Subgroups — C₃×#67615 #11771140

Order 1152.

433 conjugacy classes of subgroups.

The subgroup lattice has 271 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#376	C₂	1	1	yes	maximal, characteristic
2	C₃×#4926	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×#208	C₂	1	1	yes	maximal, characteristic
4	C₃×#1300	—	3	1	no	maximal
5	#67615	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃²×C₄²	—	2	1	no	—
7	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
8	C₂×C₃×#208	—	2	1	no	—
9	C₃²×#95	—	2	1	no	—
10	C₃²×#95	C₄	1	2	yes	—
11	C₃×#830	—	2	1	no	—
12	C₃×C₄⋊(C₃⋊C₈)	C₄	1	2	yes	complemented
13	C₃×#803	—	2	1	no	—
14	C₃×#803	C₄	1	2	yes	complemented
15	C₃×C₄×C₃⋊C₈	—	2	1	no	—
16	C₃×#432	—	3	1	no	—
17	C₃×C₄×M₁₆	—	3	1	no	—
18	C₃×#376	—	2	1	no	—
19	C₃×#376	D₃	1	1	yes	characteristic
20	C₃×#376	C₂×C₃	1	1	yes	characteristic
21	#4926	C₂×C₃	1	1	yes	characteristic
22	C₄×#208	C₂×C₃	1	1	yes	characteristic
23	C₂²×C₃²×C₄	—	2	2	no	—
24	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
26	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
27	C₃²×C₄²	—	2	4	no	—
28	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
29	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
30	C₃²×C₄²	D₄	1	1	yes	characteristic
31	C₃²×C₄²	Q₈	1	1	yes	characteristic
32	C₃×#208	—	2	4	no	—
33	C₂×C₃×C₃⋊C₈	—	2	2	no	—
34	C₂×C₃×C₃⋊C₈	—	2	2	no	—
35	#1300	—	3	1	no	Sylow
36	C₂×C₃×M₁₆	—	6	1	no	—
37	C₂×C₃×C₄²	—	2	2	no	—
38	C₂×C₃×C₄²	—	2	1	no	—
39	C₂×C₃×C₄²	—	2	1	no	—
40	C₂×C₃×C₄²	—	2	1	no	—
41	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
42	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
43	C₂×#208	—	2	1	no	—
44	C₃×C₄⋊C₈	—	3	2	no	—
45	C₃×C₂²⋊C₈	—	6	1	no	—
46	C₃×#97	—	3	2	no	—
47	C₃×#97	—	6	1	no	—
48	C₃×C₄×C₈	—	6	1	no	—
49	C₃×#95	—	2	2	no	—
50	C₃×#95	—	2	1	no	—
51	C₃×#95	—	2	1	no	—
52	C₃×#95	—	2	2	no	—
53	C₃×#95	Dic₃	1	2	yes	—
54	C₃×#95	C₃×C₄	1	2	yes	—
55	#830	—	2	1	no	—
56	C₄⋊(C₃⋊C₈)	C₃×C₄	1	2	yes	complemented
57	#803	—	2	1	no	—
58	#803	C₃×C₄	1	2	yes	complemented
59	C₄×C₃⋊C₈	—	2	1	no	—
60	C₂³×C₃²	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₃²×C₄	—	2	2	no	—
62	C₂×C₃²×C₄	—	2	4	no	—
63	C₂×C₃²×C₄	—	2	2	no	—
64	C₂×C₃²×C₄	—	4	1	no	—
65	C₂×C₃²×C₄	—	4	2	no	—
66	C₂×C₃²×C₄	—	4	2	no	—
67	C₂×C₃²×C₄	C₄²	1	1	yes	characteristic
68	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
72	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
73	C₃×C₃⋊C₈	—	2	4	no	—
74	C₃×C₃⋊C₈	—	4	2	no	—
75	#432	—	3	1	no	—
76	C₄×M₁₆	—	3	1	no	—
77	#376	C₃×D₃	1	1	yes	characteristic
78	C₂²×C₃×C₄	—	2	4	no	—
79	C₂²×C₃×C₄	—	2	2	no	—
80	C₂²×C₃×C₄	—	2	2	no	—
81	C₂²×C₃×C₄	—	2	1	no	—
82	C₂²×C₃×C₄	—	2	1	no	—
83	C₂²×C₃×C₄	—	2	1	no	—
84	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
85	C₂²×C₃×C₄	#67	1	1	yes	characteristic
86	C₂²×C₃×C₄	#67	1	1	yes	characteristic
87	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
88	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
89	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
90	C₃×M₁₆	—	6	4	no	—
91	C₂×C₃×C₈	—	6	2	no	—
92	C₂×C₃×C₈	—	6	2	no	—
93	C₃×C₄²	—	2	8	no	—
94	C₃×C₄²	—	2	4	no	—
