Subgroups — #10948292

Order 768.

600 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×#405	C₂	1	1	yes	maximal, characteristic
2	C₃×#2164	C₂	1	1	yes	maximal, characteristic, complemented
3	#69883	C₂	1	1	yes	maximal, characteristic, complemented
4	#69285	C₂	1	1	yes	maximal, characteristic, complemented
5	#69285	C₂	1	1	yes	maximal, characteristic, complemented
6	#69275	C₂	1	1	yes	maximal, characteristic, complemented
7	#69274	C₂	1	1	yes	maximal, characteristic, complemented
8	#69106	C₂	1	1	yes	maximal, characteristic
9	D₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
10	#69094	C₂	1	1	yes	maximal, characteristic, complemented
11	#69094	C₂	1	1	yes	maximal, characteristic, complemented
12	#69073	C₂	1	1	yes	maximal, characteristic, complemented
13	#69072	C₂	1	1	yes	maximal, characteristic, complemented
14	#69052	C₂	1	1	yes	maximal, characteristic, complemented
15	#69051	C₂	1	1	yes	maximal, characteristic, complemented
16	#33422	—	3	1	no	maximal, Sylow
17	C₂×D₃×M₁₆	C₄	1	1	yes	characteristic
18	C₂²×D₃×C₈	C₂²	1	1	yes	characteristic
19	D₃×#117	C₄	1	1	yes	characteristic
20	C₃×#405	C₂²	1	1	yes	characteristic
21	#5122	C₄	1	1	yes	characteristic
22	#5101	C₂²	1	1	yes	characteristic
23	#4997	C₄	1	1	yes	characteristic
24	C₂×#798	C₂²	1	1	yes	characteristic
25	C₂×#798	C₂²	1	1	yes	characteristic
26	C₂×D₃×C₁₆	C₂²	1	1	yes	characteristic
27	C₂×D₃×C₁₆	C₂²	1	1	yes	characteristic
28	#4708	C₄	1	1	yes	characteristic
29	#4708	C₄	1	1	yes	characteristic
30	D₃×#97	C₄	1	1	yes	characteristic
31	D₃×#97	C₄	1	1	yes	characteristic
32	#4689	C₂²	1	1	yes	characteristic
33	#4689	C₂²	1	1	yes	characteristic
34	C₄×D₃×C₈	C₂²	1	1	yes	characteristic
35	C₄×D₃×C₈	C₂²	1	1	yes	characteristic
36	C₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
40	C₃×#346	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₄×C₁₆	C₂²	1	1	yes	characteristic, complemented
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	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic
47	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic
48	#4502	C₂²	1	1	yes	characteristic, complemented
49	#4502	C₂²	1	1	yes	characteristic, complemented
50	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
51	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
52	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
53	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
54	Dic₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
55	Dic₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
56	C₄⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
57	C₄⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
58	#4461	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
60	C₂×#405	—	3	1	no	—
61	#2164	—	3	1	no	—
62	#2164	—	3	1	no	—
63	#2164	—	3	1	no	—
64	#2164	D₃	1	1	yes	characteristic, complemented
65	#2163	—	3	1	no	—
66	#2163	—	3	1	no	—
