Subgroups — #35558983

Order 21248.

642 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19128134	C₂	1	1	yes	maximal, characteristic, complemented
2	#504×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#24917185	C₂	1	2	yes	maximal, complemented
4	#24909596	C₂	1	2	yes	maximal, complemented
5	#24909595	C₂	1	2	yes	maximal, complemented
6	#24909585	C₂	1	1	yes	maximal, characteristic, complemented
7	#24909584	C₂	1	1	yes	maximal, characteristic, complemented
8	#24909583	C₂	1	1	yes	maximal, characteristic, complemented
9	#368×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#24909211	C₂	1	2	yes	maximal, complemented
11	C₈₃×#2222	C₂	1	1	yes	maximal, characteristic, complemented
12	#19128500	—	2	2	no	—
13	C₂×#14581815	C₂²	1	2	yes	—
14	#131×D₈₃	C₂²	1	1	yes	characteristic
15	#19128134	—	2	1	no	—
16	#19128134	—	2	1	no	—
17	#19128134	—	2	1	no	—
18	#19128134	—	2	1	no	—
19	C₂×#14581735	C₂²	1	2	yes	complemented
20	C₂×D₁₃₂₈	C₂²	1	1	yes	characteristic, complemented
21	#19128119	—	2	1	no	—
22	#19128119	C₂²	1	1	yes	characteristic
23	#19128118	C₂²	1	1	yes	characteristic
24	#19128117	—	2	1	no	—
25	#19128117	C₂²	1	1	yes	characteristic
26	M₃₂×D₈₃	—	2	1	no	—
27	M₃₂×D₈₃	C₂²	1	1	yes	characteristic
28	C₂×C₁₆×D₈₃	—	2	1	no	—
29	C₂×C₁₆×D₈₃	C₂²	1	1	yes	characteristic
30	#19127973	C₂²	1	2	yes	—
31	#19127972	C₂²	1	2	yes	—
32	#19127971	C₂²	1	2	yes	—
33	#19127967	—	2	2	no	—
34	#19127966	—	2	2	no	—
35	#108×D₈₃	C₂²	1	2	yes	—
36	#19127684	—	2	2	no	—
37	#19127531	C₂²	1	1	yes	characteristic, complemented
38	#19127530	C₂²	1	2	yes	complemented
39	#19127517	C₂²	1	2	yes	complemented
40	#19127515	C₂²	1	2	yes	complemented
41	#19127513	C₂²	1	2	yes	complemented
42	C₂×Q₃₂×C₈₃	C₂²	1	1	yes	characteristic, complemented
43	#504×C₈₃	C₂²	1	1	yes	characteristic
44	#473×C₈₃	C₂²	1	2	yes	—
45	#368×C₈₃	C₂²	1	1	yes	characteristic, complemented
46	#362×C₈₃	C₂²	1	2	yes	complemented
47	C₂×#13050591	—	2	2	no	—
48	#41×D₈₃	D₄	1	1	yes	characteristic
49	#14581824	—	4	2	no	—
50	#14581823	—	2	2	no	—
51	#14581820	—	2	2	no	—
52	#14581819	—	4	2	no	—
53	#14581817	—	2	2	no	—
54	#14581815	—	2	2	no	—
55	#14581815	—	2	2	no	—
56	#14581815	—	2	2	no	—
57	#14581815	—	2	2	no	—
58	#14581815	—	4	2	no	—
59	#14581813	—	4	2	no	—
60	C₂×#13050577	—	2	2	no	—
61	C₂×D₆₆₄	C₂³	1	2	yes	—
62	#14581800	—	2	1	no	—
63	#14581800	D₄	1	1	yes	characteristic
64	#14581799	D₄	1	1	yes	characteristic
