Subgroups — D₃×#72224648 #72254993

Order 6144.

480 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72254992	C₂	1	1	yes	maximal, characteristic, complemented
2	#72254991	C₂	1	1	yes	maximal, characteristic, complemented
3	#72254989	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#72224648	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×#93878	C₂	1	1	yes	maximal, characteristic
6	#72245424	—	2	1	no	—
7	D₃×#7456	—	2	1	no	—
8	#72245421	C₂²	1	1	yes	characteristic
9	C₃×#93878	C₂²	1	1	yes	characteristic
10	D₃×#94506	C₂	1	1	yes	maximal, characteristic
11	#72245364	C₄	1	1	yes	characteristic
12	#72245364	C₄	1	1	yes	characteristic
13	D₃×#7511	C₄	1	1	yes	characteristic
14	D₃×#7511	C₄	1	1	yes	characteristic
15	#72245357	C₂²	1	1	yes	characteristic
16	C₃×#94506	C₂²	1	1	yes	characteristic
17	C₂×#72224648	—	3	1	no	maximal, Sylow
18	C₂×#93878	—	3	1	no	—
19	C₂×#94506	—	3	1	no	—
20	D₃×#93877	C₂	1	1	yes	maximal, characteristic
21	#72244942	—	2	1	no	—
22	D₃×#7099	—	2	1	no	—
23	#72244930	C₂²	1	1	yes	characteristic
24	C₃×#93877	C₂²	1	1	yes	characteristic
25	D₃×#7330	C₂²	1	1	yes	characteristic
26	C₂×#93877	—	3	1	no	—
27	#72224648	—	3	1	no	—
28	#72224648	—	3	1	no	—
29	#72224648	—	3	1	no	—
30	#72224648	D₃	1	1	yes	characteristic, direct product factor
31	D₃×M₁₂₈	—	2	1	no	—
32	D₃×M₁₂₈	C₈	1	1	yes	characteristic
33	D₃×M₁₂₈	C₈	1	1	yes	characteristic
34	D₃×#1422	—	4	1	no	—
35	D₃×#1397	C₂×C₄	1	1	yes	characteristic
36	D₃×#1397	Q₈	1	1	yes	characteristic
37	D₃×#1367	—	4	1	no	—
38	D₃×#1311	D₄	1	1	yes	characteristic
39	#10682994	C₂×C₄	1	1	yes	characteristic
40	#10682994	C₂×C₄	1	1	yes	characteristic
41	#10682993	—	2	1	no	—
42	#10682993	C₈	1	1	yes	characteristic
43	#10682993	C₈	1	1	yes	characteristic
44	#10682855	—	2	1	no	—
45	#10682854	—	4	1	no	—
46	#10682517	D₄	1	1	yes	characteristic
47	#10682516	C₂×C₄	1	1	yes	characteristic
48	#10682516	Q₈	1	1	yes	characteristic
49	#10681925	—	2	1	no	—
50	#10681924	—	4	1	no	—
51	C₃×#7511	C₂×C₄	1	1	yes	characteristic
52	C₃×#7511	C₂×C₄	1	1	yes	characteristic
53	C₃×#7456	—	2	1	no	—
