Subgroups — #28328417

Order 13568.

668 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20291495	C₂	1	1	yes	maximal, characteristic, complemented
2	#20291474	C₂	1	1	yes	maximal, characteristic, complemented
3	#20291127	C₂	1	4	yes	maximal, complemented
4	#20291126	C₂	1	4	yes	maximal, complemented
5	#20291062	C₂	1	1	yes	maximal, characteristic, complemented
6	D₅₃⋊#361	C₂	1	1	yes	maximal, characteristic, complemented
7	#20291037	C₂	1	1	yes	maximal, characteristic, complemented
8	#20290934	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16811060	C₂	1	1	yes	maximal, characteristic
10	#16811703	—	2	1	no	—
11	#16811690	—	2	1	no	—
12	D₅₃⋊M₃₂	C₂²	1	1	yes	characteristic
13	#16811669	C₂²	1	4	yes	complemented
14	#16811667	—	2	2	no	—
15	#16811664	C₂²	1	4	yes	complemented
16	D₈×#6157	—	2	2	no	—
17	D₅₃⋊#108	C₂²	1	1	yes	characteristic
18	#16811633	C₂²	1	1	yes	characteristic
19	#16811622	—	2	1	no	—
20	#16811615	—	2	1	no	—
21	#16811586	C₂²	1	1	yes	characteristic
22	#16811548	C₂²	1	2	yes	complemented
23	#16811547	C₂²	1	2	yes	complemented
24	#16811541	C₂²	1	4	yes	complemented
25	#16811540	C₂²	1	4	yes	complemented
26	#16811514	C₂²	1	2	yes	complemented
27	#16811513	C₂²	1	2	yes	complemented
28	C₂×#13133240	C₂²	1	1	yes	characteristic
29	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic
30	#16811060	C₄	1	2	yes	complemented
31	#16811060	C₄	1	2	yes	complemented
32	#16811060	C₂²	1	2	yes	—
33	#16811060	C₂²	1	2	yes	—
34	C₂×#13133160	C₄	1	1	yes	characteristic, complemented
35	C₂×D₈₄₈	C₄	1	1	yes	characteristic, complemented
36	C₂×#13133158	C₄	1	1	yes	characteristic, complemented
37	C₂×#13133156	C₂²	1	1	yes	characteristic
38	C₂×SD₃₂×C₅₃	C₄	1	1	yes	characteristic, complemented
39	#13133305	—	2	4	no	—
40	#13133305	—	4	2	no	—
41	D₅₃⋊M₁₆	—	2	1	no	—
42	D₅₃⋊M₁₆	—	4	2	no	—
43	D₅₃⋊M₁₆	D₄	1	1	yes	characteristic
44	D₄×#6157	—	2	4	no	—
45	D₄×#6157	—	4	2	no	—
46	#13133296	—	2	1	no	—
47	#13133296	D₄	1	1	yes	characteristic
48	C₂×C₂²⋊#6157	—	4	2	no	—
49	#13133292	C₂³	1	2	yes	—
50	#13133291	—	2	1	no	—
51	D₅₃⋊C₁₆	—	2	1	no	—
52	#13133288	—	2	1	no	—
53	#13133287	C₂³	1	2	yes	—
54	#13133286	—	2	1	no	—
55	#13133285	C₂³	1	2	yes	—
56	#13133282	—	2	4	no	—
57	#13133279	—	2	4	no	—
58	#13133271	C₂³	1	2	yes	—
59	C₈×#6157	D₄	1	2	yes	—
60	C₂×#11719949	—	2	1	no	—
61	C₂×D₄×D₅₃	—	2	1	no	—
62	#13133240	—	2	1	no	—
