Subgroups — #28297948

Order 13568.

10836 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	C₂×#16811459	C₂	1	2	yes	maximal, complemented
2	#20289503	C₂	1	16	yes	maximal, complemented
3	#20289496	C₂	1	16	yes	maximal, complemented
4	#20289489	C₂	1	16	yes	maximal, complemented
5	C₂×#16811423	C₂	1	12	yes	maximal, complemented
6	C₂×C₅₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811459	—	2	8	no	—
8	#16811459	—	2	8	no	—
9	#16811459	C₂²	1	16	yes	complemented
10	#16811459	C₂²	1	16	yes	complemented
11	C₂×#13133265	—	2	2	no	—
12	C₂×#13133264	C₂²	1	8	yes	complemented
13	C₂×#13133263	C₂²	1	8	yes	complemented
14	C₂×#13133262	—	2	6	no	—
15	C₂²×#11719945	C₂²	1	12	yes	complemented
16	C₂×#41×D₅₃	—	2	8	no	—
17	#16811440	C₂²	1	64	yes	complemented
18	#16811435	C₂²	1	128	yes	complemented
19	#16811428	C₂²	1	64	yes	complemented
20	#16811423	C₂²	1	16	yes	complemented
21	#16811423	C₂²	1	96	yes	complemented
22	#16811423	C₂²	1	48	yes	complemented
23	C₂×#13133250	C₂²	1	48	yes	complemented
24	C₂×#13133245	C₂²	1	48	yes	complemented
25	C₂×#13133239	C₂²	1	48	yes	complemented
26	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
27	C₅₃×#568	C₂²	1	16	yes	complemented
28	C₂×#131×C₅₃	C₂²	1	8	yes	complemented
29	C₂²×M₁₆×C₅₃	C₂²	1	6	yes	complemented
30	#13133265	—	2	16	no	—
31	#13133265	—	2	16	no	—
32	#13133264	—	2	32	no	—
33	#13133264	C₂³	1	64	yes	complemented
34	#13133263	—	2	32	no	—
35	#13133263	C₂³	1	64	yes	complemented
36	#13133262	—	2	48	no	—
37	#13133262	—	2	48	no	—
38	C₂×#11719949	—	2	8	no	—
39	C₂×#11719945	—	2	12	no	—
40	C₂×#11719945	—	2	12	no	—
41	C₂×#11719945	—	2	24	no	—
42	C₂×#11719945	—	2	24	no	—
43	C₂×#11719945	C₂³	1	48	yes	—
44	C₂×#11719945	C₂³	1	8	yes	—
45	C₂×#11719945	C₂³	1	48	yes	complemented
46	C₂×#11719945	C₂³	1	24	yes	complemented
47	C₂×#11719947	—	2	24	no	—
48	#41×D₅₃	—	2	64	no	—
49	#41×D₅₃	—	2	64	no	—
50	C₂²×Dic₁₀₆	C₂³	1	12	yes	complemented
51	C₂×Q₈×D₅₃	—	2	8	no	—
52	C₂²×D₂₁₂	C₂³	1	12	yes	complemented
53	C₂²×C₂²⋊D₅₃	—	2	12	no	—
54	C₂×D₄×D₅₃	—	2	24	no	—
55	C₂²×C₄×D₅₃	—	2	12	no	—
56	#13133250	C₂³	1	64	yes	complemented
57	#13133250	C₂³	1	192	yes	complemented
58	#13133245	C₂³	1	64	yes	complemented