65	#14581798	—	2	1	no	—
66	#14581798	C₂³	1	1	yes	characteristic
67	M₁₆×D₈₃	—	2	1	no	—
68	M₁₆×D₈₃	—	2	2	no	—
69	M₁₆×D₈₃	D₄	1	1	yes	characteristic
70	C₂×C₈×D₈₃	—	2	1	no	—
71	C₂×C₈×D₈₃	C₂³	1	1	yes	characteristic
72	#14581735	—	2	2	no	—
73	#14581735	—	2	2	no	—
74	D₁₃₂₈	—	2	1	no	—
75	D₁₃₂₈	—	2	1	no	—
76	#14581732	—	2	1	no	—
77	#14581732	C₂³	1	1	yes	characteristic
78	#14581731	—	2	1	no	—
79	#14581731	—	2	1	no	—
80	#14581731	—	2	1	no	—
81	C₂×C₈₃⋊C₁₆	—	2	1	no	—
82	C₂×C₈₃⋊C₁₆	C₂³	1	1	yes	characteristic
83	C₁₆×D₈₃	—	2	1	no	—
84	C₁₆×D₈₃	—	2	1	no	—
85	C₁₆×D₈₃	—	2	1	no	—
86	C₁₆×D₈₃	D₄	1	1	yes	characteristic
87	C₁₆×D₈₃	D₄	1	1	yes	characteristic
88	C₁₆×D₈₃	D₄	1	1	yes	characteristic
89	C₁₆×D₈₃	D₄	1	1	yes	characteristic
90	#14581728	C₂³	1	2	yes	—
91	#14581727	—	2	2	no	—
92	#14581711	—	2	2	no	—
93	#14581708	—	2	2	no	—
94	#14581708	—	2	2	no	—
95	#137×C₈₃	—	2	2	no	—
96	C₂×Q₁₆×C₈₃	C₂³	1	2	yes	—
97	#131×C₈₃	C₂³	1	1	yes	characteristic
98	Q₃₂×C₈₃	—	2	1	no	—
99	Q₃₂×C₈₃	—	2	1	no	—
100	M₃₂×C₈₃	—	2	1	no	—
101	M₃₂×C₈₃	C₂³	1	1	yes	characteristic
102	C₂×C₁₆×C₈₃	—	2	1	no	—
103	C₂×C₁₆×C₈₃	C₂³	1	1	yes	characteristic
104	#108×C₈₃	C₂³	1	2	yes	—
105	#101×C₈₃	—	2	2	no	—
106	#13050591	—	4	2	no	—
107	#13050591	—	4	2	no	—
108	#13050591	—	4	2	no	—
109	#13050591	—	4	2	no	—
110	#13050591	D₈	1	1	yes	characteristic
111	#13050590	—	2	1	no	—
112	#13050590	C₂×D₄	1	1	yes	characteristic
113	#13050589	—	2	1	no	—
114	#13050589	D₈	1	1	yes	characteristic
115	Q₈×D₈₃	D₈	1	1	yes	characteristic
116	C₂×D₃₃₂	—	2	2	no	—
117	C₂×D₃₃₂	—	4	2	no	—
118	D₄×D₈₃	—	2	1	no	—
119	D₄×D₈₃	D₈	1	1	yes	characteristic
120	C₂×C₄×D₈₃	—	2	1	no	—
121	C₂×C₄×D₈₃	—	4	2	no	—
122	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
123	#13050580	—	4	2	no	—
124	#13050579	—	4	2	no	—
125	#13050577	—	4	2	no	—
126	#13050577	—	4	2	no	—
127	#13050577	—	4	2	no	—
128	#13050577	—	4	2	no	—
129	D₆₆₄	—	2	2	no	—
130	D₆₆₄	—	2	2	no	—
131	D₆₆₄	—	4	2	no	—
132	#13050575	—	4	2	no	—
133	#13050574	—	2	1	no	—
134	#13050574	—	2	2	no	—
135	#13050574	C₂×D₄	1	1	yes	characteristic
136	#13050573	—	2	1	no	—
137	#13050573	—	2	1	no	—
138	#13050573	—	2	1	no	—
139	#13050573	—	4	2	no	—
140	C₂×C₈₃⋊C₈	—	2	1	no	—
141	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
142	C₈×D₈₃	—	2	1	no	—
143	C₈×D₈₃	—	2	1	no	—
144	C₈×D₈₃	—	2	1	no	—
145	C₈×D₈₃	—	4	2	no	—
146	C₈×D₈₃	C₂×D₄	1	1	yes	characteristic
