Subgroups — C₉×#2084 #11766805

Order 1152.

345 conjugacy classes of subgroups.

The subgroup lattice has 231 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#106	C₂	1	2	yes	maximal
2	C₉×#389	C₂	1	1	yes	maximal, characteristic
3	C₉×#384	C₂	1	1	yes	maximal, characteristic
4	C₉×#340	C₂	1	2	yes	maximal
5	C₉×#336	C₂	1	1	yes	maximal, characteristic
6	C₃×#2084	C₃	1	1	yes	maximal, characteristic
7	C₂²×C₈×C₉	C₂²	1	2	yes	—
8	C₂×C₉×C₄⋊C₄	—	2	1	no	—
9	C₂×C₉×C₄⋊C₄	—	2	1	no	—
10	C₂×C₉×C₄⋊C₄	—	2	1	no	—
11	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
15	C₉×#106	—	2	4	no	—
16	C₉×#95	—	2	1	no	—
17	C₂×C₃×#106	C₂×C₃	1	2	yes	—
18	C₃×#389	C₂×C₃	1	1	yes	characteristic
19	C₃×#384	C₂×C₃	1	1	yes	characteristic
20	C₃×#340	C₂×C₃	1	2	yes	—
21	C₃×#336	C₂×C₃	1	1	yes	characteristic
22	C₂²×C₄×C₉	—	2	1	no	—
23	C₂²×C₄×C₉	—	2	2	no	—
24	C₂²×C₄×C₉	—	2	1	no	—
25	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
26	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
27	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
28	C₂×C₈×C₉	—	2	2	no	—
29	C₂×C₈×C₉	—	2	2	no	—
30	C₂×C₈×C₉	Q₈	1	4	yes	—
31	C₉×C₄⋊C₄	—	2	1	no	—
32	C₉×C₄⋊C₄	—	2	2	no	—
33	C₉×C₄⋊C₄	—	2	2	no	—
34	C₉×C₄⋊C₄	—	2	2	no	—
35	C₉×C₄⋊C₄	—	4	2	no	—
36	C₉×C₄⋊C₄	—	4	2	no	—
37	C₉×C₄⋊C₄	—	4	2	no	—
38	C₉×C₄⋊C₄	D₄	1	2	yes	—
39	C₄²×C₉	—	2	2	no	—
40	#2084	C₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
42	C₂×C₃×C₄⋊C₄	—	2	1	no	—
43	C₂×C₃×C₄⋊C₄	—	2	1	no	—
44	C₂×C₃×C₄⋊C₄	—	2	1	no	—
45	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
46	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
47	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
48	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
49	C₃×#106	—	2	4	no	—
50	C₃×#95	—	2	1	no	—
51	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₉	—	2	1	no	—
53	C₂×C₄×C₉	—	2	1	no	—
54	C₂×C₄×C₉	—	2	1	no	—
55	C₂×C₄×C₉	—	2	1	no	—
56	C₂×C₄×C₉	—	2	2	no	—
57	C₂×C₄×C₉	—	4	1	no	—
58	C₂×C₄×C₉	—	4	1	no	—
59	C₂×C₄×C₉	—	4	2	no	—
60	C₂×C₄×C₉	—	4	1	no	—
61	C₂×C₄×C₉	—	4	2	no	—
62	C₂×C₄×C₉	—	4	1	no	—
63	C₂×C₄×C₉	—	4	2	no	—
64	C₂×C₄×C₉	—	4	1	no	—
65	C₂×C₄×C₉	SD₁₆	1	2	yes	—
66	C₂×C₄×C₉	SD₁₆	1	2	yes	—
67	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
68	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
69	C₂×C₄×C₉	#41	1	2	yes	—
70	C₂×C₄×C₉	#41	1	1	yes	characteristic
71	C₈×C₉	—	2	4	no	—
72	C₂×#106	C₂×C₉	1	2	yes	—
73	#389	C₂×C₉	1	1	yes	characteristic
74	#384	C₂×C₉	1	1	yes	characteristic
75	#340	C₂×C₉	1	2	yes	—
76	#336	C₂×C₉	1	1	yes	characteristic
77	C₂²×C₃×C₄	—	2	1	no	—
78	C₂²×C₃×C₄	—	2	1	no	—
79	C₂²×C₃×C₄	—	2	2	no	—