59	#13133245	C₂³	1	192	yes	complemented
60	#13133239	C₂³	1	64	yes	complemented
61	#13133239	C₂³	1	192	yes	complemented
62	C₂×Dic₂₁₂	C₂³	1	48	yes	complemented
63	C₂×#11719913	C₂³	1	96	yes	complemented
64	C₂×D₄₂₄	C₂³	1	48	yes	complemented
65	C₂×#41×C₅₃	D₄	1	8	yes	—
66	C₂×#41×C₅₃	D₄	1	4	yes	—
67	C₂×#41×C₅₃	C₂³	1	4	yes	—
68	C₂×#41×C₅₃	C₂³	1	8	yes	—
69	C₂²×Q₈×C₅₃	D₄	1	1	yes	characteristic
70	C₂²×D₄×C₅₃	D₄	1	3	yes	—
71	C₂³×C₄×C₅₃	C₂³	1	3	yes	—
72	#131×C₅₃	C₂³	1	64	yes	complemented
73	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
74	C₂×M₁₆×C₅₃	C₂³	1	12	yes	complemented
75	C₂×M₁₆×C₅₃	C₂³	1	48	yes	complemented
76	C₂²×C₈×C₅₃	C₂³	1	12	yes	complemented
77	C₂⁴×C₅₃	C₂×D₄	1	3	yes	—
78	C₂³×D₅₃	—	2	12	no	—
79	#41×C₅₃	C₂×D₄	1	16	yes	—
80	#41×C₅₃	C₂×D₄	1	32	yes	—
81	#41×C₅₃	C₂⁴	1	16	yes	—
82	C₂×Q₈×C₅₃	C₂×D₄	1	8	yes	—
83	C₂×Q₈×C₅₃	C₂×D₄	1	4	yes	—
84	C₂×D₄×C₅₃	C₂×D₄	1	24	yes	—
85	C₂×D₄×C₅₃	C₂×D₄	1	12	yes	—
86	C₂²×C₄×C₅₃	C₂×D₄	1	3	yes	—
87	C₂²×C₄×C₅₃	C₂×D₄	1	12	yes	—
88	C₂²×C₄×C₅₃	C₂×D₄	1	6	yes	—
89	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
90	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
91	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
92	C₂×C₂²⋊D₅₃	—	2	24	no	—
93	C₂×C₂²⋊D₅₃	—	2	8	no	—
94	C₂×C₂²⋊D₅₃	—	2	48	no	—
95	C₂×C₂²⋊D₅₃	—	2	48	no	—
96	C₂²×Dic₅₃	—	2	12	no	—
97	#11719949	—	2	64	no	—
98	Q₈×D₅₃	—	2	64	no	—
99	#11719947	—	2	192	no	—
100	D₄×D₅₃	—	2	192	no	—
101	#11719945	—	2	48	no	—
102	#11719945	—	2	48	no	—
103	#11719945	—	2	8	no	—
104	#11719945	—	2	8	no	—
105	#11719945	—	2	48	no	—
106	#11719945	—	2	48	no	—
107	#11719945	—	2	48	no	—
108	#11719945	C₂⁴	1	16	yes	—
109	#11719945	C₂⁴	1	96	yes	—
110	#11719945	C₂⁴	1	16	yes	—
111	C₂×D₂₁₂	—	2	12	no	—
112	C₂×D₂₁₂	—	2	24	no	—
113	C₂×D₂₁₂	C₂⁴	1	48	yes	—
114	C₂×D₂₁₂	C₂⁴	1	8	yes	—
115	C₂×C₄×D₅₃	—	2	8	no	—
116	C₂×C₄×D₅₃	—	2	24	no	—
117	C₂×C₄×D₅₃	—	2	48	no	—
118	C₂×C₄×D₅₃	—	2	48	no	—
119	C₂×Dic₁₀₆	—	2	12	no	—
120	C₂×Dic₁₀₆	—	2	24	no	—
121	C₂×Dic₁₀₆	C₂⁴	1	48	yes	—
122	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
123	M₁₆×C₅₃	C₂⁴	1	16	yes	—
124	M₁₆×C₅₃	C₂⁴	1	48	yes	—
125	C₂×C₈×C₅₃	C₂⁴	1	8	yes	—
126	C₂×C₈×C₅₃	C₂⁴	1	48	yes	—
127	Dic₂₁₂	C₂⁴	1	64	yes	—
