Subgroups — #27354605

Order 13568.

750 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20285291	C₂	1	1	yes	maximal, characteristic
2	#20283424	C₂	1	2	yes	maximal, complemented
3	#20273601	C₂	1	1	yes	maximal, characteristic, complemented
4	#20273598	C₂	1	2	yes	maximal, complemented
5	D₈×#88322	C₂	1	1	yes	maximal, characteristic, complemented
6	#20273509	C₂	1	1	yes	maximal, characteristic, complemented
7	#20273507	C₂	1	2	yes	maximal, complemented
8	#20273472	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273164	C₂	1	2	yes	maximal, complemented
10	C₈²×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1589	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133225	—	2	2	no	—
13	#16811170	C₂²	1	2	yes	—
14	#16811027	C₄	1	1	yes	characteristic
15	#16810998	C₄	1	1	yes	characteristic
16	#16810968	C₄	1	2	yes	—
17	#16810860	C₄	1	1	yes	characteristic
18	#16810858	C₄	1	2	yes	—
19	#16810856	C₄	1	1	yes	characteristic
20	C₄×D₄₂₄	C₂²	1	1	yes	characteristic
21	C₄×#11719922	C₂²	1	2	yes	—
22	#16810702	C₂²	1	2	yes	—
23	#16810699	—	2	2	no	—
24	D₄×#88322	C₂²	1	2	yes	—
25	#16810688	C₂²	1	2	yes	—
26	#16810686	—	2	2	no	—
27	#16810645	C₂²	1	2	yes	—
28	#16810588	—	2	2	no	—
29	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
32	#16810376	C₂²	1	1	yes	characteristic
33	#16810375	C₂²	1	2	yes	—
34	#16810352	C₂²	1	2	yes	—
35	D₄⋊#88322	C₂²	1	2	yes	—
36	#16810350	C₂²	1	2	yes	—
37	C₈×#88322	C₂²	1	1	yes	characteristic
38	C₈×#88322	C₂²	1	1	yes	characteristic
39	C₈×#88322	C₂²	1	1	yes	characteristic
40	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#436	C₂²	1	2	yes	—
42	C₅₃×#335	C₂²	1	1	yes	characteristic
43	C₅₃×D₄⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×#11719945	—	2	2	no	—
46	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic
47	C₂×#11719922	C₂×C₄	1	2	yes	—
48	#13133225	—	4	8	no	—
49	C₂×#11719912	—	2	2	no	—
50	C₂×#11719912	—	2	2	no	—
51	C₂²×#88322	—	2	2	no	—
52	C₂×C₈×D₅₃	—	2	2	no	—
53	C₂×C₈×D₅₃	—	2	1	no	—
54	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
57	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
58	#13133216	C₂×C₄	1	2	yes	—
59	#13133213	C₂×C₄	1	2	yes	—
60	#13133203	—	2	2	no	—
61	#13133192	C₂×C₄	1	2	yes	—
62	#13133190	—	2	2	no	—
63	#13133188	C₂×C₄	1	2	yes	—
64	C₄×D₂₁₂	C₂³	1	2	yes	—
65	C₄×C₂²⋊D₅₃	—	2	2	no	—
66	C₄²×D₅₃	C₂³	1	1	yes	characteristic
67	#13133151	C₂×C₄	1	1	yes	characteristic
68	#13133150	C₂×C₄	1	2	yes	—
69	C₄⋊#88322	C₂³	1	2	yes	—
70	#13133146	—	2	2	no	—
71	#13133139	C₂×C₄	1	2	yes	—
72	#13133138	C₂×C₄	1	2	yes	—
73	#13133137	C₂×C₄	1	2	yes	—
74	C₂²⋊#88322	—	2	2	no	—
75	#13133129	—	2	2	no	—