63	#13133240	—	2	1	no	—
64	#13133240	C₂×C₄	1	2	yes	complemented
65	#13133240	C₂³	1	2	yes	—
66	C₂×#11719924	—	2	1	no	—
67	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic
68	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic, complemented
69	C₂×#11719922	—	2	1	no	—
70	D₈×D₅₃	—	2	1	no	—
71	D₈×D₅₃	—	2	1	no	—
72	D₈×D₅₃	C₂×C₄	1	2	yes	—
73	D₈×D₅₃	C₂³	1	2	yes	—
74	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
75	#13133160	C₂×C₄	1	2	yes	complemented
76	#13133160	C₂×C₄	1	2	yes	complemented
77	D₈₄₈	C₂×C₄	1	2	yes	complemented
78	D₈₄₈	C₂×C₄	1	2	yes	complemented
79	#13133158	C₂×C₄	1	2	yes	complemented
80	#13133158	C₂×C₄	1	2	yes	complemented
81	#13133156	C₂×C₄	1	1	yes	characteristic, complemented
82	#13133156	C₂×C₄	1	1	yes	characteristic, complemented
83	#13133156	C₂³	1	1	yes	characteristic
84	#13133156	C₂³	1	1	yes	characteristic
85	C₂×#11719908	C₂×C₄	1	1	yes	characteristic, complemented
86	C₂×Q₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
87	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic
88	SD₃₂×C₅₃	C₂×C₄	1	2	yes	complemented
89	SD₃₂×C₅₃	C₂×C₄	1	2	yes	complemented
90	C₂×C₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
91	C₂³×D₅₃	—	4	1	no	—
92	C₂²×#6157	—	4	4	no	—
93	C₂×Q₈×C₅₃	—	2	1	no	—
94	C₂×D₄×C₅₃	—	2	1	no	—
95	C₂×C₂²⋊D₅₃	—	4	1	no	—
96	#11719949	—	2	2	no	—
97	#11719949	—	2	2	no	—
98	#11719949	—	4	1	no	—
99	#11719949	—	4	1	no	—
100	D₄×D₅₃	—	2	2	no	—
101	D₄×D₅₃	—	2	2	no	—
102	D₄×D₅₃	—	4	1	no	—
103	D₄×D₅₃	—	4	1	no	—
104	C₂×D₂₁₂	—	2	1	no	—
105	C₂×D₂₁₂	—	2	1	no	—
106	C₂×D₂₁₂	—	4	1	no	—
107	C₂×C₄×D₅₃	—	4	1	no	—
108	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
109	C₂²⋊#6157	—	2	1	no	—
110	C₂²⋊#6157	—	4	4	no	—
111	C₂²⋊#6157	—	4	1	no	—
112	#11719940	—	2	1	no	—
113	#11719940	—	4	1	no	—
114	C₄⋊#6157	—	2	1	no	—
115	C₄⋊#6157	—	2	2	no	—
116	C₄×#6157	—	4	1	no	—
117	C₄×#6157	C₂×D₄	1	2	yes	—
118	#11719936	—	2	1	no	—
119	#11719936	—	2	2	no	—
120	#11719936	—	4	4	no	—
121	D₅₃⋊C₈	—	4	4	no	—
122	D₅₃⋊C₈	—	4	1	no	—
123	D₅₃⋊C₈	C₂×D₄	1	2	yes	—
124	Q₁₆×C₅₃	—	2	1	no	—
125	Q₁₆×C₅₃	C₂²×C₄	1	2	yes	—
126	D₈×C₅₃	—	2	1	no	—
127	D₈×C₅₃	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
129	#11719924	—	2	2	no	—
130	#11719924	—	2	2	no	—
131	#11719922	—	2	2	no	—
132	#11719922	—	2	2	no	—
133	C₂×#88322	#41	1	1	yes	characteristic