128	D₄₂₄	C₂⁴	1	64	yes	—
129	#11719913	C₂⁴	1	128	yes	—
130	C₂³×C₅₃	—	8	3	no	—
131	C₂³×C₅₃	C₂²×D₄	1	12	yes	—
132	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
133	C₂³×C₅₃	C₂²×D₄	1	6	yes	—
134	C₂²×D₅₃	—	2	8	no	—
135	C₂²×D₅₃	—	2	48	no	—
136	C₂²×D₅₃	—	8	24	no	—
137	Q₈×C₅₃	C₂²×D₄	1	16	yes	—
138	D₄×C₅₃	C₂²×D₄	1	48	yes	—
139	C₂×C₄×C₅₃	C₂²×D₄	1	12	yes	—
140	C₂×C₄×C₅₃	C₂²×D₄	1	24	yes	—
141	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
142	C₂×C₄×C₅₃	C₂²×D₄	1	12	yes	—
143	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₅₃	C₂²×D₄	1	6	yes	—
145	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
146	C₂×C₄×C₅₃	C₂⁵	1	12	yes	—
147	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
148	C₂²⋊D₅₃	—	2	16	no	—
149	C₂²⋊D₅₃	—	2	16	no	—
150	C₂²⋊D₅₃	—	2	96	no	—
151	C₂×Dic₅₃	—	2	8	no	—
152	C₂×Dic₅₃	—	2	48	no	—
153	D₂₁₂	—	2	8	no	—
154	D₂₁₂	—	2	48	no	—
155	D₂₁₂	C₂⁵	1	16	yes	—
156	C₄×D₅₃	—	2	16	no	—
157	C₄×D₅₃	—	2	16	no	—
158	C₄×D₅₃	—	2	96	no	—
159	Dic₁₀₆	—	2	8	no	—
160	Dic₁₀₆	—	2	48	no	—
161	Dic₁₀₆	C₂⁵	1	16	yes	—
162	C₈×C₅₃	C₂⁵	1	16	yes	—
163	#63090	—	53	1	no	maximal, Sylow
164	C₂²×C₅₃	—	4	12	no	—
165	C₂²×C₅₃	—	4	1	no	—
166	C₂²×C₅₃	—	4	6	no	—
167	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
168	C₂²×C₅₃	C₂³×D₄	1	12	yes	—
169	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
170	C₂×D₅₃	—	2	16	no	—
171	C₂×D₅₃	—	4	16	no	—
172	C₂×D₅₃	—	8	48	no	—
173	C₄×C₅₃	C₂³×D₄	1	2	yes	—
174	C₄×C₅₃	C₂³×D₄	1	12	yes	—
175	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
176	C₄×C₅₃	C₂⁶	1	1	yes	characteristic
177	Dic₅₃	—	2	16	no	—
178	C₂×#585	—	53	2	no	—
179	#3586	—	53	16	no	—
180	#3585	—	53	16	no	—
181	#3584	—	53	16	no	—
182	C₂×#575	—	53	12	no	—
183	C₂×#568	D₅₃	1	1	yes	characteristic, complemented
184	C₂×C₅₃	—	2	2	no	—
185	C₂×C₅₃	—	2	12	no	—
186	C₂×C₅₃	—	2	1	no	—
187	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
188	D₅₃	—	4	16	no	—
189	#585	—	53	16	no	—
190	#585	—	53	16	no	—
191	#585	—	106	8	no	—
192	#585	—	106	8	no	—
193	C₂×2₋¹⁺⁴	—	53	8	no	—
194	C₂×2₋¹⁺⁴	—	106	2	no	—
195	C₂×H(5,𝔽₂)	—	53	8	no	—
196	C₂×H(5,𝔽₂)	—	106	6	no	—
197	C₂²×#41	—	53	12	no	—
198	C₂²×#41	—	106	8	no	—
199	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic
