Subgroups — #27382663

Order 13568.

1022 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810746	C₂	1	1	yes	maximal, characteristic
2	C₂×#16810744	C₂	1	1	yes	maximal, characteristic
3	#20283486	C₂	1	1	yes	maximal, characteristic
4	#20283137	C₂	1	2	yes	maximal, complemented
5	#108×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274601	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274561	C₂	1	2	yes	maximal, complemented
8	#20274556	C₂	1	2	yes	maximal, complemented
9	#20274519	C₂	1	2	yes	maximal, complemented
10	#97×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1773	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133239	C₂²	1	1	yes	characteristic
13	C₂×#13133225	C₂²	1	2	yes	—
14	C₂×#13133223	C₂²	1	2	yes	—
15	#16811091	C₂²	1	2	yes	—
16	#16810746	C₄	1	8	yes	complemented
17	#16810744	C₄	1	8	yes	complemented
18	#16810717	C₄	1	2	yes	complemented
19	#16810710	C₄	1	4	yes	complemented
20	#16810705	C₄	1	2	yes	complemented
21	C₂×#13133153	C₂²	1	1	yes	characteristic
22	C₂×#13133145	C₂²	1	2	yes	—
23	C₂×#13133143	C₂²	1	2	yes	—
24	#16810617	C₂²	1	2	yes	—
25	#16810580	—	2	2	no	—
26	#16810579	C₂²	1	2	yes	—
27	#16810577	—	2	2	no	—
28	#16810575	—	2	2	no	—
29	M₁₆×Dic₅₃	C₂²	1	2	yes	—
30	C₂×#13133128	C₂²	1	1	yes	characteristic
31	C₂×#13133127	C₂²	1	1	yes	characteristic
32	C₂×#13133127	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₅₃	—	2	2	no	—
36	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
37	#16810387	C₂²	1	2	yes	—
38	#16810382	C₂²	1	2	yes	—
39	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
40	C₅₃×#427	C₂²	1	1	yes	characteristic
41	C₅₃×#405	C₂²	1	2	yes	—
42	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×#339	C₂²	1	2	yes	—
44	C₂×#11719945	C₂³	1	2	yes	—
45	#13133239	C₂×C₄	1	4	yes	—
46	#13133239	C₂×C₄	1	4	yes	—
47	C₂×Dic₂₁₂	C₂×C₄	1	1	yes	characteristic
48	C₂×#11719913	C₂×C₄	1	2	yes	—
49	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic
50	#13133225	—	2	4	no	—
51	#13133225	C₂×C₄	1	8	yes	complemented
52	#13133223	—	2	4	no	—
53	#13133223	C₂×C₄	1	8	yes	complemented
54	C₂×#11719917	C₂³	1	2	yes	—
55	C₂×#11719912	—	2	2	no	—
56	C₂×#11719912	—	2	2	no	—
57	C₂²×#88322	C₂³	1	1	yes	characteristic
58	C₂²×#88322	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₅₃	—	2	2	no	—
60	C₂×C₈×D₅₃	—	2	2	no	—
61	#13133182	C₂×C₄	1	4	yes	—
62	#13133179	C₂×C₄	1	4	yes	—
63	#13133177	—	2	4	no	—
64	#13133174	—	2	2	no	—
65	C₂×C₄×Dic₅₃	—	2	2	no	—
66	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
67	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
68	C₄²×D₅₃	—	2	2	no	—
69	#13133153	C₂×C₄	1	4	yes	complemented
70	#13133145	C₂×C₄	1	8	yes	complemented
