Subgroups — #28293117

Order 13568.

7474 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288556	C₂	1	24	yes	maximal, complemented
2	#20288414	C₂	1	12	yes	maximal, complemented
3	#20288405	C₂	1	12	yes	maximal, complemented
4	#20288127	C₂	1	8	yes	maximal, complemented
5	C₂×#16811185	C₂	1	3	yes	maximal, complemented
6	C₂×#16811096	C₂	1	3	yes	maximal, complemented
7	C₂×C₅₃×#543	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₂²⋊D₅₃	C₂²	1	3	yes	—
9	#16811321	C₂²	1	48	yes	complemented
10	#16811315	C₂²	1	48	yes	complemented
11	#16811300	C₂²	1	96	yes	complemented
12	#16811284	C₂²	1	16	yes	complemented
13	#16811264	C₂²	1	48	yes	complemented
14	#16811222	C₂²	1	48	yes	complemented
15	#16811213	C₂²	1	48	yes	complemented
16	#16811185	C₂²	1	12	yes	—
17	#16811185	C₂²	1	24	yes	complemented
18	#16811185	C₂²	1	12	yes	complemented
19	#16811159	C₂²	1	48	yes	complemented
20	#16811136	C₂²	1	48	yes	complemented
21	C₂×#13133201	C₂²	1	12	yes	complemented
22	C₂×#13133191	C₂²	1	12	yes	complemented
23	C₂×#13133187	C₂²	1	12	yes	complemented
24	#16811096	C₂²	1	24	yes	complemented
25	#16811096	C₂²	1	24	yes	complemented
26	C₂×C₄×C₂²⋊D₅₃	C₂²	1	12	yes	complemented
27	C₂×#13133177	C₂²	1	12	yes	complemented
28	C₂×#13133173	C₂²	1	6	yes	complemented
29	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×D₅₃	C₂²	1	6	yes	complemented
31	C₅₃×#543	C₂²	1	4	yes	complemented
32	C₅₃×#543	C₂²	1	12	yes	complemented
33	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	12	yes	complemented
34	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	3	yes	—
35	C₂⁴×D₅₃	C₂³	1	3	yes	—
36	C₂×#11719949	C₂³	1	16	yes	complemented
37	C₂²×D₂₁₂	C₂³	1	12	yes	complemented
38	C₂²×C₂²⋊D₅₃	—	2	24	no	—
39	C₂²×C₂²⋊D₅₃	C₂³	1	6	yes	—
40	C₂²×C₂²⋊D₅₃	C₂³	1	6	yes	—
41	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
42	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	—
43	C₂³×Dic₅₃	C₂³	1	3	yes	—
44	C₂³×Dic₅₃	C₂³	1	2	yes	—
45	C₂²×C₄×D₅₃	C₂³	1	12	yes	complemented
46	#13133212	C₂³	1	96	yes	complemented
47	#13133208	C₂³	1	48	yes	complemented
48	#13133206	C₂³	1	48	yes	complemented
49	#13133202	C₂³	1	96	yes	complemented
50	#13133201	C₂³	1	48	yes	—
51	#13133201	C₂³	1	48	yes	complemented
52	#13133193	C₂³	1	48	yes	complemented
53	#13133192	C₂³	1	48	yes	complemented
