Subgroups — C₃×#79933 #11895470

Order 1152.

723 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5570	C₂	1	1	yes	maximal, characteristic
2	C₃×Q₈×Dic₆	C₂	1	1	yes	maximal, characteristic
3	C₃²×C₈×Q₈	C₂	1	1	yes	maximal, characteristic
4	C₃×#4850	C₂	1	3	yes	maximal
5	C₃×#4849	C₂	1	3	yes	maximal
6	C₃×C₄×Dic₁₂	C₂	1	3	yes	maximal
7	C₃×#4681	C₂	1	3	yes	maximal
8	C₃×#3363	—	3	1	no	maximal
9	#79933	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
11	C₃×Q₈×Dic₃	—	2	1	no	—
12	C₃×Q₈×Dic₃	—	2	1	no	—
13	C₂×C₃×Dic₁₂	C₂²	1	3	yes	—
14	C₃×#890	—	2	3	no	—
15	C₃×#888	—	2	3	no	—
16	C₃×#869	C₂²	1	3	yes	—
17	C₃×#869	C₂²	1	3	yes	—
18	C₃×C₄×Dic₆	C₂²	1	3	yes	—
19	C₃×C₄×Dic₆	C₂²	1	3	yes	—
20	C₃²×C₄⋊C₈	C₂²	1	3	yes	—
21	C₃²×C₄×C₈	C₂²	1	3	yes	—
22	C₃×#818	C₂²	1	3	yes	—
23	C₃×#816	C₂²	1	3	yes	—
24	C₃×#816	C₂²	1	6	yes	—
25	C₃×#816	C₂²	1	1	yes	characteristic
26	C₃×Q₈²	—	3	1	no	—
27	C₃×#557	—	3	1	no	—
28	#5570	C₂×C₃	1	1	yes	characteristic
29	Q₈×Dic₆	C₂×C₃	1	1	yes	characteristic
30	C₃×#487	—	3	3	no	—
31	C₃×#477	—	3	3	no	—
32	C₃×#462	—	3	3	no	—
33	C₃×C₈×Q₈	—	2	1	no	—
34	C₃×C₈×Q₈	D₃	1	1	yes	characteristic
35	C₃×C₈×Q₈	C₂×C₃	1	1	yes	characteristic
36	C₃×C₄×Q₁₆	—	3	3	no	—
37	#4850	C₂×C₃	1	3	yes	—
38	#4849	C₂×C₃	1	3	yes	—
39	C₄×Dic₁₂	C₂×C₃	1	3	yes	—
40	#4681	C₂×C₃	1	3	yes	—
41	C₂×C₃²×Q₈	D₄	1	1	yes	characteristic
42	C₂×C₃×Dic₆	—	2	3	no	—
43	C₂×C₃×Dic₆	C₂³	1	3	yes	—
44	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
45	C₂×C₃²×C₈	C₂³	1	3	yes	—
46	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
47	C₃²×C₄⋊C₄	D₄	1	3	yes	—
48	C₃²×C₄²	C₂³	1	3	yes	—
49	C₃×C₄⋊Dic₃	—	2	3	no	—
50	C₃×C₄⋊Dic₃	—	2	3	no	—
51	C₃×C₄⋊Dic₃	—	2	3	no	—
52	C₃×C₄⋊Dic₃	C₂³	1	3	yes	—
53	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
54	C₃×Dic₃⋊C₄	—	2	3	no	—
55	C₃×Dic₃⋊C₄	—	2	3	no	—
56	C₃×C₄×Dic₃	—	2	3	no	—
57	C₃×C₄×Dic₃	—	2	3	no	—
58	C₃×Dic₁₂	—	2	6	no	—
59	#3363	—	3	1	no	Sylow
60	C₂×C₃×Q₁₆	—	3	3	no	—
61	C₃×C₄⋊Q₈	—	3	3	no	—
62	C₃×C₄⋊Q₈	—	3	3	no	—
63	C₃×C₄⋊Q₈	—	6	3	no	—
64	C₃×#125	—	6	3	no	—
65	C₃×C₄×Q₈	—	2	1	no	—
66	C₃×C₄×Q₈	—	3	3	no	—
67	C₃×C₄×Q₈	—	3	3	no	—
68	C₃×C₄×Q₈	—	6	1	no	—
69	C₃×C₄×Q₈	—	6	1	no	—
70	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
71	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
72	Q₈×Dic₃	—	2	1	no	—
73	Q₈×Dic₃	—	2	1	no	—
74	C₂×Dic₁₂	C₂²×C₃	1	3	yes	—
75	#890	—	2	3	no	—
76	#888	—	2	3	no	—
77	#869	C₂²×C₃	1	3	yes	—
