Subgroups — #24917090

Order 10624.

496 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14581824	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13050573	C₂	1	1	yes	maximal, characteristic, complemented
3	#19128214	C₂	1	1	yes	maximal, characteristic
4	C₂²⋊Q₈×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#19127958	C₂	1	1	yes	maximal, characteristic, complemented
6	#19127956	C₂	1	1	yes	maximal, characteristic, complemented
7	#19127950	C₂	1	1	yes	maximal, characteristic, complemented
8	#19127948	C₂	1	1	yes	maximal, characteristic, complemented
9	#19127940	C₂	1	1	yes	maximal, characteristic, complemented
10	#19127932	C₂	1	1	yes	maximal, characteristic, complemented
11	#19127930	C₂	1	1	yes	maximal, characteristic, complemented
12	#19127742	C₂	1	1	yes	maximal, characteristic, complemented
13	#19127708	C₂	1	1	yes	maximal, characteristic, complemented
14	#19127701	C₂	1	1	yes	maximal, characteristic, complemented
15	#467×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13050591	C₂²	1	1	yes	characteristic
17	C₂×Q₈×D₈₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₈₃	C₂²	1	1	yes	characteristic
19	#14581824	—	2	4	no	—
20	C₂×#13050580	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13050579	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13050577	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13050573	—	2	4	no	—
24	C₂×#13050573	C₂²	1	1	yes	characteristic
25	C₂×#13050573	C₂²	1	1	yes	characteristic
26	C₂×#13050573	C₂²	1	1	yes	characteristic
27	C₂×#13050573	C₂²	1	1	yes	characteristic
28	C₂²×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
29	#14581777	—	2	1	no	—
30	#14581772	C₂²	1	1	yes	characteristic
31	#14581771	C₂²	1	1	yes	characteristic
32	#14581770	—	2	1	no	—
33	#14581769	—	2	1	no	—
34	#14581768	C₂²	1	1	yes	characteristic
35	#14581768	C₂²	1	1	yes	characteristic
36	#14581767	C₂²	1	1	yes	characteristic
37	#14581766	C₂²	1	1	yes	characteristic
38	#14581762	—	2	1	no	—
39	#14581754	—	2	1	no	—
40	(C₂²⋊D₈₃)⋊C₄	—	2	1	no	—
41	#14581750	C₂²	1	1	yes	characteristic
42	C₄⋊C₄×D₈₃	—	2	1	no	—
43	C₄⋊C₄×D₈₃	C₂²	1	1	yes	characteristic
44	C₂²⋊C₄×D₈₃	—	2	1	no	—
45	#14581725	C₂²	1	1	yes	characteristic, complemented
46	#14581724	C₂²	1	1	yes	characteristic, complemented
47	#14581723	C₂²	1	1	yes	characteristic, complemented
48	#14581717	C₂²	1	1	yes	characteristic, complemented
49	#14581716	C₂²	1	1	yes	characteristic, complemented
50	#14581716	C₂²	1	1	yes	characteristic, complemented
51	#14581715	C₂²	1	1	yes	characteristic, complemented
52	#14581714	C₂²	1	1	yes	characteristic, complemented
53	#14581712	C₂²	1	1	yes	characteristic, complemented
