Subgroups — #24916997

Order 10624.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14581816	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14581811	C₂	1	1	yes	maximal, characteristic, complemented
3	#19128264	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128180	C₂	1	1	yes	maximal, characteristic, complemented
5	#19127924	C₂	1	1	yes	maximal, characteristic, complemented
6	#19127922	C₂	1	1	yes	maximal, characteristic, complemented
7	#19127916	C₂	1	1	yes	maximal, characteristic, complemented
8	#19127914	C₂	1	1	yes	maximal, characteristic, complemented
9	#19127900	C₂	1	1	yes	maximal, characteristic, complemented
10	#19127898	C₂	1	1	yes	maximal, characteristic, complemented
11	#19127894	C₂	1	1	yes	maximal, characteristic, complemented
12	#19127726	C₂	1	1	yes	maximal, characteristic, complemented
13	#19127699	C₂	1	1	yes	maximal, characteristic, complemented
14	#102×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#459×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13050589	C₂²	1	1	yes	characteristic
17	C₂×#13050589	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₈₃	C₂²	1	1	yes	characteristic
19	#14581816	—	2	4	no	—
20	#14581811	—	2	4	no	—
21	C₂×Dic₃₃₂	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×#13050578	C₂²	1	1	yes	characteristic, complemented
26	C₂×#13050575	C₂²	1	1	yes	characteristic
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	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic, complemented
37	#14581757	C₂²	1	1	yes	characteristic, complemented
38	D₄×Dic₈₃	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₂²⋊D₈₃	—	2	1	no	—
40	(C₂²⋊D₈₃)⋊C₄	—	2	1	no	—
41	#14581749	C₂²	1	1	yes	characteristic
42	#14581748	—	2	1	no	—
43	C₂×Dic₈₃⋊C₄	—	2	1	no	—
44	C₄⋊C₄×D₈₃	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×D₈×C₈₃	C₂²	1	1	yes	characteristic
55	C₂×D₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
56	#127×C₈₃	C₂²	1	1	yes	characteristic
57	C₄×D₄×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	#13050589	—	2	2	no	—
65	#13050589	D₄	1	4	yes	complemented
66	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
67	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
68	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊D₈₃	—	2	1	no	—
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	C₂²×Dic₈₃	—	2	1	no	—
78	C₂²×Dic₈₃	—	2	1	no	—
79	C₂×C₄×D₈₃	—	2	1	no	—
80	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
81	Dic₃₃₂	—	2	2	no	—
82	#13050579	—	2	2	no	—
83	#13050578	—	2	2	no	—
84	#13050578	—	2	2	no	—
85	#13050578	—	2	2	no	—
86	#13050575	—	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	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
92	Dic₈₃⋊C₄	—	2	1	no	—
93	Dic₈₃⋊C₄	—	2	1	no	—
94	Dic₈₃⋊C₄	—	2	1	no	—
95	Dic₈₃⋊C₄	D₄	1	1	yes	characteristic
96	Dic₈₃⋊C₄	D₄	1	1	yes	characteristic
97	C₂²⋊Dic₈₃	—	2	1	no	—
98	C₂²⋊Dic₈₃	—	2	1	no	—
99	C₂²⋊Dic₈₃	—	2	1	no	—
100	(C₂×D₈₃)⋊C₄	—	2	1	no	—
101	(C₂×D₈₃)⋊C₄	—	2	1	no	—
