Subgroups — #28293108

Order 13568.

7130 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288515	C₂	1	24	yes	maximal, complemented
2	#20288511	C₂	1	24	yes	maximal, complemented
3	#20288117	C₂	1	4	yes	maximal, complemented
4	C₂×#16811249	C₂	1	3	yes	maximal, complemented
5	#543×D₅₃	C₂	1	4	yes	maximal, complemented
6	C₂×#16811096	C₂	1	3	yes	maximal
7	C₂×C₅₃×#543	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
9	#16811331	C₂²	1	48	yes	complemented
10	#16811328	C₂²	1	48	yes	complemented
11	#16811327	C₂²	1	96	yes	complemented
12	Q₈×C₂²⋊D₅₃	C₂²	1	16	yes	complemented
13	#16811286	C₂²	1	48	yes	complemented
14	#16811252	C₂²	1	48	yes	complemented
15	#16811249	C₂²	1	12	yes	—
16	#16811249	C₂²	1	24	yes	complemented
17	#16811249	C₂²	1	12	yes	complemented
18	#16811248	C₂²	1	48	yes	complemented
19	#16811175	C₂²	1	48	yes	complemented
20	C₂×#13133196	C₂²	1	12	yes	complemented
21	C₂×#13133194	C₂²	1	24	yes	complemented
22	C₂²⋊Q₈×D₅₃	C₂²	1	48	yes	complemented
23	#16811096	C₂²	1	24	yes	—
24	#16811096	C₂²	1	24	yes	—
25	C₂×C₄×C₂²⋊D₅₃	C₂²	1	12	yes	—
26	C₂×#13133177	C₂²	1	12	yes	—
27	C₂×#13133173	C₂²	1	6	yes	—
28	C₂²×C₂²⋊Dic₅₃	C₂²	1	3	yes	—
29	C₂×C₂²⋊C₄×D₅₃	C₂²	1	6	yes	—
30	C₅₃×#543	C₂²	1	4	yes	—
31	C₅₃×#543	C₂²	1	12	yes	complemented
32	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	12	yes	complemented
33	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	3	yes	—
34	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
35	C₂²×Dic₁₀₆	C₂³	1	12	yes	complemented
36	C₂×Q₈×D₅₃	C₂³	1	16	yes	complemented
37	C₂²×C₂²⋊D₅₃	Q₈	1	16	yes	complemented
38	C₂²×C₂²⋊D₅₃	C₂³	1	6	yes	—
39	C₂²×C₂²⋊D₅₃	C₂³	1	6	yes	—
40	C₂³×Dic₅₃	C₂³	1	6	yes	—
41	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
42	C₂²×C₄×D₅₃	C₂³	1	12	yes	—
43	#13133216	C₂³	1	48	yes	complemented
44	#13133215	C₂³	1	48	yes	complemented
45	#13133207	C₂³	1	96	yes	complemented
46	#13133197	C₂³	1	48	yes	complemented
47	#13133196	C₂³	1	48	yes	—
48	#13133196	C₂³	1	48	yes	complemented
49	#13133195	C₂³	1	96	yes	complemented
50	#13133194	C₂³	1	96	yes	—
51	#13133194	C₂³	1	96	yes	complemented
