Subgroups — #27367290

Order 13568.

710 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20285856	C₂	1	1	yes	maximal, characteristic, complemented
2	#20285653	C₂	1	1	yes	maximal, characteristic
3	C₂×#16810996	C₂	1	1	yes	maximal, characteristic
4	#20274187	C₂	1	4	yes	maximal, complemented
5	#20274063	C₂	1	4	yes	maximal, complemented
6	#20273463	C₂	1	1	yes	maximal, characteristic, complemented
7	#20273388	C₂	1	1	yes	maximal, characteristic, complemented
8	#20273384	C₂	1	1	yes	maximal, characteristic
9	C₅₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#11719913	—	2	1	no	—
11	C₂²×#11719913	—	2	1	no	—
12	C₂×#13133217	C₂²	1	1	yes	characteristic
13	C₂×#13133214	C₂²	1	1	yes	characteristic
14	#16811019	—	2	1	no	—
15	#16810997	—	2	1	no	—
16	#16810996	—	2	1	no	—
17	#16810996	—	2	1	no	—
18	#16810996	C₂²	1	2	yes	—
19	#16810996	C₂²	1	2	yes	—
20	#16810973	—	2	1	no	—
21	#16810971	—	2	1	no	—
22	#16810951	—	2	2	no	—
23	#16810908	C₂²	1	4	yes	complemented
24	#16810823	C₂²	1	4	yes	—
25	#16810773	—	2	2	no	—
26	#16810676	C₂²	1	1	yes	characteristic
27	#16810676	C₂²	1	1	yes	characteristic
28	#16810376	C₂²	1	2	yes	complemented
29	#16810374	C₂²	1	2	yes	complemented
30	#16810370	C₂²	1	4	yes	complemented
31	#16810366	C₂²	1	4	yes	—
32	C₅₃×#533	C₂²	1	1	yes	characteristic
33	C₅₃×#446	—	2	1	no	—
34	C₅₃×#446	C₂²	1	2	yes	complemented
35	C₈×Q₈×C₅₃	—	2	1	no	—
36	C₈×Q₈×C₅₃	C₂²	1	2	yes	complemented
37	C₅₃×#424	—	2	1	no	—
38	C₅₃×#423	C₂²	1	1	yes	characteristic
39	C₅₃×#405	—	2	1	no	—
40	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₂²×Dic₁₀₆	—	2	1	no	—
42	C₂²×D₂₁₂	—	2	1	no	—
43	C₂²×D₂₁₂	—	2	1	no	—
44	C₂²×D₂₁₂	—	2	1	no	—
45	C₂×#11719913	—	2	2	no	—
46	C₂×#11719913	—	2	2	no	—
47	C₂×#11719913	—	2	2	no	—
48	C₂×#11719913	—	2	2	no	—
49	C₂×#11719913	—	4	4	no	—
50	C₂×#11719913	—	4	4	no	—
51	C₂×#11719924	—	2	4	no	—
52	#13133217	—	2	1	no	—
53	#13133217	—	2	1	no	—
54	#13133217	—	2	1	no	—
55	#13133217	C₂³	1	2	yes	—
56	#13133214	—	2	1	no	—
57	#13133214	—	2	1	no	—
58	#13133214	—	2	1	no	—
59	#13133214	C₂³	1	2	yes	—
60	C₂×C₄⋊Dic₅₃	—	2	1	no	—
61	C₂×C₄⋊Dic₅₃	—	2	1	no	—
62	#13133148	—	2	4	no	—
63	C₄⋊#88322	C₂³	1	2	yes	—
64	C₄⋊#88322	C₂³	1	2	yes	—
65	#13133141	—	2	4	no	—
66	#13133137	—	2	4	no	—
67	C₂²⋊#88322	—	2	1	no	—
68	C₂²⋊#88322	—	2	1	no	—
69	C₄×#88322	—	2	1	no	—
70	C₄×#88322	—	2	1	no	—
71	C₂×M₁₆×C₅₃	—	2	1	no	—
72	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
73	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
74	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
75	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