102	(C₂×D₈₃)⋊C₄	D₄	1	1	yes	characteristic
103	(C₂×D₈₃)⋊C₄	D₄	1	1	yes	characteristic
104	C₄×Dic₈₃	—	2	1	no	—
105	C₄×Dic₈₃	—	2	1	no	—
106	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
107	C₂×D₄×C₈₃	—	2	1	no	—
108	C₂×D₄×C₈₃	—	2	1	no	—
109	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
111	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₈₃	—	2	1	no	—
113	D₈×C₈₃	—	2	2	no	—
114	D₈×C₈₃	—	2	2	no	—
115	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
116	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
118	C₂²⋊C₄×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	C₂³×C₈₃	—	2	1	no	—
123	C₂²×D₈₃	—	2	1	no	—
124	C₂²×D₈₃	—	4	2	no	—
125	C₂²×D₈₃	—	8	1	no	—
126	C₂²×D₈₃	—	8	1	no	—
127	C₂²×D₈₃	C₂×D₄	1	1	yes	characteristic
128	D₄×C₈₃	—	2	1	no	—
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	D₄×C₈₃	C₂×D₄	1	2	yes	—
136	C₂×C₄×C₈₃	—	2	1	no	—
137	C₂×C₄×C₈₃	—	8	1	no	—
138	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
141	C₂²⋊D₈₃	—	2	4	no	—
142	C₂²⋊D₈₃	—	4	2	no	—
143	C₂²⋊D₈₃	—	4	2	no	—
144	C₂²⋊D₈₃	—	8	1	no	—
145	C₂²⋊D₈₃	—	8	1	no	—
146	C₂×Dic₈₃	—	2	1	no	—
147	C₂×Dic₈₃	—	2	4	no	—
148	C₂×Dic₈₃	—	2	1	no	—
149	C₂×Dic₈₃	—	2	1	no	—
150	C₂×Dic₈₃	—	4	2	no	—
151	C₂×Dic₈₃	—	8	1	no	—
152	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
153	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
154	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
155	D₃₃₂	—	2	1	no	—
156	D₃₃₂	—	2	1	no	—
157	C₄×D₈₃	—	8	1	no	—
158	C₄×D₈₃	C₂×D₄	1	2	yes	—
159	C₄×D₈₃	#41	1	2	yes	—
160	Dic₁₆₆	—	2	1	no	—
161	Dic₁₆₆	—	2	1	no	—
162	Dic₁₆₆	—	2	1	no	—
163	Dic₁₆₆	C₂×D₄	1	2	yes	—
164	C₈×C₈₃	—	2	1	no	—
165	C₈×C₈₃	—	2	1	no	—
166	C₈₃⋊C₈	—	2	1	no	—
167	C₈₃⋊C₈	—	2	1	no	—
168	C₂²×C₈₃	—	2	2	no	—
169	C₂²×C₈₃	—	4	1	no	—
170	C₂²×C₈₃	—	4	1	no	—
171	C₂²×C₈₃	—	4	1	no	—
172	C₂²×C₈₃	—	4	1	no	—
173	C₂²×C₈₃	—	4	1	no	—
174	C₂²×C₈₃	—	4	1	no	—
175	C₂²×C₈₃	—	4	1	no	—
176	C₂²×C₈₃	—	4	1	no	—
177	C₂²×C₈₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×D₈₃	—	2	1	no	—
179	C₂×D₈₃	—	2	1	no	—
180	C₂×D₈₃	—	4	1	no	—
181	C₂×D₈₃	—	4	1	no	—
182	C₂×D₈₃	—	4	1	no	—
183	C₂×D₈₃	—	8	4	no	—
184	C₂×D₈₃	#121	1	2	yes	—
185	C₄×C₈₃	—	2	1	no	—
186	C₄×C₈₃	—	2	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	2	no	—
191	Dic₈₃	—	2	1	no	—
192	Dic₈₃	—	2	1	no	—
193	Dic₈₃	—	4	1	no	—
194	Dic₈₃	—	4	1	no	—
195	Dic₈₃	#121	1	2	yes	—
196	C₂×C₈₃	—	4	2	no	—
197	C₂×C₈₃	—	8	1	no	—
198	C₂×C₈₃	—	8	1	no	—
199	C₂×C₈₃	C₂×#121	1	1	yes	characteristic
200	C₂×C₈₃	#576	1	1	yes	characteristic
201	C₂×C₈₃	#577	1	1	yes	characteristic
202	D₈₃	—	2	2	no	—
203	D₈₃	—	8	1	no	—
204	#3045	—	83	1	no	maximal, Sylow
205	C₈₃	#3045	1	1	yes	characteristic, complemented, Sylow
206	C₂×AGL(1,ℤ/8)	—	83	1	no	—
207	C₂×#135	—	83	1	no	—
208	#535	—	83	1	no	—
209	#520	—	83	1	no	—
210	#464	—	83	1	no	—
211	#464	—	83	1	no	—
212	#463	—	83	1	no	—
213	#463	—	83	1	no	—
214	#460	—	83	1	no	—
215	#460	—	83	1	no	—
216	#459	—	83	1	no	—
217	#459	D₈₃	1	1	yes	characteristic, complemented
