Subgroups — D₃×#4840 #11858805

Order 1152.

872 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×#872	C₂	1	1	yes	maximal, characteristic
2	#10592539	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#4840	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
6	D₃×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
7	#10590699	C₂	1	1	yes	maximal, characteristic, complemented
8	#10590698	C₂	1	1	yes	maximal, characteristic, complemented
9	D₃×#815	C₂	1	1	yes	maximal, characteristic, complemented
10	D₃×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#10590648	C₂	1	1	yes	maximal, characteristic, complemented
12	#10590647	C₂	1	1	yes	maximal, characteristic, complemented
13	D₃×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
14	#10590257	C₂	1	1	yes	maximal, characteristic, complemented
15	#10590253	C₂	1	1	yes	maximal, characteristic, complemented
16	D₃×#433	—	3	1	no	maximal
17	C₂×#4840	—	3	1	no	maximal
18	C₂×C₄×D₃²	C₂²	1	1	yes	characteristic
19	#64081	C₂²	1	1	yes	characteristic
20	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
22	C₃×#872	C₂²	1	1	yes	characteristic
23	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
24	D₃×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
25	D₃×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
26	#63877	C₄	1	1	yes	characteristic
27	#63877	C₄	1	1	yes	characteristic
28	D₃×Dic₃⋊C₄	C₄	1	1	yes	characteristic
29	D₃×Dic₃⋊C₄	C₄	1	1	yes	characteristic
30	C₄×D₃×Dic₃	C₂²	1	1	yes	characteristic
31	#63874	C₂²	1	1	yes	characteristic
32	#63855	C₂²	1	1	yes	characteristic
33	#63836	C₄	1	1	yes	characteristic
34	#63836	C₄	1	1	yes	characteristic
35	C₂×D₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×D₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
37	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	#63647	C₂²	1	1	yes	characteristic
39	#63647	C₂²	1	1	yes	characteristic
40	#63642	C₂²	1	1	yes	characteristic, complemented
41	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
42	C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	1	1	yes	characteristic, complemented
43	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
44	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
45	C₃×#815	C₂²	1	1	yes	characteristic, complemented
46	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
51	Dic₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
52	Dic₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
53	#63557	C₂²	1	1	yes	characteristic
54	#63557	C₂²	1	1	yes	characteristic
55	(C₂×D₃)⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
56	(C₂×D₃)⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
57	#63555	C₂²	1	1	yes	characteristic, complemented
58	#63554	C₂²	1	1	yes	characteristic, complemented
59	#63553	C₂²	1	1	yes	characteristic, complemented
60	Dic₃×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	D₃×#117	—	3	1	no	—
62	C₂×#872	—	3	1	no	—
63	C₃×#433	—	3	1	no	—
64	C₂×C₃×C₄⋊C₈	—	3	1	no	—
65	C₂×(C₂×D₃)⋊C₈	—	3	1	no	—
66	C₂×(C₂×D₃)⋊C₈	—	3	1	no	—
67	C₂×#815	—	3	1	no	—