78	#869	C₂²×C₃	1	3	yes	—
79	C₄×Dic₆	C₂²×C₃	1	3	yes	—
80	C₄×Dic₆	C₂²×C₃	1	3	yes	—
81	C₃×#107	—	3	3	no	—
82	C₃×C₄⋊C₈	—	2	3	no	—
83	C₃×C₄⋊C₈	C₂×D₃	1	3	yes	—
84	C₃×C₄⋊C₈	C₂²×C₃	1	3	yes	—
85	C₃×#103	—	3	1	no	—
86	C₃×#103	—	3	3	no	—
87	C₃×#103	—	3	6	no	—
88	C₃×C₄×C₈	—	2	3	no	—
89	C₃×C₄×C₈	C₂×D₃	1	3	yes	—
90	C₃×C₄×C₈	C₂²×C₃	1	3	yes	—
91	#818	C₂²×C₃	1	3	yes	—
92	#816	C₂²×C₃	1	3	yes	—
93	#816	C₂²×C₃	1	6	yes	—
94	#816	C₂²×C₃	1	1	yes	characteristic
95	C₃²×Q₈	Q₁₆	1	4	yes	complemented
96	C₂×C₃²×C₄	C₂×D₄	1	3	yes	—
97	C₂×C₃²×C₄	C₂×D₄	1	3	yes	—
98	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
99	C₂×C₃×Dic₃	—	2	1	no	—
100	C₂×C₃×Dic₃	—	2	1	no	—
101	C₂×C₃×Dic₃	—	2	3	no	—
102	C₂×C₃×Dic₃	—	2	3	no	—
103	C₃×Dic₆	—	2	1	no	—
104	C₃×Dic₆	—	2	3	no	—
105	C₃×Dic₆	—	2	3	no	—
106	C₃×Dic₆	—	8	3	no	—
107	C₃×Dic₆	#41	1	2	yes	—
108	C₃²×C₈	—	2	1	no	—
109	C₃²×C₈	—	2	3	no	—
110	Q₈²	—	3	1	no	—
111	#557	—	3	1	no	—
112	#487	—	3	3	no	—
113	#477	—	3	3	no	—
114	#462	—	3	3	no	—
115	C₈×Q₈	C₃×D₃	1	1	yes	characteristic
116	C₄×Q₁₆	—	3	3	no	—
117	C₂×C₃×Q₈	—	2	1	no	—
118	C₂×C₃×Q₈	—	3	1	no	—
119	C₂×C₃×Q₈	—	3	3	no	—
120	C₂×C₃×Q₈	—	6	3	no	—
121	C₂×C₃×Q₈	D₁₂	1	1	yes	characteristic
122	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
123	C₂×Dic₆	—	2	3	no	—
124	C₂×Dic₆	C₂³×C₃	1	3	yes	—
125	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
126	C₃×Q₁₆	—	6	6	no	—
127	C₂×C₃×C₈	—	2	1	no	—
128	C₂×C₃×C₈	—	2	3	no	—
129	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
130	C₂×C₃×C₈	C₂²×D₃	1	3	yes	—
131	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
132	C₂×C₃×C₈	C₂³×C₃	1	3	yes	—
133	C₃×C₄⋊C₄	—	2	3	no	—
134	C₃×C₄⋊C₄	—	3	3	no	—
135	C₃×C₄⋊C₄	—	3	1	no	—
136	C₃×C₄⋊C₄	—	6	3	no	—
137	C₃×C₄⋊C₄	—	6	3	no	—
138	C₃×C₄⋊C₄	—	6	3	no	—
139	C₃×C₄⋊C₄	—	6	3	no	—
140	C₃×C₄⋊C₄	—	6	3	no	—
141	C₃×C₄⋊C₄	D₁₂	1	3	yes	—
142	C₃×C₄⋊C₄	C₃×D₄	1	3	yes	—
143	C₃×C₄²	—	2	3	no	—
144	C₃×C₄²	—	6	3	no	—
145	C₃×C₄²	—	6	3	no	—
146	C₃×C₄²	C₂²×D₃	1	3	yes	—
147	C₃×C₄²	C₂³×C₃	1	3	yes	—
148	C₄⋊Dic₃	—	2	3	no	—
149	C₄⋊Dic₃	—	2	3	no	—
150	C₄⋊Dic₃	—	2	3	no	—
151	C₄⋊Dic₃	C₂³×C₃	1	3	yes	—
152	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
153	Dic₃⋊C₄	—	2	3	no	—
154	Dic₃⋊C₄	—	2	3	no	—
155	C₄×Dic₃	—	2	3	no	—
156	C₄×Dic₃	—	2	3	no	—
157	Dic₁₂	—	2	6	no	—
158	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
159	C₃²×C₄	—	2	3	no	—
160	C₃²×C₄	C₂×Q₁₆	1	6	yes	—
161	C₃²×C₄	C₂×#41	1	1	yes	characteristic