80	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
81	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
82	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
83	C₂×C₃×C₈	—	2	2	no	—
84	C₂×C₃×C₈	—	2	2	no	—
85	C₂×C₃×C₈	C₃×Q₈	1	4	yes	—
86	C₃×C₄⋊C₄	—	2	1	no	—
87	C₃×C₄⋊C₄	—	2	2	no	—
88	C₃×C₄⋊C₄	—	2	2	no	—
89	C₃×C₄⋊C₄	—	2	2	no	—
90	C₃×C₄⋊C₄	—	4	2	no	—
91	C₃×C₄⋊C₄	—	4	2	no	—
92	C₃×C₄⋊C₄	—	4	2	no	—
93	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
94	C₃×C₄²	—	2	2	no	—
95	C₂²×C₉	#121	1	1	yes	characteristic
96	C₂²×C₉	#123	1	1	yes	characteristic
97	C₂²×C₉	C₄⋊Q₈	1	1	yes	characteristic
98	C₂²×C₉	C₂×SD₁₆	1	1	yes	characteristic
99	C₂²×C₉	C₂×SD₁₆	1	1	yes	characteristic
100	C₂²×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
101	C₂²×C₉	#137	1	1	yes	characteristic
102	C₄×C₉	—	2	2	no	—
103	C₄×C₉	—	2	2	no	—
104	C₄×C₉	—	4	2	no	—
105	C₄×C₉	—	8	2	no	—
106	C₄×C₉	—	8	1	no	—
107	C₄×C₉	C₂²⋊Q₈	1	2	yes	—
108	C₄×C₉	#125	1	2	yes	—
109	C₂²×C₈	C₂²×C₉	1	2	yes	—
110	C₂×C₄⋊C₄	—	2	1	no	—
111	C₂×C₄⋊C₄	—	2	1	no	—
112	C₂×C₄⋊C₄	—	2	1	no	—
113	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
114	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
115	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
116	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
117	#106	—	2	4	no	—
118	#95	—	2	1	no	—
119	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
120	C₂×C₃×C₄	—	2	1	no	—
121	C₂×C₃×C₄	—	2	1	no	—
122	C₂×C₃×C₄	—	2	1	no	—
123	C₂×C₃×C₄	—	2	1	no	—
124	C₂×C₃×C₄	—	2	2	no	—
125	C₂×C₃×C₄	—	4	1	no	—
126	C₂×C₃×C₄	—	4	1	no	—
127	C₂×C₃×C₄	—	4	2	no	—
128	C₂×C₃×C₄	—	4	1	no	—
129	C₂×C₃×C₄	—	4	2	no	—
130	C₂×C₃×C₄	—	4	1	no	—
131	C₂×C₃×C₄	—	4	2	no	—
132	C₂×C₃×C₄	—	4	1	no	—
133	C₂×C₃×C₄	C₃×SD₁₆	1	2	yes	—
134	C₂×C₃×C₄	C₃×SD₁₆	1	2	yes	—
135	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
136	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
137	C₂×C₃×C₄	C₃×#41	1	2	yes	—
138	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
139	C₃×C₈	—	2	4	no	—
140	C₂×C₉	#398	1	1	yes	characteristic
141	C₂×C₉	#460	1	1	yes	characteristic
142	C₂×C₉	#461	1	1	yes	characteristic
143	C₂×C₉	#481	1	1	yes	characteristic
144	C₂×C₉	#483	1	1	yes	characteristic
145	C₂×C₉	#498	1	1	yes	characteristic
146	C₂×C₉	#501	1	1	yes	characteristic
147	C₂²×C₄	—	2	1	no	—
148	C₂²×C₄	—	2	1	no	—
149	C₂²×C₄	—	2	2	no	—
150	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
151	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
152	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
153	C₂×C₈	—	2	2	no	—
154	C₂×C₈	—	2	2	no	—
155	C₂×C₈	Q₈×C₉	1	4	yes	—
156	C₄⋊C₄	—	2	1	no	—
