Subgroups — #35404579

Order 21248.

772 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19127748	C₂	1	1	yes	maximal, characteristic
2	#24916051	C₂	1	1	yes	maximal, characteristic
3	#24915879	C₂	1	1	yes	maximal, characteristic
4	#24907588	C₂	1	1	yes	maximal, characteristic, complemented
5	#24907587	C₂	1	1	yes	maximal, characteristic, complemented
6	#24907586	C₂	1	1	yes	maximal, characteristic, complemented
7	#24907585	C₂	1	2	yes	maximal, complemented
8	#24907584	C₂	1	2	yes	maximal, complemented
9	#344×D₈₃	C₂	1	2	yes	maximal
10	H(3,ℤ/4)×D₈₃	C₂	1	2	yes	maximal
11	C₈₃×#1833	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#13050573	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×D₈₃	C₂²	1	2	yes	—
14	C₂×M₁₆×D₈₃	C₂²	1	1	yes	characteristic
15	#117×D₈₃	C₂²	1	2	yes	—
16	#117×D₈₃	C₂²	1	1	yes	characteristic
17	#19127748	—	2	2	no	—
18	#19127748	—	2	2	no	—
19	C₂×#14581728	C₂²	1	1	yes	characteristic
20	C₂×#14581727	C₂²	1	2	yes	—
21	#19127742	—	2	2	no	—
22	#19127740	—	2	2	no	—
23	#19127739	C₂²	1	1	yes	characteristic
24	#19127737	C₂²	1	2	yes	—
25	#19127659	C₂²	1	1	yes	characteristic
26	#19127658	C₄	1	2	yes	complemented
27	#19127657	C₂²	1	1	yes	characteristic
28	#19127656	C₂²	1	1	yes	characteristic
29	#19127655	C₄	1	2	yes	complemented
30	#19127653	C₄	1	2	yes	complemented
31	C₄×#13050573	C₄	1	2	yes	complemented
32	#19127473	C₂²	1	2	yes	—
33	#19127472	C₂²	1	2	yes	—
34	#19127471	C₂²	1	2	yes	—
35	#19127458	C₂²	1	2	yes	—
36	#19127457	C₂²	1	2	yes	—
37	#19127457	C₂²	1	2	yes	—
38	C₂×#108×C₈₃	C₂²	1	1	yes	characteristic
39	#427×C₈₃	C₂²	1	1	yes	characteristic
40	#405×C₈₃	C₂²	1	1	yes	characteristic
41	#344×C₈₃	C₂²	1	2	yes	—
42	H(3,ℤ/4)×C₈₃	C₂²	1	2	yes	—
43	C₂²×C₄×D₈₃	C₂³	1	1	yes	characteristic
44	C₂×#13050574	C₂³	1	2	yes	—
45	C₂×#13050574	C₂³	1	1	yes	characteristic
46	C₂×#13050573	—	2	2	no	—
47	C₂×#13050573	C₂×C₄	1	2	yes	—
48	C₂×#13050573	C₂×C₄	1	1	yes	characteristic
49	C₂×#13050573	C₂×C₄	1	1	yes	characteristic
50	C₂×#13050573	C₂×C₄	1	1	yes	characteristic
51	C₂×#13050573	C₂×C₄	1	1	yes	characteristic
52	C₂×#13050573	D₄	1	2	yes	—
53	C₂×#13050573	D₄	1	2	yes	—
54	C₂×#13050573	Q₈	1	2	yes	—
55	C₂×#13050573	Q₈	1	2	yes	—
56	M₁₆×D₈₃	—	2	2	no	—
57	M₁₆×D₈₃	—	2	2	no	—
58	M₁₆×D₈₃	—	2	2	no	—
59	M₁₆×D₈₃	—	2	2	no	—
60	M₁₆×D₈₃	—	2	2	no	—
61	M₁₆×D₈₃	—	2	2	no	—
62	C₂²×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
63	C₂×C₈×D₈₃	—	2	2	no	—
64	C₂×C₈×D₈₃	C₂×C₄	1	2	yes	—
65	#14581751	C₂³	1	2	yes	—
66	#14581751	C₂³	1	1	yes	characteristic
