Subgroups — #35374513

Order 21248.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24917535	C₂	1	1	yes	maximal, characteristic
2	#24916571	C₂	1	1	yes	maximal, characteristic
3	#24916557	C₂	1	1	yes	maximal, characteristic, complemented
4	#24906336	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906322	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906315	C₂	1	1	yes	maximal, characteristic, complemented
7	#24906301	C₂	1	1	yes	maximal, characteristic, complemented
8	#24906283	C₂	1	1	yes	maximal, characteristic, complemented
9	#24906277	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×Dic₃₃₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#13050579	C₂	1	1	yes	maximal, characteristic, complemented
12	#24906248	C₂	1	1	yes	maximal, characteristic, complemented
13	#24905898	C₂	1	1	yes	maximal, characteristic
14	#24905867	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₃×#1454	C₂	1	1	yes	maximal, characteristic, complemented
16	#19128258	C₂²	1	1	yes	characteristic
17	C₄×#13050590	C₂²	1	1	yes	characteristic
18	#19128043	C₄	1	1	yes	characteristic
19	#19128043	C₄	1	1	yes	characteristic
20	#19127987	C₄	1	1	yes	characteristic
21	#19127982	C₄	1	1	yes	characteristic
22	#19127912	C₄	1	1	yes	characteristic
23	#19127907	C₄	1	1	yes	characteristic
24	#19127865	C₄	1	1	yes	characteristic
25	#19127865	C₄	1	1	yes	characteristic
26	#19127831	C₂²	1	1	yes	characteristic
27	#19127831	C₂²	1	1	yes	characteristic
28	#19127830	—	2	1	no	—
29	#19127830	—	2	1	no	—
30	C₈×Dic₁₆₆	C₂²	1	1	yes	characteristic
31	C₈×Dic₁₆₆	C₂²	1	1	yes	characteristic
32	C₈×Dic₁₆₆	C₂²	1	1	yes	characteristic
33	C₈×Dic₁₆₆	C₂²	1	1	yes	characteristic
34	C₄×Dic₃₃₂	C₂²	1	1	yes	characteristic
35	C₄×Dic₃₃₂	C₂²	1	1	yes	characteristic
36	C₄×#13050579	C₂²	1	1	yes	characteristic
37	C₄×#13050579	C₂²	1	1	yes	characteristic
38	C₈×D₃₃₂	C₂²	1	1	yes	characteristic
39	C₈×D₃₃₂	C₂²	1	1	yes	characteristic
40	(C₂²⋊D₈₃)⋊C₈	—	2	1	no	—
41	(C₂²⋊D₈₃)⋊C₈	—	2	1	no	—
42	#19127759	—	2	1	no	—
43	#19127759	—	2	1	no	—
44	#19127758	C₂²	1	1	yes	characteristic
45	#19127753	—	2	1	no	—
46	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
47	C₄⋊C₈×D₈₃	—	2	1	no	—
48	#19127454	C₂²	1	1	yes	characteristic
49	#19127454	C₂²	1	1	yes	characteristic
50	#19127452	C₂²	1	1	yes	characteristic
51	#19127452	C₂²	1	1	yes	characteristic
52	#19127433	C₂²	1	1	yes	characteristic
53	#19127433	C₂²	1	1	yes	characteristic
54	#19127433	C₂²	1	1	yes	characteristic
55	#19127433	C₂²	1	1	yes	characteristic
56	#19127433	C₂²	1	1	yes	characteristic