76	#13133129	—	2	2	no	—
77	C₄×#88322	C₂³	1	1	yes	characteristic
78	C₄×#88322	C₂³	1	1	yes	characteristic
79	C₄×#88322	C₂³	1	1	yes	characteristic
80	C₈×Dic₅₃	—	2	1	no	—
81	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₅₃	D₄	1	1	yes	characteristic
84	C₈×Dic₅₃	D₄	1	1	yes	characteristic
85	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic
86	C₂×M₁₆×C₅₃	—	2	2	no	—
87	C₄×D₄×C₅₃	C₂³	1	2	yes	—
88	#107×C₅₃	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
90	#102×C₅₃	C₂×C₄	1	2	yes	—
91	C₂²⋊C₈×C₅₃	—	2	2	no	—
92	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
95	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₅₃	—	2	2	no	—
97	C₂×C₂²⋊D₅₃	—	2	2	no	—
98	C₂×C₂²⋊D₅₃	—	2	2	no	—
99	C₂×C₂²⋊D₅₃	—	2	2	no	—
100	#11719945	—	4	4	no	—
101	#11719945	—	4	4	no	—
102	C₂×D₂₁₂	—	2	2	no	—
103	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
104	C₂×C₄×D₅₃	—	2	2	no	—
105	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
108	C₂×Dic₁₀₆	—	2	2	no	—
109	D₈×C₅₃	—	2	2	no	—
110	M₁₆×C₅₃	—	4	4	no	—
111	C₂×C₈×C₅₃	—	2	1	no	—
112	C₂×C₈×C₅₃	—	2	2	no	—
113	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
117	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
118	C₂²⋊C₄×C₅₃	—	2	2	no	—
119	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
120	C₂²⋊Dic₅₃	—	2	2	no	—
121	#11719922	—	2	4	no	—
122	#11719921	—	2	2	no	—
123	#11719921	—	2	2	no	—
124	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
125	#11719919	—	2	2	no	—
126	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
128	C₄×Dic₅₃	#41	1	1	yes	characteristic
129	C₂×#88322	—	2	1	no	—
130	C₂×#88322	—	2	2	no	—
131	C₂×#88322	—	4	4	no	—
132	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
133	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
134	C₂×#88322	C₂×D₄	1	1	yes	characteristic
135	C₂×#88322	C₂×D₄	1	1	yes	characteristic
136	D₄₂₄	—	2	2	no	—
137	#11719912	—	4	4	no	—
138	#11719912	—	4	4	no	—
139	C₈×D₅₃	—	2	4	no	—
140	C₈×D₅₃	—	2	2	no	—
141	C₈×D₅₃	—	2	2	no	—
142	C₈×D₅₃	—	2	2	no	—
143	C₈×D₅₃	—	4	4	no	—
144	C₈×D₅₃	D₈	1	4	yes	complemented
145	C₂³×C₅₃	—	2	2	no	—
146	C₂²×D₅₃	—	2	2	no	—
147	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
148	D₄×C₅₃	—	2	2	no	—
149	D₄×C₅₃	—	2	2	no	—
150	C₂×C₄×C₅₃	—	2	2	no	—
151	C₂×C₄×C₅₃	—	4	2	no	—
152	C₂×C₄×C₅₃	—	4	2	no	—
153	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
156	C₂²⋊D₅₃	—	4	4	no	—
157	C₂²⋊D₅₃	—	4	4	no	—
158	C₂²⋊D₅₃	—	4	4	no	—
159	C₂×Dic₅₃	—	2	2	no	—
160	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
161	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
162	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
