Subgroups — C₃⋊C₈×Dic₁₂ #11777244

Order 1152.

355 conjugacy classes of subgroups.

The subgroup lattice has 235 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×Dic₁₂	C₂	1	1	yes	maximal, characteristic
2	C₃⋊C₈×Dic₆	C₂	1	2	yes	maximal
3	#10589324	C₂	1	1	yes	maximal, characteristic
4	C₃×C₈×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
5	#10589084	C₂	1	2	yes	maximal
6	Q₁₆×C₃⋊C₈	—	3	1	no	maximal
7	C₈×Dic₁₂	—	3	1	no	maximal
8	C₂×C₃×Dic₁₂	C₄	1	1	yes	characteristic
9	C₃×C₄×Dic₆	C₂²	1	2	yes	—
10	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
11	C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	1	2	yes	—
12	C₃×#818	C₄	1	1	yes	characteristic
13	C₃×#816	C₄	1	2	yes	—
14	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	Dic₃⋊(C₃⋊C₈)	—	2	2	no	—
17	Dic₃×C₃⋊C₈	—	2	2	no	—
18	C₃×C₄×Q₁₆	—	3	1	no	—
19	Q₈×C₃⋊C₈	—	3	2	no	—
20	C₄×Dic₁₂	D₃	1	1	yes	characteristic
21	C₈×Dic₆	—	3	2	no	—
22	C₃×C₈²	—	3	1	no	—
23	#4535	—	3	2	no	—
24	#4458	—	3	1	no	—
25	#4458	—	3	1	no	—
26	#4458	—	6	1	no	—
27	#4456	—	3	2	no	—
28	C₈×C₃⋊C₈	D₃	1	1	yes	characteristic
29	C₂×C₃×Dic₆	C₂×C₄	1	2	yes	—
30	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
31	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
32	C₃²×C₄²	C₂³	1	1	yes	characteristic
33	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
34	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
35	C₃×Dic₃⋊C₄	—	2	2	no	—
36	C₃×C₄×Dic₃	—	2	2	no	—
37	C₂×C₃×C₃⋊C₈	—	2	1	no	—
38	C₂×C₃×C₃⋊C₈	D₄	1	1	yes	characteristic
39	C₂×C₃×C₃⋊C₈	D₄	1	1	yes	characteristic
40	C₃×Dic₁₂	C₈	1	4	yes	complemented
41	C₈×Q₁₆	—	9	1	no	Sylow
42	C₂×C₃×Q₁₆	—	3	1	no	—
43	C₃×C₄×Q₈	—	3	2	no	—
44	C₂×Dic₁₂	Dic₃	1	1	yes	characteristic
45	C₄×Dic₆	C₂×D₃	1	2	yes	—
46	C₃×#107	—	3	1	no	—
47	C₃×#103	—	3	2	no	—
48	C₃×C₄×C₈	—	2	1	no	—
49	C₃×C₄×C₈	—	3	1	no	—
50	C₃×C₄×C₈	—	3	1	no	—
51	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
52	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
53	#818	Dic₃	1	1	yes	characteristic
54	#816	Dic₃	1	2	yes	—
55	Dic₃⋊C₈	—	6	2	no	—
56	C₈×Dic₃	—	6	2	no	—
57	C₄⋊(C₃⋊C₈)	—	3	2	no	—
58	C₄⋊(C₃⋊C₈)	—	3	2	no	—
59	C₄⋊(C₃⋊C₈)	—	6	2	no	—
60	C₄⋊(C₃⋊C₈)	—	6	2	no	—
61	C₄×C₃⋊C₈	—	6	2	no	—
62	C₄×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
63	C₄×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
64	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
66	C₂×C₃²×C₄	#41	1	1	yes	characteristic
67	C₂×C₃×Dic₃	—	2	2	no	—
68	C₂×C₃×Dic₃	—	2	2	no	—
69	C₃×Dic₆	—	2	2	no	—
70	C₃×Dic₆	C₂×C₈	1	4	yes	—
71	C₃²×C₈	—	2	1	no	—
72	C₃²×C₈	C₂×C₈	1	2	yes	—
73	C₃⋊(C₃⋊C₈)	—	4	2	no	—
74	C₃×C₃⋊C₈	—	2	2	no	—
75	C₃×C₃⋊C₈	—	2	1	no	—
76	C₃×C₃⋊C₈	Q₁₆	1	2	yes	complemented
77	C₈×Q₈	—	9	2	no	—
78	C₄×Q₁₆	—	3	1	no	—
79	#335	—	9	1	no	—
