Subgroups — C₉×#1992 #11766713

Order 1152.

390 conjugacy classes of subgroups.

The subgroup lattice has 174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#125	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#97	C₂	1	1	yes	maximal, characteristic
3	C₉×#384	C₂	1	1	yes	maximal, characteristic
4	C₉×#340	C₂	1	4	yes	maximal
5	C₃×#1992	C₃	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₉	C₂²	1	2	yes	—
7	C₉×#125	—	2	2	no	—
8	C₉×#125	C₄	1	4	yes	complemented
9	C₂×C₉×C₄⋊C₄	—	2	2	no	—
10	C₂×C₉×C₄⋊C₄	—	2	2	no	—
11	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
14	C₉×#97	—	2	2	no	—
15	C₂×C₃×#125	C₂×C₃	1	1	yes	characteristic
16	C₂×C₃×#97	C₂×C₃	1	1	yes	characteristic
17	C₃×#384	C₂×C₃	1	1	yes	characteristic
18	C₃×#340	C₂×C₃	1	4	yes	—
19	C₂²×C₄×C₉	—	2	2	no	—
20	C₂²×C₄×C₉	—	2	2	no	—
21	C₂²×C₄×C₉	D₄	1	2	yes	—
22	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
23	C₂×C₈×C₉	—	2	2	no	—
24	C₂×C₈×C₉	—	2	2	no	—
25	C₂×C₈×C₉	Q₈	1	4	yes	—
26	C₉×C₄⋊C₄	—	2	8	no	—
27	C₉×C₄⋊C₄	—	2	2	no	—
28	C₉×C₄⋊C₄	—	2	4	no	—
29	C₉×C₄⋊C₄	—	4	4	no	—
30	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
31	C₄²×C₉	C₂×C₄	1	2	yes	—
32	C₄²×C₉	D₄	1	2	yes	—
33	#1992	C₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
35	C₃×#125	—	2	2	no	—
36	C₃×#125	C₃×C₄	1	4	yes	—
37	C₂×C₃×C₄⋊C₄	—	2	2	no	—
38	C₂×C₃×C₄⋊C₄	—	2	2	no	—
39	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
40	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
41	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
42	C₃×#97	—	2	2	no	—
43	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₉	—	2	2	no	—
45	C₂×C₄×C₉	—	2	2	no	—
46	C₂×C₄×C₉	—	2	4	no	—
47	C₂×C₄×C₉	—	4	2	no	—
48	C₂×C₄×C₉	—	4	2	no	—
49	C₂×C₄×C₉	—	4	2	no	—
50	C₂×C₄×C₉	—	4	4	no	—
51	C₂×C₄×C₉	C₂²⋊C₄	1	4	yes	—
52	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
55	C₂×C₄×C₉	#41	1	2	yes	—
56	C₈×C₉	—	2	4	no	—
57	C₂×#125	C₂×C₉	1	1	yes	characteristic
58	C₂×#97	C₂×C₉	1	1	yes	characteristic
59	#384	C₂×C₉	1	1	yes	characteristic
60	#340	C₂×C₉	1	4	yes	—
61	C₂²×C₃×C₄	—	2	2	no	—
62	C₂²×C₃×C₄	—	2	2	no	—
63	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
64	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
65	C₂×C₃×C₈	—	2	2	no	—
66	C₂×C₃×C₈	—	2	2	no	—
67	C₂×C₃×C₈	C₃×Q₈	1	4	yes	—
68	C₃×C₄⋊C₄	—	2	8	no	—
69	C₃×C₄⋊C₄	—	2	2	no	—
70	C₃×C₄⋊C₄	—	2	4	no	—
71	C₃×C₄⋊C₄	—	4	4	no	—
72	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
73	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
74	C₃×C₄²	C₃×D₄	1	2	yes	—
75	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₉	#124	1	1	yes	characteristic
77	C₂²×C₉	C₄⋊Q₈	1	1	yes	characteristic
78	C₂²×C₉	AGL(1,ℤ/8)	1	2	yes	—
79	C₂²×C₉	#137	1	2	yes	—
80	C₄×C₉	—	2	4	no	—
81	C₄×C₉	—	4	4	no	—
82	C₄×C₉	—	8	2	no	—
83	C₄×C₉	C₄×Q₈	1	2	yes	—
84	C₄×C₉	C₂²⋊Q₈	1	2	yes	—
85	C₂²×C₈	C₂²×C₉	1	2	yes	—
86	#125	—	2	2	no	—
87	#125	C₄×C₉	1	4	yes	complemented
88	C₂×C₄⋊C₄	—	2	2	no	—
89	C₂×C₄⋊C₄	—	2	2	no	—
90	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
91	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