54	#13133191	C₂³	1	48	yes	—
55	#13133191	C₂³	1	48	yes	complemented
56	#13133187	C₂³	1	48	yes	—
57	#13133187	C₂³	1	48	yes	complemented
58	Q₈×Dic₅₃	C₂³	1	16	yes	complemented
59	#13133179	C₂³	1	48	yes	complemented
60	C₄×C₂²⋊D₅₃	C₂³	1	48	yes	—
61	C₄×C₂²⋊D₅₃	C₂³	1	48	yes	complemented
62	#13133177	C₂³	1	96	yes	complemented
63	#13133175	C₂³	1	48	yes	complemented
64	#13133173	C₂³	1	48	yes	complemented
65	C₂×C₄⋊Dic₅₃	C₂³	1	12	yes	complemented
66	C₂×#11719919	C₂³	1	12	yes	complemented
67	C₂×C₂²⋊Dic₅₃	C₂³	1	6	yes	—
68	C₂×C₂²⋊Dic₅₃	C₂³	1	6	yes	—
69	C₂×#11719921	C₂³	1	24	yes	complemented
70	C₂×#11719921	C₂³	1	12	yes	complemented
71	C₂²⋊C₄×D₅₃	C₂³	1	48	yes	complemented
72	C₂×C₄×Dic₅₃	C₂³	1	12	yes	complemented
73	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
74	C₂²×Q₈×C₅₃	C₂³	1	4	yes	complemented
75	C₂³×C₄×C₅₃	C₂³	1	6	yes	—
76	C₂²⋊Q₈×C₅₃	C₂³	1	48	yes	complemented
77	C₂²⋊Q₈×C₅₃	C₂³	1	48	yes	complemented
78	C₂×C₄⋊C₄×C₅₃	C₂³	1	12	yes	complemented
79	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	—
80	C₂×C₂²⋊C₄×C₅₃	C₂³	1	6	yes	—
81	C₂×C₂²⋊C₄×C₅₃	C₂³	1	6	yes	—
82	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	—
83	C₂⁴×C₅₃	—	8	2	no	—
84	C₂⁴×C₅₃	#41	1	8	yes	complemented
85	C₂⁴×C₅₃	C₂⁴	1	3	yes	—
86	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
87	C₂⁴×C₅₃	C₂⁴	1	3	yes	—
88	C₂³×D₅₃	—	2	12	no	—
89	C₂³×D₅₃	—	8	6	no	—
90	C₂³×D₅₃	C₂⁴	1	12	yes	—
91	C₂³×D₅₃	C₂⁴	1	6	yes	—
92	C₂×Q₈×C₅₃	—	8	4	no	—
93	C₂×Q₈×C₅₃	C₂⁴	1	16	yes	—
94	C₂²×C₄×C₅₃	—	8	6	no	—
95	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
96	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
97	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
98	C₂×C₂²⋊D₅₃	—	2	24	no	—
99	C₂×C₂²⋊D₅₃	—	2	24	no	—
100	C₂×C₂²⋊D₅₃	—	2	48	no	—
101	C₂×C₂²⋊D₅₃	—	2	48	no	—
102	C₂×C₂²⋊D₅₃	C₂⁴	1	24	yes	—
103	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
104	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
105	C₂²×Dic₅₃	—	2	12	no	—
106	C₂²×Dic₅₃	—	8	2	no	—
107	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
108	C₂²×Dic₅₃	C₂⁴	1	12	yes	—
109	C₂²×Dic₅₃	C₂⁴	1	12	yes	—
110	#11719949	—	8	16	no	—
111	C₂×D₂₁₂	—	8	12	no	—
112	C₂×D₂₁₂	C₂⁴	1	48	yes	—
113	C₂×C₄×D₅₃	—	8	12	no	—
114	C₂×C₄×D₅₃	C₂⁴	1	48	yes	—
115	C₄⋊C₄×C₅₃	C₂⁴	1	48	yes	—
