Subgroups — C₃×#83780 #11899412

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#131	C₂	1	1	yes	maximal, characteristic
2	C₃×#5140	C₂	1	8	yes	maximal, complemented
3	C₂×C₃×#812	C₂	1	6	yes	maximal, complemented
4	C₃×#3407	—	3	1	no	maximal
5	#83780	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃²×#41	C₄	1	1	yes	characteristic
7	C₃²×#131	C₄	1	4	yes	—
8	C₃²×#131	C₂²	1	4	yes	—
9	C₂×C₃²×M₁₆	C₄	1	3	yes	—
10	C₂²×C₃²×C₈	C₂²	1	3	yes	—
11	C₃×#812	C₂²	1	4	yes	—
12	C₃×#812	C₂²	1	12	yes	complemented
13	C₂×C₃×C₃⋊C₁₆	C₂²	1	12	yes	complemented
14	C₂×C₃×#131	—	2	1	no	—
15	C₂×C₃×#131	D₃	1	1	yes	characteristic
16	C₂×C₃×#131	C₂×C₃	1	1	yes	characteristic
17	C₃×#504	—	3	8	no	—
18	C₂×C₃×M₃₂	—	3	6	no	—
19	#5140	C₂×C₃	1	8	yes	complemented
20	C₂×#812	C₂×C₃	1	6	yes	complemented
21	C₃²×#41	C₈	1	4	yes	—
22	C₃²×#41	C₂×C₄	1	4	yes	—
23	C₂×C₃²×Q₈	C₈	1	1	yes	characteristic
24	C₂×C₃²×D₄	C₈	1	3	yes	—
25	C₂²×C₃²×C₄	C₂×C₄	1	3	yes	—
26	C₃²×M₁₆	C₂×C₄	1	12	yes	—
27	C₂×C₃²×C₈	C₂×C₄	1	3	yes	—
28	C₂×C₃²×C₈	C₂×C₄	1	6	yes	—
29	C₂×C₃²×C₈	C₂³	1	6	yes	—
30	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
31	C₃×C₃⋊C₁₆	C₂³	1	8	yes	—
32	#3407	—	3	1	no	Sylow
33	C₂×C₃×#41	—	2	1	no	—
34	C₂×C₃×#41	Dic₃	1	1	yes	characteristic
35	C₂×C₃×#41	C₃×C₄	1	1	yes	characteristic
36	C₃×#131	—	2	4	no	—
37	C₃×#131	—	2	4	no	—
38	C₃×#131	Dic₃	1	4	yes	—
39	C₃×#131	C₃×C₄	1	4	yes	—
40	C₃×#131	C₂×D₃	1	4	yes	—
41	C₃×#131	C₂²×C₃	1	4	yes	—
42	C₂×C₃×M₁₆	—	2	3	no	—
43	C₂×C₃×M₁₆	Dic₃	1	3	yes	—
44	C₂×C₃×M₁₆	C₃×C₄	1	3	yes	—
45	C₂²×C₃×C₈	—	2	3	no	—
46	C₂²×C₃×C₈	C₂×D₃	1	3	yes	—
47	C₂²×C₃×C₈	C₂²×C₃	1	3	yes	—
48	C₃×M₃₂	—	3	4	no	—
49	C₃×M₃₂	—	3	12	no	—
50	C₂×C₃×C₁₆	—	3	12	no	—
51	#812	C₂²×C₃	1	4	yes	—
52	#812	C₂²×C₃	1	12	yes	complemented
53	C₂×C₃⋊C₁₆	C₂²×C₃	1	12	yes	complemented
54	C₂³×C₃²	C₂×C₈	1	3	yes	—
55	C₃²×Q₈	C₂×C₈	1	4	yes	—
56	C₃²×D₄	C₂×C₈	1	12	yes	—
57	C₂×C₃²×C₄	C₂×C₈	1	3	yes	—
58	C₂×C₃²×C₄	C₂×C₈	1	6	yes	—
59	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₃²×C₄	C₂²×C₄	1	6	yes	—
61	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
62	C₃²×C₈	C₂²×C₄	1	6	yes	—
63	C₃²×C₈	C₂⁴	1	1	yes	characteristic
64	C₂×#131	C₃×D₃	1	1	yes	characteristic
65	#504	—	3	8	no	—
66	C₂×M₃₂	—	3	6	no	—
67	C₃×#41	—	2	4	no	—
68	C₃×#41	—	2	4	no	—
69	C₃×#41	C₃⋊C₈	1	4	yes	—
70	C₃×#41	C₃×C₈	1	4	yes	—
71	C₃×#41	C₂×Dic₃	1	4	yes	—
72	C₃×#41	C₂×C₃×C₄	1	4	yes	—
73	C₂×C₃×Q₈	—	2	1	no	—
74	C₂×C₃×Q₈	C₃⋊C₈	1	1	yes	characteristic
75	C₂×C₃×Q₈	C₃×C₈	1	1	yes	characteristic
76	C₂×C₃×D₄	—	2	3	no	—
77	C₂×C₃×D₄	C₃⋊C₈	1	3	yes	—
78	C₂×C₃×D₄	C₃×C₈	1	3	yes	—
79	C₂²×C₃×C₄	—	2	3	no	—
