Subgroups — D₃×#13656 #72245463

Order 1536.

844 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×#2262	C₂	1	1	yes	maximal, characteristic
2	D₃×#2178	C₂	1	2	yes	maximal, complemented
3	#10715801	C₂	1	1	yes	maximal, characteristic, complemented
4	#10715800	C₂	1	1	yes	maximal, characteristic, complemented
5	#10715799	C₂	1	1	yes	maximal, characteristic, complemented
6	#10715798	C₂	1	2	yes	maximal, complemented
7	#10715797	C₂	1	2	yes	maximal, complemented
8	D₃×#1425	C₂	1	1	yes	maximal, characteristic, complemented
9	D₃×#1417	C₂	1	2	yes	maximal, complemented
10	D₃×#1397	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#13656	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13656	—	3	1	no	maximal, Sylow
13	D₃×#508	C₂²	1	2	yes	—
14	D₃×#443	—	2	2	no	—
15	C₃×#2262	C₂²	1	1	yes	characteristic
16	C₃×#2178	C₂²	1	2	yes	complemented
17	#71511	C₂²	1	2	yes	complemented
18	#71508	C₂²	1	2	yes	—
19	#70921	—	2	2	no	—
20	#69383	C₄	1	1	yes	characteristic, complemented
21	D₃×Q₆₄	C₄	1	1	yes	characteristic, complemented
22	#69379	C₄	1	2	yes	complemented
23	D₃×SD₆₄	C₄	1	2	yes	complemented
24	#69376	C₄	1	1	yes	characteristic, complemented
25	D₃×D₃₂	C₄	1	1	yes	characteristic, complemented
26	#69369	C₂²	1	1	yes	characteristic
27	C₂×D₃×C₃₂	C₂²	1	1	yes	characteristic
28	C₂×D₃×C₃₂	C₂²	1	1	yes	characteristic
29	D₃×#368	C₂²	1	2	yes	—
30	#69357	C₂²	1	2	yes	complemented
31	D₃×#359	—	2	2	no	—
32	#69238	—	2	2	no	—
33	#69067	C₂²	1	2	yes	complemented
34	C₄×D₃×C₁₆	C₂²	1	1	yes	characteristic
35	C₃×#1425	C₂²	1	1	yes	characteristic, complemented
36	C₃×#1417	C₂²	1	2	yes	complemented
37	C₃×#1397	C₂²	1	1	yes	characteristic, complemented
38	#67829	C₂²	1	2	yes	complemented
39	#67598	C₂²	1	2	yes	complemented
40	#67593	C₂²	1	1	yes	characteristic, complemented
41	#67589	C₂²	1	1	yes	characteristic, complemented
42	#67589	C₂²	1	1	yes	characteristic, complemented
43	#67585	C₂²	1	2	yes	complemented
44	#67581	C₂²	1	2	yes	complemented
45	#67508	C₂²	1	1	yes	characteristic, complemented
46	C₂×#2262	—	3	1	no	—
47	C₂×#2178	—	3	2	no	—
48	#13656	—	3	1	no	—
49	#13656	—	3	1	no	—