67	#2162	—	3	1	no	—
68	#2162	—	3	1	no	—
69	#2151	—	3	1	no	—
70	#2151	—	3	1	no	—
71	#2112	—	3	1	no	—
72	C₂×C₂²⋊C₁₆	—	3	1	no	—
73	#2108	—	3	1	no	—
74	#2108	—	3	1	no	—
75	C₂²×C₄×D₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₃×M₁₆	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
78	C₃×#117	C₂×C₄	1	1	yes	characteristic
79	#926	C₂×C₄	1	1	yes	characteristic
80	C₂×#208	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
82	D₃×M₁₆	—	2	4	no	—
83	C₂×ΓL(1,𝔽₂₅)	C₂×C₄	1	1	yes	characteristic
84	C₂×ΓL(1,𝔽₂₅)	C₂×C₄	1	1	yes	characteristic
85	C₂×D₃×C₈	—	2	2	no	—
86	C₂×D₃×C₈	—	2	2	no	—
87	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
88	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
89	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
90	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
91	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
92	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
93	#892	C₈	1	1	yes	characteristic
94	#892	C₈	1	1	yes	characteristic
95	D₃×C₄⋊C₄	C₈	1	1	yes	characteristic
96	D₃×C₄⋊C₄	C₈	1	1	yes	characteristic
97	D₃×C₂²⋊C₄	C₈	1	1	yes	characteristic
98	D₃×C₂²⋊C₄	C₈	1	1	yes	characteristic
99	#877	C₈	1	1	yes	characteristic
100	#877	C₈	1	1	yes	characteristic
101	#872	C₂×C₄	1	1	yes	characteristic
102	#872	C₂×C₄	1	1	yes	characteristic
103	C₄²×D₃	C₂×C₄	1	1	yes	characteristic
104	C₄²×D₃	C₂×C₄	1	1	yes	characteristic
105	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
107	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
108	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
109	C₃×#97	C₂×C₄	1	1	yes	characteristic
110	C₃×#97	C₂×C₄	1	1	yes	characteristic
111	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
112	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
113	#815	C₂×C₄	1	1	yes	characteristic
114	#815	C₂×C₄	1	1	yes	characteristic
115	#815	C₂×C₄	1	1	yes	characteristic
116	#815	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	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
123	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
124	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
125	#803	C₂×C₄	1	1	yes	characteristic
126	#803	C₂×C₄	1	1	yes	characteristic
127	C₄×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
128	C₄×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
129	#798	—	2	2	no	—
130	#798	—	2	2	no	—
131	D₃×C₁₆	—	2	2	no	—
132	D₃×C₁₆	—	2	2	no	—
133	C₂²×M₁₆	—	3	1	no	—
134	C₂³×C₈	—	3	1	no	—
135	C₂×#117	—	3	1	no	—
136	C₂×M₃₂	—	3	1	no	—
137	C₂×M₃₂	—	3	1	no	—
138	C₂²×C₁₆	—	3	1	no	—
139	C₂²×C₁₆	—	3	1	no	—
140	#405	—	3	1	no	—
141	#405	—	3	1	no	—
142	#405	—	3	1	no	—
143	#405	—	3	1	no	—
144	#405	—	3	1	no	—
145	#405	—	3	1	no	—
146	#405	—	3	1	no	—
147	#405	C₂×D₃	1	1	yes	characteristic
148	C₂×#97	—	3	1	no	—
149	C₂×#97	—	3	1	no	—
150	C₂×C₄×C₈	—	3	1	no	—
151	C₂×C₄×C₈	—	3	1	no	—
