Subgroups — C₃×#70944 #11781142

Order 1152.

363 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₈×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#5031	C₂	1	2	yes	maximal
3	C₃×#4682	C₂	1	1	yes	maximal, characteristic
4	C₃×#4486	C₂	1	2	yes	maximal
5	C₃×#4458	C₂	1	1	yes	maximal, characteristic
6	C₃×#1674	—	3	1	no	maximal
7	#70944	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₃×#216	—	2	2	no	—
10	C₃×#869	C₂²	1	2	yes	—
11	C₃²×C₄⋊C₈	—	2	1	no	—
12	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₃²×C₄×C₈	—	2	1	no	—
14	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
15	C₃×#818	—	2	1	no	—
16	C₃×#818	—	2	1	no	—
17	C₃×#810	—	2	2	no	—
18	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
19	C₃×#500	—	3	1	no	—
20	C₃×#462	—	3	2	no	—
21	C₃×C₈×Q₈	—	2	1	no	—
22	C₃×C₈×Q₈	D₃	1	1	yes	characteristic
23	C₃×C₈×Q₈	C₂×C₃	1	1	yes	characteristic
24	#5031	C₂×C₃	1	2	yes	—
25	#4682	C₂×C₃	1	1	yes	characteristic
26	C₃×#335	—	3	1	no	—
27	C₃×#332	—	3	2	no	—
28	#4486	C₂×C₃	1	2	yes	—
29	#4458	C₂×C₃	1	1	yes	characteristic
30	C₂×C₃²×Q₈	D₄	1	1	yes	characteristic
31	C₂×C₃×Dic₆	—	2	2	no	—
32	C₂×C₃²×C₈	—	2	1	no	—
33	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
34	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
35	C₃²×C₄⋊C₄	—	2	1	no	—
36	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
37	C₃²×C₄²	—	2	1	no	—
38	C₃²×C₄²	C₂³	1	1	yes	characteristic
39	C₃×#216	—	4	4	no	—
40	C₃×C₄⋊Dic₃	—	2	2	no	—
41	C₃×C₄⋊Dic₃	—	2	2	no	—
42	C₂×C₃×C₃⋊C₈	—	2	2	no	—
43	#1674	—	3	1	no	Sylow
44	C₂×C₃×Q₁₆	—	6	2	no	—
45	C₃×C₄⋊Q₈	—	3	2	no	—
46	C₃×C₄×Q₈	—	2	1	no	—
47	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
48	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
49	C₂×#216	—	2	2	no	—
50	#869	C₂²×C₃	1	2	yes	—
51	C₃×#107	—	6	1	no	—
52	C₃×#107	—	6	1	no	—
53	C₃×C₄⋊C₈	—	2	2	no	—
54	C₃×C₄⋊C₈	—	2	1	no	—
55	C₃×C₄⋊C₈	—	2	1	no	—
56	C₃×C₄⋊C₈	—	2	1	no	—
57	C₃×C₄⋊C₈	—	3	2	no	—
58	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
59	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
60	C₃×#103	—	6	2	no	—
61	C₃×C₄×C₈	—	2	2	no	—
62	C₃×C₄×C₈	—	2	1	no	—
63	C₃×C₄×C₈	—	2	1	no	—
64	C₃×C₄×C₈	—	2	1	no	—
65	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
66	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
67	#818	—	2	1	no	—
68	#818	—	2	1	no	—
69	#810	—	2	2	no	—
70	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
71	C₃²×Q₈	—	2	1	no	—
72	C₃²×Q₈	D₈	1	2	yes	—
73	C₂×C₃²×C₄	—	2	1	no	—
74	C₂×C₃²×C₄	—	2	1	no	—
75	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
76	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
77	C₂×C₃²×C₄	#41	1	1	yes	characteristic
78	C₂×C₃×Dic₃	—	4	2	no	—
79	C₃×Dic₆	—	4	2	no	—
80	C₃×Dic₆	—	4	2	no	—
81	C₃²×C₈	—	2	1	no	—
82	C₃²×C₈	—	4	1	no	—
83	C₃²×C₈	Q₁₆	1	2	yes	complemented
84	C₃×C₃⋊C₈	—	4	2	no	—
85	#500	—	3	1	no	—
86	#462	—	3	2	no	—
87	C₈×Q₈	C₃×D₃	1	1	yes	characteristic
88	#335	—	3	1	no	—
89	#332	—	3	2	no	—
90	C₂×C₃×Q₈	—	2	1	no	—
91	C₂×C₃×Q₈	—	6	2	no	—
92	C₂×C₃×Q₈	D₁₂	1	1	yes	characteristic
