Subgroups — #35374372

Order 21248.

720 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24917506	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₃₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#24906325	C₂	1	2	yes	maximal, complemented
4	#24906318	C₂	1	2	yes	maximal, complemented
5	C₈×#13050577	C₂	1	2	yes	maximal, complemented
6	C₈×#13050575	C₂	1	2	yes	maximal, complemented
7	#24906249	C₂	1	1	yes	maximal, characteristic, complemented
8	#24905905	C₂	1	1	yes	maximal, characteristic, complemented
9	#24905876	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#13050574	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₈₃	—	2	1	no	—
13	C₂×C₄×D₃₃₂	C₂²	1	1	yes	characteristic
14	#19128034	C₄	1	1	yes	characteristic
15	#19128017	C₄	1	1	yes	characteristic
16	#19127998	C₄	1	2	yes	—
17	#19127913	C₄	1	2	yes	—
18	#19127851	C₄	1	1	yes	characteristic
19	#19127834	C₄	1	1	yes	characteristic
20	C₄×#13050577	C₂²	1	2	yes	—
21	C₄×#13050575	C₂²	1	2	yes	—
22	C₈×D₃₃₂	—	2	1	no	—
23	C₈×D₃₃₂	—	2	1	no	—
24	C₈×D₃₃₂	C₂²	1	2	yes	—
25	C₈×D₃₃₂	C₂²	1	2	yes	—
26	#19127754	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×(C₂×D₈₃)⋊C₈	—	2	1	no	—
29	C₄×#13050574	C₂²	1	1	yes	characteristic
30	#19127453	C₂²	1	2	yes	complemented
31	#19127451	C₂²	1	2	yes	complemented
32	Q₈⋊(C₈₃⋊C₈)	C₂²	1	2	yes	complemented
33	D₄⋊(C₈₃⋊C₈)	C₂²	1	2	yes	complemented
34	#19127428	C₂²	1	2	yes	—
35	#19127428	C₂²	1	2	yes	—
36	#19127423	C₂²	1	2	yes	complemented
37	C₈×C₈₃⋊C₈	C₂²	1	2	yes	complemented
38	#529×C₈₃	C₂²	1	1	yes	characteristic
39	#446×C₈₃	C₂²	1	1	yes	characteristic, complemented
40	C₈×Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
41	#436×C₈₃	C₂²	1	1	yes	characteristic, complemented
42	#435×C₈₃	—	2	1	no	—
43	C₈×D₄×C₈₃	—	2	1	no	—
44	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
45	#433×C₈₃	—	2	1	no	—
46	#432×C₈₃	C₂²	1	1	yes	characteristic
47	#405×C₈₃	—	2	1	no	—
48	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
49	C₂²×D₃₃₂	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₈₃	—	2	1	no	—
51	C₂×#13050577	C₂×C₄	1	2	yes	—
52	C₂×#13050575	C₂×C₄	1	2	yes	—
53	C₂×#13050574	—	2	1	no	—
54	C₂²×C₈₃⋊C₈	—	2	1	no	—
55	C₂×C₈×D₈₃	—	2	2	no	—
56	C₂×C₈×D₈₃	—	2	2	no	—
57	C₂×C₈×D₈₃	—	4	4	no	—
58	C₄×D₃₃₂	—	2	1	no	—
59	C₄×D₃₃₂	—	2	1	no	—
60	C₄×D₃₃₂	C₂×C₄	1	2	yes	—
61	C₄×D₃₃₂	C₂³	1	2	yes	—
62	C₂×C₄⋊Dic₈₃	C₂×C₄	1	1	yes	characteristic
63	C₂×(C₂×D₈₃)⋊C₄	—	2	1	no	—
64	#14581725	C₂×C₄	1	2	yes	—
65	#14581723	C₂×C₄	1	2	yes	—
66	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
67	C₄⋊(C₈₃⋊C₈)	C₂×C₄	1	2	yes	—
68	C₄⋊(C₈₃⋊C₈)	C₂³	1	2	yes	—
69	#14581716	C₂×C₄	1	2	yes	—
70	#14581713	C₂×C₄	1	2	yes	—
71	#14581712	C₂×C₄	1	2	yes	—
72	#14581712	C₂×C₄	1	2	yes	—
73	C₂²⋊(C₈₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
74	C₂²⋊(C₈₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
75	(C₂×D₈₃)⋊C₈	—	2	2	no	—
76	(C₂×D₈₃)⋊C₈	—	2	2	no	—
77	#14581703	—	2	1	no	—
78	C₄×C₈₃⋊C₈	C₂³	1	2	yes	—
