Subgroups — C₉×#2100 #11766821

Order 1152.

321 conjugacy classes of subgroups.

The subgroup lattice has 225 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#389	C₂	1	1	yes	maximal, characteristic
2	C₉×#384	C₂	1	1	yes	maximal, characteristic
3	C₉×#340	C₂	1	2	yes	maximal
4	C₉×#340	C₂	1	2	yes	maximal
5	C₉×#336	C₂	1	1	yes	maximal, characteristic
6	C₃×#2100	C₃	1	1	yes	maximal, characteristic
7	C₂²×C₈×C₉	C₂²	1	2	yes	—
8	C₂×C₉×C₄⋊C₄	—	2	1	no	—
9	C₂×C₉×C₄⋊C₄	—	2	1	no	—
10	C₂×C₉×C₄⋊C₄	—	2	1	no	—
11	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
15	C₉×#95	—	2	1	no	—
16	C₃×#389	C₂×C₃	1	1	yes	characteristic
17	C₃×#384	C₂×C₃	1	1	yes	characteristic
18	C₃×#340	C₂×C₃	1	2	yes	—
19	C₃×#340	C₂×C₃	1	2	yes	—
20	C₃×#336	C₂×C₃	1	1	yes	characteristic
21	C₂²×C₄×C₉	—	2	1	no	—
22	C₂²×C₄×C₉	—	2	2	no	—
23	C₂²×C₄×C₉	—	2	1	no	—
24	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
25	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
26	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
27	C₂×C₈×C₉	—	2	2	no	—
28	C₂×C₈×C₉	—	2	2	no	—
29	C₂×C₈×C₉	—	2	2	no	—
30	C₉×C₄⋊C₄	—	2	1	no	—
31	C₉×C₄⋊C₄	—	2	2	no	—
32	C₉×C₄⋊C₄	—	2	4	no	—
33	C₉×C₄⋊C₄	—	4	2	no	—
34	C₉×C₄⋊C₄	—	4	2	no	—
35	C₉×C₄⋊C₄	—	4	2	no	—
36	C₉×C₄⋊C₄	Q₈	1	2	yes	—
37	C₄²×C₉	—	2	2	no	—
38	#2100	C₉	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
40	C₂×C₃×C₄⋊C₄	—	2	1	no	—
41	C₂×C₃×C₄⋊C₄	—	2	1	no	—
42	C₂×C₃×C₄⋊C₄	—	2	1	no	—
43	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
44	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
45	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
46	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
47	C₃×#95	—	2	1	no	—
48	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₉	—	2	1	no	—
50	C₂×C₄×C₉	—	2	1	no	—
51	C₂×C₄×C₉	—	2	1	no	—
52	C₂×C₄×C₉	—	2	1	no	—
53	C₂×C₄×C₉	—	2	2	no	—
54	C₂×C₄×C₉	—	4	1	no	—
55	C₂×C₄×C₉	—	4	1	no	—
56	C₂×C₄×C₉	—	4	1	no	—
57	C₂×C₄×C₉	—	4	2	no	—
58	C₂×C₄×C₉	—	4	1	no	—
59	C₂×C₄×C₉	—	4	2	no	—
60	C₂×C₄×C₉	—	4	2	no	—
61	C₂×C₄×C₉	—	4	1	no	—
62	C₂×C₄×C₉	SD₁₆	1	2	yes	—
63	C₂×C₄×C₉	Q₁₆	1	2	yes	—
64	C₂×C₄×C₉	C₂×Q₈	1	1	yes	characteristic
65	C₂×C₄×C₉	#41	1	2	yes	—
66	C₂×C₄×C₉	#41	1	2	yes	—
67	C₂×C₄×C₉	#41	1	1	yes	characteristic
68	C₈×C₉	—	4	2	no	—
69	#389	C₂×C₉	1	1	yes	characteristic
70	#384	C₂×C₉	1	1	yes	characteristic
71	#340	C₂×C₉	1	2	yes	—
72	#340	C₂×C₉	1	2	yes	—
73	#336	C₂×C₉	1	1	yes	characteristic
74	C₂²×C₃×C₄	—	2	1	no	—
75	C₂²×C₃×C₄	—	2	1	no	—
76	C₂²×C₃×C₄	—	2	2	no	—
77	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
