Subgroups — #28328373

Order 13568.

682 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20291476	C₂	1	1	yes	maximal, characteristic, complemented
2	#20291474	C₂	1	1	yes	maximal, characteristic
3	#20291111	C₂	1	4	yes	maximal, complemented
4	SD₃₂×#6157	C₂	1	4	yes	maximal, complemented
5	#20291066	C₂	1	1	yes	maximal, characteristic, complemented
6	#20291025	C₂	1	1	yes	maximal, characteristic, complemented
7	#20291024	C₂	1	1	yes	maximal, characteristic
8	#20290923	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×SD₃₂×D₅₃	C₂	1	1	yes	maximal, characteristic
10	#16811691	—	2	1	no	—
11	#16811690	—	2	1	no	—
12	D₅₃⋊M₃₂	C₂²	1	1	yes	characteristic
13	#16811664	—	2	2	no	—
14	#16811663	—	2	2	no	—
15	Q₁₆×#6157	C₂²	1	4	yes	complemented
16	D₈×#6157	C₂²	1	4	yes	—
17	#16811633	C₂²	1	1	yes	characteristic
18	#16811633	C₂²	1	1	yes	characteristic
19	#16811616	—	2	1	no	—
20	#16811615	—	2	1	no	—
21	#16811586	C₂²	1	1	yes	characteristic
22	#16811550	C₂²	1	2	yes	complemented
23	#16811549	C₂²	1	2	yes	complemented
24	#16811536	C₂²	1	4	yes	complemented
25	#16811535	C₂²	1	4	yes	—
26	#16811510	C₂²	1	2	yes	complemented
27	C₁₆×#6157	C₂²	1	2	yes	complemented
28	C₂×Q₁₆×D₅₃	C₂²	1	1	yes	characteristic
29	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic
30	C₂×#13133162	C₄	1	1	yes	characteristic, complemented
31	C₂×#13133161	C₄	1	1	yes	characteristic, complemented
32	C₂×#13133160	C₄	1	1	yes	characteristic, complemented
33	SD₃₂×D₅₃	C₄	1	2	yes	complemented
34	SD₃₂×D₅₃	C₄	1	2	yes	complemented
35	SD₃₂×D₅₃	C₂²	1	2	yes	—
36	SD₃₂×D₅₃	C₂²	1	2	yes	—
37	C₂×C₁₆×D₅₃	C₂²	1	1	yes	characteristic
38	C₂×SD₃₂×C₅₃	C₄	1	1	yes	characteristic, complemented
39	D₅₃⋊M₁₆	D₄	1	1	yes	characteristic
40	Q₈×#6157	—	2	4	no	—
41	Q₈×#6157	—	4	2	no	—
42	D₄×#6157	—	2	4	no	—
43	D₄×#6157	—	4	2	no	—
44	#13133296	—	2	1	no	—
45	#13133296	—	2	1	no	—
46	#13133296	—	4	2	no	—
47	#13133296	D₄	1	1	yes	characteristic
48	C₂×C₂²⋊#6157	—	4	2	no	—
49	#13133292	—	2	1	no	—
50	#13133291	—	2	1	no	—
51	D₅₃⋊C₁₆	C₂³	1	2	yes	—
52	#13133286	C₂³	1	2	yes	—
53	#13133286	C₂³	1	2	yes	—
54	#13133285	—	2	1	no	—
55	#13133285	—	2	1	no	—
56	#13133280	—	2	4	no	—
57	#13133279	—	2	4	no	—
58	#13133271	D₄	1	2	yes	—
59	C₈×#6157	C₂³	1	2	yes	—
60	C₂×Q₈×D₅₃	—	2	1	no	—
61	C₂×D₄×D₅₃	—	2	1	no	—
62	C₂×Dic₂₁₂	C₂×C₄	1	1	yes	characteristic, complemented
63	C₂×#11719925	—	2	1	no	—
64	Q₁₆×D₅₃	—	2	1	no	—
65	Q₁₆×D₅₃	—	2	1	no	—