79	C₄×C₈₃⋊C₈	C₂³	1	2	yes	—
80	C₂×M₁₆×C₈₃	—	2	1	no	—
81	C₂²×C₈×C₈₃	—	2	1	no	—
82	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
83	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
84	#126×C₈₃	—	2	1	no	—
85	#125×C₈₃	C₂×C₄	1	1	yes	characteristic
86	#124×C₈₃	C₂×C₄	1	1	yes	characteristic
87	#123×C₈₃	—	2	1	no	—
88	C₂²⋊Q₈×C₈₃	C₂×C₄	1	1	yes	characteristic
89	#121×C₈₃	C₂×C₄	1	1	yes	characteristic
90	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
91	C₄×D₄×C₈₃	—	2	1	no	—
92	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
93	#117×C₈₃	—	2	1	no	—
94	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₈₃	—	2	1	no	—
96	C₄⋊C₈×C₈₃	—	2	1	no	—
97	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
99	C₂²⋊C₈×C₈₃	—	2	1	no	—
100	C₂²⋊C₈×C₈₃	—	2	1	no	—
101	C₂²⋊C₈×C₈₃	—	2	1	no	—
102	#97×C₈₃	—	2	1	no	—
103	#97×C₈₃	—	2	1	no	—
104	C₄×C₈×C₈₃	—	2	1	no	—
105	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
106	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
107	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
109	C₂³×D₈₃	—	2	1	no	—
110	C₂×D₃₃₂	—	2	1	no	—
111	C₂×D₃₃₂	—	2	4	no	—
112	C₂×D₃₃₂	C₂²×C₄	1	2	yes	—
113	C₂²×Dic₈₃	—	2	1	no	—
114	C₂×C₄×D₈₃	—	2	2	no	—
115	C₂×C₄×D₈₃	—	2	2	no	—
116	C₂×C₄×D₈₃	—	4	2	no	—
117	C₂×C₄×D₈₃	—	4	2	no	—
118	#13050577	—	2	4	no	—
119	#13050575	—	2	4	no	—
120	#13050574	—	2	4	no	—
121	C₂×C₈₃⋊C₈	—	2	2	no	—
122	C₂×C₈₃⋊C₈	—	2	2	no	—
123	C₂×C₈₃⋊C₈	—	4	2	no	—
124	C₂×C₈₃⋊C₈	C₂²×C₄	1	2	yes	—
125	C₂×C₈₃⋊C₈	C₂²×C₄	1	2	yes	—
126	C₈×D₈₃	—	4	4	no	—
127	C₈×D₈₃	—	4	4	no	—
128	C₄⋊Dic₈₃	—	2	1	no	—
129	C₄⋊Dic₈₃	C₂²×C₄	1	2	yes	—
130	(C₂×D₈₃)⋊C₄	—	2	2	no	—
131	(C₂×D₈₃)⋊C₄	—	2	2	no	—
132	C₂×Q₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×D₄×C₈₃	—	2	1	no	—
134	C₂×D₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₈₃	—	2	1	no	—
136	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
139	M₁₆×C₈₃	—	4	2	no	—
140	C₂×C₈×C₈₃	—	2	2	no	—
141	C₂×C₈×C₈₃	—	2	1	no	—
142	C₂×C₈×C₈₃	—	2	1	no	—
143	C₂×C₈×C₈₃	—	4	1	no	—
144	C₂×C₈×C₈₃	—	4	2	no	—
145	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
149	C₄⋊C₄×C₈₃	—	2	1	no	—
150	C₄⋊C₄×C₈₃	—	2	1	no	—
151	C₄⋊C₄×C₈₃	—	2	1	no	—
152	C₄⋊C₄×C₈₃	—	2	1	no	—
153	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
154	C₄⋊C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
155	C₂²⋊C₄×C₈₃	—	2	1	no	—
156	C₂²⋊C₄×C₈₃	—	2	1	no	—
157	C₂²⋊C₄×C₈₃	—	2	1	no	—
158	C₂²⋊C₄×C₈₃	—	2	1	no	—
159	C₂²⋊C₄×C₈₃	—	2	1	no	—
160	C₄²×C₈₃	—	2	1	no	—
161	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₈₃	#41	1	1	yes	characteristic
164	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
165	C₂³×C₈₃	—	2	1	no	—
166	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
167	C₂²×D₈₃	—	2	4	no	—
168	C₂²×D₈₃	—	2	2	no	—
169	C₂²×D₈₃	—	4	2	no	—
170	C₂²×D₈₃	—	4	2	no	—
171	Q₈×C₈₃	—	2	2	no	—
172	D₄×C₈₃	—	2	2	no	—
173	D₄×C₈₃	—	4	2	no	—
174	C₂×C₄×C₈₃	—	2	2	no	—
175	C₂×C₄×C₈₃	—	2	2	no	—
176	C₂×C₄×C₈₃	—	2	1	no	—
177	C₂×C₄×C₈₃	—	2	1	no	—
178	C₂×C₄×C₈₃	—	2	1	no	—