54	C₂×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₈×C₈₃	C₂²	1	1	yes	characteristic
56	C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
57	C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
58	#107×C₈₃	C₂²	1	1	yes	characteristic, complemented
59	#103×C₈₃	C₂²	1	1	yes	characteristic, complemented
60	#103×C₈₃	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₈₃	D₄	1	1	yes	characteristic
62	#13050591	—	2	2	no	—
63	#13050591	—	2	2	no	—
64	C₂×Dic₁₆₆	—	2	1	no	—
65	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
66	Q₈×D₈₃	—	2	2	no	—
67	Q₈×D₈₃	—	2	2	no	—
68	C₂×D₃₃₂	—	2	1	no	—
69	C₂×D₃₃₂	—	2	1	no	—
70	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊D₈₃	—	2	1	no	—
72	C₂²×Dic₈₃	D₄	1	1	yes	characteristic
73	C₂×C₄×D₈₃	—	2	2	no	—
74	C₂×C₄×D₈₃	—	2	2	no	—
75	C₂×C₄×D₈₃	—	2	1	no	—
76	C₂×C₄×D₈₃	—	2	1	no	—
77	C₂×C₄×D₈₃	—	2	1	no	—
78	C₂×C₄×D₈₃	D₄	1	1	yes	characteristic
79	C₂×C₄×D₈₃	D₄	1	1	yes	characteristic
80	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
81	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
82	#13050580	—	2	2	no	—
83	#13050579	—	2	2	no	—
84	#13050577	—	2	2	no	—
85	#13050573	—	2	2	no	—
86	#13050573	—	2	2	no	—
87	#13050573	—	2	2	no	—
88	#13050573	D₄	1	4	yes	complemented
89	C₂×C₈₃⋊C₈	—	2	2	no	—
90	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
91	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
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	Dic₈₃⋊C₄	—	2	1	no	—
98	Dic₈₃⋊C₄	—	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	—	2	1	no	—
103	(C₂×D₈₃)⋊C₄	—	2	1	no	—
104	(C₂×D₈₃)⋊C₄	—	2	1	no	—
105	(C₂×D₈₃)⋊C₄	—	2	1	no	—
106	C₄×Dic₈₃	—	2	1	no	—
107	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
110	Q₁₆×C₈₃	—	2	2	no	—
111	C₂×C₈×C₈₃	—	2	2	no	—
112	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
113	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
114	C₄⋊C₄×C₈₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
121	C₂²×D₈₃	—	2	2	no	—
122	C₂²×D₈₃	—	2	2	no	—
123	C₂²×D₈₃	—	2	1	no	—
124	C₂²×D₈₃	—	4	1	no	—
125	C₂²×D₈₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×D₈₃	C₂×D₄	1	1	yes	characteristic
127	Q₈×C₈₃	—	2	1	no	—
128	Q₈×C₈₃	—	2	1	no	—
129	Q₈×C₈₃	—	2	1	no	—
130	Q₈×C₈₃	—	2	1	no	—
131	C₂×C₄×C₈₃	—	2	1	no	—
132	C₂×C₄×C₈₃	—	2	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	C₂×D₄	1	1	yes	characteristic
138	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
139	C₂²⋊D₈₃	—	4	2	no	—
140	C₂×Dic₈₃	—	2	2	no	—
141	C₂×Dic₈₃	—	2	1	no	—
142	C₂×Dic₈₃	—	2	1	no	—
143	C₂×Dic₈₃	—	2	1	no	—
144	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
145	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