54	C₃×#7330	C₂³	1	1	yes	characteristic
55	C₃×#7099	—	2	1	no	—
56	C₂×#7511	—	3	1	no	—
57	C₂×#7511	—	3	1	no	—
58	C₂×#7456	—	6	1	no	—
59	C₂×#7330	—	3	1	no	—
60	C₂×#7099	—	6	1	no	—
61	#94506	—	3	1	no	—
62	#94506	—	3	1	no	—
63	#94506	—	3	1	no	—
64	#94506	C₂×D₃	1	1	yes	characteristic
65	#93878	—	3	1	no	—
66	#93878	—	6	1	no	—
67	#93878	C₂×D₃	1	1	yes	characteristic
68	#93877	—	3	1	no	—
69	#93877	—	6	1	no	—
70	#93877	C₂×D₃	1	1	yes	characteristic
71	D₃×M₆₄	—	8	1	no	—
72	C₂×D₃×C₃₂	—	2	1	no	—
73	C₂×D₃×C₃₂	C₂×C₈	1	1	yes	characteristic
74	C₂×D₃×C₃₂	M₁₆	1	1	yes	characteristic
75	D₃×C₄⋊C₁₆	—	8	1	no	—
76	C₄×D₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
77	C₄×D₃×C₁₆	SD₁₆	1	1	yes	characteristic
78	D₃×C₈²	SD₁₆	1	1	yes	characteristic
79	C₃×M₁₂₈	—	2	1	no	—
80	C₃×M₁₂₈	C₂×C₈	1	1	yes	characteristic
81	C₃×M₁₂₈	C₂×C₈	1	1	yes	characteristic
82	C₃×#1422	—	4	1	no	—
83	C₃×#1397	C₂²×C₄	1	1	yes	characteristic
84	C₃×#1397	C₂×Q₈	1	1	yes	characteristic
85	C₃×#1367	—	4	1	no	—
86	C₃×#1311	C₂×D₄	1	1	yes	characteristic
87	#67599	—	8	1	no	—
88	#67589	—	2	1	no	—
89	#67589	C₂×C₈	1	1	yes	characteristic
90	#67589	M₁₆	1	1	yes	characteristic
91	#67587	—	2	1	no	—
92	#67587	C₂×C₈	1	1	yes	characteristic
93	#67587	C₂×C₈	1	1	yes	characteristic
94	#67554	—	8	1	no	—
95	#67510	—	4	1	no	—
96	#67508	C₄⋊C₄	1	1	yes	characteristic
97	#67508	C₄⋊C₄	1	1	yes	characteristic
98	#67498	C₄⋊C₄	1	1	yes	characteristic
99	#67498	SD₁₆	1	1	yes	characteristic
100	#67439	—	4	1	no	—
101	#67437	SD₁₆	1	1	yes	characteristic
102	#67432	—	2	2	no	—
103	#67432	—	2	1	no	—
104	#67432	C₁₆	1	2	yes	complemented
105	D₃×C₆₄	—	2	2	no	—
106	D₃×C₆₄	—	2	1	no	—
107	D₃×C₆₄	C₁₆	1	2	yes	complemented
108	C₂×M₁₂₈	—	3	1	no	—
109	C₂×M₁₂₈	—	3	1	no	—
110	C₂×M₁₂₈	—	6	1	no	—
111	C₂×#1422	—	12	1	no	—
112	C₂×#1397	—	3	1	no	—
113	C₂×#1397	—	3	1	no	—
114	C₂×#1367	—	12	1	no	—
115	C₂×#1311	—	3	1	no	—
116	#7511	—	3	1	no	—
117	#7511	—	3	1	no	—
118	#7511	—	3	1	no	—
119	#7511	—	3	1	no	—
120	#7511	—	6	1	no	—
121	#7511	C₄×D₃	1	1	yes	characteristic
122	#7511	C₄×D₃	1	1	yes	characteristic
123	#7456	—	2	1	no	—
124	#7456	—	6	1	no	—
