Subgroups — #35376134

Order 21248.

648 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24916595	C₂	1	1	yes	maximal, characteristic, complemented
2	#24916593	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14581812	C₂	1	1	yes	maximal, characteristic
4	#24906374	C₂	1	2	yes	maximal, complemented
5	#24906309	C₂	1	2	yes	maximal, complemented
6	#24906303	C₂	1	2	yes	maximal, complemented
7	#24906279	C₂	1	2	yes	maximal, complemented
8	#24906218	C₂	1	1	yes	maximal, characteristic, complemented
9	#24905903	C₂	1	1	yes	maximal, characteristic, complemented
10	#24905750	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#1489	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14581812	C₄	1	1	yes	characteristic
13	C₄×#13050590	C₂²	1	1	yes	characteristic
14	Q₈×C₈₃⋊C₈	C₂²	1	2	yes	—
15	#19127825	C₂²	1	2	yes	—
16	C₄×#13050580	C₄	1	1	yes	characteristic
17	C₄×#13050580	C₂²	1	1	yes	characteristic
18	C₄×#13050577	C₄	1	1	yes	characteristic
19	C₄×#13050577	C₂²	1	1	yes	characteristic
20	C₄×#13050578	C₄	1	1	yes	characteristic
21	C₄×#13050578	C₂²	1	1	yes	characteristic
22	C₄×#13050575	C₄	1	1	yes	characteristic
23	C₄×#13050575	C₂²	1	1	yes	characteristic
24	#19127779	—	2	2	no	—
25	#19127779	C₂²	1	2	yes	—
26	#19127778	C₂²	1	2	yes	—
27	#19127777	—	2	2	no	—
28	#19127754	—	2	1	no	—
29	#19127754	C₂²	1	1	yes	characteristic
30	#19127753	—	2	1	no	—
31	#19127737	C₄	1	1	yes	characteristic
32	#19127725	—	2	1	no	—
33	#19127725	C₂²	1	1	yes	characteristic
34	#19127723	—	2	1	no	—
35	#19127697	C₄	1	1	yes	characteristic
36	#19127695	C₄	1	1	yes	characteristic
37	C₂×C₄×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
38	#19127451	C₂²	1	2	yes	—
39	#19127451	C₂²	1	2	yes	—
40	#19127433	C₂²	1	2	yes	—
41	#19127430	C₂²	1	2	yes	—
42	#19127423	C₂²	1	2	yes	—
43	#19127423	C₂²	1	2	yes	—
44	C₄×#41×C₈₃	C₂²	1	1	yes	characteristic
45	#423×C₈₃	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₈₃	C₂²	1	1	yes	characteristic
47	Q₈⋊C₈×C₈₃	C₂²	1	2	yes	—
48	D₄⋊C₈×C₈₃	C₂²	1	2	yes	—
49	C₂×#13050590	C₂×C₄	1	1	yes	characteristic
50	#14581812	—	2	4	no	—
51	C₂×#13050580	C₂×C₄	1	1	yes	characteristic
52	C₂×#13050578	C₂×C₄	1	1	yes	characteristic
53	C₂×#13050577	C₂×C₄	1	1	yes	characteristic
54	C₂×#13050575	C₂×C₄	1	1	yes	characteristic
55	C₂×#13050574	—	2	2	no	—
56	C₂×#13050574	—	2	1	no	—
57	C₂×#13050573	—	2	2	no	—
58	C₂²×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
60	C₄×Dic₁₆₆	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
62	C₄×D₃₃₂	C₂×C₄	1	1	yes	characteristic
63	C₄×D₃₃₂	C₂³	1	1	yes	characteristic
64	C₄×C₂²⋊D₈₃	—	2	1	no	—
