Subgroups — #35447004

Order 21248.

830 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	#24917193	C₂	1	2	yes	maximal, complemented
2	C₂×#19127971	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19127971	C₂	1	1	yes	maximal, characteristic, complemented
4	#24916074	C₂	1	1	yes	maximal, characteristic, complemented
5	#24908860	C₂	1	2	yes	maximal, complemented
6	#24908737	C₂	1	2	yes	maximal, complemented
7	#24908373	C₂	1	1	yes	maximal, characteristic, complemented
8	#24908253	C₂	1	1	yes	maximal, characteristic, complemented
9	#24907941	C₂	1	2	yes	maximal, complemented
10	#24907513	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#2955	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14581817	C₂²	1	2	yes	—
13	C₂×#14581817	C₂²	1	2	yes	—
14	C₂²×D₆₆₄	C₂²	1	1	yes	characteristic
15	#19128468	C₂²	1	2	yes	—
16	#19127971	—	2	2	no	—
17	#19127971	—	2	2	no	—
18	#19127971	—	2	2	no	—
19	#19127971	—	2	2	no	—
20	#19127969	—	2	4	no	—
21	#19127966	—	2	4	no	—
22	#19127750	—	2	2	no	—
23	#19127750	C₂²	1	2	yes	—
24	#19127749	C₂²	1	2	yes	—
25	C₂×#14581728	—	2	2	no	—
26	C₂×#14581728	C₂²	1	1	yes	characteristic
27	C₂×#14581728	C₂²	1	1	yes	characteristic
28	C₂×#14581728	C₂²	1	1	yes	characteristic
29	#19127705	C₂²	1	2	yes	—
30	#19127685	C₂²	1	2	yes	—
31	C₂×#14581708	C₂²	1	2	yes	—
32	C₂×#14581708	C₂²	1	2	yes	—
33	C₂×#14581708	C₂²	1	2	yes	—
34	#19127471	C₂²	1	2	yes	—
35	C₈₃⋊#338	C₂²	1	2	yes	—
36	#575×C₈₃	C₂²	1	1	yes	characteristic
37	C₂×#131×C₈₃	C₂²	1	1	yes	characteristic
38	C₂×#131×C₈₃	C₂²	1	1	yes	characteristic
39	#444×C₈₃	—	2	2	no	—
40	#443×C₈₃	—	2	2	no	—
41	#430×C₈₃	C₂²	1	1	yes	characteristic
42	#421×C₈₃	C₂²	1	1	yes	characteristic
43	#421×C₈₃	C₂²	1	1	yes	characteristic
44	#405×C₈₃	C₂²	1	1	yes	characteristic
45	C₂²×D₃₃₂	C₂³	1	2	yes	—
46	#14581817	—	2	4	no	—
47	#14581817	—	2	4	no	—
48	#14581817	—	2	4	no	—
49	#14581817	—	4	2	no	—
50	C₂×#13050577	—	2	2	no	—
51	C₂×#13050577	—	2	2	no	—
52	C₂×D₆₆₄	—	2	1	no	—
53	C₂×D₆₆₄	—	2	1	no	—
54	C₂×D₆₆₄	—	2	1	no	—
55	C₂×D₆₆₄	—	2	1	no	—
56	C₂×D₆₆₄	—	2	1	no	—
57	C₂×D₆₆₄	—	2	1	no	—
58	C₂×#13050575	—	2	2	no	—
59	C₂×#13050575	—	2	2	no	—
60	#14581799	—	2	4	no	—
61	#14581799	—	4	2	no	—
62	C₂×#13050574	—	2	4	no	—
63	C₂×#13050574	C₂³	1	2	yes	—
64	C₂×#13050574	C₂³	1	2	yes	—
65	C₂×#13050574	C₂³	1	2	yes	—
66	#14581728	—	2	4	no	—
67	#14581728	—	2	1	no	—
68	#14581728	—	2	1	no	—
69	#14581728	—	2	1	no	—
70	#14581728	—	2	1	no	—
71	#14581728	D₄	1	2	yes	—
