Subgroups — C₄×#19127973 #35411289

Order 21248.

882 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	C₂×#19127973	C₂	1	1	yes	maximal, characteristic
2	C₄×#14581823	C₂	1	2	yes	maximal
3	C₄×#14581798	C₂	1	1	yes	maximal, characteristic
4	#24908379	C₂	1	1	yes	maximal, characteristic, complemented
5	#24908246	C₂	1	1	yes	maximal, characteristic, complemented
6	#24908115	C₂	1	2	yes	maximal, complemented
7	#24907981	C₂	1	2	yes	maximal
8	#24907528	C₂	1	1	yes	maximal, characteristic
9	C₄×#14581728	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#14581711	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×Q₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14581823	C₂²	1	2	yes	—
13	C₂×#14581798	C₂²	1	1	yes	characteristic
14	C₂×#14581798	C₂²	1	1	yes	characteristic
15	C₄×#13050590	C₂²	1	1	yes	characteristic
16	#19127973	C₄	1	8	yes	direct product factor
17	#19127806	—	2	2	no	—
18	#19127799	—	2	2	no	—
19	C₄×#13050580	—	2	2	no	—
20	C₄×#13050577	—	2	2	no	—
21	C₂×#14581728	C₂²	1	1	yes	characteristic
22	C₂×#14581728	C₂²	1	1	yes	characteristic
23	#19127741	C₂²	1	2	yes	—
24	#19127710	C₂²	1	2	yes	—
25	#19127700	C₂²	1	2	yes	—
26	C₂×#14581711	C₂²	1	2	yes	—
27	C₂×#14581711	C₂²	1	2	yes	—
28	#19127656	C₂²	1	1	yes	characteristic
29	#19127656	C₂²	1	1	yes	characteristic
30	#19127655	—	2	1	no	—
31	#19127655	—	2	1	no	—
32	C₄×#13050574	C₂²	1	2	yes	—
33	C₄×#13050574	C₂²	1	1	yes	characteristic
34	C₄×#13050573	—	2	1	no	—
35	C₄×C₈×D₈₃	—	2	1	no	—
36	#19127470	C₂²	1	2	yes	—
37	#19127470	C₂²	1	2	yes	—
38	#19127466	C₂²	1	2	yes	—
39	C₂²×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₈₃	C₂²	1	2	yes	—
41	C₄×Q₁₆×C₈₃	—	2	1	no	—
42	C₄×Q₁₆×C₈₃	—	2	1	no	—
43	C₄×Q₁₆×C₈₃	—	2	1	no	—
44	C₄×Q₁₆×C₈₃	—	2	1	no	—
45	C₂×#107×C₈₃	C₂²	1	1	yes	characteristic
46	C₂×#103×C₈₃	C₂²	1	2	yes	—
47	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
48	C₂×#13050590	C₂³	1	1	yes	characteristic
49	#14581823	—	2	4	no	—
50	#14581823	C₂×C₄	1	8	yes	—
51	C₂×#13050580	—	2	2	no	—
52	C₂×#13050577	—	2	2	no	—
53	#14581798	—	2	2	no	—
54	#14581798	—	2	2	no	—
55	#14581798	—	2	2	no	—
56	#14581798	C₂×C₄	1	4	yes	—
57	C₂×#13050574	C₂³	1	2	yes	—
58	C₂×#13050574	C₂³	1	1	yes	characteristic
59	C₂×#13050574	C₂³	1	2	yes	—
60	C₂×#13050574	C₂³	1	1	yes	characteristic
61	C₂×#13050573	—	2	1	no	—
62	C₂×#13050573	—	2	1	no	—
63	C₂×C₈×D₈₃	—	2	1	no	—
64	C₂×C₈×D₈₃	—	2	1	no	—
65	C₄×Dic₁₆₆	D₄	1	1	yes	characteristic
66	C₄×Dic₁₆₆	D₄	1	1	yes	characteristic
67	C₄×D₃₃₂	D₄	1	1	yes	characteristic
68	C₄×D₃₃₂	D₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₈₃	—	2	1	no	—
70	C₄×C₂²⋊D₈₃	—	2	1	no	—
71	#14581751	C₂³	1	1	yes	characteristic
