Subgroups — #10948757

Order 768.

552 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#237	C₂	1	1	yes	maximal, characteristic
2	C₃×#2168	C₂	1	1	yes	maximal, characteristic, complemented
3	#71433	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₆×#67	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#4502	C₂	1	1	yes	maximal, characteristic, complemented
7	#70857	C₂	1	1	yes	maximal, characteristic, complemented
8	#69282	C₂	1	1	yes	maximal, characteristic, complemented
9	#69275	C₂	1	1	yes	maximal, characteristic, complemented
10	#69103	C₂	1	1	yes	maximal, characteristic, complemented
11	#67⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#69093	C₂	1	1	yes	maximal, characteristic, complemented
13	#69093	C₂	1	1	yes	maximal, characteristic, complemented
14	D₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
15	#69068	C₂	1	1	yes	maximal, characteristic, complemented
16	#33484	—	3	1	no	maximal, Sylow
17	C₄×#237	C₄	1	1	yes	characteristic
18	C₂×C₃×M₃₂	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₁₆	C₂²	1	1	yes	characteristic
20	C₃×C₈×D₄	C₂²	1	1	yes	characteristic
21	C₈×#67	C₂²	1	1	yes	characteristic
22	C₈×#67	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₃	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₃	C₂²	1	1	yes	characteristic
25	C₂×#812	C₂²	1	1	yes	characteristic
26	C₂²×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
27	D₄×C₃⋊C₈	C₄	1	1	yes	characteristic
28	C₂×D₃×C₁₆	C₂²	1	1	yes	characteristic
29	C₂×D₃×C₁₆	C₂²	1	1	yes	characteristic
30	#4833	C₄	1	1	yes	characteristic
31	#4830	C₄	1	1	yes	characteristic
32	#67⋊C₈	C₄	1	1	yes	characteristic
33	#67⋊C₈	C₄	1	1	yes	characteristic
34	#4718	C₄	1	1	yes	characteristic
35	#4718	C₄	1	1	yes	characteristic
36	C₄×D₃×C₈	C₂²	1	1	yes	characteristic
37	C₈×Dic₆	C₂²	1	1	yes	characteristic
38	C₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
40	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
41	C₃×#346	C₂²	1	1	yes	characteristic
42	#4549	C₂²	1	1	yes	characteristic
43	#4549	C₂²	1	1	yes	characteristic
44	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic
45	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic
46	#4502	C₂²	1	1	yes	characteristic
47	#4502	C₂²	1	1	yes	characteristic
48	#4502	C₂²	1	1	yes	characteristic
49	#4502	C₂²	1	1	yes	characteristic
50	#4502	C₂²	1	1	yes	characteristic
51	#4502	C₂²	1	1	yes	characteristic
52	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic
53	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic
54	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic
55	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic
56	Dic₃×C₁₆	C₂²	1	1	yes	characteristic
57	Dic₃×C₁₆	C₂²	1	1	yes	characteristic
58	C₄⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic
59	#4461	C₂²	1	1	yes	characteristic
60	C₈×#41	—	3	1	no	—
61	#2183	—	3	1	no	—
62	#2183	—	3	1	no	—
63	#2168	—	3	1	no	—
64	#2168	—	3	1	no	—
65	#2168	—	3	1	no	—
66	#2168	D₃	1	1	yes	characteristic, complemented
67	D₄×C₁₆	—	3	1	no	—
68	D₄×C₁₆	—	3	1	no	—
69	#2163	—	3	1	no	—
70	#2163	—	3	1	no	—
71	#2163	—	3	1	no	—
72	C₄×M₃₂	—	3	1	no	—
73	C₂×#346	—	3	1	no	—
74	C₂×#346	—	3	1	no	—
75	C₂×#237	C₈	1	1	yes	characteristic
76	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
78	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
79	D₄×Dic₃	C₈	1	1	yes	characteristic
80	C₄×#67	C₂×C₄	1	1	yes	characteristic
