Subgroups — #10948739

Order 768.

518 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#78556	C₂	1	1	yes	maximal, characteristic
2	C₃×#2164	C₂	1	1	yes	maximal, characteristic, complemented
3	#69881	C₂	1	1	yes	maximal, characteristic, complemented
4	#69282	C₂	1	1	yes	maximal, characteristic, complemented
5	#69281	C₂	1	1	yes	maximal, characteristic, complemented
6	#69278	C₂	1	1	yes	maximal, characteristic, complemented
7	#69277	C₂	1	1	yes	maximal, characteristic, complemented
8	#69103	C₂	1	1	yes	maximal, characteristic, complemented
9	#69103	C₂	1	1	yes	maximal, characteristic, complemented
10	#69102	C₂	1	1	yes	maximal, characteristic, complemented
11	#67⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#69074	C₂	1	1	yes	maximal, characteristic, complemented
13	D₃×#346	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	#33482	—	3	1	no	maximal, Sylow
17	#5528	C₄	1	1	yes	characteristic
18	C₃×#405	C₂²	1	1	yes	characteristic
19	#5128	C₄	1	1	yes	characteristic
20	#5127	C₄	1	1	yes	characteristic
21	C₈×#67	C₂²	1	1	yes	characteristic
22	C₈×#67	C₂²	1	1	yes	characteristic
23	C₂×#812	C₂²	1	1	yes	characteristic
24	C₂²×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
25	#5000	C₄	1	1	yes	characteristic
26	C₂×#798	C₂²	1	1	yes	characteristic
27	C₂×D₃×C₁₆	C₂²	1	1	yes	characteristic
28	C₂×D₃×C₁₆	C₂²	1	1	yes	characteristic
29	C₂×D₃×C₁₆	C₂²	1	1	yes	characteristic
30	#4709	C₄	1	1	yes	characteristic
31	#4706	C₄	1	1	yes	characteristic
32	#4705	C₄	1	1	yes	characteristic
33	#4701	C₄	1	1	yes	characteristic
34	#4689	C₂²	1	1	yes	characteristic
35	C₈×D₁₂	C₂²	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×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
40	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
41	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₃×#346	C₂²	1	1	yes	characteristic
43	C₃×C₄×C₁₆	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
49	#4502	C₂²	1	1	yes	characteristic
50	#4502	C₂²	1	1	yes	characteristic
51	Dic₃⋊C₁₆	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	#4461	C₂²	1	1	yes	characteristic
57	#4461	C₂²	1	1	yes	characteristic
58	C₄×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
59	C₄×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
60	#2966	—	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	—	3	1	no	—
67	D₄×C₁₆	—	3	1	no	—
68	D₄×C₁₆	—	3	1	no	—
69	#2164	—	3	1	no	—
70	#2164	D₃	1	1	yes	characteristic, complemented
71	#2162	—	3	1	no	—
72	#2108	—	3	1	no	—
73	#2108	—	3	1	no	—
74	C₂×#346	—	3	1	no	—
75	C₂×C₃×M₁₆	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
77	C₃×#117	C₂×C₄	1	1	yes	characteristic
78	C₄×#67	C₂×C₄	1	1	yes	characteristic
79	C₄×#67	C₂×C₄	1	1	yes	characteristic
80	C₂×ΓL(1,𝔽₂₅)	C₂×C₄	1	1	yes	characteristic
81	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
82	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
83	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
84	#898	C₈	1	1	yes	characteristic
85	#896	C₈	1	1	yes	characteristic
86	#894	C₈	1	1	yes	characteristic
87	#889	C₈	1	1	yes	characteristic
88	#885	C₈	1	1	yes	characteristic
89	#884	C₈	1	1	yes	characteristic
90	#883	C₈	1	1	yes	characteristic
91	#879	C₈	1	1	yes	characteristic
92	C₄×D₁₂	C₂×C₄	1	1	yes	characteristic
93	#872	C₂×C₄	1	1	yes	characteristic
94	C₄²×D₃	C₂×C₄	1	1	yes	characteristic
95	C₄×Dic₆	C₂×C₄	1	1	yes	characteristic
96	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
99	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
100	C₃×#97	C₂×C₄	1	1	yes	characteristic