157	C₄⋊C₄	—	2	2	no	—
158	C₄⋊C₄	—	2	2	no	—
159	C₄⋊C₄	—	2	2	no	—
160	C₄⋊C₄	—	4	2	no	—
161	C₄⋊C₄	—	4	2	no	—
162	C₄⋊C₄	—	4	2	no	—
163	C₄⋊C₄	D₄×C₉	1	2	yes	—
164	C₄²	—	2	2	no	—
165	C₂²×C₃	C₃×#121	1	1	yes	characteristic
166	C₂²×C₃	C₃×#123	1	1	yes	characteristic
167	C₂²×C₃	C₃×C₄⋊Q₈	1	1	yes	characteristic
168	C₂²×C₃	C₂×C₃×SD₁₆	1	1	yes	characteristic
169	C₂²×C₃	C₂×C₃×SD₁₆	1	1	yes	characteristic
170	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂²×C₃	C₃×#137	1	1	yes	characteristic
172	C₃×C₄	—	2	2	no	—
173	C₃×C₄	—	2	2	no	—
174	C₃×C₄	—	4	2	no	—
175	C₃×C₄	—	8	2	no	—
176	C₃×C₄	—	8	1	no	—
177	C₃×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
178	C₃×C₄	C₃×#125	1	2	yes	—
179	C₉	#2084	1	1	yes	characteristic, direct product factor, Sylow
180	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	4	1	no	—
187	C₂×C₄	—	4	1	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	4	1	no	—
190	C₂×C₄	—	4	2	no	—
191	C₂×C₄	—	4	1	no	—
192	C₂×C₄	—	4	2	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	C₉×SD₁₆	1	2	yes	—
195	C₂×C₄	C₉×SD₁₆	1	2	yes	—
196	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
197	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
198	C₂×C₄	C₉×#41	1	2	yes	—
199	C₂×C₄	C₉×#41	1	1	yes	characteristic
200	C₈	—	2	4	no	—
201	C₂×C₃	C₃×#398	1	1	yes	characteristic
202	C₂×C₃	C₃×#460	1	1	yes	characteristic
203	C₂×C₃	C₃×#461	1	1	yes	characteristic
204	C₂×C₃	C₃×#481	1	1	yes	characteristic
205	C₂×C₃	C₃×#483	1	1	yes	characteristic
206	C₂×C₃	C₃×#498	1	1	yes	characteristic
207	C₂×C₃	C₃×#501	1	1	yes	characteristic
208	C₂²	C₉×#121	1	1	yes	characteristic
209	C₂²	C₉×#123	1	1	yes	characteristic
210	C₂²	C₉×C₄⋊Q₈	1	1	yes	characteristic
211	C₂²	C₂×C₉×SD₁₆	1	1	yes	characteristic
212	C₂²	C₂×C₉×SD₁₆	1	1	yes	characteristic
213	C₂²	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₂²	C₉×#137	1	1	yes	characteristic
215	C₄	—	2	2	no	—
216	C₄	—	2	2	no	—
217	C₄	—	4	2	no	—
218	C₄	—	8	2	no	—
219	C₄	—	8	1	no	—
220	C₄	C₉×C₂²⋊Q₈	1	2	yes	—
221	C₄	C₉×#125	1	2	yes	—
222	C₃	C₃×#2084	1	1	yes	characteristic
223	C₂	C₉×#398	1	1	yes	characteristic
224	C₂	C₉×#460	1	1	yes	characteristic
225	C₂	C₉×#461	1	1	yes	characteristic
226	C₂	C₉×#481	1	1	yes	characteristic
227	C₂	C₉×#483	1	1	yes	characteristic
228	C₂	C₉×#498	1	1	yes	characteristic
229	C₂	C₉×#501	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
40. #2084	C₉	direct (N × H)
179. C₉	#2084	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×#106	2
C₉×#389	2
C₉×#384	2
C₉×#340	2
C₉×#336	2
C₃×#2084	3

Subgroups — C9×#2084 #11766805

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2084 #11766805