76	#125×C₅₃	—	2	1	no	—
77	C₂²⋊Q₈×C₅₃	—	2	1	no	—
78	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
79	C₄×Q₈×C₅₃	—	2	1	no	—
80	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
81	#117×C₅₃	—	2	1	no	—
82	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₅₃	—	2	2	no	—
84	C₄⋊C₈×C₅₃	—	2	2	no	—
85	C₄⋊C₈×C₅₃	—	2	1	no	—
86	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
87	#97×C₅₃	—	2	2	no	—
88	C₄×C₈×C₅₃	—	2	2	no	—
89	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
90	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
91	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₂³×D₅₃	—	4	1	no	—
94	C₂×Q₈×C₅₃	—	2	1	no	—
95	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
99	C₂²×Dic₅₃	—	4	1	no	—
100	C₂×D₂₁₂	—	2	2	no	—
101	C₂×D₂₁₂	—	2	2	no	—
102	C₂×D₂₁₂	—	2	2	no	—
103	C₂×D₂₁₂	—	4	2	no	—
104	C₂×D₂₁₂	—	4	2	no	—
105	C₂×D₂₁₂	—	4	1	no	—
106	C₂×D₂₁₂	—	4	1	no	—
107	C₂×D₂₁₂	—	4	1	no	—
108	C₂×D₂₁₂	—	8	2	no	—
109	C₂×D₂₁₂	—	8	2	no	—
110	C₂×Dic₁₀₆	—	2	2	no	—
111	C₂×Dic₁₀₆	—	4	2	no	—
112	C₂×Dic₁₀₆	—	4	2	no	—
113	C₂×Dic₁₀₆	—	4	1	no	—
114	M₁₆×C₅₃	—	4	2	no	—
115	C₂×C₈×C₅₃	—	2	2	no	—
116	C₂×C₈×C₅₃	—	2	2	no	—
117	C₂×C₈×C₅₃	SD₁₆	1	4	yes	complemented
118	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
122	C₄⋊C₄×C₅₃	—	2	1	no	—
123	C₄⋊C₄×C₅₃	—	2	1	no	—
124	C₄⋊C₄×C₅₃	—	2	1	no	—
125	C₄⋊C₄×C₅₃	—	2	2	no	—
126	C₄⋊C₄×C₅₃	—	2	2	no	—
127	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
128	C₂²⋊C₄×C₅₃	—	2	2	no	—
129	C₄²×C₅₃	—	2	2	no	—
130	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₅₃	#41	1	1	yes	characteristic
133	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
134	#11719924	—	8	4	no	—
135	C₄⋊Dic₅₃	—	2	2	no	—
136	C₄⋊Dic₅₃	—	2	2	no	—
137	C₄⋊Dic₅₃	—	4	1	no	—
138	C₄⋊Dic₅₃	—	4	1	no	—
139	C₂×#88322	—	2	2	no	—
140	C₂×#88322	—	2	2	no	—
141	#11719913	—	4	4	no	—
142	#11719913	—	4	4	no	—
143	#11719913	—	4	4	no	—
144	#11719913	—	4	4	no	—
145	C₂³×C₅₃	#121	1	1	yes	characteristic
146	C₂²×D₅₃	—	4	2	no	—
147	C₂²×D₅₃	—	8	2	no	—
148	C₂²×D₅₃	—	8	2	no	—
149	C₂²×D₅₃	—	8	2	no	—
150	Q₈×C₅₃	—	2	4	no	—
151	Q₈×C₅₃	—	4	2	no	—
152	C₂×C₄×C₅₃	—	2	2	no	—
153	C₂×C₄×C₅₃	—	2	2	no	—
154	C₂×C₄×C₅₃	—	2	2	no	—
155	C₂×C₄×C₅₃	—	2	2	no	—
156	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
157	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
158	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₂×SD₁₆	1	2	yes	—
160	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
161	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
164	C₂×Dic₅₃	—	4	2	no	—
165	C₂×Dic₅₃	—	8	2	no	—