50	#13656	—	3	2	no	—
51	#13656	—	3	2	no	—
52	#13656	—	3	1	no	—
53	#13656	D₃	1	1	yes	characteristic, direct product factor
54	C₂×#1425	—	3	1	no	—
55	C₂×#1417	—	3	2	no	—
56	C₂×#1397	—	3	1	no	—
57	D₃×#135	—	2	2	no	—
58	D₃×#131	—	4	2	no	—
59	C₃×#508	C₂³	1	2	yes	—
60	C₃×#443	—	2	2	no	—
61	#5196	—	2	2	no	—
62	#5194	—	2	2	no	—
63	#5144	—	4	2	no	—
64	#4919	C₂×C₄	1	2	yes	—
65	D₃×Q₃₂	C₂×C₄	1	2	yes	—
66	#4916	—	2	2	no	—
67	D₃×SD₃₂	—	2	2	no	—
68	#4912	C₂×C₄	1	2	yes	—
69	D₃×D₁₆	C₂×C₄	1	2	yes	—
70	#4904	C₂³	1	2	yes	—
71	C₂×D₃×C₁₆	D₄	1	1	yes	characteristic
72	C₂×D₃×C₁₆	C₂³	1	1	yes	characteristic
73	#4895	—	2	2	no	—
74	D₃×#108	—	2	2	no	—
75	#4824	—	4	2	no	—
76	D₃×#104	—	4	2	no	—
77	#4700	—	2	2	no	—
78	C₄×D₃×C₈	D₄	1	1	yes	characteristic
79	C₃×Q₆₄	C₂×C₄	1	1	yes	characteristic, complemented
80	C₃×SD₆₄	C₂×C₄	1	2	yes	complemented
81	C₃×D₃₂	C₂×C₄	1	1	yes	characteristic, complemented
82	C₂×C₃×C₃₂	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₃₂	C₂³	1	1	yes	characteristic
84	C₃×#368	C₂³	1	2	yes	—
85	C₃×#359	—	2	2	no	—
86	C₃×C₄×C₁₆	C₂³	1	1	yes	characteristic
87	#4567	—	2	2	no	—
88	#4522	C₂×C₄	1	2	yes	complemented
89	#4521	C₂×C₄	1	2	yes	complemented
90	#4520	C₂×C₄	1	2	yes	complemented
91	#4519	C₂×C₄	1	2	yes	complemented
92	#4510	—	2	2	no	—
93	#4506	C₂³	1	2	yes	—
94	Dic₃×C₁₆	D₄	1	1	yes	characteristic
95	Dic₃×C₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₃⋊C₃₂	C₂³	1	1	yes	characteristic
97	C₂×C₃⋊C₃₂	C₂³	1	1	yes	characteristic
98	#4497	—	2	2	no	—
99	#4493	—	2	2	no	—
100	C₄×C₃⋊C₁₆	D₄	1	1	yes	characteristic
101	Dic₄₈	C₂×C₄	1	1	yes	characteristic, complemented
102	#4449	C₂×C₄	1	2	yes	complemented
103	D₉₆	C₂×C₄	1	1	yes	characteristic, complemented
104	D₃×C₃₂	—	2	1	no	—
105	D₃×C₃₂	—	2	1	no	—
106	D₃×C₃₂	C₂×C₄	1	1	yes	characteristic
107	D₃×C₃₂	C₂×C₄	1	1	yes	characteristic
108	D₃×C₃₂	C₂×C₄	1	1	yes	characteristic
109	D₃×C₃₂	C₂×C₄	1	1	yes	characteristic
110	C₂×#508	—	3	2	no	—
111	C₂×#443	—	6	2	no	—
112	#2262	—	3	2	no	—
113	#2262	—	3	1	no	—
114	#2262	—	3	2	no	—
115	#2262	—	3	1	no	—
116	#2262	—	3	1	no	—
117	#2262	C₂×D₃	1	1	yes	characteristic
118	C₂×Q₆₄	—	3	1	no	—
