Subgroups — C₃×#67753 #11770997

Order 1152.

331 conjugacy classes of subgroups.

The subgroup lattice has 251 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#432	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×#1291	—	3	1	no	maximal
5	#67753	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
7	C₂×C₃×#208	—	2	1	no	—
8	C₃²×C₄⋊C₈	C₄	1	2	yes	—
9	C₃²×C₂²⋊C₈	—	2	1	no	—
10	C₃²×#97	—	2	1	no	—
11	C₃×#830	C₄	1	2	yes	—
12	C₃×C₄⋊(C₃⋊C₈)	—	2	1	no	—
13	C₃×#803	—	2	1	no	—
14	C₃×#803	—	2	1	no	—
15	C₃×C₄×C₃⋊C₈	C₄	1	2	yes	—
16	C₃×#432	—	2	1	no	—
17	C₃×#432	—	3	1	no	—
18	C₃×#432	D₃	1	1	yes	characteristic
19	C₃×#432	C₂×C₃	1	1	yes	characteristic
20	C₃×C₄×M₁₆	—	3	1	no	—
21	#4926	C₂×C₃	1	1	yes	characteristic
22	C₄×#208	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	C₂×C₃²×C₈	—	2	2	no	—
27	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
28	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
29	C₃²×C₄²	D₄	1	1	yes	characteristic
30	C₃²×C₄²	D₄	1	1	yes	characteristic
31	C₃×#208	—	2	4	no	—
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	—	6	1	no	—
36	C₂×C₃×C₄²	—	2	1	no	—
37	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
38	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
39	C₂×#208	—	2	1	no	—
40	C₃×C₄⋊C₈	—	2	2	no	—
41	C₃×C₄⋊C₈	—	6	1	no	—
42	C₃×C₄⋊C₈	Dic₃	1	2	yes	—
43	C₃×C₄⋊C₈	C₃×C₄	1	2	yes	—
44	C₃×C₂²⋊C₈	—	2	2	no	—
45	C₃×C₂²⋊C₈	—	2	1	no	—
46	C₃×C₂²⋊C₈	—	2	1	no	—
47	C₃×C₂²⋊C₈	—	3	2	no	—
48	C₃×#97	—	2	2	no	—
49	C₃×#97	—	2	1	no	—
50	C₃×#97	—	2	1	no	—
51	C₃×#97	—	6	1	no	—
52	C₃×#97	—	6	1	no	—
53	C₃×C₄×C₈	—	3	2	no	—
54	#830	C₃×C₄	1	2	yes	—
55	C₄⋊(C₃⋊C₈)	—	2	1	no	—
56	#803	—	2	1	no	—
57	#803	—	2	1	no	—
58	C₄×C₃⋊C₈	C₃×C₄	1	2	yes	—
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	—	4	2	no	—
70	C₃×C₃⋊C₈	—	2	4	no	—
71	C₃×C₃⋊C₈	—	4	2	no	—
72	#432	—	3	1	no	—
73	#432	C₃×D₃	1	1	yes	characteristic
74	C₄×M₁₆	—	3	1	no	—
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	—	6	4	no	—
85	C₂×C₃×C₈	—	2	4	no	—
86	C₂×C₃×C₈	—	2	2	no	—
87	C₂×C₃×C₈	—	2	2	no	—
88	C₂×C₃×C₈	—	6	2	no	—
89	C₂×C₃×C₈	—	6	2	no	—
90	C₃×C₄²	—	2	1	no	—
91	C₃×C₄²	—	2	1	no	—
92	C₃×C₄²	—	2	1	no	—
93	C₃×C₄²	—	2	1	no	—
94	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
95	C₃×C₄²	D₁₂	1	1	yes	characteristic
96	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
97	C₃×C₄²	#67	1	1	yes	characteristic
98	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
99	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
100	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
101	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
102	#208	—	2	4	no	—
103	C₂×C₃⋊C₈	—	2	2	no	—
104	C₂×C₃⋊C₈	—	2	2	no	—
105	C₂²×C₃²	—	2	1	no	—
106	C₂²×C₃²	—	2	1	no	—
107	C₂²×C₃²	—	2	1	no	—
108	C₂²×C₃²	#95	1	1	yes	characteristic
109	C₃²×C₄	—	2	1	no	—
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	#104	1	2	yes	—
115	C₂×M₁₆	—	6	1	no	—
116	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
117	C₄⋊C₈	—	6	1	no	—
118	C₄⋊C₈	C₃×Dic₃	1	2	yes	—
119	C₂²⋊C₈	—	2	1	no	—
120	C₂²⋊C₈	—	3	2	no	—
121	#97	—	2	1	no	—
122	#97	—	6	1	no	—
123	#97	—	6	1	no	—
124	C₄×C₈	—	3	2	no	—
125	C₂³×C₃	—	2	1	no	—
126	C₂³×C₃	Dic₃⋊C₄	1	1	yes	characteristic
127	C₂³×C₃	C₃×C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₃×C₄	—	2	2	no	—
129	C₂×C₃×C₄	—	2	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	—	2	1	no	—
134	C₂×C₃×C₄	—	2	1	no	—
135	C₂×C₃×C₄	—	2	1	no	—
136	C₂×C₃×C₄	—	4	2	no	—
137	C₂×C₃×C₄	—	4	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	2	no	—
142	C₂×C₃×C₄	—	4	2	no	—
143	C₂×C₃×C₄	C₄×Dic₃	1	1	yes	characteristic
144	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
