	1	2	yes	—
175	C₂×Q₈	Q₈×C₉	1	2	yes	—
176	C₂²×C₄	—	2	1	no	—
177	C₂²×C₄	—	2	1	no	—
178	C₂²×C₄	—	2	2	no	—
179	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
180	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
181	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	2	2	no	—
185	C₄⋊C₄	—	2	4	no	—
186	C₄⋊C₄	—	2	1	no	—
187	C₄⋊C₄	—	2	2	no	—
188	C₄⋊C₄	—	2	2	no	—
189	C₄⋊C₄	C₂×C₄×C₉	1	2	yes	—
190	C₄²	—	2	4	no	—
191	C₄²	C₂×C₄×C₉	1	2	yes	—
192	C₄²	D₄×C₉	1	2	yes	—
193	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
194	C₂²×C₃	C₃×#121	1	1	yes	characteristic
195	C₂²×C₃	C₃×C₂²⋊Q₈	1	1	yes	characteristic
196	C₂²×C₃	C₃×#135	1	2	yes	—
197	C₂²×C₃	C₃×#137	1	2	yes	—
198	C₃×C₄	—	2	4	no	—
199	C₃×C₄	—	2	2	no	—
200	C₃×C₄	—	2	2	no	—
201	C₃×C₄	—	4	2	no	—
202	C₃×C₄	—	8	2	no	—
203	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
204	C₃×C₄	C₃×#117	1	1	yes	characteristic
205	C₃×C₄	C₃×#121	1	1	yes	characteristic
206	C₃×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
207	C₉	#1805	1	1	yes	characteristic, direct product factor, Sylow
208	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
209	Q₈	—	2	2	no	—
210	Q₈	—	2	2	no	—
211	Q₈	—	2	2	no	—
212	Q₈	C₉×C₄⋊C₄	1	4	yes	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	C₉×C₂²⋊C₄	1	2	yes	—
224	C₂×C₄	C₉×C₂²⋊C₄	1	2	yes	—
225	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
226	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
227	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
228	C₂×C₄	C₂×Q₈×C₉	1	1	yes	characteristic
229	C₂×C₄	C₉×#41	1	1	yes	characteristic
230	C₂×C₄	C₉×#41	1	1	yes	characteristic
231	C₈	—	4	2	no	—
232	C₂×C₃	C₃×#380	1	1	yes	characteristic
233	C₂×C₃	C₃×#416	1	1	yes	characteristic
234	C₂×C₃	C₃×#419	1	1	yes	characteristic
235	C₂×C₃	C₃×#464	1	2	yes	—
236	C₂×C₃	C₃×#479	1	2	yes	—
237	C₂²	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
238	C₂²	C₉×#121	1	1	yes	characteristic
239	C₂²	C₉×C₂²⋊Q₈	1	1	yes	characteristic
240	C₂²	C₉×#135	1	2	yes	—
241	C₂²	C₉×#137	1	2	yes	—
242	C₄	—	2	4	no	—
243	C₄	—	2	2	no	—
244	C₄	—	2	2	no	—
245	C₄	—	4	2	no	—
246	C₄	—	8	2	no	—
247	C₄	C₂×C₉×C₄⋊C₄	1	1	yes	characteristic
248	C₄	C₉×#117	1	1	yes	characteristic
249	C₄	C₉×#121	1	1	yes	characteristic
250	C₄	C₉×C₂²⋊Q₈	1	1	yes	characteristic
251	C₃	C₃×#1805	1	1	yes	characteristic
252	C₂	C₉×#380	1	1	yes	characteristic
253	C₂	C₉×#416	1	1	yes	characteristic
254	C₂	C₉×#419	1	1	yes	characteristic
255	C₂	C₉×#464	1	2	yes	—
256	C₂	C₉×#479	1	2	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle, prime radical	C₂³×C₃	C₂×C₃×D₄
LCS	G ▷ C₂×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
10. C₄×Q₈×C₉	C₄	semidirect
48. #1805	C₉	direct (N × H)
131. C₄×Q₈	C₄×C₉	semidirect
207. C₉	#1805	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×C₄×Q₈×C₉	2
C₂×C₉×C₄⋊C₈	2
C₂×C₉×#103	2
C₉×#382	2
C₉×#340	2
C₃×#1805	3

Subgroups — C9×#1805 #11766526

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1805 #11766526