Subgroups — Q₈×#102×C₅₃ #27230030

Order 13568.

1314 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₄⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#1990	C₂	1	3	yes	maximal, complemented
5	C₅₃×#1988	C₂	1	3	yes	maximal, complemented
6	C₅₃×#1802	C₂	1	3	yes	maximal
7	C₄×#102×C₅₃	C₂	1	3	yes	maximal
8	C₂³×Q₈×C₅₃	—	2	1	no	—
9	D₄×Q₈×C₅₃	—	2	4	no	—
10	D₄×Q₈×C₅₃	C₄	1	8	yes	complemented
11	C₂×C₄⋊Q₈×C₅₃	C₂²	1	3	yes	—
12	C₂×C₂²⋊Q₈×C₅₃	—	2	3	no	—
13	C₂×C₄×Q₈×C₅₃	—	2	1	no	—
14	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₅₃	C₂²	1	3	yes	—
16	C₈×Q₈×C₅₃	—	2	4	no	—
17	C₂×C₄⋊C₈×C₅₃	C₂²	1	3	yes	—
18	C₂×#102×C₅₃	C₂²	1	3	yes	—
19	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₅₃	C₂²	1	3	yes	—
21	C₅₃×#389	—	2	3	no	—
22	C₅₃×#384	C₂²	1	3	yes	—
23	C₄×C₄⋊C₄×C₅₃	C₂²	1	3	yes	—
24	C₅₃×#340	C₂²	1	3	yes	—
25	C₅₃×#340	C₂²	1	6	yes	—
26	C₅₃×#340	C₂²	1	3	yes	—
27	C₂²×Q₈×C₅₃	—	2	8	no	—
28	C₂²×Q₈×C₅₃	—	2	3	no	—
29	C₂²×Q₈×C₅₃	—	4	4	no	—
30	C₂²×Q₈×C₅₃	—	4	4	no	—
31	C₂²×Q₈×C₅₃	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₅₃	—	2	3	no	—
34	C₂²×C₈×C₅₃	C₂³	1	3	yes	—
35	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
36	C₄⋊Q₈×C₅₃	—	2	6	no	—
37	C₄⋊Q₈×C₅₃	C₂×C₄	1	12	yes	—
38	C₂²⋊Q₈×C₅₃	—	2	24	no	—
39	C₄×Q₈×C₅₃	—	4	4	no	—
40	C₄×Q₈×C₅₃	C₂×C₄	1	4	yes	—
41	C₄×Q₈×C₅₃	D₄	1	4	yes	—
42	C₄×D₄×C₅₃	—	2	6	no	—
43	C₄×D₄×C₅₃	C₂×C₄	1	12	yes	—
44	C₂×C₄⋊C₄×C₅₃	—	2	3	no	—
45	C₂×C₄⋊C₄×C₅₃	—	2	3	no	—
46	C₂×C₄⋊C₄×C₅₃	—	2	3	no	—
47	C₂×C₄⋊C₄×C₅₃	D₄	1	3	yes	—
48	C₂×C₄⋊C₄×C₅₃	C₂³	1	3	yes	—
49	C₂×C₄⋊C₄×C₅₃	C₂³	1	3	yes	—
50	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×C₅₃	—	2	3	no	—
52	C₂×C₄²×C₅₃	—	2	3	no	—
53	C₂×C₄²×C₅₃	C₂³	1	3	yes	—
54	C₄⋊C₈×C₅₃	—	2	6	no	—
55	#102×C₅₃	—	2	6	no	—
56	#102×C₅₃	Q₈	1	4	yes	direct product factor
57	C₄×C₈×C₅₃	—	2	6	no	—
58	#95×C₅₃	—	2	3	no	—
59	C₂⁴×C₅₃	—	2	1	no	—
60	C₂×Q₈×C₅₃	—	2	12	no	—
61	C₂×Q₈×C₅₃	—	4	32	no	—
62	C₂×Q₈×C₅₃	—	4	6	no	—
63	C₂×Q₈×C₅₃	—	4	6	no	—
64	C₂×Q₈×C₅₃	C₂²⋊C₄	1	4	yes	—
65	C₂×Q₈×C₅₃	D₈	1	4	yes	—
66	C₂×Q₈×C₅₃	SD₁₆	1	4	yes	—
67	C₂×D₄×C₅₃	—	2	1	no	—
68	C₂×D₄×C₅₃	—	2	1	no	—
69	C₂×D₄×C₅₃	—	2	1	no	—
70	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
71	C₂×D₄×C₅₃	C₂×Q₈	1	2	yes	—
72	C₂×D₄×C₅₃	#41	1	2	yes	—
73	C₂²×C₄×C₅₃	—	2	1	no	—
74	C₂²×C₄×C₅₃	—	2	3	no	—
75	C₂²×C₄×C₅₃	—	2	12	no	—
76	C₂²×C₄×C₅₃	—	2	3	no	—
77	C₂²×C₄×C₅₃	—	4	6	no	—
78	C₂²×C₄×C₅₃	—	4	6	no	—