119	C₂×SD₆₄	—	3	2	no	—
120	C₂×D₃₂	—	3	1	no	—
121	C₂²×C₃₂	—	3	1	no	—
122	C₂²×C₃₂	—	3	1	no	—
123	#2178	—	3	2	no	—
124	#2178	—	3	2	no	—
125	#2178	—	3	2	no	—
126	#2178	—	6	2	no	—
127	#2178	—	6	2	no	—
128	#2178	C₂×D₃	1	2	yes	complemented
129	C₂×#368	—	3	2	no	—
130	C₂×#359	—	6	2	no	—
131	C₂×C₄×C₁₆	—	3	1	no	—
132	#1425	—	3	1	no	—
133	#1425	—	3	2	no	—
134	#1425	C₂×D₃	1	1	yes	characteristic, complemented
135	#1417	—	3	2	no	—
136	#1417	—	3	2	no	—
137	#1417	—	3	2	no	—
138	#1417	C₂×D₃	1	2	yes	complemented
139	#1397	—	3	1	no	—
140	#1397	—	3	1	no	—
141	#1397	—	3	1	no	—
142	#1397	C₂×D₃	1	1	yes	characteristic, complemented
143	D₃×#41	—	4	2	no	—
144	C₃×#135	—	2	2	no	—
145	C₃×#131	—	4	2	no	—
146	#950	—	4	2	no	—
147	#948	—	4	2	no	—
148	#919	—	2	2	no	—
149	D₃×Q₁₆	—	2	2	no	—
150	#916	—	4	2	no	—
151	D₃×SD₁₆	—	4	2	no	—
152	#912	—	2	2	no	—
153	D₃×D₈	—	2	2	no	—
154	#907	—	4	2	no	—
155	#907	—	8	2	no	—
156	D₃×M₁₆	—	4	2	no	—
157	D₃×M₁₆	—	8	2	no	—
158	#904	—	2	2	no	—
159	#901	—	4	2	no	—
160	#901	—	8	2	no	—
161	C₂×D₃×C₈	—	8	2	no	—
162	C₂×D₃×C₈	D₈	1	1	yes	characteristic
163	C₂×D₃×C₈	C₂×D₄	1	1	yes	characteristic
164	C₄²×D₃	D₈	1	1	yes	characteristic
165	C₃×Q₃₂	C₂²×C₄	1	2	yes	—
166	C₃×SD₃₂	—	2	2	no	—
167	C₃×D₁₆	C₂²×C₄	1	2	yes	—
168	C₂×C₃×C₁₆	C₂×D₄	1	1	yes	characteristic
169	C₂×C₃×C₁₆	C₂⁴	1	1	yes	characteristic
170	C₃×#108	—	2	2	no	—
171	C₃×#104	—	4	2	no	—
172	C₃×C₄×C₈	C₂×D₄	1	1	yes	characteristic
173	#837	—	4	2	no	—
174	#829	—	2	2	no	—
175	#828	—	2	2	no	—
176	#827	—	2	2	no	—
177	#826	—	2	2	no	—
178	#825	—	4	2	no	—
179	#822	—	4	2	no	—
180	#819	—	2	2	no	—
181	C₈×Dic₃	D₈	1	1	yes	characteristic
182	C₈×Dic₃	C₂×D₄	1	1	yes	characteristic
183	C₂×C₃⋊C₁₆	C₂×D₄	1	1	yes	characteristic
184	C₂×C₃⋊C₁₆	C₂×D₄	1	1	yes	characteristic
185	#805	—	4	2	no	—
186	C₄×C₃⋊C₈	D₈	1	1	yes	characteristic
187	Dic₂₄	C₂²×C₄	1	2	yes	—
188	#800	—	2	2	no	—
189	D₄₈	C₂²×C₄	1	2	yes	—
190	D₃×C₁₆	—	2	1	no	—
191	D₃×C₁₆	—	2	1	no	—
192	D₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
193	D₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
194	D₃×C₁₆	#41	1	1	yes	characteristic
195	D₃×C₁₆	#41	1	1	yes	characteristic