57	#19127433	C₂²	1	1	yes	characteristic
58	#19127430	C₂²	1	1	yes	characteristic
59	#19127430	C₂²	1	1	yes	characteristic
60	#431×C₈₃	C₂²	1	1	yes	characteristic
61	#431×C₈₃	C₂²	1	1	yes	characteristic
62	#431×C₈₃	C₂²	1	1	yes	characteristic
63	#322×C₈₃	C₂²	1	1	yes	characteristic
64	#322×C₈₃	C₂²	1	1	yes	characteristic
65	#322×C₈₃	C₂²	1	1	yes	characteristic
66	C₈²×C₈₃	C₂²	1	1	yes	characteristic
67	C₂×#13050590	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₃₃₂	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₃₃₂	C₂×C₄	1	1	yes	characteristic
70	C₂×#13050579	C₂×C₄	1	1	yes	characteristic
71	C₂×#13050579	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₈₃⋊C₈	—	2	1	no	—
73	C₂×C₈×D₈₃	—	2	1	no	—
74	C₂×C₈×D₈₃	—	2	1	no	—
75	#14581792	C₂×C₄	1	1	yes	characteristic
76	#14581792	C₂×C₄	1	1	yes	characteristic
77	#14581784	—	2	1	no	—
78	#14581771	—	2	1	no	—
79	#14581771	C₂×C₄	1	1	yes	characteristic
80	#14581771	C₂×C₄	1	1	yes	characteristic
81	C₄×Dic₁₆₆	—	2	1	no	—
82	C₄×Dic₁₆₆	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
84	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
85	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
86	C₄×D₃₃₂	C₂×C₄	1	1	yes	characteristic
87	C₄×D₃₃₂	C₂³	1	1	yes	characteristic
88	C₄×C₂²⋊D₈₃	—	2	1	no	—
89	C₄×C₂²⋊D₈₃	—	2	1	no	—
90	#14581751	—	2	1	no	—
91	#14581751	C₂×C₄	1	1	yes	characteristic
92	#14581749	—	2	1	no	—
93	C₄²×D₈₃	—	2	1	no	—
94	#14581726	C₂×C₄	1	1	yes	characteristic
95	#14581726	C₂×C₄	1	1	yes	characteristic
96	#14581724	C₂×C₄	1	1	yes	characteristic
97	#14581724	C₂×C₄	1	1	yes	characteristic
98	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
99	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
100	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
101	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
102	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
103	Dic₈₃⋊C₈	—	2	1	no	—
104	Dic₈₃⋊C₈	—	2	1	no	—
105	Dic₈₃⋊C₈	—	2	1	no	—
106	Dic₈₃⋊C₈	—	2	1	no	—
107	Dic₈₃⋊C₈	—	2	1	no	—
108	Dic₈₃⋊C₈	—	2	1	no	—
109	#14581717	C₂×C₄	1	1	yes	characteristic
110	#14581717	C₂×C₄	1	1	yes	characteristic
111	#14581717	C₂×C₄	1	1	yes	characteristic
112	#14581717	C₂×C₄	1	1	yes	characteristic
113	#14581717	C₂×C₄	1	1	yes	characteristic
114	#14581717	C₂×C₄	1	1	yes	characteristic
115	#14581714	C₂×C₄	1	1	yes	characteristic
116	#14581714	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
118	(C₂×D₈₃)⋊C₈	—	2	1	no	—
119	(C₂×D₈₃)⋊C₈	—	2	1	no	—
120	#14581703	—	2	1	no	—
121	#14581702	—	2	1	no	—
122	#14581702	—	2	1	no	—
