Subgroups — C₉×#3259 #11767980

Order 1152.

555 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#540	C₂	1	2	yes	maximal, complemented
2	C₉×#478	C₂	1	4	yes	maximal, complemented
3	C₉×#469	C₂	1	2	yes	maximal, complemented
4	C₉×#466	C₂	1	2	yes	maximal, complemented
5	C₉×#459	C₂	1	4	yes	maximal, complemented
6	C₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#3259	C₃	1	1	yes	maximal, characteristic
8	C₂×C₉×D₈	C₂²	1	2	yes	—
9	C₂×C₉×D₈	C₂²	1	2	yes	—
10	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
12	C₉×#127	C₂²	1	2	yes	—
13	C₉×#125	C₂²	1	2	yes	—
14	C₉×#123	—	2	4	no	—
15	C₉×#121	—	2	4	no	—
16	C₉×#121	C₂²	1	4	yes	—
17	C₄×D₄×C₉	C₂²	1	4	yes	—
18	C₉×#117	C₂²	1	1	yes	characteristic
19	C₉×#107	C₂²	1	2	yes	—
20	C₉×#106	C₂²	1	2	yes	—
21	C₉×C₄⋊C₈	C₂²	1	4	yes	—
22	C₉×#102	C₂²	1	4	yes	—
23	C₉×#102	C₂²	1	4	yes	—
24	C₃×#540	C₂×C₃	1	2	yes	—
25	C₃×#478	C₂×C₃	1	4	yes	—
26	C₃×#469	C₂×C₃	1	2	yes	—
27	C₃×#466	C₂×C₃	1	2	yes	—
28	C₃×#459	C₂×C₃	1	4	yes	—
29	C₃×#424	C₂×C₃	1	1	yes	characteristic
30	C₂×D₄×C₉	—	2	4	no	—
31	C₂×D₄×C₉	—	2	4	no	—
32	C₂×D₄×C₉	C₂³	1	4	yes	—
33	C₂²×C₄×C₉	—	2	4	no	—
34	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
35	C₉×D₈	—	4	2	no	—
36	C₉×D₈	—	4	2	no	—
37	C₉×M₁₆	—	4	1	no	—
38	C₂×C₈×C₉	—	4	1	no	—
39	C₂×C₈×C₉	C₂³	1	2	yes	—
40	C₂×C₈×C₉	C₂³	1	2	yes	—
41	C₉×C₄⋊C₄	—	2	4	no	—
42	C₉×C₄⋊C₄	D₄	1	2	yes	—
43	C₉×C₄⋊C₄	C₂³	1	4	yes	—
44	C₉×C₂²⋊C₄	—	2	4	no	—
45	C₉×C₂²⋊C₄	—	2	4	no	—
46	C₉×C₂²⋊C₄	D₄	1	2	yes	—
47	C₄²×C₉	C₂³	1	2	yes	—
48	#3259	C₉	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
50	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
51	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
52	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
53	C₃×#127	C₂²×C₃	1	2	yes	—
54	C₃×#125	C₂²×C₃	1	2	yes	—
55	C₃×#123	—	2	4	no	—
56	C₃×#121	—	2	4	no	—
57	C₃×#121	C₂²×C₃	1	4	yes	—
58	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
59	C₃×#117	C₂²×C₃	1	1	yes	characteristic
60	C₃×#107	C₂²×C₃	1	2	yes	—
61	C₃×#106	C₂²×C₃	1	2	yes	—
62	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	—
63	C₃×#102	C₂²×C₃	1	4	yes	—
64	C₃×#102	C₂²×C₃	1	4	yes	—
65	C₂³×C₉	—	2	4	no	—
66	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
67	D₄×C₉	—	2	4	no	—
68	D₄×C₉	—	2	4	no	—
69	D₄×C₉	—	8	4	no	—
70	D₄×C₉	—	8	4	no	—
71	C₂×C₄×C₉	—	2	1	no	—
72	C₂×C₄×C₉	—	2	1	no	—
73	C₂×C₄×C₉	—	2	4	no	—
74	C₂×C₄×C₉	—	8	4	no	—
75	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
76	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
78	C₈×C₉	—	2	2	no	—
79	C₈×C₉	—	2	2	no	—
80	#540	C₂×C₉	1	2	yes	complemented
81	#478	C₂×C₉	1	4	yes	complemented
82	#469	C₂×C₉	1	2	yes	complemented
83	#466	C₂×C₉	1	2	yes	complemented
84	#459	C₂×C₉	1	4	yes	complemented
85	#424	C₂×C₉	1	1	yes	characteristic, complemented
86	C₂×C₃×D₄	—	2	4	no	—
87	C₂×C₃×D₄	—	2	4	no	—
88	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
89	C₂²×C₃×C₄	—	2	4	no	—
90	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
91	C₃×D₈	—	4	2	no	—
92	C₃×D₈	—	4	2	no	—
93	C₃×M₁₆	—	4	1	no	—
94	C₂×C₃×C₈	—	4	1	no	—
95	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
96	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
97	C₃×C₄⋊C₄	—	2	4	no	—
98	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
99	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
100	C₃×C₂²⋊C₄	—	2	4	no	—
101	C₃×C₂²⋊C₄	—	2	4	no	—
102	C₃×C₂²⋊C₄	C₃×D₄	1	2	yes	—
103	C₃×C₄²	C₂³×C₃	1	2	yes	—
104	C₂²×C₉	—	2	1	no	—
105	C₂²×C₉	—	2	2	no	—
106	C₂²×C₉	—	4	4	no	—
107	C₂²×C₉	—	4	4	no	—
108	C₂²×C₉	—	4	4	no	—
109	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
110	C₄×C₉	—	2	1	no	—
111	C₄×C₉	—	2	4	no	—
112	C₄×C₉	—	4	4	no	—
113	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
114	C₄×C₉	2₋¹⁺⁴	1	1	yes	characteristic