134	D₄₂₄	—	2	1	no	—
135	D₄₂₄	—	2	1	no	—
136	D₄₂₄	C₂²×C₄	1	2	yes	—
137	D₄₂₄	C₂²×C₄	1	2	yes	—
138	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
139	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
140	C₈×D₅₃	#41	1	1	yes	characteristic
141	C₈×D₅₃	C₂⁴	1	1	yes	characteristic
142	#11719910	—	2	2	no	—
143	C₁₆×C₅₃	C₂²×C₄	1	1	yes	characteristic
144	C₁₆×C₅₃	C₂²×C₄	1	1	yes	characteristic
145	#11719908	C₂²×C₄	1	1	yes	characteristic
146	#11719908	C₂²×C₄	1	1	yes	characteristic
147	C₂³×C₅₃	—	4	1	no	—
148	C₂²×D₅₃	—	4	1	no	—
149	C₂²×D₅₃	—	4	1	no	—
150	C₂²×D₅₃	—	4	2	no	—
151	C₂²×D₅₃	—	4	2	no	—
152	C₂²×D₅₃	—	16	2	no	—
153	C₂²×D₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×#6157	—	2	2	no	—
155	C₂×#6157	—	4	2	no	—
156	C₂×#6157	—	16	4	no	—
157	Q₈×C₅₃	—	2	2	no	—
158	Q₈×C₅₃	—	4	1	no	—
159	D₄×C₅₃	—	2	2	no	—
160	D₄×C₅₃	—	4	1	no	—
161	C₂×C₄×C₅₃	—	4	1	no	—
162	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
163	C₂²⋊D₅₃	—	4	2	no	—
164	C₂²⋊D₅₃	—	4	2	no	—
165	C₂×Dic₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
166	D₂₁₂	—	2	2	no	—
167	D₂₁₂	—	2	2	no	—
168	D₂₁₂	—	4	2	no	—
169	D₂₁₂	—	4	2	no	—
170	D₂₁₂	—	4	1	no	—
171	D₂₁₂	—	4	1	no	—
172	C₄×D₅₃	—	4	2	no	—
173	C₄×D₅₃	—	4	2	no	—
174	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
175	C₄×D₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₄×D₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
178	#88324	—	2	2	no	—
179	#88324	—	4	2	no	—
180	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
181	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
182	#88322	C₄×D₄	1	1	yes	characteristic
183	#88322	C₂×#41	1	1	yes	characteristic
184	#33471	—	53	1	no	maximal, Sylow
185	C₂²×C₅₃	—	4	2	no	—
186	C₂²×C₅₃	—	16	1	no	—
187	C₂²×C₅₃	#442	1	1	yes	characteristic
188	C₂×D₅₃	—	4	1	no	—
189	C₂×D₅₃	—	4	2	no	—
190	C₂×D₅₃	—	4	2	no	—
191	C₂×D₅₃	—	8	4	no	—
192	C₂×D₅₃	—	16	2	no	—
193	C₂×D₅₃	—	16	1	no	—
194	C₂×D₅₃	—	16	1	no	—
195	C₂×D₅₃	#442	1	1	yes	characteristic
196	C₂×D₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	#6157	—	4	2	no	—
198	#6157	—	8	2	no	—
199	C₄×C₅₃	—	4	2	no	—
200	C₄×C₅₃	#442	1	1	yes	characteristic
201	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
202	Dic₅₃	#442	1	1	yes	characteristic
203	Dic₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₂×#509	—	53	1	no	—
205	#2957	—	53	1	no	—
