Subgroups — #24916979

Order 10624.

490 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14581821	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×SD₁₆×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#19128264	C₂	1	1	yes	maximal, characteristic
4	#19128177	C₂	1	1	yes	maximal, characteristic, complemented
5	#19127924	C₂	1	1	yes	maximal, characteristic, complemented
6	#19127923	C₂	1	1	yes	maximal, characteristic, complemented
7	#19127922	C₂	1	1	yes	maximal, characteristic, complemented
8	#19127921	C₂	1	1	yes	maximal, characteristic, complemented
9	#19127900	C₂	1	1	yes	maximal, characteristic, complemented
10	#19127899	C₂	1	1	yes	maximal, characteristic, complemented
11	#19127898	C₂	1	1	yes	maximal, characteristic, complemented
12	#19127726	C₂	1	1	yes	maximal, characteristic, complemented
13	#19127704	C₂	1	1	yes	maximal, characteristic, complemented
14	#19127694	C₂	1	1	yes	maximal, characteristic, complemented
15	#460×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13050589	C₂²	1	1	yes	characteristic
17	C₂×Q₈×D₈₃	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₈₃	C₂²	1	1	yes	characteristic
19	#14581821	—	2	4	no	—
20	C₂×Dic₃₃₂	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13050580	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13050579	C₂²	1	1	yes	characteristic
23	C₂×#13050578	C₂²	1	1	yes	characteristic
24	C₂×#13050578	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13050577	C₂²	1	1	yes	characteristic
26	SD₁₆×D₈₃	—	2	4	no	—
27	C₂×#13050573	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₈₃	C₂²	1	1	yes	characteristic
29	#14581788	C₂²	1	1	yes	characteristic
30	#14581780	C₂²	1	1	yes	characteristic
31	#14581779	C₂²	1	1	yes	characteristic
32	#14581764	—	2	1	no	—
33	#14581764	—	2	1	no	—
34	#14581760	—	2	1	no	—
35	#14581760	—	2	1	no	—
36	Q₈×Dic₈₃	C₂²	1	1	yes	characteristic, complemented
37	C₄×Dic₁₆₆	—	2	1	no	—
38	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic, complemented
39	#14581757	—	2	1	no	—
40	#14581757	C₂²	1	1	yes	characteristic, complemented
41	#14581750	—	2	1	no	—
42	#14581750	C₂²	1	1	yes	characteristic
43	#14581749	—	2	1	no	—
44	#14581749	C₂²	1	1	yes	characteristic
45	C₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
46	Dic₈₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	Dic₈₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	#14581717	C₂²	1	1	yes	characteristic, complemented
49	#14581715	C₂²	1	1	yes	characteristic, complemented
50	#14581714	C₂²	1	1	yes	characteristic
51	#14581713	C₂²	1	1	yes	characteristic
52	#14581713	C₂²	1	1	yes	characteristic, complemented
53	#14581712	C₂²	1	1	yes	characteristic
