Subgroups — C₉×#1982 #11766703

Order 1152.

642 conjugacy classes of subgroups.

The subgroup lattice has 255 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#102	C₂	1	4	yes	maximal, complemented
4	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#1982	C₃	1	1	yes	maximal, characteristic
6	C₂²×D₄×C₉	—	2	1	no	—
7	C₂²×D₄×C₉	—	2	1	no	—
8	C₂²×D₄×C₉	C₂²	1	2	yes	—
9	C₂²×C₈×C₉	C₂²	1	2	yes	—
10	C₉×#127	—	2	2	no	—
11	C₉×#127	C₄	1	4	yes	complemented
12	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₄²×C₉	—	2	1	no	—
14	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
15	C₉×C₄⋊C₈	—	2	2	no	—
16	C₉×#102	—	2	8	no	—
17	C₉×#95	—	2	1	no	—
18	C₂×C₃×#127	C₂×C₃	1	1	yes	characteristic
19	C₂×C₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
20	C₂×C₃×#102	C₂×C₃	1	4	yes	—
21	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
22	C₂⁴×C₉	—	2	2	no	—
23	C₂×D₄×C₉	—	2	4	no	—
24	C₂×D₄×C₉	—	2	4	no	—
25	C₂×D₄×C₉	—	2	4	no	—
26	C₂×D₄×C₉	—	2	2	no	—
27	C₂×D₄×C₉	—	2	4	no	—
28	C₂×D₄×C₉	—	4	4	no	—
29	C₂×D₄×C₉	—	4	2	no	—
30	C₂×D₄×C₉	—	4	2	no	—
31	C₂×D₄×C₉	C₂×C₄	1	4	yes	—
32	C₂²×C₄×C₉	—	2	2	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	4	no	—
37	C₂×C₈×C₉	—	2	2	no	—
38	C₉×C₄⋊C₄	—	2	2	no	—
39	C₉×C₄⋊C₄	D₄	1	4	yes	complemented
40	C₄²×C₉	—	4	2	no	—
41	C₄²×C₉	C₂×C₄	1	2	yes	—
42	C₄²×C₉	D₄	1	2	yes	—
43	#1982	C₉	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²×C₃×D₄	—	2	1	no	—
45	C₂²×C₃×D₄	—	2	1	no	—
46	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
47	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
48	C₃×#127	—	2	2	no	—
49	C₃×#127	C₃×C₄	1	4	yes	—
50	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
51	C₂×C₃×C₄²	—	2	1	no	—
52	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
53	C₃×C₄⋊C₈	—	2	2	no	—
54	C₃×#102	—	2	8	no	—
55	C₃×#95	—	2	1	no	—
56	C₂³×C₉	—	2	4	no	—
57	C₂³×C₉	—	4	4	no	—
58	C₂³×C₉	—	4	2	no	—
59	C₂³×C₉	—	4	2	no	—
60	C₂³×C₉	—	4	4	no	—
61	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
62	D₄×C₉	—	2	8	no	—
63	D₄×C₉	—	4	8	no	—
64	D₄×C₉	—	4	8	no	—
65	D₄×C₉	—	4	2	no	—
66	D₄×C₉	—	4	2	no	—
67	C₂×C₄×C₉	—	2	2	no	—
68	C₂×C₄×C₉	—	2	4	no	—
69	C₂×C₄×C₉	—	4	2	no	—
70	C₂×C₄×C₉	—	4	2	no	—
71	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
72	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
73	C₂×C₄×C₉	D₈	1	2	yes	—
74	C₂×C₄×C₉	SD₁₆	1	2	yes	—
75	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
77	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₉	#41	1	2	yes	—
79	C₈×C₉	—	4	2	no	—
80	C₂×#127	C₂×C₉	1	1	yes	characteristic
81	C₂×C₄⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
82	C₂×#102	C₂×C₉	1	4	yes	complemented
83	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
84	C₂⁴×C₃	—	2	2	no	—
85	C₂×C₃×D₄	—	2	4	no	—
86	C₂×C₃×D₄	—	2	4	no	—
87	C₂×C₃×D₄	—	2	4	no	—
88	C₂×C₃×D₄	—	2	2	no	—
89	C₂×C₃×D₄	—	2	4	no	—
90	C₂×C₃×D₄	—	4	4	no	—
91	C₂×C₃×D₄	—	4	2	no	—
92	C₂×C₃×D₄	—	4	2	no	—