200	#578	—	53	64	no	—
201	#577	—	53	128	no	—
202	#576	—	53	64	no	—
203	#575	—	53	16	no	—
204	#575	—	53	48	no	—
205	#575	—	53	96	no	—
206	C₂×#137	—	53	48	no	—
207	C₂×AGL(1,ℤ/8)	—	53	48	no	—
208	C₂×#135	—	53	48	no	—
209	#568	C₂×D₅₃	1	16	yes	complemented
210	C₂×#131	C₂×D₅₃	1	8	yes	complemented
211	C₂²×M₁₆	C₂×D₅₃	1	6	yes	complemented
212	C₅₃	#63090	1	1	yes	characteristic, complemented, Sylow
213	2₋¹⁺⁴	—	53	64	no	—
214	2₋¹⁺⁴	—	106	32	no	—
215	2₋¹⁺⁴	—	106	16	no	—
216	2₋¹⁺⁴	—	106	16	no	—
217	H(5,𝔽₂)	—	53	64	no	—
218	H(5,𝔽₂)	—	106	32	no	—
219	H(5,𝔽₂)	—	106	48	no	—
220	H(5,𝔽₂)	—	106	48	no	—
221	C₂×#41	—	53	48	no	—
222	C₂×#41	—	53	48	no	—
223	C₂×#41	—	53	8	no	—
224	C₂×#41	—	53	24	no	—
225	C₂×#41	—	106	64	no	—
226	C₂×#41	—	106	64	no	—
227	C₂×#41	—	106	8	no	—
228	C₂×#41	—	106	24	no	—
229	C₂×#41	—	106	12	no	—
230	C₂×#41	—	106	12	no	—
231	C₂×#41	—	106	24	no	—
232	C₂×#41	—	106	24	no	—
233	C₂×#41	D₂₁₂	1	8	yes	—
234	C₂×#41	D₂₁₂	1	4	yes	—
235	C₂×#41	C₂²×D₅₃	1	4	yes	—
236	C₂×#41	C₂²×D₅₃	1	8	yes	—
237	C₂²×Q₈	—	53	12	no	—
238	C₂²×Q₈	—	106	8	no	—
239	C₂²×Q₈	D₂₁₂	1	1	yes	characteristic
240	C₂²×D₄	—	53	12	no	—
241	C₂²×D₄	—	106	12	no	—
242	C₂²×D₄	—	106	24	no	—
243	C₂²×D₄	D₂₁₂	1	3	yes	—
244	C₂³×C₄	—	106	12	no	—
245	C₂³×C₄	C₂²×D₅₃	1	3	yes	—
246	#137	—	53	64	no	—
247	#137	—	53	192	no	—
248	AGL(1,ℤ/8)	—	53	64	no	—
249	AGL(1,ℤ/8)	—	53	192	no	—
250	#135	—	53	64	no	—
251	#135	—	53	192	no	—
252	C₂×Q₁₆	—	53	48	no	—
253	C₂×SD₁₆	—	53	96	no	—
254	C₂×D₈	—	53	48	no	—
255	#131	C₂²×D₅₃	1	64	yes	complemented
256	C₂×M₁₆	C₂²×D₅₃	1	4	yes	—
257	C₂×M₁₆	C₂²×D₅₃	1	12	yes	complemented
258	C₂×M₁₆	C₂²×D₅₃	1	48	yes	complemented
259	C₂²×C₈	C₂²×D₅₃	1	12	yes	complemented
260	C₂⁴	—	106	12	no	—
261	C₂⁴	C₂×D₂₁₂	1	3	yes	—
262	#41	—	53	16	no	—
263	#41	—	53	96	no	—
264	#41	—	53	16	no	—
265	#41	—	106	64	no	—
266	#41	—	106	192	no	—
267	#41	—	106	48	no	—
268	#41	—	106	8	no	—
269	#41	—	106	8	no	—
270	#41	—	106	48	no	—
271	#41	—	106	48	no	—
272	#41	—	106	48	no	—
273	#41	—	106	48	no	—
274	#41	C₂×D₂₁₂	1	16	yes	—
275	#41	C₂×D₂₁₂	1	32	yes	—
276	#41	C₂³×D₅₃	1	16	yes	—
277	C₂×Q₈	—	53	48	no	—
278	C₂×Q₈	—	53	8	no	—
279	C₂×Q₈	—	106	64	no	—
280	C₂×Q₈	—	106	12	no	—
