Subgroups — C₃×#70532 #11795293

Order 1152.

409 conjugacy classes of subgroups.

The subgroup lattice has 265 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#424	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#818	C₂	1	1	yes	maximal, characteristic
3	C₃×#4995	C₂	1	2	yes	maximal
4	C₃×#4554	C₂	1	2	yes	maximal
5	C₃×#4552	C₂	1	1	yes	maximal, characteristic
6	C₃×#2089	—	3	1	no	maximal
7	#70532	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
9	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
10	C₃²×#117	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
12	C₂×C₃×#208	C₂²	1	2	yes	—
13	C₃²×C₄⋊C₈	—	2	2	no	—
14	C₃×#818	—	2	2	no	—
15	C₃×#808	—	2	2	no	—
16	C₃×#807	—	2	2	no	—
17	C₃×#428	—	3	2	no	—
18	C₂×C₃×#107	—	3	1	no	—
19	C₃×#424	—	2	1	no	—
20	C₃×#424	D₃	1	1	yes	characteristic
21	C₃×#424	C₂×C₃	1	1	yes	characteristic
22	C₂×#818	C₂×C₃	1	1	yes	characteristic
23	#4995	C₂×C₃	1	2	yes	—
24	C₃×#343	—	3	2	no	—
25	C₃×#341	—	3	1	no	—
26	#4554	C₂×C₃	1	2	yes	—
27	#4552	C₂×C₃	1	1	yes	characteristic
28	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
29	C₂²×C₃×Dic₃	—	2	2	no	—
30	C₃²×M₁₆	—	2	2	no	—
31	C₂×C₃²×C₈	—	2	2	no	—
32	C₂×C₃²×C₈	—	2	1	no	—
33	C₂×C₃²×C₈	D₄	1	2	yes	—
34	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
35	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
36	C₃²×C₂²⋊C₄	—	2	1	no	—
37	C₃²×C₄²	—	2	1	no	—
38	C₃×C₄⋊Dic₃	—	2	2	no	—
39	C₃×C₄⋊Dic₃	—	2	2	no	—
40	C₃×#208	—	2	2	no	—
41	C₃×#208	Q₈	1	4	yes	—
42	C₂×C₃×C₃⋊C₈	—	2	2	no	—
43	#2089	—	3	1	no	Sylow
44	C₂×C₃×M₁₆	—	2	1	no	—
45	C₂×C₃×M₁₆	—	3	2	no	—
46	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
47	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
48	C₂²×C₃×C₈	—	2	1	no	—
49	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
50	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
51	C₃×#117	—	2	1	no	—
52	C₃×#117	C₂×D₃	1	1	yes	characteristic
53	C₃×#117	C₂²×C₃	1	1	yes	characteristic
54	C₂×C₃×C₄⋊C₄	—	3	2	no	—
55	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
56	C₂×#208	C₂²×C₃	1	2	yes	—
57	C₃×#107	—	6	2	no	—
58	C₃×#107	—	6	2	no	—
59	C₃×#106	—	6	2	no	—
60	C₃×C₄⋊C₈	—	2	4	no	—
61	C₃×C₄⋊C₈	—	2	2	no	—
62	C₃×C₄⋊C₈	—	2	2	no	—
63	#818	—	2	2	no	—
64	#808	—	2	2	no	—
65	#807	—	2	2	no	—
66	C₂³×C₃²	#41	1	1	yes	characteristic
67	C₂×C₃²×C₄	—	2	1	no	—
68	C₂×C₃²×C₄	—	2	1	no	—
69	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
70	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
71	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
72	C₂×C₃²×C₄	#41	1	2	yes	—
73	C₂×C₃×Dic₃	—	4	2	no	—
74	C₂×C₃×Dic₃	—	8	2	no	—
75	C₃²×C₈	—	2	2	no	—
76	C₃²×C₈	—	4	1	no	—
77	C₃×C₃⋊C₈	—	2	4	no	—
78	#428	—	3	2	no	—
79	C₂×#107	—	3	1	no	—
80	#424	C₃×D₃	1	1	yes	characteristic
81	#343	—	3	2	no	—
82	#341	—	3	1	no	—
83	C₂²×C₃×C₄	—	2	1	no	—
84	C₂²×C₃×C₄	—	6	2	no	—
85	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
86	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