163	D₂₁₂	—	2	2	no	—
164	D₂₁₂	—	2	2	no	—
165	D₂₁₂	—	4	4	no	—
166	C₄×D₅₃	—	2	1	no	—
167	C₄×D₅₃	—	2	1	no	—
168	C₄×D₅₃	—	2	2	no	—
169	C₄×D₅₃	—	4	2	no	—
170	C₄×D₅₃	—	4	2	no	—
171	C₄×D₅₃	C₂×D₈	1	2	yes	—
172	C₄×D₅₃	#135	1	2	yes	—
173	Dic₁₀₆	—	4	4	no	—
174	C₈×C₅₃	—	2	2	no	—
175	C₈×C₅₃	—	2	1	no	—
176	C₈×C₅₃	—	2	1	no	—
177	C₈×C₅₃	—	4	2	no	—
178	C₈×C₅₃	#131	1	2	yes	complemented
179	C₈×C₅₃	C₂×D₈	1	2	yes	—
180	#88322	—	2	2	no	—
181	#88322	—	2	1	no	—
182	#88322	—	2	1	no	—
183	#88322	—	4	2	no	—
184	#88322	#131	1	2	yes	complemented
185	#88322	C₂×D₈	1	2	yes	—
186	#17956	—	53	1	no	maximal, Sylow
187	C₂²×C₅₃	—	4	2	no	—
188	C₂²×C₅₃	—	4	2	no	—
189	C₂²×C₅₃	—	4	2	no	—
190	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
191	C₂×D₅₃	—	2	1	no	—
192	C₂×D₅₃	—	2	1	no	—
193	C₂×D₅₃	—	4	2	no	—
194	C₂×D₅₃	—	4	2	no	—
195	C₂×D₅₃	—	4	2	no	—
196	C₂×D₅₃	C₄×D₈	1	2	yes	—
197	C₄×C₅₃	—	2	1	no	—
198	C₄×C₅₃	—	4	2	no	—
199	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
200	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
201	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
202	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
203	Dic₅₃	—	2	1	no	—
204	Dic₅₃	—	4	2	no	—
205	Dic₅₃	C₄×D₈	1	2	yes	—
206	Dic₅₃	#443	1	2	yes	—
207	#3169	—	53	1	no	—
208	#2931	—	53	2	no	—
209	#1589	—	53	2	no	—
210	#1589	—	53	1	no	—
211	#1589	D₅₃	1	1	yes	characteristic, complemented
212	C₈×D₈	—	53	1	no	—
213	C₈×D₈	—	53	1	no	—
214	C₈×D₈	—	53	2	no	—
215	#1567	—	53	1	no	—
216	#1492	—	53	2	no	—
217	C₂×C₈²	—	53	1	no	—
218	C₂×C₅₃	—	8	2	no	—
219	C₂×C₅₃	#2931	1	1	yes	characteristic
220	C₂×C₅₃	C₂×C₄×D₈	1	1	yes	characteristic
221	C₂×C₅₃	C₂×#443	1	1	yes	characteristic
222	D₅₃	—	2	2	no	—
223	D₅₃	—	8	2	no	—
224	C₂×#131	—	106	2	no	—
225	#532	—	53	2	no	—
226	#500	—	53	1	no	—
227	#493	—	53	1	no	—
228	#486	—	53	2	no	—
229	#466	—	53	1	no	—
230	#466	—	53	1	no	—
231	#466	—	53	2	no	—
232	C₄×D₈	—	53	2	no	—
233	C₄×D₈	—	53	1	no	—
234	C₄×D₈	C₂×D₅₃	1	1	yes	characteristic
235	#436	—	53	2	no	—
236	#436	—	106	2	no	—
237	#436	C₂×D₅₃	1	2	yes	—
238	C₈×D₄	—	53	2	no	—
239	C₈×D₄	—	53	2	no	—
240	C₈×D₄	—	106	2	no	—
241	#423	—	53	2	no	—
242	#408	—	106	2	no	—
243	C₂×C₄×C₈	—	53	1	no	—
244	C₂×C₄×C₈	—	53	1	no	—
245	C₂×C₄×C₈	—	53	1	no	—
246	#335	—	53	2	no	—
247	#335	—	53	1	no	—
248	#335	C₂×D₅₃	1	1	yes	characteristic
249	D₄⋊C₈	—	53	2	no	—
250	D₄⋊C₈	—	53	2	no	—
251	D₄⋊C₈	—	53	2	no	—
252	D₄⋊C₈	C₂×D₅₃	1	2	yes	—
253	C₈²	—	53	1	no	—
254	C₈²	—	53	1	no	—
255	C₈²	—	53	1	no	—
256	C₈²	C₂×D₅₃	1	1	yes	characteristic
257	C₅₃	#17956	1	1	yes	characteristic, complemented, Sylow
258	C₂×#41	—	106	2	no	—