80	Q₈⋊C₈	—	9	2	no	—
81	C₈²	—	3	1	no	—
82	C₂×C₃×Q₈	—	3	2	no	—
83	C₂×Dic₆	C₂×Dic₃	1	2	yes	—
84	C₃×Q₁₆	—	3	4	no	—
85	C₂×C₃×C₈	—	2	1	no	—
86	C₂×C₃×C₈	—	2	1	no	—
87	C₂×C₃×C₈	—	3	1	no	—
88	C₂×C₃×C₈	—	3	1	no	—
89	C₂×C₃×C₈	—	6	1	no	—
90	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
91	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
92	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
93	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
94	C₃×C₄⋊C₄	—	3	2	no	—
95	C₃×C₄⋊C₄	—	6	2	no	—
96	C₃×C₄²	—	2	1	no	—
97	C₃×C₄²	—	6	2	no	—
98	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
99	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
100	C₄⋊Dic₃	C₂×Dic₃	1	2	yes	—
101	Dic₃⋊C₄	—	2	2	no	—
102	C₄×Dic₃	—	2	2	no	—
103	C₂×C₃⋊C₈	—	2	1	no	—
104	C₂×C₃⋊C₈	—	6	2	no	—
105	C₂×C₃⋊C₈	—	6	2	no	—
106	C₂×C₃⋊C₈	—	12	2	no	—
107	C₂×C₃⋊C₈	D₁₂	1	1	yes	characteristic
108	C₂×C₃⋊C₈	D₁₂	1	1	yes	characteristic
109	Dic₁₂	C₃⋊C₈	1	4	yes	direct product factor
110	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
111	C₃²×C₄	—	2	1	no	—
112	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
113	C₃²×C₄	#131	1	1	yes	characteristic
114	C₃²×C₄	C₂×Q₁₆	1	1	yes	characteristic
115	C₃²×C₄	#135	1	1	yes	characteristic
116	C₃×Dic₃	—	2	4	no	—
117	C₃×Dic₃	—	4	2	no	—
118	C₂×Q₁₆	—	3	1	no	—
119	C₄×Q₈	—	3	2	no	—
120	#107	—	3	1	no	—
121	C₄⋊C₈	—	9	2	no	—
122	C₄⋊C₈	—	18	2	no	—
123	#103	—	3	2	no	—
124	C₄×C₈	—	3	1	no	—
125	C₄×C₈	—	3	1	no	—
126	C₄×C₈	—	18	2	no	—
127	C₄×C₈	D₃²	1	1	yes	characteristic
128	C₃×Q₈	—	3	4	no	—
129	C₃×Q₈	—	6	2	no	—
130	C₂×C₃×C₄	—	2	1	no	—
131	C₂×C₃×C₄	—	2	1	no	—
132	C₂×C₃×C₄	—	2	1	no	—
133	C₂×C₃×C₄	—	6	2	no	—
134	C₂×C₃×C₄	—	6	2	no	—
135	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
136	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
137	C₂×C₃×C₄	#235	1	1	yes	characteristic
138	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄	#237	1	1	yes	characteristic
140	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
141	C₂×Dic₃	—	2	2	no	—
142	C₂×Dic₃	—	2	2	no	—
143	Dic₆	—	2	2	no	—
144	Dic₆	C₂×C₃⋊C₈	1	4	yes	—
145	C₃×C₈	—	2	1	no	—
146	C₃×C₈	—	2	1	no	—
147	C₃×C₈	—	2	2	no	—
148	C₃×C₈	—	3	2	no	—
149	C₃×C₈	—	4	1	no	—
150	C₃×C₈	—	6	2	no	—
151	C₃×C₈	—	6	1	no	—
152	C₃×C₈	D₃×C₈	1	2	yes	—
153	C₃×C₈	C₂×C₃⋊C₈	1	2	yes	—
154	C₃⋊C₈	—	2	2	no	—
155	C₃⋊C₈	—	2	1	no	—
156	C₃⋊C₈	—	12	2	no	—
157	C₃⋊C₈	—	12	2	no	—
158	C₃⋊C₈	—	24	2	no	—
159	C₃⋊C₈	Dic₁₂	1	2	yes	direct product factor
160	C₂×C₃²	C₈×D₄	1	1	yes	characteristic
161	C₂×C₃²	C₄×Q₁₆	1	1	yes	characteristic
162	C₂×C₃²	#443	1	1	yes	characteristic
163	C₂×Q₈	—	3	2	no	—
164	Q₁₆	—	3	4	no	—
165	C₂×C₈	—	3	1	no	—
166	C₂×C₈	—	3	1	no	—
167	C₂×C₈	—	6	1	no	—
168	C₂×C₈	—	18	2	no	—
169	C₂×C₈	D₃×Dic₃	1	1	yes	characteristic
