Subgroups — #27537331

Order 13568.

646 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811039	C₂	1	1	yes	maximal, characteristic, complemented
2	#20283616	C₂	1	1	yes	maximal, characteristic
3	#20276555	C₂	1	4	yes	maximal, complemented
4	#20276550	C₂	1	4	yes	maximal, complemented
5	#20276480	C₂	1	1	yes	maximal, characteristic, complemented
6	#20276344	C₂	1	1	yes	maximal, characteristic, complemented
7	#20276343	C₂	1	1	yes	maximal, characteristic, complemented
8	#20276311	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅₃×#504	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811421	C₄	1	1	yes	characteristic
11	C₂×#13133223	C₂²	1	1	yes	characteristic
12	#16811039	—	2	1	no	—
13	#16811039	—	2	1	no	—
14	#16811039	C₂²	1	2	yes	complemented
15	#16811039	C₂²	1	2	yes	complemented
16	C₂×#13133157	C₂²	1	1	yes	characteristic
17	C₂×#13133157	C₂²	1	1	yes	characteristic
18	C₂×#13133156	—	2	1	no	—
19	C₂×C₁₆×D₅₃	—	2	1	no	—
20	#16810743	C₄	1	4	yes	—
21	#16810738	C₂²	1	4	yes	—
22	#16810671	C₄	1	1	yes	characteristic
23	#16810640	C₄	1	1	yes	characteristic
24	#16810639	C₄	1	1	yes	characteristic
25	#16810578	C₂²	1	1	yes	characteristic
26	#16810443	C₂²	1	4	yes	complemented
27	#16810408	C₂²	1	4	yes	complemented
28	#16810407	C₂²	1	4	yes	complemented
29	#16810398	C₂²	1	2	yes	complemented
30	C₁₆×Dic₅₃	C₂²	1	2	yes	complemented
31	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
32	C₅₃×#504	—	2	1	no	—
33	C₅₃×#504	—	2	1	no	—
34	C₅₃×#504	C₂²	1	2	yes	complemented
35	C₅₃×#504	C₂²	1	2	yes	complemented
36	C₂×M₃₂×C₅₃	—	2	1	no	—
37	C₂×M₃₂×C₅₃	C₂²	1	1	yes	characteristic
38	C₂²×C₁₆×C₅₃	—	2	1	no	—
39	C₂²×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
41	#13133248	C₈	1	2	yes	—
42	#13133247	C₈	1	2	yes	—
43	#13133243	C₈	1	2	yes	—
44	#13133242	C₈	1	2	yes	—
45	#13133237	C₂×C₄	1	4	yes	—
46	#13133223	—	2	1	no	—
47	#13133223	—	2	1	no	—
48	#13133223	C₂×C₄	1	2	yes	—
49	#13133223	C₂³	1	2	yes	—
50	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
51	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
52	C₂×#11719912	—	2	1	no	—
53	C₂×C₈×D₅₃	—	2	1	no	—
54	#13133176	C₂×C₄	1	1	yes	characteristic
55	#13133157	—	2	1	no	—
56	#13133157	—	2	1	no	—
57	#13133157	—	2	1	no	—
58	#13133157	C₂³	1	2	yes	—
59	#13133156	—	2	2	no	—
60	#13133156	—	2	2	no	—
61	C₂×#11719908	—	2	1	no	—
62	C₂×#11719908	C₂³	1	2	yes	—
63	C₁₆×D₅₃	—	2	2	no	—
64	C₁₆×D₅₃	—	2	2	no	—
65	#13133152	C₂×C₄	1	4	yes	—
66	#13133144	C₂×C₄	1	4	yes	—
67	#13133143	C₂×C₄	1	4	yes	—
68	#13133127	C₂×C₄	1	2	yes	—
69	C₈×Dic₅₃	C₂³	1	2	yes	—
70	C₂×#41×C₅₃	C₂×C₄	1	1	yes	characteristic
71	#131×C₅₃	—	2	1	no	—
72	#131×C₅₃	—	2	1	no	—
73	#131×C₅₃	C₂×C₄	1	2	yes	—
74	#131×C₅₃	C₂³	1	2	yes	—
75	C₂×M₁₆×C₅₃	—	2	1	no	—
