Subgroups — #27402613

Order 13568.

812 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	#20283633	C₂	1	1	yes	maximal, characteristic
2	#20283631	C₂	1	1	yes	maximal, characteristic
3	C₂×#16810739	C₂	1	1	yes	maximal, characteristic
4	#20283325	C₂	1	2	yes	maximal, complemented
5	#20275506	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274958	C₂	1	2	yes	maximal, complemented
7	#20274952	C₂	1	2	yes	maximal, complemented
8	#20274885	C₂	1	1	yes	maximal, characteristic, complemented
9	#20274768	C₂	1	2	yes	maximal, complemented
10	#20274595	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1953	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133239	C₂²	1	1	yes	characteristic
13	#16811389	C₂²	1	2	yes	—
14	#16811389	C₂²	1	2	yes	—
15	C₂×#13133225	C₂²	1	2	yes	—
16	#16810746	—	2	2	no	—
17	#16810744	—	2	2	no	—
18	#16810741	—	2	2	no	—
19	#16810739	—	2	2	no	—
20	#16810739	C₄	1	2	yes	complemented
21	#16810739	C₄	1	2	yes	complemented
22	#16810739	C₄	1	2	yes	complemented
23	#16810739	C₄	1	2	yes	complemented
24	#16810672	C₂²	1	2	yes	—
25	#16810670	—	2	4	no	—
26	C₂×#13133153	C₂²	1	1	yes	characteristic
27	C₂×#13133152	C₂²	1	2	yes	—
28	C₂×#13133152	C₂²	1	1	yes	characteristic
29	#108×D₅₃	—	2	4	no	—
30	#16810659	C₂²	1	1	yes	characteristic
31	#16810646	C₂²	1	2	yes	—
32	#16810641	C₂²	1	2	yes	—
33	#16810639	C₂²	1	2	yes	—
34	C₂×#13133143	C₂²	1	2	yes	—
35	#16810578	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
37	#16810395	C₂²	1	2	yes	—
38	#16810384	C₂²	1	1	yes	characteristic
39	#16810382	C₂²	1	1	yes	characteristic
40	C₅₃×#430	C₂²	1	2	yes	—
41	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×#405	C₂²	1	1	yes	characteristic
44	C₅₃×#344	C₂²	1	2	yes	—
45	C₂×#11719945	C₂³	1	2	yes	—
46	#13133239	C₂×C₄	1	2	yes	—
47	#13133239	C₂×C₄	1	2	yes	—
48	#13133239	D₄	1	2	yes	—
49	#13133239	D₄	1	2	yes	—
50	C₂×Dic₂₁₂	Q₈	1	1	yes	characteristic
51	C₂×#11719913	Q₈	1	2	yes	—
52	C₂×D₄₂₄	Q₈	1	1	yes	characteristic
53	#13133225	—	2	2	no	—
54	#13133225	—	2	2	no	—
55	#13133225	—	2	4	no	—
56	#13133225	—	4	2	no	—
57	#13133225	C₂×C₄	1	4	yes	—
58	#13133225	C₂×C₄	1	4	yes	—
59	#13133223	—	2	4	no	—
60	#13133223	—	4	2	no	—
61	C₂×#11719917	C₂³	1	2	yes	—
62	C₂×#11719917	C₂³	1	1	yes	characteristic
63	C₂×#11719912	—	2	2	no	—
64	M₁₆×D₅₃	—	2	4	no	—
65	M₁₆×D₅₃	—	2	4	no	—
66	C₂²×#88322	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₅₃	—	2	2	no	—
68	#13133176	C₂³	1	1	yes	characteristic
69	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
70	#13133153	—	2	1	no	—
71	#13133153	—	2	1	no	—
72	#13133153	—	2	4	no	—
73	#13133152	—	2	2	no	—
74	#13133152	—	2	2	no	—
75	#13133152	D₄	1	2	yes	—
76	#13133152	D₄	1	2	yes	—
77	#13133150	—	2	1	no	—
78	#13133148	—	2	1	no	—
79	#13133146	—	4	2	no	—
80	#13133145	—	2	4	no	—
81	#13133143	—	2	4	no	—
82	#13133143	C₂×C₄	1	4	yes	—
83	#13133143	C₂×C₄	1	4	yes	—