116	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
117	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
118	C₂²⋊Dic₅₃	C₂⁴	1	12	yes	—
119	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
120	#11719921	C₂⁴	1	48	yes	—
121	#11719921	C₂⁴	1	96	yes	—
122	C₄⋊Dic₅₃	C₂⁴	1	48	yes	—
123	#11719919	C₂⁴	1	48	yes	—
124	C₄×Dic₅₃	C₂⁴	1	48	yes	—
125	C₂³×C₅₃	—	4	2	no	—
126	C₂³×C₅₃	—	4	6	no	—
127	C₂³×C₅₃	—	4	6	no	—
128	C₂³×C₅₃	—	8	8	no	—
129	C₂³×C₅₃	C₂×#41	1	12	yes	—
130	C₂³×C₅₃	C₂×#41	1	12	yes	—
131	C₂³×C₅₃	C₂×#41	1	4	yes	—
132	C₂³×C₅₃	C₂⁵	1	3	yes	—
133	C₂³×C₅₃	C₂⁵	1	3	yes	—
134	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
135	C₂²×D₅₃	—	2	12	no	—
136	C₂²×D₅₃	—	2	24	no	—
137	C₂²×D₅₃	—	4	12	no	—
138	C₂²×D₅₃	—	4	24	no	—
139	C₂²×D₅₃	—	8	24	no	—
140	C₂²×D₅₃	C₂⁵	1	12	yes	—
141	Q₈×C₅₃	—	4	16	no	—
142	C₂×C₄×C₅₃	—	4	12	no	—
143	C₂×C₄×C₅₃	—	4	12	no	—
144	C₂×C₄×C₅₃	—	4	12	no	—
145	C₂×C₄×C₅₃	C₂⁵	1	24	yes	—
146	C₂²⋊D₅₃	—	2	24	no	—
147	C₂²⋊D₅₃	—	2	48	no	—
148	C₂²⋊D₅₃	—	2	24	no	—
149	C₂×Dic₅₃	—	2	24	no	—
150	C₂×Dic₅₃	—	2	12	no	—
151	C₂×Dic₅₃	—	4	12	no	—
152	C₂×Dic₅₃	C₂⁵	1	8	yes	—
153	C₂×Dic₅₃	C₂⁵	1	12	yes	—
154	D₂₁₂	—	4	48	no	—
155	C₄×D₅₃	—	4	48	no	—
156	#62844	—	53	1	no	maximal, Sylow
157	C₂²×C₅₃	—	2	6	no	—
158	C₂²×C₅₃	—	2	2	no	—
159	C₂²×C₅₃	—	2	6	no	—
160	C₂²×C₅₃	—	4	12	no	—
161	C₂²×C₅₃	—	4	4	no	—
162	C₂²×C₅₃	—	4	12	no	—
163	C₂²×C₅₃	C₂²×#41	1	6	yes	—
164	C₂²×C₅₃	C₂²×#41	1	6	yes	—
165	C₂²×C₅₃	C₂²×#41	1	2	yes	—
166	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
167	C₂×D₅₃	—	2	12	no	—
168	C₂×D₅₃	—	2	24	no	—
169	C₂×D₅₃	—	4	24	no	—
170	C₂×D₅₃	—	8	24	no	—
171	C₄×C₅₃	—	2	24	no	—
172	Dic₅₃	—	2	12	no	—
173	Dic₅₃	—	2	8	no	—
174	#3505	—	53	24	no	—
175	#3491	—	53	12	no	—
176	#3490	—	53	12	no	—
177	#3459	—	53	8	no	—
178	C₂×#543	D₅₃	1	1	yes	characteristic, complemented
179	C₂×#534	—	53	3	no	—
180	C₂×#518	—	53	3	no	—
181	C₂×C₅₃	—	2	6	no	—
182	C₂×C₅₃	—	2	6	no	—
183	C₂×C₅₃	—	2	2	no	—
184	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
185	C₂×C₅₃	H(7,𝔽₂)	1	2	yes	—
186	D₅₃	—	4	12	no	—
187	C₂³×D₄	—	53	3	no	—
188	#553	—	53	48	no	—
189	#552	—	53	48	no	—
190	#551	—	53	96	no	—
191	#548	—	53	16	no	—
192	#546	—	53	48	no	—
193	#543	C₂×D₅₃	1	4	yes	complemented
194	#543	C₂×D₅₃	1	12	yes	complemented
195	#539	—	53	48	no	—
196	#538	—	53	48	no	—