72	#14581728	D₄	1	2	yes	—
73	#14581727	—	2	4	no	—
74	#14581712	—	4	2	no	—
75	#14581711	—	2	2	no	—
76	#14581709	—	2	2	no	—
77	#14581708	—	2	4	no	—
78	#14581708	—	2	4	no	—
79	#14581708	—	2	4	no	—
80	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
81	C₂×#41×C₈₃	C₂³	1	1	yes	characteristic
82	#137×C₈₃	—	2	1	no	—
83	#137×C₈₃	D₄	1	2	yes	—
84	AGL(1,ℤ/8)×C₈₃	—	2	1	no	—
85	AGL(1,ℤ/8)×C₈₃	D₄	1	2	yes	—
86	#135×C₈₃	—	2	2	no	—
87	#131×C₈₃	—	2	1	no	—
88	#131×C₈₃	—	2	1	no	—
89	#131×C₈₃	—	2	1	no	—
90	#131×C₈₃	—	2	1	no	—
91	#131×C₈₃	—	2	1	no	—
92	#131×C₈₃	—	2	1	no	—
93	#131×C₈₃	D₄	1	2	yes	—
94	#131×C₈₃	D₄	1	2	yes	—
95	C₂×M₁₆×C₈₃	—	2	1	no	—
96	C₂×M₁₆×C₈₃	—	2	1	no	—
97	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
98	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
99	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₈₃	—	2	1	no	—
101	C₂²×C₈×C₈₃	—	2	1	no	—
102	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
103	#117×C₈₃	C₂³	1	1	yes	characteristic
104	#108×C₈₃	—	2	2	no	—
105	#104×C₈₃	—	2	2	no	—
106	#104×C₈₃	—	2	2	no	—
107	#97×C₈₃	—	2	1	no	—
108	C₄×C₈×C₈₃	—	2	1	no	—
109	C₂³×D₈₃	—	2	2	no	—
110	C₂×D₃₃₂	—	2	2	no	—
111	C₂×D₃₃₂	—	2	2	no	—
112	C₂×D₃₃₂	—	2	2	no	—
113	C₂×D₃₃₂	—	2	2	no	—
114	C₂×D₃₃₂	—	2	2	no	—
115	C₂×D₃₃₂	—	2	2	no	—
116	#13050577	—	4	4	no	—
117	#13050577	—	4	4	no	—
118	D₆₆₄	—	4	1	no	—
119	D₆₆₄	—	4	1	no	—
120	D₆₆₄	—	4	1	no	—
121	D₆₆₄	—	4	1	no	—
122	#13050575	—	4	4	no	—
123	#13050575	—	4	4	no	—
124	#13050574	—	2	2	no	—
125	#13050574	—	2	2	no	—
126	#13050574	—	2	2	no	—
127	#13050574	—	2	2	no	—
128	#13050574	—	2	2	no	—
129	#13050574	—	4	4	no	—
130	#13050574	C₂×D₄	1	4	yes	—
131	C₂×C₈₃⋊C₈	—	2	2	no	—
132	C₂×C₈₃⋊C₈	—	2	2	no	—
133	C₂×C₈₃⋊C₈	—	2	2	no	—
134	C₂×C₈₃⋊C₈	—	4	4	no	—
135	#41×C₈₃	—	2	1	no	—
136	#41×C₈₃	—	2	1	no	—
137	#41×C₈₃	—	2	1	no	—
138	#41×C₈₃	—	2	1	no	—
139	#41×C₈₃	—	2	1	no	—
140	#41×C₈₃	—	2	1	no	—
141	#41×C₈₃	C₂×D₄	1	2	yes	—
142	#41×C₈₃	C₂×D₄	1	2	yes	—
143	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
144	C₂×Q₈×C₈₃	#41	1	1	yes	characteristic
145	C₂×D₄×C₈₃	—	2	1	no	—
146	C₂×D₄×C₈₃	—	2	1	no	—
147	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
148	C₂×D₄×C₈₃	#41	1	1	yes	characteristic
149	C₂²×C₄×C₈₃	—	2	1	no	—
150	C₂²×C₄×C₈₃	—	2	1	no	—
151	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
152	Q₁₆×C₈₃	—	2	2	no	—
153	SD₁₆×C₈₃	—	2	2	no	—
154	SD₁₆×C₈₃	—	2	2	no	—
155	D₈×C₈₃	—	2	2	no	—
156	M₁₆×C₈₃	—	2	1	no	—
157	M₁₆×C₈₃	—	2	1	no	—
