Subgroups — C₉×#1825 #11766546

Order 1152.

450 conjugacy classes of subgroups.

The subgroup lattice has 246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#117	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	2	yes	maximal, complemented
5	C₉×#340	C₂	1	2	yes	maximal, complemented
6	C₃×#1825	C₃	1	1	yes	maximal, characteristic
7	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₉	C₂²	1	2	yes	—
9	C₉×#117	—	2	2	no	—
10	C₉×#117	C₄	1	4	yes	complemented
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×C₉×C₂²⋊C₄	—	2	1	no	—
15	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
16	C₂×C₄²×C₉	—	2	1	no	—
17	C₉×C₂²⋊C₈	—	2	2	no	—
18	C₉×#95	—	2	1	no	—
19	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
20	C₂×C₃×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
21	C₃×#380	C₂×C₃	1	1	yes	characteristic
22	C₃×#340	C₂×C₃	1	2	yes	—
23	C₃×#340	C₂×C₃	1	2	yes	—
24	C₂⁴×C₉	D₄	1	1	yes	characteristic
25	C₂²×C₄×C₉	—	2	4	no	—
26	C₂²×C₄×C₉	—	2	1	no	—
27	C₂²×C₄×C₉	—	2	1	no	—
28	C₂²×C₄×C₉	—	2	2	no	—
29	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
30	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
31	C₂²×C₄×C₉	D₄	1	2	yes	—
32	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
33	C₂×C₈×C₉	—	2	2	no	—
34	C₂×C₈×C₉	—	2	4	no	—
35	C₉×C₄⋊C₄	—	2	1	no	—
36	C₉×C₄⋊C₄	—	2	1	no	—
37	C₉×C₄⋊C₄	—	2	4	no	—
38	C₉×C₄⋊C₄	C₂×C₄	1	2	yes	—
39	C₉×C₄⋊C₄	C₂×C₄	1	2	yes	—
40	C₉×C₂²⋊C₄	—	2	4	no	—
41	C₉×C₂²⋊C₄	—	4	2	no	—
42	C₄²×C₉	—	2	4	no	—
43	#1825	C₉	1	1	yes	characteristic, direct product factor, Sylow
44	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
45	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
46	C₃×#117	—	2	2	no	—
47	C₃×#117	C₃×C₄	1	4	yes	—
48	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
49	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
50	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
51	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
52	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
53	C₂×C₃×C₄²	—	2	1	no	—
54	C₃×C₂²⋊C₈	—	2	2	no	—
55	C₃×#95	—	2	1	no	—
56	C₂³×C₉	—	2	2	no	—
57	C₂³×C₉	—	2	2	no	—
58	C₂³×C₉	—	2	1	no	—
59	C₂³×C₉	—	2	1	no	—
60	C₂³×C₉	C₂²⋊C₄	1	2	yes	—
61	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄×C₉	—	2	2	no	—
63	C₂×C₄×C₉	—	2	4	no	—
64	C₂×C₄×C₉	—	2	4	no	—
65	C₂×C₄×C₉	—	2	2	no	—
66	C₂×C₄×C₉	—	2	2	no	—
67	C₂×C₄×C₉	—	4	2	no	—
68	C₂×C₄×C₉	—	4	1	no	—
69	C₂×C₄×C₉	—	4	1	no	—
70	C₂×C₄×C₉	—	4	2	no	—
71	C₂×C₄×C₉	—	4	2	no	—
72	C₂×C₄×C₉	—	4	2	no	—
73	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
74	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
76	C₂×C₄×C₉	#41	1	4	yes	—
77	C₈×C₉	—	4	2	no	—
78	C₂×#117	C₂×C₉	1	1	yes	characteristic