68	C₂×C₈×Dic₃	—	3	1	no	—
69	#5000	—	3	1	no	—
70	C₂×C₄⋊(C₃⋊C₈)	—	3	1	no	—
71	#4840	—	3	1	no	—
72	#4840	—	3	1	no	—
73	#4840	—	3	1	no	—
74	#4840	—	3	1	no	—
75	#4840	—	3	1	no	—
76	#4840	—	3	1	no	—
77	#4840	—	3	1	no	—
78	#4840	—	3	1	no	—
79	#4840	—	3	1	no	—
80	#4840	—	6	1	no	—
81	#4840	D₃	1	1	yes	characteristic, direct product factor
82	D₃×C₄⋊C₈	—	3	1	no	—
83	D₃×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
84	D₃×C₂²⋊C₈	—	3	1	no	—
85	D₃×C₂²⋊C₈	—	3	1	no	—
86	#4720	—	3	1	no	—
87	#4720	—	3	1	no	—
88	#4709	—	3	1	no	—
89	D₃×#97	—	3	1	no	—
90	#4690	—	3	1	no	—
91	C₄×D₃×C₈	—	3	1	no	—
92	C₂²×D₃²	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
98	C₂×#624	C₂×C₄	1	1	yes	characteristic
99	C₂×D₃×Dic₃	C₂×C₄	1	1	yes	characteristic
100	C₂×D₃×Dic₃	C₂×C₄	1	1	yes	characteristic
101	C₂×D₃×Dic₃	C₂×C₄	1	1	yes	characteristic
102	C₂×D₃×Dic₃	C₂×C₄	1	1	yes	characteristic
103	C₄×D₃²	—	2	2	no	—
104	C₄×D₃²	—	2	2	no	—
105	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
106	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
107	C₃²×C₄²	C₂³	1	1	yes	characteristic
108	#3752	C₂×C₄	1	1	yes	characteristic
109	#3752	C₂×C₄	1	1	yes	characteristic
110	#3750	C₂×C₄	1	1	yes	characteristic
111	#3750	C₂×C₄	1	1	yes	characteristic
112	C₄×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
113	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
114	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
115	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
118	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
119	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
120	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
121	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
122	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
123	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
124	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
125	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
127	C₃×D₃×C₈	—	2	2	no	—
128	C₃×D₃×C₈	—	2	2	no	—
129	#3724	C₂×C₄	1	1	yes	characteristic
130	#3724	C₂×C₄	1	1	yes	characteristic
131	Dic₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
132	Dic₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
133	#3722	C₂×C₄	1	1	yes	characteristic
134	#3722	C₂×C₄	1	1	yes	characteristic
135	(C₂×D₃)⋊Dic₃	C₂×C₄	1	1	yes	characteristic
136	(C₂×D₃)⋊Dic₃	C₂×C₄	1	1	yes	characteristic
137	Dic₃²	C₂×C₄	1	1	yes	characteristic
138	Dic₃²	C₂×C₄	1	1	yes	characteristic
139	D₃×C₃⋊C₈	—	2	2	no	—
140	D₃×C₃⋊C₈	—	2	2	no	—
141	C₂×#433	—	9	1	no	Sylow
142	C₂²×C₄×D₃	—	3	1	no	—
143	C₂²×C₄×D₃	—	3	1	no	—
144	C₂²×C₃×C₈	—	3	1	no	—
145	C₂²×C₃×C₈	—	3	1	no	—
146	C₃×#117	—	3	1	no	—
147	C₂×C₃×C₄²	—	3	1	no	—
148	C₂×(C₂×D₃)⋊C₄	—	3	1	no	—
149	C₂×(C₂×D₃)⋊C₄	—	3	1	no	—
150	#926	—	3	1	no	—
151	C₂×Dic₃⋊C₄	—	3	1	no	—
152	C₂×Dic₃⋊C₄	—	3	1	no	—
153	C₂×C₄×Dic₃	—	3	1	no	—
154	C₂²×C₃⋊C₈	—	3	1	no	—
155	C₂²×C₃⋊C₈	—	3	1	no	—
156	C₂×D₃×C₈	—	3	1	no	—
157	C₂×D₃×C₈	—	3	1	no	—
158	C₂×D₃×C₈	C₂×D₃	1	1	yes	characteristic
159	C₂×D₃×C₈	C₂×D₃	1	1	yes	characteristic
160	#892	—	3	1	no	—
