Subgroups — C₉×#3150 #11767871

Order 1152.

846 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#135	C₂	1	4	yes	maximal, complemented
2	C₉×#532	C₂	1	2	yes	maximal, complemented
3	C₉×#497	C₂	1	4	yes	maximal, complemented
4	C₉×#496	C₂	1	4	yes	maximal, complemented
5	C₂×C₉×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#3150	C₃	1	1	yes	maximal, characteristic
7	C₂×C₉×#41	C₂²	1	4	yes	—
8	C₉×#135	—	2	16	no	—
9	C₂×C₉×Q₁₆	C₂²	1	4	yes	—
10	C₂×C₉×SD₁₆	C₂²	1	8	yes	—
11	C₂×C₉×D₈	C₂²	1	4	yes	—
12	C₂²×C₈×C₉	C₂²	1	2	yes	—
13	C₉×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₉×#127	C₂²	1	2	yes	—
15	C₉×#124	C₂²	1	4	yes	—
16	C₉×#121	—	2	4	no	—
17	C₄×D₄×C₉	—	2	4	no	—
18	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
19	C₉×#97	C₂²	1	4	yes	—
20	C₂×C₃×#135	C₂×C₃	1	4	yes	—
21	C₃×#532	C₂×C₃	1	2	yes	—
22	C₃×#497	C₂×C₃	1	4	yes	—
23	C₃×#496	C₂×C₃	1	4	yes	—
24	C₂×C₃×#97	C₂×C₃	1	1	yes	characteristic
25	C₉×#41	—	2	16	no	—
26	C₂×Q₈×C₉	C₂³	1	4	yes	—
27	C₂×D₄×C₉	—	2	4	no	—
28	C₂×D₄×C₉	—	2	4	no	—
29	C₂×D₄×C₉	C₂³	1	4	yes	—
30	C₂²×C₄×C₉	—	2	4	no	—
31	C₂²×C₄×C₉	D₄	1	2	yes	—
32	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
33	C₉×Q₁₆	—	2	8	no	—
34	C₉×SD₁₆	—	2	16	no	—
35	C₉×D₈	—	2	8	no	—
36	C₂×C₈×C₉	D₄	1	8	yes	complemented
37	C₂×C₈×C₉	C₂³	1	4	yes	—
38	C₉×C₄⋊C₄	—	2	4	no	—
39	C₉×C₂²⋊C₄	—	2	8	no	—
40	C₄²×C₉	D₄	1	2	yes	—
41	C₄²×C₉	C₂³	1	2	yes	—
42	#3150	C₉	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
44	C₃×#135	—	2	16	no	—
45	C₂×C₃×Q₁₆	C₂²×C₃	1	4	yes	—
46	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	—
47	C₂×C₃×D₈	C₂²×C₃	1	4	yes	—
48	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
49	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
50	C₃×#127	C₂²×C₃	1	2	yes	—
51	C₃×#124	C₂²×C₃	1	4	yes	—
52	C₃×#121	—	2	4	no	—
53	C₃×C₄×D₄	—	2	4	no	—
54	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
55	C₃×#97	C₂²×C₃	1	4	yes	—
56	C₂³×C₉	—	2	4	no	—
57	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
58	Q₈×C₉	—	2	8	no	—
59	D₄×C₉	—	2	8	no	—
60	D₄×C₉	—	4	8	no	—
61	D₄×C₉	—	4	8	no	—
62	C₂×C₄×C₉	—	2	4	no	—
63	C₂×C₄×C₉	—	4	2	no	—
64	C₂×C₄×C₉	—	4	8	no	—
65	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
66	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
67	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
68	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
69	C₈×C₉	C₂×D₄	1	8	yes	—
70	C₂×#135	C₂×C₉	1	4	yes	complemented
71	#532	C₂×C₉	1	2	yes	complemented
72	#497	C₂×C₉	1	4	yes	complemented
73	#496	C₂×C₉	1	4	yes	complemented
74	C₂×#97	C₂×C₉	1	1	yes	characteristic, complemented
75	C₃×#41	—	2	16	no	—
76	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
77	C₂×C₃×D₄	—	2	4	no	—
78	C₂×C₃×D₄	—	2	4	no	—
79	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
80	C₂²×C₃×C₄	—	2	4	no	—
81	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
82	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
83	C₃×Q₁₆	—	2	8	no	—
84	C₃×SD₁₆	—	2	16	no	—
85	C₃×D₈	—	2	8	no	—
86	C₂×C₃×C₈	C₃×D₄	1	8	yes	—
87	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
88	C₃×C₄⋊C₄	—	2	4	no	—
89	C₃×C₂²⋊C₄	—	2	8	no	—
90	C₃×C₄²	C₃×D₄	1	2	yes	—
91	C₃×C₄²	C₂³×C₃	1	2	yes	—
92	C₂²×C₉	—	2	2	no	—
93	C₂²×C₉	—	4	4	no	—
94	C₂²×C₉	—	4	8	no	—
95	C₂²×C₉	#127	1	2	yes	—
96	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
97	C₄×C₉	—	2	4	no	—
98	C₄×C₉	—	4	4	no	—
99	C₄×C₉	#127	1	2	yes	—
100	C₄×C₉	C₂²×D₄	1	2	yes	—
101	C₂×#41	C₂²×C₉	1	4	yes	—
102	#135	—	2	16	no	—