147	C₈×D₈₃	C₂×D₄	1	1	yes	characteristic
148	C₈×D₈₃	#41	1	1	yes	characteristic
149	C₈×D₈₃	#41	1	1	yes	characteristic
150	C₈₃⋊C₁₆	—	2	1	no	—
151	C₈₃⋊C₁₆	C₂×D₄	1	1	yes	characteristic
152	C₈₃⋊C₁₆	C₂×D₄	1	1	yes	characteristic
153	#41×C₈₃	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₈₃	—	2	2	no	—
155	Q₁₆×C₈₃	—	2	2	no	—
156	Q₁₆×C₈₃	—	2	2	no	—
157	Q₁₆×C₈₃	—	4	2	no	—
158	SD₁₆×C₈₃	—	4	2	no	—
159	M₁₆×C₈₃	—	2	1	no	—
160	M₁₆×C₈₃	—	2	2	no	—
161	M₁₆×C₈₃	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₈₃	—	2	1	no	—
163	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
164	C₁₆×C₈₃	—	2	1	no	—
165	C₁₆×C₈₃	C₂×D₄	1	1	yes	characteristic
166	C₁₆×C₈₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×D₈₃	—	2	1	no	—
168	C₂²×D₈₃	—	4	2	no	—
169	C₂²×D₈₃	#135	1	1	yes	characteristic
170	Q₈×C₈₃	—	4	2	no	—
171	Q₈×C₈₃	—	4	2	no	—
172	Q₈×C₈₃	C₂×D₈	1	1	yes	characteristic
173	D₄×C₈₃	—	2	1	no	—
174	D₄×C₈₃	C₂×D₈	1	1	yes	characteristic
175	C₂×C₄×C₈₃	—	2	1	no	—
176	C₂×C₄×C₈₃	—	4	2	no	—
177	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
178	C₂²⋊D₈₃	—	2	1	no	—
179	C₂²⋊D₈₃	—	2	1	no	—
180	C₂²⋊D₈₃	—	2	1	no	—
181	C₂×Dic₈₃	—	2	1	no	—
182	C₂×Dic₈₃	#135	1	1	yes	characteristic
183	D₃₃₂	—	2	1	no	—
184	D₃₃₂	—	4	2	no	—
185	D₃₃₂	—	4	2	no	—
186	D₃₃₂	—	8	2	no	—
187	D₃₃₂	—	8	2	no	—
188	D₃₃₂	C₂×D₈	1	1	yes	characteristic
189	C₄×D₈₃	—	2	1	no	—
190	C₄×D₈₃	—	2	1	no	—
191	C₄×D₈₃	—	2	1	no	—
192	C₄×D₈₃	—	8	2	no	—
193	C₄×D₈₃	—	8	2	no	—
194	C₄×D₈₃	#121	1	1	yes	characteristic
195	C₄×D₈₃	#121	1	1	yes	characteristic
196	C₄×D₈₃	C₂×D₈	1	1	yes	characteristic
197	C₄×D₈₃	C₂×D₈	1	1	yes	characteristic
198	Dic₁₆₆	—	2	1	no	—
199	Dic₁₆₆	C₂×D₈	1	1	yes	characteristic
200	C₈×C₈₃	—	2	1	no	—
201	C₈×C₈₃	—	4	2	no	—
202	C₈×C₈₃	C₂²×D₄	1	1	yes	characteristic
203	C₈×C₈₃	C₂×#41	1	1	yes	characteristic
204	C₈₃⋊C₈	—	2	1	no	—
205	C₈₃⋊C₈	—	4	2	no	—
206	C₈₃⋊C₈	#121	1	1	yes	characteristic
207	C₈₃⋊C₈	#121	1	1	yes	characteristic
208	C₂²×C₈₃	—	2	1	no	—
209	C₂²×C₈₃	C₂×#135	1	1	yes	characteristic
210	C₂×D₈₃	—	2	1	no	—
211	C₂×D₈₃	—	4	1	no	—
212	C₂×D₈₃	—	4	2	no	—
213	C₂×D₈₃	—	8	2	no	—
214	C₂×D₈₃	—	16	2	no	—
215	C₂×D₈₃	#466	1	1	yes	characteristic
216	C₂×D₈₃	#466	1	1	yes	characteristic
217	C₄×C₈₃	—	2	1	no	—
218	C₄×C₈₃	—	8	2	no	—
219	C₄×C₈₃	C₂×#121	1	1	yes	characteristic
220	C₄×C₈₃	C₂²×D₈	1	1	yes	characteristic
221	Dic₈₃	—	2	1	no	—
222	Dic₈₃	#466	1	1	yes	characteristic