101	C₃×#97	C₂×C₄	1	1	yes	characteristic
102	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
103	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
104	#830	C₂×C₄	1	1	yes	characteristic
105	#830	C₂×C₄	1	1	yes	characteristic
106	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
107	(C₂×D₃)⋊C₈	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	#815	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	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
115	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
116	C₈×Dic₃	C₂³	1	1	yes	characteristic
117	C₈×Dic₃	C₂³	1	1	yes	characteristic
118	#812	—	2	2	no	—
119	C₂×C₃⋊C₁₆	—	2	2	no	—
120	C₂×C₃⋊C₁₆	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	C₄⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
125	C₄⋊(C₃⋊C₈)	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	#798	—	2	2	no	—
129	D₃×C₁₆	—	2	2	no	—
130	D₃×C₁₆	—	2	2	no	—
131	D₃×C₁₆	—	2	2	no	—
132	#529	—	3	1	no	—
133	C₂×M₃₂	—	3	1	no	—
134	C₂×M₃₂	—	3	1	no	—
135	C₂²×C₁₆	—	3	1	no	—
136	C₂²×C₁₆	—	3	1	no	—
137	C₂²×C₁₆	—	3	1	no	—
138	C₂²×C₁₆	—	3	1	no	—
139	#446	—	3	1	no	—
140	C₈×Q₈	—	3	1	no	—
141	#436	—	3	1	no	—
142	#435	—	3	1	no	—
143	#435	—	3	1	no	—
144	C₈×D₄	—	3	1	no	—
145	C₈×D₄	—	3	1	no	—
146	C₈×D₄	—	3	1	no	—
147	#433	—	3	1	no	—
148	#433	—	3	1	no	—
149	#432	—	3	1	no	—
150	#405	—	3	1	no	—
151	#405	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	1	1	yes	characteristic
171	C₄×C₁₆	—	3	1	no	—
172	C₄×C₁₆	—	3	1	no	—
173	C₄×C₁₆	—	3	1	no	—
174	C₄×C₁₆	C₂×D₃	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
176	C₂×#67	C₂×C₈	1	1	yes	characteristic
177	C₂×#67	C₂×C₈	1	1	yes	characteristic
178	C₂×D₁₂	C₂×C₈	1	1	yes	characteristic
179	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
180	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
181	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
183	C₂×Dic₆	C₂×C₈	1	1	yes	characteristic
184	C₃×M₁₆	—	2	2	no	—
185	C₂×C₃×C₈	—	2	1	no	—
186	C₂×C₃×C₈	—	2	1	no	—
187	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
191	C₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
192	C₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
193	C₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
194	C₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
195	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
196	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
197	#217	C₂×C₈	1	1	yes	characteristic
198	#217	C₂×C₈	1	1	yes	characteristic
199	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
200	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
201	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
202	(C₂×D₃)⋊C₄	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	C₄⋊Dic₃	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	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	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
214	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
215	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
216	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
217	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
220	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
221	ΓL(1,𝔽₂₅)	—	2	2	no	—
222	D₃×C₈	—	2	2	no	—
223	D₃×C₈	—	2	1	no	—
224	D₃×C₈	—	2	1	no	—
225	D₃×C₈	—	2	1	no	—
226	D₃×C₈	—	2	1	no	—
227	C₃×C₁₆	—	2	1	no	—
228	C₃×C₁₆	—	2	1	no	—
229	C₃×C₁₆	—	2	1	no	—
230	C₃×C₁₆	—	2	1	no	—
231	C₃⋊C₁₆	—	2	1	no	—
232	C₃⋊C₁₆	—	2	1	no	—
233	C₃⋊C₁₆	#41	1	2	yes	—
234	C₃⋊C₁₆	#41	1	2	yes	—