152	C₄⋊C₁₆	—	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, complemented
159	C₄⋊C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
160	C₂²⋊C₁₆	—	3	1	no	—
161	C₂²⋊C₁₆	—	3	1	no	—
162	C₂²⋊C₁₆	—	3	1	no	—
163	C₂²⋊C₁₆	—	3	1	no	—
164	C₂²⋊C₁₆	—	3	1	no	—
165	C₂²⋊C₁₆	—	3	1	no	—
166	C₂²⋊C₁₆	C₂×D₃	1	1	yes	characteristic
167	C₂²⋊C₁₆	C₂×D₃	1	1	yes	characteristic
168	#346	—	3	1	no	—
169	#346	—	3	1	no	—
170	#346	—	3	1	no	—
171	#346	C₂×D₃	1	1	yes	characteristic, complemented
172	C₄×C₁₆	—	3	1	no	—
173	C₄×C₁₆	—	3	1	no	—
174	C₄×C₁₆	—	3	1	no	—
175	C₄×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
176	C₂³×D₃	C₂×C₈	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
178	C₂²×Dic₃	C₂×C₈	1	1	yes	characteristic
179	C₂×C₄×D₃	—	2	2	no	—
180	C₂×C₄×D₃	—	2	2	no	—
181	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
182	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
183	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
184	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
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×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
189	C₃×M₁₆	—	2	2	no	—
190	C₂×C₃×C₈	—	2	1	no	—
191	C₂×C₃×C₈	—	2	1	no	—
192	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
196	C₃×C₄⋊C₄	C₂×C₈	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	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
202	#217	C₂×C₈	1	1	yes	characteristic
203	#217	C₂×C₈	1	1	yes	characteristic
204	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
205	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
206	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
207	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
208	C₄⋊Dic₃	C₂×C₈	1	1	yes	characteristic
209	C₄⋊Dic₃	C₂×C₈	1	1	yes	characteristic
210	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
211	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
212	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
213	Dic₃⋊C₄	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	C₂×C₈	1	1	yes	characteristic
217	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
218	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
219	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
220	#208	—	2	2	no	—
221	C₂×C₃⋊C₈	—	2	2	no	—
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	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
226	ΓL(1,𝔽₂₅)	—	2	2	no	—
227	ΓL(1,𝔽₂₅)	M₁₆	1	4	yes	—
228	D₃×C₈	—	2	2	no	—
229	D₃×C₈	—	2	2	no	—
230	D₃×C₈	—	2	1	no	—
231	D₃×C₈	—	2	1	no	—
232	D₃×C₈	—	2	2	no	—
233	D₃×C₈	—	2	2	no	—
234	D₃×C₈	#41	1	2	yes	—
235	D₃×C₈	#41	1	2	yes	—
236	C₃×C₁₆	—	2	1	no	—
237	C₃×C₁₆	—	2	1	no	—
238	C₃×C₁₆	—	2	1	no	—
239	C₃×C₁₆	—	2	1	no	—
240	C₃⋊C₁₆	—	2	1	no	—
241	C₃⋊C₁₆	—	2	1	no	—
242	C₃⋊C₁₆	—	2	1	no	—
243	C₃⋊C₁₆	—	2	1	no	—
244	C₂³×C₄	—	3	1	no	—
245	C₂×M₁₆	—	3	1	no	—
246	C₂×M₁₆	—	3	1	no	—
247	C₂×M₁₆	—	3	1	no	—
248	C₂×M₁₆	—	6	4	no	—