123	C₈×Dic₈₃	—	2	1	no	—
124	C₈×Dic₈₃	—	2	1	no	—
125	C₈×Dic₈₃	—	2	1	no	—
126	C₈×Dic₈₃	—	2	1	no	—
127	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
128	C₄⋊C₈×C₈₃	—	2	1	no	—
129	C₄⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
130	C₄⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
131	C₄⋊C₈×C₈₃	D₄	1	1	yes	characteristic
132	C₄⋊C₈×C₈₃	D₄	1	1	yes	characteristic
133	C₂²⋊C₈×C₈₃	—	2	1	no	—
134	C₂²⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
135	C₂²⋊C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
136	C₂²⋊C₈×C₈₃	D₄	1	1	yes	characteristic
137	C₂²⋊C₈×C₈₃	D₄	1	1	yes	characteristic
138	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
144	#13050590	—	2	2	no	—
145	#13050590	—	2	2	no	—
146	C₂×Dic₁₆₆	—	2	1	no	—
147	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₁₆₆	C₂²×C₄	1	1	yes	characteristic
150	C₂×D₃₃₂	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₂²⋊D₈₃	—	2	1	no	—
152	C₂×C₄×D₈₃	—	2	1	no	—
153	C₂×C₄×D₈₃	—	2	1	no	—
154	C₂×C₄×D₈₃	—	2	1	no	—
155	Dic₃₃₂	—	2	2	no	—
156	Dic₃₃₂	—	2	2	no	—
157	#13050579	—	2	2	no	—
158	#13050579	—	2	2	no	—
159	C₂×C₈₃⋊C₈	—	2	1	no	—
160	C₂×C₈₃⋊C₈	—	2	1	no	—
161	C₂×C₈₃⋊C₈	—	2	1	no	—
162	C₂×C₈₃⋊C₈	—	2	1	no	—
163	C₂×C₈₃⋊C₈	—	8	1	no	—
164	C₈×D₈₃	—	8	1	no	—
165	C₈×D₈₃	—	8	1	no	—
166	C₄⋊Dic₈₃	—	2	1	no	—
167	C₄⋊Dic₈₃	—	2	1	no	—
168	C₄⋊Dic₈₃	—	2	1	no	—
169	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
170	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
171	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
172	C₄⋊Dic₈₃	C₂²×C₄	1	1	yes	characteristic
173	Dic₈₃⋊C₄	—	2	1	no	—
174	Dic₈₃⋊C₄	—	2	1	no	—
175	Dic₈₃⋊C₄	—	2	1	no	—
176	Dic₈₃⋊C₄	—	2	1	no	—
177	Dic₈₃⋊C₄	—	2	1	no	—
178	Dic₈₃⋊C₄	—	2	1	no	—
179	C₂²⋊Dic₈₃	—	2	1	no	—
180	C₂²⋊Dic₈₃	—	2	1	no	—
181	C₂²⋊Dic₈₃	—	2	1	no	—
182	(C₂×D₈₃)⋊C₄	—	2	1	no	—
183	(C₂×D₈₃)⋊C₄	—	2	1	no	—
184	C₄×Dic₈₃	—	2	1	no	—
185	C₄×Dic₈₃	—	2	1	no	—
186	C₄×Dic₈₃	—	2	1	no	—
187	C₄×Dic₈₃	—	2	1	no	—
188	C₄×Dic₈₃	—	2	1	no	—
189	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
192	C₂×C₈×C₈₃	—	2	1	no	—
193	C₂×C₈×C₈₃	—	2	1	no	—
194	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
199	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
201	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
203	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₈₃	#41	1	1	yes	characteristic
205	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
206	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
207	C₂²×D₈₃	—	2	1	no	—
208	C₂×C₄×C₈₃	—	2	1	no	—
209	C₂×C₄×C₈₃	—	2	1	no	—