84	#13133127	—	2	1	no	—
85	C₈×Dic₅₃	—	2	1	no	—
86	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
90	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
91	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
92	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
94	#117×C₅₃	C₂³	1	1	yes	characteristic
95	#108×C₅₃	—	2	4	no	—
96	#108×C₅₃	—	2	1	no	—
97	#108×C₅₃	—	2	1	no	—
98	#108×C₅₃	C₂×C₄	1	2	yes	—
99	#108×C₅₃	C₂×C₄	1	2	yes	—
100	#97×C₅₃	—	2	1	no	—
101	C₄×C₈×C₅₃	—	2	1	no	—
102	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
103	C₂×C₂²⋊D₅₃	—	2	2	no	—
104	C₂²×Dic₅₃	—	2	1	no	—
105	#11719945	—	2	2	no	—
106	#11719945	—	2	2	no	—
107	#11719945	C₂²×C₄	1	4	yes	—
108	#11719945	C₂×D₄	1	4	yes	—
109	C₂×D₂₁₂	C₂×Q₈	1	2	yes	—
110	C₂×C₄×D₅₃	—	2	2	no	—
111	C₂×Dic₁₀₆	C₂×Q₈	1	2	yes	—
112	M₁₆×C₅₃	—	2	2	no	—
113	M₁₆×C₅₃	—	2	1	no	—
114	M₁₆×C₅₃	—	2	2	no	—
115	M₁₆×C₅₃	—	2	2	no	—
116	M₁₆×C₅₃	C₂²×C₄	1	4	yes	—
117	M₁₆×C₅₃	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₅₃	—	2	1	no	—
119	C₂×C₈×C₅₃	—	2	2	no	—
120	C₂×C₈×C₅₃	—	2	2	no	—
121	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₅₃	C₂×Q₈	1	1	yes	characteristic
126	C₂×C₈×C₅₃	C₂×Q₈	1	1	yes	characteristic
127	C₄⋊C₄×C₅₃	—	2	1	no	—
128	C₂²⋊C₄×C₅₃	—	2	1	no	—
129	C₄²×C₅₃	—	2	1	no	—
130	C₂²⋊Dic₅₃	—	2	1	no	—
131	C₄⋊Dic₅₃	—	2	1	no	—
132	C₄×Dic₅₃	—	2	1	no	—
133	C₄×Dic₅₃	—	2	1	no	—
134	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
136	#11719917	—	2	1	no	—
137	#11719917	—	2	2	no	—
138	#11719917	—	2	2	no	—
139	#11719917	C₂×D₄	1	2	yes	—
140	C₂×#88322	—	2	1	no	—
141	C₂×#88322	—	2	2	no	—
142	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
143	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
144	C₂×#88322	C₂×D₄	1	1	yes	characteristic
145	C₂×#88322	C₂×D₄	1	1	yes	characteristic
146	C₂×#88322	#41	1	1	yes	characteristic
147	C₂×#88322	#41	1	1	yes	characteristic
148	Dic₂₁₂	C₄⋊C₄	1	2	yes	—
149	Dic₂₁₂	C₄⋊C₄	1	2	yes	—
150	D₄₂₄	C₄⋊C₄	1	2	yes	—
151	D₄₂₄	C₄⋊C₄	1	2	yes	—
152	#11719913	C₄⋊C₄	1	4	yes	—
153	#11719913	C₄⋊C₄	1	4	yes	—
154	#11719912	—	2	4	no	—
155	#11719912	—	2	4	no	—
156	#11719912	—	4	4	no	—
157	#11719912	—	4	4	no	—
158	C₈×D₅₃	—	2	4	no	—
159	C₈×D₅₃	—	2	4	no	—
160	C₈×D₅₃	—	4	4	no	—
161	C₈×D₅₃	—	4	4	no	—
162	C₂³×C₅₃	2₋¹⁺⁴	1	1	yes	characteristic
163	C₂²×D₅₃	—	2	2	no	—
164	C₂×C₄×C₅₃	—	4	1	no	—
165	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂²⋊D₅₃	—	2	4	no	—
172	C₂²⋊D₅₃	—	2	4	no	—
173	C₂×Dic₅₃	—	2	1	no	—
174	C₂×Dic₅₃	—	2	2	no	—
175	C₂×Dic₅₃	—	2	1	no	—
176	C₂×Dic₅₃	—	4	2	no	—
177	C₂×Dic₅₃	—	4	1	no	—
178	D₂₁₂	—	2	2	no	—
179	D₂₁₂	C₂×C₄⋊C₄	1	4	yes	—
180	C₄×D₅₃	—	2	4	no	—
181	C₄×D₅₃	—	2	4	no	—
182	Dic₁₀₆	—	2	2	no	—
183	Dic₁₀₆	C₂×C₄⋊C₄	1	4	yes	—
184	C₈×C₅₃	—	2	4	no	—
185	C₈×C₅₃	—	2	2	no	—
186	C₈×C₅₃	—	4	2	no	—
187	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
191	#88322	—	2	2	no	—
192	#88322	—	4	2	no	—