249	C₂×M₁₆	C₄×D₃	1	1	yes	characteristic
250	C₂²×C₈	—	3	1	no	—
251	C₂²×C₈	—	3	1	no	—
252	C₂²×C₈	—	3	1	no	—
253	C₂²×C₈	—	3	1	no	—
254	C₂²×C₈	—	3	1	no	—
255	C₂²×C₈	—	3	1	no	—
256	C₂²×C₈	—	3	1	no	—
257	C₂²×C₈	—	6	2	no	—
258	C₂²×C₈	—	6	2	no	—
259	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
260	#117	—	3	1	no	—
261	#117	—	3	1	no	—
262	#117	—	3	1	no	—
263	#117	—	3	1	no	—
264	#117	—	3	1	no	—
265	#117	—	3	1	no	—
266	#117	—	3	1	no	—
267	#117	C₄×D₃	1	1	yes	characteristic
268	C₂×C₄⋊C₄	—	3	1	no	—
269	C₂×C₄⋊C₄	—	3	1	no	—
270	C₂×C₂²⋊C₄	—	3	1	no	—
271	C₂×C₂²⋊C₄	—	3	1	no	—
272	C₂×C₄²	—	3	1	no	—
273	C₂×C₄²	—	3	1	no	—
274	M₃₂	—	6	2	no	—
275	M₃₂	—	6	2	no	—
276	C₂×C₁₆	—	3	1	no	—
277	C₂×C₁₆	—	3	1	no	—
278	C₂×C₁₆	—	3	1	no	—
279	C₂×C₁₆	—	3	1	no	—
280	C₂×C₁₆	—	6	2	no	—
281	C₂×C₁₆	—	6	2	no	—
282	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
283	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
284	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
285	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
286	#97	—	3	1	no	—
287	#97	—	3	1	no	—
288	#97	—	3	1	no	—
289	#97	—	3	1	no	—
290	#97	—	3	1	no	—
291	#97	—	3	1	no	—
292	#97	C₄×D₃	1	1	yes	characteristic
293	#97	C₄×D₃	1	1	yes	characteristic
294	C₄×C₈	—	3	1	no	—
295	C₄×C₈	—	3	1	no	—
296	C₄×C₈	—	3	1	no	—
297	C₄×C₈	—	3	1	no	—
298	C₄×C₈	—	3	1	no	—
299	C₄×C₈	—	3	1	no	—
300	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
301	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
302	C₂³×C₃	C₂²×C₈	1	1	yes	characteristic
303	C₂²×D₃	—	2	2	no	—
304	C₂²×D₃	—	2	2	no	—
305	C₂²×D₃	—	4	1	no	—
306	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
307	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
308	C₂×C₃×C₄	—	2	1	no	—
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
312	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
314	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
315	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
316	C₂×Dic₃	—	2	2	no	—
317	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
318	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
319	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
320	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
321	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
322	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
323	C₄×D₃	—	2	2	no	—
324	C₄×D₃	—	2	2	no	—
325	C₄×D₃	—	2	2	no	—
326	C₄×D₃	—	2	1	no	—
327	C₄×D₃	—	2	1	no	—
328	C₄×D₃	—	2	2	no	—
329	C₄×D₃	—	4	1	no	—
330	C₄×D₃	—	4	1	no	—
331	C₄×D₃	#117	1	2	yes	—
332	C₄×D₃	C₂×M₁₆	1	2	yes	—
333	C₃×C₈	—	2	1	no	—
334	C₃×C₈	—	2	1	no	—
335	C₃×C₈	C₂×M₁₆	1	2	yes	—
336	C₃×C₈	C₂×#41	1	1	yes	characteristic
337	C₃×C₈	C₂×#41	1	1	yes	characteristic
338	C₃⋊C₈	—	2	1	no	—
339	C₃⋊C₈	—	2	1	no	—
340	C₃⋊C₈	#117	1	2	yes	—
341	C₃⋊C₈	C₂×M₁₆	1	2	yes	—
342	C₂⁴	—	3	1	no	—
343	C₂²×C₄	—	3	1	no	—
344	C₂²×C₄	—	3	1	no	—
