Subgroups — C₃×#67670 #11771000

Order 1152.

347 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	C₃²×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×#4926	C₂	1	1	yes	maximal, characteristic
3	C₃×#4926	C₂	1	1	yes	maximal, characteristic
4	C₃×#1291	—	3	1	no	maximal
5	#67670	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃²×M₁₆	—	2	1	no	—
7	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
8	C₃²×#97	—	2	1	no	—
9	C₃²×C₄×C₈	C₄	1	2	yes	—
10	C₃×#830	—	2	1	no	—
11	C₃×#830	C₄	1	2	yes	—
12	C₃×C₄⋊(C₃⋊C₈)	—	2	1	no	—
13	C₃×C₄⋊(C₃⋊C₈)	C₄	1	2	yes	—
14	C₃×#803	—	2	1	no	—
15	C₃×#803	—	2	1	no	—
16	C₃×#432	—	3	1	no	—
17	C₃×#432	—	3	1	no	—
18	C₃×C₄×M₁₆	—	2	1	no	—
19	C₃×C₄×M₁₆	D₃	1	1	yes	characteristic
20	C₃×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic
21	#4926	C₂×C₃	1	1	yes	characteristic
22	#4926	C₂×C₃	1	1	yes	characteristic
23	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
25	C₂²×C₃²×C₄	Q₈	1	1	yes	characteristic
26	C₃²×M₁₆	—	2	4	no	—
27	C₂×C₃²×C₈	—	2	2	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	D₄	1	1	yes	characteristic
32	C₂×C₃×C₃⋊C₈	—	2	2	no	—
33	C₂×C₃×C₃⋊C₈	—	2	2	no	—
34	#1291	—	3	1	no	Sylow
35	C₂×C₃×M₁₆	—	2	2	no	—
36	C₂×C₃×M₁₆	—	2	1	no	—
37	C₂×C₃×M₁₆	—	2	1	no	—
38	C₂×C₃×C₄²	—	2	1	no	—
39	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
40	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
41	C₃×C₄⋊C₈	—	3	2	no	—
42	C₃×C₄⋊C₈	—	6	1	no	—
43	C₃×C₂²⋊C₈	—	3	2	no	—
44	C₃×C₂²⋊C₈	—	6	1	no	—
45	C₃×#97	—	2	2	no	—
46	C₃×#97	—	2	1	no	—
47	C₃×#97	—	2	1	no	—
48	C₃×#97	—	6	1	no	—
49	C₃×#97	—	6	1	no	—
50	C₃×C₄×C₈	—	2	2	no	—
51	C₃×C₄×C₈	Dic₃	1	2	yes	—
52	C₃×C₄×C₈	C₃×C₄	1	2	yes	—
53	#830	—	2	1	no	—
54	#830	C₃×C₄	1	2	yes	—
55	C₄⋊(C₃⋊C₈)	—	2	1	no	—
56	C₄⋊(C₃⋊C₈)	C₃×C₄	1	2	yes	—
57	#803	—	2	1	no	—
58	#803	—	2	1	no	—
59	C₂³×C₃²	C₄⋊C₄	1	1	yes	characteristic
60	C₂×C₃²×C₄	—	2	2	no	—
61	C₂×C₃²×C₄	—	4	1	no	—
62	C₂×C₃²×C₄	—	4	1	no	—
63	C₂×C₃²×C₄	C₄²	1	1	yes	characteristic
64	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
68	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
69	C₃²×C₈	—	2	4	no	—
70	C₃×C₃⋊C₈	—	4	2	no	—
71	C₃×C₃⋊C₈	—	4	2	no	—
72	#432	—	3	1	no	—
73	#432	—	3	1	no	—
74	C₄×M₁₆	C₃×D₃	1	1	yes	characteristic
75	C₂²×C₃×C₄	—	2	1	no	—
76	C₂²×C₃×C₄	—	2	1	no	—
77	C₂²×C₃×C₄	—	2	1	no	—
78	C₂²×C₃×C₄	Dic₆	1	1	yes	characteristic
79	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
80	C₂²×C₃×C₄	#67	1	1	yes	characteristic
81	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
82	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
83	C₂²×C₃×C₄	C₃×Q₈	1	1	yes	characteristic
84	C₃×M₁₆	—	2	8	no	—
85	C₃×M₁₆	—	2	4	no	—
86	C₃×M₁₆	—	2	4	no	—
87	C₂×C₃×C₈	—	2	4	no	—
88	C₂×C₃×C₈	—	2	2	no	—
89	C₂×C₃×C₈	—	2	2	no	—
90	C₂×C₃×C₈	—	6	2	no	—
91	C₂×C₃×C₈	—	6	2	no	—