54	C₂×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic
55	C₂×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
56	#127×C₈₃	C₂²	1	1	yes	characteristic
57	C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
58	C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
59	#102×C₈₃	C₂²	1	1	yes	characteristic
60	#102×C₈₃	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₈₃	—	2	1	no	—
62	#13050589	—	2	2	no	—
63	#13050589	—	2	2	no	—
64	C₂×Dic₁₆₆	—	2	1	no	—
65	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
66	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
67	Q₈×D₈₃	—	2	2	no	—
68	Q₈×D₈₃	D₄	1	4	yes	complemented
69	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₈₃	—	2	1	no	—
71	C₂×C₂²⋊D₈₃	—	2	1	no	—
72	C₂×C₂²⋊D₈₃	—	2	1	no	—
73	C₂×C₂²⋊D₈₃	—	2	1	no	—
74	D₄×D₈₃	—	2	2	no	—
75	D₄×D₈₃	—	2	2	no	—
76	C₂²×Dic₈₃	—	2	1	no	—
77	C₂×C₄×D₈₃	—	2	1	no	—
78	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
79	Dic₃₃₂	—	2	2	no	—
80	#13050580	—	2	2	no	—
81	#13050579	—	2	2	no	—
82	#13050578	—	2	2	no	—
83	#13050578	—	2	2	no	—
84	#13050577	—	2	2	no	—
85	#13050573	—	2	2	no	—
86	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
87	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
88	C₈×D₈₃	—	2	2	no	—
89	C₄⋊Dic₈₃	—	2	1	no	—
90	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
91	Dic₈₃⋊C₄	—	2	1	no	—
92	Dic₈₃⋊C₄	—	2	1	no	—
93	Dic₈₃⋊C₄	D₄	1	1	yes	characteristic
94	Dic₈₃⋊C₄	D₄	1	1	yes	characteristic
95	C₂²⋊Dic₈₃	—	2	1	no	—
96	C₂²⋊Dic₈₃	—	2	1	no	—
97	(C₂×D₈₃)⋊C₄	—	2	1	no	—
98	(C₂×D₈₃)⋊C₄	—	2	1	no	—
99	(C₂×D₈₃)⋊C₄	—	2	1	no	—
100	(C₂×D₈₃)⋊C₄	D₄	1	1	yes	characteristic
101	(C₂×D₈₃)⋊C₄	D₄	1	1	yes	characteristic
102	C₄×Dic₈₃	—	2	1	no	—
103	C₄×Dic₈₃	—	2	1	no	—
104	C₄×Dic₈₃	—	2	1	no	—
105	C₄×Dic₈₃	—	2	1	no	—
106	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
107	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₈₃	—	2	1	no	—
109	C₂×D₄×C₈₃	—	2	1	no	—
110	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
111	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
112	SD₁₆×C₈₃	—	2	2	no	—
113	SD₁₆×C₈₃	—	2	2	no	—
114	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₈₃	—	2	1	no	—
117	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
118	C₄²×C₈₃	—	2	1	no	—
119	C₄²×C₈₃	C₂³	1	1	yes	characteristic
120	C₂³×C₈₃	—	2	1	no	—
121	C₂³×C₈₃	—	2	1	no	—
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	Q₈×C₈₃	—	2	1	no	—
128	Q₈×C₈₃	C₂×D₄	1	2	yes	—
129	D₄×C₈₃	—	2	1	no	—
130	D₄×C₈₃	—	2	1	no	—
131	D₄×C₈₃	—	2	1	no	—
132	D₄×C₈₃	—	2	1	no	—
133	D₄×C₈₃	—	8	1	no	—
134	D₄×C₈₃	—	8	1	no	—
135	C₂×C₄×C₈₃	—	2	1	no	—
136	C₂×C₄×C₈₃	—	2	1	no	—
137	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
140	C₂²⋊D₈₃	—	4	2	no	—
141	C₂²⋊D₈₃	—	4	2	no	—
