Subgroups — C₉×#2081 #11766802

Order 1152.

306 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	C₉×#430	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#418	C₂	1	1	yes	maximal, characteristic
3	C₉×#418	C₂	1	1	yes	maximal, characteristic
4	C₂×C₉×#100	C₂	1	1	yes	maximal, characteristic
5	C₉×#344	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#344	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2081	C₃	1	1	yes	maximal, characteristic
9	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
10	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
14	C₉×#117	C₂²	1	1	yes	characteristic
15	C₉×#117	C₂²	1	1	yes	characteristic
16	C₉×#108	—	2	2	no	—
17	C₉×#102	—	2	2	no	—
18	C₉×#102	—	2	2	no	—
19	C₉×#100	—	2	2	no	—
20	C₃×#430	C₂×C₃	1	1	yes	characteristic
21	C₃×#418	C₂×C₃	1	1	yes	characteristic
22	C₃×#418	C₂×C₃	1	1	yes	characteristic
23	C₂×C₃×#100	C₂×C₃	1	1	yes	characteristic
24	C₃×#344	C₂×C₃	1	1	yes	characteristic
25	C₃×#344	C₂×C₃	1	1	yes	characteristic
26	C₃×H(3,ℤ/4)	C₂×C₃	1	1	yes	characteristic
27	C₂⁴×C₉	—	2	1	no	—
28	C₂×D₄×C₉	—	2	1	no	—
29	C₂×D₄×C₉	—	2	1	no	—
30	C₂×D₄×C₉	—	2	1	no	—
31	C₂×D₄×C₉	—	2	1	no	—
32	C₂×D₄×C₉	—	2	1	no	—
33	C₂×D₄×C₉	D₄	1	2	yes	—
34	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
35	C₉×M₁₆	—	2	1	no	—
36	C₉×M₁₆	—	2	1	no	—
37	C₉×M₁₆	—	2	1	no	—
38	C₉×M₁₆	—	2	1	no	—
39	C₉×M₁₆	—	2	1	no	—
40	C₉×M₁₆	—	2	1	no	—
41	C₉×M₁₆	—	2	1	no	—
42	C₉×M₁₆	—	2	1	no	—
43	C₂×C₈×C₉	—	2	1	no	—
44	C₂×C₈×C₉	—	2	1	no	—
45	C₂×C₈×C₉	—	2	1	no	—
46	C₂×C₈×C₉	D₄	1	2	yes	—
47	C₉×C₄⋊C₄	—	2	1	no	—
48	C₉×C₄⋊C₄	—	2	1	no	—
49	C₉×C₂²⋊C₄	—	2	1	no	—
50	C₉×C₂²⋊C₄	—	2	1	no	—
51	C₄²×C₉	—	2	1	no	—
52	C₄²×C₉	—	2	1	no	—
53	#2081	C₉	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
55	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
56	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
57	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
58	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
59	C₃×#117	C₂²×C₃	1	1	yes	characteristic
60	C₃×#117	C₂²×C₃	1	1	yes	characteristic
61	C₃×#108	—	2	2	no	—
62	C₃×#102	—	2	2	no	—
63	C₃×#102	—	2	2	no	—
64	C₃×#100	—	2	2	no	—
65	C₂³×C₉	—	2	2	no	—
66	C₂³×C₉	—	4	1	no	—
67	C₂³×C₉	—	4	1	no	—
68	C₂³×C₉	—	8	2	no	—
69	C₂³×C₉	#41	1	1	yes	characteristic
70	D₄×C₉	—	2	2	no	—
71	D₄×C₉	—	2	2	no	—
72	D₄×C₉	—	4	1	no	—
73	D₄×C₉	—	4	1	no	—
74	C₂×C₄×C₉	—	4	1	no	—
75	C₂×C₄×C₉	—	4	1	no	—
76	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₉	#41	1	1	yes	characteristic
79	C₂×C₄×C₉	#41	1	1	yes	characteristic
80	C₂×C₄×C₉	#41	1	1	yes	characteristic
81	C₂×C₄×C₉	#41	1	1	yes	characteristic
82	C₈×C₉	—	2	2	no	—
83	C₈×C₉	—	4	1	no	—
84	C₈×C₉	—	4	1	no	—
85	C₈×C₉	—	4	1	no	—
86	#430	C₂×C₉	1	1	yes	characteristic, complemented
87	#418	C₂×C₉	1	1	yes	characteristic
88	#418	C₂×C₉	1	1	yes	characteristic
89	C₂×#100	C₂×C₉	1	1	yes	characteristic
