Subgroups — C₈₃×#19943 #35247767

Order 21248.

644 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3395	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×#3368	C₂	1	2	yes	maximal, complemented
3	C₈₃×#3287	C₂	1	1	yes	maximal, characteristic
4	C₈₃×#1709	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#1702	C₂	1	2	yes	maximal, complemented
6	C₈₃×#1669	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₃×#1668	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₃×#1641	C₂	1	2	yes	maximal, complemented
9	C₈₃×#1626	C₂	1	2	yes	maximal, complemented
10	C₈₃×#1591	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₈₃	—	2	1	no	—
13	#557×C₈₃	C₂²	1	2	yes	—
14	#550×C₈₃	C₂²	1	2	yes	—
15	#494×C₈₃	—	2	1	no	—
16	#494×C₈₃	C₂²	1	1	yes	characteristic
17	#493×C₈₃	C₂²	1	1	yes	characteristic
18	#490×C₈₃	—	2	2	no	—
19	#486×C₈₃	C₂²	1	2	yes	—
20	#486×C₈₃	C₂²	1	2	yes	—
21	#478×C₈₃	—	2	2	no	—
22	#474×C₈₃	C₂²	1	2	yes	—
23	#466×C₈₃	—	2	1	no	—
24	#462×C₈₃	—	2	2	no	—
25	#462×C₈₃	C₂²	1	2	yes	—
26	#460×C₈₃	—	2	2	no	—
27	#460×C₈₃	C₂²	1	2	yes	—
28	#460×C₈₃	C₂²	1	2	yes	—
29	#449×C₈₃	—	2	2	no	—
30	#446×C₈₃	C₂²	1	2	yes	—
31	C₈×Q₈×C₈₃	C₂²	1	1	yes	characteristic
32	#440×C₈₃	—	2	2	no	—
33	C₄×Q₁₆×C₈₃	—	2	1	no	—
34	C₄×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
35	C₄×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
36	C₈×D₄×C₈₃	C₂²	1	1	yes	characteristic
37	#335×C₈₃	C₂²	1	1	yes	characteristic
38	#334×C₈₃	C₂²	1	1	yes	characteristic
39	#332×C₈₃	C₂²	1	2	yes	—
40	#331×C₈₃	C₂²	1	2	yes	—
41	Q₈⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
42	Q₈⋊C₈×C₈₃	C₂²	1	2	yes	—
43	D₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
44	C₈²×C₈₃	C₂²	1	1	yes	characteristic
45	C₂×#41×C₈₃	—	2	2	no	—
46	#135×C₈₃	—	4	4	no	—
47	C₂×Q₁₆×C₈₃	—	2	2	no	—
48	C₂×Q₁₆×C₈₃	—	2	1	no	—
49	C₂×Q₁₆×C₈₃	—	2	1	no	—
50	C₂×Q₁₆×C₈₃	D₄	1	1	yes	characteristic
51	C₂×SD₁₆×C₈₃	—	2	2	no	—
52	C₂×SD₁₆×C₈₃	—	2	2	no	—
53	C₂×SD₁₆×C₈₃	D₄	1	1	yes	characteristic
54	C₂×D₈×C₈₃	—	2	1	no	—
55	C₂×D₈×C₈₃	—	2	1	no	—
56	C₂²×C₈×C₈₃	—	2	1	no	—
57	C₄⋊Q₈×C₈₃	—	2	2	no	—
58	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
59	#127×C₈₃	—	2	2	no	—
60	#127×C₈₃	C₂³	1	2	yes	—
61	#125×C₈₃	—	2	2	no	—
62	#125×C₈₃	—	4	2	no	—
63	#121×C₈₃	—	2	2	no	—
64	#121×C₈₃	—	4	2	no	—
65	C₄×Q₈×C₈₃	—	2	2	no	—
66	C₄×Q₈×C₈₃	—	2	2	no	—
67	C₄×Q₈×C₈₃	C₂³	1	2	yes	—
68	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₈₃	—	2	2	no	—