52	#13133193	C₂³	1	48	yes	complemented
53	Q₈×Dic₅₃	C₂³	1	16	yes	complemented
54	#13133182	C₂³	1	48	yes	complemented
55	C₄×C₂²⋊D₅₃	C₂³	1	48	yes	—
56	C₄×C₂²⋊D₅₃	C₂³	1	48	yes	—
57	#13133177	C₂³	1	96	yes	—
58	#13133173	C₂³	1	48	yes	—
59	C₂×C₄⋊Dic₅₃	C₂³	1	12	yes	complemented
60	C₂×#11719919	C₂³	1	12	yes	—
61	C₂×#11719919	C₂³	1	24	yes	complemented
62	C₄⋊C₄×D₅₃	C₂³	1	48	yes	complemented
63	C₂×C₂²⋊Dic₅₃	C₂³	1	6	yes	—
64	C₂×C₂²⋊Dic₅₃	C₂³	1	6	yes	—
65	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	—
66	C₂×C₂²⋊Dic₅₃	C₂³	1	12	yes	—
67	C₂×#11719921	C₂³	1	12	yes	—
68	C₂²⋊C₄×D₅₃	C₂³	1	48	yes	—
69	C₂×C₄×Dic₅₃	C₂³	1	12	yes	—
70	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₅₃	C₂³	1	4	yes	complemented
72	C₂³×C₄×C₅₃	C₂³	1	6	yes	—
73	C₂²⋊Q₈×C₅₃	C₂³	1	48	yes	—
74	C₂²⋊Q₈×C₅₃	C₂³	1	48	yes	complemented
75	C₂×C₄⋊C₄×C₅₃	C₂³	1	12	yes	complemented
76	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	—
77	C₂×C₂²⋊C₄×C₅₃	C₂³	1	6	yes	—
78	C₂×C₂²⋊C₄×C₅₃	C₂³	1	6	yes	—
79	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	—
80	C₂⁴×C₅₃	—	8	2	no	—
81	C₂⁴×C₅₃	C₂×Q₈	1	8	yes	complemented
82	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
83	C₂⁴×C₅₃	C₂⁴	1	3	yes	—
84	C₂⁴×C₅₃	C₂⁴	1	3	yes	—
85	C₂³×D₅₃	—	8	2	no	—
86	C₂³×D₅₃	C₂×Q₈	1	8	yes	complemented
87	C₂³×D₅₃	C₂⁴	1	6	yes	—
88	C₂×Q₈×C₅₃	—	8	4	no	—
89	C₂×Q₈×C₅₃	C₂⁴	1	16	yes	—
90	C₂²×C₄×C₅₃	—	8	6	no	—
91	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
92	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
93	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
94	C₂×C₂²⋊D₅₃	C₂×Q₈	1	48	yes	complemented
95	C₂×C₂²⋊D₅₃	C₂×Q₈	1	48	yes	complemented
96	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
97	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
98	C₂²×Dic₅₃	—	8	6	no	—
99	C₂²×Dic₅₃	C₂×Q₈	1	8	yes	complemented
100	C₂²×Dic₅₃	C₂⁴	1	12	yes	—
101	C₂²×Dic₅₃	C₂⁴	1	24	yes	—
102	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
103	Q₈×D₅₃	—	8	16	no	—
104	C₂×C₄×D₅₃	—	8	12	no	—
105	C₂×C₄×D₅₃	C₂⁴	1	48	yes	—
106	C₂×Dic₁₀₆	—	8	12	no	—
107	C₂×Dic₁₀₆	C₂⁴	1	48	yes	—