90	#344	C₂×C₉	1	1	yes	characteristic, complemented
91	#344	C₂×C₉	1	1	yes	characteristic, complemented
92	H(3,ℤ/4)	C₂×C₉	1	1	yes	characteristic, complemented
93	C₂⁴×C₃	—	2	1	no	—
94	C₂×C₃×D₄	—	2	1	no	—
95	C₂×C₃×D₄	—	2	1	no	—
96	C₂×C₃×D₄	—	2	1	no	—
97	C₂×C₃×D₄	—	2	1	no	—
98	C₂×C₃×D₄	—	2	1	no	—
99	C₂×C₃×D₄	C₃×D₄	1	2	yes	—
100	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
101	C₃×M₁₆	—	2	1	no	—
102	C₃×M₁₆	—	2	1	no	—
103	C₃×M₁₆	—	2	1	no	—
104	C₃×M₁₆	—	2	1	no	—
105	C₃×M₁₆	—	2	1	no	—
106	C₃×M₁₆	—	2	1	no	—
107	C₃×M₁₆	—	2	1	no	—
108	C₃×M₁₆	—	2	1	no	—
109	C₂×C₃×C₈	—	2	1	no	—
110	C₂×C₃×C₈	—	2	1	no	—
111	C₂×C₃×C₈	—	2	1	no	—
112	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
113	C₃×C₄⋊C₄	—	2	1	no	—
114	C₃×C₄⋊C₄	—	2	1	no	—
115	C₃×C₂²⋊C₄	—	2	1	no	—
116	C₃×C₂²⋊C₄	—	2	1	no	—
117	C₃×C₄²	—	2	1	no	—
118	C₃×C₄²	—	2	1	no	—
119	C₂²×C₉	—	4	1	no	—
120	C₂²×C₉	—	4	2	no	—
121	C₂²×C₉	—	8	2	no	—
122	C₂²×C₉	—	8	2	no	—
123	C₂²×C₉	—	8	2	no	—
124	C₂²×C₉	#123	1	1	yes	characteristic
125	C₂²×C₉	#124	1	1	yes	characteristic
126	C₂²×C₉	#126	1	1	yes	characteristic
127	C₄×C₉	—	8	1	no	—
128	C₄×C₉	—	8	1	no	—
129	C₄×C₉	#121	1	1	yes	characteristic
130	C₄×C₉	#123	1	1	yes	characteristic
131	C₄×C₉	#123	1	1	yes	characteristic
132	C₄×C₉	#126	1	1	yes	characteristic
133	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
134	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
135	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
136	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
137	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
138	#117	C₂²×C₉	1	1	yes	characteristic
139	#117	C₂²×C₉	1	1	yes	characteristic
140	#108	—	2	2	no	—
141	#102	—	2	2	no	—
142	#102	—	2	2	no	—
143	#100	—	2	2	no	—
144	C₂³×C₃	—	2	2	no	—
145	C₂³×C₃	—	4	1	no	—
146	C₂³×C₃	—	4	1	no	—
147	C₂³×C₃	—	8	2	no	—
148	C₂³×C₃	C₃×#41	1	1	yes	characteristic
149	C₃×D₄	—	2	2	no	—
150	C₃×D₄	—	2	2	no	—
151	C₃×D₄	—	4	1	no	—
152	C₃×D₄	—	4	1	no	—
153	C₂×C₃×C₄	—	4	1	no	—
154	C₂×C₃×C₄	—	4	1	no	—
155	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
156	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
157	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
158	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
159	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
160	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
161	C₃×C₈	—	2	2	no	—
162	C₃×C₈	—	4	1	no	—
163	C₃×C₈	—	4	1	no	—
164	C₃×C₈	—	4	1	no	—
165	C₂×C₉	—	2	1	no	—
166	C₂×C₉	—	2	1	no	—
167	C₂×C₉	—	2	1	no	—
168	C₂×C₉	—	8	2	no	—
169	C₂×C₉	#397	1	1	yes	characteristic
170	C₂⁴	—	2	1	no	—
171	C₂×D₄	—	2	1	no	—
172	C₂×D₄	—	2	1	no	—
173	C₂×D₄	—	2	1	no	—
174	C₂×D₄	—	2	1	no	—
175	C₂×D₄	—	2	1	no	—
176	C₂×D₄	D₄×C₉	1	2	yes	—
177	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
178	M₁₆	—	2	1	no	—
179	M₁₆	—	2	1	no	—
180	M₁₆	—	2	1	no	—