179	C₂×C₄×C₈₃	—	2	1	no	—
180	C₂×C₄×C₈₃	—	2	1	no	—
181	C₂×C₄×C₈₃	—	4	1	no	—
182	C₂×C₄×C₈₃	—	4	1	no	—
183	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
189	C₂×Dic₈₃	—	2	2	no	—
190	C₂×Dic₈₃	—	4	2	no	—
191	D₃₃₂	—	2	4	no	—
192	D₃₃₂	—	2	2	no	—
193	D₃₃₂	#131	1	4	yes	—
194	C₄×D₈₃	—	4	4	no	—
195	C₄×D₈₃	—	4	2	no	—
196	C₄×D₈₃	—	4	2	no	—
197	C₈×C₈₃	—	2	1	no	—
198	C₈×C₈₃	—	2	1	no	—
199	C₈×C₈₃	—	2	1	no	—
200	C₈×C₈₃	—	4	1	no	—
201	C₈×C₈₃	—	4	1	no	—
202	C₈×C₈₃	AGL(1,ℤ/8)	1	2	yes	—
203	C₈₃⋊C₈	—	2	4	no	—
204	C₈₃⋊C₈	—	2	2	no	—
205	C₈₃⋊C₈	—	2	2	no	—
206	C₈₃⋊C₈	—	4	2	no	—
207	C₂²×C₈₃	—	2	1	no	—
208	C₂²×C₈₃	—	2	1	no	—
209	C₂²×C₈₃	—	4	1	no	—
210	C₂²×C₈₃	—	4	1	no	—
211	C₂²×C₈₃	—	4	1	no	—
212	C₂²×C₈₃	#443	1	2	yes	—
213	C₂²×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
214	C₂×D₈₃	—	2	4	no	—
215	C₂×D₈₃	—	4	8	no	—
216	C₂×D₈₃	—	4	2	no	—
217	C₂×D₈₃	—	4	2	no	—
218	C₄×C₈₃	—	2	1	no	—
219	C₄×C₈₃	—	2	1	no	—
220	C₄×C₈₃	—	2	1	no	—
221	C₄×C₈₃	—	2	1	no	—
222	C₄×C₈₃	—	4	1	no	—
223	C₄×C₈₃	—	4	1	no	—
224	C₄×C₈₃	—	4	1	no	—
225	C₄×C₈₃	C₂×#131	1	2	yes	—
226	C₄×C₈₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₄×C₈₃	#575	1	1	yes	characteristic
228	Dic₈₃	—	4	2	no	—
229	#17910	—	83	1	no	maximal, Sylow
230	C₂×C₈₃	—	2	2	no	—
231	C₂×C₈₃	—	8	1	no	—
232	C₂×C₈₃	#2929	1	1	yes	characteristic
233	C₂×C₈₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
234	C₂×C₈₃	C₂×#443	1	1	yes	characteristic
235	D₈₃	—	4	4	no	—
236	#3105	—	83	1	no	—
237	#2966	D₈₃	1	1	yes	characteristic, complemented
238	C₂×C₈×D₄	—	83	1	no	—
239	#1586	—	83	2	no	—
240	#1585	—	83	2	no	—
241	C₈×SD₁₆	—	83	2	no	—
242	C₈×D₈	—	83	2	no	—
243	#1573	—	83	1	no	—
244	#1490	—	83	1	no	—
245	#1483	—	83	1	no	—
246	C₈×M₁₆	—	83	1	no	—
247	C₈₃	#17910	1	1	yes	characteristic, complemented, Sylow
248	C₂³×C₈	—	166	1	no	—
249	#529	C₂×D₈₃	1	1	yes	characteristic
250	C₂×C₄×D₄	—	83	1	no	—
251	#484	—	83	1	no	—
252	#481	—	83	1	no	—
253	#478	—	83	2	no	—
254	#463	—	83	2	no	—
255	#450	—	83	1	no	—
256	#447	—	83	1	no	—
257	#446	C₂×D₈₃	1	1	yes	characteristic, complemented
258	C₈×Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
259	C₄×SD₁₆	—	83	2	no	—
260	C₄×D₈	—	83	2	no	—
261	#436	C₂×D₈₃	1	1	yes	characteristic, complemented
262	#435	—	2	1	no	—
263	C₈×D₄	—	2	1	no	—
264	C₈×D₄	—	83	2	no	—
265	C₈×D₄	—	83	2	no	—
266	C₈×D₄	—	166	1	no	—
267	C₈×D₄	—	166	1	no	—
268	C₈×D₄	C₂×D₈₃	1	1	yes	characteristic, complemented
269	#433	—	2	1	no	—
270	#432	C₂×D₈₃	1	1	yes	characteristic
271	#431	—	83	1	no	—
272	C₂×C₄⋊C₈	—	83	1	no	—
273	C₂×C₂²⋊C₈	—	166	1	no	—
274	#405	—	2	1	no	—
275	C₄×M₁₆	—	83	1	no	—
276	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
277	#335	—	83	2	no	—
278	#334	—	83	2	no	—
279	Q₈⋊C₈	—	83	2	no	—
280	D₄⋊C₈	—	83	2	no	—
281	D₄⋊C₈	—	83	2	no	—
282	D₄⋊C₈	—	83	2	no	—
283	#322	—	83	2	no	—
284	C₈²	—	83	2	no	—
285	C₂²×D₄	—	83	1	no	—
286	C₂³×C₄	—	166	1	no	—
287	C₂×SD₁₆	—	83	2	no	—
288	C₂×D₈	—	83	2	no	—
289	C₂×M₁₆	—	2	1	no	—
290	C₂×M₁₆	—	166	1	no	—
