Subgroups — C₉×#2298 #11767019

Order 1152.

786 conjugacy classes of subgroups.

The subgroup lattice has 228 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	C₉×#388	C₂	1	4	yes	maximal
3	C₉×#387	C₂	1	4	yes	maximal, complemented
4	C₄×C₉×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₄×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal
6	C₉×#376	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄³×C₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2298	C₃	1	1	yes	maximal, characteristic
9	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
10	C₉×#117	C₄	1	8	yes	complemented
11	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
12	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	—
14	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
15	C₂×C₄²×C₉	C₂²	1	4	yes	—
16	C₂×C₄²×C₉	C₂²	1	2	yes	—
17	C₂×C₄²×C₉	C₂²	1	2	yes	—
18	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
19	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
20	C₉×#95	C₂²	1	4	yes	—
21	C₉×#95	C₂²	1	4	yes	—
22	C₉×#95	C₂²	1	4	yes	—
23	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
24	C₃×#388	C₂×C₃	1	4	yes	—
25	C₃×#387	C₂×C₃	1	4	yes	—
26	C₃×C₄×C₄⋊C₄	C₂×C₃	1	2	yes	—
27	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	2	yes	—
28	C₃×#376	C₂×C₃	1	1	yes	characteristic
29	C₃×C₄³	C₂×C₃	1	1	yes	characteristic
30	C₂⁴×C₉	C₂³	1	1	yes	characteristic
31	C₂²×C₄×C₉	—	2	4	no	—
32	C₂²×C₄×C₉	C₂×C₄	1	4	yes	—
33	C₂²×C₄×C₉	C₂³	1	4	yes	—
34	C₂²×C₄×C₉	C₂³	1	2	yes	—
35	C₂²×C₄×C₉	C₂³	1	2	yes	—
36	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
37	C₂²×C₄×C₉	C₂³	1	4	yes	—
38	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
39	C₉×C₄⋊C₄	—	2	8	no	—
40	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	—
41	C₉×C₂²⋊C₄	—	2	8	no	—
42	C₉×C₂²⋊C₄	C₂×C₄	1	8	yes	—
43	C₄²×C₉	—	2	8	no	—
44	C₄²×C₉	—	2	4	no	—
45	C₄²×C₉	—	2	4	no	—
46	C₄²×C₉	C₂×C₄	1	4	yes	—
47	C₄²×C₉	C₂×C₄	1	4	yes	—
48	#2298	C₉	1	1	yes	characteristic, direct product factor, Sylow
49	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
50	C₃×#117	C₃×C₄	1	8	yes	—
51	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
52	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
53	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
54	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
55	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
56	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
57	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
58	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
60	C₃×#95	C₂²×C₃	1	4	yes	—
61	C₃×#95	C₂²×C₃	1	4	yes	—
62	C₃×#95	C₂²×C₃	1	4	yes	—
63	C₂³×C₉	—	2	4	no	—
64	C₂³×C₉	—	2	2	no	—
65	C₂³×C₉	C₂²×C₄	1	2	yes	—
66	C₂³×C₉	C₂⁴	1	1	yes	characteristic
67	C₂×C₄×C₉	—	2	4	no	—
68	C₂×C₄×C₉	—	2	4	no	—
69	C₂×C₄×C₉	—	2	4	no	—
70	C₂×C₄×C₉	—	2	4	no	—
71	C₂×C₄×C₉	—	2	2	no	—
72	C₂×C₄×C₉	—	2	8	no	—
73	C₂×C₄×C₉	—	2	4	no	—
74	C₂×C₄×C₉	—	2	4	no	—
75	C₂×C₄×C₉	—	2	4	no	—
76	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
77	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
78	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
79	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
80	C₂×C₄×C₉	#41	1	8	yes	—
81	C₂×C₄×C₉	#41	1	4	yes	—
82	C₂×#117	C₂×C₉	1	1	yes	characteristic
83	#388	C₂×C₉	1	4	yes	—
84	#387	C₂×C₉	1	4	yes	complemented
85	C₄×C₄⋊C₄	C₂×C₉	1	2	yes	complemented
86	C₄×C₂²⋊C₄	C₂×C₉	1	2	yes	—
87	#376	C₂×C₉	1	1	yes	characteristic, complemented
88	C₄³	C₂×C₉	1	1	yes	characteristic, complemented
89	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
90	C₂²×C₃×C₄	—	2	4	no	—
91	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
92	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
93	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
94	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
95	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
96	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
97	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
98	C₃×C₄⋊C₄	—	2	8	no	—
99	C₃×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
100	C₃×C₂²⋊C₄	—	2	8	no	—
101	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
102	C₃×C₄²	—	2	8	no	—
103	C₃×C₄²	—	2	4	no	—
104	C₃×C₄²	—	2	4	no	—
105	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
106	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
107	C₂²×C₉	—	2	2	no	—
108	C₂²×C₉	—	2	4	no	—
109	C₂²×C₉	—	4	4	no	—
110	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
111	C₂²×C₉	C₂×#41	1	2	yes	—