79	C₂²×C₄×C₅₃	C₂×D₄	1	3	yes	—
80	C₂²×C₄×C₅₃	C₂×D₄	1	3	yes	—
81	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
82	C₂×C₈×C₅₃	—	2	1	no	—
83	C₂×C₈×C₅₃	—	2	1	no	—
84	C₂×C₈×C₅₃	—	2	3	no	—
85	C₂×C₈×C₅₃	—	2	3	no	—
86	C₂×C₈×C₅₃	—	2	3	no	—
87	C₂×C₈×C₅₃	C₂×Q₈	1	2	yes	complemented
88	C₄⋊C₄×C₅₃	—	2	12	no	—
89	C₄⋊C₄×C₅₃	—	2	3	no	—
90	C₄⋊C₄×C₅₃	—	2	1	no	—
91	C₄⋊C₄×C₅₃	—	2	3	no	—
92	C₄⋊C₄×C₅₃	—	2	3	no	—
93	C₄⋊C₄×C₅₃	—	4	6	no	—
94	C₄⋊C₄×C₅₃	—	8	3	no	—
95	C₄⋊C₄×C₅₃	C₂²⋊C₄	1	12	yes	—
96	C₄⋊C₄×C₅₃	C₂²×C₄	1	6	yes	—
97	C₄⋊C₄×C₅₃	C₂×Q₈	1	2	yes	complemented
98	C₂²⋊C₄×C₅₃	—	2	12	no	—
99	C₄²×C₅₃	—	4	6	no	—
100	C₄²×C₅₃	C₂²×C₄	1	6	yes	—
101	C₄²×C₅₃	C₂×D₄	1	6	yes	—
102	C₂³×C₅₃	—	2	2	no	—
103	C₂³×C₅₃	—	2	2	no	—
104	C₂³×C₅₃	—	2	2	no	—
105	C₂³×C₅₃	—	4	1	no	—
106	C₂³×C₅₃	—	4	1	no	—
107	C₂³×C₅₃	—	4	1	no	—
108	C₂³×C₅₃	—	4	1	no	—
109	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
110	Q₈×C₅₃	—	4	24	no	—
111	Q₈×C₅₃	#102	1	16	yes	direct product factor
112	D₄×C₅₃	—	2	2	no	—
113	D₄×C₅₃	—	2	2	no	—
114	D₄×C₅₃	—	2	2	no	—
115	D₄×C₅₃	C₄×Q₈	1	4	yes	complemented
116	C₂×C₄×C₅₃	—	2	3	no	—
117	C₂×C₄×C₅₃	—	2	3	no	—
118	C₂×C₄×C₅₃	—	2	6	no	—
119	C₂×C₄×C₅₃	—	2	2	no	—
120	C₂×C₄×C₅₃	—	4	3	no	—
121	C₂×C₄×C₅₃	—	4	1	no	—
122	C₂×C₄×C₅₃	—	4	3	no	—
123	C₂×C₄×C₅₃	—	4	1	no	—
124	C₂×C₄×C₅₃	—	4	24	no	—
125	C₂×C₄×C₅₃	—	4	3	no	—
126	C₂×C₄×C₅₃	—	4	3	no	—
127	C₂×C₄×C₅₃	—	4	3	no	—
128	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	6	yes	—
129	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	6	yes	—
130	C₂×C₄×C₅₃	C₂×D₈	1	6	yes	—
131	C₂×C₄×C₅₃	C₂×SD₁₆	1	6	yes	—
132	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
133	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
135	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
136	C₂×C₄×C₅₃	2₋¹⁺⁴	1	1	yes	characteristic
137	C₂×C₄×C₅₃	2₋¹⁺⁴	1	1	yes	characteristic
138	C₈×C₅₃	—	2	2	no	—
139	C₈×C₅₃	—	4	3	no	—
140	Q₈×#102	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂²×C₅₃	—	2	4	no	—
142	C₂²×C₅₃	—	4	2	no	—
143	C₂²×C₅₃	—	4	2	no	—
144	C₂²×C₅₃	—	4	2	no	—
145	C₂²×C₅₃	—	4	2	no	—
146	C₂²×C₅₃	—	4	2	no	—
147	C₂²×C₅₃	—	4	2	no	—
148	C₂²×C₅₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₅₃	#548	1	1	yes	characteristic
150	C₂²×C₅₃	D₄×Q₈	1	1	yes	characteristic
151	C₂²×C₅₃	C₂²×D₈	1	1	yes	characteristic
152	C₂²×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