92	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
93	#97	—	2	2	no	—
94	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
95	C₂×C₃×C₄	—	2	2	no	—
96	C₂×C₃×C₄	—	2	2	no	—
97	C₂×C₃×C₄	—	2	4	no	—
98	C₂×C₃×C₄	—	4	2	no	—
99	C₂×C₃×C₄	—	4	2	no	—
100	C₂×C₃×C₄	—	4	2	no	—
101	C₂×C₃×C₄	—	4	4	no	—
102	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	4	yes	—
103	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
106	C₂×C₃×C₄	C₃×#41	1	2	yes	—
107	C₃×C₈	—	2	4	no	—
108	C₂×C₉	#391	1	1	yes	characteristic
109	C₂×C₉	#417	1	2	yes	—
110	C₂×C₉	#490	1	1	yes	characteristic
111	C₂×C₉	#491	1	1	yes	characteristic
112	C₂×C₉	#501	1	2	yes	—
113	C₂²×C₄	—	2	2	no	—
114	C₂²×C₄	—	2	2	no	—
115	C₂²×C₄	D₄×C₉	1	2	yes	—
116	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	—	2	2	no	—
119	C₂×C₈	Q₈×C₉	1	4	yes	—
120	C₄⋊C₄	—	2	8	no	—
121	C₄⋊C₄	—	2	2	no	—
122	C₄⋊C₄	—	2	4	no	—
123	C₄⋊C₄	—	4	4	no	—
124	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	—
125	C₄²	C₂×C₄×C₉	1	2	yes	—
126	C₄²	D₄×C₉	1	2	yes	—
127	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×C₃	C₃×#124	1	1	yes	characteristic
129	C₂²×C₃	C₃×C₄⋊Q₈	1	1	yes	characteristic
130	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	2	yes	—
131	C₂²×C₃	C₃×#137	1	2	yes	—
132	C₃×C₄	—	2	4	no	—
133	C₃×C₄	—	4	4	no	—
134	C₃×C₄	—	8	2	no	—
135	C₃×C₄	C₃×C₄×Q₈	1	2	yes	—
136	C₃×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
137	C₉	#1992	1	1	yes	characteristic, direct product factor, Sylow
138	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
139	C₂×C₄	—	2	2	no	—
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	2	4	no	—
142	C₂×C₄	—	4	2	no	—
143	C₂×C₄	—	4	2	no	—
144	C₂×C₄	—	4	2	no	—
145	C₂×C₄	—	4	4	no	—
146	C₂×C₄	C₉×C₂²⋊C₄	1	4	yes	—
147	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
148	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
149	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
150	C₂×C₄	C₉×#41	1	2	yes	—
151	C₈	—	2	4	no	—
152	C₂×C₃	C₃×#391	1	1	yes	characteristic
153	C₂×C₃	C₃×#417	1	2	yes	—
154	C₂×C₃	C₃×#490	1	1	yes	characteristic
155	C₂×C₃	C₃×#491	1	1	yes	characteristic
156	C₂×C₃	C₃×#501	1	2	yes	—
157	C₂²	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
158	C₂²	C₉×#124	1	1	yes	characteristic
159	C₂²	C₉×C₄⋊Q₈	1	1	yes	characteristic
160	C₂²	C₉×AGL(1,ℤ/8)	1	2	yes	—
161	C₂²	C₉×#137	1	2	yes	—
162	C₄	—	2	4	no	—
163	C₄	—	4	4	no	—
164	C₄	—	8	2	no	—
165	C₄	C₄×Q₈×C₉	1	2	yes	—
166	C₄	C₉×C₂²⋊Q₈	1	2	yes	—
167	C₃	C₃×#1992	1	1	yes	characteristic
168	C₂	C₉×#391	1	1	yes	characteristic
169	C₂	C₉×#417	1	2	yes	—
170	C₂	C₉×#490	1	1	yes	characteristic
171	C₂	C₉×#491	1	1	yes	characteristic
172	C₂	C₉×#501	1	2	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle, prime radical	C₂³×C₃	C₂×C₃×D₄
LCS	G ▷ C₂×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
8. C₉×#125	C₄	semidirect
33. #1992	C₉	direct (N × H)
87. #125	C₄×C₉	semidirect
137. C₉	#1992	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×#125	2
C₂×C₉×#97	2
C₉×#384	2
C₉×#340	2
C₃×#1992	3

Subgroups — C9×#1992 #11766713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1992 #11766713