Subgroups — C₉×#2371 #11767092

Order 1152.

672 conjugacy classes of subgroups.

The subgroup lattice has 165 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	C₉×#387	C₂	1	4	yes	maximal
3	C₉×#387	C₂	1	4	yes	maximal
4	C₄×C₉×C₄⋊C₄	C₂	1	4	yes	maximal
5	C₉×#376	C₂	1	2	yes	maximal
6	C₃×#2371	C₃	1	1	yes	maximal, characteristic
7	C₉×#125	C₄	1	8	yes	complemented
8	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
9	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
10	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₄²×C₉	C₂²	1	4	yes	—
12	C₂×C₄²×C₉	C₂²	1	4	yes	—
13	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
14	C₉×#95	C₂²	1	2	yes	—
15	C₉×#95	C₂²	1	2	yes	—
16	C₉×#95	C₂²	1	4	yes	—
17	C₉×#95	C₂²	1	4	yes	—
18	C₉×#95	C₂²	1	4	yes	—
19	C₂×C₃×#125	C₂×C₃	1	1	yes	characteristic
20	C₃×#387	C₂×C₃	1	4	yes	—
21	C₃×#387	C₂×C₃	1	4	yes	—
22	C₃×C₄×C₄⋊C₄	C₂×C₃	1	4	yes	—
23	C₃×#376	C₂×C₃	1	2	yes	—
24	C₂²×C₄×C₉	C₂³	1	4	yes	—
25	C₂²×C₄×C₉	C₂³	1	2	yes	—
26	C₂²×C₄×C₉	C₂³	1	4	yes	—
27	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₉	C₂³	1	4	yes	—
29	C₉×C₄⋊C₄	—	2	8	no	—
30	C₉×C₄⋊C₄	C₂×C₄	1	16	yes	—
31	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	—
32	C₄²×C₉	—	2	8	no	—
33	C₄²×C₉	—	2	8	no	—
34	C₄²×C₉	C₂×C₄	1	4	yes	—
35	#2371	C₉	1	1	yes	characteristic, direct product factor, Sylow
36	C₃×#125	C₃×C₄	1	8	yes	—
37	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
38	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
39	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
40	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
41	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
42	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
43	C₃×#95	C₂²×C₃	1	2	yes	—
44	C₃×#95	C₂²×C₃	1	2	yes	—
45	C₃×#95	C₂²×C₃	1	4	yes	—
46	C₃×#95	C₂²×C₃	1	4	yes	—
47	C₃×#95	C₂²×C₃	1	4	yes	—
48	C₂³×C₉	C₂⁴	1	1	yes	characteristic
49	C₂×C₄×C₉	—	2	4	no	—
50	C₂×C₄×C₉	—	2	4	no	—
51	C₂×C₄×C₉	—	2	4	no	—
52	C₂×C₄×C₉	—	2	4	no	—
53	C₂×C₄×C₉	—	2	2	no	—
54	C₂×C₄×C₉	—	2	4	no	—
55	C₂×C₄×C₉	—	2	4	no	—
56	C₂×C₄×C₉	—	2	4	no	—
57	C₂×C₄×C₉	—	2	4	no	—
58	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
59	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
60	C₂×C₄×C₉	C₂²×C₄	1	8	yes	—
61	C₂×C₄×C₉	#41	1	8	yes	—
62	C₂×#125	C₂×C₉	1	1	yes	characteristic
63	#387	C₂×C₉	1	4	yes	—
64	#387	C₂×C₉	1	4	yes	—
65	C₄×C₄⋊C₄	C₂×C₉	1	4	yes	—
66	#376	C₂×C₉	1	2	yes	—
67	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
68	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
69	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
70	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
71	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
72	C₃×C₄⋊C₄	—	2	8	no	—
73	C₃×C₄⋊C₄	C₂×C₃×C₄	1	16	yes	—
74	C₃×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
75	C₃×C₄²	—	2	8	no	—
76	C₃×C₄²	—	2	8	no	—
77	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
78	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
79	C₂²×C₉	C₂×#41	1	4	yes	—
80	C₂²×C₉	2₋¹⁺⁴	1	2	yes	—
81	C₄×C₉	—	2	4	no	—