210	C₂×C₄×C₈₃	—	2	1	no	—
211	C₂×C₄×C₈₃	—	2	1	no	—
212	C₂×C₄×C₈₃	—	4	1	no	—
213	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
219	C₂²⋊D₈₃	—	2	4	no	—
220	C₂×Dic₈₃	—	2	1	no	—
221	C₂×Dic₈₃	—	2	1	no	—
222	C₂×Dic₈₃	—	2	1	no	—
223	C₂×Dic₈₃	—	2	1	no	—
224	C₂×Dic₈₃	—	2	1	no	—
225	C₂×Dic₈₃	—	2	1	no	—
226	C₂×Dic₈₃	—	2	1	no	—
227	D₃₃₂	—	2	1	no	—
228	D₃₃₂	#131	1	2	yes	—
229	C₄×D₈₃	—	2	4	no	—
230	C₄×D₈₃	—	4	1	no	—
231	C₄×D₈₃	—	4	1	no	—
232	C₄×D₈₃	—	8	1	no	—
233	Dic₁₆₆	—	2	1	no	—
234	Dic₁₆₆	—	2	1	no	—
235	Dic₁₆₆	—	2	1	no	—
236	Dic₁₆₆	—	2	1	no	—
237	Dic₁₆₆	—	2	1	no	—
238	Dic₁₆₆	—	8	1	no	—
239	Dic₁₆₆	#131	1	2	yes	—
240	C₈×C₈₃	—	2	1	no	—
241	C₈×C₈₃	—	2	1	no	—
242	C₈×C₈₃	—	2	1	no	—
243	C₈×C₈₃	—	2	1	no	—
244	C₈×C₈₃	—	2	1	no	—
245	C₈×C₈₃	—	2	1	no	—
246	C₈×C₈₃	—	2	1	no	—
247	C₈×C₈₃	—	2	1	no	—
248	C₈×C₈₃	—	4	1	no	—
249	C₈×C₈₃	—	4	1	no	—
250	C₈₃⋊C₈	—	4	1	no	—
251	C₈₃⋊C₈	—	4	1	no	—
252	C₈₃⋊C₈	—	4	1	no	—
253	C₈₃⋊C₈	—	4	1	no	—
254	C₂²×C₈₃	—	2	1	no	—
255	C₂²×C₈₃	—	2	1	no	—
256	C₂²×C₈₃	—	2	1	no	—
257	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
258	C₂×D₈₃	—	2	2	no	—
259	C₂×D₈₃	—	4	1	no	—
260	C₂×D₈₃	—	4	1	no	—
261	C₄×C₈₃	—	2	1	no	—
262	C₄×C₈₃	—	2	1	no	—
263	C₄×C₈₃	—	2	1	no	—
264	C₄×C₈₃	—	2	1	no	—
265	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
266	C₄×C₈₃	C₂×#131	1	1	yes	characteristic
267	C₄×C₈₃	#577	1	1	yes	characteristic
268	C₄×C₈₃	#578	1	1	yes	characteristic
269	Dic₈₃	—	2	2	no	—
270	Dic₈₃	—	4	1	no	—
271	Dic₈₃	—	4	1	no	—
272	Dic₈₃	—	4	1	no	—
273	Dic₈₃	—	4	1	no	—
274	Dic₈₃	—	4	1	no	—
275	Dic₈₃	—	4	1	no	—
276	#17921	—	83	1	no	maximal, Sylow
277	C₂×C₈₃	—	4	1	no	—
278	C₂×C₈₃	#2929	1	1	yes	characteristic
279	C₂×C₈₃	#2947	1	1	yes	characteristic
280	C₂×C₈₃	#2957	1	1	yes	characteristic
281	D₈₃	—	4	2	no	—
282	#3107	—	83	1	no	—
283	#2988	—	83	1	no	—
284	#2985	—	83	1	no	—
285	#1587	—	83	1	no	—
286	#1585	—	83	1	no	—
287	#1584	—	83	1	no	—
288	#1582	—	83	1	no	—
289	#1579	—	83	1	no	—
290	SD₁₆⋊C₈	—	83	1	no	—
291	C₈×Q₁₆	—	83	1	no	—
292	C₈×SD₁₆	—	83	1	no	—
293	#1573	—	83	1	no	—
294	#1488	—	83	1	no	—
295	#1481	—	83	1	no	—
296	#1454	D₈₃	1	1	yes	characteristic, complemented
297	C₈₃	#17921	1	1	yes	characteristic, complemented, Sylow
298	#533	—	83	1	no	—
299	C₄×#41	—	83	1	no	—
300	#485	—	83	1	no	—
301	#485	—	83	1	no	—
302	#475	—	83	1	no	—
303	#474	—	83	1	no	—
304	#462	—	83	1	no	—
305	#461	—	83	1	no	—
306	#452	—	83	1	no	—
307	#452	—	83	1	no	—
308	#446	—	83	1	no	—
309	#446	—	83	1	no	—
310	#446	—	166	1	no	—
311	#446	—	166	1	no	—
312	C₈×Q₈	—	83	1	no	—