93	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
94	C₂×Dic₆	—	2	2	no	—
95	C₃×Q₁₆	—	12	4	no	—
96	C₂×C₃×C₈	—	2	2	no	—
97	C₂×C₃×C₈	—	2	1	no	—
98	C₂×C₃×C₈	—	2	1	no	—
99	C₂×C₃×C₈	—	2	1	no	—
100	C₂×C₃×C₈	—	2	1	no	—
101	C₂×C₃×C₈	—	6	2	no	—
102	C₂×C₃×C₈	#67	1	1	yes	characteristic
103	C₂×C₃×C₈	#67	1	1	yes	characteristic
104	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
105	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
106	C₃×C₄⋊C₄	—	2	2	no	—
107	C₃×C₄⋊C₄	—	2	1	no	—
108	C₃×C₄⋊C₄	—	2	1	no	—
109	C₃×C₄⋊C₄	—	2	1	no	—
110	C₃×C₄⋊C₄	—	6	2	no	—
111	C₃×C₄⋊C₄	—	6	2	no	—
112	C₃×C₄⋊C₄	D₁₂	1	1	yes	characteristic
113	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
114	C₃×C₄²	—	2	2	no	—
115	C₃×C₄²	—	2	1	no	—
116	C₃×C₄²	—	2	1	no	—
117	C₃×C₄²	—	2	1	no	—
118	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
119	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
120	#216	—	4	4	no	—
121	C₄⋊Dic₃	—	2	2	no	—
122	C₄⋊Dic₃	—	2	2	no	—
123	C₂×C₃⋊C₈	—	2	2	no	—
124	C₂²×C₃²	#121	1	1	yes	characteristic
125	C₃²×C₄	—	2	2	no	—
126	C₃²×C₄	—	2	1	no	—
127	C₃²×C₄	—	4	1	no	—
128	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
129	C₃²×C₄	C₂×Q₁₆	1	1	yes	characteristic
130	C₃²×C₄	#135	1	1	yes	characteristic
131	C₃²×C₄	#137	1	1	yes	characteristic
132	C₃×Dic₃	—	8	2	no	—
133	C₂×Q₁₆	—	6	2	no	—
134	C₄⋊Q₈	—	3	2	no	—
135	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
136	#107	—	6	1	no	—
137	#107	—	6	1	no	—
138	C₄⋊C₈	—	2	1	no	—
139	C₄⋊C₈	—	3	2	no	—
140	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
141	#103	—	6	2	no	—
142	C₄×C₈	—	2	1	no	—
143	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
144	C₃×Q₈	—	2	2	no	—
145	C₃×Q₈	—	2	1	no	—
146	C₃×Q₈	—	2	1	no	—
147	C₃×Q₈	—	2	2	no	—
148	C₃×Q₈	—	12	2	no	—
149	C₃×Q₈	—	12	2	no	—
150	C₃×Q₈	D₂₄	1	2	yes	—
151	C₃×Q₈	C₃×D₈	1	2	yes	—
152	C₂×C₃×C₄	—	2	2	no	—
153	C₂×C₃×C₄	—	2	1	no	—
154	C₂×C₃×C₄	—	2	1	no	—
155	C₂×C₃×C₄	—	2	2	no	—
156	C₂×C₃×C₄	—	2	1	no	—
157	C₂×C₃×C₄	—	2	1	no	—
158	C₂×C₃×C₄	—	2	1	no	—
159	C₂×C₃×C₄	—	2	1	no	—
160	C₂×C₃×C₄	—	2	1	no	—
161	C₂×C₃×C₄	—	12	2	no	—
162	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
163	C₂×C₃×C₄	#235	1	1	yes	characteristic
164	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
165	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
166	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
167	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
168	C₂×Dic₃	—	4	2	no	—
169	Dic₆	—	4	2	no	—
170	Dic₆	—	4	2	no	—
171	C₃×C₈	—	2	1	no	—
172	C₃×C₈	—	2	1	no	—
173	C₃×C₈	—	2	2	no	—
174	C₃×C₈	—	4	1	no	—
175	C₃×C₈	—	4	2	no	—
176	C₃×C₈	—	4	1	no	—
177	C₃×C₈	—	4	1	no	—
178	C₃×C₈	—	12	2	no	—
179	C₃×C₈	#216	1	2	yes	complemented
180	C₃×C₈	C₃×Q₁₆	1	2	yes	complemented
181	C₃⋊C₈	—	4	2	no	—
182	C₂×C₃²	#462	1	1	yes	characteristic
183	C₂×C₃²	#466	1	1	yes	characteristic
184	C₂×C₃²	#473	1	1	yes	characteristic
185	C₂×Q₈	—	6	2	no	—
186	C₂×Q₈	C₃×D₁₂	1	1	yes	characteristic
187	Q₁₆	—	12	4	no	—
188	C₂×C₈	—	2	1	no	—
189	C₂×C₈	—	6	2	no	—
190	C₂×C₈	C₃×#67	1	1	yes	characteristic
