Subgroups — #27537503

Order 13568.

652 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20287849	C₂	1	1	yes	maximal, characteristic
2	C₂×#16810741	C₂	1	1	yes	maximal, characteristic, complemented
3	#20276599	C₂	1	4	yes	maximal, complemented
4	#20276594	C₂	1	4	yes	maximal, complemented
5	#20276509	C₂	1	1	yes	maximal, characteristic, complemented
6	#20276443	C₂	1	1	yes	maximal, characteristic, complemented
7	#20276442	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#13133157	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13133239	C₂²	1	1	yes	characteristic
11	C₂×#13133223	—	2	1	no	—
12	#16811064	C₄	1	2	yes	complemented
13	#16811063	C₄	1	2	yes	complemented
14	#16811059	C₄	1	2	yes	complemented
15	#16811058	C₄	1	2	yes	complemented
16	#16811053	C₂²	1	4	yes	—
17	C₂×#13133157	C₂²	1	1	yes	characteristic
18	C₂×#13133157	C₂²	1	1	yes	characteristic
19	#16810741	—	2	1	no	—
20	#16810741	—	2	1	no	—
21	#16810741	C₂²	1	2	yes	complemented
22	#16810741	C₂²	1	2	yes	complemented
23	C₂×#13133153	C₂²	1	1	yes	characteristic
24	C₂×#13133145	—	2	1	no	—
25	#16810452	C₂²	1	4	yes	complemented
26	#16810430	C₂²	1	4	yes	complemented
27	#16810429	C₂²	1	4	yes	complemented
28	#16810399	C₂²	1	2	yes	complemented
29	C₄×#11719908	C₂²	1	2	yes	complemented
30	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×#131×C₅₃	—	2	1	no	—
32	C₅₃×#443	—	2	1	no	—
33	C₅₃×#443	—	2	1	no	—
34	C₅₃×#443	C₂²	1	2	yes	complemented
35	C₅₃×#443	C₂²	1	2	yes	complemented
36	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#104×C₅₃	—	2	1	no	—
38	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#11719945	—	2	1	no	—
40	#13133239	—	2	1	no	—
41	#13133239	—	2	1	no	—
42	#13133239	C₂×C₄	1	2	yes	—
43	#13133239	C₂³	1	2	yes	—
44	C₂×Dic₂₁₂	C₂×C₄	1	1	yes	characteristic
45	C₂×#11719913	—	2	1	no	—
46	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic
47	#13133223	—	2	2	no	—
48	#13133223	—	2	2	no	—
49	#13133223	—	4	1	no	—
50	#13133223	—	4	1	no	—
51	C₂×#11719917	—	2	1	no	—
52	C₂×#11719912	—	4	1	no	—
53	C₂×C₈×D₅₃	—	4	1	no	—
54	#13133163	C₂×C₄	1	4	yes	complemented
55	#13133161	C₂×C₄	1	4	yes	complemented
56	#13133160	C₂×C₄	1	4	yes	complemented
57	#13133158	C₂×C₄	1	4	yes	complemented
58	#13133157	—	2	1	no	—
59	#13133157	—	2	1	no	—
60	#13133157	C₂×C₄	1	2	yes	—
61	#13133157	C₂×C₄	1	2	yes	—
62	C₂×#11719908	C₂³	1	2	yes	—
63	C₂×#11719908	C₂³	1	2	yes	—
64	#13133153	—	2	1	no	—
65	#13133153	C₂³	1	2	yes	—
66	#13133145	—	2	2	no	—
67	#13133145	—	2	2	no	—
68	C₂×#41×C₅₃	—	2	1	no	—
69	#135×C₅₃	—	2	1	no	—
70	#135×C₅₃	—	2	1	no	—
71	#135×C₅₃	C₂×C₄	1	2	yes	—
72	#135×C₅₃	C₂³	1	2	yes	—
73	C₂×Q₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
74	C₂×SD₁₆×C₅₃	—	2	1	no	—
75	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic
76	#131×C₅₃	—	2	2	no	—
77	#131×C₅₃	—	2	2	no	—
78	#131×C₅₃	—	4	1	no	—
79	#131×C₅₃	—	4	1	no	—
80	C₂×M₁₆×C₅₃	—	2	1	no	—
81	C₂×M₁₆×C₅₃	—	4	1	no	—