71	#13133143	C₂×C₄	1	8	yes	complemented
72	#13133140	C₂×C₄	1	4	yes	—
73	#13133137	C₂×C₄	1	4	yes	—
74	#13133128	—	2	2	no	—
75	#13133128	—	2	2	no	—
76	#13133127	—	2	2	no	—
77	#13133127	—	2	2	no	—
78	#13133127	C₂×C₄	1	4	yes	complemented
79	C₄×#88322	—	2	2	no	—
80	C₈×Dic₅₃	—	2	2	no	—
81	C₈×Dic₅₃	C₂×C₄	1	2	yes	—
82	C₈×Dic₅₃	C₂×C₄	1	2	yes	—
83	C₈×Dic₅₃	D₄	1	2	yes	—
84	C₈×Dic₅₃	D₄	1	2	yes	—
85	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
86	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
88	#117×C₅₃	C₂³	1	2	yes	—
89	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
90	#108×C₅₃	C₂×C₄	1	4	yes	complemented
91	#107×C₅₃	C₂×C₄	1	2	yes	—
92	#106×C₅₃	C₂×C₄	1	2	yes	—
93	#97×C₅₃	—	2	2	no	—
94	#97×C₅₃	C₂×C₄	1	4	yes	complemented
95	C₄×C₈×C₅₃	—	2	2	no	—
96	C₂²×C₄×C₅₃	—	2	1	no	—
97	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
98	C₂×C₂²⋊D₅₃	—	2	2	no	—
99	C₂²×Dic₅₃	—	2	1	no	—
100	C₂²×Dic₅₃	#41	1	2	yes	—
101	#11719945	—	2	2	no	—
102	#11719945	—	2	2	no	—
103	#11719945	C₂²×C₄	1	4	yes	—
104	#11719945	C₂²×C₄	1	4	yes	—
105	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
106	C₂×C₄×D₅₃	—	2	2	no	—
107	C₂×C₄×D₅₃	—	2	4	no	—
108	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
109	M₁₆×C₅₃	—	2	2	no	—
110	M₁₆×C₅₃	C₂²×C₄	1	4	yes	—
111	C₂×C₈×C₅₃	—	2	2	no	—
112	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₅₃	#41	1	2	yes	—
119	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
120	C₂²⋊C₄×C₅₃	—	2	2	no	—
121	C₄²×C₅₃	—	2	2	no	—
122	C₄²×C₅₃	—	2	1	no	—
123	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
124	#11719921	—	2	4	no	—
125	#11719919	—	2	4	no	—
126	C₄×Dic₅₃	—	2	1	no	—
127	C₄×Dic₅₃	—	2	4	no	—
128	C₄×Dic₅₃	—	4	4	no	—
129	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
130	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
131	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
132	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
133	#11719917	—	2	2	no	—
134	#11719917	C₂²×C₄	1	4	yes	—
135	C₂×#88322	—	2	2	no	—
136	C₂×#88322	—	2	1	no	—
137	C₂×#88322	—	2	1	no	—
138	C₂×#88322	C₂²×C₄	1	2	yes	—
139	C₂×#88322	C₂²×C₄	1	2	yes	—
140	C₂×#88322	C₂×D₄	1	2	yes	—
141	C₂×#88322	#41	1	2	yes	—
142	Dic₂₁₂	C₄²	1	4	yes	complemented
143	D₄₂₄	C₄²	1	4	yes	complemented
144	#11719913	C₄²	1	8	yes	complemented
145	#11719912	—	2	8	no	—
146	#11719912	—	2	8	no	—
147	C₈×D₅₃	—	2	8	no	—
148	C₈×D₅₃	—	2	8	no	—
149	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
150	C₂²×D₅₃	—	2	2	no	—
151	C₂×C₄×C₅₃	—	2	4	no	—
152	C₂×C₄×C₅₃	—	2	2	no	—
153	C₂×C₄×C₅₃	—	4	2	no	—
154	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
160	C₂²⋊D₅₃	—	2	4	no	—