79	C₂×C₂²⋊C₈	C₂×C₉	1	1	yes	characteristic
80	#380	C₂×C₉	1	1	yes	characteristic
81	#340	C₂×C₉	1	2	yes	complemented
82	#340	C₂×C₉	1	2	yes	complemented
83	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
84	C₂²×C₃×C₄	—	2	4	no	—
85	C₂²×C₃×C₄	—	2	1	no	—
86	C₂²×C₃×C₄	—	2	1	no	—
87	C₂²×C₃×C₄	—	2	2	no	—
88	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
89	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
90	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
91	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
92	C₂×C₃×C₈	—	2	2	no	—
93	C₂×C₃×C₈	—	2	4	no	—
94	C₃×C₄⋊C₄	—	2	1	no	—
95	C₃×C₄⋊C₄	—	2	1	no	—
96	C₃×C₄⋊C₄	—	2	4	no	—
97	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
98	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
99	C₃×C₂²⋊C₄	—	2	4	no	—
100	C₃×C₂²⋊C₄	—	4	2	no	—
101	C₃×C₄²	—	2	4	no	—
102	C₂²×C₉	—	2	2	no	—
103	C₂²×C₉	—	2	2	no	—
104	C₂²×C₉	—	2	2	no	—
105	C₂²×C₉	—	4	2	no	—
106	C₂²×C₉	—	4	2	no	—
107	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₉	#123	1	2	yes	—
109	C₂²×C₉	#135	1	2	yes	—
110	C₂²×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
111	C₂²×C₉	#137	1	1	yes	characteristic
112	C₄×C₉	—	2	2	no	—
113	C₄×C₉	—	4	2	no	—
114	C₄×C₉	—	4	2	no	—
115	C₄×C₉	—	8	2	no	—
116	C₄×C₉	#117	1	2	yes	—
117	C₄×C₉	#123	1	2	yes	—
118	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
119	C₂²×C₈	C₂²×C₉	1	2	yes	—
120	#117	—	2	2	no	—
121	#117	C₄×C₉	1	4	yes	complemented
122	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
123	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
124	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
125	C₂×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₄²	—	2	1	no	—
128	C₂²⋊C₈	—	2	2	no	—
129	#95	—	2	1	no	—
130	C₂³×C₃	—	2	2	no	—
131	C₂³×C₃	—	2	2	no	—
132	C₂³×C₃	—	2	1	no	—
133	C₂³×C₃	—	2	1	no	—
134	C₂³×C₃	C₃×C₂²⋊C₄	1	2	yes	—
135	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
136	C₂×C₃×C₄	—	2	2	no	—
137	C₂×C₃×C₄	—	2	4	no	—
138	C₂×C₃×C₄	—	2	4	no	—
139	C₂×C₃×C₄	—	2	2	no	—
140	C₂×C₃×C₄	—	2	2	no	—
141	C₂×C₃×C₄	—	4	2	no	—
142	C₂×C₃×C₄	—	4	1	no	—
143	C₂×C₃×C₄	—	4	1	no	—
144	C₂×C₃×C₄	—	4	2	no	—
145	C₂×C₃×C₄	—	4	2	no	—
146	C₂×C₃×C₄	—	4	2	no	—
147	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
148	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
149	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
150	C₂×C₃×C₄	C₃×#41	1	4	yes	—
151	C₃×C₈	—	4	2	no	—
152	C₂×C₉	—	4	2	no	—
153	C₂×C₉	#381	1	1	yes	characteristic
154	C₂×C₉	#416	1	1	yes	characteristic
155	C₂×C₉	#417	1	1	yes	characteristic
156	C₂×C₉	#482	1	2	yes	—
157	C₂×C₉	#485	1	2	yes	—
158	C₂⁴	D₄×C₉	1	1	yes	characteristic
159	C₂²×C₄	—	2	4	no	—