161	#892	—	3	1	no	—
162	D₃×C₄⋊C₄	—	3	1	no	—
163	D₃×C₄⋊C₄	—	3	1	no	—
164	D₃×C₂²⋊C₄	—	3	1	no	—
165	D₃×C₂²⋊C₄	—	3	1	no	—
166	#877	—	3	1	no	—
167	#877	—	3	1	no	—
168	#872	—	3	1	no	—
169	#872	—	3	1	no	—
170	#872	—	3	1	no	—
171	#872	—	3	1	no	—
172	#872	—	3	1	no	—
173	#872	—	3	1	no	—
174	#872	—	3	1	no	—
175	#872	—	3	1	no	—
176	#872	—	3	1	no	—
177	#872	—	6	1	no	—
178	#872	C₂×D₃	1	1	yes	characteristic
179	C₄²×D₃	—	3	1	no	—
180	C₄²×D₃	C₂×D₃	1	1	yes	characteristic
181	C₃×C₄⋊C₈	—	2	1	no	—
182	C₃×C₄⋊C₈	—	3	1	no	—
183	C₃×C₄⋊C₈	—	3	1	no	—
184	C₃×C₄⋊C₈	—	3	1	no	—
185	C₃×C₄⋊C₈	—	3	1	no	—
186	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
187	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
188	C₃×C₂²⋊C₈	—	3	1	no	—
189	C₃×C₂²⋊C₈	—	3	1	no	—
190	C₃×#97	—	3	1	no	—
191	C₃×C₄×C₈	—	3	1	no	—
192	#830	—	3	1	no	—
193	#830	—	3	1	no	—
194	(C₂×D₃)⋊C₈	—	3	1	no	—
195	(C₂×D₃)⋊C₈	—	3	1	no	—
196	(C₂×D₃)⋊C₈	—	3	1	no	—
197	(C₂×D₃)⋊C₈	—	3	1	no	—
198	(C₂×D₃)⋊C₈	—	3	1	no	—
199	(C₂×D₃)⋊C₈	—	3	1	no	—
200	(C₂×D₃)⋊C₈	—	3	1	no	—
201	(C₂×D₃)⋊C₈	—	3	1	no	—
202	(C₂×D₃)⋊C₈	—	3	1	no	—
203	(C₂×D₃)⋊C₈	—	3	1	no	—
204	(C₂×D₃)⋊C₈	—	6	1	no	—
205	(C₂×D₃)⋊C₈	—	6	1	no	—
206	(C₂×D₃)⋊C₈	C₂×D₃	1	1	yes	characteristic
207	(C₂×D₃)⋊C₈	C₂×D₃	1	1	yes	characteristic
208	#815	—	3	1	no	—
209	#815	—	3	1	no	—
210	#815	—	3	1	no	—
211	#815	—	3	1	no	—
212	#815	—	3	1	no	—
213	#815	—	6	1	no	—
214	#815	C₂×D₃	1	1	yes	characteristic, complemented
215	Dic₃⋊C₈	—	3	1	no	—
216	Dic₃⋊C₈	—	3	1	no	—
217	Dic₃⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
218	Dic₃⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
219	C₈×Dic₃	—	3	1	no	—
220	C₈×Dic₃	—	3	1	no	—
221	C₈×Dic₃	—	3	1	no	—
222	C₈×Dic₃	—	3	1	no	—
223	C₈×Dic₃	—	3	1	no	—
224	C₈×Dic₃	—	6	1	no	—
225	C₈×Dic₃	C₂×D₃	1	1	yes	characteristic, complemented
226	C₄⋊(C₃⋊C₈)	—	3	1	no	—
227	C₄⋊(C₃⋊C₈)	—	3	1	no	—
228	C₄⋊(C₃⋊C₈)	—	3	1	no	—
229	C₄⋊(C₃⋊C₈)	—	3	1	no	—
230	C₄⋊(C₃⋊C₈)	—	6	1	no	—
231	C₄⋊(C₃⋊C₈)	C₂×D₃	1	1	yes	characteristic, complemented
232	C₄⋊(C₃⋊C₈)	C₂×D₃	1	1	yes	characteristic, complemented
233	#803	—	3	1	no	—
234	C₄×C₃⋊C₈	—	3	1	no	—
235	C₂²×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
236	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
237	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
238	C₂×D₃²	—	2	2	no	—
239	C₂×D₃²	—	2	2	no	—
240	C₂×D₃²	—	2	2	no	—
241	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
242	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
243	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
244	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
245	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
246	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
247	C₄×C₃⋊D₃	—	2	1	no	—
248	C₄×C₃⋊D₃	—	2	1	no	—
249	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
250	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
251	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
252	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
253	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