281	C₂×Q₈	—	106	24	no	—
282	C₂×Q₈	C₂×D₂₁₂	1	8	yes	—
283	C₂×Q₈	C₂×D₂₁₂	1	4	yes	—
284	C₂×D₄	—	53	48	no	—
285	C₂×D₄	—	53	8	no	—
286	C₂×D₄	—	106	24	no	—
287	C₂×D₄	—	106	8	no	—
288	C₂×D₄	—	106	48	no	—
289	C₂×D₄	—	106	48	no	—
290	C₂×D₄	—	106	192	no	—
291	C₂×D₄	—	106	12	no	—
292	C₂×D₄	—	106	24	no	—
293	C₂×D₄	C₂×D₂₁₂	1	24	yes	—
294	C₂×D₄	C₂×D₂₁₂	1	12	yes	—
295	C₂²×C₄	—	106	12	no	—
296	C₂²×C₄	—	106	8	no	—
297	C₂²×C₄	—	106	24	no	—
298	C₂²×C₄	—	106	48	no	—
299	C₂²×C₄	—	106	48	no	—
300	C₂²×C₄	C₂×D₂₁₂	1	12	yes	—
301	C₂²×C₄	C₂×D₂₁₂	1	3	yes	—
302	C₂²×C₄	C₂×D₂₁₂	1	6	yes	—
303	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
304	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
305	C₂²×C₄	C₂³×D₅₃	1	12	yes	—
306	Q₁₆	—	53	64	no	—
307	SD₁₆	—	53	128	no	—
308	D₈	—	53	64	no	—
309	M₁₆	C₂³×D₅₃	1	16	yes	—
310	M₁₆	C₂³×D₅₃	1	48	yes	—
311	C₂×C₈	C₂³×D₅₃	1	8	yes	—
312	C₂×C₈	C₂³×D₅₃	1	48	yes	—
313	C₂³	—	8	3	no	—
314	C₂³	—	106	48	no	—
315	C₂³	—	106	8	no	—
316	C₂³	—	424	24	no	—
317	C₂³	C₂²×D₂₁₂	1	12	yes	—
318	C₂³	C₂²×D₂₁₂	1	1	yes	characteristic
319	C₂³	C₂²×D₂₁₂	1	6	yes	—
320	Q₈	—	53	16	no	—
321	Q₈	—	106	8	no	—
322	Q₈	—	106	48	no	—
323	Q₈	C₂²×D₂₁₂	1	16	yes	—
324	D₄	—	53	16	no	—
325	D₄	—	106	16	no	—
326	D₄	—	106	96	no	—
327	D₄	—	106	16	no	—
328	D₄	—	106	8	no	—
329	D₄	—	106	48	no	—
330	D₄	C₂²×D₂₁₂	1	48	yes	—
331	C₂×C₄	—	106	8	no	—
332	C₂×C₄	—	106	48	no	—
333	C₂×C₄	—	106	16	no	—
334	C₂×C₄	—	106	96	no	—
335	C₂×C₄	—	106	16	no	—
336	C₂×C₄	C₂²×D₂₁₂	1	12	yes	—
337	C₂×C₄	C₂²×D₂₁₂	1	24	yes	—
338	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₂₁₂	1	6	yes	—
340	C₂×C₄	C₂²×D₂₁₂	1	2	yes	—
341	C₂×C₄	C₂²×D₂₁₂	1	12	yes	—
342	C₂×C₄	C₂⁴×D₅₃	1	12	yes	—
343	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
344	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
345	C₈	C₂⁴×D₅₃	1	16	yes	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	12	no	—
348	C₂²	—	4	6	no	—
349	C₂²	—	106	16	no	—
350	C₂²	—	424	48	no	—
351	C₂²	—	212	16	no	—
352	C₂²	C₂³×D₂₁₂	1	2	yes	—
353	C₂²	C₂³×D₂₁₂	1	12	yes	—
354	C₂²	C₂³×D₂₁₂	1	1	yes	characteristic
355	C₄	—	106	16	no	—
356	C₄	C₂³×D₂₁₂	1	2	yes	—
357	C₄	C₂³×D₂₁₂	1	12	yes	—
358	C₄	C₂³×D₂₁₂	1	1	yes	characteristic
