Subgroups — #28291205

Order 13568.

7812 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288337	C₂	1	6	yes	maximal, complemented
2	#20288323	C₂	1	9	yes	maximal, complemented
3	#20288314	C₂	1	6	yes	maximal, complemented
4	Q₈×#11719949	C₂	1	2	yes	maximal, complemented
5	#20288272	C₂	1	18	yes	maximal, complemented
6	#20288205	C₂	1	6	yes	maximal, complemented
7	#20288010	C₂	1	9	yes	maximal, complemented
8	C₄×#41×D₅₃	C₂	1	6	yes	maximal, complemented
9	C₅₃×#3483	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#41×D₅₃	C₂²	1	6	yes	—
11	#16811359	C₂²	1	9	yes	complemented
12	#16811352	C₂²	1	6	yes	complemented
13	#16811343	C₂²	1	18	yes	complemented
14	#16811334	C₂²	1	18	yes	complemented
15	#16811320	C₂²	1	36	yes	complemented
16	#16811312	C₂²	1	36	yes	complemented
17	#16811303	C₂²	1	36	yes	complemented
18	Q₈×D₂₁₂	C₂²	1	6	yes	complemented
19	#16811280	C₂²	1	12	yes	complemented
20	#16811278	C₂²	1	18	yes	complemented
21	#16811270	C₂²	1	36	yes	complemented
22	#16811258	C₂²	1	9	yes	complemented
23	#16811180	C₂²	1	9	yes	complemented
24	#16811178	C₂²	1	18	yes	complemented
25	#16811171	C₂²	1	18	yes	complemented
26	#16811155	C₂²	1	36	yes	complemented
27	#16811154	C₂²	1	36	yes	complemented
28	#16811152	C₂²	1	36	yes	complemented
29	#16811133	C₂²	1	36	yes	complemented
30	#16811130	C₂²	1	18	yes	complemented
31	#41×Dic₅₃	C₂²	1	6	yes	complemented
32	#41×Dic₅₃	C₂²	1	6	yes	complemented
33	C₄×#11719949	C₂²	1	6	yes	—
34	C₄×#11719949	C₂²	1	2	yes	—
35	C₄×#11719945	C₂²	1	18	yes	complemented
36	#16811091	C₂²	1	18	yes	complemented
37	C₄×#11719947	C₂²	1	18	yes	complemented
38	C₄×#11719947	C₂²	1	18	yes	complemented
39	C₄×Q₈×D₅₃	C₂²	1	6	yes	complemented
40	C₄×Q₈×D₅₃	C₂²	1	6	yes	complemented
41	C₄×D₄×D₅₃	C₂²	1	18	yes	complemented
42	C₄×D₄×D₅₃	C₂²	1	18	yes	complemented
43	#117×D₅₃	C₂²	1	18	yes	complemented
44	C₂×C₄²×D₅₃	C₂²	1	9	yes	complemented
45	Q₈²×C₅₃	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#555	C₂²	1	9	yes	complemented
47	C₅₃×#550	C₂²	1	6	yes	complemented
48	C₅₃×#532	C₂²	1	9	yes	complemented
49	C₄×#41×C₅₃	C₂²	1	6	yes	complemented
50	C₂×#11719949	C₂³	1	2	yes	—
51	C₂×#11719945	C₂³	1	18	yes	—
52	C₂×#11719947	C₂³	1	18	yes	—
53	#41×D₅₃	—	2	48	no	—
54	C₂×Q₈×D₅₃	C₂³	1	6	yes	—
55	C₂×D₄×D₅₃	C₂³	1	18	yes	—
56	C₂²×C₄×D₅₃	C₂³	1	18	yes	—
57	C₂²×C₄×D₅₃	C₂³	1	9	yes	—
58	#13133217	C₂³	1	18	yes	—
59	#13133210	C₂³	1	72	yes	—
60	#13133209	C₂³	1	18	yes	—
