Subgroups — C₉×#2382 #11767103

Order 1152.

612 conjugacy classes of subgroups.

The subgroup lattice has 186 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×#389	C₂	1	4	yes	maximal
3	C₉×#387	C₂	1	4	yes	maximal
4	C₉×#387	C₂	1	4	yes	maximal
5	C₉×#382	C₂	1	2	yes	maximal
6	C₃×#2382	C₃	1	1	yes	maximal, characteristic
7	C₉×#125	C₄	1	8	yes	complemented
8	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
11	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
13	C₂×C₄²×C₉	C₂²	1	4	yes	—
14	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
15	C₉×#95	C₂²	1	4	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×#389	C₂×C₃	1	4	yes	—
21	C₃×#387	C₂×C₃	1	4	yes	—
22	C₃×#387	C₂×C₃	1	4	yes	—
23	C₃×#382	C₂×C₃	1	2	yes	—
24	C₂²×C₄×C₉	C₂³	1	4	yes	—
25	C₂²×C₄×C₉	C₂³	1	4	yes	—
26	C₂²×C₄×C₉	C₂³	1	4	yes	—
27	C₂²×C₄×C₉	C₂³	1	2	yes	—
28	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
29	C₉×C₄⋊C₄	—	4	4	no	—
30	C₉×C₄⋊C₄	—	4	2	no	—
31	C₉×C₄⋊C₄	—	4	2	no	—
32	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	—
33	C₉×C₄⋊C₄	C₂×C₄	1	16	yes	—
34	C₄²×C₉	—	4	4	no	—
35	C₄²×C₉	C₂×C₄	1	4	yes	—
36	#2382	C₉	1	1	yes	characteristic, direct product factor, Sylow
37	C₃×#125	C₃×C₄	1	8	yes	—
38	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
39	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
40	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
41	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
42	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
43	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
44	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
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	C₃×#95	C₂²×C₃	1	4	yes	—
49	C₂³×C₉	C₂⁴	1	1	yes	characteristic
50	C₂×C₄×C₉	—	2	4	no	—
51	C₂×C₄×C₉	—	2	2	no	—
52	C₂×C₄×C₉	—	2	1	no	—
53	C₂×C₄×C₉	—	2	1	no	—
54	C₂×C₄×C₉	—	2	4	no	—
55	C₂×C₄×C₉	—	2	2	no	—
56	C₂×C₄×C₉	—	2	4	no	—
57	C₂×C₄×C₉	—	2	4	no	—
58	C₂×C₄×C₉	—	2	4	no	—
59	C₂×C₄×C₉	—	2	4	no	—
60	C₂×C₄×C₉	—	2	4	no	—
61	C₂×C₄×C₉	—	2	4	no	—
62	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
63	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
64	C₂×C₄×C₉	C₂²×C₄	1	8	yes	—
65	C₂×#125	C₂×C₉	1	1	yes	characteristic
66	#389	C₂×C₉	1	4	yes	—
67	#387	C₂×C₉	1	4	yes	—
68	#387	C₂×C₉	1	4	yes	—
69	#382	C₂×C₉	1	2	yes	—
70	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
71	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
72	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
73	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
74	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
75	C₃×C₄⋊C₄	—	4	4	no	—
76	C₃×C₄⋊C₄	—	4	2	no	—
77	C₃×C₄⋊C₄	—	4	2	no	—
78	C₃×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
79	C₃×C₄⋊C₄	C₂×C₃×C₄	1	16	yes	—
80	C₃×C₄²	—	4	4	no	—
81	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
82	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
83	C₂²×C₉	H(5,𝔽₂)	1	2	yes	—
84	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
85	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
86	C₂²×C₉	2₋¹⁺⁴	1	2	yes	—
87	C₄×C₉	—	2	2	no	—
88	C₄×C₉	—	2	8	no	—
89	C₄×C₉	—	2	4	no	—
90	C₄×C₉	—	4	4	no	—
91	C₄×C₉	—	4	4	no	—
92	#125	C₄×C₉	1	8	yes	complemented
93	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
94	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