81	C₄×#67	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
87	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
88	#892	C₈	1	1	yes	characteristic
89	#887	C₈	1	1	yes	characteristic
90	#67⋊C₄	C₈	1	1	yes	characteristic
91	#67⋊C₄	C₈	1	1	yes	characteristic
92	#877	C₈	1	1	yes	characteristic
93	#877	C₈	1	1	yes	characteristic
94	C₄²×D₃	C₂×C₄	1	1	yes	characteristic
95	C₄×Dic₆	C₂×C₄	1	1	yes	characteristic
96	C₃×M₃₂	—	2	2	no	—
97	C₂×C₃×C₁₆	—	2	2	no	—
98	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
99	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
102	C₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
103	C₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
104	C₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
105	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
106	#830	C₂×C₄	1	1	yes	characteristic
107	#830	C₂×C₄	1	1	yes	characteristic
108	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
109	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
110	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
111	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
112	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
113	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
114	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
115	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
116	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
117	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
118	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
119	C₈×Dic₃	C₂³	1	1	yes	characteristic
120	C₈×Dic₃	C₂³	1	1	yes	characteristic
121	C₈×Dic₃	C₂³	1	1	yes	characteristic
122	#812	—	2	2	no	—
123	C₂×C₃⋊C₁₆	—	2	2	no	—
124	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
125	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
126	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
127	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
128	C₄⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
129	C₄×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
130	D₃×C₁₆	—	2	2	no	—
131	D₃×C₁₆	—	2	2	no	—
132	C₄×#41	—	3	1	no	—
133	C₂×M₃₂	—	3	1	no	—
134	C₂×M₃₂	C₂×D₃	1	1	yes	characteristic
135	C₂²×C₁₆	—	3	1	no	—
136	C₂²×C₁₆	—	3	1	no	—
137	C₂²×C₁₆	—	3	1	no	—
138	C₂²×C₁₆	C₂×D₃	1	1	yes	characteristic
139	C₈×Q₈	—	3	1	no	—
140	C₈×Q₈	—	3	1	no	—
141	C₈×D₄	—	3	1	no	—
142	C₈×D₄	—	3	1	no	—
143	C₈×D₄	—	3	1	no	—
144	C₈×D₄	—	3	1	no	—
145	C₈×D₄	—	3	1	no	—
146	C₈×D₄	C₂×D₃	1	1	yes	characteristic
147	#431	—	3	1	no	—
148	#431	—	3	1	no	—
149	#431	—	3	1	no	—
150	C₂×C₄×C₈	—	3	1	no	—
151	C₂×C₄×C₈	—	3	1	no	—
152	C₂×C₄×C₈	—	3	1	no	—
153	C₄⋊C₁₆	—	3	1	no	—
154	C₄⋊C₁₆	—	3	1	no	—
155	C₄⋊C₁₆	—	3	1	no	—
156	C₄⋊C₁₆	—	3	1	no	—
157	C₄⋊C₁₆	—	3	1	no	—
158	C₄⋊C₁₆	C₂×D₃	1	1	yes	characteristic
159	C₂²⋊C₁₆	—	3	1	no	—
160	C₂²⋊C₁₆	—	3	1	no	—
161	C₂²⋊C₁₆	—	3	1	no	—
162	C₂²⋊C₁₆	—	3	1	no	—
163	C₂²⋊C₁₆	C₂×D₃	1	1	yes	characteristic
164	C₂²⋊C₁₆	C₂×D₃	1	1	yes	characteristic
165	#346	—	3	1	no	—
166	#346	—	3	1	no	—
167	#346	—	3	1	no	—
168	#346	—	3	1	no	—
169	#346	—	3	1	no	—
170	#346	—	3	1	no	—
171	#346	—	3	1	no	—
172	#346	C₂×D₃	1	1	yes	characteristic
173	C₄×C₁₆	—	3	1	no	—
174	C₄×C₁₆	—	3	1	no	—
175	C₂×C₃×D₄	C₂×C₈	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
178	C₂×#67	C₂×C₈	1	1	yes	characteristic
179	C₂×#67	C₂×C₈	1	1	yes	characteristic
