Subgroups — #27382659

Order 13568.

1006 conjugacy classes of subgroups.

The subgroup lattice has 404 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×#16810741	C₂	1	1	yes	maximal, characteristic
3	#20283517	C₂	1	1	yes	maximal, characteristic
4	C₄×#13133223	C₂	1	2	yes	maximal, complemented
5	#20274621	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274599	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274594	C₂	1	1	yes	maximal, characteristic, complemented
8	#20274559	C₂	1	2	yes	maximal, complemented
9	#20274552	C₂	1	2	yes	maximal, complemented
10	#20274526	C₂	1	2	yes	maximal, complemented
11	C₅₃×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133239	C₂²	1	1	yes	characteristic
13	C₂×#13133223	C₂²	1	2	yes	—
14	C₂×#13133223	C₂²	1	2	yes	—
15	C₄×#11719945	C₂²	1	2	yes	—
16	#16810746	C₄	1	8	yes	complemented
17	#16810741	C₄	1	8	yes	complemented
18	#16810736	C₄	1	2	yes	complemented
19	#16810731	C₄	1	2	yes	complemented
20	#16810725	C₄	1	4	yes	complemented
21	C₂×#13133153	C₂²	1	1	yes	characteristic
22	C₂×#13133153	C₂²	1	1	yes	characteristic
23	#16810661	C₂²	1	1	yes	characteristic
24	C₂×#13133145	C₂²	1	2	yes	—
25	C₂×#13133145	C₂²	1	2	yes	—
26	#16810620	C₂²	1	2	yes	—
27	#16810578	C₂²	1	2	yes	—
28	#16810578	C₂²	1	2	yes	—
29	#16810577	—	2	2	no	—
30	#16810577	—	2	2	no	—
31	C₄×#11719917	C₂²	1	2	yes	—
32	C₄×#11719912	—	2	2	no	—
33	C₄×C₈×D₅₃	—	2	2	no	—
34	#16810388	C₂²	1	2	yes	—
35	#16810383	C₂²	1	2	yes	—
36	#16810383	C₂²	1	2	yes	—
37	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×#376	C₂²	1	1	yes	characteristic
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	#13133223	—	2	4	no	—
51	#13133223	—	2	4	no	—
52	#13133223	C₂×C₄	1	8	yes	complemented
53	#13133223	C₂×C₄	1	8	yes	complemented
54	C₂×#11719917	C₂³	1	2	yes	—
55	C₂×#11719917	C₂³	1	2	yes	—
56	C₂×#11719912	—	2	2	no	—
57	C₂×#11719912	—	2	2	no	—
58	C₂×C₈×D₅₃	—	2	2	no	—
59	C₂×C₈×D₅₃	—	2	2	no	—
60	C₄×Dic₁₀₆	C₂×C₄	1	4	yes	—
61	C₄×D₂₁₂	C₂×C₄	1	4	yes	—
62	C₄×C₂²⋊D₅₃	—	2	4	no	—
63	#13133176	C₂³	1	2	yes	—
64	#13133174	—	2	2	no	—
65	C₄²×D₅₃	—	2	2	no	—
66	#13133153	C₂×C₄	1	4	yes	complemented
67	#13133153	C₂×C₄	1	4	yes	complemented
68	#13133151	C₂×C₄	1	2	yes	—
69	#13133149	C₂×C₄	1	2	yes	—
70	#13133145	C₂×C₄	1	8	yes	complemented
71	#13133145	C₂×C₄	1	8	yes	complemented
72	#13133142	C₂×C₄	1	4	yes	—
73	#13133139	C₂×C₄	1	4	yes	—
74	#13133128	—	2	2	no	—
75	#13133127	—	2	2	no	—
76	#13133127	—	2	2	no	—
77	C₄×#88322	—	2	2	no	—
78	C₈×Dic₅₃	—	2	2	no	—
79	C₈×Dic₅₃	—	2	2	no	—
80	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
87	#97×C₅₃	—	2	2	no	—
88	#97×C₅₃	C₂×C₄	1	2	yes	—
89	#97×C₅₃	C₂×C₄	1	2	yes	—
90	#97×C₅₃	C₂×C₄	1	4	yes	complemented
91	C₄×C₈×C₅₃	—	2	2	no	—
92	C₄×C₈×C₅₃	C₂×C₄	1	4	yes	complemented
93	C₄×C₈×C₅₃	D₄	1	2	yes	—
94	C₄×C₈×C₅₃	D₄	1	2	yes	—
95	#95×C₅₃	—	2	2	no	—
96	C₂²×C₄×C₅₃	—	2	1	no	—
97	C₂²×C₄×C₅₃	—	2	1	no	—
98	C₂²×C₄×C₅₃	#41	1	2	yes	—
99	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
100	C₂×C₂²⋊D₅₃	—	2	2	no	—
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	C₂×C₈×C₅₃	—	2	1	no	—
