Subgroups — #35559142

Order 21248.

524 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24917972	C₂	1	1	yes	maximal, characteristic, complemented
2	#443×D₈₃	C₂	1	1	yes	maximal, characteristic
3	#24909638	C₂	1	2	yes	maximal, complemented
4	#24909637	C₂	1	2	yes	maximal, complemented
5	#24909635	C₂	1	1	yes	maximal, characteristic, complemented
6	#24909634	C₂	1	1	yes	maximal, characteristic, complemented
7	#24909631	C₂	1	1	yes	maximal, characteristic, complemented
8	#24909234	C₂	1	2	yes	maximal, complemented
9	#364×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#24909197	C₂	1	2	yes	maximal
11	C₈₃×#2230	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₈₃	C₂²	1	1	yes	characteristic
13	#131×D₈₃	—	2	1	no	—
14	#19128256	—	2	1	no	—
15	M₃₂×D₈₃	C₂²	1	2	yes	—
16	#19128104	—	2	1	no	—
17	#19128101	—	2	1	no	—
18	#19128101	C₂²	1	2	yes	complemented
19	#19128099	C₂²	1	1	yes	characteristic, complemented
20	#19127819	C₂²	1	1	yes	characteristic
21	#19127818	C₂²	1	1	yes	characteristic
22	#19127817	C₂²	1	1	yes	characteristic
23	#19127816	—	2	1	no	—
24	#19127815	—	2	1	no	—
25	#108×D₈₃	C₂²	1	1	yes	characteristic
26	#19127736	—	2	1	no	—
27	#19127736	C₂²	1	2	yes	—
28	#104×D₈₃	—	2	1	no	—
29	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
30	#19127525	C₂²	1	2	yes	complemented
31	#19127524	C₂²	1	2	yes	complemented
32	#19127523	C₂²	1	2	yes	complemented
33	#19127522	C₂²	1	1	yes	characteristic, complemented
34	#19127521	C₂²	1	2	yes	complemented
35	#19127512	C₂²	1	2	yes	—
36	#19127511	C₂²	1	2	yes	—
37	#19127510	C₂²	1	2	yes	—
38	#498×C₈₃	C₂²	1	1	yes	characteristic, complemented
39	#443×C₈₃	C₂²	1	1	yes	characteristic
40	#365×C₈₃	C₂²	1	2	yes	complemented
41	#364×C₈₃	C₂²	1	1	yes	characteristic, complemented
42	#360×C₈₃	C₂²	1	2	yes	—
43	#41×D₈₃	—	2	1	no	—
44	#14581815	Q₈	1	1	yes	characteristic, complemented
45	#14581814	C₂³	1	1	yes	characteristic
46	#14581813	—	2	1	no	—
47	#14581812	—	2	1	no	—
48	#14581811	Q₈	1	1	yes	characteristic, complemented
49	Q₁₆×D₈₃	Q₈	1	1	yes	characteristic, complemented
50	SD₁₆×D₈₃	—	2	1	no	—
51	D₈×D₈₃	Q₈	1	1	yes	characteristic, complemented
52	#14581800	—	2	1	no	—
53	#14581800	—	4	1	no	—
54	#14581799	—	2	1	no	—
55	#14581798	—	2	1	no	—
56	#14581798	—	4	1	no	—
57	M₁₆×D₈₃	—	2	1	no	—
58	M₁₆×D₈₃	—	4	1	no	—
59	C₂×C₈×D₈₃	—	4	1	no	—