180	C₂²×Dic₃	C₂×C₈	1	1	yes	characteristic
181	C₂²×Dic₃	C₂×C₈	1	1	yes	characteristic
182	C₂²×Dic₃	C₂×C₈	1	1	yes	characteristic
183	C₂²×Dic₃	C₂×C₈	1	1	yes	characteristic
184	#237	—	2	4	no	—
185	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
186	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
187	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
188	C₂×Dic₆	C₂×C₈	1	1	yes	characteristic
189	C₂×C₃×C₈	—	2	1	no	—
190	C₂×C₃×C₈	—	2	1	no	—
191	C₂×C₃×C₈	—	2	1	no	—
192	C₂×C₃×C₈	—	2	1	no	—
193	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
197	C₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
198	C₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
199	C₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
200	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
201	#217	C₂×C₈	1	1	yes	characteristic
202	#217	C₂×C₈	1	1	yes	characteristic
203	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
204	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
205	C₄⋊Dic₃	C₂×C₈	1	1	yes	characteristic
206	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
207	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
208	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
209	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
210	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
211	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
212	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
213	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
214	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
215	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
216	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
217	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
218	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₃⋊C₈	—	2	2	no	—
220	C₂×C₃⋊C₈	—	2	2	no	—
221	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
222	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
223	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
224	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
225	D₃×C₈	—	2	1	no	—
226	D₃×C₈	—	2	1	no	—
227	D₃×C₈	—	2	2	no	—
228	C₃×C₁₆	—	2	1	no	—
229	C₃×C₁₆	—	2	1	no	—
230	C₃×C₁₆	—	2	1	no	—
231	C₃×C₁₆	#41	1	2	yes	complemented
232	C₃⋊C₁₆	—	2	1	no	—
233	C₃⋊C₁₆	—	2	1	no	—
234	C₃⋊C₁₆	—	2	1	no	—
235	C₃⋊C₁₆	#41	1	2	yes	complemented
236	C₂×#41	—	3	1	no	—
237	C₂²×C₈	—	3	1	no	—
238	C₂²×C₈	—	3	1	no	—
239	C₂²×C₈	—	3	1	no	—
240	C₂²×C₈	—	3	1	no	—
241	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
242	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
243	C₄×Q₈	—	3	1	no	—
244	C₄×Q₈	—	3	1	no	—
245	C₄×D₄	—	3	1	no	—
246	C₄×D₄	—	3	1	no	—
247	C₄×D₄	—	3	1	no	—
248	C₄×D₄	—	3	1	no	—
249	C₄×D₄	—	3	1	no	—
250	C₄×D₄	C₄×D₃	1	1	yes	characteristic
251	#117	—	3	1	no	—
252	#117	—	3	1	no	—
253	#117	—	3	1	no	—
254	C₂×C₄²	—	3	1	no	—
255	C₂×C₄²	—	3	1	no	—
256	C₂×C₄²	—	3	1	no	—
257	M₃₂	—	2	2	no	—
258	M₃₂	—	6	2	no	—
259	C₂×C₁₆	—	2	2	no	—
260	C₂×C₁₆	—	3	1	no	—
261	C₂×C₁₆	—	3	1	no	—
262	C₂×C₁₆	—	3	1	no	—
263	C₂×C₁₆	—	3	1	no	—
264	C₂×C₁₆	—	6	2	no	—
265	C₂×C₁₆	—	6	2	no	—
266	C₂×C₁₆	—	6	2	no	—
267	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
268	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
269	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
270	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
271	C₄⋊C₈	—	3	1	no	—
