Subgroups — #24917097

Order 10624.

492 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14581798	C₂	1	1	yes	maximal, characteristic, complemented
3	#19128274	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128267	C₂	1	1	yes	maximal, characteristic
5	#19127950	C₂	1	1	yes	maximal, characteristic, complemented
6	#19127949	C₂	1	1	yes	maximal, characteristic, complemented
7	#19127946	C₂	1	1	yes	maximal, characteristic, complemented
8	#19127945	C₂	1	1	yes	maximal, characteristic, complemented
9	#19127931	C₂	1	1	yes	maximal, characteristic, complemented
10	#19127930	C₂	1	1	yes	maximal, characteristic, complemented
11	#19127927	C₂	1	1	yes	maximal, characteristic, complemented
12	#19127736	C₂	1	1	yes	maximal, characteristic, complemented
13	#19127708	C₂	1	1	yes	maximal, characteristic, complemented
14	#19127704	C₂	1	1	yes	maximal, characteristic, complemented
15	#465×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13050590	C₂²	1	1	yes	characteristic
17	C₂×Q₈×D₈₃	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₈₃	C₂²	1	1	yes	characteristic
19	C₂×#13050579	C₂²	1	1	yes	characteristic
20	C₂×#13050578	C₂²	1	1	yes	characteristic
21	C₂×#13050577	C₂²	1	1	yes	characteristic
22	SD₁₆×D₈₃	—	2	4	no	—
23	#14581798	—	2	4	no	—
24	C₂×#13050574	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13050573	C₂²	1	1	yes	characteristic
26	C₂×#13050573	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₈×D₈₃	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₈₃	C₂²	1	1	yes	characteristic, complemented
29	#14581791	—	2	1	no	—
30	#14581788	—	2	1	no	—
31	#14581778	—	2	1	no	—
32	#14581778	—	2	1	no	—
33	#14581777	—	2	1	no	—
34	#14581774	—	2	1	no	—
35	#14581772	C₂²	1	1	yes	characteristic, complemented
36	#14581771	C₂²	1	1	yes	characteristic, complemented
37	#14581768	C₂²	1	1	yes	characteristic, complemented
38	#14581767	C₂²	1	1	yes	characteristic
39	#14581766	C₂²	1	1	yes	characteristic
40	#14581763	C₂²	1	1	yes	characteristic
41	#14581762	—	2	1	no	—
42	#14581760	—	2	1	no	—
43	#14581750	C₂²	1	1	yes	characteristic
44	#14581750	C₂²	1	1	yes	characteristic
45	#14581725	C₂²	1	1	yes	characteristic, complemented
46	#14581725	C₂²	1	1	yes	characteristic, complemented
47	#14581724	C₂²	1	1	yes	characteristic, complemented
48	#14581717	C₂²	1	1	yes	characteristic, complemented
49	#14581716	C₂²	1	1	yes	characteristic, complemented
50	#14581715	C₂²	1	1	yes	characteristic, complemented
51	#14581714	C₂²	1	1	yes	characteristic
52	#14581713	C₂²	1	1	yes	characteristic
53	#14581712	C₂²	1	1	yes	characteristic
54	C₂×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
55	C₂²×C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
57	#121×C₈₃	C₂²	1	1	yes	characteristic
