Subgroups — #27289910

Order 13568.

1126 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×#88322	C₂	1	1	yes	maximal, characteristic
2	C₂×#16810493	C₂	1	1	yes	maximal, characteristic
3	C₂×#16810385	C₂	1	4	yes	maximal
4	C₂×C₅₃×#384	C₂	1	1	yes	maximal, characteristic
5	C₂³×#88322	C₂²	1	2	yes	—
6	C₂²×C₄⋊Dic₅₃	—	2	2	no	—
7	C₂²×C₄⋊Dic₅₃	C₂²	1	2	yes	—
8	C₂×C₄×#88322	—	2	2	no	—
9	C₂×C₄×#88322	—	2	2	no	—
10	C₂×C₄×#88322	C₄	1	4	yes	complemented
11	#16810493	—	2	2	no	—
12	#16810493	C₄	1	4	yes	complemented
13	#16810385	—	2	8	no	—
14	C₂²×C₄⋊C₄×C₅₃	—	2	2	no	—
15	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
16	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
17	C₅₃×#384	—	2	2	no	—
18	C₅₃×#384	C₄	1	4	yes	complemented
19	C₂³×Dic₅₃	—	2	2	no	—
20	C₂²×#88322	—	2	2	no	—
21	C₂²×#88322	—	2	2	no	—
22	C₂²×#88322	—	2	2	no	—
23	C₂²×#88322	—	2	2	no	—
24	C₂²×#88322	C₂×C₄	1	4	yes	—
25	C₂²×#88322	D₄	1	4	yes	—
26	C₂²×#88322	Q₈	1	4	yes	—
27	C₂×C₄⋊Dic₅₃	—	2	8	no	—
28	C₂×C₄⋊Dic₅₃	—	2	2	no	—
29	C₂×C₄⋊Dic₅₃	—	2	4	no	—
30	C₂×C₄⋊Dic₅₃	—	2	4	no	—
31	C₂×C₄⋊Dic₅₃	—	4	4	no	—
32	C₂×C₄⋊Dic₅₃	—	4	4	no	—
33	C₂×C₄⋊Dic₅₃	C₂×C₄	1	4	yes	—
34	C₄×#88322	—	2	8	no	—
35	C₂³×C₄×C₅₃	—	2	2	no	—
36	C₂³×C₄×C₅₃	D₄	1	2	yes	—
37	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₅₃	—	2	8	no	—
39	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
40	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
41	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
42	C₂×C₄⋊C₄×C₅₃	—	4	4	no	—
43	C₂×C₄⋊C₄×C₅₃	—	4	4	no	—
44	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	4	yes	—
45	C₂×C₄²×C₅₃	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₅₃	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₅₃	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₅₃	D₄	1	2	yes	—
49	C₂×C₄²×C₅₃	D₄	1	2	yes	—
50	C₂×C₄²×C₅₃	Q₈	1	2	yes	—
51	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₅₃	—	2	4	no	—
53	C₂²×C₄×C₅₃	—	4	2	no	—
54	C₂²×C₄×C₅₃	—	4	2	no	—
55	C₂²×C₄×C₅₃	—	4	4	no	—
56	C₂²×C₄×C₅₃	—	4	4	no	—
57	C₂²×C₄×C₅₃	C₂²⋊C₄	1	4	yes	—
58	C₂²×C₄×C₅₃	C₂²⋊C₄	1	4	yes	—
59	C₂²×C₄×C₅₃	C₄⋊C₄	1	4	yes	—
60	C₂²×C₄×C₅₃	D₈	1	4	yes	—
61	C₂²×C₄×C₅₃	SD₁₆	1	4	yes	—
62	C₂²×C₄×C₅₃	SD₁₆	1	4	yes	—
63	C₂²×C₄×C₅₃	Q₁₆	1	4	yes	—
64	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
70	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
71	C₂²×C₄×C₅₃	C₂×Q₈	1	2	yes	—
72	C₂²×C₄×C₅₃	#41	1	2	yes	—
73	C₂²×C₄×C₅₃	#41	1	2	yes	—