61	#13133208	C₂³	1	36	yes	—
62	#13133204	C₂³	1	36	yes	—
63	#13133199	C₂³	1	72	yes	—
64	#13133198	C₂³	1	36	yes	—
65	#13133197	C₂³	1	36	yes	—
66	#13133196	C₂³	1	36	yes	—
67	#13133193	C₂³	1	36	yes	—
68	#13133188	C₂³	1	36	yes	—
69	#13133188	C₂³	1	36	yes	—
70	#13133185	C₂³	1	36	yes	—
71	Q₈×Dic₅₃	C₂³	1	6	yes	—
72	Q₈×Dic₅₃	C₂³	1	2	yes	—
73	Q₈×Dic₅₃	C₂³	1	12	yes	—
74	C₄×Dic₁₀₆	C₂³	1	18	yes	—
75	C₄×Dic₁₀₆	C₂³	1	18	yes	—
76	#13133182	C₂³	1	18	yes	—
77	#13133182	C₂³	1	18	yes	—
78	C₄×D₂₁₂	C₂³	1	18	yes	—
79	C₄×D₂₁₂	C₂³	1	6	yes	—
80	D₄×Dic₅₃	C₂³	1	18	yes	—
81	D₄×Dic₅₃	C₂³	1	18	yes	—
82	D₄×Dic₅₃	C₂³	1	36	yes	—
83	#13133179	C₂³	1	18	yes	—
84	#13133179	C₂³	1	6	yes	—
85	C₄×C₂²⋊D₅₃	C₂³	1	36	yes	—
86	C₄×C₂²⋊D₅₃	C₂³	1	36	yes	—
87	#13133177	C₂³	1	36	yes	—
88	#13133177	C₂³	1	36	yes	—
89	#13133176	C₂³	1	18	yes	—
90	#13133176	C₂³	1	18	yes	—
91	#13133175	C₂³	1	6	yes	—
92	#13133175	C₂³	1	18	yes	—
93	#13133174	C₂³	1	36	yes	—
94	#13133173	C₂³	1	36	yes	—
95	C₄⋊C₄×D₅₃	C₂³	1	18	yes	—
96	C₄⋊C₄×D₅₃	C₂³	1	18	yes	—
97	C₂²⋊C₄×D₅₃	C₂³	1	36	yes	—
98	C₂×C₄×Dic₅₃	C₂³	1	9	yes	—
99	C₂×C₄×Dic₅₃	C₂³	1	18	yes	—
100	C₄²×D₅₃	C₂³	1	6	yes	—
101	C₄²×D₅₃	C₂³	1	18	yes	—
102	C₄²×D₅₃	C₂³	1	18	yes	—
103	C₄²×D₅₃	C₂³	1	18	yes	—
104	C₂×#41×C₅₃	C₂³	1	6	yes	—
105	C₂×#41×C₅₃	C₂³	1	6	yes	—
106	C₄⋊Q₈×C₅₃	C₂³	1	9	yes	—
107	#127×C₅₃	C₂³	1	9	yes	—
108	#124×C₅₃	C₂³	1	18	yes	—
109	#121×C₅₃	C₂³	1	36	yes	—
110	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
111	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
112	C₄×D₄×C₅₃	C₂³	1	18	yes	—
113	C₄×D₄×C₅₃	C₂³	1	18	yes	—
114	#117×C₅₃	C₂³	1	18	yes	—
115	C₂×C₄²×C₅₃	C₂³	1	9	yes	—
116	C₂³×D₅₃	C₂⁴	1	9	yes	—
117	#41×C₅₃	—	2	24	no	—
118	#41×C₅₃	—	4	12	no	—
119	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
120	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
121	C₂×D₄×C₅₃	C₂⁴	1	18	yes	—
122	C₂×D₄×C₅₃	C₂⁴	1	18	yes	—
123	C₂²×C₄×C₅₃	C₂⁴	1	18	yes	—
124	C₂²×C₄×C₅₃	C₂⁴	1	9	yes	—
125	C₂×C₂²⋊D₅₃	C₂⁴	1	36	yes	—
126	C₂²×Dic₅₃	C₂⁴	1	18	yes	—
127	C₂²×Dic₅₃	C₂⁴	1	9	yes	—
128	#11719949	#41	1	16	yes	complemented
129	Q₈×D₅₃	—	2	24	no	—
130	#11719947	—	2	72	no	—
131	D₄×D₅₃	—	2	72	no	—
132	#11719945	—	2	72	no	—
133	C₂×D₂₁₂	C₂⁴	1	6	yes	—
134	C₂×C₄×D₅₃	—	2	72	no	—
135	C₂×C₄×D₅₃	—	4	18	no	—
136	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
137	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
138	C₂×C₄×D₅₃	C₂⁴	1	18	yes	—
139	C₂×C₄×D₅₃	C₂⁴	1	18	yes	—
140	C₂×C₄×D₅₃	C₂⁴	1	18	yes	—