95	C₃×C₄²	—	2	4	no	—
96	C₃×C₄²	—	2	1	no	—
97	C₃×C₄²	—	2	1	no	—
98	C₃×C₄²	—	2	1	no	—
99	C₃×C₄²	—	2	1	no	—
100	C₃×C₄²	Dic₆	1	1	yes	characteristic
101	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
102	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
103	C₃×C₄²	D₁₂	1	1	yes	characteristic
104	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
105	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
106	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
107	C₃×C₄²	C₃×Q₈	1	1	yes	characteristic
108	#208	—	2	4	no	—
109	C₂×C₃⋊C₈	—	2	2	no	—
110	C₂×C₃⋊C₈	—	2	2	no	—
111	C₂²×C₃²	—	2	1	no	—
112	C₂²×C₃²	—	2	1	no	—
113	C₂²×C₃²	#95	1	1	yes	characteristic
114	C₂²×C₃²	#104	1	2	yes	—
115	C₃²×C₄	—	2	1	no	—
116	C₃²×C₄	—	2	1	no	—
117	C₃²×C₄	—	2	1	no	—
118	C₃²×C₄	—	2	1	no	—
119	C₃²×C₄	—	2	1	no	—
120	C₃²×C₄	—	4	4	no	—
121	C₃²×C₄	#104	1	2	yes	—
122	C₂×M₁₆	—	6	1	no	—
123	C₂×C₄²	—	2	1	no	—
124	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
125	C₄⋊C₈	—	3	2	no	—
126	C₂²⋊C₈	—	6	1	no	—
127	#97	—	3	2	no	—
128	#97	—	6	1	no	—
129	C₄×C₈	—	6	1	no	—
130	#95	—	2	1	no	—
131	#95	C₃×Dic₃	1	2	yes	—
132	C₂³×C₃	—	2	1	no	—
133	C₂³×C₃	#217	1	1	yes	characteristic
134	C₂³×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₃×C₄	—	2	4	no	—
136	C₂×C₃×C₄	—	2	2	no	—
137	C₂×C₃×C₄	—	2	2	no	—
138	C₂×C₃×C₄	—	2	2	no	—
139	C₂×C₃×C₄	—	2	2	no	—
140	C₂×C₃×C₄	—	2	8	no	—
141	C₂×C₃×C₄	—	2	4	no	—
142	C₂×C₃×C₄	—	2	4	no	—
143	C₂×C₃×C₄	—	2	1	no	—
144	C₂×C₃×C₄	—	2	1	no	—
145	C₂×C₃×C₄	—	2	1	no	—
146	C₂×C₃×C₄	—	2	1	no	—
147	C₂×C₃×C₄	—	2	1	no	—
148	C₂×C₃×C₄	—	2	1	no	—
149	C₂×C₃×C₄	—	4	2	no	—
150	C₂×C₃×C₄	—	4	1	no	—
151	C₂×C₃×C₄	—	4	1	no	—
152	C₂×C₃×C₄	—	4	2	no	—
153	C₂×C₃×C₄	—	4	4	no	—
154	C₂×C₃×C₄	—	4	2	no	—
155	C₂×C₃×C₄	—	4	2	no	—
156	C₂×C₃×C₄	—	4	4	no	—
157	C₂×C₃×C₄	—	4	2	no	—
158	C₂×C₃×C₄	—	4	2	no	—
159	C₂×C₃×C₄	C₄×Dic₃	1	1	yes	characteristic
160	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
161	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
162	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
163	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
164	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
165	C₂×C₃×C₄	C₃×C₄²	1	1	yes	characteristic
166	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₃×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₃×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₃×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
171	C₃×C₈	—	6	4	no	—
172	C₃×C₈	—	12	2	no	—
173	C₃⋊C₈	—	2	4	no	—
174	C₃⋊C₈	—	4	2	no	—
175	C₂×C₃²	—	2	2	no	—
176	C₂×C₃²	#339	1	1	yes	characteristic
177	C₂×C₃²	#339	1	1	yes	characteristic
178	C₂×C₃²	#344	1	1	yes	characteristic
179	C₂²×C₄	—	2	2	no	—
180	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
181	C₂²×C₄	C₃×#67	1	1	yes	characteristic
182	C₂²×C₄	C₃×#67	1	1	yes	characteristic
183	M₁₆	—	6	4	no	—
184	C₂×C₈	—	6	2	no	—
185	C₂×C₈	—	6	2	no	—
186	C₄²	—	2	4	no	—
187	C₄²	C₃×Dic₆	1	1	yes	characteristic
188	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
189	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