60	C₂×C₈×D₈₃	D₄	1	1	yes	characteristic
61	C₂×C₈×D₈₃	C₂³	1	1	yes	characteristic
62	#14581792	—	2	1	no	—
63	#14581783	—	2	2	no	—
64	#14581772	—	4	1	no	—
65	#14581768	—	4	1	no	—
66	Q₈×Dic₈₃	—	4	1	no	—
67	#14581757	—	4	1	no	—
68	#14581750	—	2	2	no	—
69	C₄²×D₈₃	D₄	1	1	yes	characteristic
70	#14581732	C₂³	1	2	yes	—
71	#14581731	—	2	2	no	—
72	C₁₆×D₈₃	—	2	2	no	—
73	#14581728	C₂³	1	1	yes	characteristic
74	#14581727	—	2	1	no	—
75	#14581725	—	2	2	no	—
76	#14581725	—	2	2	no	—
77	#14581724	—	2	1	no	—
78	#14581724	C₂³	1	2	yes	—
79	#14581720	—	2	1	no	—
80	#14581719	—	2	1	no	—
81	#14581718	—	2	1	no	—
82	C₄×C₈₃⋊C₈	D₄	1	1	yes	characteristic
83	C₈×Dic₈₃	D₄	1	1	yes	characteristic
84	C₈×Dic₈₃	C₂³	1	1	yes	characteristic
85	#135×C₈₃	C₂³	1	1	yes	characteristic
86	#131×C₈₃	—	2	1	no	—
87	C₄⋊Q₈×C₈₃	—	2	1	no	—
88	M₃₂×C₈₃	C₂³	1	2	yes	—
89	#108×C₈₃	C₂³	1	1	yes	characteristic
90	#106×C₈₃	—	2	1	no	—
91	#106×C₈₃	C₂³	1	2	yes	—
92	#104×C₈₃	—	2	1	no	—
93	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
94	#13050591	—	2	1	no	—
95	#13050590	—	2	1	no	—
96	#13050590	—	4	1	no	—
97	#13050589	—	2	1	no	—
98	#13050589	—	4	1	no	—
99	C₂×Dic₁₆₆	—	4	1	no	—
100	Q₈×D₈₃	—	2	1	no	—
101	D₄×D₈₃	—	2	1	no	—
102	D₄×D₈₃	—	4	1	no	—
103	C₂×C₄×D₈₃	—	2	1	no	—
104	C₂×C₄×D₈₃	—	4	1	no	—
105	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
106	Dic₃₃₂	C₂×Q₈	1	1	yes	characteristic
107	#13050580	—	2	1	no	—
108	#13050579	—	2	1	no	—
109	#13050578	—	2	1	no	—
110	#13050577	—	2	1	no	—
111	D₆₆₄	C₂×Q₈	1	1	yes	characteristic
112	#13050575	—	2	1	no	—
113	#13050574	—	2	1	no	—
114	#13050574	—	4	1	no	—
115	#13050573	—	4	1	no	—
116	#13050573	—	4	1	no	—
117	#13050573	—	4	1	no	—
118	C₂×C₈₃⋊C₈	—	4	1	no	—
119	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
121	C₈×D₈₃	—	4	1	no	—
122	C₈×D₈₃	—	4	1	no	—
123	C₈×D₈₃	—	4	1	no	—
124	C₈×D₈₃	SD₁₆	1	1	yes	characteristic
125	C₈×D₈₃	SD₁₆	1	1	yes	characteristic
126	C₈×D₈₃	SD₁₆	1	1	yes	characteristic
127	C₈×D₈₃	SD₁₆	1	1	yes	characteristic
128	C₈×D₈₃	C₂×Q₈	1	1	yes	characteristic
129	C₈×D₈₃	C₂×Q₈	1	1	yes	characteristic
130	C₈×D₈₃	#41	1	1	yes	characteristic
131	C₈×D₈₃	#41	1	1	yes	characteristic
132	C₄⋊Dic₈₃	—	2	2	no	—
133	C₄⋊Dic₈₃	—	4	2	no	—
134	C₄⋊Dic₈₃	—	4	1	no	—
135	Dic₈₃⋊C₄	—	4	2	no	—
136	(C₂×D₈₃)⋊C₄	—	4	2	no	—
137	C₄×Dic₈₃	—	2	1	no	—
138	C₄×Dic₈₃	—	4	2	no	—