72	#14581749	—	2	1	no	—
73	C₄²×D₈₃	—	2	1	no	—
74	#14581728	—	2	2	no	—
75	#14581728	C₂×C₄	1	4	yes	complemented
76	#14581725	—	2	2	no	—
77	#14581723	—	2	2	no	—
78	#14581716	—	2	2	no	—
79	#14581716	—	2	2	no	—
80	#14581715	—	2	2	no	—
81	#14581712	—	2	2	no	—
82	#14581711	—	2	4	no	—
83	#14581711	C₂×C₄	1	8	yes	complemented
84	#14581703	—	2	1	no	—
85	#14581703	—	2	2	no	—
86	#14581702	—	2	1	no	—
87	#14581702	—	2	1	no	—
88	C₄×C₈₃⋊C₈	—	2	1	no	—
89	C₄×C₈₃⋊C₈	—	2	2	no	—
90	C₈×Dic₈₃	—	2	1	no	—
91	C₈×Dic₈₃	—	2	1	no	—
92	C₂²×Q₈×C₈₃	C₂³	1	2	yes	—
93	C₂×Q₁₆×C₈₃	—	2	1	no	—
94	C₂×Q₁₆×C₈₃	—	2	1	no	—
95	C₂×Q₁₆×C₈₃	—	2	2	no	—
96	C₂×Q₁₆×C₈₃	C₂×C₄	1	4	yes	complemented
97	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
99	C₄×Q₈×C₈₃	—	2	2	no	—
100	C₄×Q₈×C₈₃	—	2	2	no	—
101	C₄×Q₈×C₈₃	—	2	2	no	—
102	C₄×Q₈×C₈₃	—	2	2	no	—
103	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
104	C₂×C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
105	C₂×C₄²×C₈₃	—	2	2	no	—
106	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
107	#107×C₈₃	—	2	1	no	—
108	#107×C₈₃	—	2	1	no	—
109	#103×C₈₃	—	2	2	no	—
110	#103×C₈₃	—	2	2	no	—
111	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
112	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
113	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
114	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
115	#13050590	—	2	1	no	—
116	#13050590	—	2	1	no	—
117	#13050590	C₂²×C₄	1	2	yes	—
118	#13050590	#41	1	2	yes	—
119	C₂×Dic₁₆₆	C₂×D₄	1	1	yes	characteristic
120	C₂×D₃₃₂	C₂×D₄	1	1	yes	characteristic
121	C₂×C₂²⋊D₈₃	—	2	1	no	—
122	C₂×C₄×D₈₃	—	2	1	no	—
123	C₂×C₄×D₈₃	—	2	1	no	—
124	C₂×C₄×D₈₃	—	2	1	no	—
125	#13050580	—	2	8	no	—
126	#13050577	—	2	8	no	—
127	#13050574	—	2	1	no	—
128	#13050574	—	2	1	no	—
129	#13050574	—	2	2	no	—
130	#13050574	—	2	2	no	—
131	#13050574	—	2	2	no	—
132	#13050574	C₂²×C₄	1	2	yes	—
133	#13050574	C₂²×C₄	1	4	yes	—
134	#13050574	#41	1	2	yes	—
135	#13050573	—	2	4	no	—
136	#13050573	—	2	4	no	—
137	C₂×C₈₃⋊C₈	—	2	1	no	—
138	C₂×C₈₃⋊C₈	—	2	1	no	—
139	C₂×C₈₃⋊C₈	—	2	2	no	—
140	C₂×C₈₃⋊C₈	—	2	2	no	—
141	C₈×D₈₃	—	2	4	no	—
142	C₈×D₈₃	—	2	4	no	—
143	C₄⋊Dic₈₃	C₂×D₄	1	1	yes	characteristic
144	C₄⋊Dic₈₃	C₂×D₄	1	1	yes	characteristic
145	Dic₈₃⋊C₄	—	2	1	no	—
146	Dic₈₃⋊C₄	—	2	1	no	—
147	C₂²⋊Dic₈₃	—	2	1	no	—
148	(C₂×D₈₃)⋊C₄	—	2	1	no	—
149	(C₂×D₈₃)⋊C₄	—	2	1	no	—
150	C₄×Dic₈₃	—	2	1	no	—
151	C₄×Dic₈₃	—	2	1	no	—
152	C₄×Dic₈₃	—	2	1	no	—
153	C₂×Q₈×C₈₃	—	2	2	no	—
154	C₂×Q₈×C₈₃	—	2	2	no	—
155	C₂×Q₈×C₈₃	—	2	2	no	—
156	C₂×Q₈×C₈₃	—	2	2	no	—
157	C₂×Q₈×C₈₃	—	2	2	no	—
158	C₂×Q₈×C₈₃	C₂²×C₄	1	4	yes	—
159	C₂²×C₄×C₈₃	—	2	2	no	—