160	C₂²×C₄	—	2	1	no	—
161	C₂²×C₄	—	2	1	no	—
162	C₂²×C₄	—	2	2	no	—
163	C₂²×C₄	C₂×C₄×C₉	1	2	yes	—
164	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
165	C₂²×C₄	D₄×C₉	1	2	yes	—
166	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	4	no	—
169	C₄⋊C₄	—	2	1	no	—
170	C₄⋊C₄	—	2	1	no	—
171	C₄⋊C₄	—	2	4	no	—
172	C₄⋊C₄	C₂×C₄×C₉	1	2	yes	—
173	C₄⋊C₄	C₂×C₄×C₉	1	2	yes	—
174	C₂²⋊C₄	—	2	4	no	—
175	C₂²⋊C₄	—	4	2	no	—
176	C₄²	—	2	4	no	—
177	C₂²×C₃	—	2	2	no	—
178	C₂²×C₃	—	2	2	no	—
179	C₂²×C₃	—	2	2	no	—
180	C₂²×C₃	—	4	2	no	—
181	C₂²×C₃	—	4	2	no	—
182	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×C₃	C₃×#123	1	2	yes	—
184	C₂²×C₃	C₃×#135	1	2	yes	—
185	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₂²×C₃	C₃×#137	1	1	yes	characteristic
187	C₃×C₄	—	2	2	no	—
188	C₃×C₄	—	4	2	no	—
189	C₃×C₄	—	4	2	no	—
190	C₃×C₄	—	8	2	no	—
191	C₃×C₄	C₃×#117	1	2	yes	—
192	C₃×C₄	C₃×#123	1	2	yes	—
193	C₉	#1825	1	1	yes	characteristic, direct product factor, Sylow
194	C₂³	—	2	2	no	—
195	C₂³	—	2	2	no	—
196	C₂³	—	2	1	no	—
197	C₂³	—	2	1	no	—
198	C₂³	C₉×C₂²⋊C₄	1	2	yes	—
199	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	4	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	C₉×C₂²⋊C₄	1	2	yes	—
212	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
213	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
214	C₂×C₄	C₉×#41	1	4	yes	—
215	C₈	—	4	2	no	—
216	C₂×C₃	—	4	2	no	—
217	C₂×C₃	C₃×#381	1	1	yes	characteristic
218	C₂×C₃	C₃×#416	1	1	yes	characteristic
219	C₂×C₃	C₃×#417	1	1	yes	characteristic
220	C₂×C₃	C₃×#482	1	2	yes	—
221	C₂×C₃	C₃×#485	1	2	yes	—
222	C₂²	—	2	2	no	—
223	C₂²	—	2	2	no	—
224	C₂²	—	2	2	no	—
225	C₂²	—	4	2	no	—
226	C₂²	—	4	2	no	—
227	C₂²	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
228	C₂²	C₉×#123	1	2	yes	—
229	C₂²	C₉×#135	1	2	yes	—
230	C₂²	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
231	C₂²	C₉×#137	1	1	yes	characteristic
232	C₄	—	2	2	no	—
233	C₄	—	4	2	no	—
234	C₄	—	4	2	no	—
235	C₄	—	8	2	no	—
236	C₄	C₉×#117	1	2	yes	—
237	C₄	C₉×#123	1	2	yes	—
238	C₃	C₃×#1825	1	1	yes	characteristic
239	C₂	—	4	2	no	—
240	C₂	C₉×#381	1	1	yes	characteristic
241	C₂	C₉×#416	1	1	yes	characteristic
242	C₂	C₉×#417	1	1	yes	characteristic
243	C₂	C₉×#482	1	2	yes	—
244	C₂	C₉×#485	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
5. C₉×#340	C₂	semidirect
10. C₉×#117	C₄	semidirect
43. #1825	C₉	direct (N × H)
81. #340	C₂×C₉	semidirect
82. #340	C₂×C₉	semidirect
121. #117	C₄×C₉	semidirect
193. C₉	#1825	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×#117	2
C₂×C₉×C₂²⋊C₈	2
C₉×#380	2
C₉×#340	2
C₃×#1825	3

Subgroups — C9×#1825 #11766546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1825 #11766546