146	D₃₃₂	—	2	1	no	—
147	D₃₃₂	—	2	1	no	—
148	D₃₃₂	—	4	2	no	—
149	D₃₃₂	—	4	2	no	—
150	C₄×D₈₃	—	2	2	no	—
151	C₄×D₈₃	—	2	1	no	—
152	C₄×D₈₃	—	2	1	no	—
153	C₄×D₈₃	—	2	2	no	—
154	C₄×D₈₃	—	4	2	no	—
155	C₄×D₈₃	—	4	2	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	1	no	—
160	Dic₁₆₆	—	2	1	no	—
161	Dic₁₆₆	—	4	2	no	—
162	C₈×C₈₃	—	2	1	no	—
163	C₈×C₈₃	C₂×D₄	1	2	yes	—
164	C₈₃⋊C₈	—	2	1	no	—
165	C₈₃⋊C₈	C₂×D₄	1	2	yes	—
166	C₂²×C₈₃	—	2	1	no	—
167	C₂²×C₈₃	—	2	1	no	—
168	C₂²×C₈₃	#137	1	2	yes	complemented
169	C₂²×C₈₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×D₈₃	—	2	1	no	—
171	C₂×D₈₃	—	2	1	no	—
172	C₂×D₈₃	—	2	1	no	—
173	C₂×D₈₃	—	2	1	no	—
174	C₂×D₈₃	—	2	1	no	—
175	C₂×D₈₃	—	4	4	no	—
176	C₂×D₈₃	—	4	1	no	—
177	C₂×D₈₃	—	4	1	no	—
178	C₂×D₈₃	—	4	1	no	—
179	C₂×D₈₃	#121	1	2	yes	—
180	C₄×C₈₃	—	2	1	no	—
181	C₄×C₈₃	—	4	1	no	—
182	C₄×C₈₃	—	4	1	no	—
183	C₄×C₈₃	—	4	1	no	—
184	C₄×C₈₃	—	4	1	no	—
185	C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
186	C₄×C₈₃	C₂×#41	1	1	yes	characteristic
187	Dic₈₃	—	2	1	no	—
188	Dic₈₃	—	4	1	no	—
189	Dic₈₃	—	4	1	no	—
190	Dic₈₃	—	4	1	no	—
191	Dic₈₃	#121	1	2	yes	—
192	C₂×C₈₃	—	2	2	no	—
193	C₂×C₈₃	C₂×#121	1	1	yes	characteristic
194	C₂×C₈₃	C₂×#137	1	1	yes	characteristic
195	C₂×C₈₃	#575	1	1	yes	characteristic
196	D₈₃	—	2	2	no	—
197	D₈₃	—	4	1	no	—
198	D₈₃	—	8	1	no	—
199	#3056	—	83	1	no	maximal, Sylow
200	C₈₃	#3056	1	1	yes	characteristic, complemented, Sylow
201	C₂×#137	—	83	1	no	—
202	C₂²×M₁₆	—	83	1	no	—
203	#525	—	83	1	no	—
204	C₂×C₂²⋊Q₈	—	83	1	no	—
205	#470	—	83	1	no	—
206	#470	—	83	1	no	—
207	#468	—	83	1	no	—
208	#468	—	83	1	no	—
209	#467	—	83	1	no	—
210	#467	D₈₃	1	1	yes	characteristic, complemented
211	#465	—	83	1	no	—
212	#465	—	83	1	no	—
213	#428	—	83	1	no	—
214	#419	—	83	1	no	—
215	#417	—	83	1	no	—
216	C₂×#41	—	83	1	no	—
217	C₂²×Q₈	—	83	1	no	—
218	C₂³×C₄	—	83	1	no	—
219	#137	—	166	4	no	—
220	C₂×Q₁₆	—	83	1	no	—
221	C₂×Q₁₆	C₂×D₈₃	1	1	yes	characteristic, complemented
222	C₂×SD₁₆	—	83	1	no	—
223	C₂×SD₁₆	—	83	1	no	—
224	C₂×M₁₆	—	83	1	no	—
225	C₂×M₁₆	—	83	1	no	—
226	C₂×M₁₆	—	83	1	no	—
227	C₂×M₁₆	—	83	1	no	—
228	C₂×M₁₆	—	166	4	no	—
229	C₂²×C₈	—	83	1	no	—
230	C₂²×C₈	C₂×D₈₃	1	1	yes	characteristic
231	#123	—	166	1	no	—
232	C₂²⋊Q₈	—	83	1	no	—
233	C₂²⋊Q₈	—	83	1	no	—
234	C₂²⋊Q₈	—	83	1	no	—
235	C₂²⋊Q₈	—	83	1	no	—
236	C₂²⋊Q₈	—	166	1	no	—
237	C₂²⋊Q₈	—	166	1	no	—
238	C₂²⋊Q₈	C₂×D₈₃	1	1	yes	characteristic
239	C₂²⋊Q₈	C₂×D₈₃	1	1	yes	characteristic
240	#121	—	83	1	no	—
241	#121	—	83	1	no	—
242	#120	—	166	1	no	—
243	C₄×D₄	—	166	1	no	—
244	C₄×D₄	—	166	1	no	—
245	#117	—	83	1	no	—
246	C₂×C₄⋊C₄	—	83	1	no	—
247	C₂×C₄⋊C₄	—	166	1	no	—
248	C₂×C₂²⋊C₄	—	166	1	no	—