197	#534	—	53	12	no	—
198	#534	—	53	12	no	—
199	#534	—	53	24	no	—
200	#529	—	53	48	no	—
201	#525	—	53	48	no	—
202	C₂×#123	—	53	12	no	—
203	C₂×C₂²⋊Q₈	C₂×D₅₃	1	12	yes	complemented
204	C₂×#121	—	53	12	no	—
205	C₂×#120	—	53	12	no	—
206	#518	—	53	24	no	—
207	#518	—	53	24	no	—
208	C₂×C₄×D₄	—	53	12	no	—
209	C₂×C₄×D₄	—	53	12	no	—
210	C₂×#117	—	53	6	no	—
211	C₂²×C₂²⋊C₄	—	53	1	no	—
212	C₂²×C₂²⋊C₄	—	53	6	no	—
213	C₂²×C₂²⋊C₄	C₂×D₅₃	1	3	yes	—
214	C₅₃	#62844	1	1	yes	characteristic, complemented, Sylow
215	C₂⁵	—	53	3	no	—
216	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
217	C₂×#41	—	53	16	no	—
218	C₂²×Q₈	C₂²×D₅₃	1	4	yes	complemented
219	C₂²×D₄	—	53	6	no	—
220	C₂²×D₄	—	53	6	no	—
221	C₂²×D₄	—	53	12	no	—
222	C₂²×D₄	—	53	12	no	—
223	C₂²×D₄	—	53	12	no	—
224	C₂²×D₄	—	106	24	no	—
225	C₂³×C₄	—	53	3	no	—
226	C₂³×C₄	—	53	2	no	—
227	C₂³×C₄	—	53	12	no	—
228	C₂³×C₄	C₂²×D₅₃	1	6	yes	—
229	#126	—	53	96	no	—
230	#125	—	53	48	no	—
231	#124	—	53	48	no	—
232	#123	—	53	96	no	—
233	#123	—	53	48	no	—
234	#123	—	53	48	no	—
235	C₂²⋊Q₈	—	53	48	no	—
236	C₂²⋊Q₈	C₂²×D₅₃	1	48	yes	complemented
237	C₂²⋊Q₈	C₂²×D₅₃	1	48	yes	complemented
238	#121	—	53	48	no	—
239	#121	—	53	48	no	—
240	#121	—	53	48	no	—
241	#120	—	53	48	no	—
242	#120	—	53	48	no	—
243	C₄×Q₈	—	53	16	no	—
244	C₄×D₄	—	53	48	no	—
245	C₄×D₄	—	53	48	no	—
246	C₄×D₄	—	53	48	no	—
247	C₄×D₄	—	53	96	no	—
248	#117	—	53	48	no	—
249	#117	—	53	48	no	—
250	C₂×C₄⋊C₄	—	53	12	no	—
251	C₂×C₄⋊C₄	—	53	12	no	—
252	C₂×C₄⋊C₄	C₂²×D₅₃	1	12	yes	complemented
253	C₂×C₂²⋊C₄	—	53	6	no	—
254	C₂×C₂²⋊C₄	—	53	6	no	—
255	C₂×C₂²⋊C₄	—	53	12	no	—
256	C₂×C₂²⋊C₄	—	53	24	no	—
257	C₂×C₂²⋊C₄	—	53	48	no	—
258	C₂×C₂²⋊C₄	C₂²×D₅₃	1	6	yes	—
259	C₂×C₂²⋊C₄	C₂²×D₅₃	1	6	yes	—
260	C₂×C₂²⋊C₄	C₂²×D₅₃	1	12	yes	—
261	C₂×C₂²⋊C₄	C₂²×D₅₃	1	12	yes	—
262	C₂×C₄²	—	53	12	no	—
263	C₂⁴	—	8	2	no	—
264	C₂⁴	—	53	12	no	—
265	C₂⁴	—	53	6	no	—
266	C₂⁴	—	106	12	no	—
267	C₂⁴	—	424	6	no	—
268	C₂⁴	#11719949	1	8	yes	complemented
269	C₂⁴	C₂³×D₅₃	1	3	yes	—
270	C₂⁴	C₂³×D₅₃	1	3	yes	—
271	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
272	#41	—	424	16	no	—
273	C₂×Q₈	—	8	4	no	—
274	C₂×Q₈	C₂³×D₅₃	1	16	yes	—
275	C₂×D₄	—	53	12	no	—
276	C₂×D₄	—	53	24	no	—
277	C₂×D₄	—	53	12	no	—
278	C₂×D₄	—	53	48	no	—
279	C₂×D₄	—	106	48	no	—
280	C₂×D₄	—	106	48	no	—