141	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
142	C₂×Dic₁₀₆	C₂⁴	1	18	yes	—
143	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
144	C₄⋊C₄×C₅₃	C₂⁴	1	18	yes	—
145	C₂²⋊C₄×C₅₃	C₂⁴	1	36	yes	—
146	C₄²×C₅₃	C₂⁴	1	6	yes	—
147	C₄²×C₅₃	C₂⁴	1	9	yes	—
148	C₄²×C₅₃	C₂⁴	1	9	yes	—
149	C₂²⋊Dic₅₃	C₂⁴	1	36	yes	—
150	C₂²⋊Dic₅₃	C₂⁴	1	36	yes	—
151	#11719921	C₂⁴	1	12	yes	—
152	#11719921	C₂⁴	1	36	yes	—
153	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
154	C₄⋊Dic₅₃	C₂⁴	1	18	yes	—
155	C₄⋊Dic₅₃	C₂⁴	1	36	yes	—
156	#11719919	C₂⁴	1	36	yes	—
157	#11719919	C₂⁴	1	36	yes	—
158	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
159	C₄×Dic₅₃	C₂⁴	1	6	yes	—
160	C₄×Dic₅₃	C₂⁴	1	6	yes	—
161	C₄×Dic₅₃	C₂⁴	1	18	yes	—
162	C₄×Dic₅₃	C₂⁴	1	18	yes	—
163	C₄×Dic₅₃	C₂⁴	1	9	yes	—
164	C₄×Dic₅₃	C₂⁴	1	18	yes	—
165	C₂³×C₅₃	C₂⁵	1	9	yes	—
166	C₂²×D₅₃	—	2	36	no	—
167	C₂²×D₅₃	—	4	9	no	—
168	C₂²×D₅₃	C₂⁵	1	6	yes	—
169	Q₈×C₅₃	—	4	6	no	—
170	Q₈×C₅₃	C₂×#41	1	8	yes	complemented
171	D₄×C₅₃	—	2	36	no	—
172	D₄×C₅₃	—	4	18	no	—
173	C₂×C₄×C₅₃	—	2	36	no	—
174	C₂×C₄×C₅₃	—	2	18	no	—
175	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
176	C₂×C₄×C₅₃	C₂⁵	1	9	yes	—
177	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
178	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
179	C₂²⋊D₅₃	—	2	72	no	—
180	C₂×Dic₅₃	—	2	36	no	—
181	C₂×Dic₅₃	—	4	9	no	—
182	C₂×Dic₅₃	C₂⁵	1	18	yes	—
183	C₂×Dic₅₃	C₂⁵	1	6	yes	—
184	C₂×Dic₅₃	C₂⁵	1	2	yes	—
185	D₂₁₂	C₂×#41	1	24	yes	complemented
186	C₄×D₅₃	—	2	36	no	—
187	C₄×D₅₃	—	2	36	no	—
188	C₄×D₅₃	—	2	12	no	—
189	C₄×D₅₃	—	2	12	no	—
190	C₄×D₅₃	—	4	18	no	—
191	C₄×D₅₃	C₂×#41	1	24	yes	complemented
192	Dic₁₀₆	—	2	36	no	—
193	#41²	—	53	1	no	maximal, Sylow
194	C₂²×C₅₃	—	2	18	no	—
195	C₂²×C₅₃	—	2	9	no	—
196	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
197	C₂×D₅₃	—	2	6	no	—
198	C₂×D₅₃	—	2	6	no	—
199	C₂×D₅₃	—	4	36	no	—
200	C₂×D₅₃	C₂²×#41	1	12	yes	—
201	C₄×C₅₃	—	2	6	no	—
202	C₄×C₅₃	—	2	9	no	—
203	C₄×C₅₃	C₂²×#41	1	12	yes	—
204	C₄×C₅₃	#585	1	2	yes	—
205	Dic₅₃	—	2	18	no	—
206	Dic₅₃	—	2	6	no	—
207	Dic₅₃	C₂²×#41	1	4	yes	—
208	#3483	D₅₃	1	1	yes	characteristic, complemented
209	#3482	—	53	6	no	—
210	#3481	—	53	9	no	—
211	#3480	—	53	6	no	—
212	Q₈×#41	—	53	2	no	—
213	#3475	—	53	18	no	—
214	D₄×#41	—	53	6	no	—
215	#3444	—	53	9	no	—
216	C₂×C₄×#41	—	53	6	no	—
217	C₂×C₅₃	—	4	9	no	—
218	C₂×C₅₃	C₂³×#41	1	2	yes	—
219	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