153	C₂²×C₅₃	#577	1	1	yes	characteristic
154	C₂²×C₅₃	#578	1	1	yes	characteristic
155	C₄×C₅₃	—	2	6	no	—
156	C₄×C₅₃	—	4	2	no	—
157	C₄×C₅₃	—	4	6	no	—
158	C₄×C₅₃	—	8	3	no	—
159	C₄×C₅₃	C₂×#102	1	12	yes	—
160	C₄×C₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
161	C₄×C₅₃	#519	1	1	yes	characteristic
162	C₄×C₅₃	#548	1	1	yes	characteristic
163	C₄×C₅₃	D₄×Q₈	1	1	yes	characteristic
164	C₂×D₄×Q₈	C₂×C₅₃	1	1	yes	characteristic
165	C₂×C₈×Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
166	Q₈×C₄⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
167	#1990	C₂×C₅₃	1	3	yes	complemented
168	#1988	C₂×C₅₃	1	3	yes	complemented
169	#1802	C₂×C₅₃	1	3	yes	—
170	C₄×#102	C₂×C₅₃	1	3	yes	—
171	C₂×C₅₃	—	4	4	no	—
172	C₂×C₅₃	Q₈×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₅₃	C₂²×#102	1	1	yes	characteristic
174	C₂×C₅₃	#2898	1	1	yes	characteristic
175	C₂×C₅₃	#3358	1	1	yes	characteristic
176	C₂×C₅₃	#3359	1	1	yes	characteristic
177	C₂×C₅₃	Q₈×D₈	1	1	yes	characteristic
178	C₂×C₅₃	Q₈×SD₁₆	1	1	yes	characteristic
179	C₂³×Q₈	—	2	1	no	—
180	D₄×Q₈	—	2	4	no	—
181	D₄×Q₈	C₄×C₅₃	1	8	yes	complemented
182	C₂×C₄⋊Q₈	C₂²×C₅₃	1	3	yes	—
183	C₂×C₂²⋊Q₈	—	2	3	no	—
184	C₂×C₄×Q₈	—	2	1	no	—
185	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
186	C₂×C₄×D₄	C₂²×C₅₃	1	3	yes	—
187	C₈×Q₈	—	2	4	no	—
188	C₂×C₄⋊C₈	C₂²×C₅₃	1	3	yes	—
189	C₂×#102	C₂²×C₅₃	1	3	yes	—
190	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
191	C₂×C₄×C₈	C₂²×C₅₃	1	3	yes	—
192	#389	—	2	3	no	—
193	#384	C₂²×C₅₃	1	3	yes	—
194	C₄×C₄⋊C₄	C₂²×C₅₃	1	3	yes	—
195	#340	C₂²×C₅₃	1	6	yes	—
196	#340	C₂²×C₅₃	1	3	yes	—
197	#340	C₂²×C₅₃	1	3	yes	—
198	C₅₃	Q₈×#102	1	1	yes	characteristic, direct product factor, Sylow
199	C₂²×Q₈	—	2	8	no	—
200	C₂²×Q₈	—	2	3	no	—
201	C₂²×Q₈	—	4	4	no	—
202	C₂²×Q₈	—	4	4	no	—
203	C₂²×Q₈	D₄×C₅₃	1	1	yes	characteristic
204	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
205	C₂³×C₄	—	2	3	no	—
206	C₂²×C₈	C₂³×C₅₃	1	3	yes	—
207	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
208	C₄⋊Q₈	—	2	6	no	—
209	C₄⋊Q₈	C₂×C₄×C₅₃	1	12	yes	—
210	C₂²⋊Q₈	—	2	24	no	—
211	C₄×Q₈	—	4	4	no	—
212	C₄×Q₈	C₂×C₄×C₅₃	1	4	yes	—
213	C₄×Q₈	D₄×C₅₃	1	4	yes	—
214	C₄×D₄	—	2	6	no	—
215	C₄×D₄	C₂×C₄×C₅₃	1	12	yes	—
216	C₂×C₄⋊C₄	—	2	3	no	—
217	C₂×C₄⋊C₄	—	2	3	no	—
218	C₂×C₄⋊C₄	—	2	3	no	—
219	C₂×C₄⋊C₄	D₄×C₅₃	1	3	yes	—
220	C₂×C₄⋊C₄	C₂³×C₅₃	1	3	yes	—
221	C₂×C₄⋊C₄	C₂³×C₅₃	1	3	yes	—
