Subgroups — C₉×#1858 #11766579

Order 1152.

378 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×#568	C₂	1	1	yes	maximal, characteristic
2	C₉×#430	C₂	1	2	yes	maximal, complemented
3	C₉×#413	C₂	1	1	yes	maximal, characteristic
4	C₉×#408	C₂	1	1	yes	maximal, characteristic
5	C₉×#341	C₂	1	2	yes	maximal, complemented
6	C₃×#1858	C₃	1	1	yes	maximal, characteristic
7	C₂×C₉×#41	C₂²	1	1	yes	characteristic
8	C₉×#131	—	2	4	no	—
9	C₂×C₉×M₁₆	—	2	2	no	—
10	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₉×M₁₆	C₂²	1	2	yes	—
12	C₂×C₉×M₁₆	C₂²	1	2	yes	—
13	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
14	C₉×#108	—	2	4	no	—
15	C₉×#101	C₄	1	2	yes	—
16	C₉×#100	C₄	1	2	yes	—
17	C₉×C₂²⋊C₈	—	2	2	no	—
18	C₃×#568	C₂×C₃	1	1	yes	characteristic
19	C₃×#430	C₂×C₃	1	2	yes	—
20	C₃×#413	C₂×C₃	1	1	yes	characteristic
21	C₃×#408	C₂×C₃	1	1	yes	characteristic
22	C₃×#341	C₂×C₃	1	2	yes	—
23	C₉×#41	—	2	2	no	—
24	C₉×#41	—	2	2	no	—
25	C₂×Q₈×C₉	C₂×C₄	1	1	yes	characteristic
26	C₂×D₄×C₉	C₂×C₄	1	1	yes	characteristic
27	C₂×D₄×C₉	Q₈	1	2	yes	—
28	C₂²×C₄×C₉	D₄	1	2	yes	—
29	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
30	C₉×M₁₆	—	2	4	no	—
31	C₉×M₁₆	—	2	2	no	—
32	C₉×M₁₆	—	2	2	no	—
33	C₉×M₁₆	—	2	2	no	—
34	C₉×M₁₆	C₂×C₄	1	4	yes	—
35	C₉×M₁₆	D₄	1	4	yes	—
36	C₂×C₈×C₉	—	2	4	no	—
37	C₂×C₈×C₉	—	2	2	no	—
38	C₂×C₈×C₉	—	2	2	no	—
39	C₂×C₈×C₉	—	2	1	no	—
40	C₂×C₈×C₉	—	2	1	no	—
41	C₂×C₈×C₉	—	2	2	no	—
42	#1858	C₉	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
44	C₃×#131	—	2	4	no	—
45	C₂×C₃×M₁₆	—	2	2	no	—
46	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
47	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
48	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
49	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
50	C₃×#108	—	2	4	no	—
51	C₃×#101	C₃×C₄	1	2	yes	—
52	C₃×#100	C₃×C₄	1	2	yes	—
53	C₃×C₂²⋊C₈	—	2	2	no	—
54	C₂³×C₉	C₄⋊C₄	1	2	yes	—
55	C₂³×C₉	C₂×Q₈	1	1	yes	characteristic
56	Q₈×C₉	—	2	2	no	—
57	D₄×C₉	—	2	4	no	—
58	D₄×C₉	—	2	2	no	—
59	C₂×C₄×C₉	—	2	2	no	—
60	C₂×C₄×C₉	—	2	2	no	—
61	C₂×C₄×C₉	C₄⋊C₄	1	2	yes	—
62	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
64	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
65	C₂×C₄×C₉	#41	1	2	yes	—
66	C₈×C₉	—	2	4	no	—
67	C₈×C₉	—	2	4	no	—
68	C₈×C₉	—	4	1	no	—
69	C₈×C₉	—	4	1	no	—
70	#568	C₂×C₉	1	1	yes	characteristic
71	#430	C₂×C₉	1	2	yes	complemented
72	#413	C₂×C₉	1	1	yes	characteristic
73	#408	C₂×C₉	1	1	yes	characteristic
74	#341	C₂×C₉	1	2	yes	complemented
75	C₃×#41	—	2	2	no	—
76	C₃×#41	—	2	2	no	—
77	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
78	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
79	C₂×C₃×D₄	C₃×Q₈	1	2	yes	—
80	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
81	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
82	C₃×M₁₆	—	2	4	no	—
83	C₃×M₁₆	—	2	2	no	—
84	C₃×M₁₆	—	2	2	no	—
85	C₃×M₁₆	—	2	2	no	—
86	C₃×M₁₆	C₂×C₃×C₄	1	4	yes	—
87	C₃×M₁₆	C₃×D₄	1	4	yes	—
88	C₂×C₃×C₈	—	2	4	no	—
89	C₂×C₃×C₈	—	2	2	no	—
90	C₂×C₃×C₈	—	2	2	no	—
91	C₂×C₃×C₈	—	2	1	no	—
92	C₂×C₃×C₈	—	2	1	no	—
93	C₂×C₃×C₈	—	2	2	no	—
94	C₂²×C₉	—	2	2	no	—
95	C₂²×C₉	—	4	1	no	—
96	C₂²×C₉	—	4	2	no	—
97	C₂²×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
98	C₂²×C₉	C₂²⋊Q₈	1	2	yes	—
99	C₄×C₉	—	2	2	no	—
100	C₄×C₉	C₄×D₄	1	2	yes	—
101	C₄×C₉	#120	1	1	yes	characteristic
102	C₄×C₉	#123	1	1	yes	characteristic
103	C₂×#41	C₂²×C₉	1	1	yes	characteristic
104	#131	—	2	4	no	—