82	C₂²×C₈×C₅₃	—	4	1	no	—
83	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
84	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
86	#108×C₅₃	—	2	1	no	—
87	#108×C₅₃	C₂³	1	2	yes	—
88	#104×C₅₃	—	2	2	no	—
89	#104×C₅₃	—	2	2	no	—
90	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
91	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
92	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
94	#41×C₅₃	—	2	2	no	—
95	#41×C₅₃	—	2	2	no	—
96	#41×C₅₃	—	4	1	no	—
97	#41×C₅₃	—	4	1	no	—
98	C₂×Q₈×C₅₃	—	2	1	no	—
99	C₂×D₄×C₅₃	—	2	1	no	—
100	C₂×D₄×C₅₃	—	4	1	no	—
101	C₂²×C₄×C₅₃	—	2	1	no	—
102	C₂²×C₄×C₅₃	—	4	1	no	—
103	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
104	C₂×C₂²⋊D₅₃	—	4	1	no	—
105	#11719945	—	2	2	no	—
106	#11719945	—	2	2	no	—
107	#11719945	—	4	1	no	—
108	#11719945	—	4	1	no	—
109	C₂×D₂₁₂	—	2	1	no	—
110	C₂×C₄×D₅₃	—	4	1	no	—
111	C₂×Dic₁₀₆	—	2	1	no	—
112	Q₁₆×C₅₃	—	2	1	no	—
113	Q₁₆×C₅₃	C₂²×C₄	1	2	yes	—
114	SD₁₆×C₅₃	—	2	2	no	—
115	SD₁₆×C₅₃	—	2	2	no	—
116	D₈×C₅₃	—	2	1	no	—
117	D₈×C₅₃	C₂²×C₄	1	2	yes	—
118	M₁₆×C₅₃	—	2	2	no	—
119	M₁₆×C₅₃	—	4	1	no	—
120	M₁₆×C₅₃	—	4	2	no	—
121	M₁₆×C₅₃	—	4	2	no	—
122	C₂×C₈×C₅₃	—	4	1	no	—
123	C₂×C₈×C₅₃	—	4	2	no	—
124	C₂×C₈×C₅₃	—	4	2	no	—
125	C₂×C₈×C₅₃	D₈	1	1	yes	characteristic
126	C₂×C₈×C₅₃	D₈	1	1	yes	characteristic
127	C₂×C₈×C₅₃	D₈	1	1	yes	characteristic
128	C₂×C₈×C₅₃	D₈	1	1	yes	characteristic
129	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
135	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
136	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
137	C₄²×C₅₃	—	2	1	no	—
138	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
140	#11719917	—	2	2	no	—
141	#11719917	—	4	1	no	—
142	C₂×#88322	—	4	1	no	—
143	Dic₂₁₂	—	2	1	no	—
144	Dic₂₁₂	C₂²×C₄	1	2	yes	—
145	D₄₂₄	—	2	1	no	—
146	D₄₂₄	C₂²×C₄	1	2	yes	—
147	#11719913	—	2	2	no	—
148	#11719913	—	2	2	no	—
149	#11719912	—	4	2	no	—
150	#11719912	—	4	2	no	—
151	C₈×D₅₃	—	4	2	no	—
152	C₈×D₅₃	—	4	2	no	—
153	#11719908	—	2	2	no	—
154	#11719908	C₂²×C₄	1	4	yes	—
155	C₂³×C₅₃	—	4	1	no	—
156	C₂³×C₅₃	#135	1	1	yes	characteristic
157	C₂²×D₅₃	—	4	1	no	—
158	Q₈×C₅₃	—	2	2	no	—
159	Q₈×C₅₃	—	4	1	no	—
160	D₄×C₅₃	—	2	2	no	—
161	D₄×C₅₃	—	4	2	no	—
162	D₄×C₅₃	—	4	2	no	—
163	D₄×C₅₃	—	4	1	no	—
164	C₂×C₄×C₅₃	—	2	1	no	—
165	C₂×C₄×C₅₃	—	2	1	no	—
166	C₂×C₄×C₅₃	—	4	2	no	—
167	C₂×C₄×C₅₃	—	4	1	no	—
168	C₂×C₄×C₅₃	—	4	2	no	—
169	C₂×C₄×C₅₃	—	4	2	no	—
170	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
173	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₅₃	#135	1	1	yes	characteristic
175	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
176	C₂²⋊D₅₃	—	4	2	no	—
177	C₂²⋊D₅₃	—	4	2	no	—
178	C₂×Dic₅₃	—	4	1	no	—
179	D₂₁₂	—	2	2	no	—
180	D₂₁₂	—	4	1	no	—
181	C₄×D₅₃	—	4	2	no	—
182	C₄×D₅₃	—	4	2	no	—
183	Dic₁₀₆	—	2	2	no	—
184	Dic₁₀₆	—	4	1	no	—
185	C₈×C₅₃	—	4	2	no	—
186	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