222	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
223	C₂×C₂²⋊C₄	—	2	3	no	—
224	C₂×C₄²	—	2	3	no	—
225	C₂×C₄²	C₂³×C₅₃	1	3	yes	—
226	C₄⋊C₈	—	2	6	no	—
227	#102	—	2	6	no	—
228	#102	Q₈×C₅₃	1	4	yes	direct product factor
229	C₄×C₈	—	2	6	no	—
230	#95	—	2	3	no	—
231	C₂⁴	—	2	1	no	—
232	C₂×Q₈	—	2	12	no	—
233	C₂×Q₈	—	4	32	no	—
234	C₂×Q₈	—	4	6	no	—
235	C₂×Q₈	—	4	6	no	—
236	C₂×Q₈	C₂²⋊C₄×C₅₃	1	4	yes	—
237	C₂×Q₈	D₈×C₅₃	1	4	yes	—
238	C₂×Q₈	SD₁₆×C₅₃	1	4	yes	—
239	C₂×D₄	—	2	1	no	—
240	C₂×D₄	—	2	1	no	—
241	C₂×D₄	—	2	1	no	—
242	C₂×D₄	C₂²×C₄×C₅₃	1	2	yes	—
243	C₂×D₄	C₂×Q₈×C₅₃	1	2	yes	—
244	C₂×D₄	#41×C₅₃	1	2	yes	—
245	C₂²×C₄	—	2	1	no	—
246	C₂²×C₄	—	2	3	no	—
247	C₂²×C₄	—	2	12	no	—
248	C₂²×C₄	—	2	3	no	—
249	C₂²×C₄	—	4	6	no	—
250	C₂²×C₄	—	4	6	no	—
251	C₂²×C₄	C₂×D₄×C₅₃	1	3	yes	—
252	C₂²×C₄	C₂×D₄×C₅₃	1	3	yes	—
253	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
254	C₂×C₈	—	2	1	no	—
255	C₂×C₈	—	2	1	no	—
256	C₂×C₈	—	2	3	no	—
257	C₂×C₈	—	2	3	no	—
258	C₂×C₈	—	2	3	no	—
259	C₂×C₈	C₂×Q₈×C₅₃	1	2	yes	complemented
260	C₄⋊C₄	—	2	12	no	—
261	C₄⋊C₄	—	2	3	no	—
262	C₄⋊C₄	—	2	1	no	—
263	C₄⋊C₄	—	2	3	no	—
264	C₄⋊C₄	—	2	3	no	—
265	C₄⋊C₄	—	4	6	no	—
266	C₄⋊C₄	—	8	3	no	—
267	C₄⋊C₄	C₂²⋊C₄×C₅₃	1	12	yes	—
268	C₄⋊C₄	C₂²×C₄×C₅₃	1	6	yes	—
269	C₄⋊C₄	C₂×Q₈×C₅₃	1	2	yes	complemented
270	C₂²⋊C₄	—	2	12	no	—
271	C₄²	—	4	6	no	—
272	C₄²	C₂²×C₄×C₅₃	1	6	yes	—
273	C₄²	C₂×D₄×C₅₃	1	6	yes	—
274	C₂³	—	2	2	no	—
275	C₂³	—	2	2	no	—
276	C₂³	—	2	2	no	—
277	C₂³	—	4	1	no	—
278	C₂³	—	4	1	no	—
279	C₂³	—	4	1	no	—
280	C₂³	—	4	1	no	—
281	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
282	Q₈	—	4	24	no	—
283	Q₈	#102×C₅₃	1	16	yes	direct product factor
284	D₄	—	2	2	no	—
285	D₄	—	2	2	no	—
286	D₄	—	2	2	no	—
287	D₄	C₄×Q₈×C₅₃	1	4	yes	complemented
288	C₂×C₄	—	2	3	no	—
289	C₂×C₄	—	2	3	no	—
290	C₂×C₄	—	2	6	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	4	1	no	—
293	C₂×C₄	—	4	3	no	—
294	C₂×C₄	—	4	3	no	—
295	C₂×C₄	—	4	1	no	—
296	C₂×C₄	—	4	24	no	—
297	C₂×C₄	—	4	3	no	—
298	C₂×C₄	—	4	3	no	—
299	C₂×C₄	—	4	3	no	—
300	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	6	yes	—
301	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	6	yes	—
302	C₂×C₄	C₂×D₈×C₅₃	1	6	yes	—
303	C₂×C₄	C₂×SD₁₆×C₅₃	1	6	yes	—
304	C₂×C₄	C₂³×C₄×C₅₃	1	1	yes	characteristic
305	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
306	C₂×C₄	C₂²×Q₈×C₅₃	1	1	yes	characteristic