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	—	332	4	no	—
293	C₂²×C₈	—	166	1	no	—
294	C₂²×C₈	—	166	2	no	—
295	C₂²×C₈	—	166	2	no	—
296	C₂²×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
297	C₂²×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
298	#126	—	2	1	no	—
299	#125	C₄×D₈₃	1	1	yes	characteristic
300	#124	C₄×D₈₃	1	1	yes	characteristic
301	#123	—	2	1	no	—
302	C₂²⋊Q₈	C₄×D₈₃	1	1	yes	characteristic
303	#121	C₄×D₈₃	1	1	yes	characteristic
304	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	—	83	2	no	—
307	C₄×D₄	—	83	2	no	—
308	C₄×D₄	—	166	1	no	—
309	C₄×D₄	—	166	1	no	—
310	C₄×D₄	C₂²×D₈₃	1	1	yes	characteristic
311	#117	—	2	1	no	—
312	C₂×C₄⋊C₄	—	83	1	no	—
313	C₂×C₂²⋊C₄	—	166	1	no	—
314	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
315	#107	—	83	2	no	—
316	#106	—	83	2	no	—
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	—	2	1	no	—
319	C₄⋊C₈	—	83	2	no	—
320	C₄⋊C₈	—	83	2	no	—
321	C₄⋊C₈	—	166	1	no	—
322	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
323	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
324	#103	—	83	2	no	—
325	#102	—	83	2	no	—
326	#102	—	83	2	no	—
327	#102	—	83	2	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	C₂²⋊C₈	—	2	1	no	—
330	C₂²⋊C₈	—	2	1	no	—
331	C₂²⋊C₈	—	83	1	no	—
332	C₂²⋊C₈	—	83	1	no	—
333	C₂²⋊C₈	—	166	2	no	—
334	C₂²⋊C₈	—	166	2	no	—
335	#97	—	2	1	no	—
336	#97	—	2	1	no	—
337	#97	—	166	1	no	—
338	C₄×C₈	—	2	1	no	—
339	C₄×C₈	—	83	2	no	—
340	C₄×C₈	—	83	2	no	—
341	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
342	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
343	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
344	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
345	C₂⁴	—	166	1	no	—
346	C₂×Q₈	C₂×C₄×D₈₃	1	1	yes	characteristic
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	83	2	no	—
349	C₂×D₄	—	166	4	no	—
350	C₂×D₄	—	166	1	no	—
351	C₂×D₄	C₂×C₄×D₈₃	1	1	yes	characteristic
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	332	2	no	—
354	C₂²×C₄	—	332	2	no	—
355	C₂²×C₄	—	166	1	no	—
356	C₂²×C₄	—	166	2	no	—
357	C₂²×C₄	—	166	2	no	—
358	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
360	C₂²×C₄	#13050590	1	1	yes	characteristic
361	SD₁₆	—	166	4	no	—
362	D₈	—	166	4	no	—
363	M₁₆	—	4	2	no	—
364	M₁₆	—	166	4	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	4	2	no	—
370	C₂×C₈	—	332	4	no	—
371	C₂×C₈	—	332	2	no	—
372	C₂×C₈	—	332	4	no	—
373	C₂×C₈	—	83	2	no	—
374	C₂×C₈	—	83	2	no	—
375	C₂×C₈	—	166	2	no	—
376	C₂×C₈	—	166	2	no	—
377	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
378	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
379	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
380	C₂×C₈	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	83	2	no	—
386	C₄⋊C₄	—	166	1	no	—
387	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
388	C₄⋊C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	2	1	no	—
394	C₂²⋊C₄	—	166	2	no	—
395	C₂²⋊C₄	—	166	2	no	—