58	#106×C₈₃	C₂²	1	1	yes	characteristic, complemented
59	#103×C₈₃	C₂²	1	1	yes	characteristic, complemented
60	#102×C₈₃	C₂²	1	1	yes	characteristic
61	C₂³×D₈₃	—	2	1	no	—
62	#13050590	—	2	2	no	—
63	#13050590	—	2	2	no	—
64	C₂×Dic₁₆₆	—	2	1	no	—
65	C₂×Dic₁₆₆	D₄	1	1	yes	characteristic
66	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
67	Q₈×D₈₃	—	2	2	no	—
68	Q₈×D₈₃	—	2	2	no	—
69	C₂×D₃₃₂	—	2	1	no	—
70	C₂×D₃₃₂	D₄	1	1	yes	characteristic
71	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊D₈₃	—	2	1	no	—
73	C₂×C₂²⋊D₈₃	—	2	1	no	—
74	C₂×C₂²⋊D₈₃	—	2	1	no	—
75	C₂×C₂²⋊D₈₃	D₄	1	1	yes	characteristic
76	C₂×C₂²⋊D₈₃	D₄	1	1	yes	characteristic
77	D₄×D₈₃	—	2	2	no	—
78	D₄×D₈₃	—	2	2	no	—
79	C₂×C₄×D₈₃	—	2	1	no	—
80	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
81	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
82	#13050579	—	2	2	no	—
83	#13050578	—	2	2	no	—
84	#13050577	—	2	2	no	—
85	#13050574	—	2	2	no	—
86	#13050573	—	2	2	no	—
87	#13050573	—	2	2	no	—
88	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
89	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
90	C₈×D₈₃	—	2	2	no	—
91	C₈×D₈₃	D₄	1	4	yes	complemented
92	C₄⋊Dic₈₃	—	2	1	no	—
93	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
94	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
95	Dic₈₃⋊C₄	—	2	1	no	—
96	Dic₈₃⋊C₄	—	2	1	no	—
97	C₂²⋊Dic₈₃	—	2	1	no	—
98	C₂²⋊Dic₈₃	—	2	1	no	—
99	(C₂×D₈₃)⋊C₄	—	2	1	no	—
100	(C₂×D₈₃)⋊C₄	—	2	1	no	—
101	(C₂×D₈₃)⋊C₄	—	2	1	no	—
102	(C₂×D₈₃)⋊C₄	—	2	1	no	—
103	(C₂×D₈₃)⋊C₄	—	2	1	no	—
104	(C₂×D₈₃)⋊C₄	—	2	1	no	—
105	C₄×Dic₈₃	—	2	1	no	—
106	C₄×Dic₈₃	—	2	1	no	—
107	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₈₃	—	2	1	no	—
109	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
110	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
111	SD₁₆×C₈₃	—	2	2	no	—
112	C₂×C₈×C₈₃	—	2	2	no	—
113	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
115	C₄⋊C₄×C₈₃	—	2	1	no	—
116	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
118	C₂²⋊C₄×C₈₃	—	2	1	no	—
119	C₂²⋊C₄×C₈₃	—	2	1	no	—
120	C₂³×C₈₃	—	2	1	no	—
121	C₂³×C₈₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×D₈₃	—	2	1	no	—
123	C₂²×D₈₃	—	4	2	no	—
124	C₂²×D₈₃	—	8	1	no	—
125	C₂²×D₈₃	—	8	1	no	—
126	C₂²×D₈₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×D₈₃	C₂×D₄	1	1	yes	characteristic
128	Q₈×C₈₃	—	2	1	no	—
129	Q₈×C₈₃	—	2	1	no	—
130	D₄×C₈₃	—	2	1	no	—
131	D₄×C₈₃	—	2	1	no	—
132	D₄×C₈₃	—	8	1	no	—
133	C₂×C₄×C₈₃	—	2	1	no	—
134	C₂×C₄×C₈₃	—	2	1	no	—
135	C₂×C₄×C₈₃	—	2	1	no	—
136	C₂×C₄×C₈₃	—	2	1	no	—
137	C₂×C₄×C₈₃	—	2	1	no	—
138	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
140	C₂²⋊D₈₃	—	2	2	no	—
141	C₂²⋊D₈₃	—	2	2	no	—
142	C₂²⋊D₈₃	—	4	2	no	—
143	C₂²⋊D₈₃	—	8	1	no	—
144	C₂²⋊D₈₃	—	8	1	no	—
145	C₂×Dic₈₃	—	2	1	no	—