235	C₂×M₁₆	—	3	1	no	—
236	C₂×M₁₆	C₄×D₃	1	1	yes	characteristic
237	C₂²×C₈	—	3	1	no	—
238	C₂²×C₈	—	3	1	no	—
239	C₂²×C₈	—	3	1	no	—
240	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
241	#126	—	3	1	no	—
242	#126	—	3	1	no	—
243	#125	—	3	1	no	—
244	#124	—	3	1	no	—
245	#123	—	3	1	no	—
246	#123	—	3	1	no	—
247	C₂²⋊Q₈	—	3	1	no	—
248	#121	—	3	1	no	—
249	C₄×Q₈	—	3	1	no	—
250	C₄×D₄	—	3	1	no	—
251	C₄×D₄	—	3	1	no	—
252	C₄×D₄	—	3	1	no	—
253	#117	—	3	1	no	—
254	#117	C₄×D₃	1	1	yes	characteristic
255	C₂×C₄²	—	3	1	no	—
256	M₃₂	—	6	2	no	—
257	M₃₂	—	6	2	no	—
258	C₂×C₁₆	—	3	1	no	—
259	C₂×C₁₆	—	3	1	no	—
260	C₂×C₁₆	—	3	1	no	—
261	C₂×C₁₆	—	3	1	no	—
262	C₂×C₁₆	—	6	2	no	—
263	C₂×C₁₆	—	6	2	no	—
264	C₂×C₁₆	—	6	2	no	—
265	C₂×C₁₆	—	6	2	no	—
266	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
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	C₄⋊C₈	—	3	1	no	—
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	C₂²⋊C₈	—	3	1	no	—
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	—	3	1	no	—
282	#97	—	3	1	no	—
283	#97	—	3	1	no	—
284	#97	C₄×D₃	1	1	yes	characteristic
285	#97	C₄×D₃	1	1	yes	characteristic
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	C₂²×D₃	1	1	yes	characteristic
291	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
292	C₂³×C₃	C₂²×C₈	1	1	yes	characteristic
293	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
294	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	1	no	—
297	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
303	#67	—	2	2	no	—
304	#67	—	4	1	no	—
305	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
306	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
307	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
308	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
309	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
310	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
311	D₁₂	—	2	2	no	—
312	C₄×D₃	—	2	2	no	—
313	C₄×D₃	—	2	1	no	—
314	C₄×D₃	—	2	1	no	—
315	C₄×D₃	—	2	1	no	—
316	C₄×D₃	—	2	1	no	—
317	C₄×D₃	—	4	1	no	—
318	Dic₆	—	4	1	no	—
319	C₃×C₈	—	2	1	no	—
320	C₃×C₈	—	2	1	no	—
321	C₃×C₈	#131	1	2	yes	—
322	C₃×C₈	C₂×#41	1	1	yes	characteristic
323	C₃×C₈	C₂×#41	1	1	yes	characteristic
324	C₃⋊C₈	—	2	1	no	—
325	C₃⋊C₈	—	2	1	no	—
326	C₃⋊C₈	—	2	1	no	—
327	C₃⋊C₈	—	2	1	no	—
328	C₂×Q₈	—	3	1	no	—
329	C₂×D₄	—	3	1	no	—
330	C₂×D₄	—	3	1	no	—
331	C₂×D₄	—	3	1	no	—
332	C₂²×C₄	—	3	1	no	—
333	C₂²×C₄	—	3	1	no	—
334	C₂²×C₄	—	3	1	no	—
335	C₂²×C₄	—	3	1	no	—
336	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
337	M₁₆	—	2	2	no	—
338	M₁₆	—	6	2	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	3	1	no	—
342	C₂×C₈	—	3	1	no	—
343	C₂×C₈	—	3	1	no	—
344	C₂×C₈	—	3	1	no	—
345	C₂×C₈	—	6	2	no	—
346	C₂×C₈	—	6	1	no	—
347	C₂×C₈	—	6	1	no	—
348	C₂×C₈	—	6	1	no	—
349	C₂×C₈	—	6	1	no	—
350	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
351	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
352	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
353	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
354	C₄⋊C₄	—	3	1	no	—
355	C₄⋊C₄	—	3	1	no	—
356	C₄⋊C₄	—	3	1	no	—
357	C₄⋊C₄	—	3	1	no	—
358	C₄⋊C₄	—	3	1	no	—
359	C₄⋊C₄	—	3	1	no	—
360	C₄⋊C₄	—	3	1	no	—
361	C₄⋊C₄	—	3	1	no	—
362	C₄⋊C₄	D₃×C₈	1	1	yes	characteristic
363	C₄⋊C₄	D₃×C₈	1	1	yes	characteristic
364	C₂²⋊C₄	—	3	1	no	—
365	C₂²⋊C₄	—	3	1	no	—
366	C₂²⋊C₄	—	3	1	no	—
367	C₂²⋊C₄	—	3	1	no	—
368	C₂²⋊C₄	—	3	1	no	—
369	C₂²⋊C₄	—	3	1	no	—
370	C₂²⋊C₄	—	3	1	no	—
371	C₂²⋊C₄	—	3	1	no	—
372	C₂²⋊C₄	D₃×C₈	1	1	yes	characteristic