65	C₄×C₂²⋊D₈₃	—	2	1	no	—
66	#14581751	C₂×C₄	1	1	yes	characteristic
67	#14581749	—	2	1	no	—
68	C₄²×D₈₃	—	2	1	no	—
69	#14581725	C₂×C₄	1	1	yes	characteristic
70	#14581725	C₂×C₄	1	1	yes	characteristic
71	#14581723	C₂×C₄	1	1	yes	characteristic
72	#14581723	C₂×C₄	1	1	yes	characteristic
73	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
74	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
75	C₄⋊(C₈₃⋊C₈)	D₄	1	1	yes	characteristic
76	C₄⋊(C₈₃⋊C₈)	D₄	1	1	yes	characteristic
77	C₄⋊(C₈₃⋊C₈)	C₂³	1	2	yes	—
78	Dic₈₃⋊C₈	—	2	2	no	—
79	#14581716	C₂×C₄	1	1	yes	characteristic
80	#14581716	C₂×C₄	1	1	yes	characteristic
81	#14581715	C₂×C₄	1	1	yes	characteristic
82	#14581715	C₂×C₄	1	1	yes	characteristic
83	#14581713	C₂×C₄	1	1	yes	characteristic
84	#14581713	C₂×C₄	1	1	yes	characteristic
85	#14581712	C₂×C₄	1	1	yes	characteristic
86	#14581712	C₂×C₄	1	1	yes	characteristic
87	C₂²⋊(C₈₃⋊C₈)	—	2	2	no	—
88	C₂²⋊(C₈₃⋊C₈)	D₄	1	2	yes	—
89	(C₂×D₈₃)⋊C₈	—	2	2	no	—
90	C₄×C₈₃⋊C₈	—	2	2	no	—
91	C₄×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
92	C₄×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
93	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
94	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
95	C₄×C₈₃⋊C₈	C₂³	1	2	yes	—
96	C₈×Dic₈₃	—	2	2	no	—
97	C₂×#41×C₈₃	C₂×C₄	1	1	yes	characteristic
98	C₂×M₁₆×C₈₃	—	2	1	no	—
99	C₂×M₁₆×C₈₃	—	2	1	no	—
100	C₄×Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
101	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
102	C₄×D₄×C₈₃	—	2	1	no	—
103	C₄×D₄×C₈₃	—	2	1	no	—
104	C₄×D₄×C₈₃	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
106	#117×C₈₃	—	2	1	no	—
107	#117×C₈₃	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₈₃	—	2	1	no	—
109	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
110	C₄⋊C₈×C₈₃	—	2	1	no	—
111	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
112	#97×C₈₃	—	2	1	no	—
113	C₄×C₈×C₈₃	C₂³	1	2	yes	—
114	#13050590	—	2	2	no	—
115	#13050590	—	4	1	no	—
116	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
117	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊D₈₃	—	2	1	no	—
119	C₂×C₄×D₈₃	—	2	1	no	—
120	C₂×C₄×D₈₃	—	2	1	no	—
121	C₂×C₄×D₈₃	—	2	1	no	—
122	#13050580	M₁₆	1	4	yes	complemented
123	#13050578	—	2	2	no	—
124	#13050577	—	2	2	no	—
125	#13050575	—	2	2	no	—
126	#13050574	—	8	2	no	—
127	#13050574	—	8	1	no	—
128	#13050573	—	8	2	no	—
129	C₂×C₈₃⋊C₈	—	2	2	no	—
130	C₂×C₈₃⋊C₈	—	2	2	no	—
131	C₂×C₈₃⋊C₈	—	4	1	no	—
132	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈₃⋊C₈	C₂×D₄	1	2	yes	—
137	C₂×C₈₃⋊C₈	C₂×D₄	1	2	yes	—