82	C₄×C₉	—	2	8	no	—
83	C₄×C₉	—	2	2	no	—
84	C₄×C₉	—	2	8	no	—
85	C₄×C₉	—	4	4	no	—
86	#125	C₄×C₉	1	8	yes	complemented
87	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
88	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
89	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
90	C₂×C₄²	C₂²×C₉	1	4	yes	—
91	C₂×C₄²	C₂²×C₉	1	4	yes	—
92	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
93	#95	C₂²×C₉	1	2	yes	—
94	#95	C₂²×C₉	1	2	yes	—
95	#95	C₂²×C₉	1	4	yes	—
96	#95	C₂²×C₉	1	4	yes	—
97	#95	C₂²×C₉	1	4	yes	—
98	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
99	C₂×C₃×C₄	—	2	4	no	—
100	C₂×C₃×C₄	—	2	4	no	—
101	C₂×C₃×C₄	—	2	4	no	—
102	C₂×C₃×C₄	—	2	4	no	—
103	C₂×C₃×C₄	—	2	2	no	—
104	C₂×C₃×C₄	—	2	4	no	—
105	C₂×C₃×C₄	—	2	4	no	—
106	C₂×C₃×C₄	—	2	4	no	—
107	C₂×C₃×C₄	—	2	4	no	—
108	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
109	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
110	C₂×C₃×C₄	C₂²×C₃×C₄	1	8	yes	—
111	C₂×C₃×C₄	C₃×#41	1	8	yes	—
112	C₂×C₉	C₄×#41	1	2	yes	—
113	C₂×C₉	#519	1	1	yes	characteristic
114	C₂×C₉	#552	1	4	yes	—
115	C₂²×C₄	C₂³×C₉	1	4	yes	—
116	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
117	C₂²×C₄	C₂³×C₉	1	2	yes	—
118	C₂²×C₄	C₂³×C₉	1	4	yes	—
119	C₂²×C₄	C₂³×C₉	1	4	yes	—
120	C₄⋊C₄	—	2	8	no	—
121	C₄⋊C₄	C₂×C₄×C₉	1	16	yes	—
122	C₄⋊C₄	C₂×C₄×C₉	1	8	yes	—
123	C₄²	—	2	8	no	—
124	C₄²	—	2	8	no	—
125	C₄²	C₂×C₄×C₉	1	4	yes	—
126	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
127	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
128	C₂²×C₃	C₃×2₋¹⁺⁴	1	2	yes	—
129	C₃×C₄	—	2	4	no	—
130	C₃×C₄	—	2	8	no	—
131	C₃×C₄	—	2	2	no	—
132	C₃×C₄	—	2	8	no	—
133	C₃×C₄	—	4	4	no	—
134	C₉	#2371	1	1	yes	characteristic, direct product factor, Sylow
135	C₂³	C₂⁴×C₉	1	1	yes	characteristic
136	C₂×C₄	—	2	4	no	—
137	C₂×C₄	—	2	4	no	—
138	C₂×C₄	—	2	4	no	—
139	C₂×C₄	—	2	4	no	—
140	C₂×C₄	—	2	4	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	4	no	—
143	C₂×C₄	—	2	4	no	—
144	C₂×C₄	—	2	4	no	—
145	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
146	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
147	C₂×C₄	C₂²×C₄×C₉	1	8	yes	—
148	C₂×C₄	C₉×#41	1	8	yes	—
149	C₂×C₃	C₃×C₄×#41	1	2	yes	—
150	C₂×C₃	C₃×#519	1	1	yes	characteristic
151	C₂×C₃	C₃×#552	1	4	yes	—
152	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
153	C₂²	C₂×C₉×#41	1	4	yes	—
154	C₂²	C₉×2₋¹⁺⁴	1	2	yes	—
155	C₄	—	2	8	no	—
156	C₄	—	2	4	no	—
157	C₄	—	2	8	no	—
158	C₄	—	2	2	no	—
159	C₄	—	4	4	no	—
160	C₃	C₃×#2371	1	1	yes	characteristic
161	C₂	C₄×C₉×#41	1	2	yes	—
162	C₂	C₉×#519	1	1	yes	characteristic
163	C₂	C₉×#552	1	4	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₉
Frattini, socle, prime radical, cosocle	C₂³×C₃	C₂⁴×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₉×#125	C₄	semidirect
35. #2371	C₉	direct (N × H)
86. #125	C₄×C₉	semidirect
134. C₉	#2371	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
C₉×#387	2
C₄×C₉×C₄⋊C₄	2
C₉×#376	2
C₃×#2371	3

Subgroups — C9×#2371 #11767092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2371 #11767092