281	C₂×D₄	—	106	24	no	—
282	C₂×D₄	—	106	24	no	—
283	C₂×D₄	—	424	12	no	—
284	C₂²×C₄	—	8	6	no	—
285	C₂²×C₄	—	53	6	no	—
286	C₂²×C₄	—	53	12	no	—
287	C₂²×C₄	—	53	12	no	—
288	C₂²×C₄	—	53	48	no	—
289	C₂²×C₄	—	106	12	no	—
290	C₂²×C₄	—	424	12	no	—
291	C₂²×C₄	—	424	2	no	—
292	C₂²×C₄	C₂³×D₅₃	1	12	yes	—
293	C₂²×C₄	C₂³×D₅₃	1	12	yes	—
294	C₂²×C₄	C₂³×D₅₃	1	12	yes	—
295	C₄⋊C₄	—	53	48	no	—
296	C₄⋊C₄	—	53	48	no	—
297	C₄⋊C₄	C₂³×D₅₃	1	48	yes	—
298	C₂²⋊C₄	—	53	12	no	—
299	C₂²⋊C₄	—	53	4	no	—
300	C₂²⋊C₄	—	53	48	no	—
301	C₂²⋊C₄	—	53	96	no	—
302	C₂²⋊C₄	C₂³×D₅₃	1	24	yes	—
303	C₂²⋊C₄	C₂³×D₅₃	1	24	yes	—
304	C₄²	—	53	48	no	—
305	C₂³	—	4	6	no	—
306	C₂³	—	4	2	no	—
307	C₂³	—	4	6	no	—
308	C₂³	—	8	8	no	—
309	C₂³	—	53	12	no	—
310	C₂³	—	106	24	no	—
311	C₂³	—	106	12	no	—
312	C₂³	—	424	24	no	—
313	C₂³	—	212	24	no	—
314	C₂³	—	212	12	no	—
315	C₂³	C₂×#11719949	1	12	yes	—
316	C₂³	C₂×#11719949	1	12	yes	—
317	C₂³	C₂×#11719949	1	4	yes	—
318	C₂³	C₂⁴×D₅₃	1	3	yes	—
319	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
320	C₂³	C₂⁴×D₅₃	1	3	yes	—
321	Q₈	—	4	16	no	—
322	D₄	—	106	24	no	—
323	D₄	—	106	48	no	—
324	D₄	—	106	24	no	—
325	D₄	—	212	48	no	—
326	C₂×C₄	—	4	12	no	—
327	C₂×C₄	—	4	12	no	—
328	C₂×C₄	—	4	12	no	—
329	C₂×C₄	—	53	8	no	—
330	C₂×C₄	—	53	12	no	—
331	C₂×C₄	—	106	24	no	—
332	C₂×C₄	—	106	12	no	—
333	C₂×C₄	—	212	48	no	—
334	C₂×C₄	—	212	12	no	—
335	C₂×C₄	C₂⁴×D₅₃	1	24	yes	—
336	C₂²	—	2	2	no	—
337	C₂²	—	2	6	no	—
338	C₂²	—	2	6	no	—
339	C₂²	—	4	12	no	—
340	C₂²	—	4	12	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	106	12	no	—
343	C₂²	—	106	24	no	—
344	C₂²	—	424	24	no	—
345	C₂²	—	212	24	no	—
346	C₂²	C₂²×#11719949	1	6	yes	—
347	C₂²	C₂²×#11719949	1	6	yes	—
348	C₂²	C₂²×#11719949	1	2	yes	—
349	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
350	C₄	—	2	24	no	—
351	C₄	—	106	12	no	—
352	C₄	—	106	8	no	—
353	C₂	—	2	6	no	—
354	C₂	—	2	6	no	—
355	C₂	—	2	2	no	—
356	C₂	—	212	12	no	—
357	C₂	C₂³×#11719949	1	1	yes	characteristic
358	C₂	#20289525	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₂×C₅₃×#543	C₂
hypercenter	C₂×#543	D₅₃
hypocenter	C₅₃	#62844
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. #20288556	C₂	semidirect
2. #20288414	C₂	semidirect
3. #20288405	C₂	semidirect
4. #20288127	C₂	semidirect
5. C₂×#16811185	C₂	semidirect
