Subgroups — C₃×C₄×#803 #11783024

Order 1152.

849 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	C₃²×C₄³	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#803	C₂	1	4	yes	maximal
3	C₂×C₃×C₄×C₃⋊C₈	C₂	1	2	yes	maximal
4	C₃×C₄×#97	—	3	1	no	maximal
5	C₄×#803	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃²×C₄²	C₄	1	4	yes	—
7	C₂×C₃²×C₄²	C₂²	1	2	yes	—
8	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₃⋊C₈	C₂²	1	4	yes	—
10	C₃×#803	C₄	1	16	yes	direct product factor
11	C₃×C₄×C₃⋊C₈	C₄	1	8	yes	complemented
12	C₂×C₃×#97	—	3	4	no	—
13	C₂×C₃×C₄×C₈	—	3	2	no	—
14	C₃×C₄³	—	2	1	no	—
15	C₃×C₄³	D₃	1	1	yes	characteristic
16	C₃×C₄³	C₂×C₃	1	1	yes	characteristic
17	C₂×#803	C₂×C₃	1	4	yes	—
18	C₂×C₄×C₃⋊C₈	C₂×C₃	1	2	yes	—
19	C₂²×C₃²×C₄	C₂×C₄	1	4	yes	—
20	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
21	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
22	C₃²×C₄²	—	2	8	no	—
23	C₃²×C₄²	C₂×C₄	1	4	yes	—
24	C₃²×C₄²	C₂×C₄	1	8	yes	—
25	C₂×C₃×C₃⋊C₈	C₂×C₄	1	8	yes	—
26	C₂×C₃×C₃⋊C₈	C₂×C₄	1	16	yes	—
27	C₄×#97	—	3	1	no	Sylow
28	C₂²×C₃×C₈	—	3	4	no	—
29	C₂×C₃×C₄²	—	2	4	no	—
30	C₂×C₃×C₄²	—	2	1	no	—
31	C₂×C₃×C₄²	—	2	2	no	—
32	C₂×C₃×C₄²	Dic₃	1	4	yes	—
33	C₂×C₃×C₄²	C₃×C₄	1	4	yes	—
34	C₂×C₃×C₄²	C₂×D₃	1	2	yes	—
35	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
36	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
37	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
38	C₂²×C₃⋊C₈	C₂²×C₃	1	4	yes	—
39	C₃×#97	—	3	16	no	—
40	C₃×C₄×C₈	—	3	8	no	—
41	#803	C₃×C₄	1	16	yes	direct product factor
42	C₄×C₃⋊C₈	C₃×C₄	1	8	yes	complemented
43	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₃²×C₄	—	2	8	no	—
45	C₂×C₃²×C₄	C₄²	1	8	yes	—
46	C₂×C₃²×C₄	C₄²	1	4	yes	—
47	C₂×C₃²×C₄	M₁₆	1	8	yes	—
48	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
49	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
50	C₃×C₃⋊C₈	C₄²	1	16	yes	complemented
51	C₂×#97	—	3	4	no	—
52	C₂×C₄×C₈	—	3	2	no	—
53	C₄³	C₃×D₃	1	1	yes	characteristic
54	C₂²×C₃×C₄	—	2	4	no	—
55	C₂²×C₃×C₄	—	2	2	no	—
56	C₂²×C₃×C₄	—	2	1	no	—
57	C₂²×C₃×C₄	C₂×Dic₃	1	4	yes	—
58	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
59	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
60	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
61	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
62	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
63	C₂×C₃×C₈	—	3	8	no	—
64	C₂×C₃×C₈	—	3	16	no	—
65	C₃×C₄²	—	2	16	no	—
66	C₃×C₄²	—	2	8	no	—
67	C₃×C₄²	—	2	8	no	—
68	C₃×C₄²	—	2	4	no	—
69	C₃×C₄²	—	2	8	no	—
70	C₃×C₄²	C₄×D₃	1	4	yes	—
71	C₃×C₄²	C₄×D₃	1	8	yes	—
72	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
73	C₃×C₄²	C₂×C₃×C₄	1	8	yes	—
74	C₂×C₃⋊C₈	C₂×C₃×C₄	1	8	yes	—
75	C₂×C₃⋊C₈	C₂×C₃×C₄	1	16	yes	—
76	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
77	C₂²×C₃²	C₂×C₄²	1	2	yes	—
78	C₂²×C₃²	C₂×M₁₆	1	4	yes	—
79	C₃²×C₄	—	2	8	no	—
80	C₃²×C₄	#97	1	8	yes	complemented
81	C₃²×C₄	C₂×C₄²	1	4	yes	—
82	C₂²×C₈	—	3	4	no	—
83	C₂×C₄²	C₃×Dic₃	1	4	yes	—
84	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
85	C₂×C₄²	C₂×C₃×D₃	1	2	yes	—
86	#97	—	3	16	no	—
87	C₄×C₈	—	3	8	no	—
88	C₂³×C₃	—	2	1	no	—
89	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
90	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
91	C₂×C₃×C₄	—	2	16	no	—
92	C₂×C₃×C₄	—	2	8	no	—
93	C₂×C₃×C₄	—	2	8	no	—
94	C₂×C₃×C₄	—	2	8	no	—
95	C₂×C₃×C₄	—	2	8	no	—
96	C₂×C₃×C₄	—	2	4	no	—
97	C₂×C₃×C₄	—	2	2	no	—
98	C₂×C₃×C₄	—	2	4	no	—