67	#14581750	—	2	1	no	—
68	#14581750	—	2	2	no	—
69	#14581749	—	2	2	no	—
70	#14581749	C₂×C₄	1	2	yes	—
71	#14581748	—	2	1	no	—
72	#14581748	—	2	2	no	—
73	C₄⋊C₄×D₈₃	—	2	1	no	—
74	C₄⋊C₄×D₈₃	—	2	2	no	—
75	C₂²⋊C₄×D₈₃	—	2	1	no	—
76	C₂²⋊C₄×D₈₃	—	2	2	no	—
77	C₄²×D₈₃	—	2	2	no	—
78	C₄²×D₈₃	C₂×C₄	1	2	yes	—
79	#14581728	—	2	1	no	—
80	#14581728	—	2	1	no	—
81	#14581727	—	2	4	no	—
82	#14581726	—	2	1	no	—
83	#14581725	—	2	2	no	—
84	#14581724	—	2	1	no	—
85	#14581723	—	2	2	no	—
86	#14581703	C₂×C₄	1	2	yes	complemented
87	#14581702	C₂×C₄	1	2	yes	complemented
88	#14581702	C₂×C₄	1	2	yes	complemented
89	C₄×C₈₃⋊C₈	C₂×C₄	1	2	yes	complemented
90	C₈×Dic₈₃	C₂×C₄	1	2	yes	complemented
91	C₈×Dic₈₃	C₂×C₄	1	2	yes	complemented
92	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
93	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
95	#117×C₈₃	C₂³	1	2	yes	—
96	#117×C₈₃	C₂³	1	1	yes	characteristic
97	#108×C₈₃	—	2	1	no	—
98	#108×C₈₃	—	2	1	no	—
99	#107×C₈₃	—	2	1	no	—
100	#106×C₈₃	—	2	1	no	—
101	#97×C₈₃	C₂×C₄	1	2	yes	complemented
102	C₄×C₈×C₈₃	C₂×C₄	1	2	yes	complemented
103	C₂³×D₈₃	#41	1	1	yes	characteristic
104	C₂²×Dic₈₃	#41	1	1	yes	characteristic
105	C₂×C₄×D₈₃	—	2	2	no	—
106	C₂×C₄×D₈₃	—	4	2	no	—
107	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₈₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₈₃	C₂×D₄	1	2	yes	—
110	C₂×C₄×D₈₃	C₂×Q₈	1	2	yes	—
111	C₂×C₄×D₈₃	#41	1	2	yes	—
112	C₂×C₄×D₈₃	#41	1	2	yes	—
113	C₂×C₄×D₈₃	#41	1	1	yes	characteristic
114	C₂×C₄×D₈₃	#41	1	1	yes	characteristic
115	#13050574	—	2	1	no	—
116	#13050574	—	2	1	no	—
117	#13050574	—	2	2	no	—
118	#13050574	—	2	2	no	—
119	#13050573	—	2	4	no	—
120	#13050573	—	4	2	no	—
121	#13050573	—	4	2	no	—
122	#13050573	C₄⋊C₄	1	2	yes	—
123	#13050573	C₄⋊C₄	1	2	yes	—
124	#13050573	C₄⋊C₄	1	2	yes	—
125	#13050573	C₄⋊C₄	1	2	yes	—
126	#13050573	C₄⋊C₄	1	2	yes	—
127	#13050573	C₄⋊C₄	1	2	yes	—
128	#13050573	C₄⋊C₄	1	2	yes	—
129	#13050573	C₄⋊C₄	1	2	yes	—
130	C₂×C₈₃⋊C₈	—	2	2	no	—
131	C₂×C₈₃⋊C₈	C₂²×C₄	1	2	yes	—
132	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈₃⋊C₈	C₂×D₄	1	2	yes	—
135	C₂×C₈₃⋊C₈	C₂×Q₈	1	2	yes	—
136	C₈×D₈₃	—	2	4	no	—
137	C₈×D₈₃	—	4	2	no	—
138	C₈×D₈₃	—	4	2	no	—
139	C₄⋊Dic₈₃	—	2	1	no	—
140	C₄⋊Dic₈₃	—	2	2	no	—
141	Dic₈₃⋊C₄	—	2	2	no	—
142	Dic₈₃⋊C₄	—	4	2	no	—
143	C₂²⋊Dic₈₃	—	2	1	no	—
144	C₂²⋊Dic₈₃	—	2	2	no	—
145	(C₂×D₈₃)⋊C₄	—	2	2	no	—
146	(C₂×D₈₃)⋊C₄	—	4	2	no	—
147	C₄×Dic₈₃	—	2	2	no	—
148	C₄×Dic₈₃	—	2	2	no	—
149	C₄×Dic₈₃	—	4	2	no	—
150	C₄×Dic₈₃	C₂²×C₄	1	2	yes	—
151	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