196	C₃×C₃₂	—	2	1	no	—
197	C₃×C₃₂	C₂²×C₄	1	1	yes	characteristic
198	C₃×C₃₂	C₂²×C₄	1	1	yes	characteristic
199	C₃⋊C₃₂	—	2	1	no	—
200	C₃⋊C₃₂	C₂²×C₄	1	1	yes	characteristic
201	C₃⋊C₃₂	C₂²×C₄	1	1	yes	characteristic
202	C₂×#135	—	6	2	no	—
203	C₂×#131	—	12	2	no	—
204	#508	—	3	2	no	—
205	#508	—	3	2	no	—
206	#508	—	3	2	no	—
207	#508	—	6	2	no	—
208	#508	—	6	2	no	—
209	#508	C₂²×D₃	1	2	yes	—
210	C₂×Q₃₂	—	3	2	no	—
211	C₂×SD₃₂	—	6	2	no	—
212	C₂×D₁₆	—	3	2	no	—
213	C₂²×C₁₆	—	3	1	no	—
214	C₂²×C₁₆	—	3	1	no	—
215	#443	—	2	2	no	—
216	#443	—	6	2	no	—
217	#443	—	6	2	no	—
218	#443	—	6	2	no	—
219	#443	—	12	2	no	—
220	#443	—	12	2	no	—
221	C₂×#108	—	6	2	no	—
222	C₂×#104	—	12	2	no	—
223	C₂×C₄×C₈	—	3	1	no	—
224	Q₆₄	—	3	2	no	—
225	Q₆₄	—	3	1	no	—
226	Q₆₄	C₄×D₃	1	1	yes	characteristic, complemented
227	SD₆₄	—	3	2	no	—
228	SD₆₄	—	3	2	no	—
229	SD₆₄	—	3	2	no	—
230	SD₆₄	C₄×D₃	1	2	yes	complemented
231	D₃₂	—	3	2	no	—
232	D₃₂	—	3	1	no	—
233	D₃₂	C₄×D₃	1	1	yes	characteristic, complemented
234	C₂×C₃₂	—	3	1	no	—
235	C₂×C₃₂	—	3	1	no	—
236	C₂×C₃₂	—	3	1	no	—
237	C₂×C₃₂	—	3	1	no	—
238	C₂×C₃₂	—	3	1	no	—
239	C₂×C₃₂	—	3	1	no	—
240	C₂×C₃₂	—	6	1	no	—
241	C₂×C₃₂	—	6	1	no	—
242	C₂×C₃₂	C₂²×D₃	1	1	yes	characteristic
243	C₂×C₃₂	C₂²×D₃	1	1	yes	characteristic
244	#368	—	3	2	no	—
245	#368	—	6	2	no	—
246	#368	C₂²×D₃	1	2	yes	—
247	#359	—	2	2	no	—
248	#359	—	6	2	no	—
249	#359	—	6	2	no	—
250	#359	—	6	2	no	—
251	C₄×C₁₆	—	3	1	no	—
252	C₄×C₁₆	—	3	1	no	—
253	C₄×C₁₆	—	3	1	no	—
254	C₄×C₁₆	C₂²×D₃	1	1	yes	characteristic
255	C₃×#41	—	4	2	no	—
256	#239	—	4	2	no	—
257	D₃×Q₈	—	4	2	no	—
258	#237	—	4	2	no	—
259	#237	—	8	2	no	—
260	D₃×D₄	—	4	2	no	—
261	D₃×D₄	—	8	2	no	—
262	#235	—	4	2	no	—
263	#235	—	8	2	no	—
264	C₂×C₄×D₃	—	2	1	no	—
265	C₂×C₄×D₃	—	8	2	no	—
266	C₂×C₄×D₃	C₂×D₈	1	1	yes	characteristic
267	C₃×Q₁₆	—	2	2	no	—
268	C₃×SD₁₆	—	4	2	no	—
269	C₃×D₈	—	2	2	no	—
270	C₃×M₁₆	—	4	2	no	—
271	C₃×M₁₆	—	8	2	no	—
272	C₂×C₃×C₈	—	8	2	no	—
273	C₂×C₃×C₈	C₂×D₈	1	1	yes	characteristic
274	C₂×C₃×C₈	C₂²×D₄	1	1	yes	characteristic
275	C₃×C₄²	C₂×D₈	1	1	yes	characteristic
276	#216	—	4	2	no	—
277	#215	—	4	2	no	—
278	#214	—	4	2	no	—