142	C₂²⋊D₈₃	—	8	1	no	—
143	C₂²⋊D₈₃	—	8	1	no	—
144	C₂×Dic₈₃	—	2	1	no	—
145	C₂×Dic₈₃	—	2	1	no	—
146	C₂×Dic₈₃	—	2	1	no	—
147	C₂×Dic₈₃	—	4	2	no	—
148	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
149	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
150	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
151	D₃₃₂	—	2	1	no	—
152	D₃₃₂	—	2	1	no	—
153	C₄×D₈₃	—	2	4	no	—
154	C₄×D₈₃	C₂×D₄	1	2	yes	—
155	C₄×D₈₃	#41	1	2	yes	—
156	Dic₁₆₆	—	2	1	no	—
157	Dic₁₆₆	—	2	4	no	—
158	Dic₁₆₆	—	2	1	no	—
159	Dic₁₆₆	—	2	1	no	—
160	Dic₁₆₆	C₂×D₄	1	2	yes	—
161	C₈×C₈₃	—	2	1	no	—
162	C₈×C₈₃	—	2	1	no	—
163	C₈₃⋊C₈	—	2	1	no	—
164	C₈₃⋊C₈	—	2	1	no	—
165	C₂²×C₈₃	—	4	1	no	—
166	C₂²×C₈₃	—	4	1	no	—
167	C₂²×C₈₃	—	4	1	no	—
168	C₂²×C₈₃	—	4	1	no	—
169	C₂²×C₈₃	—	4	1	no	—
170	C₂²×C₈₃	—	4	1	no	—
171	C₂²×C₈₃	C₂²×D₄	1	1	yes	characteristic
172	C₂×D₈₃	—	2	1	no	—
173	C₂×D₈₃	—	2	1	no	—
174	C₂×D₈₃	—	4	1	no	—
175	C₂×D₈₃	—	4	1	no	—
176	C₂×D₈₃	—	4	1	no	—
177	C₂×D₈₃	—	8	4	no	—
178	C₂×D₈₃	#121	1	2	yes	—
179	C₄×C₈₃	—	2	2	no	—
180	C₄×C₈₃	—	2	1	no	—
181	C₄×C₈₃	—	2	1	no	—
182	C₄×C₈₃	—	4	1	no	—
183	C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
184	C₄×C₈₃	C₂×#41	1	1	yes	characteristic
185	Dic₈₃	—	2	2	no	—
186	Dic₈₃	—	2	1	no	—
187	Dic₈₃	—	2	1	no	—
188	Dic₈₃	—	4	1	no	—
189	Dic₈₃	—	4	1	no	—
190	Dic₈₃	#121	1	2	yes	—
191	C₂×C₈₃	—	8	1	no	—
192	C₂×C₈₃	—	8	1	no	—
193	C₂×C₈₃	C₂×#121	1	1	yes	characteristic
194	C₂×C₈₃	#577	1	1	yes	characteristic
195	C₂×C₈₃	#577	1	1	yes	characteristic
196	D₈₃	—	2	2	no	—
197	D₈₃	—	8	1	no	—
198	#3043	—	83	1	no	maximal, Sylow
199	C₈₃	#3043	1	1	yes	characteristic, complemented, Sylow
200	C₂×#137	—	83	1	no	—
201	C₂²×SD₁₆	—	83	1	no	—
202	#535	—	83	1	no	—
203	#519	—	83	1	no	—
204	#464	—	83	1	no	—
205	#464	—	83	1	no	—
206	#464	—	83	1	no	—
207	#464	—	83	1	no	—
208	#460	—	83	1	no	—
209	#460	—	83	1	no	—
210	#460	—	83	1	no	—
211	#460	D₈₃	1	1	yes	characteristic, complemented
212	#424	—	83	1	no	—
213	#418	—	83	1	no	—
214	#416	—	83	1	no	—
215	C₂×#41	—	83	1	no	—
216	C₂²×Q₈	—	83	1	no	—
217	C₂²×D₄	—	83	1	no	—
218	#137	—	166	4	no	—
219	C₂×Q₁₆	—	83	1	no	—
220	C₂×Q₁₆	—	83	1	no	—
221	C₂×SD₁₆	—	83	1	no	—
222	C₂×SD₁₆	—	83	1	no	—
223	C₂×SD₁₆	—	83	1	no	—
224	C₂×SD₁₆	—	83	1	no	—
225	C₂×SD₁₆	—	166	4	no	—
226	C₂×SD₁₆	C₂×D₈₃	1	1	yes	characteristic
227	C₂×SD₁₆	C₂×D₈₃	1	1	yes	characteristic, complemented
228	C₂×M₁₆	—	83	1	no	—
229	C₂²×C₈	—	83	1	no	—
230	#127	—	83	1	no	—
231	#127	C₂×D₈₃	1	1	yes	characteristic
232	#124	—	83	1	no	—
233	#124	—	83	1	no	—
234	#121	—	166	1	no	—
235	#121	—	166	1	no	—
236	#120	—	166	1	no	—
237	#120	—	166	1	no	—
238	C₄×Q₈	—	83	1	no	—
239	C₄×Q₈	—	83	1	no	—
240	C₄×Q₈	—	83	1	no	—
241	C₄×Q₈	—	166	1	no	—
242	C₄×Q₈	—	166	1	no	—