80	C₂²×C₃×C₄	C₂×Dic₃	1	3	yes	—
81	C₂²×C₃×C₄	C₂×C₃×C₄	1	3	yes	—
82	C₃×M₁₆	—	2	12	no	—
83	C₃×M₁₆	C₂×Dic₃	1	12	yes	—
84	C₃×M₁₆	C₂×C₃×C₄	1	12	yes	—
85	C₂×C₃×C₈	—	2	3	no	—
86	C₂×C₃×C₈	—	2	6	no	—
87	C₂×C₃×C₈	—	2	1	no	—
88	C₂×C₃×C₈	—	2	6	no	—
89	C₂×C₃×C₈	C₂×Dic₃	1	3	yes	—
90	C₂×C₃×C₈	C₂×Dic₃	1	6	yes	—
91	C₂×C₃×C₈	C₂×C₃×C₄	1	3	yes	—
92	C₂×C₃×C₈	C₂×C₃×C₄	1	6	yes	—
93	C₂×C₃×C₈	C₂²×D₃	1	6	yes	—
94	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
95	C₂×C₃×C₈	C₂³×C₃	1	6	yes	—
96	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
97	C₃×C₁₆	—	3	8	no	—
98	C₃⋊C₁₆	C₂³×C₃	1	8	yes	—
99	C₂²×C₃²	—	4	3	no	—
100	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
101	C₂²×C₃²	C₂²×C₈	1	6	yes	—
102	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
103	C₃²×C₄	C₂²×C₈	1	6	yes	—
104	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
105	C₂×#41	C₃×Dic₃	1	1	yes	characteristic
106	#131	C₃×Dic₃	1	4	yes	—
107	#131	C₂×C₃×D₃	1	4	yes	—
108	C₂×M₁₆	C₃×Dic₃	1	3	yes	—
109	C₂²×C₈	C₂×C₃×D₃	1	3	yes	—
110	M₃₂	—	3	4	no	—
111	M₃₂	—	3	12	no	—
112	C₂×C₁₆	—	3	12	no	—
113	C₂³×C₃	—	2	3	no	—
114	C₂³×C₃	C₂×C₃⋊C₈	1	3	yes	—
115	C₂³×C₃	C₂×C₃×C₈	1	3	yes	—
116	C₃×Q₈	—	2	4	no	—
117	C₃×Q₈	C₂×C₃⋊C₈	1	4	yes	—
118	C₃×Q₈	C₂×C₃×C₈	1	4	yes	—
119	C₃×D₄	—	2	12	no	—
120	C₃×D₄	C₂×C₃⋊C₈	1	12	yes	—
121	C₃×D₄	C₂×C₃×C₈	1	12	yes	—
122	C₂×C₃×C₄	—	2	3	no	—
123	C₂×C₃×C₄	—	2	6	no	—
124	C₂×C₃×C₄	—	2	1	no	—
125	C₂×C₃×C₄	—	2	6	no	—
126	C₂×C₃×C₄	C₂×C₃⋊C₈	1	3	yes	—
127	C₂×C₃×C₄	C₂×C₃⋊C₈	1	6	yes	—
128	C₂×C₃×C₄	C₂×C₃×C₈	1	3	yes	—
129	C₂×C₃×C₄	C₂×C₃×C₈	1	6	yes	—
130	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
131	C₂×C₃×C₄	C₂²×Dic₃	1	6	yes	—
132	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
133	C₂×C₃×C₄	C₂²×C₃×C₄	1	6	yes	—
134	C₃×C₈	—	2	1	no	—
135	C₃×C₈	—	2	1	no	—
136	C₃×C₈	—	2	6	no	—
137	C₃×C₈	C₂²×Dic₃	1	1	yes	characteristic
138	C₃×C₈	C₂²×Dic₃	1	6	yes	—
139	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
140	C₃×C₈	C₂²×C₃×C₄	1	6	yes	—
141	C₃×C₈	C₂³×D₃	1	1	yes	characteristic
142	C₃×C₈	C₂⁴×C₃	1	1	yes	characteristic
143	C₂×C₃²	—	2	1	no	—
144	C₂×C₃²	—	2	6	no	—
145	C₂×C₃²	C₂³×C₈	1	1	yes	characteristic
146	#41	C₃×C₃⋊C₈	1	4	yes	—
147	#41	C₂×C₃×Dic₃	1	4	yes	—
148	C₂×Q₈	C₃×C₃⋊C₈	1	1	yes	characteristic
149	C₂×D₄	C₃×C₃⋊C₈	1	3	yes	—
150	C₂²×C₄	C₂×C₃×Dic₃	1	3	yes	—
151	M₁₆	C₂×C₃×Dic₃	1	12	yes	—
152	C₂×C₈	C₂×C₃×Dic₃	1	3	yes	—
153	C₂×C₈	C₂×C₃×Dic₃	1	6	yes	—
154	C₂×C₈	C₂²×C₃×D₃	1	6	yes	—
155	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
156	C₁₆	—	3	8	no	—
157	C₂²×C₃	—	2	1	no	—
158	C₂²×C₃	—	2	6	no	—
159	C₂²×C₃	—	4	3	no	—