160	C₂²×C₄×C₈₃	—	2	2	no	—
161	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
162	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
163	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
164	Q₁₆×C₈₃	—	2	4	no	—
165	Q₁₆×C₈₃	—	2	4	no	—
166	C₂×C₈×C₈₃	—	2	1	no	—
167	C₂×C₈×C₈₃	—	2	1	no	—
168	C₂×C₈×C₈₃	C₂²×C₄	1	2	yes	—
169	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
171	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
172	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₈₃	#41	1	2	yes	—
174	C₄⋊C₄×C₈₃	—	2	2	no	—
175	C₄⋊C₄×C₈₃	—	2	2	no	—
176	C₄⋊C₄×C₈₃	—	4	2	no	—
177	C₄⋊C₄×C₈₃	—	4	2	no	—
178	C₄²×C₈₃	—	4	2	no	—
179	C₄²×C₈₃	—	4	2	no	—
180	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
184	C₂³×C₈₃	C₂×#41	1	1	yes	characteristic
185	C₂²×D₈₃	—	2	1	no	—
186	Q₈×C₈₃	—	2	4	no	—
187	Q₈×C₈₃	—	2	4	no	—
188	Q₈×C₈₃	—	4	2	no	—
189	Q₈×C₈₃	—	4	2	no	—
190	C₂×C₄×C₈₃	—	2	2	no	—
191	C₂×C₄×C₈₃	—	2	4	no	—
192	C₂×C₄×C₈₃	—	4	1	no	—
193	C₂×C₄×C₈₃	—	4	2	no	—
194	C₂×C₄×C₈₃	—	4	2	no	—
195	C₂×C₄×C₈₃	—	4	2	no	—
196	C₂×C₄×C₈₃	—	8	2	no	—
197	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
198	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
199	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
200	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
201	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
207	C₂²⋊D₈₃	—	2	2	no	—
208	C₂²⋊D₈₃	—	2	2	no	—
209	C₂×Dic₈₃	—	2	1	no	—
210	C₂×Dic₈₃	—	2	1	no	—
211	C₂×Dic₈₃	—	2	1	no	—
212	D₃₃₂	—	2	1	no	—
213	D₃₃₂	C₄×D₄	1	2	yes	—
214	C₄×D₈₃	—	2	2	no	—
215	C₄×D₈₃	—	2	2	no	—
216	C₄×D₈₃	—	4	2	no	—
217	C₄×D₈₃	—	4	2	no	—
218	Dic₁₆₆	—	2	1	no	—
219	Dic₁₆₆	C₄×D₄	1	2	yes	—
220	C₈×C₈₃	—	2	1	no	—
221	C₈×C₈₃	—	2	1	no	—
222	C₈×C₈₃	C₄×D₄	1	2	yes	—
223	C₈×C₈₃	C₄×D₄	1	2	yes	—
224	C₈₃⋊C₈	—	2	2	no	—
225	C₈₃⋊C₈	—	2	4	no	—
226	C₈₃⋊C₈	—	2	2	no	—
227	C₈₃⋊C₈	—	4	2	no	—
228	C₂²×C₈₃	—	2	1	no	—
229	C₂²×C₈₃	—	2	1	no	—
230	C₂²×C₈₃	C₄×#41	1	1	yes	characteristic
231	C₂²×C₈₃	C₂×#121	1	1	yes	characteristic
232	C₂²×C₈₃	#529	1	1	yes	characteristic
233	C₂×D₈₃	—	2	2	no	—
234	C₂×D₈₃	—	4	1	no	—
235	C₂×D₈₃	—	4	1	no	—
236	C₄×C₈₃	—	2	1	no	—
237	C₄×C₈₃	—	2	1	no	—
238	C₄×C₈₃	—	2	1	no	—
239	C₄×C₈₃	—	4	4	no	—
240	C₄×C₈₃	—	8	2	no	—
241	C₄×C₈₃	#473	1	2	yes	complemented
242	C₄×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
243	C₄×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
244	C₄×C₈₃	#525	1	1	yes	characteristic
245	C₄×C₈₃	#532	1	1	yes	characteristic
246	Dic₈₃	—	2	2	no	—
247	Dic₈₃	—	4	1	no	—
248	Dic₈₃	—	4	1	no	—
249	C₄×#473	—	83	1	no	maximal, Sylow
250	C₂×C₈₃	—	2	1	no	—
251	C₂×C₈₃	—	2	1	no	—
252	C₂×C₈₃	C₄×#121	1	1	yes	characteristic