345	C₂²×C₄	—	3	1	no	—
346	C₂²×C₄	—	3	1	no	—
347	C₂²×C₄	—	3	1	no	—
348	C₂²×C₄	—	3	1	no	—
349	C₂²×C₄	—	3	1	no	—
350	C₂²×C₄	—	3	1	no	—
351	C₂²×C₄	—	3	1	no	—
352	C₂²×C₄	—	6	2	no	—
353	C₂²×C₄	—	6	2	no	—
354	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
355	M₁₆	—	2	2	no	—
356	M₁₆	—	3	4	no	—
357	M₁₆	—	6	2	no	—
358	M₁₆	—	6	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	3	1	no	—
362	C₂×C₈	—	3	1	no	—
363	C₂×C₈	—	3	2	no	—
364	C₂×C₈	—	3	2	no	—
365	C₂×C₈	—	3	1	no	—
366	C₂×C₈	—	3	1	no	—
367	C₂×C₈	—	6	2	no	—
368	C₂×C₈	—	6	2	no	—
369	C₂×C₈	—	6	2	no	—
370	C₂×C₈	—	6	2	no	—
371	C₂×C₈	—	6	2	no	—
372	C₂×C₈	—	6	1	no	—
373	C₂×C₈	—	6	1	no	—
374	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
375	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
376	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
377	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
378	C₄⋊C₄	—	3	1	no	—
379	C₄⋊C₄	—	3	1	no	—
380	C₄⋊C₄	—	3	1	no	—
381	C₄⋊C₄	—	3	1	no	—
382	C₄⋊C₄	—	3	1	no	—
383	C₄⋊C₄	—	3	1	no	—
384	C₄⋊C₄	D₃×C₈	1	1	yes	characteristic
385	C₄⋊C₄	D₃×C₈	1	1	yes	characteristic
386	C₂²⋊C₄	—	3	1	no	—
387	C₂²⋊C₄	—	3	1	no	—
388	C₂²⋊C₄	—	3	1	no	—
389	C₂²⋊C₄	—	3	1	no	—
390	C₂²⋊C₄	—	3	1	no	—
391	C₂²⋊C₄	—	3	1	no	—
392	C₂²⋊C₄	D₃×C₈	1	1	yes	characteristic
393	C₂²⋊C₄	D₃×C₈	1	1	yes	characteristic
394	C₄²	—	3	1	no	—
395	C₄²	—	3	1	no	—
396	C₄²	—	3	1	no	—
397	C₄²	—	3	1	no	—
398	C₄²	—	3	1	no	—
399	C₄²	—	3	1	no	—
400	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
401	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
402	C₁₆	—	2	1	no	—
403	C₁₆	—	2	1	no	—
404	C₁₆	—	2	1	no	—
405	C₁₆	—	2	1	no	—
406	C₁₆	—	6	1	no	—
407	C₁₆	—	6	1	no	—
408	C₁₆	—	6	1	no	—
409	C₁₆	—	6	1	no	—
410	C₂²×C₃	—	2	1	no	—
411	C₂²×C₃	—	2	1	no	—
412	C₂²×C₃	—	2	1	no	—
413	C₂²×C₃	C₂³×C₈	1	1	yes	characteristic
414	C₂×D₃	—	2	1	no	—
415	C₂×D₃	—	2	1	no	—
416	C₂×D₃	—	2	1	no	—
417	C₂×D₃	—	2	1	no	—
418	C₂×D₃	—	4	4	no	—
419	C₂×D₃	#431	1	2	yes	—
420	C₂×D₃	#504	1	2	yes	—
421	C₃×C₄	—	2	1	no	—
422	C₃×C₄	—	2	1	no	—
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	2	1	no	—
425	C₃×C₄	—	2	1	no	—
426	C₃×C₄	C₂×#117	1	1	yes	characteristic
427	C₃×C₄	C₂²×M₁₆	1	1	yes	characteristic
428	Dic₃	—	2	1	no	—
429	Dic₃	—	2	1	no	—
430	Dic₃	—	2	1	no	—
431	Dic₃	—	2	1	no	—
432	Dic₃	—	2	1	no	—
433	Dic₃	#431	1	2	yes	—
434	C₂³	—	3	1	no	—
435	C₂³	—	3	1	no	—
436	C₂³	—	6	2	no	—
437	C₂³	—	6	2	no	—
438	C₂³	—	12	1	no	—
439	C₂³	C₂×D₃×C₈	1	1	yes	characteristic
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	3	1	no	—
443	C₂×C₄	—	3	2	no	—
444	C₂×C₄	—	3	2	no	—
445	C₂×C₄	—	3	1	no	—
446	C₂×C₄	—	3	1	no	—
447	C₂×C₄	—	3	1	no	—
448	C₂×C₄	—	3	1	no	—
449	C₂×C₄	—	3	1	no	—
450	C₂×C₄	—	6	2	no	—
451	C₂×C₄	—	6	2	no	—
452	C₂×C₄	—	6	2	no	—
453	C₂×C₄	—	6	2	no	—
454	C₂×C₄	—	6	2	no	—
455	C₂×C₄	—	6	1	no	—
456	C₂×C₄	—	6	1	no	—
457	C₂×C₄	—	12	1	no	—
458	C₂×C₄	—	12	1	no	—