70	C₄×D₄×C₈₃	C₂³	1	1	yes	characteristic
71	#107×C₈₃	—	2	2	no	—
72	#107×C₈₃	D₄	1	1	yes	characteristic
73	#106×C₈₃	D₄	1	1	yes	characteristic
74	C₄⋊C₈×C₈₃	—	2	2	no	—
75	C₄⋊C₈×C₈₃	—	2	1	no	—
76	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
77	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
79	#103×C₈₃	—	2	2	no	—
80	#103×C₈₃	D₄	1	1	yes	characteristic
81	#103×C₈₃	D₄	1	2	yes	—
82	#102×C₈₃	—	2	2	no	—
83	#102×C₈₃	—	2	2	no	—
84	#102×C₈₃	—	2	2	no	—
85	#102×C₈₃	—	2	2	no	—
86	#102×C₈₃	—	2	2	no	—
87	#102×C₈₃	—	4	2	no	—
88	#102×C₈₃	D₄	1	1	yes	characteristic
89	C₂²⋊C₈×C₈₃	—	2	1	no	—
90	#97×C₈₃	—	2	2	no	—
91	C₄×C₈×C₈₃	—	2	1	no	—
92	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
95	#41×C₈₃	—	4	4	no	—
96	#41×C₈₃	—	8	2	no	—
97	C₂×Q₈×C₈₃	—	2	2	no	—
98	C₂×Q₈×C₈₃	C₂×D₄	1	2	yes	—
99	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
100	C₂×D₄×C₈₃	—	2	2	no	—
101	C₂×D₄×C₈₃	—	2	2	no	—
102	C₂×D₄×C₈₃	—	2	2	no	—
103	C₂×D₄×C₈₃	—	4	2	no	—
104	C₂×D₄×C₈₃	—	4	2	no	—
105	C₂×D₄×C₈₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₈₃	—	2	1	no	—
107	C₂²×C₄×C₈₃	—	4	2	no	—
108	Q₁₆×C₈₃	—	2	2	no	—
109	Q₁₆×C₈₃	—	4	2	no	—
110	Q₁₆×C₈₃	—	8	1	no	—
111	Q₁₆×C₈₃	—	8	2	no	—
112	SD₁₆×C₈₃	—	2	2	no	—
113	SD₁₆×C₈₃	—	4	4	no	—
114	SD₁₆×C₈₃	—	4	4	no	—
115	D₈×C₈₃	—	4	2	no	—
116	D₈×C₈₃	—	8	1	no	—
117	C₂×C₈×C₈₃	—	2	1	no	—
118	C₂×C₈×C₈₃	—	2	2	no	—
119	C₂×C₈×C₈₃	—	2	1	no	—
120	C₂×C₈×C₈₃	—	2	1	no	—
121	C₂×C₈×C₈₃	—	4	2	no	—
122	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
126	C₄⋊C₄×C₈₃	—	2	2	no	—
127	C₄⋊C₄×C₈₃	—	2	1	no	—
128	C₄⋊C₄×C₈₃	—	2	2	no	—
129	C₄⋊C₄×C₈₃	—	2	2	no	—
130	C₄⋊C₄×C₈₃	—	4	2	no	—
131	C₄⋊C₄×C₈₃	—	4	2	no	—
132	C₄⋊C₄×C₈₃	—	4	2	no	—
133	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
134	C₄⋊C₄×C₈₃	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
136	C₂²⋊C₄×C₈₃	—	2	1	no	—
137	C₂²⋊C₄×C₈₃	—	4	2	no	—
138	C₄²×C₈₃	—	2	1	no	—
139	C₄²×C₈₃	—	2	2	no	—
140	C₄²×C₈₃	—	4	2	no	—
141	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
142	C₂³×C₈₃	—	2	1	no	—
143	C₂³×C₈₃	—	4	2	no	—
144	Q₈×C₈₃	—	2	1	no	—
145	Q₈×C₈₃	—	2	2	no	—
146	Q₈×C₈₃	—	2	2	no	—
147	Q₈×C₈₃	—	4	2	no	—
148	Q₈×C₈₃	—	4	2	no	—
149	Q₈×C₈₃	#135	1	2	yes	complemented
150	D₄×C₈₃	—	2	1	no	—
151	D₄×C₈₃	—	2	1	no	—
152	D₄×C₈₃	—	4	2	no	—
153	D₄×C₈₃	—	4	2	no	—
154	D₄×C₈₃	—	4	2	no	—
155	D₄×C₈₃	—	4	2	no	—
156	D₄×C₈₃	—	8	2	no	—
157	D₄×C₈₃	—	8	4	no	—
158	D₄×C₈₃	—	16	2	no	—
159	C₂×C₄×C₈₃	—	2	1	no	—
160	C₂×C₄×C₈₃	—	2	2	no	—
161	C₂×C₄×C₈₃	—	2	1	no	—