139	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
140	C₈₃⋊C₁₆	—	2	2	no	—
141	#41×C₈₃	—	2	1	no	—
142	C₂×Q₈×C₈₃	—	4	1	no	—
143	Q₁₆×C₈₃	C₂×Q₈	1	1	yes	characteristic
144	SD₁₆×C₈₃	—	2	1	no	—
145	D₈×C₈₃	C₂×Q₈	1	1	yes	characteristic
146	M₁₆×C₈₃	—	2	1	no	—
147	M₁₆×C₈₃	—	4	1	no	—
148	C₂×C₈×C₈₃	—	4	1	no	—
149	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₈₃	C₂⁴	1	1	yes	characteristic
151	C₄⋊C₄×C₈₃	—	2	2	no	—
152	C₄⋊C₄×C₈₃	—	4	1	no	—
153	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
154	C₁₆×C₈₃	—	2	2	no	—
155	C₂²×D₈₃	—	4	1	no	—
156	C₂²×D₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
157	Q₈×C₈₃	—	2	1	no	—
158	Q₈×C₈₃	—	8	2	no	—
159	D₄×C₈₃	—	2	1	no	—
160	D₄×C₈₃	—	4	1	no	—
161	C₂×C₄×C₈₃	—	2	1	no	—
162	C₂×C₄×C₈₃	—	4	1	no	—
163	C₂×C₄×C₈₃	—	4	2	no	—
164	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
165	C₂²⋊D₈₃	—	4	1	no	—
166	C₂²⋊D₈₃	—	4	1	no	—
167	C₂²⋊D₈₃	—	4	1	no	—
168	C₂×Dic₈₃	—	2	1	no	—
169	C₂×Dic₈₃	—	4	1	no	—
170	C₂×Dic₈₃	—	4	2	no	—
171	C₂×Dic₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
172	D₃₃₂	—	2	1	no	—
173	D₃₃₂	—	4	1	no	—
174	C₄×D₈₃	—	4	2	no	—
175	C₄×D₈₃	—	4	1	no	—
176	C₄×D₈₃	—	4	1	no	—
177	C₄×D₈₃	—	4	1	no	—
178	C₄×D₈₃	C₂²⋊Q₈	1	1	yes	characteristic
179	C₄×D₈₃	C₂²⋊Q₈	1	1	yes	characteristic
180	C₄×D₈₃	C₂×SD₁₆	1	1	yes	characteristic
181	C₄×D₈₃	C₂×SD₁₆	1	1	yes	characteristic
182	Dic₁₆₆	—	2	1	no	—
183	Dic₁₆₆	—	4	1	no	—
184	Dic₁₆₆	—	8	2	no	—
185	C₈×C₈₃	—	4	1	no	—
186	C₈×C₈₃	C₂×SD₁₆	1	1	yes	characteristic
187	C₈×C₈₃	C₂×SD₁₆	1	1	yes	characteristic
188	C₈×C₈₃	C₂²×Q₈	1	1	yes	characteristic
189	C₈×C₈₃	C₂×#41	1	1	yes	characteristic
190	C₈₃⋊C₈	—	4	1	no	—
191	C₈₃⋊C₈	C₂²⋊Q₈	1	1	yes	characteristic
192	C₈₃⋊C₈	C₂²⋊Q₈	1	1	yes	characteristic
193	C₈₃⋊C₈	C₂×SD₁₆	1	1	yes	characteristic
194	C₈₃⋊C₈	C₂×SD₁₆	1	1	yes	characteristic
195	C₂²×C₈₃	—	4	1	no	—
196	C₂²×C₈₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₂×D₈₃	—	4	1	no	—
198	C₂×D₈₃	—	4	1	no	—
199	C₂×D₈₃	—	8	2	no	—
200	C₂×D₈₃	#476	1	1	yes	characteristic
201	C₂×D₈₃	#476	1	1	yes	characteristic
202	C₄×C₈₃	—	2	2	no	—
203	C₄×C₈₃	—	4	1	no	—
204	C₄×C₈₃	—	8	2	no	—
205	C₄×C₈₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
206	C₄×C₈₃	C₂²×SD₁₆	1	1	yes	characteristic
207	Dic₈₃	—	4	1	no	—
208	Dic₈₃	—	4	1	no	—
209	Dic₈₃	—	8	2	no	—
210	Dic₈₃	#476	1	1	yes	characteristic