74	C₂²×Dic₅₃	—	2	4	no	—
75	C₂²×Dic₅₃	—	4	2	no	—
76	C₂²×Dic₅₃	—	4	2	no	—
77	C₂²×Dic₅₃	—	4	4	no	—
78	C₂²×Dic₅₃	—	4	4	no	—
79	C₄⋊C₄×C₅₃	—	2	8	no	—
80	C₄⋊C₄×C₅₃	—	4	16	no	—
81	C₄⋊C₄×C₅₃	—	4	4	no	—
82	C₄²×C₅₃	C₄²	1	4	yes	—
83	C₄²×C₅₃	C₂²⋊C₄	1	4	yes	—
84	C₄²×C₅₃	C₄⋊C₄	1	4	yes	—
85	C₄²×C₅₃	C₄⋊C₄	1	4	yes	—
86	C₄⋊Dic₅₃	—	2	8	no	—
87	C₄⋊Dic₅₃	—	4	16	no	—
88	C₄⋊Dic₅₃	—	4	4	no	—
89	C₂×#88322	—	2	4	no	—
90	C₂×#88322	—	2	4	no	—
91	C₂×#88322	—	2	4	no	—
92	C₂×#88322	—	2	4	no	—
93	C₂×#88322	—	2	4	no	—
94	C₂×#88322	—	2	4	no	—
95	C₂×#88322	C₄⋊C₄	1	8	yes	complemented
96	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
99	C₂³×C₅₃	#124	1	1	yes	characteristic
100	C₂³×C₅₃	#124	1	1	yes	characteristic
101	C₂³×C₅₃	#127	1	1	yes	characteristic
102	C₂³×C₅₃	C₄⋊Q₈	1	1	yes	characteristic
103	C₂³×C₅₃	C₂×D₈	1	2	yes	—
104	C₂³×C₅₃	C₂×SD₁₆	1	2	yes	—
105	C₂³×C₅₃	C₂×SD₁₆	1	2	yes	—
106	C₂³×C₅₃	C₂×Q₁₆	1	2	yes	—
107	C₂×C₄×C₅₃	—	4	4	no	—
108	C₂×C₄×C₅₃	—	4	8	no	—
109	C₂×C₄×C₅₃	—	8	4	no	—
110	C₂×C₄×C₅₃	—	8	2	no	—
111	C₂×C₄×C₅₃	—	8	2	no	—
112	C₂×C₄×C₅₃	#95	1	8	yes	—
113	C₂×C₄×C₅₃	#102	1	8	yes	—
114	C₂×C₄×C₅₃	#102	1	8	yes	—
115	C₂×C₄×C₅₃	#103	1	8	yes	—
116	C₂×C₄×C₅₃	#103	1	8	yes	—
117	C₂×C₄×C₅₃	#106	1	8	yes	—
118	C₂×C₄×C₅₃	#107	1	8	yes	—
119	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
120	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
122	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₅₃	#117	1	2	yes	—
125	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
126	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
127	C₂×C₄×C₅₃	C₄×Q₈	1	2	yes	—
128	C₂×C₄×C₅₃	C₄×Q₈	1	2	yes	—
129	C₂×C₄×C₅₃	#121	1	2	yes	—
130	C₂×C₄×C₅₃	#121	1	2	yes	—
131	C₂×C₄×C₅₃	C₂²⋊Q₈	1	2	yes	—
132	C₂×C₄×C₅₃	C₂²⋊Q₈	1	2	yes	—
133	C₂×C₄×C₅₃	#125	1	2	yes	—
134	C₂×C₄×C₅₃	C₄⋊Q₈	1	2	yes	—
135	C₂×Dic₅₃	—	4	4	no	—
136	C₂×Dic₅₃	—	4	8	no	—
137	C₂×Dic₅₃	—	8	4	no	—
138	C₂×Dic₅₃	—	8	2	no	—
139	C₂×Dic₅₃	—	8	2	no	—
140	#88322	—	2	8	no	—
141	#10841	—	53	1	no	maximal, Sylow
142	C₂²×C₅₃	C₂×#95	1	1	yes	characteristic
143	C₂²×C₅₃	#382	1	1	yes	characteristic
144	C₂²×C₅₃	#384	1	1	yes	characteristic
145	C₂²×C₅₃	#390	1	1	yes	characteristic
146	C₂²×C₅₃	#390	1	1	yes	characteristic
147	C₂²×C₅₃	#391	1	1	yes	characteristic
148	C₂²×C₅₃	#391	1	1	yes	characteristic
149	C₂²×C₅₃	C₂×#102	1	2	yes	—
150	C₂²×C₅₃	C₂×#102	1	2	yes	—
151	C₂²×C₅₃	C₂×#103	1	2	yes	—
152	C₂²×C₅₃	C₂×#103	1	2	yes	—
153	C₂²×C₅₃	C₂×#106	1	2	yes	—
154	C₂²×C₅₃	C₂×#107	1	2	yes	—