125	#7456	—	12	1	no	—
126	#7330	—	3	1	no	—
127	#7330	—	3	1	no	—
128	#7330	—	3	1	no	—
129	#7330	C₂²×D₃	1	1	yes	characteristic
130	#7099	—	2	1	no	—
131	#7099	—	6	1	no	—
132	#7099	—	12	1	no	—
133	C₂×D₃×C₁₆	—	2	1	no	—
134	C₂×D₃×C₁₆	—	16	1	no	—
135	C₂×D₃×C₁₆	C₄⋊C₈	1	1	yes	characteristic
136	C₂×D₃×C₁₆	#108	1	1	yes	characteristic
137	C₄×D₃×C₈	—	2	1	no	—
138	C₄×D₃×C₈	#106	1	1	yes	characteristic
139	C₃×M₆₄	—	8	1	no	—
140	C₂×C₃×C₃₂	—	2	1	no	—
141	C₂×C₃×C₃₂	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₃×C₃₂	C₂×M₁₆	1	1	yes	characteristic
143	C₃×C₄⋊C₁₆	—	8	1	no	—
144	C₃×C₄×C₁₆	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₃×C₄×C₁₆	C₂×SD₁₆	1	1	yes	characteristic
146	C₃×C₈²	C₂×SD₁₆	1	1	yes	characteristic
147	Dic₃⋊C₁₆	—	16	1	no	—
148	Dic₃×C₁₆	—	2	1	no	—
149	Dic₃×C₁₆	C₄⋊C₈	1	1	yes	characteristic
150	Dic₃×C₁₆	#108	1	1	yes	characteristic
151	#4499	—	8	1	no	—
152	C₂×C₃⋊C₃₂	—	2	1	no	—
153	C₂×C₃⋊C₃₂	C₄⋊C₈	1	1	yes	characteristic
154	C₂×C₃⋊C₃₂	C₄⋊C₈	1	1	yes	characteristic
155	C₄⋊(C₃⋊C₁₆)	—	8	1	no	—
156	C₄×C₃⋊C₁₆	#106	1	1	yes	characteristic
157	C₄×C₃⋊C₁₆	#106	1	1	yes	characteristic
158	C₈×C₃⋊C₈	—	2	1	no	—
159	C₈×C₃⋊C₈	#106	1	1	yes	characteristic
160	#4447	—	16	1	no	—
161	D₃×C₃₂	—	2	1	no	—
162	D₃×C₃₂	—	2	1	no	—
163	D₃×C₃₂	—	4	1	no	—
164	D₃×C₃₂	—	4	1	no	—
165	D₃×C₃₂	—	16	1	no	—
166	D₃×C₃₂	C₂×C₁₆	1	1	yes	characteristic
167	D₃×C₃₂	C₂×C₁₆	1	1	yes	characteristic
168	D₃×C₃₂	M₃₂	1	1	yes	characteristic
169	D₃×C₃₂	M₃₂	1	1	yes	characteristic
170	C₃×C₆₄	—	2	2	no	—
171	C₃×C₆₄	—	2	1	no	—
172	C₃×C₆₄	C₂×C₁₆	1	2	yes	complemented
173	C₃⋊C₆₄	—	2	2	no	—
174	C₃⋊C₆₄	—	2	1	no	—
175	C₃⋊C₆₄	C₂×C₁₆	1	2	yes	complemented
176	C₂×M₆₄	—	24	1	no	—
177	C₂²×C₃₂	—	3	1	no	—
178	C₂²×C₃₂	—	3	1	no	—
179	C₂²×C₃₂	—	6	1	no	—
180	C₂×C₄⋊C₁₆	—	24	1	no	—
181	C₂×C₄×C₁₆	—	3	1	no	—
182	C₂×C₄×C₁₆	—	3	1	no	—
183	C₂×C₈²	—	3	1	no	—
184	M₁₂₈	—	2	1	no	—
185	M₁₂₈	—	3	1	no	—
186	M₁₂₈	—	3	2	no	—
187	M₁₂₈	—	3	1	no	—
188	M₁₂₈	—	6	1	no	—
189	M₁₂₈	—	6	2	no	—
190	M₁₂₈	—	6	1	no	—
191	M₁₂₈	D₃×C₈	1	1	yes	characteristic
192	M₁₂₈	D₃×C₈	1	1	yes	characteristic
193	C₂×C₆₄	—	3	2	no	—
194	C₂×C₆₄	—	6	1	no	—
