Subgroups — C₉×#1823 #11766544

Order 1152.

516 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	C₂²×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₉×#380	C₂	1	1	yes	maximal, characteristic
4	C₉×#340	C₂	1	4	yes	maximal, complemented
5	C₃×#1823	C₃	1	1	yes	maximal, characteristic
6	C₂³×C₄×C₉	—	2	1	no	—
7	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₉	C₂²	1	2	yes	—
9	C₂×C₉×C₄⋊C₄	—	2	1	no	—
10	C₂×C₉×C₄⋊C₄	—	2	2	no	—
11	C₂×C₉×C₄⋊C₄	C₄	1	4	yes	complemented
12	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
15	C₉×C₂²⋊C₈	—	2	2	no	—
16	C₉×#95	—	2	1	no	—
17	C₂²×C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
18	C₂×C₃×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
19	C₃×#380	C₂×C₃	1	1	yes	characteristic
20	C₃×#340	C₂×C₃	1	4	yes	—
21	C₂⁴×C₉	D₄	1	1	yes	characteristic
22	C₂²×C₄×C₉	—	2	4	no	—
23	C₂²×C₄×C₉	—	2	4	no	—
24	C₂²×C₄×C₉	—	2	2	no	—
25	C₂²×C₄×C₉	—	2	2	no	—
26	C₂²×C₄×C₉	—	4	2	no	—
27	C₂²×C₄×C₉	—	4	2	no	—
28	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
29	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
30	C₂²×C₄×C₉	D₄	1	2	yes	—
31	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
32	C₂×C₈×C₉	—	2	2	no	—
33	C₂×C₈×C₉	—	2	4	no	—
34	C₉×C₄⋊C₄	—	2	4	no	—
35	C₉×C₄⋊C₄	—	2	2	no	—
36	C₉×C₄⋊C₄	—	2	4	no	—
37	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
38	C₉×C₂²⋊C₄	—	4	2	no	—
39	#1823	C₉	1	1	yes	characteristic, direct product factor, Sylow
40	C₂³×C₃×C₄	—	2	1	no	—
41	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
42	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
43	C₂×C₃×C₄⋊C₄	—	2	1	no	—
44	C₂×C₃×C₄⋊C₄	—	2	2	no	—
45	C₂×C₃×C₄⋊C₄	C₃×C₄	1	4	yes	—
46	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
47	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
48	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
49	C₃×C₂²⋊C₈	—	2	2	no	—
50	C₃×#95	—	2	1	no	—
51	C₂³×C₉	—	2	2	no	—
52	C₂³×C₉	—	2	2	no	—
53	C₂³×C₉	C₂²⋊C₄	1	2	yes	—
54	C₂³×C₉	D₈	1	2	yes	—
55	C₂³×C₉	SD₁₆	1	2	yes	—
56	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₉	—	2	2	no	—
58	C₂×C₄×C₉	—	2	4	no	—
59	C₂×C₄×C₉	—	2	4	no	—
60	C₂×C₄×C₉	—	2	4	no	—
61	C₂×C₄×C₉	—	4	8	no	—
62	C₂×C₄×C₉	—	4	2	no	—
63	C₂×C₄×C₉	—	4	2	no	—
64	C₂×C₄×C₉	—	4	2	no	—
65	C₂×C₄×C₉	—	4	2	no	—
66	C₂×C₄×C₉	—	4	2	no	—
67	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
68	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₉	#41	1	4	yes	—
71	C₈×C₉	—	4	2	no	—
72	C₂²×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
73	C₂×C₂²⋊C₈	C₂×C₉	1	1	yes	characteristic
74	#380	C₂×C₉	1	1	yes	characteristic
75	#340	C₂×C₉	1	4	yes	complemented