249	#107	—	83	1	no	—
250	#107	C₂×D₈₃	1	1	yes	characteristic, complemented
251	#106	—	83	1	no	—
252	#106	—	83	1	no	—
253	#103	—	83	1	no	—
254	#103	—	83	1	no	—
255	#103	—	83	1	no	—
256	#103	—	83	1	no	—
257	#103	C₂×D₈₃	1	1	yes	characteristic, complemented
258	#103	C₂×D₈₃	1	1	yes	characteristic, complemented
259	#102	—	83	1	no	—
260	#102	—	83	1	no	—
261	C₂⁴	—	83	1	no	—
262	#41	—	166	2	no	—
263	#41	—	166	2	no	—
264	C₂×Q₈	—	83	1	no	—
265	C₂×Q₈	—	166	1	no	—
266	C₂×Q₈	—	166	2	no	—
267	C₂×Q₈	—	166	2	no	—
268	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
269	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
270	C₂×D₄	—	83	1	no	—
271	C₂×D₄	—	166	1	no	—
272	C₂×D₄	—	166	1	no	—
273	C₂×D₄	—	166	1	no	—
274	C₂²×C₄	—	83	1	no	—
275	C₂²×C₄	—	83	1	no	—
276	C₂²×C₄	—	83	1	no	—
277	C₂²×C₄	—	83	1	no	—
278	C₂²×C₄	—	83	1	no	—
279	C₂²×C₄	—	166	1	no	—
280	C₂²×C₄	—	166	1	no	—
281	C₂²×C₄	—	166	1	no	—
282	C₂²×C₄	—	166	2	no	—
283	C₂²×C₄	—	166	2	no	—
284	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
285	Q₁₆	—	2	2	no	—
286	Q₁₆	—	166	2	no	—
287	SD₁₆	—	166	2	no	—
288	SD₁₆	—	166	2	no	—
289	M₁₆	—	83	4	no	—
290	M₁₆	—	166	2	no	—
291	M₁₆	—	166	2	no	—
292	M₁₆	—	166	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	83	1	no	—
295	C₂×C₈	—	83	1	no	—
296	C₂×C₈	—	166	2	no	—
297	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
298	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	83	1	no	—
302	C₄⋊C₄	—	83	1	no	—
303	C₄⋊C₄	—	166	1	no	—
304	C₄⋊C₄	—	166	1	no	—
305	C₄⋊C₄	—	166	1	no	—
306	C₄⋊C₄	—	166	1	no	—
307	C₄⋊C₄	—	166	1	no	—
308	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
309	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
310	C₂²⋊C₄	—	2	1	no	—
311	C₂²⋊C₄	—	2	1	no	—
312	C₂²⋊C₄	—	166	1	no	—
313	C₂²⋊C₄	—	166	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	C₄²	—	166	1	no	—
320	C₂³	—	332	1	no	—
321	C₂³	—	83	1	no	—
322	C₂³	—	83	1	no	—
323	C₂³	—	166	2	no	—
324	C₂³	—	166	1	no	—
325	C₂³	—	166	2	no	—
326	C₂³	D₄×D₈₃	1	1	yes	characteristic
327	Q₈	—	2	1	no	—
328	Q₈	—	2	1	no	—
329	Q₈	—	2	1	no	—
330	Q₈	—	2	1	no	—
331	Q₈	—	332	2	no	—
332	Q₈	—	166	1	no	—
333	Q₈	—	166	1	no	—
334	D₄	—	332	2	no	—
335	D₄	—	332	2	no	—
336	D₄	—	332	2	no	—
337	D₄	—	166	1	no	—
338	D₄	—	166	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	332	2	no	—
346	C₂×C₄	—	332	2	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	—	166	2	no	—
353	C₂×C₄	—	166	2	no	—
354	C₂×C₄	—	166	1	no	—
355	C₂×C₄	—	166	1	no	—
356	C₂×C₄	—	166	1	no	—
357	C₂×C₄	—	166	2	no	—
358	C₂×C₄	—	166	1	no	—
359	C₂×C₄	—	166	1	no	—
360	C₂×C₄	D₄×D₈₃	1	1	yes	characteristic
361	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
362	C₈	—	2	1	no	—