112	C₂²×C₉	C₂×#41	1	4	yes	—
113	C₄×C₉	—	2	2	no	—
114	C₄×C₉	—	2	4	no	—
115	C₄×C₉	—	2	4	no	—
116	C₄×C₉	—	2	8	no	—
117	C₄×C₉	—	4	4	no	—
118	C₄×C₉	#117	1	4	yes	—
119	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
120	#117	C₄×C₉	1	8	yes	complemented
121	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
122	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
123	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	—
124	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
125	C₂×C₄²	C₂²×C₉	1	2	yes	—
126	C₂×C₄²	C₂²×C₉	1	4	yes	—
127	C₂×C₄²	C₂²×C₉	1	2	yes	—
128	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
129	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
130	#95	C₂²×C₉	1	4	yes	—
131	#95	C₂²×C₉	1	4	yes	—
132	#95	C₂²×C₉	1	4	yes	—
133	C₂³×C₃	—	2	4	no	—
134	C₂³×C₃	—	2	2	no	—
135	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
136	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
137	C₂×C₃×C₄	—	2	4	no	—
138	C₂×C₃×C₄	—	2	4	no	—
139	C₂×C₃×C₄	—	2	4	no	—
140	C₂×C₃×C₄	—	2	4	no	—
141	C₂×C₃×C₄	—	2	2	no	—
142	C₂×C₃×C₄	—	2	8	no	—
143	C₂×C₃×C₄	—	2	4	no	—
144	C₂×C₃×C₄	—	2	4	no	—
145	C₂×C₃×C₄	—	2	4	no	—
146	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
147	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
148	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
149	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
150	C₂×C₃×C₄	C₃×#41	1	8	yes	—
151	C₂×C₃×C₄	C₃×#41	1	4	yes	—
152	C₂×C₉	—	4	2	no	—
153	C₂×C₉	C₂×#117	1	1	yes	characteristic
154	C₂×C₉	C₄×#41	1	2	yes	—
155	C₂×C₉	#529	1	4	yes	—
156	C₂⁴	C₂³×C₉	1	1	yes	characteristic
157	C₂²×C₄	—	2	4	no	—
158	C₂²×C₄	C₂×C₄×C₉	1	4	yes	—
159	C₂²×C₄	C₂³×C₉	1	4	yes	—
160	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
161	C₂²×C₄	C₂³×C₉	1	2	yes	—
162	C₂²×C₄	C₂³×C₉	1	2	yes	—
163	C₂²×C₄	C₂³×C₉	1	4	yes	—
164	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
165	C₄⋊C₄	—	2	8	no	—
166	C₄⋊C₄	C₂×C₄×C₉	1	8	yes	—
167	C₂²⋊C₄	—	2	8	no	—
168	C₂²⋊C₄	C₂×C₄×C₉	1	8	yes	—
169	C₄²	—	2	8	no	—
170	C₄²	—	2	4	no	—
171	C₄²	—	2	4	no	—
172	C₄²	C₂×C₄×C₉	1	4	yes	—
173	C₄²	C₂×C₄×C₉	1	4	yes	—
174	C₂²×C₃	—	2	2	no	—
175	C₂²×C₃	—	2	4	no	—
176	C₂²×C₃	—	4	4	no	—
177	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
178	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
179	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
180	C₃×C₄	—	2	2	no	—
181	C₃×C₄	—	2	4	no	—
182	C₃×C₄	—	2	4	no	—
183	C₃×C₄	—	2	8	no	—
184	C₃×C₄	—	4	4	no	—
185	C₃×C₄	C₃×#117	1	4	yes	—
186	C₉	#2298	1	1	yes	characteristic, direct product factor, Sylow
187	C₂³	—	2	4	no	—
188	C₂³	—	2	2	no	—
189	C₂³	C₂²×C₄×C₉	1	2	yes	—
190	C₂³	C₂⁴×C₉	1	1	yes	characteristic
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	2	4	no	—
193	C₂×C₄	—	2	4	no	—
194	C₂×C₄	—	2	4	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	8	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	4	no	—
200	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
201	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
202	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
203	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
204	C₂×C₄	C₉×#41	1	8	yes	—
205	C₂×C₄	C₉×#41	1	4	yes	—
206	C₂×C₃	—	4	2	no	—
207	C₂×C₃	C₂×C₃×#117	1	1	yes	characteristic
208	C₂×C₃	C₃×C₄×#41	1	2	yes	—
209	C₂×C₃	C₃×#529	1	4	yes	—
210	C₂²	—	2	2	no	—
211	C₂²	—	2	4	no	—
212	C₂²	—	4	4	no	—
213	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
214	C₂²	C₂×C₉×#41	1	2	yes	—
215	C₂²	C₂×C₉×#41	1	4	yes	—
216	C₄	—	2	8	no	—
217	C₄	—	2	2	no	—
218	C₄	—	2	4	no	—
219	C₄	—	2	4	no	—
220	C₄	—	4	4	no	—
221	C₄	C₉×#117	1	4	yes	—
222	C₃	C₃×#2298	1	1	yes	characteristic
223	C₂	—	4	2	no	—
224	C₂	C₂×C₉×#117	1	1	yes	characteristic
225	C₂	C₄×C₉×#41	1	2	yes	—
226	C₂	C₉×#529	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₉	C₂³
commutator	C₂²	C₂³×C₄×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂⁴×C₃	C₂³×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉×#387	C₂	semidirect
4. C₄×C₉×C₄⋊C₄	C₂	semidirect
6. C₉×#376	C₂	semidirect
7. C₄³×C₉	C₂	semidirect
10. C₉×#117	C₄	semidirect
48. #2298	C₉	direct (N × H)
84. #387	C₂×C₉	semidirect
85. C₄×C₄⋊C₄	C₂×C₉	semidirect
87. #376	C₂×C₉	semidirect
88. C₄³	C₂×C₉	semidirect
120. #117	C₄×C₉	semidirect
186. C₉	#2298	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
C₉×#388	2
C₉×#387	2
C₄×C₉×C₄⋊C₄	2
C₄×C₉×C₂²⋊C₄	2
C₉×#376	2
C₄³×C₉	2
C₃×#2298	3

Subgroups — C9×#2298 #11767019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2298 #11767019