373	C₂²⋊C₄	D₃×C₈	1	1	yes	characteristic
374	C₄²	—	3	1	no	—
375	C₄²	—	3	1	no	—
376	C₄²	—	3	1	no	—
377	C₄²	—	3	1	no	—
378	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
379	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
380	C₁₆	—	2	1	no	—
381	C₁₆	—	2	1	no	—
382	C₁₆	—	2	1	no	—
383	C₁₆	—	2	1	no	—
384	C₁₆	—	3	2	no	—
385	C₁₆	—	3	2	no	—
386	C₁₆	—	6	1	no	—
387	C₁₆	—	6	1	no	—
388	C₂²×C₃	—	2	1	no	—
389	C₂²×C₃	—	2	1	no	—
390	C₂²×C₃	—	2	1	no	—
391	C₂²×C₃	C₂³×C₈	1	1	yes	characteristic
392	C₂×D₃	—	2	1	no	—
393	C₂×D₃	—	2	1	no	—
394	C₂×D₃	—	2	1	no	—
395	C₂×D₃	—	2	1	no	—
396	C₂×D₃	—	2	1	no	—
397	C₂×D₃	#504	1	2	yes	—
398	C₃×C₄	—	2	1	no	—
399	C₃×C₄	—	2	1	no	—
400	C₃×C₄	—	2	1	no	—
401	C₃×C₄	—	2	1	no	—
402	C₃×C₄	—	2	1	no	—
403	C₃×C₄	C₄×#41	1	1	yes	characteristic
404	C₃×C₄	C₂×#131	1	1	yes	characteristic
405	Dic₃	—	2	1	no	—
406	Dic₃	—	2	1	no	—
407	Dic₃	—	2	1	no	—
408	Dic₃	—	2	1	no	—
409	Dic₃	—	2	1	no	—
410	Dic₃	—	2	1	no	—
411	C₂³	—	3	1	no	—
412	C₂³	—	3	1	no	—
413	C₂³	C₂×D₃×C₈	1	1	yes	characteristic
414	Q₈	—	12	1	no	—
415	D₄	—	6	2	no	—
416	D₄	—	6	2	no	—
417	D₄	—	12	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	3	1	no	—
421	C₂×C₄	—	3	1	no	—
422	C₂×C₄	—	3	1	no	—
423	C₂×C₄	—	3	1	no	—
424	C₂×C₄	—	3	1	no	—
425	C₂×C₄	—	3	1	no	—
426	C₂×C₄	—	6	2	no	—
427	C₂×C₄	—	6	1	no	—
428	C₂×C₄	—	6	1	no	—
429	C₂×C₄	—	6	1	no	—
430	C₂×C₄	—	6	1	no	—
431	C₂×C₄	—	12	1	no	—
432	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
433	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
434	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
435	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
436	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
437	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
438	C₈	—	2	1	no	—
439	C₈	—	2	1	no	—
440	C₈	—	6	1	no	—
441	C₈	—	6	1	no	—
442	C₈	—	6	1	no	—
443	C₈	—	6	1	no	—
444	C₈	#907	1	2	yes	—
445	C₈	D₃×#41	1	1	yes	characteristic
446	C₈	D₃×#41	1	1	yes	characteristic
447	C₂×C₃	—	4	1	no	—
448	C₂×C₃	C₈×#41	1	1	yes	characteristic
449	C₂×C₃	C₂×#504	1	1	yes	characteristic
450	C₂×C₃	#3407	1	1	yes	characteristic
451	D₃	—	2	2	no	—
452	D₃	—	4	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	3	2	no	—
457	C₂²	—	6	1	no	—
458	C₂²	—	6	1	no	—
459	C₂²	—	6	1	no	—
460	C₂²	—	6	1	no	—
461	C₂²	—	6	1	no	—
462	C₂²	C₂²×D₃×C₈	1	1	yes	characteristic
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	6	1	no	—
469	C₄	—	6	1	no	—
470	C₄	—	6	1	no	—
471	C₄	—	6	1	no	—
472	C₄	—	6	1	no	—
473	C₄	—	6	1	no	—
474	C₄	#5522	1	1	yes	characteristic
475	C₄	C₂×#907	1	1	yes	characteristic
476	C₃	#33482	1	1	yes	characteristic, complemented, Sylow
477	C₂	—	4	1	no	—
478	C₂	—	6	2	no	—
479	C₂	—	12	1	no	—
480	C₂	#79276	1	1	yes	characteristic
481	C₂	D₃×#504	1	1	yes	characteristic
482	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	#884	C₈
cosocle	C₂×C₃×C₈	C₂⁴
hypercenter	#2164	D₃
hypocenter	C₃	#33482
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. #69881	C₂	semidirect
4. #69282	C₂	semidirect
5. #69281	C₂	semidirect
6. #69278	C₂	semidirect
7. #69277	C₂	semidirect
8. #69103	C₂	semidirect
9. #69103	C₂	semidirect
10. #69102	C₂	semidirect
11. #67⋊C₁₆	C₂	semidirect
12. #69074	C₂	semidirect
13. D₃×#346	C₂	semidirect
14. #69052	C₂	semidirect
15. #69051	C₂	semidirect
70. #2164	D₃	semidirect
476. C₃	#33482	semidirect

Maximal subgroups

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

subgroup	index
#78556	2
C₃×#2164	2
#69881	2
#69282	2
#69281	2
#69278	2
#69277	2
#69103	2
#69102	2
#67⋊C₁₆	2
#69074	2
D₃×#346	2
#69052	2
#69051	2
#33482	3