95	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
96	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
97	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
98	C₂×C₄²	C₂²×C₉	1	4	yes	—
99	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
100	#95	C₂²×C₉	1	4	yes	—
101	#95	C₂²×C₉	1	4	yes	—
102	#95	C₂²×C₉	1	4	yes	—
103	#95	C₂²×C₉	1	4	yes	—
104	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
105	C₂×C₃×C₄	—	2	4	no	—
106	C₂×C₃×C₄	—	2	2	no	—
107	C₂×C₃×C₄	—	2	1	no	—
108	C₂×C₃×C₄	—	2	1	no	—
109	C₂×C₃×C₄	—	2	4	no	—
110	C₂×C₃×C₄	—	2	2	no	—
111	C₂×C₃×C₄	—	2	4	no	—
112	C₂×C₃×C₄	—	2	4	no	—
113	C₂×C₃×C₄	—	2	4	no	—
114	C₂×C₃×C₄	—	2	4	no	—
115	C₂×C₃×C₄	—	2	4	no	—
116	C₂×C₃×C₄	—	2	4	no	—
117	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
118	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
119	C₂×C₃×C₄	C₂²×C₃×C₄	1	8	yes	—
120	C₂×C₉	#519	1	1	yes	characteristic
121	C₂×C₉	#520	1	2	yes	—
122	C₂×C₉	#562	1	1	yes	characteristic
123	C₂×C₉	#563	1	2	yes	—
124	C₂×C₉	#564	1	1	yes	characteristic
125	C₂²×C₄	C₂³×C₉	1	4	yes	—
126	C₂²×C₄	C₂³×C₉	1	4	yes	—
127	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
128	C₂²×C₄	C₂³×C₉	1	4	yes	—
129	C₂²×C₄	C₂³×C₉	1	2	yes	—
130	C₄⋊C₄	—	4	4	no	—
131	C₄⋊C₄	—	4	2	no	—
132	C₄⋊C₄	—	4	2	no	—
133	C₄⋊C₄	C₂×C₄×C₉	1	8	yes	—
134	C₄⋊C₄	C₂×C₄×C₉	1	16	yes	—
135	C₄²	—	4	4	no	—
136	C₄²	C₂×C₄×C₉	1	4	yes	—
137	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
138	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
139	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
140	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
141	C₂²×C₃	C₃×2₋¹⁺⁴	1	2	yes	—
142	C₃×C₄	—	2	2	no	—
143	C₃×C₄	—	2	8	no	—
144	C₃×C₄	—	2	4	no	—
145	C₃×C₄	—	4	4	no	—
146	C₃×C₄	—	4	4	no	—
147	C₉	#2382	1	1	yes	characteristic, direct product factor, Sylow
148	C₂³	C₂⁴×C₉	1	1	yes	characteristic
149	C₂×C₄	—	2	4	no	—
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	2	4	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	1	no	—
154	C₂×C₄	—	2	1	no	—
155	C₂×C₄	—	2	4	no	—
156	C₂×C₄	—	2	4	no	—
157	C₂×C₄	—	2	4	no	—
158	C₂×C₄	—	2	4	no	—
159	C₂×C₄	—	2	4	no	—
160	C₂×C₄	—	2	4	no	—
161	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
162	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
163	C₂×C₄	C₂²×C₄×C₉	1	8	yes	—
164	C₂×C₃	C₃×#519	1	1	yes	characteristic
165	C₂×C₃	C₃×#520	1	2	yes	—
166	C₂×C₃	C₃×#562	1	1	yes	characteristic
167	C₂×C₃	C₃×#563	1	2	yes	—
168	C₂×C₃	C₃×#564	1	1	yes	characteristic
169	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
170	C₂²	C₉×H(5,𝔽₂)	1	2	yes	—
171	C₂²	C₉×2₋¹⁺⁴	1	2	yes	—
172	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
173	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
174	C₄	—	2	8	no	—
175	C₄	—	2	4	no	—
176	C₄	—	2	2	no	—
177	C₄	—	4	4	no	—
178	C₄	—	4	4	no	—
179	C₃	C₃×#2382	1	1	yes	characteristic
180	C₂	C₉×#519	1	1	yes	characteristic
181	C₂	C₉×#520	1	2	yes	—
182	C₂	C₉×#562	1	1	yes	characteristic
183	C₂	C₉×#563	1	2	yes	—
184	C₂	C₉×#564	1	1	yes	characteristic

	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
36. #2382	C₉	direct (N × H)
92. #125	C₄×C₉	semidirect
147. C₉	#2382	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×#389	2
C₉×#387	2
C₉×#382	2
C₃×#2382	3

Subgroups — C9×#2382 #11767103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2382 #11767103