220	D₅₃	—	2	12	no	—
221	C₂²×#41	—	53	6	no	—
222	#559	—	53	9	no	—
223	Q₈²	C₂×D₅₃	1	1	yes	characteristic, complemented
224	#557	—	53	6	no	—
225	#556	—	53	18	no	—
226	#555	C₂×D₅₃	1	9	yes	complemented
227	#554	—	53	18	no	—
228	#553	—	53	36	no	—
229	#552	—	53	36	no	—
230	#551	—	53	36	no	—
231	#550	C₂×D₅₃	1	6	yes	complemented
232	D₄×Q₈	—	53	6	no	—
233	#548	—	53	12	no	—
234	#547	—	53	18	no	—
235	#546	—	53	36	no	—
236	D₄²	—	53	9	no	—
237	#533	—	53	18	no	—
238	#533	—	53	9	no	—
239	#532	—	53	18	no	—
240	#532	C₂×D₅₃	1	9	yes	complemented
241	#529	—	53	36	no	—
242	#529	—	53	36	no	—
243	#529	—	53	36	no	—
244	#525	—	53	18	no	—
245	#525	—	53	36	no	—
246	C₄×#41	—	53	6	no	—
247	C₄×#41	—	53	6	no	—
248	C₄×#41	—	53	2	no	—
249	C₄×#41	—	53	6	no	—
250	C₄×#41	—	53	18	no	—
251	C₄×#41	—	53	18	no	—
252	C₄×#41	—	53	18	no	—
253	C₄×#41	—	53	18	no	—
254	C₄×#41	C₂×D₅₃	1	6	yes	complemented
255	C₂×C₄×Q₈	—	53	6	no	—
256	C₂×C₄×Q₈	—	53	6	no	—
257	C₂×C₄×D₄	—	53	18	no	—
258	C₂×C₄×D₄	—	53	18	no	—
259	C₂×#117	—	53	18	no	—
260	C₂²×C₄²	—	53	9	no	—
261	C₅₃	#41²	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	—	53	2	no	—
263	C₂×#41	—	53	18	no	—
264	C₂×#41	—	53	18	no	—
265	C₂×#41	—	106	48	no	—
266	C₂×#41	C₂²×D₅₃	1	6	yes	—
267	C₂×#41	C₂²×D₅₃	1	6	yes	—
268	C₂²×Q₈	—	53	6	no	—
269	C₂²×D₄	—	53	18	no	—
270	C₂³×C₄	—	53	18	no	—
271	C₂³×C₄	—	53	9	no	—
272	C₄⋊Q₈	—	53	18	no	—
273	C₄⋊Q₈	C₂²×D₅₃	1	9	yes	—
274	#127	C₂²×D₅₃	1	9	yes	—
275	#126	—	53	72	no	—
276	#125	—	53	36	no	—
277	#125	—	53	18	no	—
278	#124	—	53	36	no	—
279	#124	C₂²×D₅₃	1	18	yes	—
280	#123	—	53	36	no	—
281	#123	—	53	72	no	—
282	C₂²⋊Q₈	—	53	36	no	—
283	C₂²⋊Q₈	—	53	36	no	—
284	C₂²⋊Q₈	—	53	36	no	—
285	#121	—	53	36	no	—
286	#121	—	53	36	no	—
287	#121	C₂²×D₅₃	1	36	yes	—
288	#120	—	53	36	no	—
289	C₄×Q₈	—	53	2	no	—
290	C₄×Q₈	—	53	6	no	—
291	C₄×Q₈	—	53	12	no	—
292	C₄×Q₈	—	53	18	no	—
293	C₄×Q₈	—	53	18	no	—
294	C₄×Q₈	—	53	18	no	—
295	C₄×Q₈	—	53	18	no	—
296	C₄×Q₈	C₂²×D₅₃	1	2	yes	—
297	C₄×Q₈	C₂²×D₅₃	1	6	yes	—
298	C₄×D₄	—	53	18	no	—
299	C₄×D₄	—	53	18	no	—
300	C₄×D₄	—	53	36	no	—
301	C₄×D₄	—	53	36	no	—
302	C₄×D₄	—	53	36	no	—
303	C₄×D₄	—	53	6	no	—
304	C₄×D₄	—	53	18	no	—
305	C₄×D₄	—	53	36	no	—
306	C₄×D₄	—	53	36	no	—
307	C₄×D₄	—	53	6	no	—
308	C₄×D₄	—	53	18	no	—
309	C₄×D₄	C₂²×D₅₃	1	18	yes	—
310	C₄×D₄	C₂²×D₅₃	1	18	yes	—
311	#117	—	53	18	no	—
312	#117	—	53	18	no	—
313	#117	—	53	6	no	—
314	#117	—	53	18	no	—
315	#117	—	53	36	no	—