108	C₄⋊C₄×C₅₃	C₂⁴	1	48	yes	—
109	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
110	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
111	C₂²⋊Dic₅₃	C₂⁴	1	24	yes	—
112	C₂²⋊Dic₅₃	C₂⁴	1	12	yes	—
113	C₂²⋊Dic₅₃	C₂⁴	1	12	yes	—
114	#11719921	C₂⁴	1	48	yes	—
115	C₄⋊Dic₅₃	C₂⁴	1	48	yes	—
116	#11719919	C₂⁴	1	96	yes	—
117	#11719919	C₂⁴	1	48	yes	—
118	C₄×Dic₅₃	C₂⁴	1	48	yes	—
119	C₂³×C₅₃	—	4	6	no	—
120	C₂³×C₅₃	—	4	6	no	—
121	C₂³×C₅₃	—	4	2	no	—
122	C₂³×C₅₃	—	8	8	no	—
123	C₂³×C₅₃	C₂²×Q₈	1	4	yes	—
124	C₂³×C₅₃	C₂²×Q₈	1	12	yes	—
125	C₂³×C₅₃	C₂²×Q₈	1	12	yes	—
126	C₂³×C₅₃	C₂⁵	1	3	yes	—
127	C₂³×C₅₃	C₂⁵	1	3	yes	—
128	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
129	C₂²×D₅₃	—	4	12	no	—
130	C₂²×D₅₃	—	8	8	no	—
131	C₂²×D₅₃	C₂²×Q₈	1	24	yes	—
132	C₂²×D₅₃	C₂⁵	1	4	yes	—
133	Q₈×C₅₃	—	4	16	no	—
134	C₂×C₄×C₅₃	—	4	12	no	—
135	C₂×C₄×C₅₃	—	4	12	no	—
136	C₂×C₄×C₅₃	—	4	12	no	—
137	C₂×C₄×C₅₃	C₂⁵	1	24	yes	—
138	C₂²⋊D₅₃	C₂²×Q₈	1	48	yes	—
139	C₂²⋊D₅₃	C₂²×Q₈	1	16	yes	—
140	C₂×Dic₅₃	—	4	24	no	—
141	C₂×Dic₅₃	—	4	12	no	—
142	C₂×Dic₅₃	C₂²×Q₈	1	24	yes	—
143	C₂×Dic₅₃	C₂⁵	1	24	yes	—
144	C₂×Dic₅₃	C₂⁵	1	4	yes	—
145	C₄×D₅₃	—	4	48	no	—
146	Dic₁₀₆	—	4	48	no	—
147	#62843	—	53	1	no	maximal, Sylow
148	C₂²×C₅₃	—	2	6	no	—
149	C₂²×C₅₃	—	2	6	no	—
150	C₂²×C₅₃	—	2	2	no	—
151	C₂²×C₅₃	—	4	4	no	—
152	C₂²×C₅₃	—	4	12	no	—
153	C₂²×C₅₃	—	4	12	no	—
154	C₂²×C₅₃	C₂³×Q₈	1	6	yes	—
155	C₂²×C₅₃	C₂³×Q₈	1	6	yes	—
156	C₂²×C₅₃	C₂³×Q₈	1	2	yes	—
157	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
158	C₂×D₅₃	—	2	8	no	—
159	C₂×D₅₃	—	4	24	no	—
160	C₂×D₅₃	C₂³×Q₈	1	8	yes	—
161	C₄×C₅₃	—	2	24	no	—
162	Dic₅₃	—	2	24	no	—
163	Dic₅₃	C₂³×Q₈	1	8	yes	—
164	#3501	—	53	24	no	—
165	#3501	—	53	24	no	—
166	#3458	—	53	4	no	—
167	C₂×#543	—	53	4	no	—
168	C₂×#543	—	53	3	no	—
169	C₂×#543	D₅₃	1	1	yes	characteristic, complemented
170	C₂×#518	—	53	3	no	—
171	C₂×C₅₃	—	2	6	no	—
172	C₂×C₅₃	—	2	6	no	—
173	C₂×C₅₃	—	2	2	no	—
174	C₂×C₅₃	C₂⁴×Q₈	1	1	yes	characteristic
175	C₂×C₅₃	H(7,𝔽₂)	1	2	yes	—
176	D₅₃	—	2	8	no	—
177	C₂³×D₄	—	53	1	no	—
178	#554	—	53	96	no	—
179	#554	—	53	48	no	—
180	#554	—	53	48	no	—