152	M₁₆×C₈₃	—	2	1	no	—
153	M₁₆×C₈₃	—	2	1	no	—
154	M₁₆×C₈₃	—	2	2	no	—
155	M₁₆×C₈₃	—	2	2	no	—
156	C₂×C₈×C₈₃	—	2	2	no	—
157	C₂×C₈×C₈₃	C₂²×C₄	1	2	yes	—
158	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₈₃	C₂×Q₈	1	1	yes	characteristic
163	C₂×C₈×C₈₃	C₂×Q₈	1	1	yes	characteristic
164	C₄⋊C₄×C₈₃	—	2	1	no	—
165	C₄⋊C₄×C₈₃	—	2	2	no	—
166	C₂²⋊C₄×C₈₃	—	2	1	no	—
167	C₂²⋊C₄×C₈₃	—	2	2	no	—
168	C₄²×C₈₃	—	2	2	no	—
169	C₄²×C₈₃	C₂²×C₄	1	2	yes	—
170	C₂³×C₈₃	C₂×#41	1	1	yes	characteristic
171	C₂²×D₈₃	—	8	1	no	—
172	C₂²×D₈₃	#117	1	1	yes	characteristic
173	C₂²×D₈₃	#117	1	1	yes	characteristic
174	C₂²×D₈₃	#124	1	2	yes	—
175	C₂²×D₈₃	#125	1	2	yes	—
176	C₂×C₄×C₈₃	—	2	2	no	—
177	C₂×C₄×C₈₃	—	4	2	no	—
178	C₂×C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₈₃	C₂²×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
184	C₂×Dic₈₃	—	2	2	no	—
185	C₂×Dic₈₃	—	4	2	no	—
186	C₂×Dic₈₃	#117	1	1	yes	characteristic
187	C₂×Dic₈₃	#117	1	1	yes	characteristic
188	C₂×Dic₈₃	#124	1	2	yes	—
189	C₂×Dic₈₃	#125	1	2	yes	—
190	C₄×D₈₃	—	8	2	no	—
191	C₄×D₈₃	—	8	4	no	—
192	C₄×D₈₃	C₂×C₄⋊C₄	1	2	yes	—
193	C₄×D₈₃	C₂×C₄⋊C₄	1	2	yes	—
194	C₄×D₈₃	#117	1	2	yes	—
195	C₄×D₈₃	#117	1	2	yes	—
196	C₄×D₈₃	#124	1	2	yes	—
197	C₄×D₈₃	#124	1	2	yes	—
198	C₄×D₈₃	#125	1	2	yes	—
199	C₄×D₈₃	#125	1	2	yes	—
200	C₈×C₈₃	—	2	2	no	—
201	C₈×C₈₃	—	4	2	no	—
202	C₈×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₈×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₈×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₈×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₈₃⋊C₈	—	2	2	no	—
207	C₈₃⋊C₈	—	4	2	no	—
208	C₈₃⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
209	C₈₃⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
210	C₂²×C₈₃	—	4	1	no	—
211	C₂²×C₈₃	C₂×#117	1	1	yes	characteristic
212	C₂²×C₈₃	C₂×#124	1	1	yes	characteristic
213	C₂²×C₈₃	C₂×#125	1	1	yes	characteristic
214	C₂×D₈₃	—	4	1	no	—
215	C₂×D₈₃	—	4	2	no	—
216	C₂×D₈₃	—	4	1	no	—
217	C₂×D₈₃	—	4	2	no	—
218	C₂×D₈₃	#382	1	2	yes	—
219	C₂×D₈₃	#382	1	2	yes	—
220	C₄×C₈₃	—	4	2	no	—
221	C₄×C₈₃	—	8	2	no	—
222	C₄×C₈₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
223	C₄×C₈₃	C₂×#117	1	1	yes	characteristic
224	C₄×C₈₃	C₂×#124	1	1	yes	characteristic
225	C₄×C₈₃	C₂×#125	1	1	yes	characteristic
226	Dic₈₃	—	4	2	no	—
227	Dic₈₃	—	8	2	no	—
228	Dic₈₃	#382	1	2	yes	—
229	Dic₈₃	#382	1	2	yes	—
230	#20757	—	83	1	no	maximal, Sylow
231	C₂×C₈₃	—	2	1	no	—
232	C₂×C₈₃	—	2	1	no	—
233	C₂×C₈₃	—	2	1	no	—
234	C₂×C₈₃	C₂×#382	1	1	yes	characteristic