206	#2948	—	53	1	no	—
207	AGL(1,ℤ/16)	—	53	4	no	—
208	AGL(1,ℤ/16)	—	53	4	no	—
209	#2155	—	53	1	no	—
210	C₂×#361	—	53	1	no	—
211	#2145	—	53	1	no	—
212	#2110	—	53	1	no	—
213	C₂×C₅₃	—	2	1	no	—
214	C₂×C₅₃	—	8	2	no	—
215	C₂×C₅₃	C₂×#442	1	1	yes	characteristic
216	D₅₃	—	2	1	no	—
217	D₅₃	—	2	1	no	—
218	D₅₃	—	8	2	no	—
219	D₅₃	—	8	2	no	—
220	C₂×#135	—	53	1	no	—
221	C₂²×D₈	—	53	1	no	—
222	#568	—	106	1	no	—
223	#518	—	106	1	no	—
224	#509	—	53	2	no	—
225	#509	—	53	2	no	—
226	#509	—	53	2	no	—
227	#509	—	53	2	no	—
228	C₂×SD₃₂	—	53	1	no	—
229	C₂×SD₃₂	#6157	1	1	yes	characteristic, complemented
230	C₂×D₁₆	—	53	1	no	—
231	C₂×D₁₆	—	53	1	no	—
232	C₂×M₃₂	—	53	1	no	—
233	C₂×M₃₂	—	53	1	no	—
234	#444	—	53	4	no	—
235	#443	—	106	2	no	—
236	#442	—	53	4	no	—
237	C₄×D₈	—	106	2	no	—
238	C₂×#108	—	53	1	no	—
239	#427	—	53	1	no	—
240	#421	—	106	1	no	—
241	#418	—	106	1	no	—
242	#405	—	53	1	no	—
243	#365	—	53	2	no	—
244	#365	—	53	2	no	—
245	#361	—	53	4	no	—
246	#360	—	53	4	no	—
247	#347	—	53	2	no	—
248	#347	—	53	2	no	—
249	C₅₃	#33471	1	1	yes	characteristic, complemented, Sylow
250	C₂×#41	—	106	1	no	—
251	C₂²×D₄	—	106	1	no	—
252	#135	—	53	2	no	—
253	#135	—	53	2	no	—
254	#135	—	106	1	no	—
255	#135	—	106	1	no	—
256	C₂×Q₁₆	C₂×#6157	1	1	yes	characteristic, complemented
257	C₂×SD₁₆	—	106	1	no	—
258	C₂×D₈	—	53	2	no	—
259	C₂×D₈	—	53	2	no	—
260	C₂×D₈	—	53	1	no	—
261	C₂×D₈	—	53	1	no	—
262	C₂×D₈	—	106	1	no	—
263	C₂×D₈	—	106	1	no	—
264	C₂×D₈	—	106	1	no	—
265	C₂×D₈	C₂×#6157	1	1	yes	characteristic
266	#131	—	106	4	no	—
267	#131	—	212	2	no	—
268	C₂×M₁₆	—	53	1	no	—
269	C₂×M₁₆	—	106	1	no	—
270	C₂×M₁₆	—	212	2	no	—
271	C₂²×C₈	—	53	1	no	—
272	C₄×D₄	—	106	4	no	—
273	C₄×D₄	—	212	2	no	—
274	#117	—	53	1	no	—
275	#117	—	106	1	no	—
276	C₂×C₂²⋊C₄	—	212	2	no	—
277	SD₃₂	—	53	2	no	—
278	SD₃₂	—	53	2	no	—
279	SD₃₂	C₂×#6157	1	2	yes	complemented
280	SD₃₂	C₂×#6157	1	2	yes	complemented
281	D₁₆	—	53	2	no	—
282	D₁₆	—	53	2	no	—
283	D₁₆	—	53	2	no	—
284	D₁₆	—	53	2	no	—
285	M₃₂	—	53	1	no	—
286	M₃₂	—	53	1	no	—
287	M₃₂	—	53	1	no	—
288	M₃₂	—	53	1	no	—
289	M₃₂	—	53	2	no	—
290	M₃₂	—	106	1	no	—
291	C₂×C₁₆	—	53	1	no	—
292	C₂×C₁₆	—	106	1	no	—
293	C₂×C₁₆	C₂×#6157	1	1	yes	characteristic, complemented
294	#108	—	53	2	no	—
295	#108	—	106	1	no	—
296	#107	—	106	1	no	—
297	#106	—	53	2	no	—
298	#104	—	106	4	no	—
299	#102	—	106	4	no	—
300	#97	—	53	2	no	—