6. C₂×#16811096	C₂	semidirect
7. C₂×C₅₃×#543	C₂	semidirect
9. #16811321	C₂²	semidirect
10. #16811315	C₂²	semidirect
11. #16811300	C₂²	semidirect
12. #16811284	C₂²	semidirect
13. #16811264	C₂²	semidirect
14. #16811222	C₂²	semidirect
15. #16811213	C₂²	semidirect
17. #16811185	C₂²	semidirect
18. #16811185	C₂²	semidirect
19. #16811159	C₂²	semidirect
20. #16811136	C₂²	semidirect
21. C₂×#13133201	C₂²	semidirect
22. C₂×#13133191	C₂²	semidirect
23. C₂×#13133187	C₂²	semidirect
24. #16811096	C₂²	semidirect
25. #16811096	C₂²	semidirect
26. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
27. C₂×#13133177	C₂²	semidirect
28. C₂×#13133173	C₂²	semidirect
30. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
31. C₅₃×#543	C₂²	semidirect
32. C₅₃×#543	C₂²	semidirect
33. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
36. C₂×#11719949	C₂³	semidirect
37. C₂²×D₂₁₂	C₂³	semidirect
45. C₂²×C₄×D₅₃	C₂³	semidirect
46. #13133212	C₂³	semidirect
47. #13133208	C₂³	semidirect
48. #13133206	C₂³	semidirect
49. #13133202	C₂³	semidirect
51. #13133201	C₂³	semidirect
52. #13133193	C₂³	semidirect
53. #13133192	C₂³	semidirect
55. #13133191	C₂³	semidirect
57. #13133187	C₂³	semidirect
58. Q₈×Dic₅₃	C₂³	semidirect
59. #13133179	C₂³	semidirect
61. C₄×C₂²⋊D₅₃	C₂³	semidirect
62. #13133177	C₂³	semidirect
63. #13133175	C₂³	semidirect
64. #13133173	C₂³	semidirect
65. C₂×C₄⋊Dic₅₃	C₂³	semidirect
66. C₂×#11719919	C₂³	semidirect
69. C₂×#11719921	C₂³	semidirect
70. C₂×#11719921	C₂³	semidirect
71. C₂²⋊C₄×D₅₃	C₂³	semidirect
72. C₂×C₄×Dic₅₃	C₂³	semidirect
74. C₂²×Q₈×C₅₃	C₂³	semidirect
76. C₂²⋊Q₈×C₅₃	C₂³	semidirect
77. C₂²⋊Q₈×C₅₃	C₂³	semidirect
78. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
84. C₂⁴×C₅₃	#41	semidirect
178. C₂×#543	D₅₃	semidirect
193. #543	C₂×D₅₃	semidirect
194. #543	C₂×D₅₃	semidirect
203. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
214. C₅₃	#62844	semidirect
218. C₂²×Q₈	C₂²×D₅₃	semidirect
236. C₂²⋊Q₈	C₂²×D₅₃	semidirect
237. C₂²⋊Q₈	C₂²×D₅₃	semidirect
252. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
268. C₂⁴	#11719949	semidirect

Maximal subgroups

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

subgroup	index
#20288556	2
#20288414	2
#20288405	2
#20288127	2
C₂×#16811185	2
C₂×#16811096	2
C₂×C₅₃×#543	2
#62844	53