235	D₈₃	—	2	2	no	—
236	D₈₃	—	2	2	no	—
237	C₂×#430	—	83	1	no	—
238	#2911	—	83	1	no	—
239	#2873	—	83	1	no	—
240	#1833	—	83	1	no	—
241	#1833	—	83	1	no	—
242	#1833	—	83	1	no	—
243	#1833	—	83	2	no	—
244	#1833	—	83	2	no	—
245	#1833	D₈₃	1	1	yes	characteristic, complemented
246	C₂×#344	—	83	2	no	—
247	C₂×H(3,ℤ/4)	—	83	2	no	—
248	C₈₃	#20757	1	1	yes	characteristic, complemented, Sylow
249	C₂²×M₁₆	—	83	1	no	—
250	C₂²×M₁₆	—	83	1	no	—
251	C₂²×M₁₆	—	83	2	no	—
252	C₂×#117	—	83	1	no	—
253	C₂×#117	—	83	2	no	—
254	#430	—	166	2	no	—
255	#430	—	166	2	no	—
256	C₂×#108	—	83	2	no	—
257	C₂×#108	—	83	1	no	—
258	C₂×#108	C₂×D₈₃	1	1	yes	characteristic
259	#428	—	166	2	no	—
260	#428	—	166	2	no	—
261	#427	—	83	1	no	—
262	#427	—	83	2	no	—
263	#427	C₂×D₈₃	1	1	yes	characteristic
264	#405	—	83	1	no	—
265	#405	—	83	1	no	—
266	#405	—	83	1	no	—
267	#405	—	83	2	no	—
268	#405	—	83	2	no	—
269	#405	C₂×D₈₃	1	1	yes	characteristic
270	C₄×M₁₆	—	83	2	no	—
271	C₄×M₁₆	—	83	2	no	—
272	#344	—	83	2	no	—
273	#344	—	83	2	no	—
274	#344	—	83	2	no	—
275	#344	C₂×D₈₃	1	2	yes	—
276	H(3,ℤ/4)	—	83	2	no	—
277	H(3,ℤ/4)	—	83	2	no	—
278	H(3,ℤ/4)	—	83	2	no	—
279	H(3,ℤ/4)	C₂×D₈₃	1	2	yes	—
280	C₂³×C₄	—	83	1	no	—
281	C₂×M₁₆	—	83	1	no	—
282	C₂×M₁₆	—	83	1	no	—
283	C₂×M₁₆	—	83	1	no	—
284	C₂×M₁₆	—	83	1	no	—
285	C₂×M₁₆	—	83	1	no	—
286	C₂×M₁₆	—	83	2	no	—
287	C₂×M₁₆	—	83	2	no	—
288	C₂×M₁₆	—	83	2	no	—
289	C₂×M₁₆	—	83	2	no	—
290	C₂×M₁₆	—	83	2	no	—
291	C₂×M₁₆	—	83	2	no	—
292	C₂×M₁₆	—	166	2	no	—
293	C₂×M₁₆	—	166	2	no	—
294	C₂×M₁₆	—	166	2	no	—
295	C₂×M₁₆	—	166	2	no	—
296	C₂×M₁₆	—	166	2	no	—
297	C₂×M₁₆	—	166	2	no	—
298	C₂×M₁₆	—	166	2	no	—
299	C₂×M₁₆	C₂²×D₈₃	1	2	yes	—
300	C₂×M₁₆	C₂²×D₈₃	1	1	yes	characteristic
301	C₂²×C₈	—	83	1	no	—
302	C₂²×C₈	—	83	2	no	—
303	C₂²×C₈	—	166	2	no	—
304	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
305	#117	—	83	1	no	—
306	#117	—	83	2	no	—
307	#117	—	83	2	no	—
308	#117	—	166	2	no	—
309	#117	—	166	2	no	—
310	#117	—	166	2	no	—
311	#117	—	166	1	no	—
312	#117	—	166	1	no	—
313	#117	C₂²×D₈₃	1	2	yes	—
314	#117	C₂²×D₈₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	—	166	2	no	—
316	C₂×C₄⋊C₄	—	166	1	no	—
317	C₂×C₂²⋊C₄	—	166	2	no	—
318	C₂×C₂²⋊C₄	—	166	1	no	—
319	C₂×C₄²	—	83	2	no	—
320	C₂×C₄²	—	166	2	no	—
321	#108	—	2	1	no	—
322	#108	—	2	1	no	—
323	#108	—	166	4	no	—
324	#108	—	166	1	no	—
325	#108	—	166	1	no	—
326	#107	—	2	1	no	—
327	#107	—	166	2	no	—
328	#107	—	166	1	no	—
329	#106	—	2	1	no	—
330	#106	—	166	2	no	—
331	#106	—	166	1	no	—
332	#97	—	83	2	no	—
333	#97	—	83	2	no	—