218	#424	—	83	1	no	—
219	#417	—	83	1	no	—
220	C₂×#102	—	83	1	no	—
221	C₂×#41	—	83	1	no	—
222	C₂×#41	—	83	1	no	—
223	C₂²×D₄	—	83	1	no	—
224	AGL(1,ℤ/8)	—	166	4	no	—
225	#135	—	166	4	no	—
226	C₂×Q₁₆	—	83	1	no	—
227	C₂×SD₁₆	—	83	1	no	—
228	C₂×SD₁₆	—	83	1	no	—
229	C₂×SD₁₆	—	83	1	no	—
230	C₂×SD₁₆	—	83	1	no	—
231	C₂×D₈	—	83	1	no	—
232	C₂×D₈	C₂×D₈₃	1	1	yes	characteristic
233	C₂×D₈	C₂×D₈₃	1	1	yes	characteristic, complemented
234	C₂×M₁₆	—	83	1	no	—
235	C₂²×C₈	—	83	1	no	—
236	#127	—	83	1	no	—
237	#127	C₂×D₈₃	1	1	yes	characteristic
238	#124	—	83	1	no	—
239	#124	—	83	1	no	—
240	#121	—	166	1	no	—
241	#121	—	166	1	no	—
242	#120	—	166	1	no	—
243	#120	—	166	1	no	—
244	C₄×Q₈	—	83	1	no	—
245	C₄×Q₈	—	83	1	no	—
246	C₄×D₄	—	83	1	no	—
247	C₄×D₄	—	166	1	no	—
248	C₄×D₄	—	166	1	no	—
249	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic, complemented
250	#117	—	83	1	no	—
251	#117	—	166	1	no	—
252	C₂×C₄⋊C₄	—	83	1	no	—
253	C₂×C₄⋊C₄	—	166	1	no	—
254	C₄⋊C₈	—	83	1	no	—
255	C₄⋊C₈	—	83	1	no	—
256	C₄⋊C₈	—	83	1	no	—
257	C₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic, complemented
258	#103	—	83	1	no	—
259	#103	—	83	1	no	—
260	#102	—	83	1	no	—
261	#102	—	83	1	no	—
262	#102	—	83	1	no	—
263	#102	—	83	1	no	—
264	#102	C₂×D₈₃	1	1	yes	characteristic
265	#102	C₂×D₈₃	1	1	yes	characteristic, complemented
266	C₂⁴	—	166	1	no	—
267	#41	—	83	4	no	—
268	#41	—	166	2	no	—
269	#41	—	166	2	no	—
270	#41	—	166	2	no	—
271	C₂×Q₈	—	83	1	no	—
272	C₂×Q₈	—	83	1	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	83	1	no	—
276	C₂×D₄	—	166	2	no	—
277	C₂×D₄	—	166	2	no	—
278	C₂×D₄	—	166	1	no	—
279	C₂×D₄	—	166	1	no	—
280	C₂×D₄	—	166	1	no	—
281	C₂×D₄	—	166	1	no	—
282	C₂×D₄	—	166	1	no	—
283	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
284	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
285	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	83	1	no	—
288	C₂²×C₄	—	166	1	no	—
289	C₂²×C₄	—	166	1	no	—
290	C₂²×C₄	—	166	1	no	—
291	C₂²×C₄	—	166	1	no	—
292	Q₁₆	—	166	2	no	—
293	SD₁₆	—	166	2	no	—
294	SD₁₆	—	166	2	no	—
295	SD₁₆	—	166	2	no	—
296	SD₁₆	—	166	2	no	—
297	D₈	—	2	2	no	—
298	D₈	—	2	2	no	—
299	D₈	—	166	2	no	—
300	M₁₆	—	166	2	no	—
301	C₂×C₈	—	83	1	no	—
302	C₂×C₈	—	83	1	no	—
303	C₂×C₈	—	166	2	no	—
304	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
305	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
306	C₄⋊C₄	—	83	1	no	—
307	C₄⋊C₄	—	83	1	no	—
308	C₄⋊C₄	—	83	1	no	—
309	C₄⋊C₄	—	166	1	no	—
310	C₄⋊C₄	—	166	1	no	—
311	C₄⋊C₄	—	166	1	no	—
312	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
313	C₂²⋊C₄	—	2	1	no	—
314	C₂²⋊C₄	—	83	1	no	—
315	C₂²⋊C₄	—	83	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	C₄²	—	83	1	no	—
322	C₄²	—	166	1	no	—
323	C₄²	—	166	1	no	—
324	C₄²	C₂²×D₈₃	1	1	yes	characteristic
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	1	no	—
328	C₂³	—	332	2	no	—
329	C₂³	—	83	1	no	—
330	C₂³	—	664	1	no	—
331	C₂³	—	664	1	no	—
332	C₂³	—	166	1	no	—
333	Q₈	—	83	2	no	—