211	Dic₈₃	#476	1	1	yes	characteristic
212	#33637	—	83	1	no	maximal, Sylow
213	C₂×C₈₃	—	2	1	no	—
214	C₂×C₈₃	—	8	1	no	—
215	C₂×C₈₃	C₂×#476	1	1	yes	characteristic
216	D₈₃	—	2	1	no	—
217	D₈₃	—	2	1	no	—
218	D₈₃	—	8	1	no	—
219	#3160	—	83	1	no	—
220	C₂×#443	—	83	1	no	—
221	#2231	—	83	2	no	—
222	#2231	—	83	2	no	—
223	#2230	—	83	1	no	—
224	#2230	—	83	1	no	—
225	#2230	—	83	1	no	—
226	#2230	D₈₃	1	1	yes	characteristic, complemented
227	#2155	—	83	2	no	—
228	C₂×#364	—	83	1	no	—
229	#2145	—	83	2	no	—
230	C₈₃	#33637	1	1	yes	characteristic, complemented, Sylow
231	C₂×#135	—	83	1	no	—
232	C₂×#131	—	166	1	no	—
233	#533	—	166	1	no	—
234	C₂×M₃₂	—	83	2	no	—
235	#500	—	166	1	no	—
236	#499	—	83	2	no	—
237	#499	—	166	1	no	—
238	#498	—	83	1	no	—
239	#498	C₂×D₈₃	1	1	yes	characteristic, complemented
240	#443	—	83	1	no	—
241	#443	—	83	1	no	—
242	#443	—	83	1	no	—
243	#443	—	166	1	no	—
244	#443	—	166	1	no	—
245	#443	C₂×D₈₃	1	1	yes	characteristic
246	C₂×#108	—	83	1	no	—
247	#427	—	83	2	no	—
248	#427	—	166	1	no	—
249	C₂×#104	—	166	1	no	—
250	C₂×C₄×C₈	—	83	1	no	—
251	#365	—	83	2	no	—
252	#365	—	83	2	no	—
253	#365	—	83	2	no	—
254	#365	C₂×D₈₃	1	2	yes	complemented
255	#364	—	83	2	no	—
256	#364	—	83	1	no	—
257	#364	C₂×D₈₃	1	1	yes	characteristic, complemented
258	#360	—	83	2	no	—
259	#360	—	83	2	no	—
260	#360	—	83	2	no	—
261	#360	C₂×D₈₃	1	2	yes	—
262	C₂×#41	—	166	1	no	—
263	#135	—	83	1	no	—
264	#135	—	83	1	no	—
265	#135	—	83	1	no	—
266	#135	—	166	1	no	—
267	#135	—	166	1	no	—
268	#135	C₂²×D₈₃	1	1	yes	characteristic
269	C₂×Q₁₆	—	83	1	no	—
270	C₂×SD₁₆	—	166	1	no	—
271	C₂×D₈	—	83	1	no	—
272	#131	—	2	1	no	—
273	#131	—	332	1	no	—
274	#131	—	332	1	no	—
275	#131	—	166	1	no	—
276	#131	—	166	1	no	—
277	#131	—	166	1	no	—
278	C₂×M₁₆	—	332	1	no	—
279	C₂×M₁₆	—	166	1	no	—
280	C₂²×C₈	—	332	1	no	—
281	C₂²×C₈	—	83	1	no	—
282	C₂²×C₈	—	83	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	166	1	no	—
285	#125	—	166	2	no	—
286	C₂²⋊Q₈	—	332	1	no	—
287	C₂²⋊Q₈	—	332	1	no	—
288	C₄×Q₈	—	332	1	no	—
289	C₄×Q₈	—	332	1	no	—
290	#117	—	166	2	no	—
291	C₂×C₄²	—	83	1	no	—
292	M₃₂	—	83	2	no	—
293	M₃₂	—	166	2	no	—
294	M₃₂	C₂²×D₈₃	1	2	yes	—
295	C₂×C₁₆	—	166	2	no	—
296	#108	—	83	1	no	—
297	#108	—	166	1	no	—
298	#108	C₂²×D₈₃	1	1	yes	characteristic
299	#107	—	166	2	no	—
300	#107	—	166	2	no	—