313	C₈×Q₈	—	83	1	no	—
314	C₈×Q₈	—	83	1	no	—
315	C₈×Q₈	—	83	1	no	—
316	C₄×Q₁₆	—	83	1	no	—
317	C₄×Q₁₆	—	83	1	no	—
318	C₄×SD₁₆	—	83	1	no	—
319	C₄×SD₁₆	—	83	1	no	—
320	C₈×D₄	—	83	1	no	—
321	C₈×D₄	—	83	1	no	—
322	C₈×D₄	—	166	1	no	—
323	C₈×D₄	—	166	1	no	—
324	#433	—	166	1	no	—
325	#433	—	166	1	no	—
326	#432	—	83	1	no	—
327	#431	—	166	1	no	—
328	#431	C₂×D₈₃	1	1	yes	characteristic
329	#431	C₂×D₈₃	1	1	yes	characteristic
330	#431	C₂×D₈₃	1	1	yes	characteristic
331	C₂×C₄⋊C₈	—	83	1	no	—
332	C₂×C₄⋊C₈	—	166	1	no	—
333	#335	—	83	1	no	—
334	#335	—	83	1	no	—
335	#334	—	83	1	no	—
336	#334	—	83	1	no	—
337	Q₈⋊C₈	—	83	1	no	—
338	Q₈⋊C₈	—	83	1	no	—
339	Q₈⋊C₈	—	83	1	no	—
340	Q₈⋊C₈	—	83	1	no	—
341	Q₈⋊C₈	—	83	1	no	—
342	Q₈⋊C₈	—	83	1	no	—
343	D₄⋊C₈	—	83	1	no	—
344	D₄⋊C₈	—	83	1	no	—
345	#322	C₂×D₈₃	1	1	yes	characteristic
346	#322	C₂×D₈₃	1	1	yes	characteristic
347	#322	C₂×D₈₃	1	1	yes	characteristic
348	C₈²	C₂×D₈₃	1	1	yes	characteristic
349	C₂×#41	—	83	1	no	—
350	C₂×Q₁₆	—	83	1	no	—
351	C₂×Q₁₆	—	83	1	no	—
352	C₂×SD₁₆	—	83	1	no	—
353	C₂×SD₁₆	—	83	1	no	—
354	C₂²×C₈	—	166	1	no	—
355	C₂²×C₈	—	166	1	no	—
356	C₂²×C₈	—	166	1	no	—
357	C₄⋊Q₈	—	83	1	no	—
358	C₄⋊Q₈	—	83	1	no	—
359	#125	—	166	1	no	—
360	C₂²⋊Q₈	—	83	1	no	—
361	C₂²⋊Q₈	—	83	1	no	—
362	C₂²⋊Q₈	—	166	1	no	—
363	C₄×Q₈	—	83	1	no	—
364	C₄×Q₈	—	83	1	no	—
365	C₄×Q₈	—	83	1	no	—
366	C₄×Q₈	—	83	1	no	—
367	C₄×Q₈	—	166	1	no	—
368	C₄×D₄	—	83	1	no	—
369	C₄×D₄	—	83	1	no	—
370	C₄×D₄	—	166	1	no	—
371	C₄×D₄	—	166	1	no	—
372	#117	—	83	1	no	—
373	#117	—	166	1	no	—
374	#117	—	166	1	no	—
375	C₂×C₄²	—	166	1	no	—
376	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
377	#107	—	83	1	no	—
378	#107	—	83	1	no	—
379	#106	—	83	1	no	—
380	#106	—	83	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	83	1	no	—
383	C₄⋊C₈	—	83	1	no	—
384	C₄⋊C₈	—	83	1	no	—
385	C₄⋊C₈	—	83	1	no	—
386	C₄⋊C₈	—	166	1	no	—
387	C₄⋊C₈	—	166	1	no	—
388	C₄⋊C₈	—	166	1	no	—
389	C₄⋊C₈	—	166	1	no	—
390	C₄⋊C₈	—	166	1	no	—
391	C₄⋊C₈	—	166	1	no	—
392	C₄⋊C₈	—	166	1	no	—
393	C₄⋊C₈	C₄×D₈₃	1	1	yes	characteristic
394	C₄⋊C₈	C₄×D₈₃	1	1	yes	characteristic
395	C₄⋊C₈	D₃₃₂	1	1	yes	characteristic
396	C₄⋊C₈	D₃₃₂	1	1	yes	characteristic
397	#103	—	83	1	no	—
398	#103	—	83	1	no	—
399	#103	—	83	1	no	—
400	#103	—	83	1	no	—
401	#103	—	83	1	no	—
402	#103	—	83	1	no	—
403	#102	—	83	1	no	—
404	#102	—	83	1	no	—
405	C₂²⋊C₈	—	2	1	no	—
406	C₂²⋊C₈	—	166	1	no	—
407	C₂²⋊C₈	—	166	1	no	—
408	C₂²⋊C₈	—	166	1	no	—
409	C₂²⋊C₈	C₄×D₈₃	1	1	yes	characteristic
410	C₂²⋊C₈	C₄×D₈₃	1	1	yes	characteristic
411	C₂²⋊C₈	D₃₃₂	1	1	yes	characteristic