223	Dic₈₃	#466	1	1	yes	characteristic
224	#33617	—	83	1	no	maximal, Sylow
225	C₂×C₈₃	—	2	1	no	—
226	C₂×C₈₃	—	4	1	no	—
227	C₂×C₈₃	C₂×#466	1	1	yes	characteristic
228	D₈₃	—	2	1	no	—
229	D₈₃	—	2	1	no	—
230	D₈₃	—	4	1	no	—
231	D₈₃	—	16	2	no	—
232	C₂×#508	—	83	1	no	—
233	C₂×#504	—	83	1	no	—
234	#3067	—	83	2	no	—
235	#2223	—	83	2	no	—
236	#2223	—	83	2	no	—
237	#2222	—	83	1	no	—
238	#2222	D₈₃	1	1	yes	characteristic, complemented
239	#2221	—	83	1	no	—
240	#2221	—	83	1	no	—
241	C₂×#368	—	83	1	no	—
242	#2148	—	83	2	no	—
243	C₈₃	#33617	1	1	yes	characteristic, complemented, Sylow
244	#575	—	166	2	no	—
245	C₂×#135	—	83	2	no	—
246	C₂×#131	—	83	1	no	—
247	#508	—	166	1	no	—
248	#508	—	166	1	no	—
249	#508	—	166	1	no	—
250	#508	—	166	1	no	—
251	C₂×Q₃₂	C₂×D₈₃	1	1	yes	characteristic, complemented
252	C₂×SD₃₂	—	83	2	no	—
253	C₂×D₁₆	—	83	1	no	—
254	#504	—	83	1	no	—
255	#504	—	83	1	no	—
256	#504	—	83	1	no	—
257	#504	—	166	1	no	—
258	#504	—	166	1	no	—
259	#504	C₂×D₈₃	1	1	yes	characteristic
260	C₂×M₃₂	—	83	1	no	—
261	C₂×M₃₂	—	166	1	no	—
262	C₂²×C₁₆	—	83	1	no	—
263	C₂²×C₁₆	—	166	1	no	—
264	#473	—	83	2	no	—
265	#473	C₂×D₈₃	1	2	yes	—
266	#472	—	83	2	no	—
267	#472	—	83	2	no	—
268	#471	—	166	2	no	—
269	#471	—	166	2	no	—
270	C₂×#108	—	83	2	no	—
271	#413	—	166	2	no	—
272	#368	—	83	1	no	—
273	#368	—	83	2	no	—
274	#368	C₂×D₈₃	1	1	yes	characteristic, complemented
275	#362	—	83	2	no	—
276	#362	C₂×D₈₃	1	2	yes	complemented
277	#361	—	83	2	no	—
278	#361	—	83	2	no	—
279	C₂×#41	—	83	1	no	—
280	C₂×#41	—	166	2	no	—
281	#137	—	2	2	no	—
282	#137	—	332	2	no	—
283	#137	—	166	2	no	—
284	AGL(1,ℤ/8)	—	332	2	no	—
285	AGL(1,ℤ/8)	—	166	2	no	—
286	AGL(1,ℤ/8)	—	166	2	no	—
287	#135	—	332	2	no	—
288	#135	—	332	2	no	—
289	#135	—	166	2	no	—
290	#135	—	166	2	no	—
291	#135	—	166	2	no	—
292	#135	—	166	2	no	—
293	C₂×Q₁₆	C₂²×D₈₃	1	2	yes	—
294	C₂×SD₁₆	—	166	2	no	—
295	C₂×D₈	—	83	2	no	—
296	#131	—	83	1	no	—
297	#131	—	83	1	no	—
298	#131	—	83	1	no	—
299	#131	—	166	1	no	—
300	#131	—	166	1	no	—
301	#131	C₂²×D₈₃	1	1	yes	characteristic
302	C₂×M₁₆	—	83	1	no	—
303	C₂×M₁₆	—	166	2	no	—
304	C₂×M₁₆	—	166	1	no	—
305	C₂²×C₈	—	83	1	no	—
306	C₂²×C₈	—	166	1	no	—
307	Q₃₂	—	2	1	no	—
308	Q₃₂	—	2	1	no	—
309	SD₃₂	—	166	2	no	—
310	SD₃₂	—	166	2	no	—
311	D₁₆	—	166	1	no	—
312	D₁₆	—	166	1	no	—
313	M₃₂	—	2	1	no	—
314	M₃₂	—	83	1	no	—
315	M₃₂	—	166	1	no	—
316	M₃₂	—	166	1	no	—
317	M₃₂	—	166	1	no	—