254	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
255	C₃×C₄×D₃	—	2	2	no	—
256	C₃×C₄×D₃	—	2	2	no	—
257	C₃×C₄×D₃	—	2	1	no	—
258	C₃×C₄×D₃	—	2	1	no	—
259	C₃×C₄×D₃	#41	1	2	yes	—
260	C₃×C₄×D₃	#41	1	2	yes	—
261	#624	—	2	2	no	—
262	D₃×Dic₃	—	2	2	no	—
263	D₃×Dic₃	—	2	2	no	—
264	D₃×Dic₃	—	2	2	no	—
265	D₃×Dic₃	—	2	2	no	—
266	C₃²×C₈	—	2	1	no	—
267	C₃²×C₈	—	2	1	no	—
268	C₃⋊(C₃⋊C₈)	—	2	1	no	—
269	C₃⋊(C₃⋊C₈)	—	2	1	no	—
270	C₃×C₃⋊C₈	—	2	1	no	—
271	C₃×C₃⋊C₈	—	2	1	no	—
272	C₃×C₃⋊C₈	—	2	1	no	—
273	C₃×C₃⋊C₈	—	2	1	no	—
274	C₂×#117	—	9	1	no	—
275	#433	—	3	1	no	—
276	#433	—	9	1	no	—
277	#433	—	9	1	no	—
278	#433	—	9	1	no	—
279	#433	—	9	1	no	—
280	#433	—	9	1	no	—
281	#433	—	9	1	no	—
282	#433	—	9	1	no	—
283	C₂×C₄⋊C₈	—	3	1	no	—
284	C₂×C₄⋊C₈	—	9	1	no	—
285	C₂×C₂²⋊C₈	—	9	1	no	—
286	C₂×C₂²⋊C₈	—	9	1	no	—
287	C₂×#97	—	9	1	no	—
288	C₂×C₄×C₈	—	9	1	no	—
289	C₂³×D₃	—	3	1	no	—
290	C₂³×D₃	—	3	1	no	—
291	C₂²×C₃×C₄	—	3	1	no	—
292	C₂²×C₃×C₄	—	3	1	no	—
293	C₂²×C₃×C₄	—	3	1	no	—
294	C₂²×C₃×C₄	—	3	1	no	—
295	C₂²×Dic₃	—	3	1	no	—
296	C₂²×Dic₃	—	3	1	no	—
297	C₂²×Dic₃	—	3	1	no	—
298	C₂²×Dic₃	—	3	1	no	—
299	C₂×C₄×D₃	—	3	1	no	—
300	C₂×C₄×D₃	—	3	1	no	—
301	C₂×C₄×D₃	—	3	1	no	—
302	C₂×C₄×D₃	—	3	1	no	—
303	C₂×C₄×D₃	—	3	1	no	—
304	C₂×C₄×D₃	—	3	1	no	—
305	C₂×C₄×D₃	—	3	1	no	—
306	C₂×C₄×D₃	—	3	1	no	—
307	C₂×C₄×D₃	—	6	1	no	—
308	C₂×C₄×D₃	—	6	2	no	—
309	C₂×C₄×D₃	—	6	2	no	—
310	C₂×C₄×D₃	—	6	2	no	—
311	C₂×C₄×D₃	—	6	2	no	—
312	C₂×C₄×D₃	C₄×D₃	1	1	yes	characteristic
313	C₂×C₄×D₃	C₄×D₃	1	1	yes	characteristic
314	C₂×C₄×D₃	C₂²×D₃	1	1	yes	characteristic
315	C₂×C₄×D₃	C₂²×D₃	1	1	yes	characteristic
316	C₂×C₃×C₈	—	2	1	no	—
317	C₂×C₃×C₈	—	2	1	no	—
318	C₂×C₃×C₈	—	3	1	no	—
319	C₂×C₃×C₈	—	3	1	no	—
320	C₂×C₃×C₈	—	3	1	no	—
321	C₂×C₃×C₈	—	3	1	no	—
322	C₂×C₃×C₈	—	6	2	no	—
323	C₂×C₃×C₈	—	6	2	no	—
324	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
325	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
326	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
327	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
328	C₃×C₄⋊C₄	—	3	1	no	—
329	C₃×C₄⋊C₄	—	3	1	no	—
330	C₃×C₂²⋊C₄	—	3	1	no	—
331	C₃×C₂²⋊C₄	—	3	1	no	—
332	C₃×C₄²	—	2	1	no	—
333	C₃×C₄²	—	3	1	no	—
334	C₃×C₄²	—	3	1	no	—
335	C₃×C₄²	—	3	1	no	—
336	C₃×C₄²	—	3	1	no	—
337	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
338	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
339	#217	—	3	1	no	—
340	#217	—	3	1	no	—
341	(C₂×D₃)⋊C₄	—	3	1	no	—
342	(C₂×D₃)⋊C₄	—	3	1	no	—
343	(C₂×D₃)⋊C₄	—	3	1	no	—
344	(C₂×D₃)⋊C₄	—	3	1	no	—
345	(C₂×D₃)⋊C₄	—	3	1	no	—
346	(C₂×D₃)⋊C₄	—	3	1	no	—
347	(C₂×D₃)⋊C₄	—	3	1	no	—
348	(C₂×D₃)⋊C₄	—	3	1	no	—
349	(C₂×D₃)⋊C₄	—	3	1	no	—
350	(C₂×D₃)⋊C₄	—	3	1	no	—
351	(C₂×D₃)⋊C₄	—	6	1	no	—
352	(C₂×D₃)⋊C₄	—	6	1	no	—
353	(C₂×D₃)⋊C₄	C₄×D₃	1	1	yes	characteristic
354	(C₂×D₃)⋊C₄	C₄×D₃	1	1	yes	characteristic
355	C₄⋊Dic₃	—	3	1	no	—
356	C₄⋊Dic₃	—	3	1	no	—
357	Dic₃⋊C₄	—	3	1	no	—
358	Dic₃⋊C₄	—	3	1	no	—
359	Dic₃⋊C₄	—	3	1	no	—
360	Dic₃⋊C₄	—	3	1	no	—
361	Dic₃⋊C₄	—	3	1	no	—
362	Dic₃⋊C₄	—	3	1	no	—
363	Dic₃⋊C₄	—	3	1	no	—
364	Dic₃⋊C₄	—	3	1	no	—
365	Dic₃⋊C₄	—	3	1	no	—
366	Dic₃⋊C₄	—	3	1	no	—