160	C₂²×C₃	—	4	3	no	—
161	C₂²×C₃	—	4	6	no	—
162	C₂²×C₃	C₂²×C₃⋊C₈	1	1	yes	characteristic
163	C₂²×C₃	C₂²×C₃⋊C₈	1	6	yes	—
164	C₂²×C₃	C₂²×C₃×C₈	1	1	yes	characteristic
165	C₂²×C₃	C₂²×C₃×C₈	1	6	yes	—
166	C₃×C₄	—	2	1	no	—
167	C₃×C₄	—	2	6	no	—
168	C₃×C₄	—	2	1	no	—
169	C₃×C₄	C₂²×C₃⋊C₈	1	1	yes	characteristic
170	C₃×C₄	C₂²×C₃⋊C₈	1	6	yes	—
171	C₃×C₄	C₂²×C₃×C₈	1	1	yes	characteristic
172	C₃×C₄	C₂²×C₃×C₈	1	6	yes	—
173	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
174	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
175	C₃²	#3407	1	1	yes	characteristic, complemented, Sylow
176	C₂³	C₂×C₃×C₃⋊C₈	1	3	yes	—
177	Q₈	C₂×C₃×C₃⋊C₈	1	4	yes	—
178	D₄	C₂×C₃×C₃⋊C₈	1	12	yes	—
179	C₂×C₄	C₂×C₃×C₃⋊C₈	1	3	yes	—
180	C₂×C₄	C₂×C₃×C₃⋊C₈	1	6	yes	—
181	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
182	C₂×C₄	C₂²×C₃×Dic₃	1	6	yes	—
183	C₈	C₂²×C₃×Dic₃	1	1	yes	characteristic
184	C₈	C₂²×C₃×Dic₃	1	6	yes	—
185	C₈	C₂³×C₃×D₃	1	1	yes	characteristic
186	C₂×C₃	—	2	2	no	—
187	C₂×C₃	—	2	1	no	—
188	C₂×C₃	—	2	6	no	—
189	C₂×C₃	—	2	1	no	—
190	C₂×C₃	—	2	6	no	—
191	C₂×C₃	—	2	1	no	—
192	C₂×C₃	—	4	6	no	—
193	C₂×C₃	C₂³×C₃⋊C₈	1	1	yes	characteristic
194	C₂×C₃	C₂³×C₃×C₈	1	1	yes	characteristic
195	C₂²	—	4	3	no	—
196	C₂²	C₂²×C₃×C₃⋊C₈	1	1	yes	characteristic
197	C₂²	C₂²×C₃×C₃⋊C₈	1	6	yes	—
198	C₄	C₂²×C₃×C₃⋊C₈	1	1	yes	characteristic
199	C₄	C₂²×C₃×C₃⋊C₈	1	6	yes	—
200	C₄	C₂³×C₃×Dic₃	1	1	yes	characteristic
201	C₃	—	2	1	no	—
202	C₃	#83780	1	1	yes	characteristic, direct product factor
203	C₃	C₃×#3407	1	1	yes	characteristic, complemented
204	C₂	—	2	1	no	—
205	C₂	—	2	6	no	—
206	C₂	C₂³×C₃×C₃⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₈	C₂³×D₃
commutator	C₂×C₃	C₂³×C₃×C₈
Frattini	C₈	C₂³×C₃×D₃
Fitting	C₂×C₃²×#131	C₂
socle	C₂×C₃²	C₂³×C₈
prime radical	C₂×C₃²×#41	C₄
cosocle	C₃×C₈	C₂⁴×C₃
hypercenter	C₂×C₃×#131	D₃
hypocenter	C₃	C₃×#3407
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₈ ◁ C₂×C₃×#131

Complements

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

N	H ≅ G/N	type
2. C₃×#5140	C₂	semidirect
3. C₂×C₃×#812	C₂	semidirect
5. #83780	C₃	direct (N × H)
12. C₃×#812	C₂²	semidirect
13. C₂×C₃×C₃⋊C₁₆	C₂²	semidirect
19. #5140	C₂×C₃	semidirect
20. C₂×#812	C₂×C₃	semidirect
52. #812	C₂²×C₃	semidirect
53. C₂×C₃⋊C₁₆	C₂²×C₃	semidirect
175. C₃²	#3407	semidirect
202. C₃	#83780	direct (N × H)
203. C₃	C₃×#3407	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#131	2
C₃×#5140	2
C₂×C₃×#812	2
C₃×#3407	3
#83780	3

Subgroups — C3×#83780 #11899412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#83780 #11899412