158	M₁₆×C₈₃	—	2	2	no	—
159	M₁₆×C₈₃	—	2	2	no	—
160	M₁₆×C₈₃	—	2	1	no	—
161	M₁₆×C₈₃	—	2	1	no	—
162	M₁₆×C₈₃	—	4	1	no	—
163	M₁₆×C₈₃	—	4	1	no	—
164	M₁₆×C₈₃	C₂×D₄	1	2	yes	—
165	M₁₆×C₈₃	C₂×D₄	1	2	yes	—
166	C₂×C₈×C₈₃	—	2	1	no	—
167	C₂×C₈×C₈₃	—	2	1	no	—
168	C₂×C₈×C₈₃	—	2	2	no	—
169	C₂×C₈×C₈₃	—	2	2	no	—
170	C₂×C₈×C₈₃	—	2	1	no	—
171	C₂×C₈×C₈₃	—	4	1	no	—
172	C₂×C₈×C₈₃	—	4	1	no	—
173	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
178	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
179	C₄⋊C₄×C₈₃	—	2	1	no	—
180	C₂²⋊C₄×C₈₃	—	2	1	no	—
181	C₄²×C₈₃	—	2	1	no	—
182	C₂³×C₈₃	—	2	1	no	—
183	C₂³×C₈₃	—	2	1	no	—
184	C₂³×C₈₃	2₋¹⁺⁴	1	1	yes	characteristic
185	C₂²×D₈₃	—	4	2	no	—
186	C₂²×D₈₃	—	4	2	no	—
187	C₂²×D₈₃	—	4	2	no	—
188	C₂²×D₈₃	—	16	2	no	—
189	Q₈×C₈₃	—	2	1	no	—
190	Q₈×C₈₃	—	2	1	no	—
191	Q₈×C₈₃	—	2	1	no	—
192	Q₈×C₈₃	#121	1	2	yes	—
193	D₄×C₈₃	—	2	2	no	—
194	D₄×C₈₃	—	2	2	no	—
195	D₄×C₈₃	—	2	1	no	—
196	D₄×C₈₃	—	2	1	no	—
197	D₄×C₈₃	—	2	1	no	—
198	D₄×C₈₃	—	4	1	no	—
199	D₄×C₈₃	—	4	1	no	—
200	D₄×C₈₃	#121	1	2	yes	—
201	C₂×C₄×C₈₃	—	2	1	no	—
202	C₂×C₄×C₈₃	—	2	2	no	—
203	C₂×C₄×C₈₃	—	2	2	no	—
204	C₂×C₄×C₈₃	—	2	1	no	—
205	C₂×C₄×C₈₃	—	4	1	no	—
206	C₂×C₄×C₈₃	—	4	1	no	—
207	C₂×C₄×C₈₃	—	4	1	no	—
208	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
214	D₃₃₂	—	4	2	no	—
215	D₃₃₂	—	4	2	no	—
216	D₃₃₂	—	4	2	no	—
217	D₃₃₂	—	4	2	no	—
218	C₈×C₈₃	—	2	2	no	—
219	C₈×C₈₃	—	2	2	no	—
220	C₈×C₈₃	—	4	1	no	—
221	C₈×C₈₃	#121	1	1	yes	characteristic
222	C₈×C₈₃	#121	1	1	yes	characteristic
223	C₈×C₈₃	#121	1	1	yes	characteristic
224	C₈×C₈₃	#121	1	1	yes	characteristic
225	C₈₃⋊C₈	—	2	4	no	—
226	C₈₃⋊C₈	—	4	2	no	—
227	C₈₃⋊C₈	—	4	2	no	—
228	C₂²×C₈₃	—	2	2	no	—
229	C₂²×C₈₃	—	4	1	no	—
230	C₂²×C₈₃	—	4	1	no	—
231	C₂²×C₈₃	—	8	1	no	—
232	C₂²×C₈₃	—	8	1	no	—
233	C₂²×C₈₃	#537	1	1	yes	characteristic
234	C₂²×C₈₃	#547	1	1	yes	characteristic
235	C₂²×C₈₃	#548	1	1	yes	characteristic
236	C₂×D₈₃	—	8	2	no	—
237	C₂×D₈₃	—	16	2	no	—
238	C₂×D₈₃	—	16	2	no	—
239	C₂×D₈₃	—	16	2	no	—
240	C₄×C₈₃	—	2	2	no	—
241	C₄×C₈₃	—	4	1	no	—
242	C₄×C₈₃	—	8	1	no	—
243	C₄×C₈₃	C₂×#121	1	1	yes	characteristic
244	C₄×C₈₃	C₂×#121	1	1	yes	characteristic
245	C₄×C₈₃	D₄²	1	1	yes	characteristic
246	C₄×C₈₃	#553	1	1	yes	characteristic
247	#24809	—	83	1	no	maximal, Sylow
248	C₂×C₈₃	—	2	1	no	—
249	C₂×C₈₃	—	2	1	no	—
250	C₂×C₈₃	—	2	1	no	—
251	C₂×C₈₃	—	4	2	no	—
252	C₂×C₈₃	—	8	1	no	—
253	C₂×C₈₃	#2416	1	1	yes	characteristic
254	D₈₃	—	16	2	no	—
255	#3068	—	83	2	no	—
256	C₂×#472	—	83	1	no	—