92	C₃×C₄²	—	2	1	no	—
93	C₃×C₄²	—	2	1	no	—
94	C₃×C₄²	—	2	1	no	—
95	C₃×C₄²	—	2	1	no	—
96	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
97	C₃×C₄²	D₁₂	1	1	yes	characteristic
98	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
99	C₃×C₄²	#67	1	1	yes	characteristic
100	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
101	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
102	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
103	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
104	C₂×C₃⋊C₈	—	2	2	no	—
105	C₂×C₃⋊C₈	—	2	2	no	—
106	C₂²×C₃²	—	2	1	no	—
107	C₂²×C₃²	—	2	1	no	—
108	C₂²×C₃²	—	2	1	no	—
109	C₂²×C₃²	#95	1	1	yes	characteristic
110	C₃²×C₄	—	2	1	no	—
111	C₃²×C₄	—	2	1	no	—
112	C₃²×C₄	—	2	1	no	—
113	C₃²×C₄	—	2	1	no	—
114	C₃²×C₄	—	2	1	no	—
115	C₃²×C₄	#104	1	2	yes	—
116	C₂×M₁₆	—	2	1	no	—
117	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
118	C₄⋊C₈	—	3	2	no	—
119	C₄⋊C₈	—	6	1	no	—
120	C₂²⋊C₈	—	3	2	no	—
121	C₂²⋊C₈	—	6	1	no	—
122	#97	—	2	1	no	—
123	#97	—	6	1	no	—
124	#97	—	6	1	no	—
125	C₄×C₈	C₃×Dic₃	1	2	yes	—
126	C₂³×C₃	—	2	1	no	—
127	C₂³×C₃	Dic₃⋊C₄	1	1	yes	characteristic
128	C₂³×C₃	C₃×C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₃×C₄	—	2	4	no	—
130	C₂×C₃×C₄	—	2	2	no	—
131	C₂×C₃×C₄	—	2	2	no	—
132	C₂×C₃×C₄	—	2	1	no	—
133	C₂×C₃×C₄	—	2	1	no	—
134	C₂×C₃×C₄	—	2	1	no	—
135	C₂×C₃×C₄	—	2	1	no	—
136	C₂×C₃×C₄	—	2	1	no	—
137	C₂×C₃×C₄	—	2	1	no	—
138	C₂×C₃×C₄	—	4	1	no	—
139	C₂×C₃×C₄	—	4	1	no	—
140	C₂×C₃×C₄	—	4	1	no	—
141	C₂×C₃×C₄	—	4	1	no	—
142	C₂×C₃×C₄	—	4	2	no	—
143	C₂×C₃×C₄	—	4	2	no	—
144	C₂×C₃×C₄	C₄×Dic₃	1	1	yes	characteristic
145	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
146	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
147	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
148	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
149	C₂×C₃×C₄	#217	1	1	yes	characteristic
150	C₂×C₃×C₄	C₃×C₄²	1	1	yes	characteristic
151	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₃×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₃×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
156	C₃×C₈	—	2	8	no	—
157	C₃×C₈	—	2	4	no	—
158	C₃×C₈	—	2	4	no	—
159	C₃×C₈	—	12	2	no	—
160	C₃×C₈	—	12	2	no	—
161	C₃⋊C₈	—	4	2	no	—
162	C₃⋊C₈	—	4	2	no	—
163	C₂×C₃²	—	4	1	no	—
164	C₂×C₃²	#338	1	1	yes	characteristic
165	C₂×C₃²	#339	1	1	yes	characteristic
166	C₂×C₃²	#344	1	1	yes	characteristic
167	C₂²×C₄	C₃×Dic₆	1	1	yes	characteristic
168	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
169	C₂²×C₄	C₃×#67	1	1	yes	characteristic
170	M₁₆	—	2	4	no	—
171	C₂×C₈	—	2	2	no	—
172	C₂×C₈	—	6	2	no	—
173	C₂×C₈	—	6	2	no	—
174	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
175	C₄²	C₃×D₁₂	1	1	yes	characteristic
176	C₄²	C₂×C₃×Dic₃	1	1	yes	characteristic