367	Dic₃⋊C₄	—	6	1	no	—
368	Dic₃⋊C₄	—	6	1	no	—
369	Dic₃⋊C₄	C₄×D₃	1	1	yes	characteristic
370	Dic₃⋊C₄	C₄×D₃	1	1	yes	characteristic
371	C₄×Dic₃	—	3	1	no	—
372	C₄×Dic₃	—	3	1	no	—
373	C₄×Dic₃	—	3	1	no	—
374	C₄×Dic₃	—	3	1	no	—
375	C₄×Dic₃	—	3	1	no	—
376	C₄×Dic₃	—	3	1	no	—
377	C₄×Dic₃	—	6	1	no	—
378	C₄×Dic₃	C₄×D₃	1	1	yes	characteristic
379	C₄×Dic₃	C₄×D₃	1	1	yes	characteristic
380	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
381	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
382	C₂×C₃⋊C₈	—	3	1	no	—
383	C₂×C₃⋊C₈	—	3	1	no	—
384	C₂×C₃⋊C₈	—	3	1	no	—
385	C₂×C₃⋊C₈	—	3	1	no	—
386	C₂×C₃⋊C₈	—	6	1	no	—
387	C₂×C₃⋊C₈	—	6	1	no	—
388	C₂×C₃⋊C₈	—	6	2	no	—
389	C₂×C₃⋊C₈	—	6	2	no	—
390	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
391	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
392	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
393	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
394	D₃×C₈	—	2	2	no	—
395	D₃×C₈	—	2	2	no	—
396	D₃×C₈	—	6	2	no	—
397	D₃×C₈	—	6	2	no	—
398	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
399	C₂×C₃⋊D₃	—	2	1	no	—
400	C₂×C₃⋊D₃	—	2	1	no	—
401	C₂×C₃⋊D₃	—	2	1	no	—
402	C₂×C₃×D₃	—	2	1	no	—
403	C₂×C₃×D₃	—	2	1	no	—
404	C₂×C₃×D₃	—	2	1	no	—
405	C₂×C₃×D₃	#117	1	2	yes	—
406	C₂×C₃×D₃	#131	1	2	yes	—
407	C₂×C₃×D₃	#131	1	2	yes	—
408	D₃²	—	4	4	no	—
409	C₃²×C₄	—	2	1	no	—
410	C₃²×C₄	—	2	1	no	—
411	C₃²×C₄	C₂×#41	1	1	yes	characteristic
412	C₃²×C₄	C₂×#41	1	1	yes	characteristic
413	C₃⋊Dic₃	—	2	1	no	—
414	C₃⋊Dic₃	—	2	1	no	—
415	C₃⋊Dic₃	—	2	1	no	—
416	C₃×Dic₃	—	2	1	no	—
417	C₃×Dic₃	—	2	1	no	—
418	C₃×Dic₃	—	2	1	no	—
419	C₃×Dic₃	—	2	1	no	—
420	C₃×Dic₃	—	2	1	no	—
421	C₃×Dic₃	#117	1	2	yes	—
422	C₂³×C₄	—	9	1	no	—
423	C₂²×C₈	—	3	1	no	—
424	C₂²×C₈	—	3	1	no	—
425	C₂²×C₈	—	9	1	no	—
426	C₂²×C₈	—	9	1	no	—
427	#117	—	3	1	no	—
428	#117	—	9	1	no	—
429	#117	—	9	1	no	—
430	#117	—	9	1	no	—
431	#117	—	9	1	no	—
432	#117	—	9	1	no	—
433	#117	—	9	1	no	—
434	#117	—	9	1	no	—
435	C₂×C₄⋊C₄	—	9	1	no	—
436	C₂×C₄⋊C₄	—	9	1	no	—
437	C₂×C₂²⋊C₄	—	9	1	no	—
438	C₂×C₂²⋊C₄	—	9	1	no	—
439	C₂×C₄²	—	3	1	no	—
440	C₂×C₄²	—	9	1	no	—
441	C₄⋊C₈	—	3	1	no	—
442	C₄⋊C₈	—	3	1	no	—
443	C₄⋊C₈	—	3	1	no	—
444	C₄⋊C₈	—	3	1	no	—
445	C₄⋊C₈	—	9	1	no	—
446	C₄⋊C₈	—	9	1	no	—
447	C₄⋊C₈	—	9	1	no	—
448	C₄⋊C₈	D₃²	1	1	yes	characteristic, complemented
449	C₂²⋊C₈	—	3	1	no	—
450	C₂²⋊C₈	—	3	1	no	—
451	C₂²⋊C₈	—	9	1	no	—
452	C₂²⋊C₈	—	9	1	no	—
453	C₂²⋊C₈	—	9	1	no	—
454	C₂²⋊C₈	—	9	1	no	—
455	C₂²⋊C₈	—	9	1	no	—
456	C₂²⋊C₈	—	9	1	no	—
457	#97	—	3	1	no	—
458	#97	—	9	1	no	—
459	#97	—	9	1	no	—
460	#97	—	9	1	no	—
461	C₄×C₈	—	3	1	no	—
462	C₄×C₈	—	9	1	no	—
463	C₄×C₈	—	9	1	no	—
464	C₄×C₈	—	9	1	no	—
465	C₂³×C₃	—	3	1	no	—
466	C₂³×C₃	—	3	1	no	—
467	C₂²×D₃	—	3	1	no	—
468	C₂²×D₃	—	3	1	no	—
469	C₂²×D₃	—	6	1	no	—
470	C₂²×D₃	—	6	2	no	—
471	C₂²×D₃	—	6	2	no	—
472	C₂²×D₃	—	6	2	no	—
473	C₂²×D₃	—	6	2	no	—
474	C₂²×D₃	—	6	2	no	—
475	C₂²×D₃	—	6	2	no	—
476	C₂²×D₃	C₂×C₄×D₃	1	1	yes	characteristic
477	C₂²×D₃	C₂×C₄×D₃	1	1	yes	characteristic
478	C₂×C₃×C₄	—	2	1	no	—
479	C₂×C₃×C₄	—	2	1	no	—
480	C₂×C₃×C₄	—	2	1	no	—
481	C₂×C₃×C₄	—	3	1	no	—