166	D₂₁₂	—	4	2	no	—
167	D₂₁₂	—	4	2	no	—
168	D₂₁₂	—	4	4	no	—
169	D₂₁₂	—	8	2	no	—
170	D₂₁₂	—	8	2	no	—
171	D₂₁₂	—	8	2	no	—
172	D₂₁₂	—	8	2	no	—
173	Dic₁₀₆	—	4	2	no	—
174	Dic₁₀₆	—	4	2	no	—
175	Dic₁₀₆	—	8	2	no	—
176	C₈×C₅₃	—	2	1	no	—
177	C₈×C₅₃	—	2	1	no	—
178	C₈×C₅₃	—	4	2	no	—
179	C₈×C₅₃	C₂×SD₁₆	1	2	yes	—
180	C₈×C₅₃	C₂×SD₁₆	1	2	yes	—
181	#88322	—	4	2	no	—
182	#88322	—	4	2	no	—
183	#19202	—	53	1	no	maximal, Sylow
184	C₂²×C₅₃	—	2	1	no	—
185	C₂²×C₅₃	—	2	1	no	—
186	C₂²×C₅₃	#460	1	2	yes	—
187	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
188	C₂×D₅₃	—	8	2	no	—
189	C₂×D₅₃	—	8	2	no	—
190	C₂×D₅₃	—	8	2	no	—
191	C₂×D₅₃	—	16	4	no	—
192	C₄×C₅₃	—	2	1	no	—
193	C₄×C₅₃	—	2	1	no	—
194	C₄×C₅₃	—	4	2	no	—
195	C₄×C₅₃	—	4	2	no	—
196	C₄×C₅₃	#460	1	2	yes	—
197	C₄×C₅₃	#471	1	2	yes	—
198	C₄×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
199	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
200	C₄×C₅₃	#577	1	2	yes	—
201	Dic₅₃	—	8	2	no	—
202	#3229	—	53	1	no	—
203	#3208	—	53	1	no	—
204	C₂×#492	—	53	1	no	—
205	#2960	D₅₃	1	1	yes	characteristic, complemented
206	#1686	—	53	4	no	—
207	#1666	—	53	4	no	—
208	#1564	—	53	1	no	—
209	#1546	—	53	1	no	—
210	#1545	—	53	1	no	—
211	C₂×C₅₃	—	2	2	no	—
212	C₂×C₅₃	C₂×#460	1	1	yes	characteristic
213	C₂×C₅₃	#3057	1	1	yes	characteristic
214	C₂×C₅₃	C₂×#471	1	1	yes	characteristic
215	D₅₃	—	16	2	no	—
216	C₂²×SD₁₆	—	106	1	no	—
217	C₂²×SD₁₆	—	106	1	no	—
218	#533	C₂×D₅₃	1	1	yes	characteristic
219	C₂×C₄⋊Q₈	—	53	1	no	—
220	C₂×#127	—	53	1	no	—
221	#498	—	106	1	no	—
222	#492	—	53	2	no	—
223	#492	—	53	2	no	—
224	#492	—	106	1	no	—
225	#492	—	106	1	no	—
226	#492	—	106	1	no	—
227	#487	—	106	1	no	—
228	#486	—	106	1	no	—
229	#483	—	106	2	no	—
230	#475	—	53	4	no	—
231	#460	—	53	4	no	—
232	#450	—	106	2	no	—
233	#446	—	2	1	no	—
234	#446	C₂×D₅₃	1	2	yes	complemented
235	C₈×Q₈	—	2	1	no	—
236	C₈×Q₈	C₂×D₅₃	1	2	yes	complemented
237	#431	—	53	1	no	—
238	#431	—	53	1	no	—
239	#424	—	2	1	no	—
240	#423	C₂×D₅₃	1	1	yes	characteristic
241	#405	—	2	1	no	—
242	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
243	#335	—	53	2	no	—
244	#334	—	53	2	no	—
245	#332	—	53	4	no	—
246	#331	—	53	4	no	—
247	C₅₃	#19202	1	1	yes	characteristic, complemented, Sylow
248	C₂²×Q₈	—	106	1	no	—
249	C₂²×D₄	—	106	1	no	—
250	C₂²×D₄	—	106	1	no	—
251	C₂²×D₄	—	106	1	no	—
252	C₂×SD₁₆	—	106	4	no	—
253	C₂×SD₁₆	—	106	2	no	—
254	C₂×SD₁₆	—	106	2	no	—
255	C₂×SD₁₆	—	106	2	no	—
256	C₂×SD₁₆	—	106	2	no	—
257	C₂×SD₁₆	—	212	4	no	—
258	C₂×SD₁₆	—	212	4	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