195	C₂×C₆₄	—	6	2	no	—
196	#1422	—	4	1	no	—
197	#1422	—	12	1	no	—
198	#1422	—	24	1	no	—
199	#1397	—	3	1	no	—
200	#1397	—	3	1	no	—
201	#1397	—	3	1	no	—
202	#1397	—	3	1	no	—
203	#1397	—	6	1	no	—
204	#1397	C₂×C₄×D₃	1	1	yes	characteristic
205	#1397	D₃×Q₈	1	1	yes	characteristic
206	#1367	—	4	1	no	—
207	#1367	—	12	1	no	—
208	#1367	—	24	1	no	—
209	#1311	—	3	1	no	—
210	#1311	—	3	1	no	—
211	#1311	—	3	1	no	—
212	#1311	D₃×D₄	1	1	yes	characteristic
213	C₂×D₃×C₈	—	4	1	no	—
214	C₂×D₃×C₈	#334	1	1	yes	characteristic
215	C₂×D₃×C₈	#365	1	1	yes	characteristic
216	C₄²×D₃	#365	1	1	yes	characteristic
217	C₂×C₃×C₁₆	—	2	1	no	—
218	C₂×C₃×C₁₆	—	16	1	no	—
219	C₂×C₃×C₁₆	C₂×C₄⋊C₈	1	1	yes	characteristic
220	C₂×C₃×C₁₆	C₂×#108	1	1	yes	characteristic
221	C₃×C₄×C₈	—	2	1	no	—
222	C₃×C₄×C₈	C₂×#106	1	1	yes	characteristic
223	C₈×Dic₃	—	4	1	no	—
224	C₈×Dic₃	#334	1	1	yes	characteristic
225	C₈×Dic₃	#365	1	1	yes	characteristic
226	C₂×C₃⋊C₁₆	—	2	1	no	—
227	C₂×C₃⋊C₁₆	—	16	1	no	—
228	C₂×C₃⋊C₁₆	#334	1	1	yes	characteristic
229	C₂×C₃⋊C₁₆	#334	1	1	yes	characteristic
230	C₄×C₃⋊C₈	—	2	1	no	—
231	C₄×C₃⋊C₈	#365	1	1	yes	characteristic
232	D₃×C₁₆	—	2	1	no	—
233	D₃×C₁₆	—	2	1	no	—
234	D₃×C₁₆	—	4	1	no	—
235	D₃×C₁₆	—	4	1	no	—
236	D₃×C₁₆	—	32	2	no	—
237	D₃×C₁₆	C₄⋊C₁₆	1	1	yes	characteristic
238	D₃×C₁₆	C₄⋊C₁₆	1	1	yes	characteristic
239	D₃×C₁₆	#364	1	1	yes	characteristic
240	D₃×C₁₆	#364	1	1	yes	characteristic
241	C₃×C₃₂	—	2	1	no	—
242	C₃×C₃₂	—	4	1	no	—
243	C₃×C₃₂	—	16	1	no	—
244	C₃×C₃₂	C₂²×C₁₆	1	1	yes	characteristic
245	C₃×C₃₂	C₂×M₃₂	1	1	yes	characteristic
246	C₃⋊C₃₂	—	2	1	no	—
247	C₃⋊C₃₂	—	4	1	no	—
248	C₃⋊C₃₂	—	16	1	no	—
249	C₃⋊C₃₂	C₄⋊C₁₆	1	1	yes	characteristic
250	C₃⋊C₃₂	C₄⋊C₁₆	1	1	yes	characteristic
251	C₂²×C₁₆	—	3	1	no	—
252	C₂²×C₁₆	—	3	1	no	—
253	C₂²×C₁₆	—	6	1	no	—
254	C₂²×C₁₆	—	48	1	no	—
255	C₂×C₄×C₈	—	3	1	no	—
256	C₂×C₄×C₈	—	6	1	no	—
257	M₆₄	—	8	1	no	—
258	M₆₄	—	24	1	no	—
259	M₆₄	—	48	1	no	—
260	C₂×C₃₂	—	2	1	no	—
261	C₂×C₃₂	—	3	1	no	—
262	C₂×C₃₂	—	3	1	no	—
263	C₂×C₃₂	—	3	1	no	—
264	C₂×C₃₂	—	3	1	no	—
265	C₂×C₃₂	—	3	1	no	—
266	C₂×C₃₂	—	3	1	no	—
267	C₂×C₃₂	—	6	1	no	—