66	Q₁₆×D₅₃	C₂×C₄	1	2	yes	complemented
67	Q₁₆×D₅₃	C₂³	1	2	yes	—
68	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic
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	#13133162	C₂×C₄	1	2	yes	complemented
76	#13133162	C₂×C₄	1	2	yes	complemented
77	#13133161	C₂×C₄	1	2	yes	complemented
78	#13133161	C₂×C₄	1	2	yes	complemented
79	#13133160	C₂×C₄	1	2	yes	complemented
80	#13133160	C₂×C₄	1	2	yes	complemented
81	C₂×#11719908	C₂×C₄	1	1	yes	characteristic, complemented
82	C₁₆×D₅₃	C₂×C₄	1	1	yes	characteristic, complemented
83	C₁₆×D₅₃	C₂×C₄	1	1	yes	characteristic, complemented
84	C₁₆×D₅₃	C₂³	1	1	yes	characteristic
85	C₁₆×D₅₃	C₂³	1	1	yes	characteristic
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	Q₈×D₅₃	—	2	2	no	—
97	Q₈×D₅₃	—	2	2	no	—
98	Q₈×D₅₃	—	4	1	no	—
99	Q₈×D₅₃	—	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×C₄×D₅₃	—	4	1	no	—
106	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
107	C₂×Dic₁₀₆	—	2	1	no	—
108	C₂×Dic₁₀₆	—	4	1	no	—
109	C₂²⋊#6157	—	4	1	no	—
110	C₂²⋊#6157	—	4	1	no	—
111	C₂²⋊#6157	—	4	4	no	—
112	C₂²⋊#6157	D₈	1	2	yes	—
113	#11719940	—	2	1	no	—
114	C₄⋊#6157	—	2	2	no	—
115	C₄⋊#6157	—	2	2	no	—
116	C₄⋊#6157	—	4	4	no	—
117	C₄⋊#6157	D₈	1	2	yes	—
118	C₄×#6157	—	4	4	no	—
119	C₄×#6157	—	4	1	no	—
120	C₄×#6157	—	4	1	no	—
121	C₄×#6157	C₂×D₄	1	2	yes	—
122	#11719936	—	2	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	#11719925	—	2	2	no	—
130	#11719925	—	2	2	no	—
131	#11719922	—	2	2	no	—
132	#11719922	—	2	2	no	—
133	C₂×#88322	#41	1	1	yes	characteristic
134	Dic₂₁₂	—	2	1	no	—
135	Dic₂₁₂	C₂²×C₄	1	2	yes	—
136	D₄₂₄	—	2	1	no	—
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	2	no	—
150	C₂²×D₅₃	—	4	2	no	—
151	C₂²×D₅₃	—	16	2	no	—
152	C₂²×D₅₃	C₂×D₈	1	1	yes	characteristic
153	C₂×#6157	—	4	2	no	—
154	C₂×#6157	—	4	2	no	—
155	C₂×#6157	—	16	4	no	—
156	C₂×#6157	C₂×D₈	1	4	yes	—
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	—	4	1	no	—
166	C₂×Dic₅₃	#135	1	1	yes	characteristic
167	D₂₁₂	—	2	2	no	—
168	D₂₁₂	—	4	1	no	—
169	C₄×D₅₃	—	4	2	no	—
170	C₄×D₅₃	—	4	2	no	—
171	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
172	C₄×D₅₃	C₂×D₈	1	1	yes	characteristic
173	C₄×D₅₃	#135	1	1	yes	characteristic
174	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
175	Dic₁₀₆	—	2	2	no	—
176	Dic₁₀₆	—	4	1	no	—
177	Dic₁₀₆	—	4	2	no	—
178	Dic₁₀₆	—	4	2	no	—
179	#88324	—	2	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	#33457	—	53	1	no	maximal, Sylow