272	C₄⋊C₈	—	3	1	no	—
273	C₄⋊C₈	—	3	1	no	—
274	C₄⋊C₈	—	3	1	no	—
275	C₄⋊C₈	—	3	1	no	—
276	C₄⋊C₈	C₄×D₃	1	1	yes	characteristic
277	C₂²⋊C₈	—	3	1	no	—
278	C₂²⋊C₈	—	3	1	no	—
279	C₂²⋊C₈	—	3	1	no	—
280	C₂²⋊C₈	—	3	1	no	—
281	C₂²⋊C₈	C₄×D₃	1	1	yes	characteristic
282	C₂²⋊C₈	C₄×D₃	1	1	yes	characteristic
283	C₄×C₈	—	3	1	no	—
284	C₄×C₈	—	3	1	no	—
285	C₄×C₈	—	3	1	no	—
286	C₄×C₈	—	3	1	no	—
287	C₄×C₈	—	3	1	no	—
288	C₄×C₈	—	3	1	no	—
289	C₄×C₈	—	3	1	no	—
290	C₄×C₈	—	3	1	no	—
291	C₄×C₈	—	3	1	no	—
292	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
293	C₂³×C₃	C₂²×C₈	1	1	yes	characteristic
294	C₂³×C₃	C₂²×C₈	1	1	yes	characteristic
295	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
296	C₃×D₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	1	no	—
298	C₂×C₃×C₄	—	2	1	no	—
299	C₂×C₃×C₄	—	2	1	no	—
300	C₂×C₃×C₄	—	2	1	no	—
301	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
305	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
306	#67	—	2	2	no	—
307	#67	M₃₂	1	4	yes	complemented
308	C₂×Dic₃	—	2	2	no	—
309	C₂×Dic₃	—	2	2	no	—
310	C₂×Dic₃	—	4	1	no	—
311	C₂×Dic₃	—	4	1	no	—
312	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
313	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
314	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
315	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
316	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
317	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
318	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
319	C₄×D₃	—	2	2	no	—
320	C₄×D₃	—	2	1	no	—
321	C₄×D₃	—	2	1	no	—
322	C₄×D₃	—	4	1	no	—
323	Dic₆	—	2	2	no	—
324	C₃×C₈	—	2	1	no	—
325	C₃×C₈	—	2	1	no	—
326	C₃×C₈	—	2	1	no	—
327	C₃×C₈	C₂×#41	1	1	yes	characteristic
328	C₃×C₈	C₂×#41	1	1	yes	characteristic
329	C₃⋊C₈	—	2	1	no	—
330	C₃⋊C₈	—	2	1	no	—
331	C₃⋊C₈	—	2	1	no	—
332	C₃⋊C₈	#131	1	2	yes	—
333	#41	—	6	4	no	—
334	C₂×Q₈	—	3	1	no	—
335	C₂×D₄	—	3	1	no	—
336	C₂×D₄	—	3	1	no	—
337	C₂×D₄	D₃×C₈	1	1	yes	characteristic
338	C₂²×C₄	—	3	1	no	—
339	C₂²×C₄	—	3	1	no	—
340	C₂²×C₄	—	3	1	no	—
341	C₂²×C₄	—	3	1	no	—
342	C₂²×C₄	—	3	1	no	—
343	C₂²×C₄	—	3	1	no	—
344	C₂²×C₄	—	3	1	no	—
345	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	3	1	no	—
352	C₂×C₈	—	3	1	no	—
353	C₂×C₈	—	3	1	no	—
354	C₂×C₈	—	3	1	no	—
355	C₂×C₈	—	6	2	no	—
356	C₂×C₈	—	6	2	no	—
357	C₂×C₈	—	6	2	no	—
358	C₂×C₈	—	6	1	no	—
359	C₂×C₈	—	6	1	no	—
360	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
361	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
362	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
363	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
364	C₄⋊C₄	—	3	1	no	—
365	C₄⋊C₄	—	3	1	no	—
366	C₄⋊C₄	—	3	1	no	—
367	C₄⋊C₄	—	3	1	no	—
368	C₄⋊C₄	—	3	1	no	—
369	C₄⋊C₄	D₃×C₈	1	1	yes	characteristic
370	C₂²⋊C₄	—	3	1	no	—
371	C₂²⋊C₄	—	3	1	no	—
372	C₂²⋊C₄	—	3	1	no	—
373	C₂²⋊C₄	—	3	1	no	—
374	C₂²⋊C₄	D₃×C₈	1	1	yes	characteristic
375	C₂²⋊C₄	D₃×C₈	1	1	yes	characteristic
376	C₄²	—	3	1	no	—
377	C₄²	—	3	1	no	—
378	C₄²	—	3	1	no	—
379	C₄²	—	3	1	no	—
380	C₄²	—	3	1	no	—
381	C₄²	—	3	1	no	—
382	C₄²	—	3	1	no	—
383	C₄²	—	3	1	no	—
384	C₄²	—	3	1	no	—
385	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
386	C₁₆	—	2	1	no	—
387	C₁₆	—	2	1	no	—
388	C₁₆	—	2	1	no	—
389	C₁₆	—	3	2	no	—
390	C₁₆	—	6	1	no	—
391	C₁₆	—	6	1	no	—
392	C₁₆	—	6	1	no	—
393	C₁₆	#237	1	2	yes	complemented
394	C₂²×C₃	—	2	1	no	—
395	C₂²×C₃	—	2	1	no	—