359	C₄	C₂⁵×D₅₃	1	1	yes	characteristic
360	C₂	—	2	2	no	—
361	C₂	—	2	1	no	—
362	C₂	—	2	12	no	—
363	C₂	—	212	16	no	—
364	C₂	C₂⁴×D₂₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂³×D₂₁₂
commutator, cosocle	C₄×C₅₃	C₂⁶
Frattini	C₄	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#568	C₂
socle	C₂×C₅₃	C₂⁴×D₄
hypercenter	C₂×#568	D₅₃
hypocenter	C₅₃	#63090
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄ ◁ C₂²×#41 ◁ C₂×#568

Complements

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

N	H ≅ G/N	type
1. C₂×#16811459	C₂	semidirect
2. #20289503	C₂	semidirect
3. #20289496	C₂	semidirect
4. #20289489	C₂	semidirect
5. C₂×#16811423	C₂	semidirect
6. C₂×C₅₃×#568	C₂	semidirect
9. #16811459	C₂²	semidirect
10. #16811459	C₂²	semidirect
12. C₂×#13133264	C₂²	semidirect
13. C₂×#13133263	C₂²	semidirect
15. C₂²×#11719945	C₂²	semidirect
17. #16811440	C₂²	semidirect
18. #16811435	C₂²	semidirect
19. #16811428	C₂²	semidirect
20. #16811423	C₂²	semidirect
21. #16811423	C₂²	semidirect
22. #16811423	C₂²	semidirect
23. C₂×#13133250	C₂²	semidirect
24. C₂×#13133245	C₂²	semidirect
25. C₂×#13133239	C₂²	semidirect
27. C₅₃×#568	C₂²	semidirect
28. C₂×#131×C₅₃	C₂²	semidirect
29. C₂²×M₁₆×C₅₃	C₂²	semidirect
33. #13133264	C₂³	semidirect
35. #13133263	C₂³	semidirect
45. C₂×#11719945	C₂³	semidirect
46. C₂×#11719945	C₂³	semidirect
50. C₂²×Dic₁₀₆	C₂³	semidirect
52. C₂²×D₂₁₂	C₂³	semidirect
56. #13133250	C₂³	semidirect
57. #13133250	C₂³	semidirect
58. #13133245	C₂³	semidirect
59. #13133245	C₂³	semidirect
60. #13133239	C₂³	semidirect
61. #13133239	C₂³	semidirect
62. C₂×Dic₂₁₂	C₂³	semidirect
63. C₂×#11719913	C₂³	semidirect
64. C₂×D₄₂₄	C₂³	semidirect
72. #131×C₅₃	C₂³	semidirect
74. C₂×M₁₆×C₅₃	C₂³	semidirect
75. C₂×M₁₆×C₅₃	C₂³	semidirect
76. C₂²×C₈×C₅₃	C₂³	semidirect
183. C₂×#568	D₅₃	semidirect
209. #568	C₂×D₅₃	semidirect
210. C₂×#131	C₂×D₅₃	semidirect
211. C₂²×M₁₆	C₂×D₅₃	semidirect
212. C₅₃	#63090	semidirect
255. #131	C₂²×D₅₃	semidirect
257. C₂×M₁₆	C₂²×D₅₃	semidirect
258. C₂×M₁₆	C₂²×D₅₃	semidirect
259. C₂²×C₈	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811459	2
#20289503	2
#20289496	2
#20289489	2
C₂×#16811423	2
C₂×C₅₃×#568	2
#63090	53