334	#97	—	83	2	no	—
335	#97	C₄×D₈₃	1	2	yes	complemented
336	C₄×C₈	—	83	2	no	—
337	C₄×C₈	—	83	2	no	—
338	C₄×C₈	—	83	2	no	—
339	C₄×C₈	C₄×D₈₃	1	2	yes	complemented
340	C₂⁴	—	83	1	no	—
341	C₂²×C₄	—	332	2	no	—
342	C₂²×C₄	—	83	1	no	—
343	C₂²×C₄	—	83	1	no	—
344	C₂²×C₄	—	83	1	no	—
345	C₂²×C₄	—	83	2	no	—
346	C₂²×C₄	—	83	2	no	—
347	C₂²×C₄	—	83	2	no	—
348	C₂²×C₄	—	83	1	no	—
349	C₂²×C₄	—	83	1	no	—
350	C₂²×C₄	—	83	2	no	—
351	C₂²×C₄	—	166	2	no	—
352	C₂²×C₄	C₂³×D₈₃	1	1	yes	characteristic
353	M₁₆	—	2	1	no	—
354	M₁₆	—	2	1	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	332	2	no	—
358	M₁₆	—	332	2	no	—
359	M₁₆	—	83	2	no	—
360	M₁₆	—	83	2	no	—
361	M₁₆	—	83	2	no	—
362	M₁₆	—	83	2	no	—
363	M₁₆	—	83	2	no	—
364	M₁₆	—	83	2	no	—
365	M₁₆	—	83	2	no	—
366	M₁₆	—	83	2	no	—
367	M₁₆	—	166	4	no	—
368	M₁₆	—	166	2	no	—
369	M₁₆	—	166	2	no	—
370	M₁₆	—	166	1	no	—
371	M₁₆	—	166	1	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	332	2	no	—
374	C₂×C₈	—	332	2	no	—
375	C₂×C₈	—	83	1	no	—
376	C₂×C₈	—	83	1	no	—
377	C₂×C₈	—	83	2	no	—
378	C₂×C₈	—	83	2	no	—
379	C₂×C₈	—	83	2	no	—
380	C₂×C₈	—	166	4	no	—
381	C₂×C₈	—	166	2	no	—
382	C₂×C₈	C₂×C₄×D₈₃	1	2	yes	—
383	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
384	C₂×C₈	C₂×C₄×D₈₃	1	1	yes	characteristic
385	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
386	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
387	C₂×C₈	Q₈×D₈₃	1	1	yes	characteristic
388	C₂×C₈	Q₈×D₈₃	1	1	yes	characteristic
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	332	2	no	—
392	C₄⋊C₄	—	166	2	no	—
393	C₄⋊C₄	—	166	2	no	—
394	C₄⋊C₄	—	166	1	no	—
395	C₂²⋊C₄	—	2	1	no	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	332	2	no	—
398	C₂²⋊C₄	—	166	2	no	—
399	C₂²⋊C₄	—	166	2	no	—
400	C₂²⋊C₄	—	166	1	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	332	2	no	—
403	C₄²	—	83	2	no	—
404	C₄²	—	166	2	no	—
405	C₄²	—	166	2	no	—
406	C₄²	C₂×C₄×D₈₃	1	2	yes	—
407	C₂³	—	83	1	no	—
408	C₂³	—	83	1	no	—
409	C₂³	—	83	2	no	—
410	C₂³	—	83	2	no	—
411	C₂³	—	664	1	no	—
412	C₂³	#41×D₈₃	1	1	yes	characteristic
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	332	2	no	—
416	C₂×C₄	—	83	1	no	—
417	C₂×C₄	—	83	1	no	—
418	C₂×C₄	—	83	2	no	—
419	C₂×C₄	—	83	2	no	—
420	C₂×C₄	—	83	2	no	—
421	C₂×C₄	—	83	2	no	—
422	C₂×C₄	—	83	2	no	—
423	C₂×C₄	—	83	2	no	—
424	C₂×C₄	—	83	2	no	—
425	C₂×C₄	—	83	2	no	—
426	C₂×C₄	—	83	2	no	—
427	C₂×C₄	—	83	2	no	—
428	C₂×C₄	—	664	2	no	—
429	C₂×C₄	—	664	4	no	—
430	C₂×C₄	—	166	2	no	—
431	C₂×C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