138	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
139	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
140	Dic₈₃⋊C₄	—	2	1	no	—
141	Dic₈₃⋊C₄	—	2	1	no	—
142	C₂²⋊Dic₈₃	—	2	1	no	—
143	(C₂×D₈₃)⋊C₄	—	2	1	no	—
144	(C₂×D₈₃)⋊C₄	—	2	1	no	—
145	C₄×Dic₈₃	—	2	1	no	—
146	C₄×Dic₈₃	—	2	1	no	—
147	C₄×Dic₈₃	—	2	1	no	—
148	#41×C₈₃	—	2	2	no	—
149	#41×C₈₃	—	4	1	no	—
150	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×D₄×C₈₃	—	2	1	no	—
152	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₈₃	—	2	1	no	—
154	C₂²×C₄×C₈₃	—	2	1	no	—
155	C₂²×C₄×C₈₃	—	2	1	no	—
156	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
159	M₁₆×C₈₃	—	4	2	no	—
160	M₁₆×C₈₃	—	8	1	no	—
161	C₂×C₈×C₈₃	—	2	2	no	—
162	C₂×C₈×C₈₃	—	2	2	no	—
163	C₄⋊C₄×C₈₃	—	2	1	no	—
164	C₄⋊C₄×C₈₃	—	2	1	no	—
165	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
166	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
167	C₂²⋊C₄×C₈₃	—	2	1	no	—
168	C₂²⋊C₄×C₈₃	—	2	1	no	—
169	C₂²⋊C₄×C₈₃	—	2	1	no	—
170	C₄²×C₈₃	—	2	1	no	—
171	C₄²×C₈₃	—	2	1	no	—
172	C₄²×C₈₃	—	2	1	no	—
173	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₈₃	#41	1	1	yes	characteristic
176	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
177	C₂³×C₈₃	—	2	1	no	—
178	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
179	C₂²×D₈₃	—	2	1	no	—
180	Q₈×C₈₃	—	2	1	no	—
181	Q₈×C₈₃	C₂×M₁₆	1	2	yes	—
182	D₄×C₈₃	—	2	1	no	—
183	D₄×C₈₃	—	2	1	no	—
184	D₄×C₈₃	—	4	2	no	—
185	C₂×C₄×C₈₃	—	2	1	no	—
186	C₂×C₄×C₈₃	—	2	1	no	—
187	C₂×C₄×C₈₃	—	2	1	no	—
188	C₂×C₄×C₈₃	—	2	1	no	—
189	C₂×C₄×C₈₃	—	2	1	no	—
190	C₂×C₄×C₈₃	—	2	2	no	—
191	C₂×C₄×C₈₃	—	2	1	no	—
192	C₂×C₄×C₈₃	—	2	1	no	—
193	C₂×C₄×C₈₃	—	4	2	no	—
194	C₂×C₄×C₈₃	—	4	1	no	—
195	C₂×C₄×C₈₃	—	4	1	no	—
196	C₂×C₄×C₈₃	—	4	2	no	—
197	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
203	C₂²⋊D₈₃	—	4	2	no	—
204	C₂×Dic₈₃	—	2	1	no	—
205	C₂×Dic₈₃	—	2	1	no	—
206	C₂×Dic₈₃	—	2	1	no	—
207	D₃₃₂	—	2	1	no	—
208	D₃₃₂	—	2	1	no	—
209	C₄×D₈₃	—	4	2	no	—
210	C₄×D₈₃	—	4	1	no	—
211	C₄×D₈₃	—	4	1	no	—
212	C₄×D₈₃	—	4	2	no	—
213	Dic₁₆₆	—	2	1	no	—
214	Dic₁₆₆	C₂×M₁₆	1	2	yes	—
215	C₈×C₈₃	—	4	2	no	—
216	C₈×C₈₃	—	4	2	no	—
217	C₈₃⋊C₈	—	2	1	no	—
218	C₈₃⋊C₈	—	2	1	no	—
219	C₈₃⋊C₈	—	2	1	no	—
220	C₈₃⋊C₈	—	2	2	no	—
221	C₈₃⋊C₈	—	2	2	no	—
222	C₈₃⋊C₈	—	4	2	no	—
223	C₈₃⋊C₈	C₂×M₁₆	1	2	yes	—
224	C₂²×C₈₃	—	2	1	no	—
225	C₂²×C₈₃	—	2	1	no	—
226	C₂²×C₈₃	—	2	1	no	—
227	C₂²×C₈₃	—	4	1	no	—
228	C₂²×C₈₃	—	4	1	no	—
229	C₂²×C₈₃	—	4	1	no	—
230	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
231	C₂×D₈₃	—	4	1	no	—
232	C₂×D₈₃	—	4	1	no	—
233	C₂×D₈₃	—	4	1	no	—
234	C₄×C₈₃	—	2	1	no	—