318	M₃₂	—	166	1	no	—
319	M₃₂	C₂²×D₈₃	1	1	yes	characteristic
320	C₂×C₁₆	—	2	1	no	—
321	C₂×C₁₆	—	83	1	no	—
322	C₂×C₁₆	—	83	1	no	—
323	C₂×C₁₆	—	83	1	no	—
324	C₂×C₁₆	—	83	1	no	—
325	C₂×C₁₆	—	83	1	no	—
326	C₂×C₁₆	—	166	1	no	—
327	C₂×C₁₆	—	166	1	no	—
328	C₂×C₁₆	—	166	1	no	—
329	C₂×C₁₆	—	166	1	no	—
330	C₂×C₁₆	C₂²×D₈₃	1	1	yes	characteristic
331	#108	—	83	2	no	—
332	#108	—	166	2	no	—
333	#108	C₂²×D₈₃	1	2	yes	—
334	#101	—	2	2	no	—
335	#101	—	166	2	no	—
336	#100	—	166	2	no	—
337	#100	—	166	2	no	—
338	#41	—	332	2	no	—
339	#41	—	332	2	no	—
340	#41	—	332	2	no	—
341	#41	—	332	2	no	—
342	#41	—	83	1	no	—
343	#41	—	83	1	no	—
344	#41	—	83	1	no	—
345	#41	—	166	1	no	—
346	#41	—	166	1	no	—
347	#41	D₄×D₈₃	1	1	yes	characteristic
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	83	1	no	—
350	C₂×D₄	—	332	2	no	—
351	C₂×D₄	—	83	1	no	—
352	C₂×D₄	—	166	1	no	—
353	C₂×D₄	—	166	2	no	—
354	C₂²×C₄	—	332	2	no	—
355	C₂²×C₄	—	83	1	no	—
356	C₂²×C₄	—	166	1	no	—
357	Q₁₆	—	2	2	no	—
358	Q₁₆	—	2	2	no	—
359	Q₁₆	—	4	2	no	—
360	Q₁₆	—	332	2	no	—
361	SD₁₆	—	4	2	no	—
362	SD₁₆	—	332	2	no	—
363	SD₁₆	—	332	2	no	—
364	SD₁₆	—	332	2	no	—
365	SD₁₆	—	332	2	no	—
366	SD₁₆	—	332	2	no	—
367	D₈	—	332	2	no	—
368	D₈	—	332	2	no	—
369	D₈	—	166	2	no	—
370	D₈	—	166	2	no	—
371	M₁₆	—	2	1	no	—
372	M₁₆	—	2	2	no	—
373	M₁₆	—	332	2	no	—
374	M₁₆	—	83	1	no	—
375	M₁₆	—	166	1	no	—
376	M₁₆	—	166	1	no	—
377	M₁₆	—	166	2	no	—
378	M₁₆	—	166	1	no	—
379	M₁₆	—	166	1	no	—
380	M₁₆	D₄×D₈₃	1	1	yes	characteristic
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	332	2	no	—
383	C₂×C₈	—	83	1	no	—
384	C₂×C₈	—	83	1	no	—
385	C₂×C₈	—	83	1	no	—
386	C₂×C₈	—	83	1	no	—
387	C₂×C₈	—	83	1	no	—
388	C₂×C₈	—	166	1	no	—
389	C₂×C₈	—	166	1	no	—
390	C₂×C₈	—	166	1	no	—
391	C₂×C₈	—	166	1	no	—
392	C₂×C₈	C₂³×D₈₃	1	1	yes	characteristic
393	C₁₆	—	2	1	no	—
394	C₁₆	—	83	1	no	—
395	C₁₆	—	83	1	no	—
396	C₁₆	—	166	1	no	—
397	C₁₆	D₄×D₈₃	1	1	yes	characteristic
398	C₁₆	D₄×D₈₃	1	1	yes	characteristic
399	C₂³	—	332	2	no	—
400	C₂³	—	83	1	no	—
401	C₂³	—	166	1	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	83	1	no	—
405	Q₈	—	166	1	no	—
406	Q₈	D₈×D₈₃	1	1	yes	characteristic
407	D₄	—	2	1	no	—
408	D₄	—	332	2	no	—
409	D₄	—	332	2	no	—
410	D₄	—	83	1	no	—
411	D₄	—	664	2	no	—
412	D₄	—	664	2	no	—
413	D₄	—	166	1	no	—
414	D₄	—	166	1	no	—
415	D₄	—	166	1	no	—
416	D₄	—	166	1	no	—
417	D₄	D₈×D₈₃	1	1	yes	characteristic
