Subgroups — C₉×#2327 #11767048

Order 1152.

774 conjugacy classes of subgroups.

The subgroup lattice has 201 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈×C₉	C₂	1	2	yes	maximal
3	C₉×#391	C₂	1	2	yes	maximal
4	C₉×#387	C₂	1	8	yes	maximal
5	C₉×#382	C₂	1	1	yes	maximal, characteristic
6	C₉×#376	C₂	1	1	yes	maximal, characteristic
7	C₃×#2327	C₃	1	1	yes	maximal, characteristic
8	C₂²×Q₈×C₉	C₂²	1	2	yes	—
9	C₉×C₄⋊Q₈	C₄	1	8	yes	complemented
10	C₄×Q₈×C₉	—	2	8	no	—
11	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
13	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
14	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₉	C₂²	1	4	yes	—
16	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
18	C₉×#95	C₂²	1	4	yes	—
19	C₉×#95	C₂²	1	4	yes	—
20	C₉×#95	C₂²	1	8	yes	—
21	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
22	C₂×C₃×C₄×Q₈	C₂×C₃	1	2	yes	—
23	C₃×#391	C₂×C₃	1	2	yes	—
24	C₃×#387	C₂×C₃	1	8	yes	—
25	C₃×#382	C₂×C₃	1	1	yes	characteristic
26	C₃×#376	C₂×C₃	1	1	yes	characteristic
27	C₂×Q₈×C₉	—	2	4	no	—
28	C₂×Q₈×C₉	—	2	4	no	—
29	C₂×Q₈×C₉	C₂×C₄	1	8	yes	—
30	C₂²×C₄×C₉	C₂³	1	4	yes	—
31	C₂²×C₄×C₉	C₂³	1	2	yes	—
32	C₂²×C₄×C₉	C₂³	1	4	yes	—
33	C₂²×C₄×C₉	C₂³	1	2	yes	—
34	C₂²×C₄×C₉	C₂³	1	2	yes	—
35	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
36	C₉×C₄⋊C₄	—	2	8	no	—
37	C₉×C₄⋊C₄	—	2	4	no	—
38	C₉×C₄⋊C₄	C₂×C₄	1	16	yes	—
39	C₄²×C₉	—	2	8	no	—
40	C₄²×C₉	—	2	2	no	—
41	C₄²×C₉	C₂×C₄	1	4	yes	—
42	C₄²×C₉	D₄	1	4	yes	—
43	#2327	C₉	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
45	C₃×C₄⋊Q₈	C₃×C₄	1	8	yes	—
46	C₃×C₄×Q₈	—	2	8	no	—
47	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
48	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
49	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
50	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
51	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
52	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
53	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
54	C₃×#95	C₂²×C₃	1	4	yes	—
55	C₃×#95	C₂²×C₃	1	4	yes	—
56	C₃×#95	C₂²×C₃	1	8	yes	—
57	C₂³×C₉	C₂⁴	1	1	yes	characteristic
58	Q₈×C₉	—	2	16	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	—	2	4	no	—
63	C₂×C₄×C₉	—	2	4	no	—
64	C₂×C₄×C₉	—	2	2	no	—
65	C₂×C₄×C₉	—	2	8	no	—
66	C₂×C₄×C₉	—	2	4	no	—
67	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
68	C₂×C₄×C₉	C₂²×C₄	1	8	yes	—
69	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
70	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
71	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
72	C₂×C₄×C₉	#41	1	2	yes	—
73	C₂×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic
74	C₂×C₄×Q₈	C₂×C₉	1	2	yes	—
75	#391	C₂×C₉	1	2	yes	—
76	#387	C₂×C₉	1	8	yes	—
77	#382	C₂×C₉	1	1	yes	characteristic
78	#376	C₂×C₉	1	1	yes	characteristic
79	C₂×C₃×Q₈	—	2	4	no	—
80	C₂×C₃×Q₈	—	2	4	no	—
81	C₂×C₃×Q₈	C₂×C₃×C₄	1	8	yes	—
82	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
83	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
84	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
85	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
86	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
87	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
88	C₃×C₄⋊C₄	—	2	8	no	—
89	C₃×C₄⋊C₄	—	2	4	no	—
90	C₃×C₄⋊C₄	C₂×C₃×C₄	1	16	yes	—
91	C₃×C₄²	—	2	8	no	—
92	C₃×C₄²	—	2	2	no	—
93	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
94	C₃×C₄²	C₃×D₄	1	4	yes	—
95	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
96	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
97	C₂²×C₉	C₂×#41	1	1	yes	characteristic
98	C₂²×C₉	2₋¹⁺⁴	1	4	yes	—
99	C₄×C₉	—	2	8	no	—
100	C₄×C₉	—	2	4	no	—
101	C₄×C₉	—	2	4	no	—
102	C₄×C₉	—	4	4	no	—