155	C₂²×C₅₃	#486	1	2	yes	—
156	C₂²×C₅₃	#486	1	2	yes	—
157	C₂²×C₅₃	#487	1	2	yes	—
158	C₂²×C₅₃	#487	1	2	yes	—
159	C₂²×C₅₃	#492	1	1	yes	characteristic
160	C₂²×C₅₃	#492	1	1	yes	characteristic
161	C₂²×C₅₃	#493	1	1	yes	characteristic
162	C₂²×C₅₃	#494	1	1	yes	characteristic
163	C₂²×C₅₃	#498	1	2	yes	—
164	C₂²×C₅₃	#500	1	2	yes	—
165	C₄×C₅₃	—	8	4	no	—
166	C₄×C₅₃	#340	1	16	yes	complemented
167	C₄×C₅₃	C₄×C₄⋊C₄	1	2	yes	—
168	C₄×C₅₃	#380	1	2	yes	—
169	C₄×C₅₃	#389	1	2	yes	—
170	C₄×C₅₃	#389	1	2	yes	—
171	Dic₅₃	—	8	4	no	—
172	C₂²×C₄×C₈	—	53	1	no	—
173	C₂×#384	—	53	1	no	—
174	C₂×#384	D₅₃	1	1	yes	characteristic
175	C₂×#340	—	53	4	no	—
176	C₂×C₅₃	C₄⋊#95	1	1	yes	characteristic
177	C₂×C₅₃	C₂×#340	1	2	yes	—
178	C₂×C₅₃	#1834	1	2	yes	—
179	C₂×C₅₃	#1844	1	1	yes	characteristic
180	C₂×C₅₃	#1845	1	1	yes	characteristic
181	C₂×C₅₃	#1956	1	1	yes	characteristic
182	C₂×C₅₃	#1956	1	1	yes	characteristic
183	C₂×C₅₃	#1957	1	1	yes	characteristic
184	C₂×C₅₃	#1957	1	1	yes	characteristic
185	C₂×C₅₃	#1990	1	2	yes	—
186	C₂×C₅₃	#1990	1	2	yes	—
187	C₂³×C₈	—	53	2	no	—
188	C₂²×C₄⋊C₄	—	2	2	no	—
189	C₂²×C₄⋊C₄	—	53	2	no	—
190	C₂²×C₄⋊C₄	—	106	2	no	—
191	C₂²×C₄⋊C₄	C₂×D₅₃	1	2	yes	—
192	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic
193	C₂×C₄×C₈	—	53	4	no	—
194	C₂×C₄×C₈	—	106	2	no	—
195	C₂×C₄×C₈	—	106	2	no	—
196	#384	—	2	2	no	—
197	#384	—	53	4	no	—
198	#384	—	106	2	no	—
199	#384	Dic₅₃	1	4	yes	complemented
200	#340	—	106	8	no	—
201	C₅₃	#10841	1	1	yes	characteristic, complemented, Sylow
202	C₂³×C₄	—	2	2	no	—
203	C₂³×C₄	—	106	2	no	—
204	C₂³×C₄	C₂²⋊D₅₃	1	2	yes	—
205	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
206	C₂²×C₈	—	53	4	no	—
207	C₂²×C₈	—	53	4	no	—
208	C₂²×C₈	—	53	4	no	—
209	C₂²×C₈	—	106	2	no	—
210	C₂²×C₈	—	106	2	no	—
211	C₂²×C₈	—	106	2	no	—
212	C₂²×C₈	—	106	2	no	—
213	C₂×C₄⋊C₄	—	2	4	no	—
214	C₂×C₄⋊C₄	—	2	4	no	—
215	C₂×C₄⋊C₄	—	2	2	no	—
216	C₂×C₄⋊C₄	—	2	8	no	—
217	C₂×C₄⋊C₄	—	4	4	no	—
218	C₂×C₄⋊C₄	—	4	4	no	—
219	C₂×C₄⋊C₄	—	53	4	no	—
220	C₂×C₄⋊C₄	—	106	4	no	—
221	C₂×C₄⋊C₄	—	106	4	no	—
222	C₂×C₄⋊C₄	—	106	2	no	—
223	C₂×C₄⋊C₄	—	106	8	no	—
224	C₂×C₄⋊C₄	—	212	4	no	—
225	C₂×C₄⋊C₄	—	212	4	no	—
226	C₂×C₄⋊C₄	C₂×Dic₅₃	1	4	yes	—
227	C₂×C₄²	Dic₁₀₆	1	2	yes	—
228	C₂×C₄²	C₄×D₅₃	1	2	yes	—
229	C₂×C₄²	C₄×D₅₃	1	2	yes	—
230	C₂×C₄²	D₂₁₂	1	2	yes	—
231	C₂×C₄²	C₂×Dic₅₃	1	2	yes	—
232	C₂×C₄²	C₂²⋊D₅₃	1	2	yes	—
233	C₄×C₈	—	106	8	no	—
234	C₂⁴	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	4	2	no	—