191	C₂×C₈	C₃×#67	1	1	yes	characteristic
192	C₄⋊C₄	—	2	1	no	—
193	C₄⋊C₄	—	6	2	no	—
194	C₄⋊C₄	—	6	2	no	—
195	C₄⋊C₄	C₃×D₁₂	1	1	yes	characteristic
196	C₄²	—	2	1	no	—
197	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
198	C₂²×C₃	—	2	1	no	—
199	C₂²×C₃	#930	1	1	yes	characteristic
200	C₂²×C₃	C₃×#121	1	1	yes	characteristic
201	C₃×C₄	—	2	4	no	—
202	C₃×C₄	—	2	1	no	—
203	C₃×C₄	—	2	2	no	—
204	C₃×C₄	—	2	1	no	—
205	C₃×C₄	—	2	2	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	—	4	1	no	—
211	C₃×C₄	—	4	2	no	—
212	C₃×C₄	—	4	1	no	—
213	C₃×C₄	—	4	1	no	—
214	C₃×C₄	—	24	2	no	—
215	C₃×C₄	C₂×D₂₄	1	1	yes	characteristic
216	C₃×C₄	#904	1	1	yes	characteristic
217	C₃×C₄	C₂×#216	1	1	yes	characteristic
218	C₃×C₄	#951	1	1	yes	characteristic
219	C₃×C₄	C₂×C₃×D₈	1	1	yes	characteristic
220	C₃×C₄	C₂×C₃×Q₁₆	1	1	yes	characteristic
221	C₃×C₄	C₃×#135	1	1	yes	characteristic
222	C₃×C₄	C₃×#137	1	1	yes	characteristic
223	Dic₃	—	8	2	no	—
224	C₃²	#1674	1	1	yes	characteristic, complemented, Sylow
225	Q₈	—	2	1	no	—
226	Q₈	—	12	2	no	—
227	Q₈	—	12	2	no	—
228	Q₈	C₃×D₂₄	1	2	yes	—
229	C₂×C₄	—	2	1	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	12	2	no	—
232	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
233	C₂×C₄	C₃×#235	1	1	yes	characteristic
234	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
235	C₈	—	2	1	no	—
236	C₈	—	4	1	no	—
237	C₈	—	12	2	no	—
238	C₈	C₃×#216	1	2	yes	complemented
239	C₂×C₃	—	2	1	no	—
240	C₂×C₃	—	2	1	no	—
241	C₂×C₃	—	2	1	no	—
242	C₂×C₃	#5031	1	1	yes	characteristic
243	C₂×C₃	#5115	1	1	yes	characteristic
244	C₂×C₃	#5143	1	1	yes	characteristic
245	C₂×C₃	C₃×#462	1	1	yes	characteristic
246	C₂×C₃	C₃×#466	1	1	yes	characteristic
247	C₂×C₃	C₃×#473	1	1	yes	characteristic
248	C₂²	C₃×#930	1	1	yes	characteristic
249	C₄	—	2	2	no	—
250	C₄	—	2	1	no	—
251	C₄	—	4	1	no	—
252	C₄	—	24	2	no	—
253	C₄	C₂×C₃×D₂₄	1	1	yes	characteristic
254	C₄	C₃×#904	1	1	yes	characteristic
255	C₄	C₂×C₃×#216	1	1	yes	characteristic
256	C₄	C₃×#951	1	1	yes	characteristic
257	C₃	—	2	1	no	—
258	C₃	#70944	1	1	yes	characteristic, direct product factor
259	C₃	C₃×#1674	1	1	yes	characteristic, complemented
260	C₂	C₃×#5031	1	1	yes	characteristic
261	C₂	C₃×#5115	1	1	yes	characteristic
262	C₂	C₃×#5143	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#930
commutator, cosocle	C₃×C₄²	C₂³×C₃
Frattini	C₄²	C₂²×C₃×D₃
Fitting	C₃²×C₈×Q₈	C₂
socle, prime radical	C₂²×C₃²	#121
hypercenter	C₃×C₈×Q₈	D₃
hypocenter	C₃	C₃×#1674
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₈×Q₈

Complements

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

N	H ≅ G/N	type
7. #70944	C₃	direct (N × H)
83. C₃²×C₈	Q₁₆	semidirect
179. C₃×C₈	#216	semidirect
180. C₃×C₈	C₃×Q₁₆	semidirect
224. C₃²	#1674	semidirect
238. C₈	C₃×#216	semidirect
258. C₃	#70944	direct (N × H)
259. C₃	C₃×#1674	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₈×Q₈	2
C₃×#5031	2
C₃×#4682	2
C₃×#4486	2
C₃×#4458	2
C₃×#1674	3
#70944	3

Subgroups — C3×#70944 #11781142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#70944 #11781142