243	C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
244	#117	—	83	1	no	—
245	#117	—	83	1	no	—
246	#117	—	166	1	no	—
247	#117	—	166	1	no	—
248	C₄⋊C₈	—	83	1	no	—
249	C₄⋊C₈	—	83	1	no	—
250	C₄⋊C₈	—	83	1	no	—
251	C₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic, complemented
252	#103	—	83	1	no	—
253	#103	—	83	1	no	—
254	#102	—	83	1	no	—
255	#102	—	83	1	no	—
256	#102	—	83	1	no	—
257	#102	—	83	1	no	—
258	#102	C₂×D₈₃	1	1	yes	characteristic
259	#102	C₂×D₈₃	1	1	yes	characteristic, complemented
260	C₂⁴	—	166	1	no	—
261	#41	—	166	2	no	—
262	#41	—	166	2	no	—
263	C₂×Q₈	—	83	4	no	—
264	C₂×Q₈	—	83	1	no	—
265	C₂×Q₈	—	83	1	no	—
266	C₂×Q₈	—	166	1	no	—
267	C₂×Q₈	—	166	2	no	—
268	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	83	1	no	—
272	C₂×D₄	—	166	2	no	—
273	C₂×D₄	—	166	2	no	—
274	C₂×D₄	—	166	1	no	—
275	C₂×D₄	—	166	1	no	—
276	C₂×D₄	—	166	1	no	—
277	C₂×D₄	—	166	1	no	—
278	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
279	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
280	C₂²×C₄	—	83	1	no	—
281	C₂²×C₄	—	166	1	no	—
282	C₂²×C₄	—	166	1	no	—
283	Q₁₆	—	166	2	no	—
284	Q₁₆	—	166	2	no	—
285	SD₁₆	—	2	2	no	—
286	SD₁₆	—	2	2	no	—
287	SD₁₆	—	166	2	no	—
288	SD₁₆	—	166	2	no	—
289	SD₁₆	—	166	2	no	—
290	SD₁₆	—	166	2	no	—
291	M₁₆	—	166	2	no	—
292	C₂×C₈	—	83	1	no	—
293	C₂×C₈	—	83	1	no	—
294	C₂×C₈	—	166	2	no	—
295	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
296	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	83	1	no	—
299	C₄⋊C₄	—	83	1	no	—
300	C₄⋊C₄	—	83	1	no	—
301	C₄⋊C₄	—	166	1	no	—
302	C₄⋊C₄	—	166	1	no	—
303	C₄⋊C₄	—	166	1	no	—
304	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
305	C₂²⋊C₄	—	83	1	no	—
306	C₂²⋊C₄	—	83	1	no	—
307	C₂²⋊C₄	—	166	1	no	—
308	C₂²⋊C₄	—	166	1	no	—
309	C₂²⋊C₄	—	166	1	no	—
310	C₂²⋊C₄	—	166	1	no	—
311	C₂²⋊C₄	—	166	1	no	—
312	C₄²	—	2	1	no	—
313	C₄²	—	83	1	no	—
314	C₄²	—	166	1	no	—
315	C₄²	—	166	1	no	—
316	C₄²	—	166	1	no	—
317	C₄²	—	166	1	no	—
318	C₄²	C₂²×D₈₃	1	1	yes	characteristic
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	332	2	no	—
322	C₂³	—	83	1	no	—
323	C₂³	—	664	1	no	—
324	C₂³	—	664	1	no	—
325	C₂³	—	166	1	no	—
326	Q₈	—	2	1	no	—
327	Q₈	—	83	2	no	—
328	Q₈	—	166	4	no	—
329	Q₈	—	166	1	no	—
330	Q₈	—	166	1	no	—
331	Q₈	—	166	1	no	—
332	Q₈	D₄×D₈₃	1	2	yes	—
333	D₄	—	2	1	no	—
334	D₄	—	2	1	no	—
335	D₄	—	2	1	no	—
336	D₄	—	2	1	no	—
337	D₄	—	8	1	no	—
338	D₄	—	8	1	no	—
339	D₄	—	332	2	no	—
340	D₄	—	332	2	no	—
341	D₄	—	664	1	no	—
342	D₄	—	664	1	no	—
343	D₄	—	166	1	no	—
344	D₄	—	166	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	332	2	no	—
348	C₂×C₄	—	83	1	no	—
349	C₂×C₄	—	83	2	no	—
350	C₂×C₄	—	83	2	no	—
351	C₂×C₄	—	83	1	no	—
352	C₂×C₄	—	83	1	no	—
353	C₂×C₄	—	166	4	no	—