187	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
188	C₈×C₅₃	C₂×D₈	1	1	yes	characteristic
189	C₈×C₅₃	C₂×D₈	1	1	yes	characteristic
190	C₈×C₅₃	C₂×D₈	1	1	yes	characteristic
191	C₈×C₅₃	C₂×D₈	1	1	yes	characteristic
192	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
193	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
194	#88322	—	4	2	no	—
195	#33463	—	53	1	no	maximal, Sylow
196	C₂²×C₅₃	—	4	1	no	—
197	C₂²×C₅₃	—	4	2	no	—
198	C₂²×C₅₃	—	8	2	no	—
199	C₂²×C₅₃	C₄×D₈	1	1	yes	characteristic
200	C₂²×C₅₃	C₄×D₈	1	1	yes	characteristic
201	C₂²×C₅₃	C₂×#135	1	1	yes	characteristic
202	C₂×D₅₃	—	4	2	no	—
203	C₂×D₅₃	—	8	2	no	—
204	C₄×C₅₃	—	2	2	no	—
205	C₄×C₅₃	—	4	1	no	—
206	C₄×C₅₃	—	4	2	no	—
207	C₄×C₅₃	C₄×D₈	1	1	yes	characteristic
208	C₄×C₅₃	C₄×D₈	1	1	yes	characteristic
209	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
210	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
211	Dic₅₃	—	4	2	no	—
212	#3414	—	53	1	no	—
213	C₂×#443	—	53	1	no	—
214	C₂×#443	D₅₃	1	1	yes	characteristic, complemented
215	#2179	—	53	4	no	—
216	#2178	—	53	4	no	—
217	#2161	—	53	1	no	—
218	#2143	—	53	1	no	—
219	#2143	—	53	1	no	—
220	C₄×M₃₂	—	53	1	no	—
221	C₂×C₅₃	—	2	1	no	—
222	C₂×C₅₃	—	2	1	no	—
223	C₂×C₅₃	—	2	1	no	—
224	C₂×C₅₃	—	8	2	no	—
225	C₂×C₅₃	C₂×C₄×D₈	1	1	yes	characteristic
226	D₅₃	—	8	2	no	—
227	C₂×#135	—	53	1	no	—
228	C₂×#135	C₂×D₅₃	1	1	yes	characteristic
229	C₂×#131	—	2	1	no	—
230	C₂×#131	—	106	1	no	—
231	#510	—	53	2	no	—
232	#510	—	53	2	no	—
233	#509	—	53	2	no	—
234	#509	—	53	2	no	—
235	#508	—	53	4	no	—
236	C₂×M₃₂	—	53	1	no	—
237	C₂×M₃₂	—	53	1	no	—
238	#443	—	2	1	no	—
239	#443	—	2	1	no	—
240	#443	—	53	2	no	—
241	#443	—	53	2	no	—
242	#443	—	106	1	no	—
243	#443	—	106	1	no	—
244	#443	C₂×D₅₃	1	2	yes	complemented
245	#443	C₂×D₅₃	1	2	yes	complemented
246	C₂×#108	—	53	1	no	—
247	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
248	C₂×#104	—	2	1	no	—
249	C₂×#104	—	106	1	no	—
250	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
251	#368	—	53	4	no	—
252	#359	—	53	4	no	—
253	#359	—	53	4	no	—
254	#346	—	53	2	no	—
255	C₄×C₁₆	—	53	2	no	—
256	C₅₃	#33463	1	1	yes	characteristic, complemented, Sylow
257	C₂×#41	—	2	1	no	—
258	C₂×#41	—	106	1	no	—
259	#135	—	2	1	no	—
260	#135	—	2	1	no	—
261	#135	—	53	2	no	—
262	#135	—	53	2	no	—
263	#135	—	106	1	no	—
264	#135	—	106	1	no	—
265	#135	C₄×D₅₃	1	2	yes	—
266	#135	C₂²×D₅₃	1	2	yes	—
267	C₂×Q₁₆	—	53	1	no	—
268	C₂×Q₁₆	C₄×D₅₃	1	1	yes	characteristic
269	C₂×SD₁₆	—	2	1	no	—
270	C₂×SD₁₆	—	106	1	no	—
271	C₂×D₈	—	53	1	no	—
272	C₂×D₈	C₄×D₅₃	1	1	yes	characteristic
273	#131	—	2	2	no	—
274	#131	—	2	2	no	—
275	#131	—	4	1	no	—
276	#131	—	4	1	no	—
277	#131	—	106	2	no	—
278	#131	—	106	2	no	—
279	#131	—	212	1	no	—
280	#131	—	212	1	no	—
281	C₂×M₁₆	—	2	1	no	—
282	C₂×M₁₆	—	4	1	no	—
283	C₂×M₁₆	—	106	1	no	—
284	C₂×M₁₆	—	212	1	no	—
285	C₂²×C₈	—	4	1	no	—
286	C₂²×C₈	—	212	1	no	—
287	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