162	C₂×C₄×C₈₃	—	2	2	no	—
163	C₂×C₄×C₈₃	—	2	1	no	—
164	C₂×C₄×C₈₃	—	4	1	no	—
165	C₂×C₄×C₈₃	—	4	1	no	—
166	C₂×C₄×C₈₃	—	4	2	no	—
167	C₂×C₄×C₈₃	—	8	4	no	—
168	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
171	C₈×C₈₃	—	2	1	no	—
172	C₈×C₈₃	—	2	1	no	—
173	C₈×C₈₃	—	2	1	no	—
174	C₈×C₈₃	—	4	1	no	—
175	C₈×C₈₃	—	4	2	no	—
176	C₈×C₈₃	—	4	1	no	—
177	C₈×C₈₃	—	4	1	no	—
178	C₈×C₈₃	AGL(1,ℤ/8)	1	2	yes	—
179	C₂²×C₈₃	—	4	1	no	—
180	C₂²×C₈₃	—	4	1	no	—
181	C₂²×C₈₃	—	4	1	no	—
182	C₂²×C₈₃	—	8	2	no	—
183	C₂²×C₈₃	—	8	2	no	—
184	C₂²×C₈₃	—	8	2	no	—
185	C₂²×C₈₃	D₄²	1	1	yes	characteristic
186	C₄×C₈₃	—	2	2	no	—
187	C₄×C₈₃	—	2	1	no	—
188	C₄×C₈₃	—	4	1	no	—
189	C₄×C₈₃	—	4	2	no	—
190	C₄×C₈₃	—	4	1	no	—
191	C₄×C₈₃	—	4	2	no	—
192	C₄×C₈₃	—	8	2	no	—
193	C₄×C₈₃	C₂×#135	1	1	yes	characteristic
194	C₄×C₈₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₄×C₈₃	#576	1	1	yes	characteristic
196	C₄×C₈₃	#578	1	1	yes	characteristic
197	#19943	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂×C₈₃	—	8	1	no	—
199	C₂×C₈₃	—	16	2	no	—
200	C₂×C₈₃	#3274	1	1	yes	characteristic
201	C₂×C₈₃	#3285	1	1	yes	characteristic
202	C₂×C₈₃	#3290	1	1	yes	characteristic
203	#3395	C₂×C₈₃	1	1	yes	characteristic, complemented
204	#3368	C₂×C₈₃	1	2	yes	complemented
205	#3287	C₂×C₈₃	1	1	yes	characteristic
206	#1709	C₂×C₈₃	1	1	yes	characteristic, complemented
207	#1702	C₂×C₈₃	1	2	yes	complemented
208	#1669	C₂×C₈₃	1	1	yes	characteristic, complemented
209	#1668	C₂×C₈₃	1	1	yes	characteristic, complemented
210	#1641	C₂×C₈₃	1	2	yes	complemented
211	#1626	C₂×C₈₃	1	2	yes	complemented
212	#1591	C₂×C₈₃	1	1	yes	characteristic, complemented
213	C₈×SD₁₆	C₂×C₈₃	1	1	yes	characteristic, complemented
214	C₈₃	#19943	1	1	yes	characteristic, direct product factor, Sylow
215	C₂×#135	—	2	1	no	—
216	#557	C₂²×C₈₃	1	2	yes	—
217	#550	C₂²×C₈₃	1	2	yes	—
218	#494	—	2	1	no	—
219	#494	C₂²×C₈₃	1	1	yes	characteristic
220	#493	C₂²×C₈₃	1	1	yes	characteristic
221	#490	—	2	2	no	—
222	#486	C₂²×C₈₃	1	2	yes	—
223	#486	C₂²×C₈₃	1	2	yes	—
224	#478	—	2	2	no	—
225	#474	C₂²×C₈₃	1	2	yes	—
226	#466	—	2	1	no	—
227	#462	—	2	2	no	—
228	#462	C₂²×C₈₃	1	2	yes	—
229	#460	—	2	2	no	—
230	#460	C₂²×C₈₃	1	2	yes	—
231	#460	C₂²×C₈₃	1	2	yes	—
232	#449	—	2	2	no	—
233	#446	C₂²×C₈₃	1	2	yes	—
234	C₈×Q₈	C₂²×C₈₃	1	1	yes	characteristic
235	#440	—	2	2	no	—
236	C₄×Q₁₆	—	2	1	no	—
237	C₄×Q₁₆	C₂²×C₈₃	1	1	yes	characteristic
238	C₄×SD₁₆	C₂²×C₈₃	1	1	yes	characteristic