396	C₄²	—	2	1	no	—
397	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
398	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
399	C₄²	#13050590	1	1	yes	characteristic
400	C₄²	C₂³×D₈₃	1	1	yes	characteristic
401	C₂³	—	2	1	no	—
402	C₂³	—	332	2	no	—
403	C₂³	—	332	2	no	—
404	C₂³	—	166	4	no	—
405	C₂³	—	166	2	no	—
406	C₂³	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
407	Q₈	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	83	4	no	—
411	D₄	—	166	4	no	—
412	D₄	—	166	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	332	4	no	—
423	C₂×C₄	—	332	2	no	—
424	C₂×C₄	—	332	2	no	—
425	C₂×C₄	—	332	2	no	—
426	C₂×C₄	—	166	2	no	—
427	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
428	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
429	C₂×C₄	C₄×C₂²⋊D₈₃	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
431	C₂×C₄	C₂²×C₂²⋊D₈₃	1	1	yes	characteristic
432	C₂×C₄	C₂×#13050590	1	1	yes	characteristic
433	C₈	—	2	1	no	—
434	C₈	—	2	1	no	—
435	C₈	—	2	1	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	1	no	—
438	C₈	—	332	2	no	—
439	C₈	—	166	4	no	—
440	C₈	—	166	2	no	—
441	C₈	—	166	2	no	—
442	C₈	#14581817	1	2	yes	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	332	8	no	—
449	C₂²	—	332	2	no	—
450	C₂²	—	332	2	no	—
451	C₂²	—	166	4	no	—
452	C₂²	#19127816	1	2	yes	—
453	C₂²	C₂×C₄×C₂²⋊D₈₃	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	1	no	—
461	C₄	—	332	2	no	—
462	C₄	#131×D₈₃	1	2	yes	—
463	C₄	C₂×#14581817	1	1	yes	characteristic
464	C₄	#19128499	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	8	1	no	—
467	C₂	—	332	4	no	—
468	C₂	#24916155	1	1	yes	characteristic
469	C₂	C₄×#14581817	1	1	yes	characteristic
470	C₂	C₂×#19127816	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₄²	C₂³×D₈₃
Fitting	C₈₃×#2966	C₂
socle	C₂²×C₈₃	C₂×C₄×D₄
prime radical	#19127834	C₄
cosocle	C₄²×C₈₃	C₂⁴
hypercenter	#2966	D₈₃
hypocenter	C₈₃	#17910
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2966

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×D₃₃₂	C₂	semidirect
3. #24906325	C₂	semidirect
4. #24906318	C₂	semidirect
5. C₈×#13050577	C₂	semidirect
6. C₈×#13050575	C₂	semidirect
7. #24906249	C₂	semidirect
8. #24905905	C₂	semidirect
9. #24905876	C₂	semidirect
10. C₈×#13050574	C₂	semidirect
11. C₈₃×#2966	C₂	semidirect
30. #19127453	C₂²	semidirect
31. #19127451	C₂²	semidirect
32. Q₈⋊(C₈₃⋊C₈)	C₂²	semidirect
33. D₄⋊(C₈₃⋊C₈)	C₂²	semidirect
36. #19127423	C₂²	semidirect
37. C₈×C₈₃⋊C₈	C₂²	semidirect
39. #446×C₈₃	C₂²	semidirect
40. C₈×Q₈×C₈₃	C₂²	semidirect
41. #436×C₈₃	C₂²	semidirect
44. C₈×D₄×C₈₃	C₂²	semidirect
237. #2966	D₈₃	semidirect
247. C₈₃	#17910	semidirect
257. #446	C₂×D₈₃	semidirect
258. C₈×Q₈	C₂×D₈₃	semidirect
261. #436	C₂×D₈₃	semidirect
268. C₈×D₄	C₂×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#24917506	2
C₂×C₈×D₃₃₂	2
#24906325	2
#24906318	2
C₈×#13050577	2
C₈×#13050575	2
#24906249	2
#24905905	2
#24905876	2
C₈×#13050574	2
C₈₃×#2966	2
#17910	83