115	C₂×D₈	C₂²×C₉	1	2	yes	—
116	C₂×D₈	C₂²×C₉	1	2	yes	—
117	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
118	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
119	#127	C₂²×C₉	1	2	yes	—
120	#125	C₂²×C₉	1	2	yes	—
121	#123	—	2	4	no	—
122	#121	—	2	4	no	—
123	#121	C₂²×C₉	1	4	yes	—
124	C₄×D₄	C₂²×C₉	1	4	yes	—
125	#117	C₂²×C₉	1	1	yes	characteristic
126	#107	C₂²×C₉	1	2	yes	—
127	#106	C₂²×C₉	1	2	yes	—
128	C₄⋊C₈	C₂²×C₉	1	4	yes	—
129	#102	C₂²×C₉	1	4	yes	—
130	#102	C₂²×C₉	1	4	yes	—
131	C₂³×C₃	—	2	4	no	—
132	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
133	C₃×D₄	—	2	4	no	—
134	C₃×D₄	—	2	4	no	—
135	C₃×D₄	—	8	4	no	—
136	C₃×D₄	—	8	4	no	—
137	C₂×C₃×C₄	—	2	1	no	—
138	C₂×C₃×C₄	—	2	1	no	—
139	C₂×C₃×C₄	—	2	4	no	—
140	C₂×C₃×C₄	—	8	4	no	—
141	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
142	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
143	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
144	C₃×C₈	—	2	2	no	—
145	C₃×C₈	—	2	2	no	—
146	C₂×C₉	—	4	1	no	—
147	C₂×C₉	—	8	4	no	—
148	C₂×C₉	#537	1	1	yes	characteristic
149	C₂×C₉	#576	1	2	yes	—
150	C₂×D₄	—	2	4	no	—
151	C₂×D₄	—	2	4	no	—
152	C₂×D₄	C₂³×C₉	1	4	yes	—
153	C₂²×C₄	—	2	4	no	—
154	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
155	D₈	—	4	2	no	—
156	D₈	—	4	2	no	—
157	M₁₆	—	4	1	no	—
158	C₂×C₈	—	4	1	no	—
159	C₂×C₈	C₂³×C₉	1	2	yes	—
160	C₂×C₈	C₂³×C₉	1	2	yes	—
161	C₄⋊C₄	—	2	4	no	—
162	C₄⋊C₄	D₄×C₉	1	2	yes	—
163	C₄⋊C₄	C₂³×C₉	1	4	yes	—
164	C₂²⋊C₄	—	2	4	no	—
165	C₂²⋊C₄	—	2	4	no	—
166	C₂²⋊C₄	D₄×C₉	1	2	yes	—
167	C₄²	C₂³×C₉	1	2	yes	—
168	C₂²×C₃	—	2	2	no	—
169	C₂²×C₃	—	2	1	no	—
170	C₂²×C₃	—	4	4	no	—
171	C₂²×C₃	—	4	4	no	—
172	C₂²×C₃	—	4	4	no	—
173	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
174	C₃×C₄	—	2	4	no	—
175	C₃×C₄	—	2	1	no	—
176	C₃×C₄	—	4	4	no	—
177	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
178	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
179	C₉	#3259	1	1	yes	characteristic, direct product factor, Sylow
180	C₂³	—	2	4	no	—
181	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
182	D₄	—	2	4	no	—
183	D₄	—	2	4	no	—
184	D₄	—	8	4	no	—
185	D₄	—	8	4	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	2	1	no	—
188	C₂×C₄	—	2	4	no	—
189	C₂×C₄	—	8	4	no	—
190	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
191	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
192	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
193	C₈	—	2	2	no	—
194	C₈	—	2	2	no	—
195	C₂×C₃	—	4	1	no	—
196	C₂×C₃	—	8	4	no	—
197	C₂×C₃	C₃×#537	1	1	yes	characteristic
198	C₂×C₃	C₃×#576	1	2	yes	—
199	C₂²	—	2	1	no	—
200	C₂²	—	2	2	no	—
201	C₂²	—	4	4	no	—
202	C₂²	—	4	4	no	—
203	C₂²	—	4	4	no	—
204	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
205	C₄	—	2	1	no	—
206	C₄	—	2	4	no	—
207	C₄	—	4	4	no	—
208	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
209	C₄	C₉×2₋¹⁺⁴	1	1	yes	characteristic
210	C₃	C₃×#3259	1	1	yes	characteristic
211	C₂	—	4	1	no	—
212	C₂	—	8	4	no	—
213	C₂	C₉×#537	1	1	yes	characteristic
214	C₂	C₉×#576	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂²×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₃×#3259	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#540	C₂	semidirect
2. C₉×#478	C₂	semidirect
3. C₉×#469	C₂	semidirect
4. C₉×#466	C₂	semidirect
5. C₉×#459	C₂	semidirect
6. C₉×#424	C₂	semidirect
48. #3259	C₉	direct (N × H)
80. #540	C₂×C₉	semidirect
81. #478	C₂×C₉	semidirect
82. #469	C₂×C₉	semidirect
83. #466	C₂×C₉	semidirect
84. #459	C₂×C₉	semidirect
85. #424	C₂×C₉	semidirect
179. C₉	#3259	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×#540	2
C₉×#478	2
C₉×#469	2
C₉×#466	2
C₉×#459	2
C₉×#424	2
C₃×#3259	3

Subgroups — C9×#3259 #11767980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3259 #11767980