181	M₁₆	—	2	1	no	—
182	M₁₆	—	2	1	no	—
183	M₁₆	—	2	1	no	—
184	M₁₆	—	2	1	no	—
185	M₁₆	—	2	1	no	—
186	C₂×C₈	—	2	1	no	—
187	C₂×C₈	—	2	1	no	—
188	C₂×C₈	—	2	1	no	—
189	C₂×C₈	D₄×C₉	1	2	yes	—
190	C₄⋊C₄	—	2	1	no	—
191	C₄⋊C₄	—	2	1	no	—
192	C₂²⋊C₄	—	2	1	no	—
193	C₂²⋊C₄	—	2	1	no	—
194	C₄²	—	2	1	no	—
195	C₄²	—	2	1	no	—
196	C₂²×C₃	—	4	1	no	—
197	C₂²×C₃	—	4	2	no	—
198	C₂²×C₃	—	8	2	no	—
199	C₂²×C₃	—	8	2	no	—
200	C₂²×C₃	—	8	2	no	—
201	C₂²×C₃	C₃×#123	1	1	yes	characteristic
202	C₂²×C₃	C₃×#124	1	1	yes	characteristic
203	C₂²×C₃	C₃×#126	1	1	yes	characteristic
204	C₃×C₄	—	8	1	no	—
205	C₃×C₄	—	8	1	no	—
206	C₃×C₄	C₃×#121	1	1	yes	characteristic
207	C₃×C₄	C₃×#123	1	1	yes	characteristic
208	C₃×C₄	C₃×#123	1	1	yes	characteristic
209	C₃×C₄	C₃×#126	1	1	yes	characteristic
210	C₉	#2081	1	1	yes	characteristic, direct product factor, Sylow
211	C₂³	—	2	2	no	—
212	C₂³	—	4	1	no	—
213	C₂³	—	4	1	no	—
214	C₂³	—	8	2	no	—
215	C₂³	C₉×#41	1	1	yes	characteristic
216	D₄	—	2	2	no	—
217	D₄	—	2	2	no	—
218	D₄	—	4	1	no	—
219	D₄	—	4	1	no	—
220	C₂×C₄	—	4	1	no	—
221	C₂×C₄	—	4	1	no	—
222	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
223	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
224	C₂×C₄	C₉×#41	1	1	yes	characteristic
225	C₂×C₄	C₉×#41	1	1	yes	characteristic
226	C₂×C₄	C₉×#41	1	1	yes	characteristic
227	C₂×C₄	C₉×#41	1	1	yes	characteristic
228	C₈	—	2	2	no	—
229	C₈	—	4	1	no	—
230	C₈	—	4	1	no	—
231	C₈	—	4	1	no	—
232	C₂×C₃	—	2	1	no	—
233	C₂×C₃	—	2	1	no	—
234	C₂×C₃	—	2	1	no	—
235	C₂×C₃	—	8	2	no	—
236	C₂×C₃	C₃×#397	1	1	yes	characteristic
237	C₂²	—	4	1	no	—
238	C₂²	—	4	2	no	—
239	C₂²	—	8	2	no	—
240	C₂²	—	8	2	no	—
241	C₂²	—	8	2	no	—
242	C₂²	C₉×#123	1	1	yes	characteristic
243	C₂²	C₉×#124	1	1	yes	characteristic
244	C₂²	C₉×#126	1	1	yes	characteristic
245	C₄	—	8	1	no	—
246	C₄	—	8	1	no	—
247	C₄	C₉×#121	1	1	yes	characteristic
248	C₄	C₉×#123	1	1	yes	characteristic
249	C₄	C₉×#123	1	1	yes	characteristic
250	C₄	C₉×#126	1	1	yes	characteristic
251	C₃	C₃×#2081	1	1	yes	characteristic
252	C₂	—	2	1	no	—
253	C₂	—	2	1	no	—
254	C₂	—	2	1	no	—
255	C₂	—	8	2	no	—
256	C₂	C₉×#397	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	#397
commutator	C₂²×C₄	C₂³×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂×C₃	C₃×#397
prime radical	C₂²×C₃×D₄	C₂²×C₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₉ ◁ C₂²×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#430	C₂	semidirect
5. C₉×#344	C₂	semidirect
6. C₉×#344	C₂	semidirect
7. C₉×H(3,ℤ/4)	C₂	semidirect
53. #2081	C₉	direct (N × H)
86. #430	C₂×C₉	semidirect
90. #344	C₂×C₉	semidirect
91. #344	C₂×C₉	semidirect
92. H(3,ℤ/4)	C₂×C₉	semidirect
210. C₉	#2081	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#430	2
C₉×#418	2
C₂×C₉×#100	2
C₉×#344	2
C₉×H(3,ℤ/4)	2
C₃×#2081	3

Subgroups — C9×#2081 #11766802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2081 #11766802