181	D₄×Q₈	—	53	16	no	—
182	D₄×Q₈	—	53	48	no	—
183	#544	—	53	48	no	—
184	#543	—	53	48	no	—
185	#543	—	53	12	no	—
186	#543	—	53	24	no	—
187	#543	—	53	12	no	—
188	#543	C₂×D₅₃	1	4	yes	—
189	#543	C₂×D₅₃	1	12	yes	complemented
190	#533	—	53	48	no	—
191	C₂×C₂²⋊Q₈	—	53	12	no	—
192	C₂×C₂²⋊Q₈	—	53	48	no	—
193	C₂×C₂²⋊Q₈	—	53	24	no	—
194	C₂×C₂²⋊Q₈	C₂×D₅₃	1	12	yes	complemented
195	#518	—	53	24	no	—
196	#518	—	53	24	no	—
197	C₂×C₄×D₄	—	53	12	no	—
198	C₂×C₄×D₄	—	53	12	no	—
199	C₂×#117	—	53	6	no	—
200	C₂²×C₂²⋊C₄	—	53	3	no	—
201	C₂²×C₂²⋊C₄	—	53	6	no	—
202	C₂²×C₂²⋊C₄	C₂×D₅₃	1	3	yes	—
203	C₅₃	#62843	1	1	yes	characteristic, complemented, Sylow
204	C₂⁵	—	53	1	no	—
205	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
206	C₂²×Q₈	—	53	16	no	—
207	C₂²×Q₈	—	53	12	no	—
208	C₂²×Q₈	C₂²×D₅₃	1	4	yes	complemented
209	C₂²×D₄	—	53	16	no	—
210	C₂²×D₄	—	53	6	no	—
211	C₂²×D₄	—	53	6	no	—
212	C₂³×C₄	—	53	1	no	—
213	C₂³×C₄	—	53	6	no	—
214	C₂³×C₄	—	53	12	no	—
215	C₂³×C₄	C₂²×D₅₃	1	6	yes	—
216	C₄⋊Q₈	—	53	48	no	—
217	C₄⋊Q₈	—	53	48	no	—
218	#125	—	53	96	no	—
219	C₂²⋊Q₈	—	53	48	no	—
220	C₂²⋊Q₈	—	53	48	no	—
221	C₂²⋊Q₈	—	53	48	no	—
222	C₂²⋊Q₈	—	53	96	no	—
223	C₂²⋊Q₈	—	53	48	no	—
224	C₂²⋊Q₈	—	53	96	no	—
225	C₂²⋊Q₈	—	53	96	no	—
226	C₂²⋊Q₈	C₂²×D₅₃	1	48	yes	—
227	C₂²⋊Q₈	C₂²×D₅₃	1	48	yes	complemented
228	C₄×Q₈	—	53	16	no	—
229	C₄×Q₈	—	53	48	no	—
230	C₄×D₄	—	53	48	no	—
231	C₄×D₄	—	53	48	no	—
232	C₄×D₄	—	53	96	no	—
233	#117	—	53	48	no	—
234	C₂×C₄⋊C₄	—	53	12	no	—
235	C₂×C₄⋊C₄	—	53	24	no	—
236	C₂×C₄⋊C₄	—	53	12	no	—
237	C₂×C₄⋊C₄	—	53	48	no	—
238	C₂×C₄⋊C₄	C₂²×D₅₃	1	12	yes	complemented
239	C₂×C₂²⋊C₄	—	53	6	no	—
240	C₂×C₂²⋊C₄	—	53	6	no	—
241	C₂×C₂²⋊C₄	—	53	12	no	—
242	C₂×C₂²⋊C₄	—	53	12	no	—
243	C₂×C₂²⋊C₄	—	53	12	no	—
244	C₂×C₂²⋊C₄	—	53	48	no	—
245	C₂×C₂²⋊C₄	C₂²×D₅₃	1	6	yes	—
246	C₂×C₂²⋊C₄	C₂²×D₅₃	1	6	yes	—
247	C₂×C₂²⋊C₄	C₂²×D₅₃	1	12	yes	—
248	C₂×C₂²⋊C₄	C₂²×D₅₃	1	12	yes	—
249	C₂×C₄²	—	53	12	no	—
250	C₂⁴	—	8	2	no	—
251	C₂⁴	—	53	8	no	—
252	C₂⁴	—	53	6	no	—
253	C₂⁴	—	424	2	no	—
254	C₂⁴	Q₈×D₅₃	1	8	yes	complemented
255	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
