Subgroups — C₉×#2983 #11767704

Order 1152.

534 conjugacy classes of subgroups.

The subgroup lattice has 180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₉×#446	C₂	1	8	yes	maximal, complemented
3	C₉×#432	C₂	1	4	yes	maximal
4	C₉×#431	C₂	1	2	yes	maximal
5	C₃×#2983	C₃	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₉	C₄	1	1	yes	characteristic
7	C₄×Q₈×C₉	C₄	1	4	yes	—
8	C₄×Q₈×C₉	C₂²	1	4	yes	—
9	C₂×C₉×C₄⋊C₄	C₄	1	2	yes	—
10	C₂×C₉×C₄⋊C₄	C₄	1	1	yes	characteristic
11	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₉	C₂²	1	2	yes	—
13	C₉×C₄⋊C₈	C₂²	1	4	yes	—
14	C₉×C₄⋊C₈	C₂²	1	8	yes	—
15	C₉×C₂²⋊C₈	C₂²	1	4	yes	—
16	C₉×#97	C₂²	1	8	yes	—
17	C₄×C₈×C₉	C₂²	1	4	yes	—
18	C₂×C₃×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
19	C₃×#446	C₂×C₃	1	8	yes	—
20	C₃×#432	C₂×C₃	1	4	yes	—
21	C₃×#431	C₂×C₃	1	2	yes	—
22	C₂×Q₈×C₉	—	2	4	no	—
23	C₂×Q₈×C₉	C₂×C₄	1	4	yes	—
24	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
27	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
29	C₂×C₈×C₉	C₂³	1	8	yes	—
30	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	—
31	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
32	C₄²×C₉	C₂×C₄	1	4	yes	—
33	C₄²×C₉	C₂×C₄	1	2	yes	—
34	C₄²×C₉	C₂³	1	2	yes	—
35	C₄²×C₉	C₂³	1	4	yes	—
36	#2983	C₉	1	1	yes	characteristic, direct product factor, Sylow
37	C₂²×C₃×Q₈	C₃×C₄	1	1	yes	characteristic
38	C₃×C₄×Q₈	C₃×C₄	1	4	yes	—
39	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
40	C₂×C₃×C₄⋊C₄	C₃×C₄	1	2	yes	—
41	C₂×C₃×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
42	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
43	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
44	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	—
45	C₃×C₄⋊C₈	C₂²×C₃	1	8	yes	—
46	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
47	C₃×#97	C₂²×C₃	1	8	yes	—
48	C₃×C₄×C₈	C₂²×C₃	1	4	yes	—
49	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
50	Q₈×C₉	—	2	8	no	—
51	C₂×C₄×C₉	—	2	4	no	—
52	C₂×C₄×C₉	—	2	2	no	—
53	C₂×C₄×C₉	—	4	1	no	—
54	C₂×C₄×C₉	—	4	2	no	—
55	C₂×C₄×C₉	M₁₆	1	4	yes	—
56	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
58	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
59	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
60	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
61	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
62	C₈×C₉	—	2	8	no	—
63	C₂×C₄×Q₈	C₂×C₉	1	1	yes	characteristic
64	#446	C₂×C₉	1	8	yes	complemented
65	#432	C₂×C₉	1	4	yes	—
66	#431	C₂×C₉	1	2	yes	—
67	C₂×C₃×Q₈	—	2	4	no	—
68	C₂×C₃×Q₈	C₂×C₃×C₄	1	4	yes	—
69	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
70	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
71	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
72	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
73	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
74	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
75	C₃×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
76	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
77	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
78	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
79	C₃×C₄²	C₂³×C₃	1	2	yes	—
80	C₃×C₄²	C₂³×C₃	1	4	yes	—
81	C₂²×C₉	—	2	1	no	—
82	C₂²×C₉	—	2	1	no	—
83	C₂²×C₉	C₂×M₁₆	1	2	yes	—
84	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
85	C₄×C₉	—	2	1	no	—
86	C₄×C₉	—	2	4	no	—
87	C₄×C₉	—	2	2	no	—
88	C₄×C₉	—	2	4	no	—
89	C₄×C₉	C₂×M₁₆	1	4	yes	—
90	C₄×C₉	2₋¹⁺⁴	1	2	yes	—
91	C₂²×Q₈	C₄×C₉	1	1	yes	characteristic