93	C₂×C₃×D₄	C₂×C₃×C₄	1	4	yes	—
94	C₂²×C₃×C₄	—	2	2	no	—
95	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
96	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
97	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
98	C₂×C₃×C₈	—	2	4	no	—
99	C₂×C₃×C₈	—	2	2	no	—
100	C₃×C₄⋊C₄	—	2	2	no	—
101	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
102	C₃×C₄²	—	4	2	no	—
103	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
104	C₃×C₄²	C₃×D₄	1	2	yes	—
105	C₂²×C₉	—	4	4	no	—
106	C₂²×C₉	—	4	4	no	—
107	C₂²×C₉	—	4	4	no	—
108	C₂²×C₉	—	8	4	no	—
109	C₂²×C₉	—	8	4	no	—
110	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₉	#121	1	2	yes	—
112	C₂²×C₉	C₂×D₈	1	1	yes	characteristic
113	C₂²×C₉	C₂×SD₁₆	1	1	yes	characteristic
114	C₂²×C₉	AGL(1,ℤ/8)	1	2	yes	—
115	C₄×C₉	—	2	2	no	—
116	C₄×C₉	—	4	4	no	—
117	C₄×C₉	#102	1	4	yes	complemented
118	C₄×C₉	C₄×D₄	1	2	yes	—
119	C₄×C₉	#124	1	1	yes	characteristic
120	C₄×C₉	#127	1	1	yes	characteristic
121	C₂²×D₄	—	2	1	no	—
122	C₂²×D₄	—	2	1	no	—
123	C₂²×D₄	C₂²×C₉	1	2	yes	—
124	C₂²×C₈	C₂²×C₉	1	2	yes	—
125	#127	—	2	2	no	—
126	#127	C₄×C₉	1	4	yes	complemented
127	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
128	C₂×C₄²	—	2	1	no	—
129	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
130	C₄⋊C₈	—	2	2	no	—
131	#102	—	2	8	no	—
132	#95	—	2	1	no	—
133	C₂³×C₃	—	2	4	no	—
134	C₂³×C₃	—	4	4	no	—
135	C₂³×C₃	—	4	2	no	—
136	C₂³×C₃	—	4	2	no	—
137	C₂³×C₃	—	4	4	no	—
138	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
139	C₃×D₄	—	2	8	no	—
140	C₃×D₄	—	4	8	no	—
141	C₃×D₄	—	4	8	no	—
142	C₃×D₄	—	4	2	no	—
143	C₃×D₄	—	4	2	no	—
144	C₂×C₃×C₄	—	2	2	no	—
145	C₂×C₃×C₄	—	2	4	no	—
146	C₂×C₃×C₄	—	4	2	no	—
147	C₂×C₃×C₄	—	4	2	no	—
148	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
149	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
150	C₂×C₃×C₄	C₃×D₈	1	2	yes	—
151	C₂×C₃×C₄	C₃×SD₁₆	1	2	yes	—
152	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
153	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
154	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
155	C₂×C₃×C₄	C₃×#41	1	2	yes	—
156	C₃×C₈	—	4	2	no	—
157	C₂×C₉	—	8	4	no	—
158	C₂×C₉	#390	1	1	yes	characteristic
159	C₂×C₉	C₂×#102	1	1	yes	characteristic
160	C₂×C₉	#418	1	1	yes	characteristic
161	C₂×C₉	#459	1	2	yes	—
162	C₂×C₉	#460	1	2	yes	—
163	C₂⁴	—	2	2	no	—
164	C₂×D₄	—	2	4	no	—
165	C₂×D₄	—	2	4	no	—
166	C₂×D₄	—	2	4	no	—
167	C₂×D₄	—	2	2	no	—
168	C₂×D₄	—	2	4	no	—
169	C₂×D₄	—	4	4	no	—
170	C₂×D₄	—	4	2	no	—
171	C₂×D₄	—	4	2	no	—
172	C₂×D₄	C₂×C₄×C₉	1	4	yes	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
175	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
176	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
177	C₂×C₈	—	2	4	no	—
178	C₂×C₈	—	2	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	D₄×C₉	1	4	yes	complemented
181	C₄²	—	4	2	no	—
182	C₄²	C₂×C₄×C₉	1	2	yes	—
183	C₄²	D₄×C₉	1	2	yes	—
184	C₂²×C₃	—	4	4	no	—
185	C₂²×C₃	—	4	4	no	—
186	C₂²×C₃	—	4	4	no	—