253	C₂×C₈₃	C₂×#473	1	1	yes	characteristic
254	C₂×C₈₃	#3067	1	1	yes	characteristic
255	D₈₃	—	4	2	no	—
256	C₂×#473	—	83	1	no	—
257	C₄×#137	—	83	2	no	—
258	C₂×C₄×Q₁₆	D₈₃	1	1	yes	characteristic, complemented
259	C₄×#131	—	83	1	no	—
260	#1979	—	83	1	no	—
261	#1952	—	83	1	no	—
262	#1930	—	83	2	no	—
263	#1908	—	83	2	no	—
264	#1816	—	83	1	no	—
265	C₄×#108	—	83	1	no	—
266	C₄×#101	—	83	2	no	—
267	C₈₃	C₄×#473	1	1	yes	characteristic, complemented, Sylow
268	C₂×#137	—	83	2	no	—
269	C₂²×Q₁₆	C₂×D₈₃	1	1	yes	characteristic
270	C₂×#131	—	83	1	no	—
271	C₂×#131	—	83	1	no	—
272	C₄×#41	—	83	1	no	—
273	C₂×C₄×Q₈	C₂×D₈₃	1	2	yes	—
274	#473	—	83	8	no	—
275	#441	—	166	2	no	—
276	#440	—	166	2	no	—
277	C₄×Q₁₆	—	2	1	no	—
278	C₄×Q₁₆	—	2	1	no	—
279	C₄×Q₁₆	—	2	1	no	—
280	C₄×Q₁₆	—	2	1	no	—
281	C₄×Q₁₆	—	166	2	no	—
282	C₄×SD₁₆	—	166	2	no	—
283	C₂×#108	—	83	1	no	—
284	C₂×#108	—	83	1	no	—
285	#428	—	83	2	no	—
286	C₂×#107	C₂×D₈₃	1	1	yes	characteristic
287	#419	—	83	2	no	—
288	#417	—	83	2	no	—
289	C₂×#103	C₂×D₈₃	1	2	yes	—
290	C₂×#101	—	83	2	no	—
291	C₂×#101	—	83	2	no	—
292	#405	—	83	1	no	—
293	#405	—	83	1	no	—
294	#405	—	166	1	no	—
295	#405	—	166	1	no	—
296	C₄×M₁₆	—	83	1	no	—
297	C₄×M₁₆	—	83	2	no	—
298	C₄×M₁₆	—	166	1	no	—
299	C₂×C₄×C₈	—	166	1	no	—
300	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
301	#343	—	83	2	no	—
302	#343	—	83	2	no	—
303	#341	—	83	2	no	—
304	C₂×#41	—	83	1	no	—
305	C₂²×Q₈	C₂²×D₈₃	1	2	yes	—
306	#137	—	83	8	no	—
307	#137	—	166	4	no	—
308	C₂×Q₁₆	—	2	1	no	—
309	C₂×Q₁₆	—	2	1	no	—
310	C₂×Q₁₆	—	2	2	no	—
311	C₂×Q₁₆	—	166	2	no	—
312	C₂×Q₁₆	C₄×D₈₃	1	4	yes	complemented
313	C₂×SD₁₆	—	166	2	no	—
314	#131	—	83	4	no	—
315	#131	—	166	2	no	—
316	#131	—	166	2	no	—
317	#131	—	166	2	no	—
318	C₂×M₁₆	—	83	1	no	—
319	C₂×M₁₆	—	83	1	no	—
320	C₂×M₁₆	—	83	2	no	—
321	C₂×M₁₆	—	83	2	no	—
322	C₂×M₁₆	—	166	1	no	—
323	C₂×M₁₆	—	166	1	no	—
324	C₂²×C₈	—	166	1	no	—
325	C₂²×C₈	—	166	1	no	—
326	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
327	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	2	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	—	83	1	no	—
333	C₄×Q₈	—	83	1	no	—
334	C₄×D₄	—	83	1	no	—
335	C₄×D₄	—	83	1	no	—
336	C₄×D₄	—	166	1	no	—
337	C₄×D₄	—	166	1	no	—
338	#117	—	83	1	no	—
339	#117	—	166	1	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	—	166	1	no	—
344	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
345	#108	—	83	4	no	—
346	#108	—	166	2	no	—
347	#107	—	2	1	no	—
348	#107	—	2	1	no	—
349	#107	—	166	2	no	—
350	#106	—	166	2	no	—
351	#103	—	2	2	no	—
352	#103	—	2	2	no	—
353	#103	—	166	2	no	—
354	#103	—	166	2	no	—
355	#103	—	166	2	no	—