235	C₄×C₈₃	—	2	2	no	—
236	C₄×C₈₃	—	2	1	no	—
237	C₄×C₈₃	—	2	1	no	—
238	C₄×C₈₃	—	4	1	no	—
239	C₄×C₈₃	—	4	1	no	—
240	C₄×C₈₃	#444	1	2	yes	—
241	C₄×C₈₃	C₂²×M₁₆	1	1	yes	characteristic
242	C₄×C₈₃	#568	1	1	yes	characteristic
243	C₄×C₈₃	#577	1	1	yes	characteristic
244	C₄×C₈₃	#577	1	1	yes	characteristic
245	Dic₈₃	—	2	2	no	—
246	Dic₈₃	—	4	1	no	—
247	Dic₈₃	—	4	1	no	—
248	#18063	—	83	1	no	maximal, Sylow
249	C₂×C₈₃	—	4	1	no	—
250	C₂×C₈₃	—	8	1	no	—
251	C₂×C₈₃	D₄×M₁₆	1	1	yes	characteristic
252	C₂×C₈₃	#2952	1	1	yes	characteristic
253	C₂×C₈₃	C₂×#444	1	1	yes	characteristic
254	D₈₃	—	8	1	no	—
255	#2991	—	83	1	no	—
256	#2991	—	83	1	no	—
257	C₄×#135	—	83	1	no	—
258	#1594	—	83	2	no	—
259	#1583	—	83	2	no	—
260	#1583	—	83	2	no	—
261	#1579	—	83	2	no	—
262	#1566	—	83	1	no	—
263	#1489	—	83	1	no	—
264	#1489	D₈₃	1	1	yes	characteristic, complemented
265	#1451	—	83	1	no	—
266	C₈₃	#18063	1	1	yes	characteristic, complemented, Sylow
267	C₂×#135	—	83	1	no	—
268	C₄×#41	—	83	1	no	—
269	C₄×#41	C₂×D₈₃	1	1	yes	characteristic
270	C₈×Q₈	—	83	2	no	—
271	C₈×Q₈	—	83	2	no	—
272	C₄×Q₁₆	—	83	1	no	—
273	C₄×Q₁₆	—	83	1	no	—
274	C₄×SD₁₆	—	83	1	no	—
275	C₄×SD₁₆	—	83	1	no	—
276	C₄×SD₁₆	—	83	1	no	—
277	C₄×SD₁₆	—	83	1	no	—
278	C₄×D₈	—	83	1	no	—
279	C₄×D₈	—	83	1	no	—
280	#436	—	83	2	no	—
281	#436	—	83	2	no	—
282	#436	—	166	2	no	—
283	#436	—	166	2	no	—
284	#431	—	83	1	no	—
285	#431	—	166	1	no	—
286	#431	—	166	1	no	—
287	#427	—	83	1	no	—
288	#423	—	83	1	no	—
289	#423	—	166	1	no	—
290	#423	—	166	1	no	—
291	#423	C₂×D₈₃	1	1	yes	characteristic
292	#416	—	83	1	no	—
293	#416	—	83	1	no	—
294	C₄×M₁₆	C₂×D₈₃	1	1	yes	characteristic
295	C₂×C₄×C₈	—	83	1	no	—
296	#334	—	83	2	no	—
297	#334	—	83	2	no	—
298	Q₈⋊C₈	—	83	2	no	—
299	Q₈⋊C₈	C₂×D₈₃	1	2	yes	—
300	D₄⋊C₈	—	83	2	no	—
301	D₄⋊C₈	C₂×D₈₃	1	2	yes	—
302	#322	—	83	2	no	—
303	#322	—	83	2	no	—
304	C₂×#41	—	83	1	no	—
305	C₂×#41	C₄×D₈₃	1	1	yes	characteristic
306	#135	—	166	4	no	—
307	C₂×Q₁₆	—	83	1	no	—
308	C₂×SD₁₆	—	83	1	no	—
309	C₂×SD₁₆	—	83	1	no	—
310	C₂×D₈	—	83	1	no	—
311	C₂×M₁₆	—	2	1	no	—
312	C₂×M₁₆	—	2	1	no	—
313	C₂×M₁₆	—	166	2	no	—
314	C₂×M₁₆	—	166	2	no	—
315	C₂×M₁₆	—	166	1	no	—
316	C₂²×C₈	—	83	1	no	—
317	C₂²×C₈	—	83	1	no	—
318	C₄×Q₈	—	83	1	no	—
319	C₄×Q₈	—	83	1	no	—
320	C₄×Q₈	C₄×D₈₃	1	1	yes	characteristic
321	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
322	C₄×D₄	—	2	1	no	—
323	C₄×D₄	—	2	1	no	—
324	C₄×D₄	—	83	1	no	—
325	C₄×D₄	—	83	1	no	—
326	C₄×D₄	—	166	1	no	—
327	C₄×D₄	—	166	1	no	—
328	C₄×D₄	C₄×D₈₃	1	1	yes	characteristic
329	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
330	#117	—	2	1	no	—