412	C₂²⋊C₈	D₃₃₂	1	1	yes	characteristic
413	#97	—	166	1	no	—
414	#97	—	166	1	no	—
415	#97	—	166	1	no	—
416	C₄×C₈	—	166	1	no	—
417	C₄×C₈	—	166	1	no	—
418	C₄×C₈	—	166	1	no	—
419	C₄×C₈	—	166	1	no	—
420	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
421	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
422	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
423	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
424	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
425	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
426	#41	—	166	2	no	—
427	#41	—	166	2	no	—
428	C₂×Q₈	—	83	1	no	—
429	C₂×Q₈	—	83	1	no	—
430	C₂×Q₈	—	83	1	no	—
431	C₂×Q₈	—	166	1	no	—
432	C₂×D₄	—	83	1	no	—
433	C₂×D₄	—	166	1	no	—
434	C₂²×C₄	—	166	1	no	—
435	C₂²×C₄	—	166	1	no	—
436	C₂²×C₄	—	166	1	no	—
437	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₃₃₂	1	1	yes	characteristic
439	C₂²×C₄	#13050590	1	1	yes	characteristic
440	Q₁₆	—	166	2	no	—
441	Q₁₆	—	166	2	no	—
442	SD₁₆	—	166	2	no	—
443	SD₁₆	—	166	2	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	664	1	no	—
447	C₂×C₈	—	664	1	no	—
448	C₂×C₈	—	664	1	no	—
449	C₂×C₈	—	166	1	no	—
450	C₂×C₈	—	166	1	no	—
451	C₂×C₈	—	166	1	no	—
452	C₂×C₈	—	166	1	no	—
453	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
454	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
455	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
456	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
457	C₂×C₈	C₂×D₃₃₂	1	1	yes	characteristic
458	C₂×C₈	C₂×D₃₃₂	1	1	yes	characteristic
459	C₂×C₈	C₂×D₃₃₂	1	1	yes	characteristic
460	C₂×C₈	C₂×D₃₃₂	1	1	yes	characteristic
461	C₄⋊C₄	—	83	1	no	—
462	C₄⋊C₄	—	83	1	no	—
463	C₄⋊C₄	—	83	1	no	—
464	C₄⋊C₄	—	83	1	no	—
465	C₄⋊C₄	—	166	1	no	—
466	C₄⋊C₄	—	166	1	no	—
467	C₄⋊C₄	—	166	1	no	—
468	C₄⋊C₄	—	166	1	no	—
469	C₄⋊C₄	—	166	1	no	—
470	C₄⋊C₄	—	166	1	no	—
471	C₄⋊C₄	—	166	1	no	—
472	C₄⋊C₄	—	166	1	no	—
473	C₄⋊C₄	—	166	1	no	—
474	C₂²⋊C₄	—	166	1	no	—
475	C₂²⋊C₄	—	166	1	no	—
476	C₂²⋊C₄	—	166	1	no	—
477	C₂²⋊C₄	—	166	1	no	—
478	C₂²⋊C₄	—	166	1	no	—
479	C₄²	—	166	1	no	—
480	C₄²	—	166	1	no	—
481	C₄²	—	166	1	no	—
482	C₄²	—	166	1	no	—
483	C₄²	—	166	1	no	—
484	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
485	C₄²	C₂×D₃₃₂	1	1	yes	characteristic
486	C₄²	#13050590	1	1	yes	characteristic
487	C₄²	C₂³×D₈₃	1	1	yes	characteristic
488	C₂³	—	166	1	no	—
489	C₂³	C₄×D₃₃₂	1	1	yes	characteristic
490	Q₈	—	83	2	no	—
491	Q₈	—	664	1	no	—
492	Q₈	—	166	1	no	—
493	Q₈	—	166	1	no	—
494	Q₈	—	166	1	no	—
495	Q₈	—	166	1	no	—
496	Q₈	—	166	1	no	—