92	C₄×Q₈	C₄×C₉	1	4	yes	—
93	C₄×Q₈	C₂²×C₉	1	4	yes	—
94	C₂×C₄⋊C₄	C₄×C₉	1	2	yes	—
95	C₂×C₄⋊C₄	C₄×C₉	1	1	yes	characteristic
96	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
97	C₂×C₄²	C₂²×C₉	1	2	yes	—
98	C₄⋊C₈	C₂²×C₉	1	4	yes	—
99	C₄⋊C₈	C₂²×C₉	1	8	yes	—
100	C₂²⋊C₈	C₂²×C₉	1	4	yes	—
101	#97	C₂²×C₉	1	8	yes	—
102	C₄×C₈	C₂²×C₉	1	4	yes	—
103	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
104	C₃×Q₈	—	2	8	no	—
105	C₂×C₃×C₄	—	2	4	no	—
106	C₂×C₃×C₄	—	2	2	no	—
107	C₂×C₃×C₄	—	4	1	no	—
108	C₂×C₃×C₄	—	4	2	no	—
109	C₂×C₃×C₄	C₃×M₁₆	1	4	yes	—
110	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
112	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
113	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
114	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
115	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
116	C₃×C₈	—	2	8	no	—
117	C₂×C₉	—	2	2	no	—
118	C₂×C₉	#519	1	1	yes	characteristic
119	C₂×C₉	C₂²×M₁₆	1	1	yes	characteristic
120	C₂×C₉	#568	1	1	yes	characteristic
121	C₂×Q₈	—	2	4	no	—
122	C₂×Q₈	C₂×C₄×C₉	1	4	yes	—
123	C₂²×C₄	C₂×C₄×C₉	1	2	yes	—
124	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
125	C₂²×C₄	C₂×C₄×C₉	1	2	yes	—
126	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
127	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
128	C₂×C₈	C₂³×C₉	1	8	yes	—
129	C₄⋊C₄	C₂×C₄×C₉	1	8	yes	—
130	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	—
131	C₄²	C₂×C₄×C₉	1	4	yes	—
132	C₄²	C₂×C₄×C₉	1	2	yes	—
133	C₄²	C₂³×C₉	1	2	yes	—
134	C₄²	C₂³×C₉	1	4	yes	—
135	C₂²×C₃	—	2	1	no	—
136	C₂²×C₃	—	2	1	no	—
137	C₂²×C₃	C₂×C₃×M₁₆	1	2	yes	—
138	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
139	C₃×C₄	—	2	4	no	—
140	C₃×C₄	—	2	2	no	—
141	C₃×C₄	—	2	4	no	—
142	C₃×C₄	—	2	1	no	—
143	C₃×C₄	C₂×C₃×M₁₆	1	4	yes	—
144	C₃×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
145	C₉	#2983	1	1	yes	characteristic, direct product factor, Sylow
146	C₂³	C₂²×C₄×C₉	1	1	yes	characteristic
147	Q₈	—	2	8	no	—
148	C₂×C₄	—	2	4	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	4	1	no	—
151	C₂×C₄	—	4	2	no	—
152	C₂×C₄	C₉×M₁₆	1	4	yes	—
153	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
154	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
155	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
156	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
157	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
158	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
159	C₈	—	2	8	no	—
160	C₂×C₃	—	2	2	no	—
161	C₂×C₃	C₃×#519	1	1	yes	characteristic
162	C₂×C₃	C₂²×C₃×M₁₆	1	1	yes	characteristic
163	C₂×C₃	C₃×#568	1	1	yes	characteristic
164	C₂²	—	2	1	no	—
165	C₂²	—	2	1	no	—
166	C₂²	C₂×C₉×M₁₆	1	2	yes	—
167	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
168	C₄	—	2	4	no	—
169	C₄	—	2	2	no	—
170	C₄	—	2	4	no	—
171	C₄	—	2	1	no	—
172	C₄	C₂×C₉×M₁₆	1	4	yes	—
173	C₄	C₉×2₋¹⁺⁴	1	2	yes	—
174	C₃	C₃×#2983	1	1	yes	characteristic
175	C₂	—	2	2	no	—
176	C₂	C₉×#519	1	1	yes	characteristic
177	C₂	C₂²×C₉×M₁₆	1	1	yes	characteristic
178	C₂	C₉×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂³×C₃×C₄
prime radical	C₂³×C₃	C₂²×C₃×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×#446	C₂	semidirect
36. #2983	C₉	direct (N × H)
64. #446	C₂×C₉	semidirect
145. C₉	#2983	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×C₄×Q₈×C₉	2
C₉×#446	2
C₉×#432	2
C₉×#431	2
C₃×#2983	3

Subgroups — C9×#2983 #11767704

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2983 #11767704