145	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
146	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
147	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
148	C₂×C₃×C₄	#217	1	1	yes	characteristic
149	C₂×C₃×C₄	C₃×C₄²	1	1	yes	characteristic
150	C₂×C₃×C₄	C₃×C₂²⋊C₄	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×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₃×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
155	C₃×C₈	—	4	4	no	—
156	C₃×C₈	—	4	2	no	—
157	C₃×C₈	—	4	2	no	—
158	C₃×C₈	—	6	4	no	—
159	C₃×C₈	—	12	2	no	—
160	C₃⋊C₈	—	2	4	no	—
161	C₃⋊C₈	—	4	2	no	—
162	C₂×C₃²	—	4	1	no	—
163	C₂×C₃²	#338	1	1	yes	characteristic
164	C₂×C₃²	#339	1	1	yes	characteristic
165	C₂×C₃²	#344	1	1	yes	characteristic
166	C₂²×C₄	C₃×Dic₆	1	1	yes	characteristic
167	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
168	C₂²×C₄	C₃×#67	1	1	yes	characteristic
169	M₁₆	—	6	4	no	—
170	C₂×C₈	—	2	2	no	—
171	C₂×C₈	—	6	2	no	—
172	C₂×C₈	—	6	2	no	—
173	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
174	C₄²	C₃×D₁₂	1	1	yes	characteristic
175	C₄²	C₂×C₃×Dic₃	1	1	yes	characteristic
176	C₄²	C₃×#67	1	1	yes	characteristic
177	C₂²×C₃	—	2	2	no	—
178	C₂²×C₃	—	2	1	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	—	4	1	no	—
186	C₂²×C₃	—	4	1	no	—
187	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
188	C₂²×C₃	C₃×#95	1	1	yes	characteristic
189	C₃×C₄	—	2	2	no	—
190	C₃×C₄	—	2	1	no	—
191	C₃×C₄	—	2	1	no	—
192	C₃×C₄	—	2	1	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	2	no	—
201	C₃×C₄	—	4	1	no	—
202	C₃×C₄	—	4	1	no	—
203	C₃×C₄	—	4	1	no	—
204	C₃×C₄	—	4	1	no	—
205	C₃×C₄	#837	1	2	yes	—
206	C₃×C₄	C₃×#104	1	2	yes	—
207	C₃²	#1291	1	1	yes	characteristic, complemented, Sylow
208	C₂³	C₃×Dic₃⋊C₄	1	1	yes	characteristic
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	C₃×C₄×Dic₃	1	1	yes	characteristic
213	C₂×C₄	C₃×Dic₃⋊C₄	1	1	yes	characteristic
214	C₂×C₄	C₃×C₄⋊Dic₃	1	1	yes	characteristic
215	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
216	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
217	C₂×C₄	C₃×#217	1	1	yes	characteristic
218	C₈	—	4	2	no	—
219	C₈	—	6	4	no	—
220	C₈	—	12	2	no	—
221	C₂×C₃	—	2	1	no	—
222	C₂×C₃	—	2	1	no	—
223	C₂×C₃	—	2	1	no	—
224	C₂×C₃	—	4	2	no	—
225	C₂×C₃	—	4	1	no	—
226	C₂×C₃	—	4	1	no	—
227	C₂×C₃	#4532	1	1	yes	characteristic
228	C₂×C₃	#4559	1	1	yes	characteristic
229	C₂×C₃	C₃⋊#338	1	1	yes	characteristic
230	C₂×C₃	C₃×#338	1	1	yes	characteristic
231	C₂×C₃	C₃×#339	1	1	yes	characteristic
232	C₂×C₃	C₃×#344	1	1	yes	characteristic
233	C₂²	—	2	1	no	—
234	C₂²	—	2	1	no	—
235	C₂²	—	2	1	no	—
236	C₂²	C₃×C₃⋊#95	1	1	yes	characteristic
237	C₄	—	2	1	no	—
238	C₄	—	2	1	no	—
239	C₄	—	2	1	no	—
240	C₄	—	2	1	no	—
241	C₄	—	2	1	no	—
242	C₄	C₃×#837	1	2	yes	—
243	C₃	—	2	1	no	—
244	C₃	#67753	1	1	yes	characteristic, direct product factor
245	C₃	C₃×#1291	1	1	yes	characteristic, complemented
246	C₂	—	4	1	no	—
247	C₂	C₃×#4532	1	1	yes	characteristic
248	C₂	C₃×#4559	1	1	yes	characteristic
249	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×#432	C₂
socle	C₂²×C₃²	#95
prime radical	C₂³×C₃²	C₄⋊C₄
cosocle	C₂×C₃×C₄²	C₂²×C₃
hypercenter	C₃×#432	D₃
hypocenter	C₃	C₃×#1291
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ C₃×#432

Complements

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

N	H ≅ G/N	type
5. #67753	C₃	direct (N × H)
207. C₃²	#1291	semidirect
244. C₃	#67753	direct (N × H)
245. 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×#432	2
C₃×#4926	2
C₃×C₄×#208	2
C₃×#1291	3
#67753	3

Subgroups — C3×#67753 #11770997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#67753 #11770997