110	C₂×C₈×C₅₃	—	2	1	no	—
111	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
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	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₅₃	#41	1	2	yes	—
122	C₂×C₈×C₅₃	#41	1	2	yes	—
123	C₄²×C₅₃	—	2	1	no	—
124	C₄²×C₅₃	—	2	1	no	—
125	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
126	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
127	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
128	C₄²×C₅₃	C₂×D₄	1	2	yes	—
129	C₂²⋊Dic₅₃	—	2	2	no	—
130	#11719921	—	2	4	no	—
131	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
132	#11719919	—	2	4	no	—
133	C₄×Dic₅₃	—	2	4	no	—
134	C₄×Dic₅₃	—	2	2	no	—
135	#11719917	—	2	2	no	—
136	#11719917	—	2	2	no	—
137	#11719917	C₂²×C₄	1	4	yes	—
138	#11719917	C₂²×C₄	1	4	yes	—
139	C₂×#88322	—	2	2	no	—
140	C₂×#88322	—	2	2	no	—
141	Dic₂₁₂	C₄²	1	4	yes	—
142	D₄₂₄	C₄²	1	4	yes	—
143	#11719913	C₄²	1	8	yes	—
144	#11719912	—	2	8	no	—
145	#11719912	—	2	8	no	—
146	C₈×D₅₃	—	2	8	no	—
147	C₈×D₅₃	—	2	8	no	—
148	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
149	C₂²×D₅₃	—	2	2	no	—
150	C₂×C₄×C₅₃	—	2	2	no	—
151	C₂×C₄×C₅₃	—	2	2	no	—
152	C₂×C₄×C₅₃	—	4	2	no	—
153	C₂×C₄×C₅₃	—	4	2	no	—
154	C₂×C₄×C₅₃	—	4	2	no	—
155	C₂×C₄×C₅₃	C₄×D₄	1	4	yes	—
156	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
162	C₂²⋊D₅₃	—	2	4	no	—
163	C₂²⋊D₅₃	—	2	4	no	—
164	C₂×Dic₅₃	—	2	2	no	—
165	C₂×Dic₅₃	—	2	4	no	—
166	D₂₁₂	—	2	2	no	—
167	D₂₁₂	C₂×C₄²	1	4	yes	—
168	C₄×D₅₃	—	2	4	no	—
169	C₄×D₅₃	—	2	4	no	—
170	C₄×D₅₃	—	4	8	no	—
171	Dic₁₀₆	—	2	2	no	—
172	Dic₁₀₆	C₂×C₄²	1	4	yes	—
173	C₈×C₅₃	—	2	2	no	—
174	C₈×C₅₃	C₂×C₄²	1	2	yes	—
175	C₈×C₅₃	C₂×C₄²	1	2	yes	—
176	C₈×C₅₃	C₄×D₄	1	2	yes	—
177	C₈×C₅₃	C₄×D₄	1	4	yes	—
178	C₈×C₅₃	C₄×D₄	1	2	yes	—
179	#88322	—	2	4	no	—
180	#88322	—	2	4	no	—
181	#20510	—	53	1	no	maximal, Sylow
182	C₂²×C₅₃	—	2	2	no	—
183	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
184	C₂²×C₅₃	C₄×#41	1	1	yes	characteristic
185	C₂²×C₅₃	C₄×#41	1	1	yes	characteristic
186	C₂×D₅₃	—	2	4	no	—
187	C₂×D₅₃	—	4	4	no	—
188	C₄×C₅₃	—	2	4	no	—
189	C₄×C₅₃	—	4	2	no	—
190	C₄×C₅₃	—	4	2	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	4	no	—
196	Dic₅₃	—	4	4	no	—
197	C₂×#444	—	53	1	no	—
198	C₂×#443	—	53	1	no	—
199	#2943	—	53	1	no	—
200	C₄×#131	—	53	2	no	—
201	#1778	—	53	1	no	—
202	#1773	—	53	1	no	—
203	#1772	—	53	1	no	—
204	#1765	—	53	2	no	—
205	#1764	—	53	2	no	—
206	#1759	—	53	2	no	—
207	#1726	D₅₃	1	1	yes	characteristic, complemented
208	C₂×C₅₃	—	2	1	no	—
209	C₂×C₅₃	—	2	1	no	—
210	C₂×C₅₃	C₄²×D₄	1	1	yes	characteristic
211	C₂×C₅₃	#2955	1	2	yes	—
212	D₅₃	—	4	4	no	—
213	C₂×#135	—	53	1	no	—
214	C₂×#131	—	53	2	no	—
215	C₂×#131	—	53	2	no	—
216	C₄×#41	—	53	2	no	—
217	#444	—	53	8	no	—
218	#443	—	53	8	no	—
219	#442	—	53	2	no	—
220	#441	—	53	2	no	—
221	#440	—	53	4	no	—
222	C₂×#108	—	53	1	no	—
223	C₂×#108	—	53	1	no	—
224	#427	—	53	1	no	—
225	C₂×#104	—	53	2	no	—
226	C₂×#104	—	53	2	no	—
227	#416	—	53	2	no	—
228	#405	—	53	2	no	—
229	#405	—	53	2	no	—
230	#405	—	106	2	no	—
231	#405	—	106	2	no	—