105	C₂×M₁₆	—	2	2	no	—
106	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
107	C₂×M₁₆	C₂²×C₉	1	2	yes	—
108	C₂×M₁₆	C₂²×C₉	1	2	yes	—
109	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
110	#108	—	2	4	no	—
111	#101	C₄×C₉	1	2	yes	—
112	#100	C₄×C₉	1	2	yes	—
113	C₂²⋊C₈	—	2	2	no	—
114	C₂³×C₃	C₃×C₄⋊C₄	1	2	yes	—
115	C₂³×C₃	C₂×C₃×Q₈	1	1	yes	characteristic
116	C₃×Q₈	—	2	2	no	—
117	C₃×D₄	—	2	4	no	—
118	C₃×D₄	—	2	2	no	—
119	C₂×C₃×C₄	—	2	2	no	—
120	C₂×C₃×C₄	—	2	2	no	—
121	C₂×C₃×C₄	C₃×C₄⋊C₄	1	2	yes	—
122	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
123	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
124	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
125	C₂×C₃×C₄	C₃×#41	1	2	yes	—
126	C₃×C₈	—	2	4	no	—
127	C₃×C₈	—	2	4	no	—
128	C₃×C₈	—	4	1	no	—
129	C₃×C₈	—	4	1	no	—
130	C₂×C₉	—	2	1	no	—
131	C₂×C₉	—	2	2	no	—
132	C₂×C₉	—	4	2	no	—
133	C₂×C₉	#385	1	1	yes	characteristic
134	#41	—	2	2	no	—
135	#41	—	2	2	no	—
136	C₂×Q₈	C₂×C₄×C₉	1	1	yes	characteristic
137	C₂×D₄	C₂×C₄×C₉	1	1	yes	characteristic
138	C₂×D₄	Q₈×C₉	1	2	yes	—
139	C₂²×C₄	D₄×C₉	1	2	yes	—
140	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
141	M₁₆	—	2	4	no	—
142	M₁₆	—	2	2	no	—
143	M₁₆	—	2	2	no	—
144	M₁₆	—	2	2	no	—
145	M₁₆	C₂×C₄×C₉	1	4	yes	—
146	M₁₆	D₄×C₉	1	4	yes	—
147	C₂×C₈	—	2	4	no	—
148	C₂×C₈	—	2	2	no	—
149	C₂×C₈	—	2	2	no	—
150	C₂×C₈	—	2	1	no	—
151	C₂×C₈	—	2	1	no	—
152	C₂×C₈	—	2	2	no	—
153	C₂²×C₃	—	2	2	no	—
154	C₂²×C₃	—	4	1	no	—
155	C₂²×C₃	—	4	2	no	—
156	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
157	C₂²×C₃	C₃×C₂²⋊Q₈	1	2	yes	—
158	C₃×C₄	—	2	2	no	—
159	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
160	C₃×C₄	C₃×#120	1	1	yes	characteristic
161	C₃×C₄	C₃×#123	1	1	yes	characteristic
162	C₉	#1858	1	1	yes	characteristic, direct product factor, Sylow
163	C₂³	C₉×C₄⋊C₄	1	2	yes	—
164	C₂³	C₂×Q₈×C₉	1	1	yes	characteristic
165	Q₈	—	2	2	no	—
166	D₄	—	2	4	no	—
167	D₄	—	2	2	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	C₉×C₄⋊C₄	1	2	yes	—
171	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
172	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
173	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
174	C₂×C₄	C₉×#41	1	2	yes	—
175	C₈	—	2	4	no	—
176	C₈	—	2	4	no	—
177	C₈	—	4	1	no	—
178	C₈	—	4	1	no	—
179	C₂×C₃	—	2	1	no	—
180	C₂×C₃	—	2	2	no	—
181	C₂×C₃	—	4	2	no	—
182	C₂×C₃	C₃×#385	1	1	yes	characteristic
183	C₂²	—	2	2	no	—
184	C₂²	—	4	1	no	—
185	C₂²	—	4	2	no	—
186	C₂²	C₂×C₉×C₄⋊C₄	1	1	yes	characteristic
187	C₂²	C₉×C₂²⋊Q₈	1	2	yes	—
188	C₄	—	2	2	no	—
189	C₄	C₄×D₄×C₉	1	2	yes	—
190	C₄	C₉×#120	1	1	yes	characteristic
191	C₄	C₉×#123	1	1	yes	characteristic
192	C₃	C₃×#1858	1	1	yes	characteristic
193	C₂	—	2	1	no	—
194	C₂	—	2	2	no	—
195	C₂	—	4	2	no	—
196	C₂	C₉×#385	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₉	#120
commutator	C₂×C₄	C₂²×C₄×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂×C₃	C₃×#385
prime radical	C₂×C₃×#41	C₂²×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₉ ◁ C₂²×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×#430	C₂	semidirect
5. C₉×#341	C₂	semidirect
42. #1858	C₉	direct (N × H)
71. #430	C₂×C₉	semidirect
74. #341	C₂×C₉	semidirect
162. C₉	#1858	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×#568	2
C₉×#430	2
C₉×#413	2
C₉×#408	2
C₉×#341	2
C₃×#1858	3

Subgroups — C9×#1858 #11766579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1858 #11766579