301	#106	—	2	1	no	—
302	#106	—	83	2	no	—
303	#106	—	166	1	no	—
304	#106	C₂²×D₈₃	1	2	yes	—
305	#104	—	2	1	no	—
306	#104	—	166	1	no	—
307	#104	—	166	1	no	—
308	#104	—	166	1	no	—
309	C₄×C₈	—	83	1	no	—
310	C₄×C₈	—	83	1	no	—
311	C₄×C₈	—	83	1	no	—
312	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
313	#41	—	2	1	no	—
314	#41	—	332	1	no	—
315	#41	—	332	1	no	—
316	#41	—	166	1	no	—
317	#41	—	166	1	no	—
318	#41	—	166	1	no	—
319	C₂×Q₈	—	4	1	no	—
320	C₂×Q₈	—	332	1	no	—
321	C₂×Q₈	—	166	1	no	—
322	C₂×D₄	—	332	1	no	—
323	C₂×D₄	—	166	1	no	—
324	C₂²×C₄	—	332	1	no	—
325	C₂²×C₄	—	83	1	no	—
326	C₂²×C₄	—	166	1	no	—
327	Q₁₆	—	83	1	no	—
328	Q₁₆	—	166	1	no	—
329	Q₁₆	Q₈×D₈₃	1	1	yes	characteristic
330	SD₁₆	—	2	1	no	—
331	SD₁₆	—	166	1	no	—
332	SD₁₆	—	166	1	no	—
333	SD₁₆	—	166	1	no	—
334	D₈	—	83	1	no	—
335	D₈	—	166	1	no	—
336	D₈	Q₈×D₈₃	1	1	yes	characteristic
337	M₁₆	—	2	1	no	—
338	M₁₆	—	4	1	no	—
339	M₁₆	—	332	1	no	—
340	M₁₆	—	332	1	no	—
341	M₁₆	—	332	1	no	—
342	M₁₆	—	332	1	no	—
343	M₁₆	—	166	1	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	332	1	no	—
346	C₂×C₈	—	332	1	no	—
347	C₂×C₈	—	332	1	no	—
348	C₂×C₈	—	332	1	no	—
349	C₂×C₈	—	83	1	no	—
350	C₂×C₈	—	83	1	no	—
351	C₂×C₈	—	83	1	no	—
352	C₂×C₈	—	83	1	no	—
353	C₂×C₈	—	83	1	no	—
354	C₂×C₈	—	83	1	no	—
355	C₂×C₈	—	83	1	no	—
356	C₂×C₈	—	83	1	no	—
357	C₂×C₈	—	83	1	no	—
358	C₂×C₈	—	83	1	no	—
359	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
360	C₂×C₈	C₂³×D₈₃	1	1	yes	characteristic
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	—	332	1	no	—
364	C₄⋊C₄	—	332	2	no	—
365	C₄⋊C₄	—	332	2	no	—
366	C₄⋊C₄	—	166	2	no	—
367	C₂²⋊C₄	—	332	2	no	—
368	C₄²	—	332	2	no	—
369	C₄²	—	83	1	no	—
370	C₄²	—	166	1	no	—
371	C₄²	D₄×D₈₃	1	1	yes	characteristic
372	C₁₆	—	2	2	no	—
373	C₁₆	—	166	2	no	—
374	C₂³	—	332	1	no	—
375	C₂³	—	83	1	no	—
376	Q₈	—	2	1	no	—
377	Q₈	—	8	2	no	—
378	Q₈	—	332	1	no	—
379	Q₈	—	664	2	no	—
380	Q₈	—	166	1	no	—
381	D₄	—	2	1	no	—
382	D₄	—	4	1	no	—
383	D₄	—	332	1	no	—
384	D₄	—	332	1	no	—
385	D₄	—	332	1	no	—
386	D₄	—	332	1	no	—
387	D₄	—	166	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	332	2	no	—
392	C₂×C₄	—	332	1	no	—
393	C₂×C₄	—	332	1	no	—
394	C₂×C₄	—	332	1	no	—
395	C₂×C₄	—	332	1	no	—
396	C₂×C₄	—	332	2	no	—
397	C₂×C₄	—	83	1	no	—
398	C₂×C₄	—	83	1	no	—
399	C₂×C₄	—	83	1	no	—