354	C₂×C₄	—	166	1	no	—
355	C₂×C₄	—	166	1	no	—
356	C₂×C₄	—	166	1	no	—
357	C₂×C₄	D₄×D₈₃	1	1	yes	characteristic
358	C₂×C₄	D₄×D₈₃	1	1	yes	characteristic
359	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	—	166	1	no	—
363	C₈	—	166	1	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	1	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	332	1	no	—
371	C₂²	—	332	1	no	—
372	C₂²	—	332	1	no	—
373	C₂²	—	83	2	no	—
374	C₂²	—	664	4	no	—
375	C₂²	—	166	1	no	—
376	C₂²	—	166	1	no	—
377	C₂²	C₂×D₄×D₈₃	1	1	yes	characteristic
378	C₄	—	2	2	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	332	1	no	—
383	C₄	—	332	1	no	—
384	C₄	—	83	2	no	—
385	C₄	—	166	2	no	—
386	C₄	—	166	1	no	—
387	C₄	—	166	1	no	—
388	C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
389	C₄	#41×D₈₃	1	1	yes	characteristic
390	C₂	—	8	1	no	—
391	C₂	—	8	1	no	—
392	C₂	—	664	1	no	—
393	C₂	—	166	2	no	—
394	C₂	#121×D₈₃	1	1	yes	characteristic
395	C₂	#19128507	1	1	yes	characteristic
396	C₂	#19128511	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₃
commutator, cosocle	C₂×C₄×C₈₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₃
Fitting	#460×C₈₃	C₂
socle	C₂²×C₈₃	C₂²×D₄
prime radical	#19128264	C₂
hypercenter	#460	D₈₃
hypocenter	C₈₃	#3043
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #460

Complements

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

N	H ≅ G/N	type
1. C₂×#14581821	C₂	semidirect
2. C₂×SD₁₆×D₈₃	C₂	semidirect
4. #19128177	C₂	semidirect
5. #19127924	C₂	semidirect
6. #19127923	C₂	semidirect
7. #19127922	C₂	semidirect
8. #19127921	C₂	semidirect
9. #19127900	C₂	semidirect
10. #19127899	C₂	semidirect
11. #19127898	C₂	semidirect
12. #19127726	C₂	semidirect
13. #19127704	C₂	semidirect
14. #19127694	C₂	semidirect
15. #460×C₈₃	C₂	semidirect
20. C₂×Dic₃₃₂	C₂²	semidirect
21. C₂×#13050580	C₂²	semidirect
24. C₂×#13050578	C₂²	semidirect
36. Q₈×Dic₈₃	C₂²	semidirect
38. C₄×Dic₁₆₆	C₂²	semidirect
40. #14581757	C₂²	semidirect
45. C₄⋊(C₈₃⋊C₈)	C₂²	semidirect
46. Dic₈₃⋊C₈	C₂²	semidirect
47. Dic₈₃⋊C₈	C₂²	semidirect
48. #14581717	C₂²	semidirect
49. #14581715	C₂²	semidirect
52. #14581713	C₂²	semidirect
55. C₂×SD₁₆×C₈₃	C₂²	semidirect
57. C₄×Q₈×C₈₃	C₂²	semidirect
58. C₄⋊C₈×C₈₃	C₂²	semidirect
60. #102×C₈₃	C₂²	semidirect
68. Q₈×D₈₃	D₄	semidirect
199. C₈₃	#3043	semidirect
211. #460	D₈₃	semidirect
227. C₂×SD₁₆	C₂×D₈₃	semidirect
243. C₄×Q₈	C₂×D₈₃	semidirect
251. C₄⋊C₈	C₂×D₈₃	semidirect
259. #102	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×#14581821	2
C₂×SD₁₆×D₈₃	2
#19128264	2
#19128177	2
#19127924	2
#19127923	2
#19127922	2
#19127921	2
#19127900	2
#19127899	2
#19127898	2
#19127726	2
#19127704	2
#19127694	2
#460×C₈₃	2
#3043	83