Subgroups — C₃²×#1283 #11768332

Order 1152.

480 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	C₃²×#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₃²×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₃×#1283	C₃	1	4	yes	maximal, direct product factor
5	C₂×C₃²×M₁₆	C₄	1	2	yes	—
6	C₂²×C₃²×C₈	C₄	1	2	yes	—
7	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
8	C₃²×C₄⋊C₈	—	2	1	no	—
9	C₃²×C₄⋊C₈	—	2	1	no	—
10	C₃²×C₄⋊C₈	—	2	1	no	—
11	C₃²×C₂²⋊C₈	C₄	1	2	yes	—
12	C₃²×#97	—	2	1	no	—
13	C₃²×C₄×C₈	—	2	1	no	—
14	C₃²×C₄×C₈	—	2	1	no	—
15	C₃×#431	C₂×C₃	1	4	yes	—
16	C₂×C₃×C₄⋊C₈	C₂×C₃	1	4	yes	—
17	C₃×C₄×M₁₆	C₂×C₃	1	4	yes	—
18	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
21	C₃²×M₁₆	—	2	2	no	—
22	C₃²×M₁₆	C₈	1	4	yes	complemented
23	C₂×C₃²×C₈	—	2	2	no	—
24	C₂×C₃²×C₈	—	2	2	no	—
25	C₂×C₃²×C₈	—	2	2	no	—
26	C₂×C₃²×C₈	—	4	2	no	—
27	C₃²×C₄²	D₄	1	1	yes	characteristic
28	C₃²×C₄²	D₄	1	1	yes	characteristic
29	C₃²×C₄²	D₄	1	1	yes	characteristic
30	C₃²×C₄²	Q₈	1	1	yes	characteristic
31	#1283	C₃²	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₃×M₁₆	C₃×C₄	1	8	yes	—
33	C₂²×C₃×C₈	C₃×C₄	1	8	yes	—
34	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
35	C₃×C₄⋊C₈	—	2	4	no	—
36	C₃×C₄⋊C₈	—	2	4	no	—
37	C₃×C₄⋊C₈	—	2	4	no	—
38	C₃×C₂²⋊C₈	C₃×C₄	1	8	yes	—
39	C₃×#97	—	2	4	no	—
40	C₃×C₄×C₈	—	2	4	no	—
41	C₃×C₄×C₈	—	2	4	no	—
42	C₂³×C₃²	C₄²	1	1	yes	characteristic
43	C₂×C₃²×C₄	—	2	1	no	—
44	C₂×C₃²×C₄	—	2	1	no	—
45	C₂×C₃²×C₄	—	4	1	no	—
46	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
53	C₂×C₃²×C₄	M₁₆	1	2	yes	—
54	C₃²×C₈	—	2	4	no	—
55	C₃²×C₈	—	4	2	no	—
56	C₃²×C₈	—	4	2	no	—
57	#431	C₂×C₃²	1	1	yes	characteristic
58	C₂×C₄⋊C₈	C₂×C₃²	1	1	yes	characteristic
59	C₄×M₁₆	C₂×C₃²	1	1	yes	characteristic
60	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
61	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
62	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
63	C₃×M₁₆	—	2	8	no	—
64	C₃×M₁₆	C₃×C₈	1	16	yes	complemented
65	C₂×C₃×C₈	—	2	8	no	—
66	C₂×C₃×C₈	—	2	8	no	—
67	C₂×C₃×C₈	—	2	8	no	—
68	C₂×C₃×C₈	—	4	8	no	—
69	C₃×C₄²	C₃×D₄	1	4	yes	—
70	C₃×C₄²	C₃×D₄	1	4	yes	—
71	C₃×C₄²	C₃×D₄	1	4	yes	—
72	C₃×C₄²	C₃×Q₈	1	4	yes	—
73	C₂²×C₃²	—	2	1	no	—
74	C₂²×C₃²	—	2	1	no	—
75	C₂²×C₃²	#95	1	1	yes	characteristic
76	C₂²×C₃²	C₄×C₈	1	1	yes	characteristic
77	C₂²×C₃²	#97	1	1	yes	characteristic
78	C₃²×C₄	—	2	1	no	—
79	C₃²×C₄	—	2	1	no	—
80	C₃²×C₄	—	2	1	no	—
81	C₃²×C₄	C₂²⋊C₈	1	2	yes	—
82	C₃²×C₄	#100	1	1	yes	characteristic
83	C₃²×C₄	#101	1	1	yes	characteristic
84	C₃²×C₄	C₄⋊C₈	1	2	yes	—
85	C₂×M₁₆	C₃²×C₄	1	2	yes	—
86	C₂²×C₈	C₃²×C₄	1	2	yes	—
87	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
88	C₄⋊C₈	—	2	1	no	—
89	C₄⋊C₈	—	2	1	no	—
90	C₄⋊C₈	—	2	1	no	—
91	C₂²⋊C₈	C₃²×C₄	1	2	yes	—
92	#97	—	2	1	no	—
93	C₄×C₈	—	2	1	no	—
94	C₄×C₈	—	2	1	no	—
95	C₂³×C₃	C₃×C₄²	1	4	yes	—
96	C₂×C₃×C₄	—	2	4	no	—
97	C₂×C₃×C₄	—	2	4	no	—
98	C₂×C₃×C₄	—	4	4	no	—
99	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	4	yes	—
100	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	4	yes	—
101	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	4	yes	—
102	C₂×C₃×C₄	C₃×C₄⋊C₄	1	4	yes	—