497	D₄	—	83	2	no	—
498	D₄	—	166	4	no	—
499	D₄	—	166	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	332	1	no	—
506	C₂×C₄	—	332	1	no	—
507	C₂×C₄	—	664	1	no	—
508	C₂×C₄	—	166	4	no	—
509	C₂×C₄	—	166	1	no	—
510	C₂×C₄	—	166	1	no	—
511	C₂×C₄	—	166	1	no	—
512	C₂×C₄	—	166	1	no	—
513	C₂×C₄	—	166	1	no	—
514	C₂×C₄	—	166	1	no	—
515	C₂×C₄	—	166	1	no	—
516	C₂×C₄	C₄×D₃₃₂	1	1	yes	characteristic
517	C₂×C₄	C₄×D₃₃₂	1	1	yes	characteristic
518	C₂×C₄	C₄×D₃₃₂	1	1	yes	characteristic
519	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₃₃₂	1	1	yes	characteristic
521	C₂×C₄	C₂×#13050590	1	1	yes	characteristic
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	2	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	—	332	1	no	—
533	C₈	—	332	1	no	—
534	C₈	—	332	1	no	—
535	C₈	—	332	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	332	1	no	—
540	C₂²	—	332	1	no	—
541	C₂²	—	166	2	no	—
542	C₂²	C₂×C₄×D₃₃₂	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	332	1	no	—
548	C₄	—	332	1	no	—
549	C₄	—	332	1	no	—
550	C₄	—	332	1	no	—
551	C₄	—	332	1	no	—
552	C₄	—	332	1	no	—
553	C₄	—	166	2	no	—
554	C₄	#131×D₈₃	1	1	yes	characteristic
555	C₄	#131×D₈₃	1	1	yes	characteristic
556	C₄	#19128513	1	1	yes	characteristic
557	C₄	#19128518	1	1	yes	characteristic
558	C₂	—	4	1	no	—
559	C₂	—	332	2	no	—
560	C₂	#24916159	1	1	yes	characteristic
561	C₂	#24916308	1	1	yes	characteristic
562	C₂	#24916381	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₃₂
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₄²	C₂³×D₈₃
Fitting	C₈₃×#1454	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	C₂×#13050590	C₂×C₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#1454	D₈₃
hypocenter	C₈₃	#17921
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #1454

Complements

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

N	H ≅ G/N	type
3. #24916557	C₂	semidirect
4. #24906336	C₂	semidirect
5. #24906322	C₂	semidirect
6. #24906315	C₂	semidirect
7. #24906301	C₂	semidirect
8. #24906283	C₂	semidirect
9. #24906277	C₂	semidirect
10. C₈×Dic₃₃₂	C₂	semidirect
11. C₈×#13050579	C₂	semidirect
12. #24906248	C₂	semidirect
14. #24905867	C₂	semidirect
15. C₈₃×#1454	C₂	semidirect
296. #1454	D₈₃	semidirect
297. C₈₃	#17921	semidirect

Maximal subgroups

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

subgroup	index
#24917535	2
#24916571	2
#24916557	2
#24906336	2
#24906322	2
#24906315	2
#24906301	2
#24906283	2
#24906277	2
C₈×Dic₃₃₂	2
C₈×#13050579	2
#24906248	2
#24905898	2
#24905867	2
C₈₃×#1454	2
#17921	83