187	C₂²×C₃	—	8	4	no	—
188	C₂²×C₃	—	8	4	no	—
189	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×C₃	C₃×#121	1	2	yes	—
191	C₂²×C₃	C₂×C₃×D₈	1	1	yes	characteristic
192	C₂²×C₃	C₂×C₃×SD₁₆	1	1	yes	characteristic
193	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	2	yes	—
194	C₃×C₄	—	2	2	no	—
195	C₃×C₄	—	4	4	no	—
196	C₃×C₄	C₃×#102	1	4	yes	—
197	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
198	C₃×C₄	C₃×#124	1	1	yes	characteristic
199	C₃×C₄	C₃×#127	1	1	yes	characteristic
200	C₉	#1982	1	1	yes	characteristic, direct product factor, Sylow
201	C₂³	—	2	4	no	—
202	C₂³	—	4	4	no	—
203	C₂³	—	4	2	no	—
204	C₂³	—	4	2	no	—
205	C₂³	—	4	4	no	—
206	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
207	D₄	—	2	8	no	—
208	D₄	—	4	8	no	—
209	D₄	—	4	2	no	—
210	D₄	—	4	2	no	—
211	D₄	—	4	8	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	4	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	C₉×C₂²⋊C₄	1	2	yes	—
217	C₂×C₄	C₉×C₂²⋊C₄	1	2	yes	—
218	C₂×C₄	C₉×D₈	1	2	yes	—
219	C₂×C₄	C₉×SD₁₆	1	2	yes	—
220	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
221	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
222	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
223	C₂×C₄	C₉×#41	1	2	yes	—
224	C₈	—	4	2	no	—
225	C₂×C₃	—	8	4	no	—
226	C₂×C₃	C₃×#390	1	1	yes	characteristic
227	C₂×C₃	C₂×C₃×#102	1	1	yes	characteristic
228	C₂×C₃	C₃×#418	1	1	yes	characteristic
229	C₂×C₃	C₃×#459	1	2	yes	—
230	C₂×C₃	C₃×#460	1	2	yes	—
231	C₂²	—	4	4	no	—
232	C₂²	—	4	4	no	—
233	C₂²	—	4	4	no	—
234	C₂²	—	8	4	no	—
235	C₂²	—	8	4	no	—
236	C₂²	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
237	C₂²	C₉×#121	1	2	yes	—
238	C₂²	C₂×C₉×D₈	1	1	yes	characteristic
239	C₂²	C₂×C₉×SD₁₆	1	1	yes	characteristic
240	C₂²	C₉×AGL(1,ℤ/8)	1	2	yes	—
241	C₄	—	2	2	no	—
242	C₄	—	4	4	no	—
243	C₄	C₉×#102	1	4	yes	complemented
244	C₄	C₄×D₄×C₉	1	2	yes	—
245	C₄	C₉×#124	1	1	yes	characteristic
246	C₄	C₉×#127	1	1	yes	characteristic
247	C₃	C₃×#1982	1	1	yes	characteristic
248	C₂	—	8	4	no	—
249	C₂	C₉×#390	1	1	yes	characteristic
250	C₂	C₂×C₉×#102	1	1	yes	characteristic
251	C₂	C₉×#418	1	1	yes	characteristic
252	C₂	C₉×#459	1	2	yes	—
253	C₂	C₉×#460	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	C₂³×C₃	C₂×C₃×D₄
prime radical	C₂×C₃×#127	C₂×C₃
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
2. C₂×C₉×C₄⋊C₈	C₂	semidirect
3. C₂×C₉×#102	C₂	semidirect
4. C₄×C₉×C₄⋊C₄	C₂	semidirect
11. C₉×#127	C₄	semidirect
39. C₉×C₄⋊C₄	D₄	semidirect
43. #1982	C₉	direct (N × H)
81. C₂×C₄⋊C₈	C₂×C₉	semidirect
82. C₂×#102	C₂×C₉	semidirect
83. C₄×C₄⋊C₄	C₂×C₉	semidirect
117. C₄×C₉	#102	semidirect
126. #127	C₄×C₉	semidirect
180. C₄⋊C₄	D₄×C₉	semidirect
200. C₉	#1982	direct (N × H)
243. C₄	C₉×#102	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₉×#127	2
C₂×C₉×C₄⋊C₈	2
C₂×C₉×#102	2
C₄×C₉×C₄⋊C₄	2
C₃×#1982	3

Subgroups — C9×#1982 #11766703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1982 #11766703