185	C₂²×C₅₃	—	4	2	no	—
186	C₂²×C₅₃	—	16	1	no	—
187	C₂²×C₅₃	C₄×D₈	1	1	yes	characteristic
188	C₂×D₅₃	—	2	2	no	—
189	C₂×D₅₃	—	4	2	no	—
190	C₂×D₅₃	—	8	4	no	—
191	C₂×D₅₃	—	16	2	no	—
192	C₂×D₅₃	—	16	1	no	—
193	C₂×D₅₃	C₄×D₈	1	1	yes	characteristic
194	C₂×D₅₃	C₂²×D₈	1	1	yes	characteristic
195	#6157	—	2	4	no	—
196	#6157	—	8	2	no	—
197	#6157	—	8	2	no	—
198	C₄×C₅₃	—	4	2	no	—
199	C₄×C₅₃	C₄×D₈	1	1	yes	characteristic
200	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
201	Dic₅₃	—	4	2	no	—
202	Dic₅₃	C₄×D₈	1	1	yes	characteristic
203	Dic₅₃	C₂×#135	1	1	yes	characteristic
204	C₂²×SD₃₂	—	53	1	no	—
205	#2950	—	53	1	no	—
206	#2948	—	53	1	no	—
207	#2175	—	53	4	no	—
208	C₄×SD₃₂	—	53	4	no	—
209	#2158	—	53	1	no	—
210	#2141	—	53	1	no	—
211	#2140	—	53	1	no	—
212	#2108	—	53	1	no	—
213	C₂×C₅₃	—	2	1	no	—
214	C₂×C₅₃	—	8	2	no	—
215	C₂×C₅₃	C₂×C₄×D₈	1	1	yes	characteristic
216	D₅₃	—	2	1	no	—
217	D₅₃	—	8	2	no	—
218	D₅₃	#3416	1	2	yes	—
219	C₂²×Q₁₆	—	53	1	no	—
220	C₂²×D₈	—	53	1	no	—
221	#519	—	106	1	no	—
222	#518	—	106	1	no	—
223	C₂×SD₃₂	—	53	1	no	—
224	C₂×SD₃₂	—	53	1	no	—
225	C₂×SD₃₂	—	53	2	no	—
226	C₂×SD₃₂	—	53	2	no	—
227	C₂×SD₃₂	—	53	2	no	—
228	C₂×SD₃₂	—	53	2	no	—
229	C₂×SD₃₂	—	53	1	no	—
230	C₂×SD₃₂	#6157	1	1	yes	characteristic, complemented
231	C₂×M₃₂	—	53	1	no	—
232	C₂²×C₁₆	—	53	1	no	—
233	#442	—	106	2	no	—
234	#441	—	106	2	no	—
235	C₄×Q₁₆	—	53	4	no	—
236	C₄×D₈	—	53	4	no	—
237	#427	—	53	1	no	—
238	#427	—	53	1	no	—
239	#419	—	106	1	no	—
240	#418	—	106	1	no	—
241	#405	—	53	1	no	—
242	#367	—	53	2	no	—
243	#366	—	53	2	no	—
244	#358	—	53	4	no	—
245	#357	—	53	4	no	—
246	#346	—	53	2	no	—
247	C₄×C₁₆	—	53	2	no	—
248	C₅₃	#33457	1	1	yes	characteristic, complemented, Sylow
249	C₂²×Q₈	—	106	1	no	—
250	C₂²×D₄	—	106	1	no	—
251	C₂×Q₁₆	—	53	2	no	—
252	C₂×Q₁₆	—	53	2	no	—
253	C₂×Q₁₆	—	53	1	no	—
254	C₂×Q₁₆	—	106	1	no	—
255	C₂×Q₁₆	—	106	1	no	—
256	C₂×Q₁₆	—	106	1	no	—
257	C₂×Q₁₆	C₂×#6157	1	1	yes	characteristic, complemented
258	C₂×D₈	—	53	2	no	—
259	C₂×D₈	—	53	2	no	—
260	C₂×D₈	—	53	1	no	—
261	C₂×D₈	—	106	1	no	—
262	C₂×D₈	—	106	1	no	—
263	C₂×D₈	—	106	1	no	—
264	C₂×D₈	C₂×#6157	1	1	yes	characteristic
265	C₂×M₁₆	—	53	1	no	—
266	C₂²×C₈	—	53	1	no	—
267	C₄×Q₈	—	106	4	no	—
268	C₄×Q₈	—	212	2	no	—
269	C₄×D₄	—	106	4	no	—
270	C₄×D₄	—	212	2	no	—
271	#117	—	53	1	no	—
272	#117	—	106	1	no	—
273	#117	—	106	1	no	—
274	#117	—	212	2	no	—
275	C₂×C₂²⋊C₄	—	212	2	no	—
276	SD₃₂	—	53	2	no	—