301	C₄×C₈	—	53	2	no	—
302	C₂⁴	—	212	1	no	—
303	#41	—	106	2	no	—
304	#41	—	106	2	no	—
305	#41	—	212	1	no	—
306	#41	—	212	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	106	2	no	—
310	C₂×D₄	—	106	2	no	—
311	C₂×D₄	—	106	1	no	—
312	C₂×D₄	—	106	1	no	—
313	C₂×D₄	—	212	1	no	—
314	C₂×D₄	—	212	1	no	—
315	C₂×D₄	—	212	1	no	—
316	C₂×D₄	—	212	1	no	—
317	C₂²×C₄	—	53	1	no	—
318	C₂²×C₄	—	212	1	no	—
319	C₂²×C₄	—	212	4	no	—
320	Q₁₆	—	2	1	no	—
321	Q₁₆	C₂²×#6157	1	2	yes	—
322	SD₁₆	—	106	2	no	—
323	SD₁₆	—	106	2	no	—
324	D₈	—	2	1	no	—
325	D₈	—	53	2	no	—
326	D₈	—	53	2	no	—
327	D₈	—	106	2	no	—
328	D₈	—	106	2	no	—
329	D₈	—	106	1	no	—
330	D₈	—	106	1	no	—
331	D₈	C₂²×#6157	1	2	yes	—
332	M₁₆	—	106	1	no	—
333	M₁₆	—	106	1	no	—
334	M₁₆	—	106	2	no	—
335	M₁₆	—	212	4	no	—
336	M₁₆	—	212	1	no	—
337	C₂×C₈	—	53	1	no	—
338	C₂×C₈	—	53	1	no	—
339	C₂×C₈	—	53	1	no	—
340	C₂×C₈	—	53	1	no	—
341	C₂×C₈	—	53	1	no	—
342	C₂×C₈	—	53	2	no	—
343	C₂×C₈	—	212	4	no	—
344	C₂×C₈	—	212	1	no	—
345	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
346	C₄⋊C₄	—	106	1	no	—
347	C₄⋊C₄	—	106	2	no	—
348	C₂²⋊C₄	—	106	1	no	—
349	C₂²⋊C₄	—	212	4	no	—
350	C₂²⋊C₄	—	212	1	no	—
351	C₄²	—	53	2	no	—
352	C₄²	—	212	1	no	—
353	C₁₆	—	53	1	no	—
354	C₁₆	—	53	1	no	—
355	C₁₆	—	106	2	no	—
356	C₁₆	C₂²×#6157	1	1	yes	characteristic
357	C₁₆	C₂²×#6157	1	1	yes	characteristic
358	C₂³	—	4	1	no	—
359	C₂³	—	53	1	no	—
360	C₂³	—	848	2	no	—
361	C₂³	—	212	2	no	—
362	C₂³	—	212	2	no	—
363	C₂³	—	212	1	no	—
364	C₂³	—	212	1	no	—
365	Q₈	—	2	2	no	—
366	Q₈	—	4	1	no	—
367	D₄	—	2	2	no	—
368	D₄	—	4	1	no	—
369	D₄	—	106	2	no	—
370	D₄	—	106	2	no	—
371	D₄	—	212	2	no	—
372	D₄	—	212	2	no	—
373	D₄	—	212	2	no	—
374	D₄	—	212	2	no	—
375	D₄	—	212	1	no	—
376	D₄	—	212	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	53	1	no	—
379	C₂×C₄	—	53	1	no	—
380	C₂×C₄	—	53	1	no	—
381	C₂×C₄	—	53	1	no	—
382	C₂×C₄	—	53	1	no	—
383	C₂×C₄	—	848	4	no	—
384	C₂×C₄	—	106	2	no	—
385	C₂×C₄	—	212	2	no	—
386	C₂×C₄	—	212	2	no	—
387	C₂×C₄	—	212	2	no	—
388	C₂×C₄	D₄×#6157	1	1	yes	characteristic
389	C₈	—	53	1	no	—
390	C₈	—	53	1	no	—
391	C₈	—	106	2	no	—
392	C₈	—	212	2	no	—
393	C₈	D₄×#6157	1	1	yes	characteristic
394	C₈	C₂³×#6157	1	1	yes	characteristic
395	C₂²	—	4	2	no	—
396	C₂²	—	16	1	no	—
397	C₂²	—	53	1	no	—
398	C₂²	—	53	1	no	—
399	C₂²	—	848	1	no	—
400	C₂²	—	848	1	no	—
401	C₂²	—	848	2	no	—