334	Q₈	—	166	1	no	—
335	Q₈	—	166	1	no	—
336	Q₈	—	166	1	no	—
337	D₄	—	2	1	no	—
338	D₄	—	2	1	no	—
339	D₄	—	2	1	no	—
340	D₄	—	2	1	no	—
341	D₄	—	2	1	no	—
342	D₄	—	8	1	no	—
343	D₄	—	8	1	no	—
344	D₄	—	332	2	no	—
345	D₄	—	332	2	no	—
346	D₄	—	664	1	no	—
347	D₄	—	664	1	no	—
348	D₄	—	166	4	no	—
349	D₄	—	166	1	no	—
350	D₄	—	166	1	no	—
351	D₄	D₄×D₈₃	1	2	yes	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	8	1	no	—
354	C₂×C₄	—	332	2	no	—
355	C₂×C₄	—	83	1	no	—
356	C₂×C₄	—	83	2	no	—
357	C₂×C₄	—	83	2	no	—
358	C₂×C₄	—	83	1	no	—
359	C₂×C₄	—	83	1	no	—
360	C₂×C₄	—	664	1	no	—
361	C₂×C₄	—	664	1	no	—
362	C₂×C₄	—	166	1	no	—
363	C₂×C₄	—	166	1	no	—
364	C₂×C₄	—	166	4	no	—
365	C₂×C₄	—	166	1	no	—
366	C₂×C₄	D₄×D₈₃	1	1	yes	characteristic
367	C₂×C₄	D₄×D₈₃	1	1	yes	characteristic
368	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	166	1	no	—
372	C₈	—	166	1	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	332	1	no	—
383	C₂²	—	332	1	no	—
384	C₂²	—	332	1	no	—
385	C₂²	—	83	2	no	—
386	C₂²	—	664	4	no	—
387	C₂²	—	166	1	no	—
388	C₂²	—	166	1	no	—
389	C₂²	C₂×D₄×D₈₃	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	332	1	no	—
394	C₄	—	332	1	no	—
395	C₄	—	83	2	no	—
396	C₄	—	166	2	no	—
397	C₄	—	166	1	no	—
398	C₄	—	166	1	no	—
399	C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
400	C₄	#41×D₈₃	1	1	yes	characteristic
401	C₂	—	4	2	no	—
402	C₂	—	8	1	no	—
403	C₂	—	8	1	no	—
404	C₂	—	664	1	no	—
405	C₂	—	166	2	no	—
406	C₂	#121×D₈₃	1	1	yes	characteristic
407	C₂	#19128502	1	1	yes	characteristic
408	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	#459×C₈₃	C₂
socle	C₂²×C₈₃	C₂²×D₄
hypercenter	#459	D₈₃
hypocenter	C₈₃	#3045
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #459

Complements

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

N	H ≅ G/N	type
1. C₂×#14581816	C₂	semidirect
2. C₂×#14581811	C₂	semidirect
3. #19128264	C₂	semidirect
4. #19128180	C₂	semidirect
5. #19127924	C₂	semidirect
6. #19127922	C₂	semidirect
7. #19127916	C₂	semidirect
8. #19127914	C₂	semidirect
9. #19127900	C₂	semidirect
10. #19127898	C₂	semidirect
11. #19127894	C₂	semidirect
12. #19127726	C₂	semidirect
13. #19127699	C₂	semidirect
14. #102×D₈₃	C₂	semidirect
15. #459×C₈₃	C₂	semidirect
21. C₂×Dic₃₃₂	C₂²	semidirect
24. C₂×#13050578	C₂²	semidirect
25. C₂×#13050578	C₂²	semidirect
36. C₄×Dic₁₆₆	C₂²	semidirect
37. #14581757	C₂²	semidirect
38. D₄×Dic₈₃	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×D₈×C₈₃	C₂²	semidirect
57. C₄×D₄×C₈₃	C₂²	semidirect
58. C₄⋊C₈×C₈₃	C₂²	semidirect
60. #102×C₈₃	C₂²	semidirect
65. #13050589	D₄	semidirect
205. C₈₃	#3045	semidirect
217. #459	D₈₃	semidirect
233. C₂×D₈	C₂×D₈₃	semidirect
249. C₄×D₄	C₂×D₈₃	semidirect
257. C₄⋊C₈	C₂×D₈₃	semidirect
265. #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×#14581816	2
C₂×#14581811	2
#19128264	2
#19128180	2
#19127924	2
#19127922	2
#19127916	2
#19127914	2
#19127900	2
#19127898	2
#19127894	2
#19127726	2
#19127699	2
#102×D₈₃	2
#459×C₈₃	2
#3045	83