146	C₂×Dic₈₃	—	2	1	no	—
147	C₂×Dic₈₃	—	2	1	no	—
148	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
149	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
150	D₃₃₂	—	2	2	no	—
151	D₃₃₂	—	2	1	no	—
152	D₃₃₂	—	2	1	no	—
153	D₃₃₂	—	8	1	no	—
154	C₄×D₈₃	—	2	1	no	—
155	C₄×D₈₃	—	2	1	no	—
156	C₄×D₈₃	—	4	2	no	—
157	C₄×D₈₃	C₂×D₄	1	2	yes	—
158	C₄×D₈₃	#41	1	2	yes	—
159	Dic₁₆₆	—	2	2	no	—
160	Dic₁₆₆	—	2	1	no	—
161	Dic₁₆₆	—	2	1	no	—
162	Dic₁₆₆	—	4	2	no	—
163	C₈×C₈₃	—	2	1	no	—
164	C₈×C₈₃	C₂×D₄	1	2	yes	—
165	C₈₃⋊C₈	—	2	1	no	—
166	C₈₃⋊C₈	C₂×D₄	1	2	yes	—
167	C₂²×C₈₃	—	2	1	no	—
168	C₂²×C₈₃	—	2	1	no	—
169	C₂²×C₈₃	—	2	1	no	—
170	C₂²×C₈₃	—	4	1	no	—
171	C₂²×C₈₃	—	4	1	no	—
172	C₂²×C₈₃	—	4	1	no	—
173	C₂²×C₈₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×D₈₃	—	2	1	no	—
175	C₂×D₈₃	—	2	1	no	—
176	C₂×D₈₃	—	2	1	no	—
177	C₂×D₈₃	—	2	1	no	—
178	C₂×D₈₃	—	2	1	no	—
179	C₂×D₈₃	—	4	1	no	—
180	C₂×D₈₃	—	4	1	no	—
181	C₂×D₈₃	—	4	1	no	—
182	C₂×D₈₃	—	8	4	no	—
183	C₂×D₈₃	#121	1	2	yes	—
184	C₄×C₈₃	—	2	1	no	—
185	C₄×C₈₃	—	4	1	no	—
186	C₄×C₈₃	—	4	1	no	—
187	C₄×C₈₃	—	4	1	no	—
188	C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
189	C₄×C₈₃	C₂×#41	1	1	yes	characteristic
190	Dic₈₃	—	2	1	no	—
191	Dic₈₃	—	4	1	no	—
192	Dic₈₃	—	4	1	no	—
193	Dic₈₃	—	4	1	no	—
194	Dic₈₃	#121	1	2	yes	—
195	C₂×C₈₃	—	4	1	no	—
196	C₂×C₈₃	—	8	1	no	—
197	C₂×C₈₃	C₂×#121	1	1	yes	characteristic
198	C₂×C₈₃	#577	1	1	yes	characteristic
199	C₂×C₈₃	#577	1	1	yes	characteristic
200	D₈₃	—	2	2	no	—
201	D₈₃	—	4	1	no	—
202	D₈₃	—	8	1	no	—
203	#3057	—	83	1	no	maximal, Sylow
204	C₈₃	#3057	1	1	yes	characteristic, complemented, Sylow
205	C₂²×SD₁₆	—	83	1	no	—
206	C₂×#131	—	83	1	no	—
207	#536	—	83	1	no	—
208	#535	—	83	1	no	—
209	#468	—	83	1	no	—
210	#468	—	83	1	no	—
211	#468	—	83	1	no	—
212	#468	—	83	1	no	—
213	#465	—	83	1	no	—
214	#465	—	83	1	no	—
215	#465	—	83	1	no	—
216	#465	D₈₃	1	1	yes	characteristic, complemented
217	#427	—	83	1	no	—
218	#419	—	83	1	no	—
219	#418	—	83	1	no	—
220	C₂×#41	—	83	1	no	—
221	C₂²×Q₈	—	83	1	no	—
222	C₂²×D₄	—	83	1	no	—
223	C₂×SD₁₆	—	83	1	no	—
224	C₂×SD₁₆	—	83	1	no	—
225	C₂×SD₁₆	—	83	1	no	—
226	C₂×SD₁₆	—	166	4	no	—
227	C₂×SD₁₆	C₂×D₈₃	1	1	yes	characteristic
228	#131	—	166	4	no	—
229	C₂×M₁₆	—	83	1	no	—
230	C₂×M₁₆	—	83	1	no	—
231	C₂×M₁₆	—	83	1	no	—
232	C₂²×C₈	—	83	1	no	—
233	C₂²×C₈	—	83	1	no	—
234	C₂²×C₈	C₂×D₈₃	1	1	yes	characteristic, complemented
235	C₄⋊Q₈	—	166	1	no	—
236	#127	—	166	1	no	—
237	#124	—	166	1	no	—
238	#124	—	166	1	no	—
239	#123	—	166	1	no	—
240	#123	—	166	1	no	—
241	C₂²⋊Q₈	—	83	1	no	—
242	C₂²⋊Q₈	—	83	1	no	—
243	C₂²⋊Q₈	—	83	1	no	—
244	C₂²⋊Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
245	#121	—	83	1	no	—
246	#121	—	83	1	no	—
247	#121	—	83	1	no	—