331	#117	—	83	1	no	—
332	#117	—	166	1	no	—
333	#117	C₄×D₈₃	1	1	yes	characteristic
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	—	166	1	no	—
336	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
337	#107	—	83	1	no	—
338	#107	—	83	1	no	—
339	#106	—	83	1	no	—
340	#106	—	83	1	no	—
341	C₄⋊C₈	—	2	1	no	—
342	C₄⋊C₈	—	83	1	no	—
343	C₄⋊C₈	—	83	1	no	—
344	C₄⋊C₈	—	83	2	no	—
345	C₄⋊C₈	—	166	2	no	—
346	C₄⋊C₈	—	166	2	no	—
347	C₄⋊C₈	—	166	1	no	—
348	C₄⋊C₈	C₂²×D₈₃	1	2	yes	—
349	#103	—	83	1	no	—
350	#103	—	83	1	no	—
351	#103	—	83	1	no	—
352	#103	—	83	1	no	—
353	#102	—	83	1	no	—
354	#102	—	83	1	no	—
355	#102	—	83	1	no	—
356	#102	—	83	1	no	—
357	C₂²⋊C₈	—	83	2	no	—
358	C₂²⋊C₈	—	166	2	no	—
359	C₂²⋊C₈	—	166	2	no	—
360	#97	—	2	1	no	—
361	C₄×C₈	—	83	1	no	—
362	C₄×C₈	—	83	1	no	—
363	C₄×C₈	—	83	1	no	—
364	C₄×C₈	—	83	1	no	—
365	C₄×C₈	—	83	2	no	—
366	C₄×C₈	—	166	2	no	—
367	C₄×C₈	—	166	2	no	—
368	C₄×C₈	C₂²×D₈₃	1	2	yes	—
369	#41	—	2	2	no	—
370	#41	—	4	1	no	—
371	#41	—	332	1	no	—
372	#41	—	166	2	no	—
373	C₂×Q₈	—	83	1	no	—
374	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	83	1	no	—
377	C₂×D₄	—	166	1	no	—
378	C₂×D₄	C₂×C₄×D₈₃	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	166	1	no	—
383	C₂²×C₄	—	166	1	no	—
384	C₂²×C₄	—	166	1	no	—
385	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
386	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
387	C₂²×C₄	#13050589	1	1	yes	characteristic
388	Q₁₆	—	83	4	no	—
389	SD₁₆	—	166	2	no	—
390	SD₁₆	—	166	2	no	—
391	D₈	—	166	2	no	—
392	M₁₆	—	4	2	no	—
393	M₁₆	—	8	1	no	—
394	M₁₆	—	664	2	no	—
395	M₁₆	—	664	1	no	—
396	M₁₆	—	664	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	332	1	no	—
400	C₂×C₈	—	83	1	no	—
401	C₂×C₈	—	83	1	no	—
402	C₂×C₈	—	83	1	no	—
403	C₂×C₈	—	83	1	no	—
404	C₂×C₈	—	83	2	no	—
405	C₂×C₈	—	83	2	no	—
406	C₂×C₈	—	166	2	no	—
407	C₂×C₈	—	166	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	83	1	no	—
411	C₄⋊C₄	—	83	1	no	—
412	C₄⋊C₄	—	166	1	no	—
413	C₄⋊C₄	—	166	1	no	—
414	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
415	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	166	1	no	—
420	C₂²⋊C₄	—	166	1	no	—
421	C₂²⋊C₄	—	166	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	166	1	no	—
426	C₄²	—	166	1	no	—
427	C₄²	—	166	1	no	—
428	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
429	C₄²	D₄×D₈₃	1	1	yes	characteristic
430	C₄²	#13050589	1	1	yes	characteristic
431	C₄²	C₂³×D₈₃	1	1	yes	characteristic
432	C₂³	—	2	1	no	—
433	C₂³	—	166	1	no	—
434	C₂³	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
435	Q₈	—	2	1	no	—