103	C₂×Q₁₆	C₂²×C₉	1	4	yes	—
104	C₂×SD₁₆	C₂²×C₉	1	8	yes	—
105	C₂×D₈	C₂²×C₉	1	4	yes	—
106	C₂²×C₈	C₂²×C₉	1	2	yes	—
107	C₄⋊Q₈	C₂²×C₉	1	2	yes	—
108	#127	C₂²×C₉	1	2	yes	—
109	#124	C₂²×C₉	1	4	yes	—
110	#121	—	2	4	no	—
111	C₄×D₄	—	2	4	no	—
112	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
113	#97	C₂²×C₉	1	4	yes	—
114	C₂³×C₃	—	2	4	no	—
115	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
116	C₃×Q₈	—	2	8	no	—
117	C₃×D₄	—	2	8	no	—
118	C₃×D₄	—	4	8	no	—
119	C₃×D₄	—	4	8	no	—
120	C₂×C₃×C₄	—	2	4	no	—
121	C₂×C₃×C₄	—	4	2	no	—
122	C₂×C₃×C₄	—	4	8	no	—
123	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
124	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
125	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
126	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
127	C₃×C₈	C₂×C₃×D₄	1	8	yes	—
128	C₂×C₉	—	2	2	no	—
129	C₂×C₉	—	8	4	no	—
130	C₂×C₉	C₂×#127	1	1	yes	characteristic
131	C₂×C₉	#575	1	2	yes	—
132	#41	—	2	16	no	—
133	C₂×Q₈	C₂³×C₉	1	4	yes	—
134	C₂×D₄	—	2	4	no	—
135	C₂×D₄	—	2	4	no	—
136	C₂×D₄	C₂³×C₉	1	4	yes	—
137	C₂²×C₄	—	2	4	no	—
138	C₂²×C₄	D₄×C₉	1	2	yes	—
139	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
140	Q₁₆	—	2	8	no	—
141	SD₁₆	—	2	16	no	—
142	D₈	—	2	8	no	—
143	C₂×C₈	D₄×C₉	1	8	yes	complemented
144	C₂×C₈	C₂³×C₉	1	4	yes	—
145	C₄⋊C₄	—	2	4	no	—
146	C₂²⋊C₄	—	2	8	no	—
147	C₄²	D₄×C₉	1	2	yes	—
148	C₄²	C₂³×C₉	1	2	yes	—
149	C₂²×C₃	—	2	2	no	—
150	C₂²×C₃	—	4	8	no	—
151	C₂²×C₃	—	4	4	no	—
152	C₂²×C₃	C₃×#127	1	2	yes	—
153	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
154	C₃×C₄	—	2	4	no	—
155	C₃×C₄	—	4	4	no	—
156	C₃×C₄	C₃×#127	1	2	yes	—
157	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
158	C₉	#3150	1	1	yes	characteristic, direct product factor, Sylow
159	C₂³	—	2	4	no	—
160	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
161	Q₈	—	2	8	no	—
162	D₄	—	2	8	no	—
163	D₄	—	4	8	no	—
164	D₄	—	4	8	no	—
165	C₂×C₄	—	2	4	no	—
166	C₂×C₄	—	4	2	no	—
167	C₂×C₄	—	4	8	no	—
168	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
169	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
170	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
171	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
172	C₈	C₂×D₄×C₉	1	8	yes	—
173	C₂×C₃	—	2	2	no	—
174	C₂×C₃	—	8	4	no	—
175	C₂×C₃	C₂×C₃×#127	1	1	yes	characteristic
176	C₂×C₃	C₃×#575	1	2	yes	—
177	C₂²	—	2	2	no	—
178	C₂²	—	4	4	no	—
179	C₂²	—	4	8	no	—
180	C₂²	C₉×#127	1	2	yes	—
181	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
182	C₄	—	2	4	no	—
183	C₄	—	4	4	no	—
184	C₄	C₉×#127	1	2	yes	—
185	C₄	C₂²×D₄×C₉	1	2	yes	—
186	C₃	C₃×#3150	1	1	yes	characteristic
187	C₂	—	2	2	no	—
188	C₂	—	8	4	no	—
189	C₂	C₂×C₉×#127	1	1	yes	characteristic
190	C₂	C₉×#575	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₉	C₂×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₃×#3150	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#135	C₂	semidirect
2. C₉×#532	C₂	semidirect
3. C₉×#497	C₂	semidirect
4. C₉×#496	C₂	semidirect
5. C₂×C₉×#97	C₂	semidirect
36. C₂×C₈×C₉	D₄	semidirect
42. #3150	C₉	direct (N × H)
70. C₂×#135	C₂×C₉	semidirect
71. #532	C₂×C₉	semidirect
72. #497	C₂×C₉	semidirect
73. #496	C₂×C₉	semidirect
74. C₂×#97	C₂×C₉	semidirect
143. C₂×C₈	D₄×C₉	semidirect
158. C₉	#3150	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×#135	2
C₉×#532	2
C₉×#497	2
C₉×#496	2
C₂×C₉×#97	2
C₃×#3150	3

Subgroups — C9×#3150 #11767871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3150 #11767871