363	C₈	—	83	2	no	—
364	C₈	—	166	1	no	—
365	C₈	D₄×D₈₃	1	2	yes	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	332	4	no	—
369	C₂²	—	332	1	no	—
370	C₂²	—	332	1	no	—
371	C₂²	—	332	1	no	—
372	C₂²	—	83	2	no	—
373	C₂²	—	166	1	no	—
374	C₂²	—	166	1	no	—
375	C₂²	—	166	1	no	—
376	C₂²	—	166	1	no	—
377	C₂²	—	166	1	no	—
378	C₂²	#14581824	1	2	yes	complemented
379	C₂²	C₂×D₄×D₈₃	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	4	1	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	1	no	—
385	C₄	—	332	1	no	—
386	C₄	—	332	1	no	—
387	C₄	—	332	1	no	—
388	C₄	—	83	2	no	—
389	C₄	—	166	1	no	—
390	C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
391	C₄	#41×D₈₃	1	1	yes	characteristic
392	C₂	—	2	2	no	—
393	C₂	—	332	1	no	—
394	C₂	—	664	1	no	—
395	C₂	—	166	2	no	—
396	C₂	#121×D₈₃	1	1	yes	characteristic
397	C₂	C₂×#14581824	1	1	yes	characteristic
398	C₂	#19128498	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₃
commutator, cosocle	C₂×C₄×C₈₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₃
Fitting	#467×C₈₃	C₂
socle	C₂²×C₈₃	C₂²×D₄
prime radical	#19128214	C₂
hypercenter	#467	D₈₃
hypocenter	C₈₃	#3056
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #467

Complements

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

N	H ≅ G/N	type
1. C₂×#14581824	C₂	semidirect
2. C₂²×#13050573	C₂	semidirect
4. C₂²⋊Q₈×D₈₃	C₂	semidirect
5. #19127958	C₂	semidirect
6. #19127956	C₂	semidirect
7. #19127950	C₂	semidirect
8. #19127948	C₂	semidirect
9. #19127940	C₂	semidirect
10. #19127932	C₂	semidirect
11. #19127930	C₂	semidirect
12. #19127742	C₂	semidirect
13. #19127708	C₂	semidirect
14. #19127701	C₂	semidirect
15. #467×C₈₃	C₂	semidirect
20. C₂×#13050580	C₂²	semidirect
21. C₂×#13050579	C₂²	semidirect
22. C₂×#13050577	C₂²	semidirect
45. #14581725	C₂²	semidirect
46. #14581724	C₂²	semidirect
47. #14581723	C₂²	semidirect
48. #14581717	C₂²	semidirect
49. #14581716	C₂²	semidirect
50. #14581716	C₂²	semidirect
51. #14581715	C₂²	semidirect
52. #14581714	C₂²	semidirect
53. #14581712	C₂²	semidirect
54. C₂×Q₁₆×C₈₃	C₂²	semidirect
58. #107×C₈₃	C₂²	semidirect
59. #103×C₈₃	C₂²	semidirect
60. #103×C₈₃	C₂²	semidirect
88. #13050573	D₄	semidirect
168. C₂²×C₈₃	#137	semidirect
200. C₈₃	#3056	semidirect
210. #467	D₈₃	semidirect
221. C₂×Q₁₆	C₂×D₈₃	semidirect
250. #107	C₂×D₈₃	semidirect
257. #103	C₂×D₈₃	semidirect
258. #103	C₂×D₈₃	semidirect
378. C₂²	#14581824	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14581824	2
C₂²×#13050573	2
#19128214	2
C₂²⋊Q₈×D₈₃	2
#19127958	2
#19127956	2
#19127950	2
#19127948	2
#19127940	2
#19127932	2
#19127930	2
#19127742	2
#19127708	2
#19127701	2
#467×C₈₃	2
#3056	83