76	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₈×C₅₃	—	2	1	no	—
78	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
79	M₃₂×C₅₃	—	2	1	no	—
80	M₃₂×C₅₃	—	2	2	no	—
81	M₃₂×C₅₃	—	2	2	no	—
82	M₃₂×C₅₃	C₂³	1	2	yes	—
83	C₂×C₁₆×C₅₃	—	2	1	no	—
84	C₂×C₁₆×C₅₃	—	2	2	no	—
85	C₂×C₁₆×C₅₃	—	2	2	no	—
86	C₂×C₁₆×C₅₃	D₄	1	1	yes	characteristic
87	C₂×C₁₆×C₅₃	D₄	1	1	yes	characteristic
88	C₂×C₁₆×C₅₃	D₄	1	1	yes	characteristic
89	C₂×C₁₆×C₅₃	D₄	1	1	yes	characteristic
90	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
91	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
92	#41×C₅₃	—	2	1	no	—
93	#41×C₅₃	—	2	1	no	—
94	#41×C₅₃	C₂×C₈	1	2	yes	—
95	#41×C₅₃	C₂²×C₄	1	2	yes	—
96	C₂×Q₈×C₅₃	C₂×C₈	1	1	yes	characteristic
97	C₂×D₄×C₅₃	—	2	1	no	—
98	C₂×D₄×C₅₃	C₂×C₈	1	1	yes	characteristic
99	C₂²×C₄×C₅₃	—	2	1	no	—
100	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊D₅₃	—	2	1	no	—
102	#11719945	—	2	1	no	—
103	#11719945	—	2	1	no	—
104	#11719945	C₂×C₈	1	2	yes	—
105	#11719945	C₂²×C₄	1	2	yes	—
106	C₂×D₂₁₂	C₂×C₈	1	1	yes	characteristic
107	C₂×C₄×D₅₃	—	2	1	no	—
108	C₂×Dic₁₀₆	C₂×C₈	1	1	yes	characteristic
109	M₁₆×C₅₃	—	2	1	no	—
110	M₁₆×C₅₃	—	2	2	no	—
111	M₁₆×C₅₃	—	2	2	no	—
112	M₁₆×C₅₃	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₅₃	—	2	1	no	—
114	C₂×C₈×C₅₃	—	2	2	no	—
115	C₂×C₈×C₅₃	—	2	2	no	—
116	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
120	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
121	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
122	C₂²⋊Dic₅₃	—	2	1	no	—
123	#11719925	C₂×C₈	1	4	yes	—
124	#11719924	C₂×C₈	1	4	yes	—
125	#11719923	C₂×C₈	1	4	yes	—
126	#11719922	C₂×C₈	1	4	yes	—
127	C₄⋊Dic₅₃	—	2	1	no	—
128	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
129	#11719917	—	2	1	no	—
130	#11719917	C₂×C₈	1	2	yes	—
131	#11719917	C₂×C₈	1	2	yes	—
132	#11719917	C₂²×C₄	1	2	yes	—
133	C₂×#88322	—	2	1	no	—
134	C₂×#88322	C₂²×C₄	1	2	yes	—
135	#11719912	—	2	2	no	—
136	#11719912	—	2	2	no	—
137	C₈×D₅₃	—	2	2	no	—
138	C₈×D₅₃	—	2	2	no	—
139	C₁₆×C₅₃	—	2	2	no	—
140	C₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
141	C₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
142	C₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
143	C₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
144	#11719908	—	2	2	no	—
145	#11719908	—	2	2	no	—
146	C₂³×C₅₃	—	2	1	no	—
147	C₂³×C₅₃	#131	1	1	yes	characteristic
148	C₂²×D₅₃	—	2	1	no	—
149	Q₈×C₅₃	—	2	1	no	—
150	Q₈×C₅₃	C₂²×C₈	1	2	yes	—
151	D₄×C₅₃	—	2	2	no	—
152	D₄×C₅₃	—	2	2	no	—
153	D₄×C₅₃	—	2	1	no	—
154	D₄×C₅₃	C₂²×C₈	1	2	yes	—
155	C₂×C₄×C₅₃	—	2	1	no	—
156	C₂×C₄×C₅₃	—	2	2	no	—
157	C₂×C₄×C₅₃	—	2	2	no	—
158	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
161	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
162	C₂×C₄×C₅₃	#131	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
