Subgroups — C₉×#3139 #11767860

Order 1152.

570 conjugacy classes of subgroups.

The subgroup lattice has 204 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	1	yes	maximal, characteristic
2	C₂×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₉×#491	C₂	1	4	yes	maximal, complemented
4	C₉×#487	C₂	1	4	yes	maximal, complemented
5	C₉×#419	C₂	1	4	yes	maximal
6	C₄×C₉×M₁₆	C₂	1	1	yes	maximal, characteristic
7	C₃×#3139	C₃	1	1	yes	maximal, characteristic
8	C₂²×Q₈×C₉	C₂²	1	2	yes	—
9	C₂×C₉×M₁₆	C₂²	1	2	yes	—
10	C₉×C₄⋊Q₈	—	2	2	no	—
11	C₉×C₄⋊Q₈	C₂²	1	2	yes	—
12	C₉×C₄⋊Q₈	C₂²	1	2	yes	—
13	C₉×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₉×#125	C₂²	1	2	yes	—
15	C₉×C₂²⋊Q₈	—	2	2	no	—
16	C₄×Q₈×C₉	—	2	2	no	—
17	C₉×#117	C₂²	1	2	yes	—
18	C₂×C₉×C₄⋊C₄	—	2	2	no	—
19	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
20	C₉×#103	C₂²	1	16	yes	—
21	C₉×#97	C₂²	1	2	yes	—
22	C₄×C₈×C₉	C₂²	1	2	yes	—
23	C₃×#533	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
25	C₃×#491	C₂×C₃	1	4	yes	—
26	C₃×#487	C₂×C₃	1	4	yes	—
27	C₃×#419	C₂×C₃	1	4	yes	—
28	C₃×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic
29	C₂×Q₈×C₉	—	2	2	no	—
30	C₂×Q₈×C₉	—	2	2	no	—
31	C₂×Q₈×C₉	—	2	8	no	—
32	C₂×Q₈×C₉	C₂³	1	4	yes	—
33	C₂²×C₄×C₉	—	2	2	no	—
34	C₂²×C₄×C₉	D₄	1	2	yes	—
35	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
36	C₉×M₁₆	—	2	4	no	—
37	C₂×C₈×C₉	C₂³	1	4	yes	—
38	C₉×C₄⋊C₄	—	2	4	no	—
39	C₉×C₄⋊C₄	—	2	4	no	—
40	C₉×C₄⋊C₄	—	2	4	no	—
41	C₉×C₄⋊C₄	—	2	2	no	—
42	C₉×C₄⋊C₄	C₂³	1	4	yes	—
43	C₉×C₂²⋊C₄	—	2	2	no	—
44	C₄²×C₉	—	2	2	no	—
45	C₄²×C₉	D₄	1	2	yes	—
46	C₄²×C₉	C₂³	1	1	yes	characteristic
47	C₄²×C₉	C₂³	1	1	yes	characteristic
48	#3139	C₉	1	1	yes	characteristic, direct product factor, Sylow
49	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
50	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
51	C₃×C₄⋊Q₈	—	2	2	no	—
52	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
53	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
54	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
55	C₃×#125	C₂²×C₃	1	2	yes	—
56	C₃×C₂²⋊Q₈	—	2	2	no	—
57	C₃×C₄×Q₈	—	2	2	no	—
58	C₃×#117	C₂²×C₃	1	2	yes	—
59	C₂×C₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
61	C₃×#103	C₂²×C₃	1	16	yes	—
62	C₃×#97	C₂²×C₃	1	2	yes	—
63	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
64	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
65	Q₈×C₉	—	2	8	no	—
66	Q₈×C₉	—	4	4	no	—
67	Q₈×C₉	—	4	4	no	—
68	C₂×C₄×C₉	—	2	4	no	—
69	C₂×C₄×C₉	—	2	4	no	—
70	C₂×C₄×C₉	—	2	4	no	—
71	C₂×C₄×C₉	—	4	4	no	—
72	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
73	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
74	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
75	C₂×C₄×C₉	#41	1	4	yes	—
76	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
77	C₈×C₉	—	2	4	no	—
78	#533	C₂×C₉	1	1	yes	characteristic
79	C₂×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic
80	#491	C₂×C₉	1	4	yes	complemented
81	#487	C₂×C₉	1	4	yes	complemented
82	#419	C₂×C₉	1	4	yes	—
83	C₄×M₁₆	C₂×C₉	1	1	yes	characteristic
84	C₂×C₃×Q₈	—	2	2	no	—
85	C₂×C₃×Q₈	—	2	2	no	—
86	C₂×C₃×Q₈	—	2	8	no	—
87	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
88	C₂²×C₃×C₄	—	2	2	no	—
89	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
90	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
91	C₃×M₁₆	—	2	4	no	—
92	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
93	C₃×C₄⋊C₄	—	2	4	no	—
94	C₃×C₄⋊C₄	—	2	4	no	—
95	C₃×C₄⋊C₄	—	2	4	no	—
96	C₃×C₄⋊C₄	—	2	2	no	—
97	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
98	C₃×C₂²⋊C₄	—	2	2	no	—
99	C₃×C₄²	—	2	2	no	—