316	#117	—	53	36	no	—
317	#117	C₂²×D₅₃	1	18	yes	—
318	C₂×C₄⋊C₄	—	53	18	no	—
319	C₂×C₄⋊C₄	—	53	18	no	—
320	C₂×C₂²⋊C₄	—	53	36	no	—
321	C₂×C₄²	—	53	9	no	—
322	C₂×C₄²	—	53	18	no	—
323	C₂×C₄²	—	53	18	no	—
324	C₂×C₄²	—	53	18	no	—
325	C₂×C₄²	—	53	18	no	—
326	C₂×C₄²	—	53	6	no	—
327	C₂×C₄²	C₂²×D₅₃	1	9	yes	—
328	C₂⁴	—	53	9	no	—
329	#41	—	2	24	no	—
330	#41	—	4	12	no	—
331	#41	—	53	16	no	—
332	#41	—	106	72	no	—
333	#41	—	106	72	no	—
334	C₂×Q₈	—	53	18	no	—
335	C₂×Q₈	—	106	24	no	—
336	C₂×Q₈	C₂³×D₅₃	1	6	yes	—
337	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
338	C₂×D₄	—	53	36	no	—
339	C₂×D₄	—	53	6	no	—
340	C₂×D₄	—	106	72	no	—
341	C₂×D₄	C₂³×D₅₃	1	18	yes	—
342	C₂×D₄	C₂³×D₅₃	1	18	yes	—
343	C₂²×C₄	—	53	6	no	—
344	C₂²×C₄	—	53	18	no	—
345	C₂²×C₄	—	53	9	no	—
346	C₂²×C₄	—	53	6	no	—
347	C₂²×C₄	—	53	18	no	—
348	C₂²×C₄	—	53	18	no	—
349	C₂²×C₄	—	53	6	no	—
350	C₂²×C₄	—	53	18	no	—
351	C₂²×C₄	—	106	72	no	—
352	C₂²×C₄	—	212	18	no	—
353	C₂²×C₄	C₂³×D₅₃	1	18	yes	—
354	C₂²×C₄	C₂³×D₅₃	1	9	yes	—
355	C₄⋊C₄	—	53	6	no	—
356	C₄⋊C₄	—	53	18	no	—
357	C₄⋊C₄	—	53	36	no	—
358	C₄⋊C₄	—	53	36	no	—
359	C₄⋊C₄	—	53	36	no	—
360	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
361	C₄⋊C₄	C₂³×D₅₃	1	18	yes	—
362	C₂²⋊C₄	—	53	36	no	—
363	C₂²⋊C₄	—	53	36	no	—
364	C₂²⋊C₄	—	53	12	no	—
365	C₂²⋊C₄	—	53	36	no	—
366	C₂²⋊C₄	C₂³×D₅₃	1	36	yes	—
367	C₄²	—	53	6	no	—
368	C₄²	—	53	6	no	—
369	C₄²	—	53	18	no	—
370	C₄²	—	53	18	no	—
371	C₄²	—	53	18	no	—
372	C₄²	—	53	1	no	—
373	C₄²	—	53	9	no	—
374	C₄²	C₂³×D₅₃	1	9	yes	—
375	C₄²	C₂³×D₅₃	1	9	yes	—
376	C₄²	C₂³×D₅₃	1	6	yes	—
377	C₂³	—	53	6	no	—
378	C₂³	—	106	36	no	—
379	C₂³	—	212	9	no	—
380	C₂³	C₂⁴×D₅₃	1	9	yes	—
381	Q₈	—	4	6	no	—
382	Q₈	—	106	36	no	—
383	Q₈	#41×D₅₃	1	8	yes	complemented
384	D₄	—	2	36	no	—
385	D₄	—	4	18	no	—
386	D₄	—	53	24	no	—
387	D₄	—	106	72	no	—
388	C₂×C₄	—	2	36	no	—
389	C₂×C₄	—	2	18	no	—
390	C₂×C₄	—	53	2	no	—
391	C₂×C₄	—	53	24	no	—
392	C₂×C₄	—	53	6	no	—
393	C₂×C₄	—	53	18	no	—
394	C₂×C₄	—	106	12	no	—
395	C₂×C₄	—	106	36	no	—
396	C₂×C₄	—	106	36	no	—
397	C₂×C₄	—	106	36	no	—
398	C₂×C₄	—	106	12	no	—
399	C₂×C₄	—	212	18	no	—
400	C₂×C₄	—	212	9	no	—
401	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
402	C₂×C₄	C₂⁴×D₅₃	1	9	yes	—
403	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
404	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
405	C₂²	—	2	18	no	—
406	C₂²	—	2	9	no	—
407	C₂²	—	53	12	no	—
408	C₂²	—	106	6	no	—
409	C₂²	—	106	6	no	—