248	#121	C₂×D₈₃	1	1	yes	characteristic
249	#120	—	166	1	no	—
250	#120	—	166	1	no	—
251	#117	—	83	1	no	—
252	#117	—	83	1	no	—
253	#107	—	83	1	no	—
254	#107	—	83	1	no	—
255	#106	—	83	1	no	—
256	#106	C₂×D₈₃	1	1	yes	characteristic, complemented
257	#103	—	83	1	no	—
258	#103	—	83	1	no	—
259	#103	—	83	1	no	—
260	#103	C₂×D₈₃	1	1	yes	characteristic, complemented
261	#102	—	83	1	no	—
262	#102	—	83	1	no	—
263	#102	—	83	1	no	—
264	#102	C₂×D₈₃	1	1	yes	characteristic
265	C₂⁴	—	166	1	no	—
266	#41	—	166	2	no	—
267	#41	—	166	2	no	—
268	C₂×Q₈	—	83	1	no	—
269	C₂×Q₈	—	83	1	no	—
270	C₂×Q₈	—	166	1	no	—
271	C₂×Q₈	—	166	2	no	—
272	C₂×Q₈	—	166	2	no	—
273	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	83	1	no	—
276	C₂×D₄	—	83	1	no	—
277	C₂×D₄	—	83	1	no	—
278	C₂×D₄	—	83	1	no	—
279	C₂×D₄	—	166	1	no	—
280	C₂×D₄	—	166	2	no	—
281	C₂×D₄	—	166	2	no	—
282	C₂×D₄	—	166	1	no	—
283	C₂×D₄	—	166	1	no	—
284	C₂×D₄	—	166	1	no	—
285	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
286	C₂²×C₄	—	83	1	no	—
287	C₂²×C₄	—	83	1	no	—
288	C₂²×C₄	—	166	1	no	—
289	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
290	SD₁₆	—	2	2	no	—
291	SD₁₆	—	166	2	no	—
292	SD₁₆	—	166	2	no	—
293	SD₁₆	—	166	2	no	—
294	M₁₆	—	166	2	no	—
295	M₁₆	—	166	2	no	—
296	M₁₆	—	166	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	83	1	no	—
299	C₂×C₈	—	83	4	no	—
300	C₂×C₈	—	83	1	no	—
301	C₂×C₈	—	166	2	no	—
302	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
303	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	83	1	no	—
306	C₄⋊C₄	—	83	1	no	—
307	C₄⋊C₄	—	166	1	no	—
308	C₄⋊C₄	—	166	1	no	—
309	C₄⋊C₄	—	166	1	no	—
310	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
311	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
312	C₂²⋊C₄	—	2	1	no	—
313	C₂²⋊C₄	—	2	1	no	—
314	C₂²⋊C₄	—	166	1	no	—
315	C₂²⋊C₄	—	166	1	no	—
316	C₂²⋊C₄	—	166	1	no	—
317	C₂²⋊C₄	—	166	1	no	—
318	C₂²⋊C₄	—	166	1	no	—
319	C₂²⋊C₄	—	166	1	no	—
320	C₂²⋊C₄	—	166	1	no	—
321	C₂²⋊C₄	—	166	1	no	—
322	C₄²	—	166	1	no	—
323	C₄²	—	166	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	332	2	no	—
326	C₂³	—	83	1	no	—
327	C₂³	—	83	1	no	—
328	C₂³	—	664	1	no	—
329	C₂³	—	664	1	no	—
330	C₂³	—	166	1	no	—
331	C₂³	D₄×D₈₃	1	1	yes	characteristic
332	Q₈	—	2	1	no	—
333	Q₈	—	2	1	no	—
334	Q₈	—	332	2	no	—
335	Q₈	—	166	2	no	—
336	Q₈	—	166	1	no	—
337	Q₈	—	166	1	no	—
338	D₄	—	2	1	no	—
339	D₄	—	2	1	no	—
340	D₄	—	8	1	no	—
341	D₄	—	332	2	no	—
342	D₄	—	664	1	no	—
343	D₄	—	664	1	no	—
344	D₄	—	664	1	no	—
345	D₄	—	166	2	no	—
346	D₄	—	166	2	no	—
347	D₄	—	166	2	no	—
348	D₄	—	166	1	no	—
349	D₄	—	166	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	332	2	no	—
356	C₂×C₄	—	83	1	no	—
357	C₂×C₄	—	83	2	no	—
358	C₂×C₄	—	83	2	no	—
359	C₂×C₄	—	83	1	no	—
360	C₂×C₄	—	166	1	no	—