482	C₂×C₃×C₄	—	3	2	no	—
483	C₂×C₃×C₄	—	3	2	no	—
484	C₂×C₃×C₄	—	3	1	no	—
485	C₂×C₃×C₄	—	3	1	no	—
486	C₂×C₃×C₄	—	3	1	no	—
487	C₂×C₃×C₄	—	3	1	no	—
488	C₂×C₃×C₄	—	3	1	no	—
489	C₂×C₃×C₄	—	6	2	no	—
490	C₂×C₃×C₄	—	6	2	no	—
491	C₂×C₃×C₄	—	6	1	no	—
492	C₂×C₃×C₄	—	6	1	no	—
493	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
494	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
495	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
496	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
497	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
498	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
499	C₂×Dic₃	—	3	1	no	—
500	C₂×Dic₃	—	3	1	no	—
501	C₂×Dic₃	—	3	1	no	—
502	C₂×Dic₃	—	3	1	no	—
503	C₂×Dic₃	—	3	1	no	—
504	C₂×Dic₃	—	3	1	no	—
505	C₂×Dic₃	—	6	1	no	—
506	C₂×Dic₃	—	6	1	no	—
507	C₂×Dic₃	—	6	1	no	—
508	C₂×Dic₃	—	6	2	no	—
509	C₂×Dic₃	—	6	2	no	—
510	C₂×Dic₃	—	6	2	no	—
511	C₂×Dic₃	—	6	2	no	—
512	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
513	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
514	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
515	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
516	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
517	C₂×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
518	C₄×D₃	—	2	2	no	—
519	C₄×D₃	—	2	2	no	—
520	C₄×D₃	—	2	1	no	—
521	C₄×D₃	—	2	1	no	—
522	C₄×D₃	—	6	2	no	—
523	C₄×D₃	—	6	2	no	—
524	C₄×D₃	—	6	2	no	—
525	C₄×D₃	—	6	2	no	—
526	C₄×D₃	—	6	2	no	—
527	C₄×D₃	—	6	1	no	—
528	C₄×D₃	—	6	1	no	—
529	C₄×D₃	—	6	1	no	—
530	C₄×D₃	—	6	1	no	—
531	C₄×D₃	—	6	2	no	—
532	C₄×D₃	—	12	1	no	—
533	C₄×D₃	—	12	1	no	—
534	C₄×D₃	#237	1	2	yes	—
535	C₄×D₃	#239	1	2	yes	—
536	C₃×C₈	—	2	1	no	—
537	C₃×C₈	—	2	1	no	—
538	C₃×C₈	—	2	1	no	—
539	C₃×C₈	—	2	1	no	—
540	C₃×C₈	—	4	1	no	—
541	C₃×C₈	—	4	1	no	—
542	C₃×C₈	—	6	1	no	—
543	C₃×C₈	—	6	1	no	—
544	C₃×C₈	—	6	1	no	—
545	C₃×C₈	—	6	1	no	—
546	C₃⋊C₈	—	2	1	no	—
547	C₃⋊C₈	—	2	1	no	—
548	C₃⋊C₈	—	2	1	no	—
549	C₃⋊C₈	—	2	1	no	—
550	C₃⋊C₈	—	6	1	no	—
551	C₃⋊C₈	—	6	1	no	—
552	C₃⋊C₈	—	6	1	no	—
553	C₃⋊C₈	—	6	1	no	—
554	C₃⋊C₈	—	12	1	no	—
555	C₃⋊C₈	—	12	1	no	—
556	C₂×C₃²	C₂×#117	1	1	yes	characteristic
557	C₂×C₃²	C₂×#131	1	1	yes	characteristic
558	C₂×C₃²	C₂×#131	1	1	yes	characteristic
559	C₃⋊D₃	—	4	1	no	—
560	C₃×D₃	—	4	1	no	—
561	C₃×D₃	#433	1	4	yes	complemented
562	C₂⁴	—	9	1	no	—
563	C₂²×C₄	—	3	1	no	—
564	C₂²×C₄	—	3	1	no	—
565	C₂²×C₄	—	3	1	no	—
566	C₂²×C₄	—	3	1	no	—
567	C₂²×C₄	—	9	1	no	—
568	C₂²×C₄	—	9	1	no	—
569	C₂²×C₄	—	9	1	no	—
570	C₂²×C₄	—	9	1	no	—
571	C₂²×C₄	—	9	1	no	—
572	C₂²×C₄	—	9	1	no	—
573	C₂²×C₄	—	18	2	no	—
574	C₂²×C₄	—	18	2	no	—
575	C₂×C₈	—	3	1	no	—
576	C₂×C₈	—	3	1	no	—
577	C₂×C₈	—	3	1	no	—
578	C₂×C₈	—	3	1	no	—
579	C₂×C₈	—	6	2	no	—
580	C₂×C₈	—	6	2	no	—
581	C₂×C₈	—	9	1	no	—
582	C₂×C₈	—	9	1	no	—
583	C₂×C₈	—	18	2	no	—
584	C₂×C₈	—	18	2	no	—
585	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
586	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
587	C₄⋊C₄	—	3	1	no	—
588	C₄⋊C₄	—	3	1	no	—
589	C₄⋊C₄	—	9	1	no	—
590	C₄⋊C₄	—	9	1	no	—
591	C₄⋊C₄	—	9	1	no	—