162	C₃²×C₄	2₋¹⁺⁴	1	1	yes	characteristic
163	C₃×Dic₃	—	2	2	no	—
164	C₃×Dic₃	—	4	3	no	—
165	C₃×Dic₃	—	4	3	no	—
166	C₃×Dic₃	—	4	1	no	—
167	C₂×Q₁₆	—	3	3	no	—
168	C₄⋊Q₈	—	3	3	no	—
169	C₄⋊Q₈	—	3	3	no	—
170	C₄⋊Q₈	—	6	3	no	—
171	#125	—	6	3	no	—
172	C₄×Q₈	—	3	3	no	—
173	C₄×Q₈	—	3	3	no	—
174	C₄×Q₈	—	6	1	no	—
175	C₄×Q₈	—	6	1	no	—
176	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
177	#107	—	3	3	no	—
178	C₄⋊C₈	C₂×C₃×D₃	1	3	yes	—
179	#103	—	3	1	no	—
180	#103	—	3	3	no	—
181	#103	—	3	6	no	—
182	C₄×C₈	C₂×C₃×D₃	1	3	yes	—
183	C₃×Q₈	—	2	4	no	—
184	C₃×Q₈	—	3	2	no	—
185	C₃×Q₈	—	6	1	no	—
186	C₃×Q₈	—	6	3	no	—
187	C₃×Q₈	—	6	3	no	—
188	C₃×Q₈	—	24	3	no	—
189	C₃×Q₈	Dic₁₂	1	4	yes	complemented
190	C₃×Q₈	C₃×Q₁₆	1	4	yes	complemented
191	C₂×C₃×C₄	—	2	1	no	—
192	C₂×C₃×C₄	—	2	3	no	—
193	C₂×C₃×C₄	—	2	3	no	—
194	C₂×C₃×C₄	—	6	1	no	—
195	C₂×C₃×C₄	—	6	1	no	—
196	C₂×C₃×C₄	—	6	3	no	—
197	C₂×C₃×C₄	—	6	3	no	—
198	C₂×C₃×C₄	C₂×D₁₂	1	3	yes	—
199	C₂×C₃×C₄	C₂×D₁₂	1	3	yes	—
200	C₂×C₃×C₄	C₂×C₃×D₄	1	3	yes	—
201	C₂×C₃×C₄	C₂×C₃×D₄	1	3	yes	—
202	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
203	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
204	C₂×Dic₃	—	2	1	no	—
205	C₂×Dic₃	—	2	1	no	—
206	C₂×Dic₃	—	2	3	no	—
207	C₂×Dic₃	—	2	3	no	—
208	Dic₆	—	2	1	no	—
209	Dic₆	—	2	3	no	—
210	Dic₆	—	2	3	no	—
211	Dic₆	—	8	3	no	—
212	Dic₆	C₃×#41	1	2	yes	—
213	C₃×C₈	—	2	2	no	—
214	C₃×C₈	—	2	1	no	—
215	C₃×C₈	—	2	3	no	—
216	C₃×C₈	—	2	3	no	—
217	C₃×C₈	—	2	1	no	—
218	C₃×C₈	—	4	3	no	—
219	C₂×C₃²	#548	1	1	yes	characteristic
220	C₂×C₃²	C₂²×Q₁₆	1	1	yes	characteristic
221	C₂×C₃²	#577	1	1	yes	characteristic
222	C₂×Q₈	—	3	1	no	—
223	C₂×Q₈	—	3	3	no	—
224	C₂×Q₈	—	6	3	no	—
225	C₂×Q₈	C₃×D₁₂	1	1	yes	characteristic
226	Q₁₆	—	6	6	no	—
227	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
228	C₂×C₈	C₂²×C₃×D₃	1	3	yes	—
229	C₄⋊C₄	—	3	3	no	—
230	C₄⋊C₄	—	3	1	no	—
231	C₄⋊C₄	—	6	3	no	—
232	C₄⋊C₄	—	6	3	no	—
233	C₄⋊C₄	—	6	3	no	—
234	C₄⋊C₄	—	6	3	no	—
235	C₄⋊C₄	—	6	3	no	—
236	C₄⋊C₄	C₃×D₁₂	1	3	yes	—
237	C₄²	—	6	3	no	—
238	C₄²	—	6	3	no	—
239	C₄²	C₂²×C₃×D₃	1	3	yes	—
240	C₂²×C₃	—	2	1	no	—
241	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
242	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
243	C₃×C₄	—	2	3	no	—
244	C₃×C₄	—	2	3	no	—
245	C₃×C₄	—	2	6	no	—
246	C₃×C₄	—	2	1	no	—
247	C₃×C₄	—	2	1	no	—
248	C₃×C₄	—	4	3	no	—
249	C₃×C₄	—	6	2	no	—
250	C₃×C₄	—	12	3	no	—
251	C₃×C₄	—	12	1	no	—