239	C₈×D₄	C₂²×C₈₃	1	1	yes	characteristic
240	#335	C₂²×C₈₃	1	1	yes	characteristic
241	#334	C₂²×C₈₃	1	1	yes	characteristic
242	#332	C₂²×C₈₃	1	2	yes	—
243	#331	C₂²×C₈₃	1	2	yes	—
244	Q₈⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
245	Q₈⋊C₈	C₂²×C₈₃	1	2	yes	—
246	D₄⋊C₈	C₂²×C₈₃	1	1	yes	characteristic
247	C₈²	C₂²×C₈₃	1	1	yes	characteristic
248	C₂×#41	—	2	2	no	—
249	#135	—	4	4	no	—
250	C₂×Q₁₆	—	2	2	no	—
251	C₂×Q₁₆	—	2	1	no	—
252	C₂×Q₁₆	—	2	1	no	—
253	C₂×Q₁₆	D₄×C₈₃	1	1	yes	characteristic
254	C₂×SD₁₆	—	2	2	no	—
255	C₂×SD₁₆	—	2	2	no	—
256	C₂×SD₁₆	D₄×C₈₃	1	1	yes	characteristic
257	C₂×D₈	—	2	1	no	—
258	C₂×D₈	—	2	1	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₄⋊Q₈	—	2	2	no	—
261	C₄⋊Q₈	C₂³×C₈₃	1	2	yes	—
262	#127	—	2	2	no	—
263	#127	C₂³×C₈₃	1	2	yes	—
264	#125	—	2	2	no	—
265	#125	—	4	2	no	—
266	#121	—	2	2	no	—
267	#121	—	4	2	no	—
268	C₄×Q₈	—	2	2	no	—
269	C₄×Q₈	—	2	2	no	—
270	C₄×Q₈	C₂³×C₈₃	1	2	yes	—
271	C₄×Q₈	C₂³×C₈₃	1	1	yes	characteristic
272	C₄×D₄	—	2	2	no	—
273	C₄×D₄	C₂³×C₈₃	1	1	yes	characteristic
274	#107	—	2	2	no	—
275	#107	D₄×C₈₃	1	1	yes	characteristic
276	#106	D₄×C₈₃	1	1	yes	characteristic
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
280	C₄⋊C₈	C₂³×C₈₃	1	2	yes	—
281	C₄⋊C₈	C₂³×C₈₃	1	1	yes	characteristic
282	#103	—	2	2	no	—
283	#103	D₄×C₈₃	1	1	yes	characteristic
284	#103	D₄×C₈₃	1	2	yes	—
285	#102	—	2	2	no	—
286	#102	—	2	2	no	—
287	#102	—	2	2	no	—
288	#102	—	2	2	no	—
289	#102	—	2	2	no	—
290	#102	—	4	2	no	—
291	#102	D₄×C₈₃	1	1	yes	characteristic
292	C₂²⋊C₈	—	2	1	no	—
293	#97	—	2	2	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
296	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
297	C₄×C₈	C₂³×C₈₃	1	1	yes	characteristic
298	#41	—	4	4	no	—
299	#41	—	8	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	C₂×D₄×C₈₃	1	2	yes	—
302	C₂×Q₈	C₂×D₄×C₈₃	1	1	yes	characteristic
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	C₂×D₄×C₈₃	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	4	2	no	—
311	Q₁₆	—	2	2	no	—
312	Q₁₆	—	4	2	no	—
313	Q₁₆	—	8	1	no	—
314	Q₁₆	—	8	2	no	—
315	SD₁₆	—	2	2	no	—
316	SD₁₆	—	4	4	no	—
317	SD₁₆	—	4	4	no	—
318	D₈	—	4	2	no	—
319	D₈	—	8	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	4	2	no	—
325	C₂×C₈	C₂×D₄×C₈₃	1	1	yes	characteristic
326	C₂×C₈	C₂×D₄×C₈₃	1	1	yes	characteristic
327	C₂×C₈	C₂×D₄×C₈₃	1	1	yes	characteristic
328	C₂×C₈	C₂×D₄×C₈₃	1	1	yes	characteristic
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