268	C₂×C₃₂	—	6	1	no	—
269	C₂×C₃₂	—	6	1	no	—
270	C₂×C₃₂	—	12	1	no	—
271	C₂×C₃₂	—	12	1	no	—
272	C₂×C₃₂	—	48	1	no	—
273	C₂×C₃₂	C₂×D₃×C₈	1	1	yes	characteristic
274	C₂×C₃₂	D₃×M₁₆	1	1	yes	characteristic
275	C₄⋊C₁₆	—	8	1	no	—
276	C₄⋊C₁₆	—	24	1	no	—
277	C₄⋊C₁₆	—	48	1	no	—
278	C₄×C₁₆	—	3	1	no	—
279	C₄×C₁₆	—	3	1	no	—
280	C₄×C₁₆	—	3	1	no	—
281	C₄×C₁₆	—	3	1	no	—
282	C₄×C₁₆	—	6	1	no	—
283	C₄×C₁₆	D₃×C₄⋊C₄	1	1	yes	characteristic
284	C₄×C₁₆	D₃×SD₁₆	1	1	yes	characteristic
285	C₈²	—	3	1	no	—
286	C₈²	—	6	1	no	—
287	C₈²	D₃×SD₁₆	1	1	yes	characteristic
288	C₆₄	—	2	2	no	—
289	C₆₄	—	2	1	no	—
290	C₆₄	—	3	2	no	—
291	C₆₄	—	6	2	no	—
292	C₆₄	—	6	1	no	—
293	C₆₄	D₃×C₁₆	1	2	yes	complemented
294	C₂×C₄×D₃	—	2	1	no	—
295	C₂×C₄×D₃	#1368	1	1	yes	characteristic
296	C₂×C₃×C₈	—	4	1	no	—
297	C₂×C₃×C₈	C₂×#334	1	1	yes	characteristic
298	C₂×C₃×C₈	C₂×#365	1	1	yes	characteristic
299	C₃×C₄²	C₂×#365	1	1	yes	characteristic
300	C₄×Dic₃	—	2	1	no	—
301	C₄×Dic₃	#1368	1	1	yes	characteristic
302	C₂×C₃⋊C₈	—	4	1	no	—
303	C₂×C₃⋊C₈	#1368	1	1	yes	characteristic
304	C₂×C₃⋊C₈	#1368	1	1	yes	characteristic
305	D₃×C₈	—	2	1	no	—
306	D₃×C₈	—	2	1	no	—
307	D₃×C₈	—	8	2	no	—
308	D₃×C₈	#1367	1	1	yes	characteristic
309	D₃×C₈	#1367	1	1	yes	characteristic
310	D₃×C₈	#1369	1	1	yes	characteristic
311	D₃×C₈	#1369	1	1	yes	characteristic
312	C₃×C₁₆	—	2	1	no	—
313	C₃×C₁₆	—	4	1	no	—
314	C₃×C₁₆	—	32	1	no	—
315	C₃×C₁₆	C₂×C₄⋊C₁₆	1	1	yes	characteristic
316	C₃×C₁₆	C₂×#364	1	1	yes	characteristic
317	C₃⋊C₁₆	—	2	1	no	—
318	C₃⋊C₁₆	—	4	1	no	—
319	C₃⋊C₁₆	—	32	1	no	—
320	C₃⋊C₁₆	#1367	1	1	yes	characteristic
321	C₃⋊C₁₆	#1367	1	1	yes	characteristic
322	C₂²×C₈	—	3	1	no	—
323	C₂²×C₈	—	3	1	no	—
324	C₂²×C₈	—	12	1	no	—
325	C₂×C₄²	—	3	1	no	—
326	C₂×C₁₆	—	2	1	no	—
327	C₂×C₁₆	—	3	1	no	—
328	C₂×C₁₆	—	3	1	no	—
329	C₂×C₁₆	—	3	1	no	—
330	C₂×C₁₆	—	3	1	no	—
331	C₂×C₁₆	—	3	1	no	—
332	C₂×C₁₆	—	3	1	no	—
333	C₂×C₁₆	—	6	1	no	—
334	C₂×C₁₆	—	6	1	no	—
335	C₂×C₁₆	—	6	1	no	—
336	C₂×C₁₆	—	12	1	no	—
337	C₂×C₁₆	—	12	1	no	—
338	C₂×C₁₆	—	16	1	no	—
339	C₂×C₁₆	—	48	1	no	—
340	C₂×C₁₆	—	96	2	no	—
341	C₂×C₁₆	D₃×C₄⋊C₈	1	1	yes	characteristic