459	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
460	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
461	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
462	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
463	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
464	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
465	C₈	—	2	1	no	—
466	C₈	—	2	1	no	—
467	C₈	—	3	2	no	—
468	C₈	—	3	2	no	—
469	C₈	—	6	1	no	—
470	C₈	—	6	1	no	—
471	C₈	D₃×M₁₆	1	2	yes	—
472	C₈	D₃×#41	1	1	yes	characteristic
473	C₈	D₃×#41	1	1	yes	characteristic
474	C₂×C₃	—	4	1	no	—
475	C₂×C₃	C₂×#431	1	1	yes	characteristic
476	C₂×C₃	C₂×#504	1	1	yes	characteristic
477	C₂×C₃	#3407	1	1	yes	characteristic
478	D₃	—	2	2	no	—
479	D₃	—	2	2	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	3	2	no	—
484	C₂²	—	3	2	no	—
485	C₂²	—	6	1	no	—
486	C₂²	—	6	1	no	—
487	C₂²	—	6	1	no	—
488	C₂²	—	6	1	no	—
489	C₂²	—	12	4	no	—
490	C₂²	C₂²×D₃×C₈	1	1	yes	characteristic
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	3	2	no	—
497	C₄	—	6	1	no	—
498	C₄	—	6	1	no	—
499	C₄	—	6	1	no	—
500	C₄	—	6	1	no	—
501	C₄	—	6	1	no	—
502	C₄	D₃×#117	1	1	yes	characteristic
503	C₄	C₂×D₃×M₁₆	1	1	yes	characteristic
504	C₃	#33422	1	1	yes	characteristic, complemented, Sylow
505	C₂	—	4	1	no	—
506	C₂	—	6	2	no	—
507	C₂	—	6	2	no	—
508	C₂	D₃×#431	1	1	yes	characteristic
509	C₂	D₃×#504	1	1	yes	characteristic
510	C₂	#82012	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₃
commutator, socle	C₂²×C₃	C₂³×C₈
Fitting	C₃×#2164	C₂
prime radical	C₂³×D₃	C₂×C₈
cosocle	C₂×C₃×C₈	C₂⁴
hypercenter	#2164	D₃
hypocenter	C₃	#33422
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₈ ◁ #2164

Complements

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

N	H ≅ G/N	type
2. C₃×#2164	C₂	semidirect
3. #69883	C₂	semidirect
4. #69285	C₂	semidirect
5. #69285	C₂	semidirect
6. #69275	C₂	semidirect
7. #69274	C₂	semidirect
10. #69094	C₂	semidirect
11. #69094	C₂	semidirect
12. #69073	C₂	semidirect
13. #69072	C₂	semidirect
14. #69052	C₂	semidirect
15. #69051	C₂	semidirect
36. C₃×C₄⋊C₁₆	C₂²	semidirect
37. C₃×C₄⋊C₁₆	C₂²	semidirect
40. C₃×#346	C₂²	semidirect
41. C₃×C₄×C₁₆	C₂²	semidirect
48. #4502	C₂²	semidirect
49. #4502	C₂²	semidirect
50. Dic₃⋊C₁₆	C₂²	semidirect
51. Dic₃⋊C₁₆	C₂²	semidirect
52. Dic₃⋊C₁₆	C₂²	semidirect
53. Dic₃⋊C₁₆	C₂²	semidirect
54. Dic₃×C₁₆	C₂²	semidirect
55. Dic₃×C₁₆	C₂²	semidirect
56. C₄⋊(C₃⋊C₁₆)	C₂²	semidirect
57. C₄⋊(C₃⋊C₁₆)	C₂²	semidirect
58. #4461	C₂²	semidirect
59. C₄×C₃⋊C₁₆	C₂²	semidirect
64. #2164	D₃	semidirect
158. C₄⋊C₁₆	C₂×D₃	semidirect
159. C₄⋊C₁₆	C₂×D₃	semidirect
171. #346	C₂×D₃	semidirect
175. C₄×C₁₆	C₂×D₃	semidirect
504. C₃	#33422	semidirect

Maximal subgroups

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

subgroup	index
D₃×#405	2
C₃×#2164	2
#69883	2
#69285	2
#69275	2
#69274	2
#69106	2
D₃×C₂²⋊C₁₆	2
#69094	2
#69073	2
#69072	2
#69052	2
#69051	2
#33422	3