396	C₂²×C₃	—	2	1	no	—
397	C₂²×C₃	—	2	1	no	—
398	C₂²×C₃	—	2	1	no	—
399	C₂²×C₃	C₂×M₃₂	1	2	yes	—
400	C₂²×C₃	C₂³×C₈	1	1	yes	characteristic
401	C₂×D₃	—	2	1	no	—
402	C₂×D₃	—	2	1	no	—
403	C₂×D₃	C₂×M₃₂	1	2	yes	—
404	C₃×C₄	—	2	1	no	—
405	C₃×C₄	—	2	1	no	—
406	C₃×C₄	—	2	1	no	—
407	C₃×C₄	—	2	1	no	—
408	C₃×C₄	C₄×#41	1	1	yes	characteristic
409	C₃×C₄	C₂×#131	1	1	yes	characteristic
410	Dic₃	—	2	1	no	—
411	Dic₃	—	2	1	no	—
412	Dic₃	—	2	1	no	—
413	Dic₃	—	2	1	no	—
414	Dic₃	—	2	1	no	—
415	Dic₃	—	2	1	no	—
416	Dic₃	C₂×M₃₂	1	2	yes	—
417	C₂³	—	3	1	no	—
418	C₂³	C₂×D₃×C₈	1	1	yes	characteristic
419	C₂³	C₂×D₃×C₈	1	1	yes	characteristic
420	Q₈	—	6	2	no	—
421	D₄	—	2	2	no	—
422	D₄	—	3	4	no	—
423	D₄	—	6	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	3	1	no	—
429	C₂×C₄	—	3	1	no	—
430	C₂×C₄	—	3	1	no	—
431	C₂×C₄	—	3	1	no	—
432	C₂×C₄	—	3	1	no	—
433	C₂×C₄	—	3	1	no	—
434	C₂×C₄	—	3	1	no	—
435	C₂×C₄	—	6	2	no	—
436	C₂×C₄	—	6	2	no	—
437	C₂×C₄	—	6	2	no	—
438	C₂×C₄	—	6	1	no	—
439	C₂×C₄	—	6	1	no	—
440	C₂×C₄	—	12	1	no	—
441	C₂×C₄	—	12	1	no	—
442	C₂×C₄	—	12	1	no	—
443	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
444	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
445	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
446	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
447	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
448	C₈	—	2	1	no	—
449	C₈	—	2	1	no	—
450	C₈	—	2	1	no	—
451	C₈	—	3	2	no	—
452	C₈	—	6	1	no	—
453	C₈	—	6	1	no	—
454	C₈	—	6	1	no	—
455	C₈	C₂×#237	1	1	yes	characteristic
456	C₈	D₃×#41	1	1	yes	characteristic
457	C₂×C₃	—	2	2	no	—
458	C₂×C₃	—	4	1	no	—
459	C₂×C₃	C₈×#41	1	1	yes	characteristic
460	C₂×C₃	C₂²×M₃₂	1	1	yes	characteristic
461	C₂×C₃	#3407	1	1	yes	characteristic
462	D₃	—	2	2	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	3	2	no	—
469	C₂²	—	6	1	no	—
470	C₂²	—	6	1	no	—
471	C₂²	D₃×M₃₂	1	2	yes	—
472	C₂²	C₂²×D₃×C₈	1	1	yes	characteristic
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	3	2	no	—
478	C₄	—	6	1	no	—
479	C₄	—	6	1	no	—
480	C₄	—	6	1	no	—
481	C₄	—	6	1	no	—
482	C₄	—	6	1	no	—
483	C₄	—	6	1	no	—
484	C₄	C₄×#237	1	1	yes	characteristic
485	C₄	D₃×#131	1	1	yes	characteristic
486	C₃	#33484	1	1	yes	characteristic, complemented, Sylow
487	C₂	—	2	2	no	—
488	C₂	—	4	1	no	—
489	C₂	—	6	2	no	—
490	C₂	C₈×#237	1	1	yes	characteristic
491	C₂	C₂×D₃×M₃₂	1	1	yes	characteristic
492	C₂	#82012	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₃
commutator, socle	C₂²×C₃	C₂³×C₈
Fitting	C₃×#2168	C₂
prime radical	C₂×#237	C₈
cosocle	C₂×C₃×C₈	C₂⁴
hypercenter	#2168	D₃
hypocenter	C₃	#33484
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
2. C₃×#2168	C₂	semidirect
3. #71433	C₂	semidirect
4. Dic₃×M₃₂	C₂	semidirect
5. C₁₆×#67	C₂	semidirect
6. C₂×#4502	C₂	semidirect
7. #70857	C₂	semidirect
8. #69282	C₂	semidirect
9. #69275	C₂	semidirect
10. #69103	C₂	semidirect
11. #67⋊C₁₆	C₂	semidirect
12. #69093	C₂	semidirect
13. #69093	C₂	semidirect
14. D₃×#346	C₂	semidirect
15. #69068	C₂	semidirect
66. #2168	D₃	semidirect
231. C₃×C₁₆	#41	semidirect
235. C₃⋊C₁₆	#41	semidirect
307. #67	M₃₂	semidirect
393. C₁₆	#237	semidirect
486. C₃	#33484	semidirect

Maximal subgroups

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

subgroup	index
C₈×#237	2
C₃×#2168	2
#71433	2
Dic₃×M₃₂	2
C₁₆×#67	2
C₂×#4502	2
#70857	2
#69282	2
#69275	2
#69103	2
#67⋊C₁₆	2
#69093	2
D₃×#346	2
#69068	2
#33484	3