277	SD₃₂	—	53	2	no	—
278	SD₃₂	—	53	2	no	—
279	SD₃₂	—	53	2	no	—
280	SD₃₂	—	53	2	no	—
281	SD₃₂	—	53	2	no	—
282	SD₃₂	C₂×#6157	1	2	yes	complemented
283	SD₃₂	C₂×#6157	1	2	yes	complemented
284	M₃₂	—	106	1	no	—
285	M₃₂	—	106	1	no	—
286	C₂×C₁₆	—	53	1	no	—
287	C₂×C₁₆	—	53	1	no	—
288	C₂×C₁₆	—	53	1	no	—
289	C₂×C₁₆	—	53	1	no	—
290	C₂×C₁₆	—	53	1	no	—
291	C₂×C₁₆	—	53	2	no	—
292	C₂×C₁₆	C₂×#6157	1	1	yes	characteristic, complemented
293	#107	—	53	2	no	—
294	#107	—	53	2	no	—
295	#106	—	106	1	no	—
296	#106	—	106	1	no	—
297	#103	—	106	4	no	—
298	#102	—	106	4	no	—
299	#97	—	53	2	no	—
300	C₄×C₈	—	53	2	no	—
301	C₂⁴	—	212	1	no	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	106	2	no	—
304	C₂×Q₈	—	106	2	no	—
305	C₂×Q₈	—	106	1	no	—
306	C₂×Q₈	—	212	1	no	—
307	C₂×Q₈	—	212	1	no	—
308	C₂×Q₈	—	212	1	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	106	2	no	—
311	C₂×D₄	—	106	2	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	C₂²×C₄	—	53	1	no	—
317	C₂²×C₄	—	212	1	no	—
318	C₂²×C₄	—	212	4	no	—
319	Q₁₆	—	2	1	no	—
320	Q₁₆	—	53	2	no	—
321	Q₁₆	—	106	2	no	—
322	Q₁₆	—	106	2	no	—
323	Q₁₆	—	106	1	no	—
324	Q₁₆	C₂²×#6157	1	2	yes	—
325	D₈	—	2	1	no	—
326	D₈	—	53	2	no	—
327	D₈	—	106	2	no	—
328	D₈	—	106	2	no	—
329	D₈	—	106	1	no	—
330	D₈	C₂²×#6157	1	2	yes	—
331	M₁₆	—	106	1	no	—
332	M₁₆	—	106	1	no	—
333	C₂×C₈	—	53	1	no	—
334	C₂×C₈	—	53	1	no	—
335	C₂×C₈	—	53	1	no	—
336	C₂×C₈	—	53	1	no	—
337	C₂×C₈	—	53	1	no	—
338	C₂×C₈	—	53	2	no	—
339	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
340	C₄⋊C₄	—	53	2	no	—
341	C₄⋊C₄	—	106	2	no	—
342	C₄⋊C₄	—	106	2	no	—
343	C₄⋊C₄	—	212	4	no	—
344	C₂²⋊C₄	—	53	2	no	—
345	C₂²⋊C₄	—	212	4	no	—
346	C₂²⋊C₄	—	212	1	no	—
347	C₂²⋊C₄	—	212	1	no	—
348	C₄²	—	53	2	no	—
349	C₄²	—	212	1	no	—
350	C₄²	—	212	1	no	—
351	C₄²	—	212	4	no	—
352	C₁₆	—	53	1	no	—
353	C₁₆	—	53	1	no	—
354	C₁₆	—	106	2	no	—
355	C₁₆	C₂²×#6157	1	1	yes	characteristic
356	C₁₆	C₂²×#6157	1	1	yes	characteristic
357	C₂³	—	4	1	no	—
358	C₂³	—	53	1	no	—
359	C₂³	—	848	2	no	—
360	C₂³	—	212	2	no	—
361	C₂³	—	212	2	no	—
362	C₂³	—	212	1	no	—
363	Q₈	—	2	2	no	—
364	Q₈	—	4	1	no	—
365	Q₈	—	106	2	no	—
366	Q₈	—	212	2	no	—
367	Q₈	—	212	2	no	—
368	Q₈	—	212	1	no	—
369	D₄	—	2	2	no	—
370	D₄	—	4	1	no	—
371	D₄	—	106	2	no	—
372	D₄	—	212	2	no	—
373	D₄	—	212	2	no	—
374	D₄	—	212	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	53	1	no	—
377	C₂×C₄	—	53	1	no	—
378	C₂×C₄	—	53	1	no	—
379	C₂×C₄	—	53	1	no	—