252	C₃×C₄	—	12	3	no	—
253	C₃×C₄	C₂×Dic₁₂	1	6	yes	—
254	C₃×C₄	C₂×C₃×Q₁₆	1	6	yes	—
255	C₃×C₄	#1007	1	1	yes	characteristic
256	C₃×C₄	D₃×#41	1	1	yes	characteristic
257	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
258	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
259	Dic₃	—	2	2	no	—
260	Dic₃	—	4	3	no	—
261	Dic₃	—	4	1	no	—
262	Dic₃	—	4	3	no	—
263	C₃²	#3363	1	1	yes	characteristic, complemented, Sylow
264	Q₈	—	3	2	no	—
265	Q₈	—	6	1	no	—
266	Q₈	—	6	3	no	—
267	Q₈	—	6	3	no	—
268	Q₈	—	24	3	no	—
269	Q₈	C₃×Dic₁₂	1	4	yes	complemented
270	C₂×C₄	—	6	1	no	—
271	C₂×C₄	—	6	1	no	—
272	C₂×C₄	—	6	3	no	—
273	C₂×C₄	—	6	3	no	—
274	C₂×C₄	C₂×C₃×D₁₂	1	3	yes	—
275	C₂×C₄	C₂×C₃×D₁₂	1	3	yes	—
276	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
277	C₈	—	2	1	no	—
278	C₈	—	2	3	no	—
279	C₂×C₃	—	2	1	no	—
280	C₂×C₃	—	2	1	no	—
281	C₂×C₃	—	2	1	no	—
282	C₂×C₃	#5576	1	1	yes	characteristic
283	C₂×C₃	C₂²×Dic₁₂	1	1	yes	characteristic
284	C₂×C₃	#5751	1	1	yes	characteristic
285	C₂×C₃	C₃×#548	1	1	yes	characteristic
286	C₂×C₃	C₂²×C₃×Q₁₆	1	1	yes	characteristic
287	C₂×C₃	C₃×#577	1	1	yes	characteristic
288	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
289	C₄	—	2	3	no	—
290	C₄	—	6	2	no	—
291	C₄	—	12	3	no	—
292	C₄	—	12	1	no	—
293	C₄	—	12	3	no	—
294	C₄	C₂×C₃×Dic₁₂	1	6	yes	—
295	C₄	C₃×#1007	1	1	yes	characteristic
296	C₄	C₃×D₃×#41	1	1	yes	characteristic
297	C₃	—	2	1	no	—
298	C₃	#79933	1	1	yes	characteristic, direct product factor
299	C₃	C₃×#3363	1	1	yes	characteristic, complemented
300	C₂	C₃×#5576	1	1	yes	characteristic
301	C₂	C₂²×C₃×Dic₁₂	1	1	yes	characteristic
302	C₂	C₃×#5751	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₈×Q₈	C₂
socle, prime radical	C₂²×C₃²	C₂²×D₄
hypercenter	C₃×C₈×Q₈	D₃
hypocenter	C₃	C₃×#3363
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×Q₈ ◁ C₃×C₈×Q₈

Complements

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

N	H ≅ G/N	type
9. #79933	C₃	direct (N × H)
95. C₃²×Q₈	Q₁₆	semidirect
189. C₃×Q₈	Dic₁₂	semidirect
190. C₃×Q₈	C₃×Q₁₆	semidirect
263. C₃²	#3363	semidirect
269. Q₈	C₃×Dic₁₂	semidirect
298. C₃	#79933	direct (N × H)
299. C₃	C₃×#3363	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5570	2
C₃×Q₈×Dic₆	2
C₃²×C₈×Q₈	2
C₃×#4850	2
C₃×#4849	2
C₃×C₄×Dic₁₂	2
C₃×#4681	2
C₃×#3363	3
#79933	3

Subgroups — C3×#79933 #11895470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79933 #11895470