337	C₄⋊C₄	C₂×D₄×C₈₃	1	2	yes	—
338	C₄⋊C₄	C₂×D₄×C₈₃	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	4	2	no	—
344	C₄²	C₂⁴×C₈₃	1	1	yes	characteristic
345	C₂³	—	2	1	no	—
346	C₂³	—	4	2	no	—
347	Q₈	—	2	1	no	—
348	Q₈	—	2	2	no	—
349	Q₈	—	2	2	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	#135×C₈₃	1	2	yes	complemented
353	D₄	—	2	1	no	—
354	D₄	—	2	1	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	D₄	—	8	2	no	—
360	D₄	—	8	4	no	—
361	D₄	—	16	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	4	no	—
371	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₈₃	1	1	yes	characteristic
373	C₂×C₄	H(5,𝔽₂)×C₈₃	1	1	yes	characteristic
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	2	no	—
379	C₈	—	4	1	no	—
380	C₈	—	4	1	no	—
381	C₈	AGL(1,ℤ/8)×C₈₃	1	2	yes	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	D₄²×C₈₃	1	1	yes	characteristic
389	C₄	—	2	2	no	—
390	C₄	—	2	1	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	2	no	—
395	C₄	—	8	2	no	—
396	C₄	C₂×#135×C₈₃	1	1	yes	characteristic
397	C₄	C₂×AGL(1,ℤ/8)×C₈₃	1	1	yes	characteristic
398	C₄	#576×C₈₃	1	1	yes	characteristic
399	C₄	#578×C₈₃	1	1	yes	characteristic
400	C₂	—	8	1	no	—
401	C₂	—	16	2	no	—
402	C₂	C₈₃×#3274	1	1	yes	characteristic
403	C₂	C₈₃×#3285	1	1	yes	characteristic
404	C₂	C₈₃×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₈₃
prime radical	C₈₃×#3287	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₄²×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3395	C₂	semidirect
2. C₈₃×#3368	C₂	semidirect
4. C₈₃×#1709	C₂	semidirect
5. C₈₃×#1702	C₂	semidirect
6. C₈₃×#1669	C₂	semidirect
7. C₈₃×#1668	C₂	semidirect
8. C₈₃×#1641	C₂	semidirect
9. C₈₃×#1626	C₂	semidirect
10. C₈₃×#1591	C₂	semidirect
11. C₈×SD₁₆×C₈₃	C₂	semidirect
149. Q₈×C₈₃	#135	semidirect
197. #19943	C₈₃	direct (N × H)
203. #3395	C₂×C₈₃	semidirect
204. #3368	C₂×C₈₃	semidirect
206. #1709	C₂×C₈₃	semidirect
207. #1702	C₂×C₈₃	semidirect
208. #1669	C₂×C₈₃	semidirect
209. #1668	C₂×C₈₃	semidirect
210. #1641	C₂×C₈₃	semidirect
211. #1626	C₂×C₈₃	semidirect
212. #1591	C₂×C₈₃	semidirect
213. C₈×SD₁₆	C₂×C₈₃	semidirect
214. C₈₃	#19943	direct (N × H)
352. Q₈	#135×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₈₃×#3395	2
C₈₃×#3368	2
C₈₃×#3287	2
C₈₃×#1709	2
C₈₃×#1702	2
C₈₃×#1669	2
C₈₃×#1668	2
C₈₃×#1641	2
C₈₃×#1626	2
C₈₃×#1591	2
C₈×SD₁₆×C₈₃	2
#19943	83

Subgroups — C83×#19943 #35247767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#19943 #35247767