99	C₂×C₃×C₄	#208	1	8	yes	—
100	C₂×C₃×C₄	C₄×Dic₃	1	8	yes	—
101	C₂×C₃×C₄	C₄×Dic₃	1	4	yes	—
102	C₂×C₃×C₄	C₃×C₄²	1	8	yes	—
103	C₂×C₃×C₄	C₃×C₄²	1	4	yes	—
104	C₂×C₃×C₄	C₃×M₁₆	1	8	yes	—
105	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
106	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
107	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
108	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
109	C₃×C₈	—	3	16	no	—
110	C₃⋊C₈	C₃×C₄²	1	16	yes	complemented
111	C₂×C₃²	C₄³	1	1	yes	characteristic
112	C₂×C₃²	C₂×#97	1	2	yes	—
113	C₂×C₃²	C₄×M₁₆	1	4	yes	—
114	C₂²×C₄	C₂×C₃×Dic₃	1	4	yes	—
115	C₂²×C₄	C₂×C₃×Dic₃	1	2	yes	—
116	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
117	C₂×C₈	—	3	8	no	—
118	C₂×C₈	—	3	16	no	—
119	C₄²	—	2	8	no	—
120	C₄²	C₃×C₄×D₃	1	4	yes	—
121	C₄²	C₃×C₄×D₃	1	8	yes	—
122	C₂²×C₃	—	2	4	no	—
123	C₂²×C₃	—	2	1	no	—
124	C₂²×C₃	—	2	2	no	—
125	C₂²×C₃	C₂×#208	1	4	yes	—
126	C₂²×C₃	C₂×C₄×Dic₃	1	1	yes	characteristic
127	C₂²×C₃	C₂×C₄×Dic₃	1	2	yes	—
128	C₂²×C₃	C₂×C₃×C₄²	1	1	yes	characteristic
129	C₂²×C₃	C₂×C₃×C₄²	1	2	yes	—
130	C₂²×C₃	C₂×C₃×M₁₆	1	4	yes	—
131	C₃×C₄	—	2	16	no	—
132	C₃×C₄	—	2	8	no	—
133	C₃×C₄	—	2	8	no	—
134	C₃×C₄	—	2	8	no	—
135	C₃×C₄	—	2	4	no	—
136	C₃×C₄	#803	1	8	yes	direct product factor
137	C₃×C₄	C₃×#97	1	8	yes	complemented
138	C₃×C₄	C₄²×D₃	1	4	yes	—
139	C₃×C₄	C₂×C₃×C₄²	1	4	yes	—
140	C₃²	C₄×#97	1	1	yes	characteristic, complemented, Sylow
141	C₂³	C₂²×C₃×Dic₃	1	1	yes	characteristic
142	C₂×C₄	—	2	8	no	—
143	C₂×C₄	C₃×#208	1	8	yes	—
144	C₂×C₄	C₃×C₄×Dic₃	1	8	yes	—
145	C₂×C₄	C₃×C₄×Dic₃	1	4	yes	—
146	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
147	C₂×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
148	C₈	—	3	16	no	—
149	C₂×C₃	—	2	2	no	—
150	C₂×C₃	—	2	4	no	—
151	C₂×C₃	—	2	1	no	—
152	C₂×C₃	C₂×#803	1	2	yes	—
153	C₂×C₃	C₄×#208	1	4	yes	—
154	C₂×C₃	C₄²×Dic₃	1	1	yes	characteristic
155	C₂×C₃	C₃×C₄³	1	1	yes	characteristic
156	C₂×C₃	C₂×C₃×#97	1	2	yes	—
157	C₂×C₃	C₃×C₄×M₁₆	1	4	yes	—
158	C₂²	C₂×C₃×#208	1	4	yes	—
159	C₂²	C₂×C₃×C₄×Dic₃	1	1	yes	characteristic
160	C₂²	C₂×C₃×C₄×Dic₃	1	2	yes	—
161	C₄	—	2	8	no	—
162	C₄	C₃×#803	1	8	yes	direct product factor
163	C₄	C₃×C₄²×D₃	1	4	yes	—
164	C₃	—	2	1	no	—
165	C₃	C₄×#803	1	1	yes	characteristic, direct product factor
166	C₃	C₃×C₄×#97	1	1	yes	characteristic, complemented
167	C₂	C₂×C₃×#803	1	2	yes	—
168	C₂	C₃×C₄×#208	1	4	yes	—
169	C₂	C₃×C₄²×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄²	C₂×D₃
commutator	C₂×C₃	C₃×C₄³
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₃²×C₄³	C₂
socle, prime radical	C₂³×C₃²	C₂²×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₃×C₄³	D₃
hypocenter	C₃	C₃×C₄×#97
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄² ◁ C₃×C₄³

Complements

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

N	H ≅ G/N	type
5. C₄×#803	C₃	direct (N × H)
10. C₃×#803	C₄	direct (N × H)
11. C₃×C₄×C₃⋊C₈	C₄	semidirect
41. #803	C₃×C₄	direct (N × H)
42. C₄×C₃⋊C₈	C₃×C₄	semidirect
50. C₃×C₃⋊C₈	C₄²	semidirect
80. C₃²×C₄	#97	semidirect
110. C₃⋊C₈	C₃×C₄²	semidirect
136. C₃×C₄	#803	direct (N × H)
137. C₃×C₄	C₃×#97	semidirect
140. C₃²	C₄×#97	semidirect
162. C₄	C₃×#803	direct (N × H)
165. C₃	C₄×#803	direct (N × H)
166. C₃	C₃×C₄×#97	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₄³	2
C₂×C₃×#803	2
C₂×C₃×C₄×C₃⋊C₈	2
C₃×C₄×#97	3
C₄×#803	3

Subgroups — C3×C4×#803 #11783024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#803 #11783024