256	C₂⁴	C₂³×D₅₃	1	3	yes	—
257	C₂⁴	C₂³×D₅₃	1	3	yes	—
258	C₂×Q₈	—	8	4	no	—
259	C₂×Q₈	—	53	48	no	—
260	C₂×Q₈	—	424	12	no	—
261	C₂×Q₈	—	424	16	no	—
262	C₂×Q₈	C₂³×D₅₃	1	16	yes	—
263	C₂×D₄	—	53	48	no	—
264	C₂×D₄	—	53	48	no	—
265	C₂×D₄	—	53	4	no	—
266	C₂×D₄	—	53	12	no	—
267	C₂²×C₄	—	8	6	no	—
268	C₂²×C₄	—	53	8	no	—
269	C₂²×C₄	—	53	6	no	—
270	C₂²×C₄	—	53	12	no	—
271	C₂²×C₄	—	53	24	no	—
272	C₂²×C₄	—	53	48	no	—
273	C₂²×C₄	—	424	12	no	—
274	C₂²×C₄	—	424	6	no	—
275	C₂²×C₄	C₂³×D₅₃	1	12	yes	—
276	C₂²×C₄	C₂³×D₅₃	1	12	yes	—
277	C₂²×C₄	C₂³×D₅₃	1	12	yes	—
278	C₄⋊C₄	—	53	96	no	—
279	C₄⋊C₄	—	53	48	no	—
280	C₄⋊C₄	—	53	48	no	—
281	C₄⋊C₄	C₂³×D₅₃	1	48	yes	—
282	C₂²⋊C₄	—	53	24	no	—
283	C₂²⋊C₄	—	53	12	no	—
284	C₂²⋊C₄	—	53	12	no	—
285	C₂²⋊C₄	—	53	48	no	—
286	C₂²⋊C₄	C₂³×D₅₃	1	24	yes	—
287	C₂²⋊C₄	C₂³×D₅₃	1	24	yes	—
288	C₄²	—	53	48	no	—
289	C₂³	—	4	6	no	—
290	C₂³	—	4	6	no	—
291	C₂³	—	4	2	no	—
292	C₂³	—	8	8	no	—
293	C₂³	—	53	4	no	—
294	C₂³	—	53	24	no	—
295	C₂³	—	424	8	no	—
296	C₂³	—	212	12	no	—
297	C₂³	C₂×Q₈×D₅₃	1	4	yes	—
298	C₂³	C₂×Q₈×D₅₃	1	12	yes	—
299	C₂³	C₂×Q₈×D₅₃	1	12	yes	—
300	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
301	C₂³	C₂⁴×D₅₃	1	3	yes	—
302	C₂³	C₂⁴×D₅₃	1	3	yes	—
303	Q₈	—	4	16	no	—
304	Q₈	—	212	48	no	—
305	D₄	—	53	16	no	—
306	D₄	—	53	48	no	—
307	C₂×C₄	—	4	12	no	—
308	C₂×C₄	—	4	12	no	—
309	C₂×C₄	—	4	12	no	—
310	C₂×C₄	—	53	24	no	—
311	C₂×C₄	—	53	4	no	—
312	C₂×C₄	—	53	24	no	—
313	C₂×C₄	—	212	48	no	—
314	C₂×C₄	—	212	12	no	—
315	C₂×C₄	—	212	24	no	—
316	C₂×C₄	C₂⁴×D₅₃	1	24	yes	—
317	C₂²	—	2	2	no	—
318	C₂²	—	2	6	no	—
319	C₂²	—	2	6	no	—
320	C₂²	—	4	4	no	—
321	C₂²	—	4	12	no	—
322	C₂²	—	4	12	no	—
323	C₂²	—	53	8	no	—
324	C₂²	—	106	8	no	—
325	C₂²	—	212	24	no	—
326	C₂²	C₂²×Q₈×D₅₃	1	6	yes	—
327	C₂²	C₂²×Q₈×D₅₃	1	2	yes	—
328	C₂²	C₂²×Q₈×D₅₃	1	6	yes	—
329	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
330	C₄	—	2	24	no	—
331	C₄	—	53	8	no	—
332	C₄	—	106	24	no	—
333	C₂	—	2	6	no	—
334	C₂	—	2	2	no	—
335	C₂	—	2	6	no	—
336	C₂	—	106	8	no	—
337	C₂	C₂³×Q₈×D₅₃	1	1	yes	characteristic
338	C₂	#20289525	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₂×C₅₃×#543	C₂