76	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
77	C₂²×C₃×C₄	—	2	4	no	—
78	C₂²×C₃×C₄	—	2	4	no	—
79	C₂²×C₃×C₄	—	2	2	no	—
80	C₂²×C₃×C₄	—	2	2	no	—
81	C₂²×C₃×C₄	—	4	2	no	—
82	C₂²×C₃×C₄	—	4	2	no	—
83	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
84	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
85	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
86	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
87	C₂×C₃×C₈	—	2	2	no	—
88	C₂×C₃×C₈	—	2	4	no	—
89	C₃×C₄⋊C₄	—	2	4	no	—
90	C₃×C₄⋊C₄	—	2	2	no	—
91	C₃×C₄⋊C₄	—	2	4	no	—
92	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
93	C₃×C₂²⋊C₄	—	4	2	no	—
94	C₂²×C₉	—	2	2	no	—
95	C₂²×C₉	—	2	2	no	—
96	C₂²×C₉	—	2	4	no	—
97	C₂²×C₉	—	2	4	no	—
98	C₂²×C₉	#102	1	4	yes	—
99	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₉	#123	1	2	yes	—
101	C₂²×C₉	C₂×D₈	1	1	yes	characteristic
102	C₂²×C₉	C₂×SD₁₆	1	1	yes	characteristic
103	C₂²×C₉	#137	1	2	yes	—
104	C₄×C₉	—	2	2	no	—
105	C₄×C₉	—	4	4	no	—
106	C₄×C₉	—	8	2	no	—
107	C₄×C₉	#117	1	2	yes	—
108	C₄×C₉	#123	1	2	yes	—
109	C₂³×C₄	—	2	1	no	—
110	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
111	C₂²×C₈	C₂²×C₉	1	2	yes	—
112	C₂×C₄⋊C₄	—	2	1	no	—
113	C₂×C₄⋊C₄	—	2	2	no	—
114	C₂×C₄⋊C₄	C₄×C₉	1	4	yes	complemented
115	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
116	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
117	C₂×C₂²⋊C₄	—	2	1	no	—
118	C₂²⋊C₈	—	2	2	no	—
119	#95	—	2	1	no	—
120	C₂³×C₃	—	2	2	no	—
121	C₂³×C₃	—	2	2	no	—
122	C₂³×C₃	C₃×C₂²⋊C₄	1	2	yes	—
123	C₂³×C₃	C₃×D₈	1	2	yes	—
124	C₂³×C₃	C₃×SD₁₆	1	2	yes	—
125	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
126	C₂×C₃×C₄	—	2	2	no	—
127	C₂×C₃×C₄	—	2	4	no	—
128	C₂×C₃×C₄	—	2	4	no	—
129	C₂×C₃×C₄	—	2	4	no	—
130	C₂×C₃×C₄	—	4	8	no	—
131	C₂×C₃×C₄	—	4	2	no	—
132	C₂×C₃×C₄	—	4	2	no	—
133	C₂×C₃×C₄	—	4	2	no	—
134	C₂×C₃×C₄	—	4	2	no	—
135	C₂×C₃×C₄	—	4	2	no	—
136	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
137	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
138	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄	C₃×#41	1	4	yes	—
140	C₃×C₈	—	4	2	no	—
141	C₂×C₉	—	2	4	no	—
142	C₂×C₉	#381	1	1	yes	characteristic
143	C₂×C₉	C₂×#102	1	1	yes	characteristic
144	C₂×C₉	#419	1	1	yes	characteristic
145	C₂×C₉	#480	1	2	yes	—
146	C₂×C₉	#483	1	2	yes	—
147	C₂⁴	D₄×C₉	1	1	yes	characteristic
148	C₂²×C₄	—	2	4	no	—
149	C₂²×C₄	—	2	4	no	—
150	C₂²×C₄	—	2	2	no	—
151	C₂²×C₄	—	2	2	no	—
152	C₂²×C₄	—	4	2	no	—
153	C₂²×C₄	—	4	2	no	—
154	C₂²×C₄	C₂×C₄×C₉	1	2	yes	—
155	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
156	C₂²×C₄	D₄×C₉	1	2	yes	—
157	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