164	C₂²⋊D₅₃	—	2	2	no	—
165	C₂²⋊D₅₃	—	2	2	no	—
166	C₂×Dic₅₃	—	2	1	no	—
167	C₂×Dic₅₃	—	2	2	no	—
168	D₂₁₂	—	2	1	no	—
169	D₂₁₂	C₂²×C₈	1	2	yes	—
170	C₄×D₅₃	—	2	2	no	—
171	C₄×D₅₃	—	2	2	no	—
172	Dic₁₀₆	—	2	1	no	—
173	Dic₁₀₆	C₂²×C₈	1	2	yes	—
174	C₈×C₅₃	—	2	2	no	—
175	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
176	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
177	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
178	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
179	#88322	—	2	2	no	—
180	#88322	C₂²×C₈	1	4	yes	—
181	#33441	—	53	1	no	maximal, Sylow
182	C₂²×C₅₃	—	2	2	no	—
183	C₂²×C₅₃	—	4	1	no	—
184	C₂²×C₅₃	—	4	2	no	—
185	C₂²×C₅₃	C₈×D₄	1	1	yes	characteristic
186	C₂²×C₅₃	C₈×D₄	1	1	yes	characteristic
187	C₂²×C₅₃	C₂×#131	1	1	yes	characteristic
188	C₂×D₅₃	—	2	2	no	—
189	C₂×D₅₃	—	4	2	no	—
190	C₄×C₅₃	—	2	2	no	—
191	C₄×C₅₃	C₈×D₄	1	1	yes	characteristic
192	C₄×C₅₃	C₈×D₄	1	1	yes	characteristic
193	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
194	C₄×C₅₃	C₂³×C₈	1	1	yes	characteristic
195	Dic₅₃	—	2	2	no	—
196	Dic₅₃	—	4	2	no	—
197	C₂×#504	—	53	1	no	—
198	C₂×#504	D₅₃	1	1	yes	characteristic, complemented
199	#2955	—	53	1	no	—
200	#2171	—	53	4	no	—
201	#2170	—	53	4	no	—
202	#2153	—	53	1	no	—
203	#2117	—	53	1	no	—
204	#2117	—	53	1	no	—
205	#2108	—	53	1	no	—
206	C₂×C₅₃	—	2	1	no	—
207	C₂×C₅₃	—	2	1	no	—
208	C₂×C₅₃	—	2	1	no	—
209	C₂×C₅₃	—	4	2	no	—
210	C₂×C₅₃	C₂×C₈×D₄	1	1	yes	characteristic
211	D₅₃	—	4	2	no	—
212	#575	—	53	1	no	—
213	C₂×#131	—	53	1	no	—
214	C₂×#131	C₂×D₅₃	1	1	yes	characteristic
215	#504	—	2	1	no	—
216	#504	—	2	1	no	—
217	#504	—	53	2	no	—
218	#504	—	53	2	no	—
219	#504	—	106	1	no	—
220	#504	—	106	1	no	—
221	#504	C₂×D₅₃	1	2	yes	complemented
222	#504	C₂×D₅₃	1	2	yes	complemented
223	C₂×M₃₂	—	2	1	no	—
224	C₂×M₃₂	—	53	1	no	—
225	C₂×M₃₂	—	53	1	no	—
226	C₂×M₃₂	—	106	1	no	—
227	C₂×M₃₂	C₂×D₅₃	1	1	yes	characteristic
228	C₂²×C₁₆	—	2	1	no	—
229	C₂²×C₁₆	—	106	1	no	—
230	C₂²×C₁₆	C₂×D₅₃	1	1	yes	characteristic
231	#444	—	53	4	no	—
232	#443	—	53	4	no	—
233	#430	—	53	1	no	—
234	#421	—	53	1	no	—
235	#421	—	53	1	no	—
236	#405	—	53	1	no	—
237	#364	—	53	4	no	—
238	#350	—	53	4	no	—
239	#350	—	53	4	no	—
240	#346	—	53	2	no	—
241	C₄×C₁₆	—	53	2	no	—
242	C₅₃	#33441	1	1	yes	characteristic, complemented, Sylow
243	C₂×#41	—	53	1	no	—
244	C₂×#41	C₄×D₅₃	1	1	yes	characteristic
245	#137	—	53	2	no	—
246	#137	—	53	2	no	—
247	AGL(1,ℤ/8)	—	53	2	no	—
248	AGL(1,ℤ/8)	—	53	2	no	—
249	#135	—	53	4	no	—
250	#131	—	2	1	no	—
251	#131	—	2	1	no	—
252	#131	—	53	2	no	—
253	#131	—	53	2	no	—
254	#131	—	106	1	no	—
255	#131	—	106	1	no	—
256	#131	C₄×D₅₃	1	2	yes	—
257	#131	C₂²×D₅₃	1	2	yes	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	53	1	no	—