78	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
79	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
80	C₂×C₃×C₈	—	2	2	no	—
81	C₂×C₃×C₈	—	2	2	no	—
82	C₂×C₃×C₈	—	2	2	no	—
83	C₃×C₄⋊C₄	—	2	1	no	—
84	C₃×C₄⋊C₄	—	2	2	no	—
85	C₃×C₄⋊C₄	—	2	4	no	—
86	C₃×C₄⋊C₄	—	4	2	no	—
87	C₃×C₄⋊C₄	—	4	2	no	—
88	C₃×C₄⋊C₄	—	4	2	no	—
89	C₃×C₄⋊C₄	C₃×Q₈	1	2	yes	—
90	C₃×C₄²	—	2	2	no	—
91	C₂²×C₉	C₂²⋊Q₈	1	1	yes	characteristic
92	C₂²×C₉	#123	1	1	yes	characteristic
93	C₂²×C₉	#124	1	1	yes	characteristic
94	C₂²×C₉	C₂×SD₁₆	1	1	yes	characteristic
95	C₂²×C₉	C₂×Q₁₆	1	1	yes	characteristic
96	C₂²×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
97	C₂²×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
98	C₄×C₉	—	2	2	no	—
99	C₄×C₉	—	2	2	no	—
100	C₄×C₉	—	4	2	no	—
101	C₄×C₉	—	8	1	no	—
102	C₄×C₉	—	8	2	no	—
103	C₄×C₉	#125	1	2	yes	—
104	C₄×C₉	#126	1	2	yes	—
105	C₂²×C₈	C₂²×C₉	1	2	yes	—
106	C₂×C₄⋊C₄	—	2	1	no	—
107	C₂×C₄⋊C₄	—	2	1	no	—
108	C₂×C₄⋊C₄	—	2	1	no	—
109	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
110	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
111	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
112	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
113	#95	—	2	1	no	—
114	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄	—	2	1	no	—
116	C₂×C₃×C₄	—	2	1	no	—
117	C₂×C₃×C₄	—	2	1	no	—
118	C₂×C₃×C₄	—	2	1	no	—
119	C₂×C₃×C₄	—	2	2	no	—
120	C₂×C₃×C₄	—	4	1	no	—
121	C₂×C₃×C₄	—	4	1	no	—
122	C₂×C₃×C₄	—	4	1	no	—
123	C₂×C₃×C₄	—	4	2	no	—
124	C₂×C₃×C₄	—	4	1	no	—
125	C₂×C₃×C₄	—	4	2	no	—
126	C₂×C₃×C₄	—	4	2	no	—
127	C₂×C₃×C₄	—	4	1	no	—
128	C₂×C₃×C₄	C₃×SD₁₆	1	2	yes	—
129	C₂×C₃×C₄	C₃×Q₁₆	1	2	yes	—
130	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
131	C₂×C₃×C₄	C₃×#41	1	2	yes	—
132	C₂×C₃×C₄	C₃×#41	1	2	yes	—
133	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
134	C₃×C₈	—	4	2	no	—
135	C₂×C₉	#400	1	1	yes	characteristic
136	C₂×C₉	#476	1	1	yes	characteristic
137	C₂×C₉	#477	1	1	yes	characteristic
138	C₂×C₉	#481	1	1	yes	characteristic
139	C₂×C₉	#484	1	1	yes	characteristic
140	C₂×C₉	#487	1	1	yes	characteristic
141	C₂×C₉	#490	1	1	yes	characteristic
142	C₂²×C₄	—	2	1	no	—
143	C₂²×C₄	—	2	1	no	—
144	C₂²×C₄	—	2	2	no	—
145	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
146	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
147	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
148	C₂×C₈	—	2	2	no	—
149	C₂×C₈	—	2	2	no	—
150	C₂×C₈	—	2	2	no	—
151	C₄⋊C₄	—	2	1	no	—
152	C₄⋊C₄	—	2	2	no	—
153	C₄⋊C₄	—	2	4	no	—
154	C₄⋊C₄	—	4	2	no	—
155	C₄⋊C₄	—	4	2	no	—
156	C₄⋊C₄	—	4	2	no	—