158	C₂×C₈	—	2	2	no	—
159	C₂×C₈	—	2	4	no	—
160	C₄⋊C₄	—	2	4	no	—
161	C₄⋊C₄	—	2	2	no	—
162	C₄⋊C₄	—	2	4	no	—
163	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	—
164	C₂²⋊C₄	—	4	2	no	—
165	C₂²×C₃	—	2	2	no	—
166	C₂²×C₃	—	2	2	no	—
167	C₂²×C₃	—	2	4	no	—
168	C₂²×C₃	—	2	4	no	—
169	C₂²×C₃	C₃×#102	1	4	yes	—
170	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₃	C₃×#123	1	2	yes	—
172	C₂²×C₃	C₂×C₃×D₈	1	1	yes	characteristic
173	C₂²×C₃	C₂×C₃×SD₁₆	1	1	yes	characteristic
174	C₂²×C₃	C₃×#137	1	2	yes	—
175	C₃×C₄	—	2	2	no	—
176	C₃×C₄	—	4	4	no	—
177	C₃×C₄	—	8	2	no	—
178	C₃×C₄	C₃×#117	1	2	yes	—
179	C₃×C₄	C₃×#123	1	2	yes	—
180	C₉	#1823	1	1	yes	characteristic, direct product factor, Sylow
181	C₂³	—	2	2	no	—
182	C₂³	—	2	2	no	—
183	C₂³	C₉×C₂²⋊C₄	1	2	yes	—
184	C₂³	C₉×D₈	1	2	yes	—
185	C₂³	C₉×SD₁₆	1	2	yes	—
186	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	4	no	—
189	C₂×C₄	—	2	4	no	—
190	C₂×C₄	—	2	4	no	—
191	C₂×C₄	—	4	2	no	—
192	C₂×C₄	—	4	2	no	—
193	C₂×C₄	—	4	8	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	C₉×C₂²⋊C₄	1	2	yes	—
198	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
199	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
200	C₂×C₄	C₉×#41	1	4	yes	—
201	C₈	—	4	2	no	—
202	C₂×C₃	—	2	4	no	—
203	C₂×C₃	C₃×#381	1	1	yes	characteristic
204	C₂×C₃	C₂×C₃×#102	1	1	yes	characteristic
205	C₂×C₃	C₃×#419	1	1	yes	characteristic
206	C₂×C₃	C₃×#480	1	2	yes	—
207	C₂×C₃	C₃×#483	1	2	yes	—
208	C₂²	—	2	2	no	—
209	C₂²	—	2	2	no	—
210	C₂²	—	2	4	no	—
211	C₂²	—	2	4	no	—
212	C₂²	C₉×#102	1	4	yes	—
213	C₂²	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
214	C₂²	C₉×#123	1	2	yes	—
215	C₂²	C₂×C₉×D₈	1	1	yes	characteristic
216	C₂²	C₂×C₉×SD₁₆	1	1	yes	characteristic
217	C₂²	C₉×#137	1	2	yes	—
218	C₄	—	2	2	no	—
219	C₄	—	4	4	no	—
220	C₄	—	8	2	no	—
221	C₄	C₉×#117	1	2	yes	—
222	C₄	C₉×#123	1	2	yes	—
223	C₃	C₃×#1823	1	1	yes	characteristic
224	C₂	—	2	4	no	—
225	C₂	C₉×#381	1	1	yes	characteristic
226	C₂	C₂×C₉×#102	1	1	yes	characteristic
227	C₂	C₉×#419	1	1	yes	characteristic
228	C₂	C₉×#480	1	2	yes	—
229	C₂	C₉×#483	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	C₂⁴×C₃	C₃×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ C₂³×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₉×#340	C₂	semidirect
11. C₂×C₉×C₄⋊C₄	C₄	semidirect
39. #1823	C₉	direct (N × H)
75. #340	C₂×C₉	semidirect
114. C₂×C₄⋊C₄	C₄×C₉	semidirect
180. C₉	#1823	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₉×C₄⋊C₄	2
C₂×C₉×C₂²⋊C₈	2
C₉×#380	2
C₉×#340	2
C₃×#1823	3

Subgroups — C9×#1823 #11766544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1823 #11766544