161	C₂²⋊D₅₃	—	2	4	no	—
162	C₂×Dic₅₃	—	2	2	no	—
163	C₂×Dic₅₃	—	2	4	no	—
164	C₂×Dic₅₃	—	2	2	no	—
165	C₂×Dic₅₃	—	4	2	no	—
166	C₂×Dic₅₃	C₄×D₄	1	2	yes	—
167	C₂×Dic₅₃	C₄×D₄	1	2	yes	—
168	D₂₁₂	—	2	2	no	—
169	D₂₁₂	C₂×C₄²	1	4	yes	—
170	C₄×D₅₃	—	2	4	no	—
171	C₄×D₅₃	—	2	4	no	—
172	C₄×D₅₃	—	4	8	no	—
173	Dic₁₀₆	—	2	2	no	—
174	Dic₁₀₆	C₂×C₄²	1	4	yes	—
175	C₈×C₅₃	—	2	4	no	—
176	C₈×C₅₃	C₂×C₄²	1	2	yes	—
177	C₈×C₅₃	C₂×C₄²	1	2	yes	—
178	C₈×C₅₃	C₄×D₄	1	4	yes	—
179	#88322	—	2	4	no	—
180	#88322	—	2	2	no	—
181	#88322	C₄×D₄	1	4	yes	—
182	C₄×#444	—	53	1	no	maximal, Sylow
183	C₂²×C₅₃	—	2	2	no	—
184	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
185	C₂²×C₅₃	C₄×#41	1	1	yes	characteristic
186	C₂²×C₅₃	C₄×#41	1	1	yes	characteristic
187	C₂×D₅₃	—	2	4	no	—
188	C₂×D₅₃	—	4	4	no	—
189	C₄×C₅₃	—	4	2	no	—
190	C₄×C₅₃	—	4	4	no	—
191	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
192	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
194	C₄×C₅₃	C₄×#41	1	1	yes	characteristic
195	Dic₅₃	—	2	2	no	—
196	Dic₅₃	—	2	4	no	—
197	Dic₅₃	—	4	2	no	—
198	Dic₅₃	#444	1	4	yes	complemented
199	C₂×#444	—	53	1	no	—
200	C₂×#444	—	53	1	no	—
201	C₄×#135	—	53	1	no	—
202	C₄×#131	—	53	2	no	—
203	C₄×#108	—	53	1	no	—
204	#1773	—	53	1	no	—
205	#1773	D₅₃	1	1	yes	characteristic, complemented
206	#1765	—	53	2	no	—
207	#1765	—	53	2	no	—
208	C₄×#104	—	53	2	no	—
209	C₄×#97	—	53	1	no	—
210	C₂×C₅₃	—	2	1	no	—
211	C₂×C₅₃	—	2	1	no	—
212	C₂×C₅₃	C₄²×D₄	1	1	yes	characteristic
213	C₂×C₅₃	C₂×#444	1	2	yes	—
214	D₅₃	—	4	4	no	—
215	C₂×#135	—	53	1	no	—
216	C₂×#131	—	53	2	no	—
217	C₂×#131	—	53	2	no	—
218	C₄×#41	—	53	2	no	—
219	#444	—	53	8	no	—
220	#444	—	53	8	no	—
221	C₄×Q₁₆	—	53	2	no	—
222	C₄×SD₁₆	—	53	4	no	—
223	C₄×D₈	—	53	2	no	—
224	C₂×#108	—	53	1	no	—
225	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
226	#427	C₂×D₅₃	1	1	yes	characteristic
227	C₂×#104	—	53	2	no	—
228	C₂×#104	—	53	2	no	—
229	#416	—	53	2	no	—
230	#405	—	53	2	no	—
231	#405	—	106	2	no	—
232	#405	—	106	2	no	—
233	#405	C₂×D₅₃	1	2	yes	—
234	C₄×M₁₆	—	53	2	no	—
235	C₄×M₁₆	—	106	2	no	—
236	C₂×#97	—	53	1	no	—
237	C₂×#97	—	53	1	no	—
238	C₂×#97	—	53	1	no	—
239	C₂×#97	C₂×D₅₃	1	1	yes	characteristic
240	C₂×C₄×C₈	—	53	1	no	—
241	C₂×C₄×C₈	—	53	1	no	—
242	C₂×C₄×C₈	—	106	2	no	—
243	C₄³	—	53	1	no	—
244	#341	—	53	2	no	—
245	#339	—	53	2	no	—
246	#339	C₂×D₅₃	1	2	yes	—
247	C₅₃	C₄×#444	1	1	yes	characteristic, complemented, Sylow
248	C₂×#41	—	53	2	no	—
249	#135	—	53	4	no	—
250	#135	—	53	4	no	—
251	C₂×Q₁₆	—	53	1	no	—
252	C₂×SD₁₆	—	53	2	no	—
253	C₂×D₈	—	53	1	no	—
254	#131	—	53	8	no	—
255	#131	—	53	8	no	—
256	#131	—	106	4	no	—
257	#131	—	106	4	no	—
258	C₂×M₁₆	—	53	2	no	—
259	C₂×M₁₆	—	106	2	no	—