592	C₄⋊C₄	—	9	1	no	—
593	C₄⋊C₄	—	9	1	no	—
594	C₄⋊C₄	—	9	1	no	—
595	C₂²⋊C₄	—	3	1	no	—
596	C₂²⋊C₄	—	3	1	no	—
597	C₂²⋊C₄	—	9	1	no	—
598	C₂²⋊C₄	—	9	1	no	—
599	C₂²⋊C₄	—	9	1	no	—
600	C₂²⋊C₄	—	9	1	no	—
601	C₂²⋊C₄	—	9	1	no	—
602	C₂²⋊C₄	—	9	1	no	—
603	C₄²	—	3	1	no	—
604	C₄²	—	3	1	no	—
605	C₄²	—	3	1	no	—
606	C₄²	—	3	1	no	—
607	C₄²	—	9	1	no	—
608	C₄²	—	9	1	no	—
609	C₄²	—	9	1	no	—
610	C₄²	C₂×D₃²	1	1	yes	characteristic
611	C₂²×C₃	—	2	1	no	—
612	C₂²×C₃	—	3	2	no	—
613	C₂²×C₃	—	3	2	no	—
614	C₂²×C₃	—	3	2	no	—
615	C₂²×C₃	—	6	1	no	—
616	C₂²×C₃	—	6	1	no	—
617	C₂²×C₃	—	6	1	no	—
618	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
619	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
620	C₂×D₃	—	2	1	no	—
621	C₂×D₃	—	2	1	no	—
622	C₂×D₃	—	2	1	no	—
623	C₂×D₃	—	6	1	no	—
624	C₂×D₃	—	6	1	no	—
625	C₂×D₃	—	6	1	no	—
626	C₂×D₃	—	6	1	no	—
627	C₂×D₃	—	6	1	no	—
628	C₂×D₃	—	6	1	no	—
629	C₂×D₃	—	12	1	no	—
630	C₂×D₃	—	12	1	no	—
631	C₂×D₃	—	12	1	no	—
632	C₂×D₃	—	12	4	no	—
633	C₂×D₃	—	12	4	no	—
634	C₂×D₃	#892	1	2	yes	—
635	C₂×D₃	#901	1	2	yes	—
636	C₂×D₃	#907	1	2	yes	—
637	C₃×C₄	—	2	1	no	—
638	C₃×C₄	—	2	1	no	—
639	C₃×C₄	—	2	1	no	—
640	C₃×C₄	—	2	1	no	—
641	C₃×C₄	—	2	1	no	—
642	C₃×C₄	—	2	1	no	—
643	C₃×C₄	—	3	2	no	—
644	C₃×C₄	—	4	1	no	—
645	C₃×C₄	—	4	1	no	—
646	C₃×C₄	—	6	1	no	—
647	C₃×C₄	—	6	1	no	—
648	C₃×C₄	—	6	1	no	—
649	C₃×C₄	—	6	1	no	—
650	C₃×C₄	—	6	1	no	—
651	C₃×C₄	C₂×#237	1	1	yes	characteristic
652	C₃×C₄	C₂×#239	1	1	yes	characteristic
653	C₃×C₄	D₃×#41	1	1	yes	characteristic
654	C₃×C₄	D₃×#41	1	1	yes	characteristic
655	Dic₃	—	2	1	no	—
656	Dic₃	—	2	1	no	—
657	Dic₃	—	2	1	no	—
658	Dic₃	—	2	1	no	—
659	Dic₃	—	2	1	no	—
660	Dic₃	—	6	1	no	—
661	Dic₃	—	6	1	no	—
662	Dic₃	—	6	1	no	—
663	Dic₃	—	6	1	no	—
664	Dic₃	—	6	1	no	—
665	Dic₃	—	6	1	no	—
666	Dic₃	—	12	1	no	—
667	Dic₃	—	12	1	no	—
668	Dic₃	—	12	1	no	—
669	Dic₃	#892	1	2	yes	—
670	C₃²	C₂×#433	1	1	yes	characteristic, complemented, Sylow
671	C₂³	—	3	1	no	—
672	C₂³	—	3	1	no	—
673	C₂³	—	9	1	no	—
674	C₂³	—	18	2	no	—
675	C₂³	—	18	2	no	—
676	C₂³	—	18	2	no	—
677	C₂×C₄	—	3	1	no	—
678	C₂×C₄	—	3	2	no	—
679	C₂×C₄	—	3	2	no	—
680	C₂×C₄	—	3	1	no	—
681	C₂×C₄	—	3	1	no	—
682	C₂×C₄	—	3	1	no	—
683	C₂×C₄	—	3	1	no	—
684	C₂×C₄	—	3	1	no	—
685	C₂×C₄	—	6	2	no	—
686	C₂×C₄	—	6	2	no	—
687	C₂×C₄	—	6	1	no	—
688	C₂×C₄	—	6	1	no	—
689	C₂×C₄	—	9	1	no	—
690	C₂×C₄	—	9	1	no	—
691	C₂×C₄	—	9	1	no	—
692	C₂×C₄	—	18	2	no	—
693	C₂×C₄	—	18	2	no	—
694	C₂×C₄	—	18	2	no	—
695	C₂×C₄	—	18	2	no	—
696	C₂×C₄	—	18	2	no	—
697	C₂×C₄	—	18	1	no	—
698	C₂×C₄	—	18	1	no	—
699	C₂×C₄	C₄×D₃²	1	1	yes	characteristic
700	C₂×C₄	C₄×D₃²	1	1	yes	characteristic
701	C₂×C₄	C₂²×D₃²	1	1	yes	characteristic
702	C₈	—	2	1	no	—
703	C₈	—	2	1	no	—
704	C₈	—	6	1	no	—
705	C₈	—	6	1	no	—
706	C₈	—	6	1	no	—
707	C₈	—	6	1	no	—
708	C₈	—	18	1	no	—
709	C₈	—	18	1	no	—
710	C₂×C₃	—	2	1	no	—
711	C₂×C₃	—	2	1	no	—
712	C₂×C₃	—	2	1	no	—
713	C₂×C₃	—	3	4	no	—
714	C₂×C₃	—	12	1	no	—
715	C₂×C₃	C₂×#892	1	1	yes	characteristic
716	C₂×C₃	D₃×#117	1	1	yes	characteristic
717	C₂×C₃	C₂×#901	1	1	yes	characteristic
718	C₂×C₃	C₂×#907	1	1	yes	characteristic