279	#213	—	4	2	no	—
280	C₄×Dic₃	—	2	1	no	—
281	C₄×Dic₃	C₂×D₈	1	1	yes	characteristic
282	#208	—	4	2	no	—
283	#208	—	8	2	no	—
284	C₂×C₃⋊C₈	—	8	2	no	—
285	C₂×C₃⋊C₈	C₂×D₈	1	1	yes	characteristic
286	C₂×C₃⋊C₈	C₂×D₈	1	1	yes	characteristic
287	Dic₁₂	—	2	2	no	—
288	D₂₄	—	2	2	no	—
289	#204	—	4	2	no	—
290	ΓL(1,𝔽₂₅)	—	8	2	no	—
291	ΓL(1,𝔽₂₅)	—	8	2	no	—
292	ΓL(1,𝔽₂₅)	—	8	2	no	—
293	D₃×C₈	—	8	2	no	—
294	D₃×C₈	—	8	2	no	—
295	D₃×C₈	—	8	2	no	—
296	D₃×C₈	D₁₆	1	2	yes	—
297	D₃×C₈	D₁₆	1	2	yes	—
298	D₃×C₈	C₄×D₄	1	1	yes	characteristic
299	D₃×C₈	C₄×D₄	1	1	yes	characteristic
300	D₃×C₈	#135	1	1	yes	characteristic
301	D₃×C₈	#135	1	1	yes	characteristic
302	C₃×C₁₆	—	2	1	no	—
303	C₃×C₁₆	C₂³×C₄	1	1	yes	characteristic
304	C₃×C₁₆	C₂×#41	1	1	yes	characteristic
305	C₃⋊C₁₆	—	2	1	no	—
306	C₃⋊C₁₆	C₄×D₄	1	1	yes	characteristic
307	C₃⋊C₁₆	C₄×D₄	1	1	yes	characteristic
308	C₂×#41	—	12	2	no	—
309	#135	—	2	2	no	—
310	#135	—	6	2	no	—
311	#135	—	6	2	no	—
312	#135	—	6	2	no	—
313	#135	—	12	2	no	—
314	#135	—	12	2	no	—
315	C₂×Q₁₆	—	6	2	no	—
316	C₂×SD₁₆	—	12	2	no	—
317	C₂×D₈	—	6	2	no	—
318	#131	—	4	2	no	—
319	#131	—	12	2	no	—
320	#131	—	12	2	no	—
321	#131	—	12	2	no	—
322	#131	—	24	2	no	—
323	#131	—	24	2	no	—
324	C₂×M₁₆	—	12	2	no	—
325	C₂×M₁₆	—	24	2	no	—
326	C₂²×C₈	—	3	1	no	—
327	C₂²×C₈	—	3	1	no	—
328	C₂²×C₈	—	24	2	no	—
329	C₂×C₄²	—	3	1	no	—
330	Q₃₂	—	3	2	no	—
331	Q₃₂	—	6	2	no	—
332	Q₃₂	C₂×C₄×D₃	1	2	yes	—
333	SD₃₂	—	2	2	no	—
334	SD₃₂	—	6	2	no	—
335	SD₃₂	—	6	2	no	—
336	SD₃₂	—	6	2	no	—
337	D₁₆	—	3	2	no	—
338	D₁₆	—	6	2	no	—
339	D₁₆	C₂×C₄×D₃	1	2	yes	—
340	C₂×C₁₆	—	3	1	no	—
341	C₂×C₁₆	—	3	1	no	—
342	C₂×C₁₆	—	3	1	no	—
343	C₂×C₁₆	—	3	1	no	—
344	C₂×C₁₆	—	3	1	no	—
345	C₂×C₁₆	—	3	1	no	—
346	C₂×C₁₆	—	6	1	no	—
347	C₂×C₁₆	—	6	1	no	—
348	C₂×C₁₆	D₃×D₄	1	1	yes	characteristic
349	C₂×C₁₆	C₂³×D₃	1	1	yes	characteristic
350	#108	—	2	2	no	—
351	#108	—	6	2	no	—
352	#108	—	12	2	no	—
353	#104	—	4	2	no	—
354	#104	—	12	2	no	—
355	#104	—	12	2	no	—
356	#104	—	12	2	no	—
357	C₄×C₈	—	3	1	no	—
358	C₄×C₈	—	3	1	no	—
359	C₄×C₈	—	3	1	no	—
360	C₄×C₈	D₃×D₄	1	1	yes	characteristic
361	C₃₂	—	2	1	no	—
362	C₃₂	—	3	1	no	—
363	C₃₂	—	3	1	no	—