259	C₂×D₈	—	53	2	no	—
260	C₂×D₈	—	53	1	no	—
261	C₂×D₈	C₄×D₅₃	1	1	yes	characteristic
262	#131	—	212	8	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	—	106	2	no	—
265	C₂×M₁₆	—	106	2	no	—
266	C₂²×C₈	—	53	1	no	—
267	C₂²×C₈	—	53	1	no	—
268	C₂²×C₈	—	53	1	no	—
269	C₂²×C₈	—	53	1	no	—
270	C₂²×C₈	—	106	2	no	—
271	C₂²×C₈	—	106	1	no	—
272	C₂²×C₈	—	106	2	no	—
273	C₄⋊Q₈	—	53	2	no	—
274	#127	—	53	2	no	—
275	#124	—	106	2	no	—
276	#121	—	53	2	no	—
277	#121	—	53	2	no	—
278	#121	—	106	2	no	—
279	C₄×D₄	—	53	2	no	—
280	C₄×D₄	—	106	2	no	—
281	C₄×D₄	C₂²×D₅₃	1	2	yes	—
282	C₂×C₄²	—	53	1	no	—
283	#107	—	53	1	no	—
284	#107	—	53	2	no	—
285	#107	C₄×D₅₃	1	1	yes	characteristic
286	C₄⋊C₈	—	53	2	no	—
287	C₄⋊C₈	—	106	2	no	—
288	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
289	#102	—	53	2	no	—
290	#102	—	53	2	no	—
291	#102	—	53	2	no	—
292	#102	C₄×D₅₃	1	2	yes	—
293	C₂²⋊C₈	—	2	2	no	—
294	C₂²⋊C₈	—	106	2	no	—
295	C₂²⋊C₈	—	106	2	no	—
296	C₂²⋊C₈	—	106	2	no	—
297	C₄×C₈	—	53	1	no	—
298	C₄×C₈	—	53	1	no	—
299	C₄×C₈	—	53	1	no	—
300	C₄×C₈	—	53	1	no	—
301	C₄×C₈	—	53	1	no	—
302	C₄×C₈	—	53	1	no	—
303	C₄×C₈	—	53	1	no	—
304	C₄×C₈	—	106	1	no	—
305	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
306	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
307	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
308	#41	—	212	4	no	—
309	#41	—	212	4	no	—
310	C₂×Q₈	—	106	2	no	—
311	C₂×D₄	—	53	2	no	—
312	C₂×D₄	—	106	2	no	—
313	C₂×D₄	—	106	2	no	—
314	C₂×D₄	—	106	2	no	—
315	C₂×D₄	—	106	2	no	—
316	C₂×D₄	C₂×C₄×D₅₃	1	2	yes	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	53	1	no	—
319	C₂²×C₄	—	53	1	no	—
320	C₂²×C₄	—	53	1	no	—
321	C₂²×C₄	—	106	2	no	—
322	D₈	—	2	2	no	—
323	D₈	—	106	4	no	—
324	D₈	—	106	2	no	—
325	M₁₆	—	4	4	no	—
326	M₁₆	—	212	4	no	—
327	M₁₆	—	212	4	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	53	1	no	—
331	C₂×C₈	—	53	1	no	—
332	C₂×C₈	—	53	4	no	—
333	C₂×C₈	—	53	1	no	—
334	C₂×C₈	—	53	1	no	—
335	C₂×C₈	—	106	2	no	—
336	C₂×C₈	—	106	2	no	—
337	C₂×C₈	—	106	4	no	—
338	C₂×C₈	—	106	1	no	—
339	C₂×C₈	—	106	2	no	—
340	C₂×C₈	—	106	2	no	—
341	C₂×C₈	—	212	4	no	—
342	C₂×C₈	—	212	4	no	—
343	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
344	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
345	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
346	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
347	C₄⋊C₄	—	53	2	no	—
348	C₄⋊C₄	—	106	2	no	—
349	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	106	2	no	—
352	C₂²⋊C₄	—	106	2	no	—
353	C₂²⋊C₄	—	106	2	no	—
354	C₄²	—	53	1	no	—
355	C₄²	—	53	1	no	—
356	C₄²	—	53	1	no	—