87	C₂²×Dic₃	—	2	2	no	—
88	C₃×M₁₆	—	2	2	no	—
89	C₃×M₁₆	—	2	2	no	—
90	C₃×M₁₆	—	3	4	no	—
91	C₃×M₁₆	—	4	2	no	—
92	C₃×M₁₆	—	6	2	no	—
93	C₂×C₃×C₈	—	2	2	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	—	2	1	no	—
98	C₂×C₃×C₈	—	2	2	no	—
99	C₂×C₃×C₈	—	4	2	no	—
100	C₂×C₃×C₈	—	6	2	no	—
101	C₂×C₃×C₈	#67	1	2	yes	—
102	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
103	C₃×C₄⋊C₄	—	2	1	no	—
104	C₃×C₄⋊C₄	—	2	1	no	—
105	C₃×C₄⋊C₄	—	6	2	no	—
106	C₃×C₄⋊C₄	—	6	2	no	—
107	C₃×C₄⋊C₄	D₁₂	1	1	yes	characteristic
108	C₃×C₄⋊C₄	D₁₂	1	1	yes	characteristic
109	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
110	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
111	C₃×C₂²⋊C₄	—	2	2	no	—
112	C₃×C₂²⋊C₄	—	2	1	no	—
113	C₃×C₂²⋊C₄	—	2	1	no	—
114	C₃×C₄²	—	2	2	no	—
115	C₃×C₄²	—	2	1	no	—
116	C₃×C₄²	—	2	1	no	—
117	C₄⋊Dic₃	—	2	2	no	—
118	C₄⋊Dic₃	—	2	2	no	—
119	#208	—	2	2	no	—
120	#208	C₃×Q₈	1	4	yes	—
121	C₂×C₃⋊C₈	—	2	2	no	—
122	C₂²×C₃²	—	2	1	no	—
123	C₂²×C₃²	—	2	1	no	—
124	C₂²×C₃²	#121	1	1	yes	characteristic
125	C₂²×C₃²	#125	1	2	yes	—
126	C₃²×C₄	—	4	1	no	—
127	C₃²×C₄	—	4	1	no	—
128	C₃²×C₄	C₂²⋊Q₈	1	2	yes	—
129	C₃²×C₄	#123	1	1	yes	characteristic
130	C₃²×C₄	C₄⋊Q₈	1	1	yes	characteristic
131	C₃×Dic₃	—	8	2	no	—
132	C₂×M₁₆	—	3	2	no	—
133	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
134	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
135	#117	C₂×C₃×D₃	1	1	yes	characteristic
136	C₂×C₄⋊C₄	—	3	2	no	—
137	#107	—	6	2	no	—
138	#107	—	6	2	no	—
139	#106	—	6	2	no	—
140	C₄⋊C₈	—	2	2	no	—
141	C₂³×C₃	—	2	1	no	—
142	C₂³×C₃	#235	1	1	yes	characteristic
143	C₂³×C₃	C₃×#41	1	1	yes	characteristic
144	C₂×C₃×C₄	—	2	2	no	—
145	C₂×C₃×C₄	—	2	2	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	—	2	1	no	—
150	C₂×C₃×C₄	—	2	1	no	—
151	C₂×C₃×C₄	—	2	2	no	—
152	C₂×C₃×C₄	—	2	2	no	—
153	C₂×C₃×C₄	—	2	1	no	—
154	C₂×C₃×C₄	—	12	2	no	—
155	C₂×C₃×C₄	—	24	2	no	—
156	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
157	C₂×C₃×C₄	#237	1	2	yes	—
158	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
159	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
160	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
161	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
162	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
163	C₂×C₃×C₄	C₃×#41	1	2	yes	—
164	C₂×Dic₃	—	4	2	no	—
165	C₂×Dic₃	—	8	2	no	—
166	C₃×C₈	—	2	2	no	—
167	C₃×C₈	—	2	2	no	—
168	C₃×C₈	—	4	2	no	—
169	C₃×C₈	—	4	2	no	—
170	C₃×C₈	—	4	1	no	—
171	C₃×C₈	—	4	1	no	—
172	C₃×C₈	—	6	4	no	—
173	C₃⋊C₈	—	2	4	no	—
174	C₂×C₃²	—	2	2	no	—
175	C₂×C₃²	#398	1	1	yes	characteristic
176	C₂×C₃²	#472	1	1	yes	characteristic
177	C₂×C₃²	#473	1	1	yes	characteristic
178	C₂²×C₄	—	6	2	no	—
179	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
180	M₁₆	—	2	2	no	—
181	M₁₆	—	3	4	no	—
182	M₁₆	—	6	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	2	1	no	—
185	C₂×C₈	—	6	2	no	—
186	C₂×C₈	C₃×#67	1	2	yes	—
187	C₄⋊C₄	—	6	2	no	—