361	C₂×C₄	—	166	1	no	—
362	C₂×C₄	—	166	1	no	—
363	C₂×C₄	—	166	1	no	—
364	C₂×C₄	—	166	1	no	—
365	C₂×C₄	D₄×D₈₃	1	1	yes	characteristic
366	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
367	C₈	—	2	1	no	—
368	C₈	—	83	2	no	—
369	C₈	—	166	1	no	—
370	C₈	D₄×D₈₃	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	332	1	no	—
378	C₂²	—	332	1	no	—
379	C₂²	—	332	1	no	—
380	C₂²	—	83	2	no	—
381	C₂²	—	664	4	no	—
382	C₂²	—	166	1	no	—
383	C₂²	—	166	1	no	—
384	C₂²	—	166	1	no	—
385	C₂²	—	166	1	no	—
386	C₂²	—	166	1	no	—
387	C₂²	C₂×D₄×D₈₃	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	4	1	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	332	1	no	—
393	C₄	—	332	1	no	—
394	C₄	—	332	1	no	—
395	C₄	—	83	2	no	—
396	C₄	—	166	1	no	—
397	C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
398	C₄	#41×D₈₃	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	8	1	no	—
401	C₂	—	332	1	no	—
402	C₂	—	664	1	no	—
403	C₂	—	166	2	no	—
404	C₂	#121×D₈₃	1	1	yes	characteristic
405	C₂	#19128507	1	1	yes	characteristic
406	C₂	#19128508	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₃
commutator, cosocle	C₂×C₄×C₈₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₃
Fitting	#465×C₈₃	C₂
socle	C₂²×C₈₃	C₂²×D₄
prime radical	#19128267	C₂
hypercenter	#465	D₈₃
hypocenter	C₈₃	#3057
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #465

Complements

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

N	H ≅ G/N	type
1. C₂×SD₁₆×D₈₃	C₂	semidirect
2. C₂×#14581798	C₂	semidirect
3. #19128274	C₂	semidirect
5. #19127950	C₂	semidirect
6. #19127949	C₂	semidirect
7. #19127946	C₂	semidirect
8. #19127945	C₂	semidirect
9. #19127931	C₂	semidirect
10. #19127930	C₂	semidirect
11. #19127927	C₂	semidirect
12. #19127736	C₂	semidirect
13. #19127708	C₂	semidirect
14. #19127704	C₂	semidirect
15. #465×C₈₃	C₂	semidirect
24. C₂×#13050574	C₂²	semidirect
26. C₂×#13050573	C₂²	semidirect
28. C₂×C₈×D₈₃	C₂²	semidirect
35. #14581772	C₂²	semidirect
36. #14581771	C₂²	semidirect
37. #14581768	C₂²	semidirect
45. #14581725	C₂²	semidirect
46. #14581725	C₂²	semidirect
47. #14581724	C₂²	semidirect
48. #14581717	C₂²	semidirect
49. #14581716	C₂²	semidirect
50. #14581715	C₂²	semidirect
55. C₂²×C₈×C₈₃	C₂²	semidirect
56. C₂²⋊Q₈×C₈₃	C₂²	semidirect
58. #106×C₈₃	C₂²	semidirect
59. #103×C₈₃	C₂²	semidirect
91. C₈×D₈₃	D₄	semidirect
204. C₈₃	#3057	semidirect
216. #465	D₈₃	semidirect
234. C₂²×C₈	C₂×D₈₃	semidirect
244. C₂²⋊Q₈	C₂×D₈₃	semidirect
256. #106	C₂×D₈₃	semidirect
260. #103	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×SD₁₆×D₈₃	2
C₂×#14581798	2
#19128274	2
#19128267	2
#19127950	2
#19127949	2
#19127946	2
#19127945	2
#19127931	2
#19127930	2
#19127927	2
#19127736	2
#19127708	2
#19127704	2
#465×C₈₃	2
#3057	83