170	C₂×C₈	D₃×Dic₃	1	1	yes	characteristic
171	C₄⋊C₄	—	3	2	no	—
172	C₄⋊C₄	—	6	2	no	—
173	C₄²	—	6	2	no	—
174	C₄²	C₂×D₃²	1	1	yes	characteristic
175	C₂²×C₃	—	2	1	no	—
176	C₂²×C₃	C₄×D₁₂	1	1	yes	characteristic
177	C₂²×C₃	D₄×Dic₃	1	1	yes	characteristic
178	C₃×C₄	—	2	1	no	—
179	C₃×C₄	—	2	1	no	—
180	C₃×C₄	—	2	1	no	—
181	C₃×C₄	—	2	1	no	—
182	C₃×C₄	—	2	1	no	—
183	C₃×C₄	—	2	1	no	—
184	C₃×C₄	—	4	1	no	—
185	C₃×C₄	—	6	4	no	—
186	C₃×C₄	—	12	2	no	—
187	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
188	C₃×C₄	#901	1	1	yes	characteristic
189	C₃×C₄	#904	1	1	yes	characteristic
190	C₃×C₄	C₂×Dic₁₂	1	1	yes	characteristic
191	C₃×C₄	D₃×Q₁₆	1	1	yes	characteristic
192	C₃×C₄	#919	1	1	yes	characteristic
193	C₃×C₄	C₂²×C₃⋊C₈	1	1	yes	characteristic
194	C₃×C₄	#948	1	1	yes	characteristic
195	Dic₃	—	2	4	no	—
196	Dic₃	—	4	2	no	—
197	C₃²	C₈×Q₁₆	1	1	yes	characteristic, complemented, Sylow
198	Q₈	—	3	4	no	—
199	Q₈	—	6	2	no	—
200	C₂×C₄	—	6	2	no	—
201	C₂×C₄	—	6	2	no	—
202	C₂×C₄	#3795	1	1	yes	characteristic
203	C₂×C₄	D₃×D₁₂	1	1	yes	characteristic
204	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
205	C₈	—	2	1	no	—
206	C₈	—	3	2	no	—
207	C₈	—	6	2	no	—
208	C₈	—	6	1	no	—
209	C₈	—	36	2	no	—
210	C₈	D₃×C₃⋊C₈	1	2	yes	—
211	C₂×C₃	—	2	1	no	—
212	C₂×C₃	—	2	1	no	—
213	C₂×C₃	—	2	1	no	—
214	C₂×C₃	C₈×D₁₂	1	1	yes	characteristic
215	C₂×C₃	C₄×Dic₁₂	1	1	yes	characteristic
216	C₂×C₃	#4700	1	1	yes	characteristic
217	C₂×C₃	D₄×C₃⋊C₈	1	1	yes	characteristic
218	C₂×C₃	Dic₃×Q₁₆	1	1	yes	characteristic
219	C₂×C₃	#5196	1	1	yes	characteristic
220	C₂²	Dic₃×D₁₂	1	1	yes	characteristic
221	C₄	—	2	1	no	—
222	C₄	—	6	4	no	—
223	C₄	—	12	2	no	—
224	C₄	D₃×Dic₁₂	1	1	yes	characteristic
225	C₄	#63808	1	1	yes	characteristic
226	C₄	C₂×D₃×C₃⋊C₈	1	1	yes	characteristic
227	C₄	#63814	1	1	yes	characteristic
228	C₃	—	2	1	no	—
229	C₃	C₈×Dic₁₂	1	1	yes	characteristic, complemented
230	C₃	Q₁₆×C₃⋊C₈	1	1	yes	characteristic, complemented
231	C₂	C₃⋊C₈×D₁₂	1	1	yes	characteristic
232	C₂	Dic₃×Dic₁₂	1	1	yes	characteristic
233	C₂	#10590915	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃×D₁₂
commutator	C₃²×C₄	C₂²×C₈
Frattini	C₄²	C₂×D₃²
Fitting	C₃²×C₄×C₈	C₂²
socle, prime radical	C₂²×C₃²	C₄×D₄
cosocle	C₃²×C₄²	C₂³
hypercenter	C₄×C₈	D₃²
hypocenter	C₃²	C₈×Q₁₆
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
40. C₃×Dic₁₂	C₈	semidirect
76. C₃×C₃⋊C₈	Q₁₆	semidirect
109. Dic₁₂	C₃⋊C₈	direct (N × H)
159. C₃⋊C₈	Dic₁₂	direct (N × H)
197. C₃²	C₈×Q₁₆	semidirect
229. C₃	C₈×Dic₁₂	semidirect
230. C₃	Q₁₆×C₃⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×Dic₁₂	2
C₃⋊C₈×Dic₆	2
#10589324	2
C₃×C₈×C₃⋊C₈	2
#10589084	2
Q₁₆×C₃⋊C₈	3
C₈×Dic₁₂	3

Subgroups — C3⋊C8×Dic12 #11777244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊C₈×Dic₁₂ #11777244