232	C₄×M₁₆	—	53	2	no	—
233	C₄×M₁₆	—	106	2	no	—
234	C₂×#97	C₂×D₅₃	1	1	yes	characteristic
235	C₂×#97	C₂×D₅₃	1	1	yes	characteristic
236	C₂×#97	C₂×D₅₃	1	1	yes	characteristic
237	C₂×C₄×C₈	—	106	2	no	—
238	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
239	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
240	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
241	#376	C₂×D₅₃	1	1	yes	characteristic
242	#341	—	53	2	no	—
243	#339	—	53	2	no	—
244	#339	—	53	2	no	—
245	C₅₃	#20510	1	1	yes	characteristic, complemented, Sylow
246	C₂×#41	—	53	2	no	—
247	#135	—	53	4	no	—
248	#135	—	53	4	no	—
249	C₂×Q₁₆	—	53	1	no	—
250	C₂×SD₁₆	—	53	2	no	—
251	C₂×D₈	—	53	1	no	—
252	#131	—	53	8	no	—
253	#131	—	53	8	no	—
254	#131	—	106	4	no	—
255	#131	—	106	4	no	—
256	C₂×M₁₆	—	53	2	no	—
257	C₂×M₁₆	—	53	2	no	—
258	C₂×M₁₆	—	106	2	no	—
259	C₂×M₁₆	—	106	2	no	—
260	C₂²×C₈	—	106	2	no	—
261	C₂²×C₈	—	106	2	no	—
262	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
263	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
264	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
266	C₄×Q₈	—	53	4	no	—
267	C₄×D₄	—	53	4	no	—
268	C₄×D₄	—	106	4	no	—
269	#117	—	53	2	no	—
270	#117	—	106	2	no	—
271	C₂×C₄²	—	106	2	no	—
272	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
273	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
274	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
275	#108	—	53	4	no	—
276	#108	—	53	4	no	—
277	#107	—	53	2	no	—
278	#106	—	53	2	no	—
279	#104	—	53	8	no	—
280	#104	—	53	8	no	—
281	#103	—	53	4	no	—
282	#102	—	53	4	no	—
283	#97	—	2	2	no	—
284	#97	—	106	2	no	—
285	#97	—	106	2	no	—
286	#97	—	106	2	no	—
287	#97	C₄×D₅₃	1	2	yes	—
288	#97	C₄×D₅₃	1	2	yes	—
289	#97	C₄×D₅₃	1	4	yes	complemented
290	C₄×C₈	—	2	2	no	—
291	C₄×C₈	—	106	2	no	—
292	C₄×C₈	—	106	2	no	—
293	C₄×C₈	—	106	2	no	—
294	C₄×C₈	C₄×D₅₃	1	4	yes	complemented
295	C₄×C₈	D₂₁₂	1	2	yes	—
296	C₄×C₈	D₂₁₂	1	2	yes	—
297	#95	—	2	2	no	—
298	#41	—	53	4	no	—
299	#41	—	53	4	no	—
300	#41	—	106	2	no	—
301	#41	—	106	2	no	—
302	C₂×Q₈	—	53	2	no	—
303	C₂×D₄	—	53	2	no	—
304	C₂×D₄	—	106	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	106	2	no	—
308	C₂²×C₄	—	106	4	no	—
309	C₂²×C₄	#11719945	1	2	yes	—
310	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
311	Q₁₆	—	53	4	no	—
312	SD₁₆	—	53	8	no	—
313	D₈	—	53	4	no	—
314	M₁₆	—	53	4	no	—
315	M₁₆	—	53	4	no	—
316	M₁₆	—	106	2	no	—
317	M₁₆	—	106	2	no	—
318	M₁₆	—	106	8	no	—
319	M₁₆	—	106	8	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	106	2	no	—
323	C₂×C₈	—	106	2	no	—
324	C₂×C₈	—	106	8	no	—
325	C₂×C₈	—	106	8	no	—
326	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
327	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
328	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
329	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
330	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
331	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
332	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
333	C₂×C₈	C₂×D₂₁₂	1	2	yes	—