364	C₃₂	—	6	1	no	—
365	C₃₂	C₂×C₄×D₃	1	1	yes	characteristic
366	C₃₂	C₂×C₄×D₃	1	1	yes	characteristic
367	C₂²×D₃	—	8	2	no	—
368	C₂²×D₃	#508	1	1	yes	characteristic
369	C₃×Q₈	—	4	2	no	—
370	C₃×D₄	—	4	2	no	—
371	C₃×D₄	—	8	2	no	—
372	C₂×C₃×C₄	—	2	1	no	—
373	C₂×C₃×C₄	—	8	2	no	—
374	C₂×C₃×C₄	C₂²×D₈	1	1	yes	characteristic
375	#67	—	8	2	no	—
376	#67	—	8	2	no	—
377	#67	—	8	2	no	—
378	C₂×Dic₃	—	2	1	no	—
379	C₂×Dic₃	—	8	2	no	—
380	C₂×Dic₃	#508	1	1	yes	characteristic
381	D₁₂	—	4	2	no	—
382	D₁₂	—	8	2	no	—
383	C₄×D₃	—	4	2	no	—
384	C₄×D₃	—	8	2	no	—
385	C₄×D₃	—	8	2	no	—
386	C₄×D₃	—	8	2	no	—
387	C₄×D₃	C₄×D₈	1	1	yes	characteristic
388	C₄×D₃	C₄×D₈	1	1	yes	characteristic
389	C₄×D₃	C₂×D₁₆	1	1	yes	characteristic
390	C₄×D₃	C₂×D₁₆	1	1	yes	characteristic
391	Dic₆	—	4	2	no	—
392	Dic₆	—	8	2	no	—
393	C₃×C₈	—	8	2	no	—
394	C₃×C₈	C₂×D₁₆	1	2	yes	—
395	C₃×C₈	C₂×C₄×D₄	1	1	yes	characteristic
396	C₃×C₈	C₂×#135	1	1	yes	characteristic
397	C₃⋊C₈	—	8	2	no	—
398	C₃⋊C₈	C₄×D₈	1	1	yes	characteristic
399	C₃⋊C₈	C₄×D₈	1	1	yes	characteristic
400	C₃⋊C₈	C₂×D₁₆	1	2	yes	—
401	#41	—	4	2	no	—
402	#41	—	12	2	no	—
403	#41	—	12	2	no	—
404	#41	—	12	2	no	—
405	#41	—	24	2	no	—
406	#41	—	24	2	no	—
407	C₂×Q₈	—	12	2	no	—
408	C₂×D₄	—	12	2	no	—
409	C₂×D₄	—	24	2	no	—
410	C₂²×C₄	—	3	1	no	—
411	C₂²×C₄	—	6	1	no	—
412	C₂²×C₄	—	24	2	no	—
413	Q₁₆	—	2	2	no	—
414	Q₁₆	—	6	2	no	—
415	Q₁₆	—	12	2	no	—
416	SD₁₆	—	4	2	no	—
417	SD₁₆	—	12	2	no	—
418	SD₁₆	—	12	2	no	—
419	SD₁₆	—	12	2	no	—
420	D₈	—	2	2	no	—
421	D₈	—	6	2	no	—
422	D₈	—	12	2	no	—
423	M₁₆	—	4	2	no	—
424	M₁₆	—	8	2	no	—
425	M₁₆	—	12	2	no	—
426	M₁₆	—	24	2	no	—
427	M₁₆	—	24	2	no	—
428	M₁₆	—	24	2	no	—
429	M₁₆	—	24	2	no	—
430	C₂×C₈	—	3	1	no	—
431	C₂×C₈	—	3	1	no	—
432	C₂×C₈	—	3	2	no	—
433	C₂×C₈	—	3	2	no	—
434	C₂×C₈	—	3	1	no	—
435	C₂×C₈	—	3	1	no	—
436	C₂×C₈	—	3	1	no	—
437	C₂×C₈	—	3	1	no	—
438	C₂×C₈	—	8	2	no	—
439	C₂×C₈	—	24	2	no	—
440	C₂×C₈	—	24	2	no	—
441	C₂×C₈	—	24	2	no	—
442	C₂×C₈	—	24	2	no	—
443	C₂×C₈	D₃×D₈	1	1	yes	characteristic
444	C₂×C₈	C₂×D₃×D₄	1	1	yes	characteristic
445	C₄²	—	3	1	no	—
446	C₄²	—	6	1	no	—
447	C₄²	D₃×D₈	1	1	yes	characteristic
448	C₁₆	—	2	1	no	—