307	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
308	C₂×C₄	2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
309	C₂×C₄	2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
310	C₈	—	2	2	no	—
311	C₈	—	4	3	no	—
312	C₂²	—	2	4	no	—
313	C₂²	—	4	2	no	—
314	C₂²	—	4	2	no	—
315	C₂²	—	4	2	no	—
316	C₂²	—	4	2	no	—
317	C₂²	—	4	2	no	—
318	C₂²	—	4	2	no	—
319	C₂²	C₂²×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
320	C₂²	C₅₃×#548	1	1	yes	characteristic
321	C₂²	D₄×Q₈×C₅₃	1	1	yes	characteristic
322	C₂²	C₂²×D₈×C₅₃	1	1	yes	characteristic
323	C₂²	C₂²×SD₁₆×C₅₃	1	1	yes	characteristic
324	C₂²	C₅₃×#577	1	1	yes	characteristic
325	C₂²	C₅₃×#578	1	1	yes	characteristic
326	C₄	—	2	6	no	—
327	C₄	—	4	2	no	—
328	C₄	—	4	6	no	—
329	C₄	—	8	3	no	—
330	C₄	C₂×#102×C₅₃	1	12	yes	—
331	C₄	C₂×C₄×Q₈×C₅₃	1	1	yes	characteristic
332	C₄	C₅₃×#519	1	1	yes	characteristic
333	C₄	C₅₃×#548	1	1	yes	characteristic
334	C₄	D₄×Q₈×C₅₃	1	1	yes	characteristic
335	C₂	—	4	4	no	—
336	C₂	Q₈×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
337	C₂	C₂²×#102×C₅₃	1	1	yes	characteristic
338	C₂	C₅₃×#2898	1	1	yes	characteristic
339	C₂	C₅₃×#3358	1	1	yes	characteristic
340	C₂	C₅₃×#3359	1	1	yes	characteristic
341	C₂	Q₈×D₈×C₅₃	1	1	yes	characteristic
342	C₂	Q₈×SD₁₆×C₅₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
prime radical	C₂²×D₄×C₅₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×C₄×Q₈×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×Q₈×C₅₃	C₂	semidirect
3. Q₈×C₄⋊C₄×C₅₃	C₂	semidirect
4. C₅₃×#1990	C₂	semidirect
5. C₅₃×#1988	C₂	semidirect
10. D₄×Q₈×C₅₃	C₄	semidirect
56. #102×C₅₃	Q₈	direct (N × H)
87. C₂×C₈×C₅₃	C₂×Q₈	semidirect
97. C₄⋊C₄×C₅₃	C₂×Q₈	semidirect
111. Q₈×C₅₃	#102	direct (N × H)
115. D₄×C₅₃	C₄×Q₈	semidirect
140. Q₈×#102	C₅₃	direct (N × H)
165. C₂×C₈×Q₈	C₂×C₅₃	semidirect
166. Q₈×C₄⋊C₄	C₂×C₅₃	semidirect
167. #1990	C₂×C₅₃	semidirect
168. #1988	C₂×C₅₃	semidirect
181. D₄×Q₈	C₄×C₅₃	semidirect
198. C₅₃	Q₈×#102	direct (N × H)
228. #102	Q₈×C₅₃	direct (N × H)
259. C₂×C₈	C₂×Q₈×C₅₃	semidirect
269. C₄⋊C₄	C₂×Q₈×C₅₃	semidirect
283. Q₈	#102×C₅₃	direct (N × H)
287. D₄	C₄×Q₈×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₅₃	2
C₂×C₈×Q₈×C₅₃	2
Q₈×C₄⋊C₄×C₅₃	2
C₅₃×#1990	2
C₅₃×#1988	2
C₅₃×#1802	2
C₄×#102×C₅₃	2
Q₈×#102	53

Subgroups — Q8×#102×C53 #27230030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#102×C₅₃ #27230030