400	C₂×C₄	—	83	1	no	—
401	C₂×C₄	—	83	1	no	—
402	C₂×C₄	—	166	1	no	—
403	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
404	C₈	—	4	1	no	—
405	C₈	—	332	1	no	—
406	C₈	—	83	1	no	—
407	C₈	—	83	1	no	—
408	C₈	—	83	1	no	—
409	C₈	—	83	1	no	—
410	C₈	SD₁₆×D₈₃	1	1	yes	characteristic
411	C₈	SD₁₆×D₈₃	1	1	yes	characteristic
412	C₈	C₂×Q₈×D₈₃	1	1	yes	characteristic
413	C₈	#41×D₈₃	1	1	yes	characteristic
414	C₂²	—	4	1	no	—
415	C₂²	—	332	1	no	—
416	C₂²	—	332	1	no	—
417	C₂²	—	83	1	no	—
418	C₂²	—	83	1	no	—
419	C₂²	—	664	2	no	—
420	C₂²	AGL(1,ℤ/8)×D₈₃	1	1	yes	characteristic
421	C₄	—	2	2	no	—
422	C₄	—	4	1	no	—
423	C₄	—	8	2	no	—
424	C₄	—	332	1	no	—
425	C₄	—	332	1	no	—
426	C₄	—	83	1	no	—
427	C₄	—	83	1	no	—
428	C₄	—	664	2	no	—
429	C₄	C₂²⋊Q₈×D₈₃	1	1	yes	characteristic
430	C₄	C₂×SD₁₆×D₈₃	1	1	yes	characteristic
431	C₂	—	2	1	no	—
432	C₂	—	8	1	no	—
433	C₂	—	664	1	no	—
434	C₂	—	166	1	no	—
435	C₂	—	166	1	no	—
436	C₂	#476×D₈₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#476×D₈₃
commutator, cosocle	C₂×C₈×C₈₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₃
Fitting	C₈₃×#2230	C₂
socle	C₂×C₈₃	C₂×#476
prime radical	#135×D₈₃	C₂²
hypercenter	#2230	D₈₃
hypocenter	C₈₃	#33637
LCS	G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2230

Complements

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

N	H ≅ G/N	type
1. #24917972	C₂	semidirect
3. #24909638	C₂	semidirect
4. #24909637	C₂	semidirect
5. #24909635	C₂	semidirect
6. #24909634	C₂	semidirect
7. #24909631	C₂	semidirect
8. #24909234	C₂	semidirect
9. #364×D₈₃	C₂	semidirect
11. C₈₃×#2230	C₂	semidirect
18. #19128101	C₂²	semidirect
19. #19128099	C₂²	semidirect
30. #19127525	C₂²	semidirect
31. #19127524	C₂²	semidirect
32. #19127523	C₂²	semidirect
33. #19127522	C₂²	semidirect
34. #19127521	C₂²	semidirect
38. #498×C₈₃	C₂²	semidirect
40. #365×C₈₃	C₂²	semidirect
41. #364×C₈₃	C₂²	semidirect
44. #14581815	Q₈	semidirect
48. #14581811	Q₈	semidirect
49. Q₁₆×D₈₃	Q₈	semidirect
51. D₈×D₈₃	Q₈	semidirect
226. #2230	D₈₃	semidirect
230. C₈₃	#33637	semidirect
239. #498	C₂×D₈₃	semidirect
254. #365	C₂×D₈₃	semidirect
257. #364	C₂×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#24917972	2
#443×D₈₃	2
#24909638	2
#24909637	2
#24909635	2
#24909634	2
#24909631	2
#24909234	2
#364×D₈₃	2
#24909197	2
C₈₃×#2230	2
#33637	83