237	C₂²×C₄	—	4	2	no	—
238	C₂²×C₄	—	4	4	no	—
239	C₂²×C₄	—	4	4	no	—
240	C₂²×C₄	—	106	4	no	—
241	C₂²×C₄	—	212	2	no	—
242	C₂²×C₄	—	212	2	no	—
243	C₂²×C₄	—	212	4	no	—
244	C₂²×C₄	—	212	4	no	—
245	C₂²×C₄	#11719919	1	4	yes	—
246	C₂²×C₄	#11719921	1	4	yes	—
247	C₂²×C₄	#11719922	1	4	yes	—
248	C₂²×C₄	#11719923	1	4	yes	—
249	C₂²×C₄	#11719924	1	4	yes	—
250	C₂²×C₄	#11719925	1	4	yes	—
251	C₂²×C₄	C₂²⋊Dic₅₃	1	4	yes	—
252	C₂²×C₄	C₂×Dic₁₀₆	1	1	yes	characteristic
253	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
254	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
255	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
256	C₂²×C₄	D₄×D₅₃	1	2	yes	—
257	C₂²×C₄	#11719947	1	2	yes	—
258	C₂²×C₄	Q₈×D₅₃	1	2	yes	—
259	C₂²×C₄	#11719949	1	2	yes	—
260	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
261	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
262	C₂×C₈	—	53	8	no	—
263	C₂×C₈	—	106	4	no	—
264	C₂×C₈	—	106	4	no	—
265	C₂×C₈	—	106	4	no	—
266	C₂×C₈	—	106	4	no	—
267	C₂×C₈	—	106	4	no	—
268	C₂×C₈	—	106	4	no	—
269	C₄⋊C₄	—	2	8	no	—
270	C₄⋊C₄	—	4	16	no	—
271	C₄⋊C₄	—	4	4	no	—
272	C₄⋊C₄	—	106	8	no	—
273	C₄⋊C₄	—	212	16	no	—
274	C₄⋊C₄	—	212	4	no	—
275	C₄²	C₄×Dic₅₃	1	4	yes	—
276	C₄²	#11719919	1	4	yes	—
277	C₄²	C₄⋊Dic₅₃	1	4	yes	—
278	C₄²	#11719921	1	4	yes	—
279	C₂³	C₂×#11719921	1	1	yes	characteristic
280	C₂³	C₂×C₂²⋊Dic₅₃	1	1	yes	characteristic
281	C₂³	C₂×#11719919	1	1	yes	characteristic
282	C₂³	#13133204	1	1	yes	characteristic
283	C₂³	#13133206	1	1	yes	characteristic
284	C₂³	#13133213	1	1	yes	characteristic
285	C₂³	#13133215	1	1	yes	characteristic
286	C₂³	C₂×#11719922	1	2	yes	—
287	C₂³	C₂×#11719924	1	2	yes	—
288	C₂³	C₂×#11719923	1	2	yes	—
289	C₂³	C₂×#11719925	1	2	yes	—
290	C₂×C₄	—	4	4	no	—
291	C₂×C₄	—	4	8	no	—
292	C₂×C₄	—	8	4	no	—
293	C₂×C₄	—	8	2	no	—
294	C₂×C₄	—	8	2	no	—
295	C₂×C₄	—	424	4	no	—
296	C₂×C₄	—	424	2	no	—
297	C₂×C₄	—	424	2	no	—
298	C₂×C₄	—	212	4	no	—
299	C₂×C₄	—	212	8	no	—
300	C₂×C₄	#13133124	1	8	yes	—
301	C₂×C₄	#13133137	1	8	yes	—
302	C₂×C₄	#13133138	1	8	yes	—
303	C₂×C₄	#13133140	1	8	yes	—
304	C₂×C₄	#13133141	1	8	yes	—
305	C₂×C₄	#13133148	1	8	yes	—
306	C₂×C₄	#13133150	1	8	yes	—
307	C₂×C₄	C₂×C₄×Dic₅₃	1	1	yes	characteristic
308	C₂×C₄	C₂×#11719921	1	1	yes	characteristic
309	C₂×C₄	C₄⋊C₄×D₅₃	1	2	yes	—
310	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
311	C₂×C₄	C₂×C₄⋊Dic₅₃	1	1	yes	characteristic
312	C₂×C₄	#13133175	1	2	yes	—
313	C₂×C₄	#13133179	1	2	yes	—
