Subgroups — Dic₃×#812 #11795865

Order 1152.

437 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63639	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#812	C₂	1	1	yes	maximal, characteristic
4	#10589103	C₂	1	2	yes	maximal, complemented
5	Dic₃×C₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
6	Dic₃×M₃₂	—	3	1	no	maximal
7	C₄×#812	—	3	1	no	maximal
8	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄×Dic₃	C₄	1	1	yes	characteristic
10	C₂²×C₃×C₃⋊C₈	C₄	1	1	yes	characteristic
11	#63639	C₄	1	4	yes	complemented
12	C₂×C₃⋊(C₃⋊C₁₆)	C₂²	1	2	yes	—
13	C₃×C₈×Dic₃	C₄	1	1	yes	characteristic
14	C₃×C₈×Dic₃	C₄	1	1	yes	characteristic
15	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
16	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
17	C₃×#812	C₄	1	4	yes	complemented
18	C₂×C₃×C₃⋊C₁₆	C₂²	1	2	yes	—
19	C₂×C₃×M₃₂	—	3	1	no	—
20	C₂×C₃×C₄×C₈	—	3	1	no	—
21	C₂×C₈×Dic₃	D₃	1	1	yes	characteristic
22	C₂×#812	—	3	1	no	—
23	C₂×#812	—	3	1	no	—
24	C₂×#812	—	6	1	no	—
25	C₂×#812	D₃	1	1	yes	characteristic
26	#4502	—	3	2	no	—
27	Dic₃×C₁₆	—	3	2	no	—
28	#4461	—	3	2	no	—
29	C₄×C₃⋊C₁₆	—	3	2	no	—
30	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×Dic₃	C₈	1	2	yes	—
32	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
33	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
34	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
35	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
36	C₃×C₄×Dic₃	C₈	1	2	yes	—
37	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
38	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×C₃⋊C₈	C₈	1	4	yes	—
40	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
42	C₃⋊(C₃⋊C₁₆)	C₂×C₄	1	4	yes	complemented
43	C₃×C₃⋊C₁₆	C₂×C₄	1	4	yes	complemented
44	C₄×M₃₂	—	9	1	no	Sylow
45	C₂²×C₃×C₈	—	2	1	no	—
46	C₂²×C₃×C₈	—	3	1	no	—
47	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
48	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
49	C₂×C₃×C₄²	—	3	1	no	—
50	C₂×C₄×Dic₃	Dic₃	1	1	yes	characteristic
51	C₂²×C₃⋊C₈	Dic₃	1	1	yes	characteristic
52	C₃×M₃₂	—	3	4	no	—
53	C₂×C₃×C₁₆	—	3	2	no	—
54	C₃×C₄×C₈	—	3	1	no	—
55	C₃×C₄×C₈	—	3	1	no	—
56	C₃×C₄×C₈	—	3	1	no	—
57	C₃×C₄×C₈	—	3	1	no	—
58	C₈×Dic₃	Dic₃	1	1	yes	characteristic
59	C₈×Dic₃	Dic₃	1	1	yes	characteristic
60	C₈×Dic₃	C₂×D₃	1	1	yes	characteristic
61	C₈×Dic₃	C₂×D₃	1	1	yes	characteristic
62	#812	—	3	4	no	—
63	#812	—	3	4	no	—
64	#812	—	6	4	no	—
65	#812	Dic₃	1	4	yes	direct product factor
66	C₂×C₃⋊C₁₆	—	3	2	no	—
67	C₂×C₃⋊C₁₆	—	3	2	no	—
68	C₂×C₃⋊C₁₆	—	6	2	no	—
69	C₂×C₃⋊C₁₆	C₂×D₃	1	2	yes	—
70	C₂³×C₃²	C₂×C₈	1	1	yes	characteristic
71	C₂×C₃²×C₄	C₄²	1	2	yes	—
72	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
73	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
74	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₃×Dic₃	—	2	4	no	—
76	C₂×C₃×Dic₃	C₂×C₈	1	2	yes	—
77	C₂×C₃×Dic₃	C₂×C₈	1	2	yes	—
78	C₃²×C₈	C₄²	1	2	yes	—
79	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
80	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
81	C₃×C₃⋊C₈	C₂×C₈	1	2	yes	—
82	C₃×C₃⋊C₈	C₂×C₈	1	2	yes	—
83	C₂×M₃₂	—	3	1	no	—
84	C₂×M₃₂	—	9	1	no	—