449	C₁₆	—	3	1	no	—
450	C₁₆	—	3	1	no	—
451	C₁₆	—	6	1	no	—
452	C₁₆	C₂²×C₄×D₃	1	1	yes	characteristic
453	C₁₆	D₃×#41	1	1	yes	characteristic
454	C₂²×C₃	—	8	2	no	—
455	C₂²×C₃	C₂×#508	1	1	yes	characteristic
456	C₂×D₃	—	2	2	no	—
457	C₂×D₃	—	8	2	no	—
458	C₂×D₃	—	16	4	no	—
459	C₂×D₃	C₄×D₁₆	1	1	yes	characteristic
460	C₂×D₃	C₄×D₁₆	1	1	yes	characteristic
461	C₃×C₄	—	4	1	no	—
462	C₃×C₄	—	8	2	no	—
463	C₃×C₄	C₂×C₄×D₈	1	1	yes	characteristic
464	C₃×C₄	C₂²×D₁₆	1	1	yes	characteristic
465	Dic₃	—	4	1	no	—
466	Dic₃	—	8	2	no	—
467	Dic₃	C₄×D₁₆	1	1	yes	characteristic
468	Dic₃	C₄×D₁₆	1	1	yes	characteristic
469	C₂³	—	3	1	no	—
470	C₂³	—	24	2	no	—
471	Q₈	—	4	2	no	—
472	Q₈	—	12	2	no	—
473	Q₈	—	24	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	8	2	no	—
476	D₄	—	12	2	no	—
477	D₄	—	24	2	no	—
478	D₄	—	24	2	no	—
479	D₄	—	24	2	no	—
480	D₄	—	24	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	3	1	no	—
483	C₂×C₄	—	3	1	no	—
484	C₂×C₄	—	3	1	no	—
485	C₂×C₄	—	3	1	no	—
486	C₂×C₄	—	3	1	no	—
487	C₂×C₄	—	6	1	no	—
488	C₂×C₄	—	8	2	no	—
489	C₂×C₄	—	12	2	no	—
490	C₂×C₄	—	24	2	no	—
491	C₂×C₄	—	24	2	no	—
492	C₂×C₄	—	24	2	no	—
493	C₂×C₄	—	24	2	no	—
494	C₂×C₄	C₂×D₃×D₈	1	1	yes	characteristic
495	C₈	—	3	2	no	—
496	C₈	—	3	1	no	—
497	C₈	—	3	1	no	—
498	C₈	—	8	2	no	—
499	C₈	—	24	2	no	—
500	C₈	D₃×D₁₆	1	2	yes	—
501	C₈	C₄×D₃×D₄	1	1	yes	characteristic
502	C₈	D₃×#135	1	1	yes	characteristic
503	C₂×C₃	—	2	1	no	—
504	C₂×C₃	—	16	2	no	—
505	C₂×C₃	C₂×C₄×D₁₆	1	1	yes	characteristic
506	D₃	—	2	1	no	—
507	D₃	—	16	2	no	—
508	D₃	#13656	1	2	yes	direct product factor
509	C₂²	—	3	1	no	—
510	C₂²	—	3	1	no	—
511	C₂²	—	6	2	no	—
512	C₂²	—	8	2	no	—
513	C₂²	—	24	2	no	—
514	C₂²	—	48	4	no	—
515	C₂²	D₃×#508	1	1	yes	characteristic
516	C₄	—	3	1	no	—
517	C₄	—	3	1	no	—
518	C₄	—	4	1	no	—
519	C₄	—	8	2	no	—
520	C₄	—	12	1	no	—
521	C₄	—	24	2	no	—
522	C₄	C₄×D₃×D₈	1	1	yes	characteristic
523	C₄	C₂×D₃×D₁₆	1	1	yes	characteristic
524	C₃	C₂×#13656	1	1	yes	characteristic, complemented, Sylow
525	C₂	—	2	1	no	—
526	C₂	—	3	2	no	—
527	C₂	—	6	1	no	—
528	C₂	—	16	2	no	—
529	C₂	—	48	2	no	—
530	C₂	C₄×D₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₃×D₁₆