357	C₄²	C₂³×D₅₃	1	1	yes	characteristic
358	C₂³	—	2	2	no	—
359	C₂³	—	53	1	no	—
360	C₂³	—	106	2	no	—
361	Q₈	—	212	4	no	—
362	D₄	—	2	2	no	—
363	D₄	—	2	2	no	—
364	D₄	—	106	2	no	—
365	D₄	—	106	2	no	—
366	D₄	—	212	4	no	—
367	D₄	—	212	4	no	—
368	D₄	—	212	4	no	—
369	D₄	—	212	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	53	1	no	—
374	C₂×C₄	—	53	1	no	—
375	C₂×C₄	—	53	2	no	—
376	C₂×C₄	—	53	2	no	—
377	C₂×C₄	—	53	1	no	—
378	C₂×C₄	—	106	2	no	—
379	C₂×C₄	—	106	1	no	—
380	C₂×C₄	—	106	1	no	—
381	C₂×C₄	—	106	2	no	—
382	C₂×C₄	—	212	2	no	—
383	C₂×C₄	—	212	2	no	—
384	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
385	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
386	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	—	4	2	no	—
391	C₈	—	53	2	no	—
392	C₈	—	53	2	no	—
393	C₈	—	106	2	no	—
394	C₈	—	106	1	no	—
395	C₈	—	106	1	no	—
396	C₈	—	212	2	no	—
397	C₈	#13133225	1	2	yes	complemented
398	C₈	D₈×D₅₃	1	2	yes	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	53	2	no	—
403	C₂²	—	106	1	no	—
404	C₂²	—	106	1	no	—
405	C₂²	—	212	2	no	—
406	C₂²	—	212	2	no	—
407	C₂²	—	212	2	no	—
408	C₂²	C₄×D₄×D₅₃	1	1	yes	characteristic
409	C₄	—	2	1	no	—
410	C₄	—	4	2	no	—
411	C₄	—	53	2	no	—
412	C₄	—	53	2	no	—
413	C₄	—	106	1	no	—
414	C₄	—	212	2	no	—
415	C₄	#131×D₅₃	1	1	yes	characteristic
416	C₄	C₂×#13133225	1	1	yes	characteristic
417	C₄	C₂×D₈×D₅₃	1	1	yes	characteristic
418	C₄	#135×D₅₃	1	1	yes	characteristic
419	C₂	—	8	2	no	—
420	C₂	—	106	2	no	—
421	C₂	—	424	2	no	—
422	C₂	#20283424	1	1	yes	characteristic
423	C₂	C₄×D₈×D₅₃	1	1	yes	characteristic
424	C₂	#443×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1589	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	#20285291	C₂
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	#1589	D₅₃
hypocenter	C₅₃	#17956
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1589

Complements

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

N	H ≅ G/N	type
2. #20283424	C₂	semidirect
3. #20273601	C₂	semidirect
4. #20273598	C₂	semidirect
5. D₈×#88322	C₂	semidirect
6. #20273509	C₂	semidirect
7. #20273507	C₂	semidirect
8. #20273472	C₂	semidirect
9. #20273164	C₂	semidirect
10. C₈²×D₅₃	C₂	semidirect
11. C₅₃×#1589	C₂	semidirect
144. C₈×D₅₃	D₈	semidirect
178. C₈×C₅₃	#131	semidirect
184. #88322	#131	semidirect
211. #1589	D₅₃	semidirect
257. C₅₃	#17956	semidirect
397. C₈	#13133225	semidirect

Maximal subgroups

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

subgroup	index
#20285291	2
#20283424	2
#20273601	2
#20273598	2
D₈×#88322	2
#20273509	2
#20273507	2
#20273472	2
#20273164	2
C₈²×D₅₃	2
C₅₃×#1589	2
#17956	53