prime radical	C₂³×C₂²⋊D₅₃	C₂²
hypercenter	C₂×#543	D₅₃
hypocenter	C₅₃	#62843
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×#543

Complements

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

N	H ≅ G/N	type
1. #20288515	C₂	semidirect
2. #20288511	C₂	semidirect
3. #20288117	C₂	semidirect
4. C₂×#16811249	C₂	semidirect
5. #543×D₅₃	C₂	semidirect
7. C₂×C₅₃×#543	C₂	semidirect
9. #16811331	C₂²	semidirect
10. #16811328	C₂²	semidirect
11. #16811327	C₂²	semidirect
12. Q₈×C₂²⋊D₅₃	C₂²	semidirect
13. #16811286	C₂²	semidirect
14. #16811252	C₂²	semidirect
16. #16811249	C₂²	semidirect
17. #16811249	C₂²	semidirect
18. #16811248	C₂²	semidirect
19. #16811175	C₂²	semidirect
20. C₂×#13133196	C₂²	semidirect
21. C₂×#13133194	C₂²	semidirect
22. C₂²⋊Q₈×D₅₃	C₂²	semidirect
31. C₅₃×#543	C₂²	semidirect
32. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
35. C₂²×Dic₁₀₆	C₂³	semidirect
36. C₂×Q₈×D₅₃	C₂³	semidirect
37. C₂²×C₂²⋊D₅₃	Q₈	semidirect
43. #13133216	C₂³	semidirect
44. #13133215	C₂³	semidirect
45. #13133207	C₂³	semidirect
46. #13133197	C₂³	semidirect
48. #13133196	C₂³	semidirect
49. #13133195	C₂³	semidirect
51. #13133194	C₂³	semidirect
52. #13133193	C₂³	semidirect
53. Q₈×Dic₅₃	C₂³	semidirect
54. #13133182	C₂³	semidirect
59. C₂×C₄⋊Dic₅₃	C₂³	semidirect
61. C₂×#11719919	C₂³	semidirect
62. C₄⋊C₄×D₅₃	C₂³	semidirect
71. C₂²×Q₈×C₅₃	C₂³	semidirect
74. C₂²⋊Q₈×C₅₃	C₂³	semidirect
75. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
81. C₂⁴×C₅₃	C₂×Q₈	semidirect
86. C₂³×D₅₃	C₂×Q₈	semidirect
94. C₂×C₂²⋊D₅₃	C₂×Q₈	semidirect
95. C₂×C₂²⋊D₅₃	C₂×Q₈	semidirect
99. C₂²×Dic₅₃	C₂×Q₈	semidirect
169. C₂×#543	D₅₃	semidirect
189. #543	C₂×D₅₃	semidirect
194. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
203. C₅₃	#62843	semidirect
208. C₂²×Q₈	C₂²×D₅₃	semidirect
227. C₂²⋊Q₈	C₂²×D₅₃	semidirect
238. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
254. C₂⁴	Q₈×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20288515	2
#20288511	2
#20288117	2
C₂×#16811249	2
#543×D₅₃	2
C₂×#16811096	2
C₂×C₅₃×#543	2
#62843	53