260	C₂×M₁₆	—	106	2	no	—
261	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
262	C₂²×C₈	—	53	1	no	—
263	C₂²×C₈	—	53	1	no	—
264	C₂²×C₈	—	106	2	no	—
265	C₂²×C₈	—	106	2	no	—
266	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
268	C₄×Q₈	—	53	4	no	—
269	C₄×D₄	—	53	4	no	—
270	C₄×D₄	—	106	4	no	—
271	#117	—	106	2	no	—
272	#117	C₂²×D₅₃	1	2	yes	—
273	C₂×C₄²	—	53	1	no	—
274	C₂×C₄²	—	53	1	no	—
275	C₂×C₄²	—	106	2	no	—
276	C₂×C₄²	—	106	2	no	—
277	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
278	#108	—	53	4	no	—
279	#108	C₄×D₅₃	1	4	yes	complemented
280	#107	C₄×D₅₃	1	2	yes	—
281	#106	C₄×D₅₃	1	2	yes	—
282	#104	—	53	8	no	—
283	#104	—	53	8	no	—
284	#103	—	53	4	no	—
285	#102	—	53	4	no	—
286	#97	—	2	2	no	—
287	#97	—	53	4	no	—
288	#97	—	106	2	no	—
289	#97	—	106	2	no	—
290	#97	—	106	2	no	—
291	#97	—	106	2	no	—
292	#97	C₄×D₅₃	1	4	yes	complemented
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	—	53	2	no	—
295	C₄×C₈	—	53	2	no	—
296	C₄×C₈	—	53	2	no	—
297	C₄×C₈	—	53	2	no	—
298	C₄×C₈	—	106	2	no	—
299	C₄×C₈	—	106	2	no	—
300	#41	—	53	4	no	—
301	#41	—	53	4	no	—
302	#41	—	106	2	no	—
303	#41	—	106	2	no	—
304	C₂×Q₈	—	53	2	no	—
305	C₂×D₄	—	53	2	no	—
306	C₂×D₄	—	106	2	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	53	2	no	—
309	C₂²×C₄	—	106	4	no	—
310	C₂²×C₄	—	106	2	no	—
311	C₂²×C₄	—	106	1	no	—
312	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
313	Q₁₆	—	53	4	no	—
314	SD₁₆	—	53	8	no	—
315	D₈	—	53	4	no	—
316	M₁₆	—	2	2	no	—
317	M₁₆	—	53	4	no	—
318	M₁₆	—	106	8	no	—
319	M₁₆	—	106	2	no	—
320	M₁₆	—	106	8	no	—
321	M₁₆	C₂×C₄×D₅₃	1	4	yes	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	53	2	no	—
324	C₂×C₈	—	53	2	no	—
325	C₂×C₈	—	53	2	no	—
326	C₂×C₈	—	53	2	no	—
327	C₂×C₈	—	106	8	no	—
328	C₂×C₈	—	106	2	no	—
329	C₂×C₈	—	106	1	no	—
330	C₂×C₈	—	106	1	no	—
331	C₂×C₈	—	106	8	no	—
332	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
333	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
335	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
336	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
337	C₂×C₈	D₄×D₅₃	1	2	yes	—
338	C₂×C₈	#11719949	1	2	yes	—
339	C₄⋊C₄	—	106	4	no	—
340	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	106	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	53	2	no	—
346	C₄²	—	53	1	no	—
347	C₄²	—	53	1	no	—
348	C₄²	—	53	2	no	—
349	C₄²	—	106	4	no	—
350	C₄²	—	106	1	no	—
351	C₄²	—	212	4	no	—
352	C₄²	C₂×C₄×D₅₃	1	2	yes	—
353	C₂³	—	106	2	no	—
354	C₂³	#41×D₅₃	1	1	yes	characteristic
355	Q₈	—	53	4	no	—
356	Q₈	—	106	2	no	—
357	D₄	—	53	4	no	—
358	D₄	—	106	4	no	—
359	D₄	—	106	4	no	—
360	D₄	—	106	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	53	2	no	—