190	C₄²	C₃×D₁₂	1	1	yes	characteristic
191	C₂²×C₃	—	2	2	no	—
192	C₂²×C₃	—	2	2	no	—
193	C₂²×C₃	—	2	1	no	—
194	C₂²×C₃	—	2	1	no	—
195	C₂²×C₃	—	2	1	no	—
196	C₂²×C₃	—	2	1	no	—
197	C₂²×C₃	—	2	1	no	—
198	C₂²×C₃	—	2	2	no	—
199	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
200	C₂²×C₃	#837	1	2	yes	—
201	C₂²×C₃	C₃×#95	1	1	yes	characteristic
202	C₂²×C₃	C₃×#104	1	2	yes	—
203	C₃×C₄	—	2	2	no	—
204	C₃×C₄	—	2	1	no	—
205	C₃×C₄	—	2	1	no	—
206	C₃×C₄	—	2	1	no	—
207	C₃×C₄	—	2	1	no	—
208	C₃×C₄	—	2	1	no	—
209	C₃×C₄	—	2	1	no	—
210	C₃×C₄	—	2	1	no	—
211	C₃×C₄	—	2	1	no	—
212	C₃×C₄	—	2	1	no	—
213	C₃×C₄	—	2	1	no	—
214	C₃×C₄	—	2	2	no	—
215	C₃×C₄	—	4	1	no	—
216	C₃×C₄	—	4	1	no	—
217	C₃×C₄	—	4	1	no	—
218	C₃×C₄	—	4	1	no	—
219	C₃×C₄	—	4	8	no	—
220	C₃×C₄	—	4	4	no	—
221	C₃×C₄	—	4	4	no	—
222	C₃×C₄	#805	1	2	yes	—
223	C₃×C₄	C₃×#104	1	2	yes	—
224	C₃²	#1300	1	1	yes	characteristic, complemented, Sylow
225	C₂³	C₃×#217	1	1	yes	characteristic
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	4	no	—
229	C₂×C₄	—	4	1	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	C₃×C₄×Dic₃	1	1	yes	characteristic
233	C₂×C₄	C₃×Dic₃⋊C₄	1	1	yes	characteristic
234	C₂×C₄	C₃×Dic₃⋊C₄	1	1	yes	characteristic
235	C₂×C₄	C₃×C₄⋊Dic₃	1	1	yes	characteristic
236	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
237	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
238	C₈	—	6	4	no	—
239	C₈	—	12	2	no	—
240	C₂×C₃	—	2	4	no	—
241	C₂×C₃	—	2	2	no	—
242	C₂×C₃	—	2	2	no	—
243	C₂×C₃	—	2	1	no	—
244	C₂×C₃	—	2	1	no	—
245	C₂×C₃	—	2	1	no	—
246	C₂×C₃	#4523	1	1	yes	characteristic
247	C₂×C₃	#4532	1	1	yes	characteristic
248	C₂×C₃	#4533	1	1	yes	characteristic
249	C₂×C₃	C₃×#339	1	1	yes	characteristic
250	C₂×C₃	C₃×#339	1	1	yes	characteristic
251	C₂×C₃	C₃×#344	1	1	yes	characteristic
252	C₂²	—	2	1	no	—
253	C₂²	—	2	1	no	—
254	C₂²	C₃×C₃⋊#95	1	1	yes	characteristic
255	C₂²	C₃×#837	1	2	yes	—
256	C₄	—	2	1	no	—
257	C₄	—	2	1	no	—
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	2	1	no	—
261	C₄	—	4	4	no	—
262	C₄	C₃×#805	1	2	yes	—
263	C₃	—	2	1	no	—
264	C₃	#67615	1	1	yes	characteristic, direct product factor
265	C₃	C₃×#1300	1	1	yes	characteristic, complemented
266	C₂	—	2	2	no	—
267	C₂	C₃×#4523	1	1	yes	characteristic
268	C₂	C₃×#4532	1	1	yes	characteristic
269	C₂	C₃×#4533	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	(C₂×D₃)⋊C₄
commutator	C₂×C₃×C₄	C₃×C₄²
Frattini	C₂×C₄²	C₂×C₃×D₃
Fitting	C₃²×#376	C₂
socle	C₂²×C₃²	#95
prime radical	C₂³×C₃²	C₂²⋊C₄
cosocle	C₂×C₃×C₄²	C₂²×C₃
hypercenter	C₃×#376	D₃
hypocenter	C₃	C₃×#1300
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×#376

Complements

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

N	H ≅ G/N	type
5. #67615	C₃	direct (N × H)
12. C₃×C₄⋊(C₃⋊C₈)	C₄	semidirect
14. C₃×#803	C₄	semidirect
56. C₄⋊(C₃⋊C₈)	C₃×C₄	semidirect
58. #803	C₃×C₄	semidirect
224. C₃²	#1300	semidirect
264. C₃	#67615	direct (N × H)
265. C₃	C₃×#1300	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#376	2
C₃×#4926	2
C₃×C₄×#208	2
C₃×#1300	3
#67615	3

Subgroups — C3×#67615 #11771140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#67615 #11771140