103	C₂×C₃×C₄	C₃×C₄⋊C₄	1	4	yes	—
104	C₂×C₃×C₄	C₃×C₄⋊C₄	1	4	yes	—
105	C₂×C₃×C₄	C₂×C₃×C₈	1	8	yes	—
106	C₂×C₃×C₄	C₃×M₁₆	1	8	yes	—
107	C₃×C₈	—	2	16	no	—
108	C₃×C₈	—	4	8	no	—
109	C₃×C₈	—	4	8	no	—
110	C₂×C₃²	—	2	1	no	—
111	C₂×C₃²	—	2	1	no	—
112	C₂×C₃²	#336	1	1	yes	characteristic
113	C₂×C₃²	#343	1	1	yes	characteristic
114	C₂×C₃²	#344	1	1	yes	characteristic
115	C₂²×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
116	C₂²×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
117	C₂²×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
118	M₁₆	—	2	2	no	—
119	M₁₆	C₃²×C₈	1	4	yes	complemented
120	C₂×C₈	—	2	2	no	—
121	C₂×C₈	—	2	2	no	—
122	C₂×C₈	—	2	2	no	—
123	C₂×C₈	—	4	2	no	—
124	C₄²	C₃²×D₄	1	1	yes	characteristic
125	C₄²	C₃²×D₄	1	1	yes	characteristic
126	C₄²	C₃²×D₄	1	1	yes	characteristic
127	C₄²	C₃²×Q₈	1	1	yes	characteristic
128	C₂²×C₃	—	2	4	no	—
129	C₂²×C₃	—	2	4	no	—
130	C₂²×C₃	C₃×#95	1	4	yes	—
131	C₂²×C₃	C₃×C₄×C₈	1	4	yes	—
132	C₂²×C₃	C₃×#97	1	4	yes	—
133	C₃×C₄	—	2	4	no	—
134	C₃×C₄	—	2	4	no	—
135	C₃×C₄	—	2	4	no	—
136	C₃×C₄	C₃×C₂²⋊C₈	1	8	yes	—
137	C₃×C₄	C₃×#100	1	4	yes	—
138	C₃×C₄	C₃×#101	1	4	yes	—
139	C₃×C₄	C₃×C₄⋊C₈	1	8	yes	—
140	C₃²	#1283	1	1	yes	characteristic, direct product factor, Sylow
141	C₂³	C₃²×C₄²	1	1	yes	characteristic
142	C₂×C₄	—	2	1	no	—
143	C₂×C₄	—	2	1	no	—
144	C₂×C₄	—	4	1	no	—
145	C₂×C₄	C₃²×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄	C₃²×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄	C₃²×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄	C₃²×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄	C₃²×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄	C₃²×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄	C₂×C₃²×C₈	1	2	yes	—
152	C₂×C₄	C₃²×M₁₆	1	2	yes	—
153	C₈	—	2	4	no	—
154	C₈	—	4	2	no	—
155	C₈	—	4	2	no	—
156	C₂×C₃	—	2	4	no	—
157	C₂×C₃	—	2	4	no	—
158	C₂×C₃	C₃×#336	1	4	yes	—
159	C₂×C₃	C₃×#343	1	4	yes	—
160	C₂×C₃	C₃×#344	1	4	yes	—
161	C₂²	—	2	1	no	—
162	C₂²	—	2	1	no	—
163	C₂²	C₃²×#95	1	1	yes	characteristic
164	C₂²	C₃²×C₄×C₈	1	1	yes	characteristic
165	C₂²	C₃²×#97	1	1	yes	characteristic
166	C₄	—	2	1	no	—
167	C₄	—	2	1	no	—
168	C₄	—	2	1	no	—
169	C₄	C₃²×C₂²⋊C₈	1	2	yes	—
170	C₄	C₃²×#100	1	1	yes	characteristic
171	C₄	C₃²×#101	1	1	yes	characteristic
172	C₄	C₃²×C₄⋊C₈	1	2	yes	—
173	C₃	C₃×#1283	1	4	yes	direct product factor
174	C₂	—	2	1	no	—
175	C₂	—	2	1	no	—
176	C₂	C₃²×#336	1	1	yes	characteristic
177	C₂	C₃²×#343	1	1	yes	characteristic
178	C₂	C₃²×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₄	C₂²⋊C₄
commutator	C₂²	C₃²×C₄×C₈
Frattini, cosocle	C₂×C₄²	C₂²×C₃²
socle	C₂²×C₃²	#95
prime radical	C₂³×C₃²	C₄²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₂×C₃²×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃×#1283	C₃	direct (N × H)
22. C₃²×M₁₆	C₈	semidirect
31. #1283	C₃²	direct (N × H)
64. C₃×M₁₆	C₃×C₈	semidirect
119. M₁₆	C₃²×C₈	semidirect
140. C₃²	#1283	direct (N × H)
173. C₃	C₃×#1283	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×#431	2
C₂×C₃²×C₄⋊C₈	2
C₃²×C₄×M₁₆	2
C₃×#1283	3

Subgroups — C32×#1283 #11768332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#1283 #11768332