Subgroups — C₉×#3255 #11767976

Order 1152.

513 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#533	C₂	1	2	yes	maximal
2	C₉×#475	C₂	1	4	yes	maximal, complemented
3	C₉×#470	C₂	1	4	yes	maximal
4	C₉×#462	C₂	1	4	yes	maximal, complemented
5	C₉×#423	C₂	1	1	yes	maximal, characteristic
6	C₃×#3255	C₃	1	1	yes	maximal, characteristic
7	C₂×C₉×Q₁₆	C₂²	1	4	yes	—
8	C₂×C₉×M₁₆	C₂²	1	2	yes	—
9	C₉×C₄⋊Q₈	C₂²	1	2	yes	—
10	C₉×C₄⋊Q₈	C₂²	1	2	yes	—
11	C₉×#125	—	2	2	no	—
12	C₉×C₂²⋊Q₈	—	2	2	no	—
13	C₉×C₂²⋊Q₈	C₂²	1	4	yes	—
14	C₄×Q₈×C₉	—	2	2	no	—
15	C₄×Q₈×C₉	C₂²	1	4	yes	—
16	C₉×#117	—	2	2	no	—
17	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
18	C₉×#106	C₂²	1	4	yes	—
19	C₉×C₄⋊C₈	C₂²	1	4	yes	—
20	C₉×#103	C₂²	1	8	yes	—
21	C₃×#533	C₂×C₃	1	2	yes	—
22	C₃×#475	C₂×C₃	1	4	yes	—
23	C₃×#470	C₂×C₃	1	4	yes	—
24	C₃×#462	C₂×C₃	1	4	yes	—
25	C₃×#423	C₂×C₃	1	1	yes	characteristic
26	C₂×Q₈×C₉	—	2	2	no	—
27	C₂×Q₈×C₉	C₂³	1	4	yes	—
28	C₂²×C₄×C₉	D₄	1	2	yes	—
29	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
30	C₉×Q₁₆	—	4	4	no	—
31	C₉×M₁₆	—	4	2	no	—
32	C₂×C₈×C₉	C₂³	1	4	yes	—
33	C₉×C₄⋊C₄	—	2	2	no	—
34	C₉×C₄⋊C₄	—	2	2	no	—
35	C₉×C₄⋊C₄	—	2	2	no	—
36	C₉×C₄⋊C₄	—	2	4	no	—
37	C₉×C₄⋊C₄	—	2	4	no	—
38	C₉×C₄⋊C₄	C₂³	1	4	yes	—
39	C₉×C₂²⋊C₄	—	2	4	no	—
40	C₄²×C₉	—	2	4	no	—
41	C₄²×C₉	D₄	1	1	yes	characteristic
42	C₄²×C₉	D₄	1	1	yes	characteristic
43	C₄²×C₉	C₂³	1	2	yes	—
44	#3255	C₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₂×C₃×Q₁₆	C₂²×C₃	1	4	yes	—
46	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
47	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
48	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
49	C₃×#125	—	2	2	no	—
50	C₃×C₂²⋊Q₈	—	2	2	no	—
51	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
52	C₃×C₄×Q₈	—	2	2	no	—
53	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
54	C₃×#117	—	2	2	no	—
55	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
56	C₃×#106	C₂²×C₃	1	4	yes	—
57	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	—
58	C₃×#103	C₂²×C₃	1	8	yes	—
59	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
60	Q₈×C₉	—	2	4	no	—
61	Q₈×C₉	—	2	4	no	—
62	Q₈×C₉	—	4	4	no	—
63	C₂×C₄×C₉	—	2	4	no	—
64	C₂×C₄×C₉	—	2	1	no	—
65	C₂×C₄×C₉	—	2	1	no	—
66	C₂×C₄×C₉	—	2	4	no	—
67	C₂×C₄×C₉	—	2	4	no	—
68	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
70	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
71	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
72	C₈×C₉	—	2	4	no	—
73	#533	C₂×C₉	1	2	yes	—
74	#475	C₂×C₉	1	4	yes	complemented
75	#470	C₂×C₉	1	4	yes	—
76	#462	C₂×C₉	1	4	yes	complemented
77	#423	C₂×C₉	1	1	yes	characteristic
78	C₂×C₃×Q₈	—	2	2	no	—
79	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
80	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
81	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
82	C₃×Q₁₆	—	4	4	no	—
83	C₃×M₁₆	—	4	2	no	—
84	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
85	C₃×C₄⋊C₄	—	2	2	no	—
86	C₃×C₄⋊C₄	—	2	2	no	—
87	C₃×C₄⋊C₄	—	2	2	no	—
88	C₃×C₄⋊C₄	—	2	4	no	—
89	C₃×C₄⋊C₄	—	2	4	no	—
90	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
91	C₃×C₂²⋊C₄	—	2	4	no	—
92	C₃×C₄²	—	2	4	no	—
93	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
94	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
95	C₃×C₄²	C₂³×C₃	1	2	yes	—
96	C₂²×C₉	—	2	1	no	—
97	C₂²×C₉	—	2	2	no	—
98	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
99	C₄×C₉	—	2	1	no	—
100	C₄×C₉	—	2	2	no	—
101	C₄×C₉	—	4	4	no	—
