Subgroups — C₉×#1831 #11766552

Order 1152.

390 conjugacy classes of subgroups.

The subgroup lattice has 171 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₄⋊C₈	C₂	1	2	yes	maximal
2	C₄³×C₉	C₂	1	1	yes	maximal, characteristic
3	C₉×#336	C₂	1	4	yes	maximal
4	C₃×#1831	C₃	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₉	C₂²	1	4	yes	—
6	C₂×C₄²×C₉	C₄	1	2	yes	—
7	C₂×C₄²×C₉	C₄	1	1	yes	characteristic
8	C₂×C₄²×C₉	C₄	1	1	yes	characteristic
9	C₂×C₄²×C₉	C₂²	1	2	yes	—
10	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
11	C₉×C₄⋊C₈	—	2	4	no	—
12	C₂×C₃×C₄⋊C₈	C₂×C₃	1	2	yes	—
13	C₃×C₄³	C₂×C₃	1	1	yes	characteristic
14	C₃×#336	C₂×C₃	1	4	yes	—
15	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
20	C₂×C₈×C₉	—	2	4	no	—
21	C₂×C₈×C₉	—	2	8	no	—
22	C₄²×C₉	—	2	4	no	—
23	C₄²×C₉	—	2	2	no	—
24	C₄²×C₉	—	2	4	no	—
25	C₄²×C₉	C₈	1	4	yes	complemented
26	C₄²×C₉	D₄	1	2	yes	—
27	C₄²×C₉	Q₈	1	2	yes	—
28	#1831	C₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
30	C₂×C₃×C₄²	C₃×C₄	1	2	yes	—
31	C₂×C₃×C₄²	C₃×C₄	1	1	yes	characteristic
32	C₂×C₃×C₄²	C₃×C₄	1	1	yes	characteristic
33	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
34	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
35	C₃×C₄⋊C₈	—	2	4	no	—
36	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₉	—	2	2	no	—
38	C₂×C₄×C₉	—	2	2	no	—
39	C₂×C₄×C₉	—	2	2	no	—
40	C₂×C₄×C₉	—	2	2	no	—
41	C₂×C₄×C₉	—	2	2	no	—
42	C₂×C₄×C₉	C₄⋊C₄	1	2	yes	—
43	C₂×C₄×C₉	C₄⋊C₄	1	2	yes	—
44	C₂×C₄×C₉	C₂×C₈	1	4	yes	—
45	C₂×C₄×C₉	C₂×C₈	1	2	yes	—
46	C₂×C₄×C₉	M₁₆	1	4	yes	—
47	C₂×C₄×C₉	M₁₆	1	2	yes	—
48	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₉	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₄×C₉	#41	1	4	yes	—
51	C₈×C₉	—	4	4	no	—
52	C₂×C₄⋊C₈	C₂×C₉	1	2	yes	—
53	C₄³	C₂×C₉	1	1	yes	characteristic
54	#336	C₂×C₉	1	4	yes	—
55	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
56	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
57	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
58	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
59	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
60	C₂×C₃×C₈	—	2	4	no	—
61	C₂×C₃×C₈	—	2	8	no	—
62	C₃×C₄²	—	2	4	no	—
63	C₃×C₄²	—	2	2	no	—
64	C₃×C₄²	—	2	4	no	—
65	C₃×C₄²	C₃×C₈	1	4	yes	—
66	C₃×C₄²	C₃×D₄	1	2	yes	—
67	C₃×C₄²	C₃×Q₈	1	2	yes	—
68	C₂²×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
69	C₂²×C₉	#117	1	2	yes	—
70	C₂²×C₉	C₂²×C₈	1	1	yes	characteristic
71	C₂²×C₉	C₂×M₁₆	1	1	yes	characteristic
72	C₂²×C₉	C₂×M₁₆	1	2	yes	—
73	C₄×C₉	—	2	2	no	—
74	C₄×C₉	—	2	4	no	—
75	C₄×C₉	—	2	4	no	—
76	C₄×C₉	C₄⋊C₈	1	4	yes	—
77	C₄×C₉	#124	1	2	yes	—
78	C₄×C₉	#125	1	2	yes	—
79	C₂²×C₈	C₂²×C₉	1	4	yes	—
80	C₂×C₄²	C₄×C₉	1	2	yes	—
81	C₂×C₄²	C₄×C₉	1	1	yes	characteristic
82	C₂×C₄²	C₄×C₉	1	1	yes	characteristic
83	C₂×C₄²	C₂²×C₉	1	2	yes	—
84	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
85	C₄⋊C₈	—	2	4	no	—
86	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
87	C₂×C₃×C₄	—	2	2	no	—
88	C₂×C₃×C₄	—	2	2	no	—
89	C₂×C₃×C₄	—	2	2	no	—