356	#102	—	166	2	no	—
357	#101	—	83	8	no	—
358	#101	—	166	4	no	—
359	#97	—	166	1	no	—
360	#97	—	166	1	no	—
361	#97	—	166	2	no	—
362	#97	—	166	1	no	—
363	C₄×C₈	—	166	1	no	—
364	C₄×C₈	—	166	1	no	—
365	C₄×C₈	—	166	2	no	—
366	C₄×C₈	—	166	1	no	—
367	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
368	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
369	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
370	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
371	#41	—	83	2	no	—
372	#41	—	83	2	no	—
373	#41	—	166	1	no	—
374	#41	—	166	1	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	83	1	no	—
381	C₂×Q₈	C₂×C₄×D₈₃	1	4	yes	—
382	C₂×D₄	—	83	1	no	—
383	C₂×D₄	—	166	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	166	1	no	—
387	C₂²×C₄	—	166	1	no	—
388	C₂²×C₄	—	166	1	no	—
389	C₂²×C₄	#13050589	1	1	yes	characteristic
390	C₂²×C₄	#13050589	1	1	yes	characteristic
391	C₂²×C₄	C₂³×D₈₃	1	1	yes	characteristic
392	Q₁₆	—	2	4	no	—
393	Q₁₆	—	2	4	no	—
394	Q₁₆	—	166	8	no	—
395	SD₁₆	—	166	8	no	—
396	M₁₆	—	83	2	no	—
397	M₁₆	—	83	4	no	—
398	M₁₆	—	83	2	no	—
399	M₁₆	—	166	4	no	—
400	M₁₆	—	166	2	no	—
401	M₁₆	—	166	2	no	—
402	M₁₆	—	166	1	no	—
403	M₁₆	—	166	2	no	—
404	M₁₆	—	166	1	no	—
405	M₁₆	—	166	4	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	166	4	no	—
409	C₂×C₈	—	166	2	no	—
410	C₂×C₈	—	166	2	no	—
411	C₂×C₈	—	166	1	no	—
412	C₂×C₈	—	166	1	no	—
413	C₂×C₈	—	166	4	no	—
414	C₂×C₈	C₂×C₄×D₈₃	1	2	yes	—
415	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
416	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
417	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
418	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
419	C₂×C₈	#13050590	1	2	yes	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	4	2	no	—
423	C₄⋊C₄	—	4	2	no	—
424	C₄⋊C₄	—	83	1	no	—
425	C₄⋊C₄	—	83	1	no	—
426	C₄⋊C₄	—	166	1	no	—
427	C₄⋊C₄	—	166	1	no	—
428	C₂²⋊C₄	—	166	1	no	—
429	C₂²⋊C₄	—	166	1	no	—
430	C₂²⋊C₄	—	166	1	no	—
431	C₄²	—	4	2	no	—
432	C₄²	—	4	2	no	—
433	C₄²	—	166	1	no	—
434	C₄²	—	166	1	no	—
435	C₄²	—	166	1	no	—
436	C₄²	D₄×D₈₃	1	1	yes	characteristic
437	C₄²	D₄×D₈₃	1	1	yes	characteristic
438	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
439	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
440	C₂³	—	166	1	no	—
441	C₂³	C₂×#13050589	1	1	yes	characteristic
442	Q₈	—	2	4	no	—
443	Q₈	—	2	4	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	83	2	no	—
447	Q₈	—	166	1	no	—
448	D₄	—	83	2	no	—
449	D₄	—	166	2	no	—
450	D₄	—	166	2	no	—
451	D₄	—	166	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	8	2	no	—
459	C₂×C₄	—	332	2	no	—
460	C₂×C₄	—	332	2	no	—
