Subgroups — C₃²×#2401 #11769450

Order 1152.

1296 conjugacy classes of subgroups.

The subgroup lattice has 213 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#401	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#400	C₂	1	3	yes	maximal, complemented
3	C₃²×#397	C₂	1	3	yes	maximal
4	C₃²×#396	C₂	1	1	yes	maximal, characteristic
5	C₃²×C₄×C₄⋊C₄	C₂	1	3	yes	maximal, complemented
6	C₃²×C₄×C₂²⋊C₄	C₂	1	3	yes	maximal
7	C₃²×#376	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2401	C₃	1	4	yes	maximal, direct product factor
9	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
10	C₂×C₃²×C₄⋊C₄	C₂²	1	3	yes	—
11	C₂×C₃²×C₄⋊C₄	C₂²	1	3	yes	—
12	C₂×C₃²×C₂²⋊C₄	C₂²	1	3	yes	—
13	C₂×C₃²×C₂²⋊C₄	C₂²	1	3	yes	—
14	C₂×C₃²×C₄²	C₂²	1	3	yes	—
15	C₂×C₃²×C₄²	C₂²	1	3	yes	—
16	C₃²×#95	C₂²	1	1	yes	characteristic
17	C₃²×#95	C₂²	1	3	yes	—
18	C₃²×#95	C₂²	1	3	yes	—
19	C₃²×#95	C₂²	1	3	yes	—
20	C₃²×#95	C₂²	1	3	yes	—
21	C₃²×#95	C₂²	1	3	yes	—
22	C₃×#401	C₂×C₃	1	4	yes	complemented
23	C₃×#400	C₂×C₃	1	12	yes	complemented
24	C₃×#397	C₂×C₃	1	12	yes	—
25	C₃×#396	C₂×C₃	1	4	yes	—
26	C₃×C₄×C₄⋊C₄	C₂×C₃	1	12	yes	complemented
27	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	12	yes	—
28	C₃×#376	C₂×C₃	1	4	yes	complemented
29	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
30	C₂²×C₃²×C₄	—	2	6	no	—
31	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
32	C₂²×C₃²×C₄	C₂³	1	3	yes	—
33	C₂²×C₃²×C₄	C₂³	1	3	yes	—
34	C₂²×C₃²×C₄	C₂³	1	3	yes	—
35	C₂²×C₃²×C₄	C₂³	1	3	yes	—
36	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
37	C₃²×C₄⋊C₄	—	2	6	no	—
38	C₃²×C₄⋊C₄	—	2	6	no	—
39	C₃²×C₂²⋊C₄	—	2	6	no	—
40	C₃²×C₂²⋊C₄	—	2	6	no	—
41	C₃²×C₄²	—	2	6	no	—
42	C₃²×C₄²	—	2	6	no	—
43	#2401	C₃²	1	1	yes	characteristic, direct product factor, Sylow
44	C₂³×C₃×C₄	C₂²×C₃	1	4	yes	—
45	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	12	yes	—
46	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	12	yes	—
47	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	12	yes	—
48	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	12	yes	—
49	C₂×C₃×C₄²	C₂²×C₃	1	12	yes	—
50	C₂×C₃×C₄²	C₂²×C₃	1	12	yes	—
51	C₃×#95	C₂²×C₃	1	4	yes	—
52	C₃×#95	C₂²×C₃	1	12	yes	—
53	C₃×#95	C₂²×C₃	1	12	yes	—
54	C₃×#95	C₂²×C₃	1	12	yes	—
55	C₃×#95	C₂²×C₃	1	12	yes	—
56	C₃×#95	C₂²×C₃	1	12	yes	—
57	C₂³×C₃²	—	2	3	no	—
58	C₂³×C₃²	—	2	3	no	—
59	C₂³×C₃²	#41	1	2	yes	—
60	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
61	C₂×C₃²×C₄	—	2	3	no	—
62	C₂×C₃²×C₄	—	2	3	no	—
63	C₂×C₃²×C₄	—	2	3	no	—
64	C₂×C₃²×C₄	—	2	3	no	—
65	C₂×C₃²×C₄	—	2	3	no	—
66	C₂×C₃²×C₄	—	2	3	no	—
67	C₂×C₃²×C₄	—	2	3	no	—
68	C₂×C₃²×C₄	—	2	3	no	—
69	C₂×C₃²×C₄	—	2	3	no	—
70	C₂×C₃²×C₄	—	2	3	no	—
71	C₂×C₃²×C₄	—	2	3	no	—
72	C₂×C₃²×C₄	—	2	3	no	—
73	C₂×C₃²×C₄	—	4	4	no	—
74	C₂×C₃²×C₄	#41	1	6	yes	—
75	C₂×C₃²×C₄	#41	1	6	yes	—
76	#401	C₂×C₃²	1	1	yes	characteristic, complemented
77	#400	C₂×C₃²	1	3	yes	complemented
78	#397	C₂×C₃²	1	3	yes	—
79	#396	C₂×C₃²	1	1	yes	characteristic
80	C₄×C₄⋊C₄	C₂×C₃²	1	3	yes	complemented
81	C₄×C₂²⋊C₄	C₂×C₃²	1	3	yes	—
82	#376	C₂×C₃²	1	1	yes	characteristic, complemented
83	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
84	C₂²×C₃×C₄	—	2	24	no	—
85	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
86	C₂²×C₃×C₄	C₂³×C₃	1	12	yes	—
87	C₂²×C₃×C₄	C₂³×C₃	1	12	yes	—
88	C₂²×C₃×C₄	C₂³×C₃	1	12	yes	—
89	C₂²×C₃×C₄	C₂³×C₃	1	12	yes	—
90	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