257	C₂×#472	—	83	1	no	—
258	#2955	D₈₃	1	1	yes	characteristic, complemented
259	#2916	—	83	1	no	—
260	#2069	—	83	2	no	—
261	#2048	—	83	2	no	—
262	#1978	—	83	1	no	—
263	#1953	—	83	1	no	—
264	#1903	—	83	2	no	—
265	#1813	—	83	1	no	—
266	C₈₃	#24809	1	1	yes	characteristic, complemented, Sylow
267	#575	C₂×D₈₃	1	1	yes	characteristic
268	C₂×AGL(1,ℤ/8)	—	83	2	no	—
269	C₂×AGL(1,ℤ/8)	—	83	2	no	—
270	C₂²×D₈	—	83	1	no	—
271	#568	—	83	2	no	—
272	C₂×#131	C₂×D₈₃	1	1	yes	characteristic
273	C₂×#131	C₂×D₈₃	1	1	yes	characteristic
274	#472	—	166	2	no	—
275	#472	—	166	2	no	—
276	#472	—	166	4	no	—
277	#472	—	166	2	no	—
278	#472	—	166	2	no	—
279	#471	—	166	4	no	—
280	#444	—	2	2	no	—
281	#443	—	2	2	no	—
282	#430	—	83	2	no	—
283	#430	—	83	2	no	—
284	#430	—	166	2	no	—
285	#430	C₂×D₈₃	1	1	yes	characteristic
286	C₂×#108	—	83	1	no	—
287	C₂×#108	—	83	1	no	—
288	C₂×#108	—	83	1	no	—
289	C₂×#108	—	166	2	no	—
290	#421	C₂×D₈₃	1	1	yes	characteristic
291	#421	C₂×D₈₃	1	1	yes	characteristic
292	#418	—	83	2	no	—
293	#413	—	83	2	no	—
294	C₂×#100	—	83	2	no	—
295	C₂×#100	—	83	2	no	—
296	C₂×#100	—	83	2	no	—
297	#405	C₂×D₈₃	1	1	yes	characteristic
298	#344	—	83	2	no	—
299	#338	—	83	2	no	—
300	C₂×#41	C₂²×D₈₃	1	1	yes	characteristic
301	C₂×#41	C₂²×D₈₃	1	1	yes	characteristic
302	C₂²×D₄	—	83	2	no	—
303	#137	—	2	1	no	—
304	#137	D₃₃₂	1	2	yes	—
305	AGL(1,ℤ/8)	—	2	1	no	—
306	AGL(1,ℤ/8)	—	332	2	no	—
307	AGL(1,ℤ/8)	—	166	4	no	—
308	AGL(1,ℤ/8)	—	166	4	no	—
309	AGL(1,ℤ/8)	—	166	4	no	—
310	AGL(1,ℤ/8)	D₃₃₂	1	2	yes	—
311	#135	—	2	2	no	—
312	C₂×SD₁₆	—	166	2	no	—
313	C₂×SD₁₆	—	166	2	no	—
314	C₂×D₈	—	166	2	no	—
315	C₂×D₈	—	166	2	no	—
316	C₂×D₈	—	166	1	no	—
317	C₂×D₈	—	166	1	no	—
318	C₂×D₈	—	166	1	no	—
319	C₂×D₈	—	166	1	no	—
320	C₂×D₈	—	166	1	no	—
321	C₂×D₈	—	166	1	no	—
322	#131	—	2	1	no	—
323	#131	—	2	1	no	—
324	#131	—	2	1	no	—
325	#131	—	2	1	no	—
326	#131	—	2	1	no	—
327	#131	—	2	1	no	—
328	#131	—	332	2	no	—
329	#131	—	166	4	no	—
330	#131	C₂²⋊D₈₃	1	2	yes	—
331	#131	C₂²⋊D₈₃	1	2	yes	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	83	2	no	—
335	C₂×M₁₆	—	83	2	no	—
336	C₂×M₁₆	—	83	2	no	—
337	C₂×M₁₆	—	166	4	no	—
338	C₂×M₁₆	C₂²×D₈₃	1	1	yes	characteristic
339	C₂×M₁₆	C₂²×D₈₃	1	1	yes	characteristic
340	C₂×M₁₆	C₂²×D₈₃	1	1	yes	characteristic
341	C₂²×C₈	—	2	1	no	—
342	C₂²×C₈	—	2	1	no	—
343	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
344	#117	C₂²×D₈₃	1	1	yes	characteristic
345	#108	—	2	2	no	—
346	#108	—	83	2	no	—