260	C₂×M₁₆	—	53	1	no	—
261	C₂×M₁₆	—	106	1	no	—
262	C₂×M₁₆	C₄×D₅₃	1	1	yes	characteristic
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	106	1	no	—
265	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
266	#117	—	53	1	no	—
267	M₃₂	—	2	1	no	—
268	M₃₂	—	2	2	no	—
269	M₃₂	—	2	2	no	—
270	M₃₂	—	53	2	no	—
271	M₃₂	—	106	1	no	—
272	M₃₂	—	106	1	no	—
273	M₃₂	—	106	1	no	—
274	M₃₂	—	106	2	no	—
275	M₃₂	—	106	2	no	—
276	M₃₂	C₂²×D₅₃	1	2	yes	—
277	C₂×C₁₆	—	2	1	no	—
278	C₂×C₁₆	—	2	2	no	—
279	C₂×C₁₆	—	2	2	no	—
280	C₂×C₁₆	—	53	2	no	—
281	C₂×C₁₆	—	106	1	no	—
282	C₂×C₁₆	—	106	2	no	—
283	C₂×C₁₆	—	106	2	no	—
284	C₂×C₁₆	C₂²⋊D₅₃	1	1	yes	characteristic
285	C₂×C₁₆	C₂²⋊D₅₃	1	1	yes	characteristic
286	C₂×C₁₆	C₂²⋊D₅₃	1	1	yes	characteristic
287	C₂×C₁₆	C₂²⋊D₅₃	1	1	yes	characteristic
288	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
289	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
290	#108	—	53	4	no	—
291	#104	—	53	4	no	—
292	#104	—	53	4	no	—
293	#97	—	53	2	no	—
294	C₄×C₈	—	53	2	no	—
295	#41	—	2	1	no	—
296	#41	—	2	1	no	—
297	#41	—	53	2	no	—
298	#41	—	53	2	no	—
299	#41	—	106	1	no	—
300	#41	—	106	1	no	—
301	#41	C₈×D₅₃	1	2	yes	—
302	#41	C₂×C₄×D₅₃	1	2	yes	—
303	C₂×Q₈	—	53	1	no	—
304	C₂×Q₈	C₈×D₅₃	1	1	yes	characteristic
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	53	1	no	—
307	C₂×D₄	—	106	1	no	—
308	C₂×D₄	C₈×D₅₃	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	106	1	no	—
311	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
312	Q₁₆	—	53	4	no	—
313	SD₁₆	—	53	4	no	—
314	SD₁₆	—	53	4	no	—
315	D₈	—	53	4	no	—
316	M₁₆	—	2	1	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	—	53	2	no	—
320	M₁₆	—	53	2	no	—
321	M₁₆	—	53	2	no	—
322	M₁₆	—	106	1	no	—
323	M₁₆	—	106	2	no	—
324	M₁₆	—	106	2	no	—
325	M₁₆	C₂×C₄×D₅₃	1	2	yes	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	53	2	no	—
330	C₂×C₈	—	106	1	no	—
331	C₂×C₈	—	106	2	no	—
332	C₂×C₈	—	106	2	no	—
333	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
334	C₂×C₈	#11719945	1	1	yes	characteristic
335	C₂×C₈	#11719945	1	1	yes	characteristic
336	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
337	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
338	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
339	C₄⋊C₄	—	106	1	no	—
340	C₂²⋊C₄	—	106	1	no	—
341	C₄²	—	53	2	no	—
342	C₁₆	—	2	2	no	—
343	C₁₆	—	106	2	no	—
344	C₁₆	—	106	2	no	—
345	C₁₆	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
346	C₁₆	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
347	C₁₆	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
348	C₁₆	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
349	C₂³	—	2	1	no	—
350	C₂³	—	106	1	no	—
351	C₂³	#13133223	1	1	yes	characteristic
352	Q₈	—	2	1	no	—
353	Q₈	—	53	2	no	—
354	Q₈	—	106	1	no	—