91	C₃×C₄⋊C₄	—	2	24	no	—
92	C₃×C₄⋊C₄	—	2	24	no	—
93	C₃×C₂²⋊C₄	—	2	24	no	—
94	C₃×C₂²⋊C₄	—	2	24	no	—
95	C₃×C₄²	—	2	24	no	—
96	C₃×C₄²	—	2	24	no	—
97	C₂²×C₃²	—	2	6	no	—
98	C₂²×C₃²	—	4	1	no	—
99	C₂²×C₃²	—	4	3	no	—
100	C₂²×C₃²	C₂×#41	1	3	yes	—
101	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
102	C₂²×C₃²	C₂×#41	1	3	yes	—
103	C₃²×C₄	—	2	6	no	—
104	C₃²×C₄	—	4	1	no	—
105	C₃²×C₄	—	4	3	no	—
106	C₃²×C₄	—	4	3	no	—
107	C₃²×C₄	—	4	3	no	—
108	C₃²×C₄	#126	1	4	yes	—
109	C₂³×C₄	C₂²×C₃²	1	1	yes	characteristic
110	C₂×C₄⋊C₄	C₂²×C₃²	1	3	yes	—
111	C₂×C₄⋊C₄	C₂²×C₃²	1	3	yes	—
112	C₂×C₂²⋊C₄	C₂²×C₃²	1	3	yes	—
113	C₂×C₂²⋊C₄	C₂²×C₃²	1	3	yes	—
114	C₂×C₄²	C₂²×C₃²	1	3	yes	—
115	C₂×C₄²	C₂²×C₃²	1	3	yes	—
116	#95	C₂²×C₃²	1	1	yes	characteristic
117	#95	C₂²×C₃²	1	3	yes	—
118	#95	C₂²×C₃²	1	3	yes	—
119	#95	C₂²×C₃²	1	3	yes	—
120	#95	C₂²×C₃²	1	3	yes	—
121	#95	C₂²×C₃²	1	3	yes	—
122	C₂³×C₃	—	2	12	no	—
123	C₂³×C₃	—	2	12	no	—
124	C₂³×C₃	C₃×#41	1	8	yes	—
125	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
126	C₂×C₃×C₄	—	2	12	no	—
127	C₂×C₃×C₄	—	2	12	no	—
128	C₂×C₃×C₄	—	2	12	no	—
129	C₂×C₃×C₄	—	2	12	no	—
130	C₂×C₃×C₄	—	2	12	no	—
131	C₂×C₃×C₄	—	2	12	no	—
132	C₂×C₃×C₄	—	2	12	no	—
133	C₂×C₃×C₄	—	2	12	no	—
134	C₂×C₃×C₄	—	2	12	no	—
135	C₂×C₃×C₄	—	2	12	no	—
136	C₂×C₃×C₄	—	2	12	no	—
137	C₂×C₃×C₄	—	2	12	no	—
138	C₂×C₃×C₄	—	4	16	no	—
139	C₂×C₃×C₄	C₃×#41	1	24	yes	—
140	C₂×C₃×C₄	C₃×#41	1	24	yes	—
141	C₂×C₃²	—	4	2	no	—
142	C₂×C₃²	C₂×#126	1	1	yes	characteristic
143	C₂×C₃²	#529	1	3	yes	—
144	C₂×C₃²	#529	1	3	yes	—
145	C₂⁴	C₂³×C₃²	1	1	yes	characteristic
146	C₂²×C₄	—	2	6	no	—
147	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
148	C₂²×C₄	C₂³×C₃²	1	3	yes	—
149	C₂²×C₄	C₂³×C₃²	1	3	yes	—
150	C₂²×C₄	C₂³×C₃²	1	3	yes	—
151	C₂²×C₄	C₂³×C₃²	1	3	yes	—
152	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
153	C₄⋊C₄	—	2	6	no	—
154	C₄⋊C₄	—	2	6	no	—
155	C₂²⋊C₄	—	2	6	no	—
156	C₂²⋊C₄	—	2	6	no	—
157	C₄²	—	2	6	no	—
158	C₄²	—	2	6	no	—
159	C₂²×C₃	—	2	24	no	—
160	C₂²×C₃	—	4	4	no	—
161	C₂²×C₃	—	4	12	no	—
162	C₂²×C₃	C₂×C₃×#41	1	12	yes	—
163	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
164	C₂²×C₃	C₂×C₃×#41	1	12	yes	—
165	C₃×C₄	—	2	24	no	—
166	C₃×C₄	—	4	4	no	—
167	C₃×C₄	—	4	12	no	—
168	C₃×C₄	—	4	12	no	—
169	C₃×C₄	—	4	12	no	—
170	C₃×C₄	C₃×#126	1	16	yes	—
171	C₃²	#2401	1	1	yes	characteristic, direct product factor, Sylow
172	C₂³	—	2	3	no	—
173	C₂³	—	2	3	no	—
174	C₂³	C₃²×#41	1	2	yes	—
175	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
176	C₂×C₄	—	2	3	no	—
177	C₂×C₄	—	2	3	no	—
178	C₂×C₄	—	2	3	no	—
179	C₂×C₄	—	2	3	no	—
180	C₂×C₄	—	2	3	no	—
181	C₂×C₄	—	2	3	no	—
182	C₂×C₄	—	2	3	no	—
183	C₂×C₄	—	2	3	no	—
184	C₂×C₄	—	2	3	no	—
185	C₂×C₄	—	2	3	no	—
186	C₂×C₄	—	2	3	no	—
187	C₂×C₄	—	2	3	no	—
188	C₂×C₄	—	4	4	no	—
189	C₂×C₄	C₃²×#41	1	6	yes	—
190	C₂×C₄	C₃²×#41	1	6	yes	—
191	C₂×C₃	—	4	8	no	—
192	C₂×C₃	C₂×C₃×#126	1	4	yes	—
193	C₂×C₃	C₃×#529	1	12	yes	—
194	C₂×C₃	C₃×#529	1	12	yes	—
195	C₂²	—	2	6	no	—
196	C₂²	—	4	1	no	—
197	C₂²	—	4	3	no	—
198	C₂²	C₂×C₃²×#41	1	3	yes	—
199	C₂²	C₂×C₃²×#41	1	1	yes	characteristic
200	C₂²	C₂×C₃²×#41	1	3	yes	—
201	C₄	—	2	6	no	—
202	C₄	—	4	1	no	—
203	C₄	—	4	3	no	—
204	C₄	—	4	3	no	—
205	C₄	—	4	3	no	—
206	C₄	C₃²×#126	1	4	yes	—
207	C₃	C₃×#2401	1	4	yes	direct product factor
208	C₂	—	4	2	no	—
209	C₂	C₂×C₃²×#126	1	1	yes	characteristic
210	C₂	C₃²×#529	1	3	yes	—
211	C₂	C₃²×#529	1	3	yes	—