402	C₂²	—	424	4	no	—
403	C₂²	—	212	1	no	—
404	C₂²	—	212	2	no	—
405	C₂²	—	212	2	no	—
406	C₂²	#16811664	1	1	yes	characteristic
407	C₄	—	4	2	no	—
408	C₄	—	53	1	no	—
409	C₄	—	53	1	no	—
410	C₄	—	424	2	no	—
411	C₄	—	212	2	no	—
412	C₄	#16811664	1	1	yes	characteristic
413	C₄	C₂×D₄×#6157	1	1	yes	characteristic
414	C₂	—	2	1	no	—
415	C₂	—	8	2	no	—
416	C₂	—	106	1	no	—
417	C₂	—	106	1	no	—
418	C₂	—	424	2	no	—
419	C₂	—	424	2	no	—
420	C₂	C₂×#16811664	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#16811664
commutator	C₈×C₅₃	C₂³×C₄
Frattini	C₈	C₂³×#6157
Fitting	C₂×SD₃₂×C₅₃	C₄
socle	C₂×C₅₃	C₂×#442
prime radical	C₂×#16811060	C₂
cosocle	C₈×D₅₃	C₂⁴
hypercenter	C₂×SD₃₂	#6157
hypocenter	C₅₃	#33471
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×SD₃₂

Complements

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

N	H ≅ G/N	type
1. #20291495	C₂	semidirect
2. #20291474	C₂	semidirect
3. #20291127	C₂	semidirect
4. #20291126	C₂	semidirect
5. #20291062	C₂	semidirect
6. D₅₃⋊#361	C₂	semidirect
7. #20291037	C₂	semidirect
8. #20290934	C₂	semidirect
13. #16811669	C₂²	semidirect
15. #16811664	C₂²	semidirect
22. #16811548	C₂²	semidirect
23. #16811547	C₂²	semidirect
24. #16811541	C₂²	semidirect
25. #16811540	C₂²	semidirect
26. #16811514	C₂²	semidirect
27. #16811513	C₂²	semidirect
30. #16811060	C₄	semidirect
31. #16811060	C₄	semidirect
34. C₂×#13133160	C₄	semidirect
35. C₂×D₈₄₈	C₄	semidirect
36. C₂×#13133158	C₄	semidirect
38. C₂×SD₃₂×C₅₃	C₄	semidirect
64. #13133240	C₂×C₄	semidirect
68. C₂×D₄₂₄	C₂×C₄	semidirect
75. #13133160	C₂×C₄	semidirect
76. #13133160	C₂×C₄	semidirect
77. D₈₄₈	C₂×C₄	semidirect
78. D₈₄₈	C₂×C₄	semidirect
79. #13133158	C₂×C₄	semidirect
80. #13133158	C₂×C₄	semidirect
81. #13133156	C₂×C₄	semidirect
82. #13133156	C₂×C₄	semidirect
85. C₂×#11719908	C₂×C₄	semidirect
86. C₂×Q₁₆×C₅₃	C₂×C₄	semidirect
88. SD₃₂×C₅₃	C₂×C₄	semidirect
89. SD₃₂×C₅₃	C₂×C₄	semidirect
90. C₂×C₁₆×C₅₃	C₂×C₄	semidirect
229. C₂×SD₃₂	#6157	semidirect
249. C₅₃	#33471	semidirect
256. C₂×Q₁₆	C₂×#6157	semidirect
279. SD₃₂	C₂×#6157	semidirect
280. SD₃₂	C₂×#6157	semidirect
293. C₂×C₁₆	C₂×#6157	semidirect

Maximal subgroups

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

subgroup	index
#20291495	2
#20291474	2
#20291127	2
#20291126	2
#20291062	2
D₅₃⋊#361	2
#20291037	2
#20290934	2
C₂×#16811060	2
#33471	53