365	C₂×C₄	—	53	2	no	—
366	C₂×C₄	—	106	4	no	—
367	C₂×C₄	—	106	2	no	—
368	C₂×C₄	—	106	4	no	—
369	C₂×C₄	—	106	4	no	—
370	C₂×C₄	—	106	2	no	—
371	C₂×C₄	—	212	8	no	—
372	C₂×C₄	—	212	2	no	—
373	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
376	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
377	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
378	C₂×C₄	C₂×#11719949	1	1	yes	characteristic
379	C₈	—	2	4	no	—
380	C₈	—	53	4	no	—
381	C₈	—	106	4	no	—
382	C₈	—	106	2	no	—
383	C₈	C₄²×D₅₃	1	2	yes	—
384	C₈	C₄²×D₅₃	1	2	yes	—
385	C₈	#13133179	1	4	yes	—
386	C₂²	—	2	2	no	—
387	C₂²	—	106	4	no	—
388	C₂²	—	212	4	no	—
389	C₂²	C₄×D₄×D₅₃	1	1	yes	characteristic
390	C₂²	#16811091	1	1	yes	characteristic
391	C₂²	C₄×#11719949	1	1	yes	characteristic
392	C₄	—	4	2	no	—
393	C₄	—	4	4	no	—
394	C₄	—	53	4	no	—
395	C₄	—	106	4	no	—
396	C₄	—	106	2	no	—
397	C₄	—	212	2	no	—
398	C₄	C₂×C₄²×D₅₃	1	1	yes	characteristic
399	C₄	C₄×D₄×D₅₃	1	1	yes	characteristic
400	C₄	C₂×#13133179	1	1	yes	characteristic
401	C₄	C₄×#11719949	1	1	yes	characteristic
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	—	212	4	no	—
405	C₂	C₄×#13133179	1	1	yes	characteristic
406	C₂	#444×D₅₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₃
commutator	C₄×C₅₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1773	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂×#13133239	C₂²
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1773	D₅₃
hypocenter	C₅₃	C₄×#444
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1773

Complements

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

N	H ≅ G/N	type
4. #20283137	C₂	semidirect
5. #108×Dic₅₃	C₂	semidirect
6. #20274601	C₂	semidirect
7. #20274561	C₂	semidirect
8. #20274556	C₂	semidirect
9. #20274519	C₂	semidirect
10. #97×Dic₅₃	C₂	semidirect
11. C₅₃×#1773	C₂	semidirect
16. #16810746	C₄	semidirect
17. #16810744	C₄	semidirect
18. #16810717	C₄	semidirect
19. #16810710	C₄	semidirect
20. #16810705	C₄	semidirect
51. #13133225	C₂×C₄	semidirect
53. #13133223	C₂×C₄	semidirect
69. #13133153	C₂×C₄	semidirect
70. #13133145	C₂×C₄	semidirect
71. #13133143	C₂×C₄	semidirect
78. #13133127	C₂×C₄	semidirect
90. #108×C₅₃	C₂×C₄	semidirect
94. #97×C₅₃	C₂×C₄	semidirect
142. Dic₂₁₂	C₄²	semidirect
143. D₄₂₄	C₄²	semidirect
144. #11719913	C₄²	semidirect
198. Dic₅₃	#444	semidirect
205. #1773	D₅₃	semidirect
247. C₅₃	C₄×#444	semidirect
279. #108	C₄×D₅₃	semidirect
292. #97	C₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16810746	2
C₂×#16810744	2
#20283486	2
#20283137	2
#108×Dic₅₃	2
#20274601	2
#20274561	2
#20274556	2
#20274519	2
#97×Dic₅₃	2
C₅₃×#1773	2
C₄×#444	53