342	C₂×C₁₆	D₃×#108	1	1	yes	characteristic
343	C₄×C₈	—	2	1	no	—
344	C₄×C₈	—	3	1	no	—
345	C₄×C₈	—	3	1	no	—
346	C₄×C₈	—	3	1	no	—
347	C₄×C₈	—	6	1	no	—
348	C₄×C₈	—	12	1	no	—
349	C₄×C₈	D₃×#106	1	1	yes	characteristic
350	C₃₂	—	2	1	no	—
351	C₃₂	—	3	1	no	—
352	C₃₂	—	3	1	no	—
353	C₃₂	—	4	1	no	—
354	C₃₂	—	6	1	no	—
355	C₃₂	—	12	1	no	—
356	C₃₂	—	16	1	no	—
357	C₃₂	—	48	1	no	—
358	C₃₂	C₂×D₃×C₁₆	1	1	yes	characteristic
359	C₃₂	D₃×M₃₂	1	1	yes	characteristic
360	C₂²×D₃	#7457	1	1	yes	characteristic
361	C₂×C₃×C₄	—	2	1	no	—
362	C₂×C₃×C₄	C₂×#1368	1	1	yes	characteristic
363	C₂×Dic₃	—	2	1	no	—
364	C₂×Dic₃	#7457	1	1	yes	characteristic
365	C₄×D₃	—	4	2	no	—
366	C₄×D₃	#7099	1	1	yes	characteristic
367	C₄×D₃	#7099	1	1	yes	characteristic
368	C₄×D₃	#7457	1	1	yes	characteristic
369	C₄×D₃	#7457	1	1	yes	characteristic
370	C₃×C₈	—	2	1	no	—
371	C₃×C₈	—	8	1	no	—
372	C₃×C₈	C₂×#1367	1	1	yes	characteristic
373	C₃×C₈	C₂×#1369	1	1	yes	characteristic
374	C₃⋊C₈	—	2	1	no	—
375	C₃⋊C₈	—	8	1	no	—
376	C₃⋊C₈	#7099	1	1	yes	characteristic
377	C₃⋊C₈	#7099	1	1	yes	characteristic
378	C₂²×C₄	—	3	1	no	—
379	C₂²×C₄	—	6	1	no	—
380	C₂×C₈	—	3	1	no	—
381	C₂×C₈	—	3	1	no	—
382	C₂×C₈	—	3	1	no	—
383	C₂×C₈	—	3	1	no	—
384	C₂×C₈	—	3	1	no	—
385	C₂×C₈	—	3	1	no	—
386	C₂×C₈	—	4	1	no	—
387	C₂×C₈	—	6	1	no	—
388	C₂×C₈	—	6	1	no	—
389	C₂×C₈	—	12	1	no	—
390	C₂×C₈	—	24	2	no	—
391	C₂×C₈	D₃×#334	1	1	yes	characteristic
392	C₂×C₈	D₃×#365	1	1	yes	characteristic
393	C₄²	—	3	1	no	—
394	C₄²	—	6	1	no	—
395	C₄²	D₃×#365	1	1	yes	characteristic
396	C₁₆	—	2	1	no	—
397	C₁₆	—	3	1	no	—
398	C₁₆	—	3	1	no	—
399	C₁₆	—	4	1	no	—
400	C₁₆	—	6	1	no	—
401	C₁₆	—	12	1	no	—
402	C₁₆	—	32	1	no	—
403	C₁₆	—	96	1	no	—
404	C₁₆	D₃×C₄⋊C₁₆	1	1	yes	characteristic
405	C₁₆	D₃×#364	1	1	yes	characteristic
406	C₂²×C₃	C₂×#7457	1	1	yes	characteristic
407	C₂×D₃	—	2	2	no	—
408	C₂×D₃	#93877	1	1	yes	characteristic
409	C₂×D₃	#93877	1	1	yes	characteristic
410	C₃×C₄	—	4	1	no	—
411	C₃×C₄	C₂×#7099	1	1	yes	characteristic
412	C₃×C₄	C₂×#7457	1	1	yes	characteristic
413	Dic₃	—	4	1	no	—
414	Dic₃	#93877	1	1	yes	characteristic
415	Dic₃	#93877	1	1	yes	characteristic