261	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
262	C₄⋊Q₈	—	53	2	no	—
263	C₄⋊Q₈	—	106	1	no	—
264	C₄⋊Q₈	—	106	1	no	—
265	C₄⋊Q₈	—	106	1	no	—
266	C₄⋊Q₈	D₂₁₂	1	1	yes	characteristic
267	C₄⋊Q₈	D₂₁₂	1	1	yes	characteristic
268	#127	—	53	2	no	—
269	#127	—	106	1	no	—
270	#127	—	106	1	no	—
271	#127	—	106	1	no	—
272	#125	—	2	1	no	—
273	C₂²⋊Q₈	—	2	1	no	—
274	C₂²⋊Q₈	D₂₁₂	1	2	yes	—
275	C₄×Q₈	—	2	1	no	—
276	C₄×Q₈	C₂²×D₅₃	1	2	yes	—
277	#117	—	2	1	no	—
278	C₂×C₄⋊C₄	—	106	1	no	—
279	C₂×C₄⋊C₄	—	106	1	no	—
280	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
281	#106	—	106	4	no	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	53	2	no	—
286	C₄⋊C₈	—	53	2	no	—
287	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
288	#103	—	106	4	no	—
289	#102	—	106	4	no	—
290	C₂²⋊C₈	—	106	1	no	—
291	C₂²⋊C₈	—	106	1	no	—
292	#97	—	2	2	no	—
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	—	106	1	no	—
295	C₄×C₈	—	106	1	no	—
296	C₄×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
297	C₄×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
299	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
300	C₂⁴	—	212	1	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	—	106	2	no	—
303	C₂×Q₈	—	212	2	no	—
304	C₂×Q₈	—	212	2	no	—
305	C₂×Q₈	—	212	1	no	—
306	C₂×Q₈	C₂×D₂₁₂	1	2	yes	—
307	C₂×D₄	—	106	2	no	—
308	C₂×D₄	—	106	2	no	—
309	C₂×D₄	—	106	2	no	—
310	C₂×D₄	—	424	2	no	—
311	C₂×D₄	—	424	2	no	—
312	C₂×D₄	—	212	1	no	—
313	C₂×D₄	—	212	1	no	—
314	C₂×D₄	—	212	1	no	—
315	C₂×D₄	—	212	2	no	—
316	C₂×D₄	—	212	2	no	—
317	C₂²×C₄	—	212	1	no	—
318	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
319	C₂²×C₄	#11719945	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
321	SD₁₆	—	424	4	no	—
322	SD₁₆	—	212	4	no	—
323	SD₁₆	—	212	4	no	—
324	SD₁₆	—	212	4	no	—
325	SD₁₆	—	212	4	no	—
326	M₁₆	—	4	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	106	2	no	—
330	C₂×C₈	—	106	2	no	—
331	C₂×C₈	#11719924	1	4	yes	complemented
332	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
333	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
334	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
335	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	106	2	no	—
342	C₄⋊C₄	—	106	2	no	—
343	C₄⋊C₄	—	212	1	no	—
344	C₄⋊C₄	—	212	1	no	—
345	C₄⋊C₄	C₂×D₂₁₂	1	2	yes	—
346	C₂²⋊C₄	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
349	C₄²	#11719945	1	1	yes	characteristic
350	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
351	C₄²	C₂³×D₅₃	1	1	yes	characteristic
352	C₂³	—	424	2	no	—
353	C₂³	—	424	2	no	—
354	C₂³	—	424	2	no	—