314	C₂×C₄	D₄×Dic₅₃	1	2	yes	—
315	C₂×C₄	#13133182	1	2	yes	—
316	C₂×C₄	Q₈×Dic₅₃	1	2	yes	—
317	C₂×C₄	#13133188	1	2	yes	—
318	C₂×C₄	#13133192	1	2	yes	—
319	C₂×C₄	#13133193	1	2	yes	—
320	C₂×C₄	#13133197	1	2	yes	—
321	C₂×C₄	#13133208	1	2	yes	—
322	C₂×C₄	#13133216	1	2	yes	—
323	C₈	—	106	8	no	—
324	C₂²	C₂×#13133124	1	1	yes	characteristic
325	C₂²	#16810488	1	1	yes	characteristic
326	C₂²	#16810492	1	1	yes	characteristic
327	C₂²	#16810524	1	1	yes	characteristic
328	C₂²	#16810526	1	1	yes	characteristic
329	C₂²	#16810528	1	1	yes	characteristic
330	C₂²	#16810530	1	1	yes	characteristic
331	C₂²	C₂×#13133137	1	2	yes	—
332	C₂²	C₂×#13133138	1	2	yes	—
333	C₂²	C₂×#13133140	1	2	yes	—
334	C₂²	C₂×#13133141	1	2	yes	—
335	C₂²	C₂×#13133148	1	2	yes	—
336	C₂²	C₂×#13133150	1	2	yes	—
337	C₂²	#16810969	1	2	yes	—
338	C₂²	#16810971	1	2	yes	—
339	C₂²	#16810973	1	2	yes	—
340	C₂²	#16810975	1	2	yes	—
341	C₂²	#16810995	1	1	yes	characteristic
342	C₂²	#16810997	1	1	yes	characteristic
343	C₂²	#16810999	1	1	yes	characteristic
344	C₂²	#16811002	1	1	yes	characteristic
345	C₂²	#16811019	1	2	yes	—
346	C₂²	#16811026	1	2	yes	—
347	C₄	—	8	4	no	—
348	C₄	—	424	4	no	—
349	C₄	#16810385	1	16	yes	complemented
350	C₄	C₄⋊C₄×Dic₅₃	1	2	yes	—
351	C₄	#16810480	1	2	yes	—
352	C₄	#16810519	1	2	yes	—
353	C₄	#16810522	1	2	yes	—
354	C₂	#20272944	1	1	yes	characteristic
355	C₂	C₂×#16810385	1	2	yes	—
356	C₂	#20274842	1	2	yes	—
357	C₂	#20274871	1	1	yes	characteristic
358	C₂	#20274874	1	1	yes	characteristic
359	C₂	#20275516	1	1	yes	characteristic
360	C₂	#20275518	1	1	yes	characteristic
361	C₂	#20275520	1	1	yes	characteristic
362	C₂	#20275522	1	1	yes	characteristic
363	C₂	#20275675	1	2	yes	—
364	C₂	#20275677	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₅₃
commutator	C₂×C₄×C₅₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₅₃
Fitting	C₂×C₅₃×#384	C₂
socle, prime radical	C₂⁴×C₅₃	C₂×D₄
cosocle	C₂³×C₄×C₅₃	C₂³
hypercenter	C₂×#384	D₅₃
hypocenter	C₅₃	#10841
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#384

Complements

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

N	H ≅ G/N	type
10. C₂×C₄×#88322	C₄	semidirect
12. #16810493	C₄	semidirect
18. C₅₃×#384	C₄	semidirect
95. C₂×#88322	C₄⋊C₄	semidirect
166. C₄×C₅₃	#340	semidirect
199. #384	Dic₅₃	semidirect
201. C₅₃	#10841	semidirect
349. C₄	#16810385	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×#88322	2
C₂×#16810493	2
C₂×#16810385	2
C₂×C₅₃×#384	2
#10841	53