347	#108	—	83	2	no	—
348	#108	—	166	4	no	—
349	#108	—	166	4	no	—
350	#108	—	166	1	no	—
351	#108	—	166	1	no	—
352	#108	—	166	1	no	—
353	#108	—	166	1	no	—
354	#104	—	2	2	no	—
355	#104	—	2	2	no	—
356	#102	—	332	2	no	—
357	#101	—	166	2	no	—
358	#100	—	166	4	no	—
359	#100	—	166	2	no	—
360	#100	—	166	4	no	—
361	#100	—	166	4	no	—
362	#97	—	2	1	no	—
363	C₄×C₈	—	2	1	no	—
364	C₂⁴	—	166	2	no	—
365	#41	—	2	1	no	—
366	#41	—	2	1	no	—
367	#41	—	2	1	no	—
368	#41	—	2	1	no	—
369	#41	—	2	1	no	—
370	#41	—	2	1	no	—
371	#41	C₂×C₂²⋊D₈₃	1	2	yes	—
372	#41	C₂×D₃₃₂	1	2	yes	—
373	C₂×Q₈	C₂×D₃₃₂	1	1	yes	characteristic
374	C₂×Q₈	#13050590	1	1	yes	characteristic
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	166	2	no	—
378	C₂×D₄	—	166	2	no	—
379	C₂×D₄	—	166	2	no	—
380	C₂×D₄	—	166	2	no	—
381	C₂×D₄	—	166	2	no	—
382	C₂×D₄	—	166	2	no	—
383	C₂×D₄	C₂×D₃₃₂	1	1	yes	characteristic
384	C₂×D₄	#13050590	1	1	yes	characteristic
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	C₂³×D₈₃	1	1	yes	characteristic
388	Q₁₆	—	2	2	no	—
389	SD₁₆	—	2	2	no	—
390	SD₁₆	—	2	2	no	—
391	SD₁₆	—	332	4	no	—
392	SD₁₆	—	332	4	no	—
393	D₈	—	2	2	no	—
394	D₈	—	332	4	no	—
395	D₈	—	332	4	no	—
396	D₈	—	332	1	no	—
397	D₈	—	332	1	no	—
398	D₈	—	332	1	no	—
399	D₈	—	332	1	no	—
400	M₁₆	—	2	1	no	—
401	M₁₆	—	2	1	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	2	no	—
404	M₁₆	—	2	1	no	—
405	M₁₆	—	2	1	no	—
406	M₁₆	—	4	1	no	—
407	M₁₆	—	4	1	no	—
408	M₁₆	—	332	4	no	—
409	M₁₆	—	83	4	no	—
410	M₁₆	—	166	2	no	—
411	M₁₆	—	166	2	no	—
412	M₁₆	—	166	2	no	—
413	M₁₆	—	166	2	no	—
414	M₁₆	—	166	2	no	—
415	M₁₆	C₂×C₂²⋊D₈₃	1	2	yes	—
416	M₁₆	C₂×D₃₃₂	1	2	yes	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	4	1	no	—
423	C₂×C₈	—	4	1	no	—
424	C₂×C₈	—	332	4	no	—
425	C₂×C₈	—	166	2	no	—
426	C₂×C₈	—	166	2	no	—
427	C₂×C₈	—	166	2	no	—
428	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
429	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
430	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
431	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
432	C₂×C₈	#13050589	1	1	yes	characteristic
433	C₂×C₈	#13050589	1	1	yes	characteristic
434	C₄⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₄²	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	1328	2	no	—
440	C₂³	—	332	2	no	—
441	C₂³	—	332	2	no	—
442	C₂³	—	332	2	no	—
443	C₂³	#14581839	1	1	yes	characteristic
444	Q₈	—	2	1	no	—
445	Q₈	—	2	1	no	—
446	Q₈	—	2	1	no	—
447	Q₈	#14581766	1	2	yes	—