commutator	C₃×C₁₆	C₂³×C₄
Frattini	C₂×C₁₆	C₂³×D₃
Fitting	C₃×#13656	C₂
socle	C₂×C₃	C₂×C₄×D₁₆
prime radical	D₃×#2262	C₂
cosocle	C₂×C₃×C₁₆	C₂⁴
hypercenter	#13656	D₃
hypocenter	C₃	C₂×#13656
LCS	G ▷ C₃×C₁₆ ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #13656

Complements

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

N	H ≅ G/N	type
2. D₃×#2178	C₂	semidirect
3. #10715801	C₂	semidirect
4. #10715800	C₂	semidirect
5. #10715799	C₂	semidirect
6. #10715798	C₂	semidirect
7. #10715797	C₂	semidirect
8. D₃×#1425	C₂	semidirect
9. D₃×#1417	C₂	semidirect
10. D₃×#1397	C₂	semidirect
11. C₃×#13656	C₂	semidirect
16. C₃×#2178	C₂²	semidirect
17. #71511	C₂²	semidirect
20. #69383	C₄	semidirect
21. D₃×Q₆₄	C₄	semidirect
22. #69379	C₄	semidirect
23. D₃×SD₆₄	C₄	semidirect
24. #69376	C₄	semidirect
25. D₃×D₃₂	C₄	semidirect
30. #69357	C₂²	semidirect
33. #69067	C₂²	semidirect
35. C₃×#1425	C₂²	semidirect
36. C₃×#1417	C₂²	semidirect
37. C₃×#1397	C₂²	semidirect
38. #67829	C₂²	semidirect
39. #67598	C₂²	semidirect
40. #67593	C₂²	semidirect
41. #67589	C₂²	semidirect
42. #67589	C₂²	semidirect
43. #67585	C₂²	semidirect
44. #67581	C₂²	semidirect
45. #67508	C₂²	semidirect
53. #13656	D₃	direct (N × H)
79. C₃×Q₆₄	C₂×C₄	semidirect
80. C₃×SD₆₄	C₂×C₄	semidirect
81. C₃×D₃₂	C₂×C₄	semidirect
88. #4522	C₂×C₄	semidirect
89. #4521	C₂×C₄	semidirect
90. #4520	C₂×C₄	semidirect
91. #4519	C₂×C₄	semidirect
101. Dic₄₈	C₂×C₄	semidirect
102. #4449	C₂×C₄	semidirect
103. D₉₆	C₂×C₄	semidirect
128. #2178	C₂×D₃	semidirect
134. #1425	C₂×D₃	semidirect
138. #1417	C₂×D₃	semidirect
142. #1397	C₂×D₃	semidirect
226. Q₆₄	C₄×D₃	semidirect
230. SD₆₄	C₄×D₃	semidirect
233. D₃₂	C₄×D₃	semidirect
508. D₃	#13656	direct (N × H)
524. C₃	C₂×#13656	semidirect

Maximal subgroups

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

subgroup	index
D₃×#2262	2
D₃×#2178	2
#10715801	2
#10715800	2
#10715799	2
#10715798	2
#10715797	2
D₃×#1425	2
D₃×#1417	2
D₃×#1397	2
C₃×#13656	2
C₂×#13656	3

Subgroups — D3×#13656 #72245463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#13656 #72245463