461	C₂×C₄	—	166	1	no	—
462	C₂×C₄	—	166	1	no	—
463	C₂×C₄	—	166	1	no	—
464	C₂×C₄	—	166	2	no	—
465	C₂×C₄	—	166	2	no	—
466	C₂×C₄	#14581763	1	1	yes	characteristic
467	C₂×C₄	#14581763	1	1	yes	characteristic
468	C₂×C₄	#14581763	1	1	yes	characteristic
469	C₂×C₄	#14581763	1	1	yes	characteristic
470	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
471	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₂²⋊D₈₃	1	1	yes	characteristic
473	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
474	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
475	C₂×C₄	C₂×#13050590	1	1	yes	characteristic
476	C₈	—	2	1	no	—
477	C₈	—	2	1	no	—
478	C₈	—	332	2	no	—
479	C₈	—	166	4	no	—
480	C₈	—	166	2	no	—
481	C₈	—	166	2	no	—
482	C₈	C₄×C₂²⋊D₈₃	1	2	yes	—
483	C₈	C₄×C₂²⋊D₈₃	1	2	yes	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	332	1	no	—
487	C₂²	—	332	1	no	—
488	C₂²	—	166	2	no	—
489	C₂²	C₄×#13050589	1	1	yes	characteristic
490	C₂²	C₂×#14581763	1	1	yes	characteristic
491	C₂²	#19128233	1	1	yes	characteristic
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	4	4	no	—
496	C₄	—	8	2	no	—
497	C₄	—	332	1	no	—
498	C₄	—	332	1	no	—
499	C₄	—	166	2	no	—
500	C₄	#19127973	1	2	yes	direct product factor
501	C₄	C₄×D₄×D₈₃	1	1	yes	characteristic
502	C₄	C₂×C₄×C₂²⋊D₈₃	1	1	yes	characteristic
503	C₄	#19128208	1	1	yes	characteristic
504	C₄	#19128248	1	1	yes	characteristic
505	C₂	—	2	1	no	—
506	C₂	—	2	1	no	—
507	C₂	—	332	2	no	—
508	C₂	C₄×#14581763	1	1	yes	characteristic
509	C₂	C₂×#19127973	1	1	yes	characteristic
510	C₂	#24917179	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14581763
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₃
Fitting	C₂×C₄×Q₁₆×C₈₃	C₂
socle	C₂²×C₈₃	C₂×#121
prime radical	C₂×#13050590	C₂³
cosocle	C₂²×C₄×C₈₃	C₂⁴
hypercenter	C₂×C₄×Q₁₆	D₈₃
hypocenter	C₈₃	C₄×#473
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
4. #24908379	C₂	semidirect
5. #24908246	C₂	semidirect
6. #24908115	C₂	semidirect
9. C₄×#14581728	C₂	semidirect
10. C₄×#14581711	C₂	semidirect
11. C₂×C₄×Q₁₆×C₈₃	C₂	semidirect
16. #19127973	C₄	direct (N × H)
75. #14581728	C₂×C₄	semidirect
83. #14581711	C₂×C₄	semidirect
96. C₂×Q₁₆×C₈₃	C₂×C₄	semidirect
241. C₄×C₈₃	#473	semidirect
258. C₂×C₄×Q₁₆	D₈₃	semidirect
267. C₈₃	C₄×#473	semidirect
312. C₂×Q₁₆	C₄×D₈₃	semidirect
500. C₄	#19127973	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#19127973	2
C₄×#14581823	2
C₄×#14581798	2
#24908379	2
#24908246	2
#24908115	2
#24907981	2
#24907528	2
C₄×#14581728	2
C₄×#14581711	2
C₂×C₄×Q₁₆×C₈₃	2
C₄×#473	83

Subgroups — C4×#19127973 #35411289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19127973 #35411289