334	C₂×C₈	C₂×D₂₁₂	1	1	yes	characteristic
335	C₂×C₈	C₂×D₂₁₂	1	1	yes	characteristic
336	C₂×C₈	#11719945	1	2	yes	—
337	C₂×C₈	#11719945	1	2	yes	—
338	C₄⋊C₄	—	53	4	no	—
339	C₄⋊C₄	—	106	4	no	—
340	C₂²⋊C₄	—	106	2	no	—
341	C₂²⋊C₄	—	106	4	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	106	4	no	—
345	C₄²	—	106	2	no	—
346	C₄²	C₂×C₄×D₅₃	1	2	yes	—
347	C₄²	C₂×C₄×D₅₃	1	2	yes	—
348	C₄²	C₂×C₄×D₅₃	1	2	yes	—
349	C₄²	C₂×D₂₁₂	1	2	yes	—
350	C₂³	—	106	2	no	—
351	C₂³	C₂×#11719945	1	1	yes	characteristic
352	Q₈	—	53	4	no	—
353	Q₈	—	106	2	no	—
354	D₄	—	53	4	no	—
355	D₄	—	106	4	no	—
356	D₄	—	106	4	no	—
357	D₄	—	106	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	106	2	no	—
364	C₂×C₄	—	106	4	no	—
365	C₂×C₄	—	106	4	no	—
366	C₂×C₄	—	106	4	no	—
367	C₂×C₄	—	212	8	no	—
368	C₂×C₄	C₄×D₂₁₂	1	4	yes	—
369	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
373	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
374	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	106	4	no	—
377	C₈	—	106	4	no	—
378	C₈	C₄²×D₅₃	1	2	yes	—
379	C₈	C₄²×D₅₃	1	2	yes	—
380	C₈	C₄×D₂₁₂	1	2	yes	—
381	C₈	C₄×D₂₁₂	1	4	yes	—
382	C₈	C₄×D₂₁₂	1	2	yes	—
383	C₂²	—	2	2	no	—
384	C₂²	—	106	4	no	—
385	C₂²	—	212	4	no	—
386	C₂²	C₂×C₄×D₂₁₂	1	1	yes	characteristic
387	C₂²	C₄×#11719945	1	1	yes	characteristic
388	C₂²	C₄×#11719945	1	1	yes	characteristic
389	C₄	—	2	4	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	106	4	no	—
393	C₄	—	212	4	no	—
394	C₄	C₂×C₄²×D₅₃	1	1	yes	characteristic
395	C₄	C₂×C₄×D₂₁₂	1	1	yes	characteristic
396	C₄	C₂×C₄×D₂₁₂	1	1	yes	characteristic
397	C₄	C₄×#11719945	1	1	yes	characteristic
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	—	212	4	no	—
401	C₂	C₄²×D₂₁₂	1	1	yes	characteristic
402	C₂	#20283619	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂×D₂₁₂
commutator	C₄×C₅₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1726	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂×#13133239	C₂²
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1726	D₅₃
hypocenter	C₅₃	#20510
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #1726

Complements

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

N	H ≅ G/N	type
4. C₄×#13133223	C₂	semidirect
5. #20274621	C₂	semidirect
6. #20274599	C₂	semidirect
7. #20274594	C₂	semidirect
8. #20274559	C₂	semidirect
9. #20274552	C₂	semidirect
10. #20274526	C₂	semidirect
11. C₅₃×#1726	C₂	semidirect
16. #16810746	C₄	semidirect
17. #16810741	C₄	semidirect
18. #16810736	C₄	semidirect
19. #16810731	C₄	semidirect
20. #16810725	C₄	semidirect
52. #13133223	C₂×C₄	semidirect
53. #13133223	C₂×C₄	semidirect
66. #13133153	C₂×C₄	semidirect
67. #13133153	C₂×C₄	semidirect
70. #13133145	C₂×C₄	semidirect
71. #13133145	C₂×C₄	semidirect
90. #97×C₅₃	C₂×C₄	semidirect
92. C₄×C₈×C₅₃	C₂×C₄	semidirect
207. #1726	D₅₃	semidirect
245. C₅₃	#20510	semidirect
289. #97	C₄×D₅₃	semidirect
294. C₄×C₈	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×#16810741	2
#20283517	2
C₄×#13133223	2
#20274621	2
#20274599	2
#20274594	2
#20274559	2
#20274552	2
#20274526	2
C₅₃×#1726	2
#20510	53