380	C₂×C₄	—	53	1	no	—
381	C₂×C₄	—	53	4	no	—
382	C₂×C₄	—	848	4	no	—
383	C₂×C₄	—	212	2	no	—
384	C₂×C₄	—	212	2	no	—
385	C₂×C₄	—	212	2	no	—
386	C₂×C₄	—	212	2	no	—
387	C₂×C₄	—	212	1	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	D₄×#6157	1	1	yes	characteristic
393	C₈	C₂³×#6157	1	1	yes	characteristic
394	C₂²	—	4	2	no	—
395	C₂²	—	16	1	no	—
396	C₂²	—	53	1	no	—
397	C₂²	—	53	1	no	—
398	C₂²	—	848	1	no	—
399	C₂²	—	848	2	no	—
400	C₂²	—	106	2	no	—
401	C₂²	—	424	4	no	—
402	C₂²	—	212	2	no	—
403	C₂²	D₈×#6157	1	1	yes	characteristic
404	C₄	—	4	2	no	—
405	C₄	—	53	1	no	—
406	C₄	—	53	1	no	—
407	C₄	—	106	4	no	—
408	C₄	—	424	2	no	—
409	C₄	—	424	2	no	—
410	C₄	—	212	2	no	—
411	C₄	D₈×#6157	1	1	yes	characteristic
412	C₄	C₂×D₄×#6157	1	1	yes	characteristic
413	C₂	—	2	1	no	—
414	C₂	—	8	2	no	—
415	C₂	—	53	2	no	—
416	C₂	—	106	1	no	—
417	C₂	—	424	2	no	—
418	C₂	C₂×D₈×#6157	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₈×#6157
commutator	C₈×C₅₃	C₂³×C₄
Frattini	C₈	C₂³×#6157
Fitting	C₂×SD₃₂×C₅₃	C₄
socle	C₂×C₅₃	C₂×C₄×D₈
prime radical	C₂×D₈×D₅₃	C₂²
cosocle	C₈×D₅₃	C₂⁴
hypercenter	C₂×SD₃₂	#6157
hypocenter	C₅₃	#33457
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. #20291476	C₂	semidirect
3. #20291111	C₂	semidirect
4. SD₃₂×#6157	C₂	semidirect
5. #20291066	C₂	semidirect
6. #20291025	C₂	semidirect
8. #20290923	C₂	semidirect
15. Q₁₆×#6157	C₂²	semidirect
22. #16811550	C₂²	semidirect
23. #16811549	C₂²	semidirect
24. #16811536	C₂²	semidirect
26. #16811510	C₂²	semidirect
27. C₁₆×#6157	C₂²	semidirect
30. C₂×#13133162	C₄	semidirect
31. C₂×#13133161	C₄	semidirect
32. C₂×#13133160	C₄	semidirect
33. SD₃₂×D₅₃	C₄	semidirect
34. SD₃₂×D₅₃	C₄	semidirect
38. C₂×SD₃₂×C₅₃	C₄	semidirect
62. C₂×Dic₂₁₂	C₂×C₄	semidirect
66. Q₁₆×D₅₃	C₂×C₄	semidirect
75. #13133162	C₂×C₄	semidirect
76. #13133162	C₂×C₄	semidirect
77. #13133161	C₂×C₄	semidirect
78. #13133161	C₂×C₄	semidirect
79. #13133160	C₂×C₄	semidirect
80. #13133160	C₂×C₄	semidirect
81. C₂×#11719908	C₂×C₄	semidirect
82. C₁₆×D₅₃	C₂×C₄	semidirect
83. C₁₆×D₅₃	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
230. C₂×SD₃₂	#6157	semidirect
248. C₅₃	#33457	semidirect
257. C₂×Q₁₆	C₂×#6157	semidirect
282. SD₃₂	C₂×#6157	semidirect
283. SD₃₂	C₂×#6157	semidirect
292. 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
#20291476	2
#20291474	2
#20291111	2
SD₃₂×#6157	2
#20291066	2
#20291025	2
#20291024	2
#20290923	2
C₂×SD₃₂×D₅₃	2
#33457	53