	subgroup	G/H
center	C₂²×C₃²×C₄	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃²
socle	C₂³×C₃²	C₂⁴
prime radical	C₂⁴×C₃²	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₃²×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×#401	C₂	semidirect
2. C₃²×#400	C₂	semidirect
5. C₃²×C₄×C₄⋊C₄	C₂	semidirect
7. C₃²×#376	C₂	semidirect
8. C₃×#2401	C₃	direct (N × H)
22. C₃×#401	C₂×C₃	semidirect
23. C₃×#400	C₂×C₃	semidirect
26. C₃×C₄×C₄⋊C₄	C₂×C₃	semidirect
28. C₃×#376	C₂×C₃	semidirect
43. #2401	C₃²	direct (N × H)
76. #401	C₂×C₃²	semidirect
77. #400	C₂×C₃²	semidirect
80. C₄×C₄⋊C₄	C₂×C₃²	semidirect
82. #376	C₂×C₃²	semidirect
171. C₃²	#2401	direct (N × H)
207. C₃	C₃×#2401	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×#401	2
C₃²×#400	2
C₃²×#397	2
C₃²×#396	2
C₃²×C₄×C₄⋊C₄	2
C₃²×C₄×C₂²⋊C₄	2
C₃²×#376	2
C₃×#2401	3

Subgroups — C32×#2401 #11769450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#2401 #11769450