100	C₃×C₄²	C₃×D₄	1	2	yes	—
101	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
102	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
103	C₂²×C₉	—	2	2	no	—
104	C₂²×C₉	#124	1	2	yes	—
105	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
106	C₄×C₉	—	2	2	no	—
107	C₄×C₉	—	4	4	no	—
108	C₄×C₉	—	4	4	no	—
109	C₄×C₉	#124	1	2	yes	—
110	C₄×C₉	#137	1	4	yes	—
111	C₄×C₉	C₂×#41	1	2	yes	—
112	C₂²×Q₈	C₂²×C₉	1	2	yes	—
113	C₂×M₁₆	C₂²×C₉	1	2	yes	—
114	C₄⋊Q₈	—	2	2	no	—
115	C₄⋊Q₈	C₂²×C₉	1	2	yes	—
116	C₄⋊Q₈	C₂²×C₉	1	2	yes	—
117	C₄⋊Q₈	C₂²×C₉	1	2	yes	—
118	#125	C₂²×C₉	1	2	yes	—
119	C₂²⋊Q₈	—	2	2	no	—
120	C₄×Q₈	—	2	2	no	—
121	#117	C₂²×C₉	1	2	yes	—
122	C₂×C₄⋊C₄	—	2	2	no	—
123	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
124	#103	C₂²×C₉	1	16	yes	—
125	#97	C₂²×C₉	1	2	yes	—
126	C₄×C₈	C₂²×C₉	1	2	yes	—
127	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
128	C₃×Q₈	—	2	8	no	—
129	C₃×Q₈	—	4	4	no	—
130	C₃×Q₈	—	4	4	no	—
131	C₂×C₃×C₄	—	2	4	no	—
132	C₂×C₃×C₄	—	2	4	no	—
133	C₂×C₃×C₄	—	2	4	no	—
134	C₂×C₃×C₄	—	4	4	no	—
135	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
136	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
137	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
138	C₂×C₃×C₄	C₃×#41	1	4	yes	—
139	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
140	C₃×C₈	—	2	4	no	—
141	C₂×C₉	—	2	2	no	—
142	C₂×C₉	C₂×#124	1	1	yes	characteristic
143	C₂×C₉	C₂×#137	1	2	yes	—
144	C₂×Q₈	—	2	2	no	—
145	C₂×Q₈	—	2	2	no	—
146	C₂×Q₈	—	2	8	no	—
147	C₂×Q₈	C₂³×C₉	1	4	yes	—
148	C₂²×C₄	—	2	2	no	—
149	C₂²×C₄	D₄×C₉	1	2	yes	—
150	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
151	M₁₆	—	2	4	no	—
152	C₂×C₈	C₂³×C₉	1	4	yes	—
153	C₄⋊C₄	—	2	4	no	—
154	C₄⋊C₄	—	2	4	no	—
155	C₄⋊C₄	—	2	4	no	—
156	C₄⋊C₄	—	2	2	no	—
157	C₄⋊C₄	C₂³×C₉	1	4	yes	—
158	C₂²⋊C₄	—	2	2	no	—
159	C₄²	—	2	2	no	—
160	C₄²	D₄×C₉	1	2	yes	—
161	C₄²	C₂³×C₉	1	1	yes	characteristic
162	C₄²	C₂³×C₉	1	1	yes	characteristic
163	C₂²×C₃	—	2	2	no	—
164	C₂²×C₃	C₃×#124	1	2	yes	—
165	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
166	C₃×C₄	—	2	2	no	—
167	C₃×C₄	—	4	4	no	—
168	C₃×C₄	—	4	4	no	—
169	C₃×C₄	C₃×#124	1	2	yes	—
170	C₃×C₄	C₃×#137	1	4	yes	—
171	C₃×C₄	C₂×C₃×#41	1	2	yes	—
172	C₉	#3139	1	1	yes	characteristic, direct product factor, Sylow
173	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
174	Q₈	—	2	8	no	—
175	Q₈	—	4	4	no	—
176	Q₈	—	4	4	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	4	4	no	—
181	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
182	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
183	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
184	C₂×C₄	C₉×#41	1	4	yes	—
185	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
186	C₈	—	2	4	no	—
187	C₂×C₃	—	2	2	no	—
188	C₂×C₃	C₂×C₃×#124	1	1	yes	characteristic
189	C₂×C₃	C₂×C₃×#137	1	2	yes	—
190	C₂²	—	2	2	no	—
191	C₂²	C₉×#124	1	2	yes	—
192	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
193	C₄	—	2	2	no	—
194	C₄	—	4	4	no	—
195	C₄	—	4	4	no	—
196	C₄	C₉×#124	1	2	yes	—
197	C₄	C₉×#137	1	4	yes	—
198	C₄	C₂×C₉×#41	1	2	yes	—
199	C₃	C₃×#3139	1	1	yes	characteristic
200	C₂	—	2	2	no	—
201	C₂	C₂×C₉×#124	1	1	yes	characteristic
202	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
3. C₉×#491	C₂	semidirect
4. C₉×#487	C₂	semidirect
48. #3139	C₉	direct (N × H)
80. #491	C₂×C₉	semidirect
81. #487	C₂×C₉	semidirect
172. C₉	#3139	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
C₂×C₉×C₄⋊Q₈	2
C₉×#491	2
C₉×#487	2
C₉×#419	2
C₄×C₉×M₁₆	2
C₃×#3139	3

Subgroups — C9×#3139 #11767860

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3139 #11767860