448	D₄	—	2	2	no	—
449	D₄	—	2	2	no	—
450	D₄	—	2	1	no	—
451	D₄	—	2	1	no	—
452	D₄	—	2	1	no	—
453	D₄	—	4	1	no	—
454	D₄	—	4	1	no	—
455	D₄	—	332	2	no	—
456	D₄	—	332	2	no	—
457	D₄	—	332	2	no	—
458	D₄	—	332	2	no	—
459	D₄	#14581766	1	2	yes	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
468	C₂×C₄	C₂²×C₂²⋊D₈₃	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₃₃₂	1	1	yes	characteristic
470	C₂×C₄	C₂×#13050589	1	1	yes	characteristic
471	C₂×C₄	C₂×#13050590	1	1	yes	characteristic
472	C₂×C₄	#14581838	1	1	yes	characteristic
473	C₈	—	2	2	no	—
474	C₈	—	2	2	no	—
475	C₈	—	4	1	no	—
476	C₈	—	332	2	no	—
477	C₈	—	332	2	no	—
478	C₈	—	166	4	no	—
479	C₈	#14581764	1	1	yes	characteristic
480	C₈	#14581764	1	1	yes	characteristic
481	C₈	#14581764	1	1	yes	characteristic
482	C₈	#14581764	1	1	yes	characteristic
483	C₂²	—	2	2	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	—	8	1	no	—
488	C₂²	—	1328	2	no	—
489	C₂²	—	1328	2	no	—
490	C₂²	—	1328	2	no	—
491	C₂²	—	664	2	no	—
492	C₂²	#19128279	1	1	yes	characteristic
493	C₂²	#19128355	1	1	yes	characteristic
494	C₂²	#19128360	1	1	yes	characteristic
495	C₄	—	2	2	no	—
496	C₄	—	4	1	no	—
497	C₄	—	8	1	no	—
498	C₄	C₂×#14581764	1	1	yes	characteristic
499	C₄	C₂×#14581766	1	1	yes	characteristic
500	C₄	D₄×D₃₃₂	1	1	yes	characteristic
501	C₄	#19128397	1	1	yes	characteristic
502	C₂	—	2	1	no	—
503	C₂	—	2	1	no	—
504	C₂	—	2	1	no	—
505	C₂	—	4	2	no	—
506	C₂	—	8	1	no	—
507	C₂	—	1328	2	no	—
508	C₂	#24910903	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#24910903
commutator, cosocle	C₂²×C₄×C₈₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₈₃
Fitting	C₈₃×#2955	C₂
socle	C₂×C₈₃	#2416
hypercenter	#2955	D₈₃
hypocenter	C₈₃	#24809
LCS	G ▷ C₂²×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #2955

Complements

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

N	H ≅ G/N	type
1. #24917193	C₂	semidirect
2. C₂×#19127971	C₂	semidirect
3. C₂×#19127971	C₂	semidirect
4. #24916074	C₂	semidirect
5. #24908860	C₂	semidirect
6. #24908737	C₂	semidirect
7. #24908373	C₂	semidirect
8. #24908253	C₂	semidirect
9. #24907941	C₂	semidirect
10. #24907513	C₂	semidirect
11. C₈₃×#2955	C₂	semidirect
258. #2955	D₈₃	semidirect
266. C₈₃	#24809	semidirect

Maximal subgroups

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

subgroup	index
#24917193	2
C₂×#19127971	2
#24916074	2
#24908860	2
#24908737	2
#24908373	2
#24908253	2
#24907941	2
#24907513	2
C₈₃×#2955	2
#24809	83