355	C₂³	—	212	2	no	—
356	C₂³	#13133191	1	1	yes	characteristic
357	Q₈	—	2	4	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	424	2	no	—
360	Q₈	—	212	2	no	—
361	Q₈	—	212	2	no	—
362	D₄	—	424	2	no	—
363	D₄	—	424	2	no	—
364	D₄	—	424	2	no	—
365	D₄	—	424	2	no	—
366	D₄	—	212	2	no	—
367	D₄	—	212	2	no	—
368	D₄	—	212	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	424	2	no	—
374	C₂×C₄	—	212	2	no	—
375	C₂×C₄	#13133191	1	1	yes	characteristic
376	C₂×C₄	#13133191	1	1	yes	characteristic
377	C₂×C₄	#13133191	1	1	yes	characteristic
378	C₂×C₄	C₂×#11719924	1	2	yes	—
379	C₂×C₄	#13133242	1	2	yes	—
380	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
381	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
382	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	4	2	no	—
386	C₈	—	212	2	no	—
387	C₈	—	212	2	no	—
388	C₈	C₂×#11719924	1	2	yes	—
389	C₈	C₂×#11719924	1	2	yes	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	848	4	no	—
393	C₂²	—	424	2	no	—
394	C₂²	—	424	2	no	—
395	C₂²	—	424	2	no	—
396	C₂²	#16810823	1	2	yes	—
397	C₂²	C₂×#13133191	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	2	no	—
402	C₄	—	424	2	no	—
403	C₄	#16810823	1	2	yes	—
404	C₄	#16810886	1	2	yes	—
405	C₄	C₂²×#11719924	1	1	yes	characteristic
406	C₄	C₂×#13133242	1	1	yes	characteristic
407	C₄	#16811435	1	2	yes	—
408	C₂	—	2	2	no	—
409	C₂	—	848	2	no	—
410	C₂	C₂×#16810823	1	1	yes	characteristic
411	C₂	#20284354	1	1	yes	characteristic
412	C₂	C₂×#16810886	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13133191
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#2960	C₂
socle	C₂²×C₅₃	C₂×#121
prime radical	C₂×#13133214	C₂²
hypercenter	#2960	D₅₃
hypocenter	C₅₃	#19202
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2960

Complements

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

N	H ≅ G/N	type
1. #20285856	C₂	semidirect
4. #20274187	C₂	semidirect
5. #20274063	C₂	semidirect
6. #20273463	C₂	semidirect
7. #20273388	C₂	semidirect
9. C₅₃×#2960	C₂	semidirect
23. #16810908	C₂²	semidirect
28. #16810376	C₂²	semidirect
29. #16810374	C₂²	semidirect
30. #16810370	C₂²	semidirect
34. C₅₃×#446	C₂²	semidirect
36. C₈×Q₈×C₅₃	C₂²	semidirect
117. C₂×C₈×C₅₃	SD₁₆	semidirect
205. #2960	D₅₃	semidirect
234. #446	C₂×D₅₃	semidirect
236. C₈×Q₈	C₂×D₅₃	semidirect
247. C₅₃	#19202	semidirect
331. C₂×C₈	#11719924	semidirect

Maximal subgroups

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

subgroup	index
#20285856	2
#20285653	2
C₂×#16810996	2
#20274187	2
#20274063	2
#20273463	2
#20273388	2
#20273384	2
C₅₃×#2960	2
#19202	53