157	C₄⋊C₄	Q₈×C₉	1	2	yes	—
158	C₄²	—	2	2	no	—
159	C₂²×C₃	C₃×C₂²⋊Q₈	1	1	yes	characteristic
160	C₂²×C₃	C₃×#123	1	1	yes	characteristic
161	C₂²×C₃	C₃×#124	1	1	yes	characteristic
162	C₂²×C₃	C₂×C₃×SD₁₆	1	1	yes	characteristic
163	C₂²×C₃	C₂×C₃×Q₁₆	1	1	yes	characteristic
164	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
166	C₃×C₄	—	2	2	no	—
167	C₃×C₄	—	2	2	no	—
168	C₃×C₄	—	4	2	no	—
169	C₃×C₄	—	8	1	no	—
170	C₃×C₄	—	8	2	no	—
171	C₃×C₄	C₃×#125	1	2	yes	—
172	C₃×C₄	C₃×#126	1	2	yes	—
173	C₉	#2100	1	1	yes	characteristic, direct product factor, Sylow
174	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	4	1	no	—
181	C₂×C₄	—	4	1	no	—
182	C₂×C₄	—	4	1	no	—
183	C₂×C₄	—	4	2	no	—
184	C₂×C₄	—	4	1	no	—
185	C₂×C₄	—	4	2	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	1	no	—
188	C₂×C₄	C₉×SD₁₆	1	2	yes	—
189	C₂×C₄	C₉×Q₁₆	1	2	yes	—
190	C₂×C₄	C₂×Q₈×C₉	1	1	yes	characteristic
191	C₂×C₄	C₉×#41	1	2	yes	—
192	C₂×C₄	C₉×#41	1	2	yes	—
193	C₂×C₄	C₉×#41	1	1	yes	characteristic
194	C₈	—	4	2	no	—
195	C₂×C₃	C₃×#400	1	1	yes	characteristic
196	C₂×C₃	C₃×#476	1	1	yes	characteristic
197	C₂×C₃	C₃×#477	1	1	yes	characteristic
198	C₂×C₃	C₃×#481	1	1	yes	characteristic
199	C₂×C₃	C₃×#484	1	1	yes	characteristic
200	C₂×C₃	C₃×#487	1	1	yes	characteristic
201	C₂×C₃	C₃×#490	1	1	yes	characteristic
202	C₂²	C₉×C₂²⋊Q₈	1	1	yes	characteristic
203	C₂²	C₉×#123	1	1	yes	characteristic
204	C₂²	C₉×#124	1	1	yes	characteristic
205	C₂²	C₂×C₉×SD₁₆	1	1	yes	characteristic
206	C₂²	C₂×C₉×Q₁₆	1	1	yes	characteristic
207	C₂²	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
208	C₂²	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
209	C₄	—	2	2	no	—
210	C₄	—	2	2	no	—
211	C₄	—	4	2	no	—
212	C₄	—	8	1	no	—
213	C₄	—	8	2	no	—
214	C₄	C₉×#125	1	2	yes	—
215	C₄	C₉×#126	1	2	yes	—
216	C₃	C₃×#2100	1	1	yes	characteristic
217	C₂	C₉×#400	1	1	yes	characteristic
218	C₂	C₉×#476	1	1	yes	characteristic
219	C₂	C₉×#477	1	1	yes	characteristic
220	C₂	C₉×#481	1	1	yes	characteristic
221	C₂	C₉×#484	1	1	yes	characteristic
222	C₂	C₉×#487	1	1	yes	characteristic
223	C₂	C₉×#490	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂×D₄
commutator	C₂²×C₄	C₂³×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle, prime radical	C₂³×C₃	C₂×C₃×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
38. #2100	C₉	direct (N × H)
173. C₉	#2100	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×#389	2
C₉×#384	2
C₉×#340	2
C₉×#336	2
C₃×#2100	3

Subgroups — C9×#2100 #11766821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2100 #11766821