432	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
433	C₂×C₄	C₂×Q₈×D₈₃	1	1	yes	characteristic
434	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
435	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
436	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
437	C₈	—	2	2	no	—
438	C₈	—	4	2	no	—
439	C₈	—	332	2	no	—
440	C₈	—	83	2	no	—
441	C₈	—	83	2	no	—
442	C₈	—	166	2	no	—
443	C₈	C₄⋊C₄×D₈₃	1	1	yes	characteristic
444	C₈	C₄⋊C₄×D₈₃	1	1	yes	characteristic
445	C₈	C₄⋊C₄×D₈₃	1	1	yes	characteristic
446	C₈	C₄⋊C₄×D₈₃	1	1	yes	characteristic
447	C₂²	—	4	1	no	—
448	C₂²	—	332	1	no	—
449	C₂²	—	332	2	no	—
450	C₂²	—	332	1	no	—
451	C₂²	—	332	2	no	—
452	C₂²	—	83	2	no	—
453	C₂²	—	83	2	no	—
454	C₂²	#117×D₈₃	1	1	yes	characteristic
455	C₂²	#124×D₈₃	1	1	yes	characteristic
456	C₂²	#125×D₈₃	1	1	yes	characteristic
457	C₄	—	4	2	no	—
458	C₄	—	8	2	no	—
459	C₄	—	332	2	no	—
460	C₄	—	83	2	no	—
461	C₄	—	83	2	no	—
462	C₄	—	664	2	no	—
463	C₄	C₂×C₄⋊C₄×D₈₃	1	1	yes	characteristic
464	C₄	#117×D₈₃	1	1	yes	characteristic
465	C₄	#124×D₈₃	1	1	yes	characteristic
466	C₄	#125×D₈₃	1	1	yes	characteristic
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	—	2	1	no	—
470	C₂	—	166	2	no	—
471	C₂	—	166	2	no	—
472	C₂	#382×D₈₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#117×D₈₃
commutator	C₂×C₄×C₈₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₃
Fitting	C₈₃×#1833	C₂
socle	C₂×C₈₃	C₂×#382
prime radical	C₂³×D₈₃	#41
cosocle	C₂²×C₄×C₈₃	C₂⁴
hypercenter	#1833	D₈₃
hypocenter	C₈₃	#20757
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₄ ◁ #117 ◁ #1833

Complements

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

N	H ≅ G/N	type
4. #24907588	C₂	semidirect
5. #24907587	C₂	semidirect
6. #24907586	C₂	semidirect
7. #24907585	C₂	semidirect
8. #24907584	C₂	semidirect
11. C₈₃×#1833	C₂	semidirect
26. #19127658	C₄	semidirect
29. #19127655	C₄	semidirect
30. #19127653	C₄	semidirect
31. C₄×#13050573	C₄	semidirect
86. #14581703	C₂×C₄	semidirect
87. #14581702	C₂×C₄	semidirect
88. #14581702	C₂×C₄	semidirect
89. C₄×C₈₃⋊C₈	C₂×C₄	semidirect
90. C₈×Dic₈₃	C₂×C₄	semidirect
91. C₈×Dic₈₃	C₂×C₄	semidirect
101. #97×C₈₃	C₂×C₄	semidirect
102. C₄×C₈×C₈₃	C₂×C₄	semidirect
245. #1833	D₈₃	semidirect
248. C₈₃	#20757	semidirect
335. #97	C₄×D₈₃	semidirect
339. C₄×C₈	C₄×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19127748	2
#24916051	2
#24915879	2
#24907588	2
#24907587	2
#24907586	2
#24907585	2
#24907584	2
#344×D₈₃	2
H(3,ℤ/4)×D₈₃	2
C₈₃×#1833	2
#20757	83