355	Q₈	C₂×C₈×D₅₃	1	2	yes	—
356	D₄	—	2	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	2	1	no	—
359	D₄	—	53	2	no	—
360	D₄	—	106	2	no	—
361	D₄	—	106	2	no	—
362	D₄	—	106	1	no	—
363	D₄	C₂×C₈×D₅₃	1	2	yes	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	106	1	no	—
368	C₂×C₄	—	106	2	no	—
369	C₂×C₄	—	106	2	no	—
370	C₂×C₄	—	106	2	no	—
371	C₂×C₄	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
372	C₂×C₄	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
373	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
374	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
375	C₂×C₄	#13133223	1	1	yes	characteristic
376	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	53	4	no	—
379	C₈	—	106	2	no	—
380	C₈	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
381	C₈	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
382	C₈	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
383	C₈	C₂×#11719945	1	1	yes	characteristic
384	C₂²	—	2	2	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	106	2	no	—
388	C₂²	—	212	2	no	—
389	C₂²	C₈×C₂²⋊D₅₃	1	1	yes	characteristic
390	C₂²	C₈×C₂²⋊D₅₃	1	1	yes	characteristic
391	C₂²	C₂×#13133223	1	1	yes	characteristic
392	C₄	—	2	2	no	—
393	C₄	—	106	2	no	—
394	C₄	—	212	2	no	—
395	C₄	C₈×C₂²⋊D₅₃	1	1	yes	characteristic
396	C₄	C₈×C₂²⋊D₅₃	1	1	yes	characteristic
397	C₄	C₂×C₄×C₂²⋊D₅₃	1	1	yes	characteristic
398	C₄	C₂²×C₈×D₅₃	1	1	yes	characteristic
399	C₂	—	2	1	no	—
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	4	2	no	—
403	C₂	—	212	2	no	—
404	C₂	C₂×C₈×C₂²⋊D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂×C₂²⋊D₅₃
commutator	C₄×C₅₃	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₂×C₅₃×#504	C₂
socle	C₂×C₅₃	C₂×C₈×D₄
prime radical	#16811421	C₄
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	C₂×#504	D₅₃
hypocenter	C₅₃	#33441
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₁₆ ◁ C₂²×C₁₆ ◁ C₂×#504

Complements

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

N	H ≅ G/N	type
1. C₂×#16811039	C₂	semidirect
3. #20276555	C₂	semidirect
4. #20276550	C₂	semidirect
5. #20276480	C₂	semidirect
6. #20276344	C₂	semidirect
7. #20276343	C₂	semidirect
8. #20276311	C₂	semidirect
9. C₂×C₅₃×#504	C₂	semidirect
14. #16811039	C₂²	semidirect
15. #16811039	C₂²	semidirect
26. #16810443	C₂²	semidirect
27. #16810408	C₂²	semidirect
28. #16810407	C₂²	semidirect
29. #16810398	C₂²	semidirect
30. C₁₆×Dic₅₃	C₂²	semidirect
34. C₅₃×#504	C₂²	semidirect
35. C₅₃×#504	C₂²	semidirect
198. C₂×#504	D₅₃	semidirect
221. #504	C₂×D₅₃	semidirect
222. #504	C₂×D₅₃	semidirect
242. C₅₃	#33441	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811039	2
#20283616	2
#20276555	2
#20276550	2
#20276480	2
#20276344	2
#20276343	2
#20276311	2
C₂×C₅₃×#504	2
#33441	53