177	C₄²	C₃×#67	1	1	yes	characteristic
178	C₂²×C₃	—	2	2	no	—
179	C₂²×C₃	—	2	1	no	—
180	C₂²×C₃	—	2	1	no	—
181	C₂²×C₃	—	2	1	no	—
182	C₂²×C₃	—	2	1	no	—
183	C₂²×C₃	—	2	1	no	—
184	C₂²×C₃	—	2	1	no	—
185	C₂²×C₃	—	2	1	no	—
186	C₂²×C₃	—	4	1	no	—
187	C₂²×C₃	—	4	1	no	—
188	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
189	C₂²×C₃	C₃×#95	1	1	yes	characteristic
190	C₃×C₄	—	2	2	no	—
191	C₃×C₄	—	2	2	no	—
192	C₃×C₄	—	2	2	no	—
193	C₃×C₄	—	2	1	no	—
194	C₃×C₄	—	2	1	no	—
195	C₃×C₄	—	2	1	no	—
196	C₃×C₄	—	2	1	no	—
197	C₃×C₄	—	2	1	no	—
198	C₃×C₄	—	2	1	no	—
199	C₃×C₄	—	2	1	no	—
200	C₃×C₄	—	2	1	no	—
201	C₃×C₄	—	2	1	no	—
202	C₃×C₄	—	2	1	no	—
203	C₃×C₄	—	2	2	no	—
204	C₃×C₄	—	4	1	no	—
205	C₃×C₄	—	4	1	no	—
206	C₃×C₄	#805	1	2	yes	—
207	C₃×C₄	C₃×#104	1	2	yes	—
208	C₃²	#1291	1	1	yes	characteristic, complemented, Sylow
209	C₂³	C₃×Dic₃⋊C₄	1	1	yes	characteristic
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	C₃×C₄×Dic₃	1	1	yes	characteristic
214	C₂×C₄	C₃×Dic₃⋊C₄	1	1	yes	characteristic
215	C₂×C₄	C₃×C₄⋊Dic₃	1	1	yes	characteristic
216	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
217	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
218	C₂×C₄	C₃×#217	1	1	yes	characteristic
219	C₈	—	2	4	no	—
220	C₈	—	12	2	no	—
221	C₈	—	12	2	no	—
222	C₂×C₃	—	2	1	no	—
223	C₂×C₃	—	2	1	no	—
224	C₂×C₃	—	2	1	no	—
225	C₂×C₃	—	4	2	no	—
226	C₂×C₃	—	4	1	no	—
227	C₂×C₃	—	4	1	no	—
228	C₂×C₃	#4523	1	1	yes	characteristic
229	C₂×C₃	#4556	1	1	yes	characteristic
230	C₂×C₃	C₃⋊#338	1	1	yes	characteristic
231	C₂×C₃	C₃×#338	1	1	yes	characteristic
232	C₂×C₃	C₃×#339	1	1	yes	characteristic
233	C₂×C₃	C₃×#344	1	1	yes	characteristic
234	C₂²	—	2	1	no	—
235	C₂²	—	2	1	no	—
236	C₂²	—	2	1	no	—
237	C₂²	C₃×C₃⋊#95	1	1	yes	characteristic
238	C₄	—	2	1	no	—
239	C₄	—	2	1	no	—
240	C₄	—	2	1	no	—
241	C₄	—	2	1	no	—
242	C₄	—	2	1	no	—
243	C₄	C₃×#805	1	2	yes	—
244	C₃	—	2	1	no	—
245	C₃	#67670	1	1	yes	characteristic, direct product factor
246	C₃	C₃×#1291	1	1	yes	characteristic, complemented
247	C₂	—	4	1	no	—
248	C₂	C₃×#4523	1	1	yes	characteristic
249	C₂	C₃×#4556	1	1	yes	characteristic
250	C₂	C₃×C₃⋊#338	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₃⋊#95
commutator	C₂×C₃×C₄	C₃×C₄²
Frattini	C₂×C₄²	C₂×C₃×D₃
Fitting	C₃²×C₄×M₁₆	C₂
socle	C₂²×C₃²	#95
prime radical	C₂³×C₃²	C₄⋊C₄
cosocle	C₂×C₃×C₄²	C₂²×C₃
hypercenter	C₃×C₄×M₁₆	D₃
hypocenter	C₃	C₃×#1291
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ C₃×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
5. #67670	C₃	direct (N × H)
208. C₃²	#1291	semidirect
245. C₃	#67670	direct (N × H)
246. C₃	C₃×#1291	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₄×M₁₆	2
C₃×#4926	2
C₃×#1291	3
#67670	3

Subgroups — C3×#67670 #11771000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#67670 #11771000