90	C₂×C₃×C₄	—	2	2	no	—
91	C₂×C₃×C₄	—	2	2	no	—
92	C₂×C₃×C₄	C₃×C₄⋊C₄	1	2	yes	—
93	C₂×C₃×C₄	C₃×C₄⋊C₄	1	2	yes	—
94	C₂×C₃×C₄	C₂×C₃×C₈	1	4	yes	—
95	C₂×C₃×C₄	C₂×C₃×C₈	1	2	yes	—
96	C₂×C₃×C₄	C₃×M₁₆	1	4	yes	—
97	C₂×C₃×C₄	C₃×M₁₆	1	2	yes	—
98	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
100	C₂×C₃×C₄	C₃×#41	1	4	yes	—
101	C₃×C₈	—	4	4	no	—
102	C₂×C₉	#382	1	1	yes	characteristic
103	C₂×C₉	C₂×C₄⋊C₈	1	1	yes	characteristic
104	C₂×C₉	#423	1	1	yes	characteristic
105	C₂×C₉	#431	1	2	yes	—
106	C₂×C₉	#432	1	2	yes	—
107	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
108	C₂²×C₄	C₂×C₄×C₉	1	2	yes	—
109	C₂²×C₄	C₂×C₄×C₉	1	2	yes	—
110	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
111	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
112	C₂×C₈	—	2	4	no	—
113	C₂×C₈	—	2	8	no	—
114	C₄²	—	2	4	no	—
115	C₄²	—	2	2	no	—
116	C₄²	—	2	4	no	—
117	C₄²	C₈×C₉	1	4	yes	complemented
118	C₄²	D₄×C₉	1	2	yes	—
119	C₄²	Q₈×C₉	1	2	yes	—
120	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
121	C₂²×C₃	C₃×#117	1	2	yes	—
122	C₂²×C₃	C₂²×C₃×C₈	1	1	yes	characteristic
123	C₂²×C₃	C₂×C₃×M₁₆	1	1	yes	characteristic
124	C₂²×C₃	C₂×C₃×M₁₆	1	2	yes	—
125	C₃×C₄	—	2	2	no	—
126	C₃×C₄	—	2	4	no	—
127	C₃×C₄	—	2	4	no	—
128	C₃×C₄	C₃×C₄⋊C₈	1	4	yes	—
129	C₃×C₄	C₃×#124	1	2	yes	—
130	C₃×C₄	C₃×#125	1	2	yes	—
131	C₉	#1831	1	1	yes	characteristic, direct product factor, Sylow
132	C₂³	C₂²×C₄×C₉	1	1	yes	characteristic
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	—	2	2	no	—
138	C₂×C₄	C₉×C₄⋊C₄	1	2	yes	—
139	C₂×C₄	C₉×C₄⋊C₄	1	2	yes	—
140	C₂×C₄	C₂×C₈×C₉	1	4	yes	—
141	C₂×C₄	C₂×C₈×C₉	1	2	yes	—
142	C₂×C₄	C₉×M₁₆	1	4	yes	—
143	C₂×C₄	C₉×M₁₆	1	2	yes	—
144	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
145	C₂×C₄	C₂×Q₈×C₉	1	1	yes	characteristic
146	C₂×C₄	C₉×#41	1	4	yes	—
147	C₈	—	4	4	no	—
148	C₂×C₃	C₃×#382	1	1	yes	characteristic
149	C₂×C₃	C₂×C₃×C₄⋊C₈	1	1	yes	characteristic
150	C₂×C₃	C₃×#423	1	1	yes	characteristic
151	C₂×C₃	C₃×#431	1	2	yes	—
152	C₂×C₃	C₃×#432	1	2	yes	—
153	C₂²	C₂×C₉×C₄⋊C₄	1	1	yes	characteristic
154	C₂²	C₉×#117	1	2	yes	—
155	C₂²	C₂²×C₈×C₉	1	1	yes	characteristic
156	C₂²	C₂×C₉×M₁₆	1	1	yes	characteristic
157	C₂²	C₂×C₉×M₁₆	1	2	yes	—
158	C₄	—	2	2	no	—
159	C₄	—	2	4	no	—
160	C₄	—	2	4	no	—
161	C₄	C₉×C₄⋊C₈	1	4	yes	—
162	C₄	C₉×#124	1	2	yes	—
163	C₄	C₉×#125	1	2	yes	—
164	C₃	C₃×#1831	1	1	yes	characteristic
165	C₂	C₉×#382	1	1	yes	characteristic
166	C₂	C₂×C₉×C₄⋊C₈	1	1	yes	characteristic
167	C₂	C₉×#423	1	1	yes	characteristic
168	C₂	C₉×#431	1	2	yes	—
169	C₂	C₉×#432	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₉	C₂³
commutator	C₂²	C₂²×C₈×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle, prime radical	C₂³×C₃	C₂²×C₃×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
25. C₄²×C₉	C₈	semidirect
28. #1831	C₉	direct (N × H)
117. C₄²	C₈×C₉	semidirect
131. C₉	#1831	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×C₄⋊C₈	2
C₄³×C₉	2
C₉×#336	2
C₃×#1831	3

Subgroups — C9×#1831 #11766552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1831 #11766552