188	C₄⋊C₄	—	6	2	no	—
189	C₄⋊C₄	C₃×D₁₂	1	1	yes	characteristic
190	C₄⋊C₄	C₃×D₁₂	1	1	yes	characteristic
191	C₂²⋊C₄	—	2	1	no	—
192	C₄²	—	2	1	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	2	no	—
198	C₂²×C₃	—	2	1	no	—
199	C₂²×C₃	—	4	1	no	—
200	C₂²×C₃	—	4	1	no	—
201	C₂²×C₃	#889	1	2	yes	—
202	C₂²×C₃	#930	1	1	yes	characteristic
203	C₂²×C₃	C₃×#121	1	1	yes	characteristic
204	C₂²×C₃	C₃×#125	1	2	yes	—
205	C₃×C₄	—	2	2	no	—
206	C₃×C₄	—	2	1	no	—
207	C₃×C₄	—	2	1	no	—
208	C₃×C₄	—	4	2	no	—
209	C₃×C₄	—	4	2	no	—
210	C₃×C₄	—	4	1	no	—
211	C₃×C₄	—	4	1	no	—
212	C₃×C₄	—	4	1	no	—
213	C₃×C₄	—	4	1	no	—
214	C₃×C₄	—	24	2	no	—
215	C₃×C₄	#897	1	2	yes	—
216	C₃×C₄	#935	1	1	yes	characteristic
217	C₃×C₄	#944	1	1	yes	characteristic
218	C₃×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
219	C₃×C₄	C₃×#123	1	1	yes	characteristic
220	C₃×C₄	C₃×C₄⋊Q₈	1	1	yes	characteristic
221	Dic₃	—	8	2	no	—
222	C₃²	#2089	1	1	yes	characteristic, complemented, Sylow
223	C₂³	C₃×#235	1	1	yes	characteristic
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	12	2	no	—
227	C₂×C₄	—	24	2	no	—
228	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
229	C₂×C₄	C₃×#237	1	2	yes	—
230	C₂×C₄	C₃×D₃×Q₈	1	2	yes	—
231	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
232	C₈	—	2	2	no	—
233	C₈	—	4	1	no	—
234	C₈	—	6	4	no	—
235	C₂×C₃	—	2	2	no	—
236	C₂×C₃	—	2	2	no	—
237	C₂×C₃	—	2	1	no	—
238	C₂×C₃	—	2	1	no	—
239	C₂×C₃	—	2	1	no	—
240	C₂×C₃	—	4	2	no	—
241	C₂×C₃	#4981	1	1	yes	characteristic
242	C₂×C₃	#5142	1	1	yes	characteristic
243	C₂×C₃	#5143	1	1	yes	characteristic
244	C₂×C₃	C₃×#398	1	1	yes	characteristic
245	C₂×C₃	C₃×#472	1	1	yes	characteristic
246	C₂×C₃	C₃×#473	1	1	yes	characteristic
247	C₂²	—	2	1	no	—
248	C₂²	—	2	1	no	—
249	C₂²	C₃×#889	1	2	yes	—
250	C₂²	C₃×#930	1	1	yes	characteristic
251	C₄	—	4	1	no	—
252	C₄	—	4	1	no	—
253	C₄	—	24	2	no	—
254	C₄	C₃×#897	1	2	yes	—
255	C₄	C₃×#935	1	1	yes	characteristic
256	C₄	C₃×#944	1	1	yes	characteristic
257	C₃	—	2	1	no	—
258	C₃	#70532	1	1	yes	characteristic, direct product factor
259	C₃	C₃×#2089	1	1	yes	characteristic, complemented
260	C₂	—	2	2	no	—
261	C₂	C₃×#4981	1	1	yes	characteristic
262	C₂	C₃×#5142	1	1	yes	characteristic
263	C₂	C₃×#5143	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#930
commutator, cosocle	C₂²×C₃×C₄	C₂³×C₃
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₃²×#424	C₂
socle	C₂²×C₃²	#121
prime radical	C₂³×C₃²	#41
hypercenter	C₃×#424	D₃
hypocenter	C₃	C₃×#2089
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#424

Complements

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

N	H ≅ G/N	type
7. #70532	C₃	direct (N × H)
222. C₃²	#2089	semidirect
258. C₃	#70532	direct (N × H)
259. C₃	C₃×#2089	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#424	2
C₂×C₃×#818	2
C₃×#4995	2
C₃×#4554	2
C₃×#4552	2
C₃×#2089	3
#70532	3

Subgroups — C3×#70532 #11795293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#70532 #11795293