85	C₂×C₄×C₈	—	3	1	no	—
86	#346	—	9	2	no	—
87	C₄×C₁₆	—	9	2	no	—
88	C₂²×C₃×C₄	—	2	1	no	—
89	C₂²×C₃×C₄	—	3	2	no	—
90	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
91	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
92	C₂²×Dic₃	C₃⋊C₈	1	2	yes	—
93	C₂×C₃×C₈	—	2	1	no	—
94	C₂×C₃×C₈	—	2	2	no	—
95	C₂×C₃×C₈	—	2	2	no	—
96	C₂×C₃×C₈	—	2	1	no	—
97	C₂×C₃×C₈	—	3	4	no	—
98	C₂×C₃×C₈	—	3	1	no	—
99	C₂×C₃×C₈	—	3	1	no	—
100	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
101	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
102	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
103	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
104	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
105	C₂×C₃×C₈	C₂×Dic₃	1	2	yes	—
106	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
107	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
108	C₃×C₄²	—	3	2	no	—
109	C₃×C₄²	—	3	1	no	—
110	C₃×C₄²	—	3	1	no	—
111	C₄×Dic₃	C₃⋊C₈	1	2	yes	—
112	C₄×Dic₃	C₂×Dic₃	1	1	yes	characteristic
113	C₄×Dic₃	C₂×Dic₃	1	1	yes	characteristic
114	C₂×C₃⋊C₈	C₃⋊C₈	1	4	yes	—
115	C₂×C₃⋊C₈	C₂×Dic₃	1	1	yes	characteristic
116	C₂×C₃⋊C₈	C₂×Dic₃	1	1	yes	characteristic
117	C₃×C₁₆	—	3	4	no	—
118	C₃⋊C₁₆	—	3	4	no	—
119	C₃⋊C₁₆	—	3	4	no	—
120	C₃⋊C₁₆	—	6	4	no	—
121	C₃⋊C₁₆	C₂×Dic₃	1	4	yes	complemented
122	C₂²×C₃²	—	2	2	no	—
123	C₂²×C₃²	C₄×C₈	1	2	yes	—
124	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
125	C₃²×C₄	C₄×C₈	1	2	yes	—
126	C₃²×C₄	C₂×C₄²	1	1	yes	characteristic
127	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
128	C₃×Dic₃	—	2	2	no	—
129	C₃×Dic₃	M₃₂	1	4	yes	complemented
130	C₂²×C₈	—	3	1	no	—
131	C₂²×C₈	D₃²	1	1	yes	characteristic
132	C₂×C₄²	—	3	1	no	—
133	M₃₂	—	3	4	no	—
134	M₃₂	—	9	4	no	—
135	C₂×C₁₆	—	3	2	no	—
136	C₂×C₁₆	—	9	2	no	—
137	C₄×C₈	—	3	1	no	—
138	C₄×C₈	—	3	1	no	—
139	C₄×C₈	—	3	1	no	—
140	C₄×C₈	—	3	1	no	—
141	C₂³×C₃	—	2	1	no	—
142	C₂³×C₃	D₃×C₈	1	1	yes	characteristic
143	C₂³×C₃	C₂×C₃⋊C₈	1	1	yes	characteristic
144	C₂×C₃×C₄	—	2	1	no	—
145	C₂×C₃×C₄	—	2	2	no	—
146	C₂×C₃×C₄	—	2	2	no	—
147	C₂×C₃×C₄	—	2	1	no	—
148	C₂×C₃×C₄	—	3	2	no	—
149	C₂×C₃×C₄	—	3	2	no	—
150	C₂×C₃×C₄	—	6	4	no	—
151	C₂×C₃×C₄	D₃×C₈	1	1	yes	characteristic
152	C₂×C₃×C₄	D₃×C₈	1	2	yes	—
153	C₂×C₃×C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
154	C₂×C₃×C₄	C₂×C₃⋊C₈	1	2	yes	—
155	C₂×C₃×C₄	C₄×Dic₃	1	2	yes	—
156	C₂×C₃×C₄	C₄×Dic₃	1	2	yes	—
157	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
158	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
159	C₂×Dic₃	—	2	4	no	—
160	C₂×Dic₃	C₂×C₃⋊C₈	1	2	yes	—
161	C₂×Dic₃	C₂×C₃⋊C₈	1	2	yes	—
162	C₃×C₈	—	2	2	no	—
163	C₃×C₈	—	2	1	no	—
164	C₃×C₈	—	2	1	no	—
165	C₃×C₈	—	3	2	no	—
166	C₃×C₈	—	3	2	no	—
167	C₃×C₈	C₄×Dic₃	1	2	yes	—
168	C₃×C₈	C₄×Dic₃	1	2	yes	—
169	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
170	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
171	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
172	C₃×C₈	C₂²×Dic₃	1	1	yes	characteristic
173	C₃⋊C₈	C₂×C₃⋊C₈	1	2	yes	—
174	C₃⋊C₈	C₂×C₃⋊C₈	1	2	yes	—
175	C₂×C₃²	—	2	2	no	—
176	C₂×C₃²	C₂×C₄×C₈	1	1	yes	characteristic
177	C₂×C₃²	C₂×M₃₂	1	2	yes	—