436	Q₈	—	83	2	no	—
437	Q₈	—	166	1	no	—
438	Q₈	M₁₆×D₈₃	1	2	yes	—
439	D₄	—	2	1	no	—
440	D₄	—	2	1	no	—
441	D₄	—	4	2	no	—
442	D₄	—	332	2	no	—
443	D₄	—	166	1	no	—
444	D₄	—	166	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	332	2	no	—
458	C₂×C₄	—	332	2	no	—
459	C₂×C₄	—	332	1	no	—
460	C₂×C₄	—	332	1	no	—
461	C₂×C₄	—	166	1	no	—
462	C₂×C₄	—	166	1	no	—
463	C₂×C₄	—	166	1	no	—
464	C₂×C₄	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
465	C₂×C₄	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
466	C₂×C₄	(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
467	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
468	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
469	C₂×C₄	C₂×#13050589	1	1	yes	characteristic
470	C₈	—	4	2	no	—
471	C₈	—	4	2	no	—
472	C₈	—	332	2	no	—
473	C₈	—	83	2	no	—
474	C₈	—	166	1	no	—
475	C₈	—	166	1	no	—
476	C₈	—	166	1	no	—
477	C₈	—	166	2	no	—
478	C₈	—	166	2	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	332	1	no	—
486	C₂²	—	332	1	no	—
487	C₂²	—	332	1	no	—
488	C₂²	C₂×(C₂²⋊D₈₃)⋊C₄	1	1	yes	characteristic
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	2	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	332	1	no	—
496	C₄	—	332	1	no	—
497	C₄	—	166	2	no	—
498	C₄	#19127820	1	2	yes	—
499	C₄	C₂×M₁₆×D₈₃	1	1	yes	characteristic
500	C₄	#19128467	1	1	yes	characteristic
501	C₄	#19128510	1	1	yes	characteristic
502	C₄	#19128511	1	1	yes	characteristic
503	C₂	—	4	1	no	—
504	C₂	—	8	1	no	—
505	C₂	—	664	1	no	—
506	C₂	#24916195	1	1	yes	characteristic
507	C₂	#24916342	1	1	yes	characteristic
508	C₂	C₂×#19127820	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₄²	C₂³×D₈₃
Fitting	C₈₃×#1489	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	C₂×#14581812	C₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#1489	D₈₃
hypocenter	C₈₃	#18063
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1489

Complements

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

N	H ≅ G/N	type
1. #24916595	C₂	semidirect
2. #24916593	C₂	semidirect
4. #24906374	C₂	semidirect
5. #24906309	C₂	semidirect
6. #24906303	C₂	semidirect
7. #24906279	C₂	semidirect
8. #24906218	C₂	semidirect
9. #24905903	C₂	semidirect
10. #24905750	C₂	semidirect
11. C₈₃×#1489	C₂	semidirect
122. #13050580	M₁₆	semidirect
264. #1489	D₈₃	semidirect
266. C₈₃	#18063	semidirect

Maximal subgroups

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

subgroup	index
#24916595	2
#24916593	2
C₄×#14581812	2
#24906374	2
#24906309	2
#24906303	2
#24906279	2
#24906218	2
#24905903	2
#24905750	2
C₈₃×#1489	2
#18063	83