719	C₂×C₃	D₃×#131	1	1	yes	characteristic
720	C₂×C₃	D₃×#131	1	1	yes	characteristic
721	D₃	—	4	1	no	—
722	D₃	—	12	1	no	—
723	D₃	—	12	1	no	—
724	D₃	—	24	1	no	—
725	D₃	#4840	1	4	yes	direct product factor
726	C₂²	—	3	2	no	—
727	C₂²	—	3	2	no	—
728	C₂²	—	3	2	no	—
729	C₂²	—	6	1	no	—
730	C₂²	—	6	1	no	—
731	C₂²	—	6	1	no	—
732	C₂²	—	18	1	no	—
733	C₂²	—	18	1	no	—
734	C₂²	—	18	1	no	—
735	C₂²	—	36	4	no	—
736	C₂²	C₂×C₄×D₃²	1	1	yes	characteristic
737	C₄	—	2	1	no	—
738	C₄	—	2	1	no	—
739	C₄	—	3	2	no	—
740	C₄	—	6	1	no	—
741	C₄	—	6	1	no	—
742	C₄	—	6	1	no	—
743	C₄	—	6	1	no	—
744	C₄	—	6	1	no	—
745	C₄	—	18	1	no	—
746	C₄	—	18	1	no	—
747	C₄	—	18	1	no	—
748	C₄	D₃×#237	1	1	yes	characteristic
749	C₄	D₃×#239	1	1	yes	characteristic
750	C₃	—	2	1	no	—
751	C₃	C₂×#4840	1	1	yes	characteristic, complemented
752	C₃	D₃×#433	1	1	yes	characteristic, complemented
753	C₂	—	3	4	no	—
754	C₂	—	12	1	no	—
755	C₂	—	36	1	no	—
756	C₂	D₃×#892	1	1	yes	characteristic
757	C₂	D₃×#901	1	1	yes	characteristic
758	C₂	D₃×#907	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃²
commutator, socle	C₂²×C₃²	C₂³×C₄
Fitting	C₃²×C₄⋊C₈	C₂²
prime radical	C₂²×D₃²	C₂×C₄
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	C₄⋊C₈	D₃²
hypocenter	C₃²	C₂×#433
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. #10592539	C₂	semidirect
3. C₃×#4840	C₂	semidirect
4. C₃×D₃×C₄⋊C₈	C₂	semidirect
7. #10590699	C₂	semidirect
8. #10590698	C₂	semidirect
9. D₃×#815	C₂	semidirect
10. D₃×C₈×Dic₃	C₂	semidirect
11. #10590648	C₂	semidirect
12. #10590647	C₂	semidirect
13. D₃×C₄⋊(C₃⋊C₈)	C₂	semidirect
14. #10590257	C₂	semidirect
15. #10590253	C₂	semidirect
37. C₃²×C₄⋊C₈	C₂²	semidirect
40. #63642	C₂²	semidirect
41. C₈×C₃⋊Dic₃	C₂²	semidirect
42. C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	semidirect
45. C₃×#815	C₂²	semidirect
46. C₃×Dic₃⋊C₈	C₂²	semidirect
47. C₃×Dic₃⋊C₈	C₂²	semidirect
48. C₃×C₈×Dic₃	C₂²	semidirect
49. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
50. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
51. Dic₃⋊(C₃⋊C₈)	C₂²	semidirect
52. Dic₃⋊(C₃⋊C₈)	C₂²	semidirect
57. #63555	C₂²	semidirect
58. #63554	C₂²	semidirect
59. #63553	C₂²	semidirect
60. Dic₃×C₃⋊C₈	C₂²	semidirect
81. #4840	D₃	direct (N × H)
83. D₃×C₄⋊C₈	D₃	semidirect
186. C₃×C₄⋊C₈	C₂×D₃	semidirect
187. C₃×C₄⋊C₈	C₂×D₃	semidirect
214. #815	C₂×D₃	semidirect
217. Dic₃⋊C₈	C₂×D₃	semidirect
218. Dic₃⋊C₈	C₂×D₃	semidirect
225. C₈×Dic₃	C₂×D₃	semidirect
231. C₄⋊(C₃⋊C₈)	C₂×D₃	semidirect
232. C₄⋊(C₃⋊C₈)	C₂×D₃	semidirect
448. C₄⋊C₈	D₃²	semidirect
561. C₃×D₃	#433	semidirect
670. C₃²	C₂×#433	semidirect
725. D₃	#4840	direct (N × H)
751. C₃	C₂×#4840	semidirect
752. C₃	D₃×#433	semidirect

Maximal subgroups

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

subgroup	index
D₃×#872	2
#10592539	2
C₃×#4840	2
C₃×D₃×C₄⋊C₈	2
D₃×(C₂×D₃)⋊C₈	2
#10590699	2
#10590698	2
D₃×#815	2
D₃×C₈×Dic₃	2
#10590648	2
#10590647	2
D₃×C₄⋊(C₃⋊C₈)	2
#10590257	2
#10590253	2
D₃×#433	3
C₂×#4840	3

Subgroups — D3×#4840 #11858805

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#4840 #11858805