288	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
289	C₂×C₄²	C₂²⋊D₅₃	1	1	yes	characteristic
290	Q₃₂	—	53	4	no	—
291	SD₃₂	—	53	4	no	—
292	SD₃₂	—	53	4	no	—
293	D₁₆	—	53	4	no	—
294	M₃₂	—	53	2	no	—
295	M₃₂	—	53	2	no	—
296	M₃₂	—	106	1	no	—
297	M₃₂	—	106	1	no	—
298	C₂×C₁₆	—	53	2	no	—
299	C₂×C₁₆	—	53	2	no	—
300	#108	—	2	1	no	—
301	#108	—	53	2	no	—
302	#108	—	106	1	no	—
303	#108	C₂²×D₅₃	1	2	yes	—
304	#104	—	2	2	no	—
305	#104	—	2	2	no	—
306	#104	—	106	2	no	—
307	#104	—	106	2	no	—
308	C₄×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
309	C₄×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
310	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
311	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
312	#41	—	2	2	no	—
313	#41	—	2	2	no	—
314	#41	—	4	1	no	—
315	#41	—	4	1	no	—
316	#41	—	106	2	no	—
317	#41	—	106	2	no	—
318	#41	—	212	1	no	—
319	#41	—	212	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	106	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	106	1	no	—
325	C₂×D₄	—	212	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	212	1	no	—
329	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
330	Q₁₆	—	2	1	no	—
331	Q₁₆	—	53	2	no	—
332	Q₁₆	—	106	1	no	—
333	Q₁₆	C₂×C₄×D₅₃	1	2	yes	—
334	SD₁₆	—	2	2	no	—
335	SD₁₆	—	2	2	no	—
336	SD₁₆	—	106	2	no	—
337	SD₁₆	—	106	2	no	—
338	D₈	—	2	1	no	—
339	D₈	—	53	2	no	—
340	D₈	—	106	1	no	—
341	D₈	C₂×C₄×D₅₃	1	2	yes	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	4	1	no	—
344	M₁₆	—	4	2	no	—
345	M₁₆	—	4	2	no	—
346	M₁₆	—	106	2	no	—
347	M₁₆	—	212	1	no	—
348	M₁₆	—	212	2	no	—
349	M₁₆	—	212	2	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	2	no	—
352	C₂×C₈	—	4	2	no	—
353	C₂×C₈	—	212	1	no	—
354	C₂×C₈	—	212	2	no	—
355	C₂×C₈	—	212	2	no	—
356	C₂×C₈	#11719922	1	1	yes	characteristic
357	C₂×C₈	#11719922	1	1	yes	characteristic
358	C₂×C₈	#11719922	1	1	yes	characteristic
359	C₂×C₈	#11719922	1	1	yes	characteristic
360	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
361	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
362	C₂×C₈	#11719945	1	1	yes	characteristic
363	C₂×C₈	#11719945	1	1	yes	characteristic
364	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
365	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
366	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
367	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
368	C₄²	—	2	1	no	—
369	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
370	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
371	C₁₆	—	53	4	no	—
372	C₁₆	—	106	2	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	212	1	no	—
375	C₂³	#13133237	1	1	yes	characteristic
376	Q₈	—	2	2	no	—
377	Q₈	—	4	1	no	—
378	Q₈	—	106	2	no	—
379	Q₈	—	212	1	no	—
380	D₄	—	2	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	1	no	—
384	D₄	—	106	2	no	—
385	D₄	—	212	2	no	—
386	D₄	—	212	2	no	—