416	C₂³	—	3	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	3	1	no	—
419	C₂×C₄	—	3	1	no	—
420	C₂×C₄	—	3	1	no	—
421	C₂×C₄	—	3	1	no	—
422	C₂×C₄	—	3	1	no	—
423	C₂×C₄	—	6	1	no	—
424	C₂×C₄	—	12	2	no	—
425	C₂×C₄	D₃×#1368	1	1	yes	characteristic
426	C₈	—	2	1	no	—
427	C₈	—	3	1	no	—
428	C₈	—	3	1	no	—
429	C₈	—	6	1	no	—
430	C₈	—	8	1	no	—
431	C₈	—	24	1	no	—
432	C₈	D₃×#1367	1	1	yes	characteristic
433	C₈	D₃×#1369	1	1	yes	characteristic
434	C₂×C₃	—	2	1	no	—
435	C₂×C₃	C₂×#93877	1	1	yes	characteristic
436	D₃	—	2	1	no	—
437	D₃	#72224648	1	2	yes	direct product factor
438	C₂²	—	3	1	no	—
439	C₂²	—	3	1	no	—
440	C₂²	—	6	2	no	—
441	C₂²	D₃×#7457	1	1	yes	characteristic
442	C₄	—	3	1	no	—
443	C₄	—	3	1	no	—
444	C₄	—	4	1	no	—
445	C₄	—	12	1	no	—
446	C₄	D₃×#7457	1	1	yes	characteristic
447	C₄	D₃×#7099	1	1	yes	characteristic
448	C₃	C₂×#72224648	1	1	yes	characteristic, complemented, Sylow
449	C₂	—	2	1	no	—
450	C₂	—	3	2	no	—
451	C₂	—	6	1	no	—
452	C₂	D₃×#93877	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃×#93877
commutator	C₃×C₃₂	C₂²×C₁₆
Frattini	#7330	C₂²×D₃
Fitting	C₃×#72224648	C₂
socle	C₂×C₃	C₂×#93877
prime radical	C₂²×D₃	#7457
cosocle	C₃×#7330	C₂³
hypercenter	#72224648	D₃
hypocenter	C₃	C₂×#72224648
LCS	G ▷ C₃×C₃₂ ▷ C₃×C₁₆ ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1311 ◁ #7330 ◁ #72224648

Complements

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

N	H ≅ G/N	type
1. #72254992	C₂	semidirect
2. #72254991	C₂	semidirect
3. #72254989	C₂	semidirect
4. C₃×#72224648	C₂	semidirect
30. #72224648	D₃	direct (N × H)
104. #67432	C₁₆	semidirect
107. D₃×C₆₄	C₁₆	semidirect
172. C₃×C₆₄	C₂×C₁₆	semidirect
175. C₃⋊C₆₄	C₂×C₁₆	semidirect
293. C₆₄	D₃×C₁₆	semidirect
437. D₃	#72224648	direct (N × H)
448. C₃	C₂×#72224648	semidirect

Maximal subgroups

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

subgroup	index
#72254992	2
#72254991	2
#72254989	2
C₃×#72224648	2
D₃×#93878	2
D₃×#94506	2
C₂×#72224648	3
D₃×#93877	2

Subgroups — D3×#72224648 #72254993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#72224648 #72254993