410	C₂²	—	212	36	no	—
411	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
412	C₄	—	2	6	no	—
413	C₄	—	2	9	no	—
414	C₄	—	53	4	no	—
415	C₄	—	106	18	no	—
416	C₄	—	106	6	no	—
417	C₄	C₂×#41×D₅₃	1	12	yes	—
418	C₄	#16811458	1	2	yes	—
419	C₂	—	4	9	no	—
420	C₂	—	106	12	no	—
421	C₂	C₂²×#41×D₅₃	1	2	yes	—
422	C₂	C₂×#16811458	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₅₃×#3483	C₂
hypercenter	#3483	D₅₃
hypocenter	C₅₃	#41²
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #3483

Complements

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

N	H ≅ G/N	type
1. #20288337	C₂	semidirect
2. #20288323	C₂	semidirect
3. #20288314	C₂	semidirect
4. Q₈×#11719949	C₂	semidirect
5. #20288272	C₂	semidirect
6. #20288205	C₂	semidirect
7. #20288010	C₂	semidirect
8. C₄×#41×D₅₃	C₂	semidirect
9. C₅₃×#3483	C₂	semidirect
11. #16811359	C₂²	semidirect
12. #16811352	C₂²	semidirect
13. #16811343	C₂²	semidirect
14. #16811334	C₂²	semidirect
15. #16811320	C₂²	semidirect
16. #16811312	C₂²	semidirect
17. #16811303	C₂²	semidirect
18. Q₈×D₂₁₂	C₂²	semidirect
19. #16811280	C₂²	semidirect
20. #16811278	C₂²	semidirect
21. #16811270	C₂²	semidirect
22. #16811258	C₂²	semidirect
23. #16811180	C₂²	semidirect
24. #16811178	C₂²	semidirect
25. #16811171	C₂²	semidirect
26. #16811155	C₂²	semidirect
27. #16811154	C₂²	semidirect
28. #16811152	C₂²	semidirect
29. #16811133	C₂²	semidirect
30. #16811130	C₂²	semidirect
31. #41×Dic₅₃	C₂²	semidirect
32. #41×Dic₅₃	C₂²	semidirect
35. C₄×#11719945	C₂²	semidirect
36. #16811091	C₂²	semidirect
37. C₄×#11719947	C₂²	semidirect
38. C₄×#11719947	C₂²	semidirect
39. C₄×Q₈×D₅₃	C₂²	semidirect
40. C₄×Q₈×D₅₃	C₂²	semidirect
41. C₄×D₄×D₅₃	C₂²	semidirect
42. C₄×D₄×D₅₃	C₂²	semidirect
43. #117×D₅₃	C₂²	semidirect
44. C₂×C₄²×D₅₃	C₂²	semidirect
45. Q₈²×C₅₃	C₂²	semidirect
46. C₅₃×#555	C₂²	semidirect
47. C₅₃×#550	C₂²	semidirect
48. C₅₃×#532	C₂²	semidirect
49. C₄×#41×C₅₃	C₂²	semidirect
128. #11719949	#41	semidirect
170. Q₈×C₅₃	C₂×#41	semidirect
185. D₂₁₂	C₂×#41	semidirect
191. C₄×D₅₃	C₂×#41	semidirect
208. #3483	D₅₃	semidirect
223. Q₈²	C₂×D₅₃	semidirect
226. #555	C₂×D₅₃	semidirect
231. #550	C₂×D₅₃	semidirect
240. #532	C₂×D₅₃	semidirect
254. C₄×#41	C₂×D₅₃	semidirect
261. C₅₃	#41²	semidirect
383. Q₈	#41×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20288337	2
#20288323	2
#20288314	2
Q₈×#11719949	2
#20288272	2
#20288205	2
#20288010	2
C₄×#41×D₅₃	2
C₅₃×#3483	2
#41²	53