387	D₄	—	212	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	212	1	no	—
395	C₂×C₄	—	212	2	no	—
396	C₂×C₄	—	212	2	no	—
397	C₂×C₄	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
398	C₂×C₄	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
399	C₂×C₄	C₂×#11719922	1	1	yes	characteristic
400	C₂×C₄	C₂×#11719922	1	1	yes	characteristic
401	C₂×C₄	#13133237	1	1	yes	characteristic
402	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
403	C₈	—	4	2	no	—
404	C₈	—	212	2	no	—
405	C₈	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
406	C₈	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
407	C₈	C₂×#11719922	1	1	yes	characteristic
408	C₈	C₂×#11719922	1	1	yes	characteristic
409	C₈	C₂×#11719922	1	1	yes	characteristic
410	C₈	C₂×#11719922	1	1	yes	characteristic
411	C₈	C₂²×C₄×D₅₃	1	1	yes	characteristic
412	C₈	C₂×#11719945	1	1	yes	characteristic
413	C₂²	—	4	1	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	424	2	no	—
417	C₂²	—	212	2	no	—
418	C₂²	C₄×#11719922	1	1	yes	characteristic
419	C₂²	C₄×#11719922	1	1	yes	characteristic
420	C₂²	C₂×#13133237	1	1	yes	characteristic
421	C₄	—	2	2	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	2	no	—
424	C₄	—	212	2	no	—
425	C₄	C₄×#11719922	1	1	yes	characteristic
426	C₄	C₄×#11719922	1	1	yes	characteristic
427	C₄	C₂×C₄×C₂²⋊D₅₃	1	1	yes	characteristic
428	C₄	C₂²×#11719922	1	1	yes	characteristic
429	C₂	—	2	1	no	—
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	8	2	no	—
433	C₂	—	424	2	no	—
434	C₂	C₂×C₄×#11719922	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×#11719922
commutator	C₈×C₅₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₂×C₅₃×#443	C₂
socle	C₂×C₅₃	C₂×C₄×D₈
prime radical	#20287849	C₂
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	C₂×#443	D₅₃
hypocenter	C₅₃	#33463
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
2. C₂×#16810741	C₂	semidirect
3. #20276599	C₂	semidirect
4. #20276594	C₂	semidirect
5. #20276509	C₂	semidirect
6. #20276443	C₂	semidirect
7. #20276442	C₂	semidirect
8. C₄×#13133157	C₂	semidirect
9. C₂×C₅₃×#443	C₂	semidirect
12. #16811064	C₄	semidirect
13. #16811063	C₄	semidirect
14. #16811059	C₄	semidirect
15. #16811058	C₄	semidirect
21. #16810741	C₂²	semidirect
22. #16810741	C₂²	semidirect
25. #16810452	C₂²	semidirect
26. #16810430	C₂²	semidirect
27. #16810429	C₂²	semidirect
28. #16810399	C₂²	semidirect
29. C₄×#11719908	C₂²	semidirect
34. C₅₃×#443	C₂²	semidirect
35. C₅₃×#443	C₂²	semidirect
54. #13133163	C₂×C₄	semidirect
55. #13133161	C₂×C₄	semidirect
56. #13133160	C₂×C₄	semidirect
57. #13133158	C₂×C₄	semidirect
214. C₂×#443	D₅₃	semidirect
244. #443	C₂×D₅₃	semidirect
245. #443	C₂×D₅₃	semidirect
256. C₅₃	#33463	semidirect

Maximal subgroups

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

subgroup	index
#20287849	2
C₂×#16810741	2
#20276599	2
#20276594	2
#20276509	2
#20276443	2
#20276442	2
C₄×#13133157	2
C₂×C₅₃×#443	2
#33463	53