102	C₄×C₉	—	4	4	no	—
103	C₄×C₉	#137	1	4	yes	—
104	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
105	C₄×C₉	2₋¹⁺⁴	1	1	yes	characteristic
106	C₂×Q₁₆	C₂²×C₉	1	4	yes	—
107	C₂×M₁₆	C₂²×C₉	1	2	yes	—
108	C₄⋊Q₈	C₂²×C₉	1	2	yes	—
109	C₄⋊Q₈	C₂²×C₉	1	2	yes	—
110	#125	—	2	2	no	—
111	C₂²⋊Q₈	—	2	2	no	—
112	C₂²⋊Q₈	C₂²×C₉	1	4	yes	—
113	C₄×Q₈	—	2	2	no	—
114	C₄×Q₈	C₂²×C₉	1	4	yes	—
115	#117	—	2	2	no	—
116	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
117	#106	C₂²×C₉	1	4	yes	—
118	C₄⋊C₈	C₂²×C₉	1	4	yes	—
119	#103	C₂²×C₉	1	8	yes	—
120	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
121	C₃×Q₈	—	2	4	no	—
122	C₃×Q₈	—	2	4	no	—
123	C₃×Q₈	—	4	4	no	—
124	C₂×C₃×C₄	—	2	4	no	—
125	C₂×C₃×C₄	—	2	1	no	—
126	C₂×C₃×C₄	—	2	1	no	—
127	C₂×C₃×C₄	—	2	4	no	—
128	C₂×C₃×C₄	—	2	4	no	—
129	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
130	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
131	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
132	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
133	C₃×C₈	—	2	4	no	—
134	C₂×C₉	—	4	1	no	—
135	C₂×C₉	#537	1	1	yes	characteristic
136	C₂×C₉	C₂×#137	1	2	yes	—
137	C₂×Q₈	—	2	2	no	—
138	C₂×Q₈	C₂³×C₉	1	4	yes	—
139	C₂²×C₄	D₄×C₉	1	2	yes	—
140	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
141	Q₁₆	—	4	4	no	—
142	M₁₆	—	4	2	no	—
143	C₂×C₈	C₂³×C₉	1	4	yes	—
144	C₄⋊C₄	—	2	2	no	—
145	C₄⋊C₄	—	2	2	no	—
146	C₄⋊C₄	—	2	2	no	—
147	C₄⋊C₄	—	2	4	no	—
148	C₄⋊C₄	—	2	4	no	—
149	C₄⋊C₄	C₂³×C₉	1	4	yes	—
150	C₂²⋊C₄	—	2	4	no	—
151	C₄²	—	2	4	no	—
152	C₄²	D₄×C₉	1	1	yes	characteristic
153	C₄²	D₄×C₉	1	1	yes	characteristic
154	C₄²	C₂³×C₉	1	2	yes	—
155	C₂²×C₃	—	2	2	no	—
156	C₂²×C₃	—	2	1	no	—
157	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
158	C₃×C₄	—	2	2	no	—
159	C₃×C₄	—	2	1	no	—
160	C₃×C₄	—	4	4	no	—
161	C₃×C₄	—	4	4	no	—
162	C₃×C₄	C₃×#137	1	4	yes	—
163	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
164	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
165	C₉	#3255	1	1	yes	characteristic, direct product factor, Sylow
166	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
167	Q₈	—	2	4	no	—
168	Q₈	—	2	4	no	—
169	Q₈	—	4	4	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	2	4	no	—
174	C₂×C₄	—	2	4	no	—
175	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
176	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
177	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
178	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
179	C₈	—	2	4	no	—
180	C₂×C₃	—	4	1	no	—
181	C₂×C₃	C₃×#537	1	1	yes	characteristic
182	C₂×C₃	C₂×C₃×#137	1	2	yes	—
183	C₂²	—	2	1	no	—
184	C₂²	—	2	2	no	—
185	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
186	C₄	—	2	1	no	—
187	C₄	—	2	2	no	—
188	C₄	—	4	4	no	—
189	C₄	—	4	4	no	—
190	C₄	C₉×#137	1	4	yes	—
191	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
192	C₄	C₉×2₋¹⁺⁴	1	1	yes	characteristic
193	C₃	C₃×#3255	1	1	yes	characteristic
194	C₂	—	4	1	no	—
195	C₂	C₉×#537	1	1	yes	characteristic
196	C₂	C₂×C₉×#137	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	C₂³×C₃	C₂×C₃×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×#475	C₂	semidirect
4. C₉×#462	C₂	semidirect
44. #3255	C₉	direct (N × H)
74. #475	C₂×C₉	semidirect
76. #462	C₂×C₉	semidirect
165. C₉	#3255	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×#533	2
C₉×#475	2
C₉×#470	2
C₉×#462	2
C₉×#423	2
C₃×#3255	3

Subgroups — C9×#3255 #11767976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3255 #11767976