103	C₄×C₉	—	4	2	no	—
104	C₄×C₉	C₄×D₄	1	4	yes	—
105	C₂²×Q₈	C₂²×C₉	1	2	yes	—
106	C₄⋊Q₈	C₄×C₉	1	8	yes	complemented
107	C₄×Q₈	—	2	8	no	—
108	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
109	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
110	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
111	C₂×C₄²	C₂²×C₉	1	4	yes	—
112	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
113	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
114	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
115	#95	C₂²×C₉	1	4	yes	—
116	#95	C₂²×C₉	1	4	yes	—
117	#95	C₂²×C₉	1	8	yes	—
118	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
119	C₃×Q₈	—	2	16	no	—
120	C₂×C₃×C₄	—	2	4	no	—
121	C₂×C₃×C₄	—	2	4	no	—
122	C₂×C₃×C₄	—	2	4	no	—
123	C₂×C₃×C₄	—	2	4	no	—
124	C₂×C₃×C₄	—	2	4	no	—
125	C₂×C₃×C₄	—	2	2	no	—
126	C₂×C₃×C₄	—	2	8	no	—
127	C₂×C₃×C₄	—	2	4	no	—
128	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
129	C₂×C₃×C₄	C₂²×C₃×C₄	1	8	yes	—
130	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
131	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
132	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
133	C₂×C₃×C₄	C₃×#41	1	2	yes	—
134	C₂×C₉	C₂×C₄×D₄	1	1	yes	characteristic
135	C₂×C₉	#519	1	2	yes	—
136	C₂×C₉	#536	1	2	yes	—
137	C₂×C₉	#541	1	2	yes	—
138	C₂×Q₈	—	2	4	no	—
139	C₂×Q₈	—	2	4	no	—
140	C₂×Q₈	C₂×C₄×C₉	1	8	yes	—
141	C₂²×C₄	C₂³×C₉	1	2	yes	—
142	C₂²×C₄	C₂³×C₉	1	4	yes	—
143	C₂²×C₄	C₂³×C₉	1	2	yes	—
144	C₂²×C₄	C₂³×C₉	1	4	yes	—
145	C₂²×C₄	C₂³×C₉	1	2	yes	—
146	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
147	C₄⋊C₄	—	2	8	no	—
148	C₄⋊C₄	—	2	4	no	—
149	C₄⋊C₄	C₂×C₄×C₉	1	16	yes	—
150	C₄²	—	2	8	no	—
151	C₄²	—	2	2	no	—
152	C₄²	C₂×C₄×C₉	1	4	yes	—
153	C₄²	D₄×C₉	1	4	yes	—
154	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
155	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
156	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
157	C₂²×C₃	C₃×2₋¹⁺⁴	1	4	yes	—
158	C₃×C₄	—	2	8	no	—
159	C₃×C₄	—	2	4	no	—
160	C₃×C₄	—	2	4	no	—
161	C₃×C₄	—	4	4	no	—
162	C₃×C₄	—	4	2	no	—
163	C₃×C₄	C₃×C₄×D₄	1	4	yes	—
164	C₉	#2327	1	1	yes	characteristic, direct product factor, Sylow
165	C₂³	C₂⁴×C₉	1	1	yes	characteristic
166	Q₈	—	2	16	no	—
167	C₂×C₄	—	2	4	no	—
168	C₂×C₄	—	2	4	no	—
169	C₂×C₄	—	2	4	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	2	4	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	8	no	—
174	C₂×C₄	—	2	4	no	—
175	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
176	C₂×C₄	C₂²×C₄×C₉	1	8	yes	—
177	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
178	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
179	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
180	C₂×C₄	C₉×#41	1	2	yes	—
181	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
182	C₂×C₃	C₃×#519	1	2	yes	—
183	C₂×C₃	C₃×#536	1	2	yes	—
184	C₂×C₃	C₃×#541	1	2	yes	—
185	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
186	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
187	C₂²	C₂×C₉×#41	1	1	yes	characteristic
188	C₂²	C₉×2₋¹⁺⁴	1	4	yes	—
189	C₄	—	2	4	no	—
190	C₄	—	2	8	no	—
191	C₄	—	2	4	no	—
192	C₄	—	4	4	no	—
193	C₄	—	4	2	no	—
194	C₄	C₄×D₄×C₉	1	4	yes	—
195	C₃	C₃×#2327	1	1	yes	characteristic
196	C₂	C₂×C₄×D₄×C₉	1	1	yes	characteristic
197	C₂	C₉×#519	1	2	yes	—
198	C₂	C₉×#536	1	2	yes	—
199	C₂	C₉×#541	1	2	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
9. C₉×C₄⋊Q₈	C₄	semidirect
43. #2327	C₉	direct (N × H)
106. C₄⋊Q₈	C₄×C₉	semidirect
164. C₉	#2327	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⋊Q₈	2
C₂×C₄×Q₈×C₉	2
C₉×#391	2
C₉×#387	2
C₉×#382	2
C₉×#376	2
C₃×#2327	3

Subgroups — C9×#2327 #11767048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2327 #11767048