178	C₂²×C₄	—	3	2	no	—
179	C₂²×C₄	D₃×Dic₃	1	1	yes	characteristic
180	C₂×C₈	—	3	4	no	—
181	C₂×C₈	—	3	1	no	—
182	C₂×C₈	—	3	1	no	—
183	C₂×C₈	D₃×Dic₃	1	1	yes	characteristic
184	C₂×C₈	D₃×Dic₃	1	2	yes	—
185	C₂×C₈	#624	1	2	yes	—
186	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
187	C₄²	—	3	2	no	—
188	C₄²	—	3	1	no	—
189	C₄²	—	3	1	no	—
190	C₁₆	—	3	4	no	—
191	C₁₆	—	9	4	no	—
192	C₂²×C₃	—	2	2	no	—
193	C₂²×C₃	—	2	2	no	—
194	C₂²×C₃	—	2	2	no	—
195	C₂²×C₃	—	2	1	no	—
196	C₂²×C₃	—	4	2	no	—
197	C₂²×C₃	C₄×C₃⋊C₈	1	2	yes	—
198	C₂²×C₃	C₈×Dic₃	1	2	yes	—
199	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
200	C₂²×C₃	C₂²×C₃⋊C₈	1	1	yes	characteristic
201	C₃×C₄	—	2	2	no	—
202	C₃×C₄	—	2	1	no	—
203	C₃×C₄	—	2	1	no	—
204	C₃×C₄	—	3	4	no	—
205	C₃×C₄	—	6	2	no	—
206	C₃×C₄	C₄×C₃⋊C₈	1	2	yes	—
207	C₃×C₄	C₈×Dic₃	1	2	yes	—
208	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
209	C₃×C₄	C₂²×C₃⋊C₈	1	1	yes	characteristic
210	C₃×C₄	C₂×C₄×Dic₃	1	1	yes	characteristic
211	C₃×C₄	C₂×C₄×Dic₃	1	1	yes	characteristic
212	Dic₃	—	2	2	no	—
213	Dic₃	#812	1	4	yes	direct product factor
214	C₃²	C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
215	C₂³	D₃×C₃⋊C₈	1	1	yes	characteristic
216	C₂×C₄	—	3	2	no	—
217	C₂×C₄	—	3	2	no	—
218	C₂×C₄	—	6	4	no	—
219	C₂×C₄	D₃×C₃⋊C₈	1	1	yes	characteristic
220	C₂×C₄	D₃×C₃⋊C₈	1	2	yes	—
221	C₂×C₄	Dic₃²	1	2	yes	—
222	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
223	C₈	—	3	2	no	—
224	C₈	—	3	2	no	—
225	C₈	Dic₃²	1	2	yes	—
226	C₈	C₂×D₃×Dic₃	1	1	yes	characteristic
227	C₈	C₂×#624	1	1	yes	characteristic
228	C₂×C₃	—	2	2	no	—
229	C₂×C₃	—	2	2	no	—
230	C₂×C₃	—	2	1	no	—
231	C₂×C₃	—	2	2	no	—
232	C₂×C₃	—	4	2	no	—
233	C₂×C₃	D₃×M₃₂	1	2	yes	—
234	C₂×C₃	C₂×C₄×C₃⋊C₈	1	1	yes	characteristic
235	C₂×C₃	C₂×#812	1	2	yes	—
236	C₂×C₃	C₂×C₈×Dic₃	1	1	yes	characteristic
237	C₂²	—	2	2	no	—
238	C₂²	Dic₃×C₃⋊C₈	1	2	yes	—
239	C₂²	C₂×D₃×C₃⋊C₈	1	1	yes	characteristic
240	C₄	—	3	4	no	—
241	C₄	—	6	2	no	—
242	C₄	Dic₃×C₃⋊C₈	1	2	yes	—
243	C₄	C₂×D₃×C₃⋊C₈	1	1	yes	characteristic
244	C₄	C₂×Dic₃²	1	1	yes	characteristic
245	C₃	—	2	1	no	—
246	C₃	C₄×#812	1	1	yes	characteristic, complemented
247	C₃	Dic₃×M₃₂	1	1	yes	characteristic, complemented
248	C₂	—	2	2	no	—
249	C₂	D₃×#812	1	2	yes	—
250	C₂	C₂×Dic₃×C₃⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₃²
commutator	C₂×C₃²	C₂×C₄×C₈
Fitting	C₂²×C₃²×C₈	C₂²
socle	C₂²×C₃²	C₂²×C₈
prime radical	C₂³×C₃²	C₂×C₈
cosocle	C₂×C₃²×C₈	C₂³
hypercenter	C₂²×C₈	D₃²
hypocenter	C₃²	C₄×M₃₂
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. #10589103	C₂	semidirect
5. Dic₃×C₃⋊C₁₆	C₂	semidirect
11. #63639	C₄	semidirect
17. C₃×#812	C₄	semidirect
42. C₃⋊(C₃⋊C₁₆)	C₂×C₄	semidirect
43. C₃×C₃⋊C₁₆	C₂×C₄	semidirect
65. #812	Dic₃	direct (N × H)
121. C₃⋊C₁₆	C₂×Dic₃	semidirect
129. C₃×Dic₃	M₃₂	semidirect
213. Dic₃	#812	direct (N × H)
214. C₃²	C₄×M₃₂	semidirect
246. C₃	C₄×#812	semidirect
247. C₃	Dic₃×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63639	2
C₂×C₃×C₈×Dic₃	2
C₂×C₃×#812	2
#10589103	2
Dic₃×C₃⋊C₁₆	2
Dic₃×M₃₂	3
C₄×#812	3

Subgroups — Dic3×#812 #11795865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×#812 #11795865