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	83	1	no	—
421	C₂×C₄	—	83	1	no	—
422	C₂×C₄	—	83	1	no	—
423	C₂×C₄	—	83	1	no	—
424	C₂×C₄	—	83	1	no	—
425	C₂×C₄	—	664	2	no	—
426	C₂×C₄	—	664	2	no	—
427	C₂×C₄	—	166	1	no	—
428	C₂×C₄	—	166	1	no	—
429	C₂×C₄	—	166	1	no	—
430	C₂×C₄	—	166	1	no	—
431	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
432	C₈	—	2	1	no	—
433	C₈	—	4	2	no	—
434	C₈	—	332	2	no	—
435	C₈	—	83	1	no	—
436	C₈	—	83	1	no	—
437	C₈	—	166	1	no	—
438	C₈	C₂×D₄×D₈₃	1	1	yes	characteristic
439	C₈	#41×D₈₃	1	1	yes	characteristic
440	C₂²	—	2	1	no	—
441	C₂²	—	1328	2	no	—
442	C₂²	—	332	1	no	—
443	C₂²	—	332	2	no	—
444	C₂²	—	83	1	no	—
445	C₂²	—	83	1	no	—
446	C₂²	—	664	2	no	—
447	C₂²	—	166	1	no	—
448	C₂²	#135×D₈₃	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	8	2	no	—
451	C₄	—	83	1	no	—
452	C₄	—	83	1	no	—
453	C₄	—	166	1	no	—
454	C₄	#121×D₈₃	1	1	yes	characteristic
455	C₄	C₂×D₈×D₈₃	1	1	yes	characteristic
456	C₂	—	2	1	no	—
457	C₂	—	4	1	no	—
458	C₂	—	1328	2	no	—
459	C₂	—	332	1	no	—
460	C₂	—	166	1	no	—
461	C₂	—	166	1	no	—
462	C₂	#466×D₈₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#466×D₈₃
commutator, cosocle	C₂×C₈×C₈₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₃
Fitting	C₈₃×#2222	C₂
socle	C₂×C₈₃	C₂×#466
hypercenter	#2222	D₈₃
hypocenter	C₈₃	#33617
LCS	G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #2222

Complements

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

N	H ≅ G/N	type
1. C₂×#19128134	C₂	semidirect
2. #504×D₈₃	C₂	semidirect
3. #24917185	C₂	semidirect
4. #24909596	C₂	semidirect
5. #24909595	C₂	semidirect
6. #24909585	C₂	semidirect
7. #24909584	C₂	semidirect
8. #24909583	C₂	semidirect
9. #368×D₈₃	C₂	semidirect
10. #24909211	C₂	semidirect
11. C₈₃×#2222	C₂	semidirect
19. C₂×#14581735	C₂²	semidirect
20. C₂×D₁₃₂₈	C₂²	semidirect
37. #19127531	C₂²	semidirect
38. #19127530	C₂²	semidirect
39. #19127517	C₂²	semidirect
40. #19127515	C₂²	semidirect
41. #19127513	C₂²	semidirect
42. C₂×Q₃₂×C₈₃	C₂²	semidirect
45. #368×C₈₃	C₂²	semidirect
46. #362×C₈₃	C₂²	semidirect
238. #2222	D₈₃	semidirect
243. C₈₃	#33617	semidirect
251. C₂×Q₃₂	C₂×D₈₃	semidirect
274. #368	C₂×D₈₃	semidirect
276. #362	C₂×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19128134	2
#504×D₈₃	2
#24917185	2
#24909596	2
#24909595	2
#24909585	2
#24909584	2
#24909583	2
#368×D₈₃	2
#24909211	2
C₈₃×#2222	2
#33617	83