193	#88322	C₄×D₄	1	1	yes	characteristic
194	#88322	C₄×D₄	1	1	yes	characteristic
195	#88322	C₄×D₄	1	1	yes	characteristic
196	#88322	C₄×D₄	1	1	yes	characteristic
197	#22694	—	53	1	no	maximal, Sylow
198	C₂²×C₅₃	—	4	1	no	—
199	C₂²×C₅₃	#520	1	1	yes	characteristic
200	C₂²×C₅₃	#547	1	1	yes	characteristic
201	C₂²×C₅₃	D₄×Q₈	1	1	yes	characteristic
202	C₂×D₅₃	—	2	4	no	—
203	C₂×D₅₃	—	8	2	no	—
204	C₄×C₅₃	—	8	1	no	—
205	C₄×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
206	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
207	C₄×C₅₃	D₄²	1	1	yes	characteristic
208	C₄×C₅₃	#554	1	1	yes	characteristic
209	Dic₅₃	—	2	2	no	—
210	Dic₅₃	—	2	4	no	—
211	Dic₅₃	—	4	1	no	—
212	Dic₅₃	—	8	1	no	—
213	#2957	—	53	1	no	—
214	#2957	—	53	1	no	—
215	C₂×#443	—	53	1	no	—
216	#2916	—	53	2	no	—
217	#1953	—	53	1	no	—
218	#1953	D₅₃	1	1	yes	characteristic, complemented
219	#1861	—	53	2	no	—
220	#1861	—	53	2	no	—
221	#1848	—	53	1	no	—
222	#1814	—	53	2	no	—
223	#1772	—	53	1	no	—
224	C₂×C₅₃	—	2	1	no	—
225	C₂×C₅₃	—	2	1	no	—
226	C₂×C₅₃	—	2	1	no	—
227	C₂×C₅₃	D₄×C₄⋊C₄	1	1	yes	characteristic
228	D₅₃	—	4	4	no	—
229	C₂×#135	—	53	1	no	—
230	#568	—	53	2	no	—
231	#568	—	53	2	no	—
232	C₂×#131	—	53	2	no	—
233	#444	—	106	2	no	—
234	#444	—	106	2	no	—
235	#443	—	53	2	no	—
236	#443	—	53	2	no	—
237	#443	—	53	2	no	—
238	#443	—	53	2	no	—
239	#443	—	106	2	no	—
240	#443	—	106	2	no	—
241	#430	—	53	2	no	—
242	#430	—	106	4	no	—
243	#430	C₂×D₅₃	1	2	yes	—
244	C₂×#108	—	53	1	no	—
245	C₂×#108	—	53	2	no	—
246	C₂×#108	—	53	1	no	—
247	C₂×#108	—	106	4	no	—
248	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
249	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
250	#427	—	53	1	no	—
251	#423	—	53	2	no	—
252	#421	—	53	2	no	—
253	#421	—	53	2	no	—
254	C₂×#104	—	53	2	no	—
255	#405	—	53	1	no	—
256	#405	C₂×D₅₃	1	1	yes	characteristic
257	C₂×C₄×C₈	—	53	1	no	—
258	#344	—	53	2	no	—
259	#344	C₂×D₅₃	1	2	yes	—
260	#339	—	53	1	no	—
261	#339	—	53	1	no	—
262	C₅₃	#22694	1	1	yes	characteristic, complemented, Sylow
263	C₂×#41	—	53	2	no	—
264	#135	—	53	2	no	—
265	#135	—	53	2	no	—
266	#135	—	53	2	no	—
267	#135	—	53	2	no	—
268	C₂×Q₁₆	—	53	1	no	—
269	C₂×SD₁₆	—	53	2	no	—
270	C₂×D₈	—	53	1	no	—
271	#131	—	53	4	no	—
272	#131	—	53	4	no	—
273	#131	—	106	4	no	—
274	#131	—	106	2	no	—
275	#131	—	106	2	no	—
276	#131	—	106	4	no	—
277	#131	—	212	2	no	—
278	#131	—	212	2	no	—
279	C₂×M₁₆	—	53	1	no	—
280	C₂×M₁₆	—	53	2	no	—
281	C₂×M₁₆	—	106	2	no	—
282	C₂×M₁₆	—	106	4	no	—
283	C₂×M₁₆	—	106	4	no	—
284	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
285	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
286	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
287	C₂²×C₈	—	53	1	no	—
288	C₂²×C₈	—	106	2	no	—
289	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
290	#117	—	53	1	no	—
291	#117	C₂²×D₅₃	1	1	yes	characteristic
292	C₂×C₄²	—	53	1	no	—
293	#108	—	2	4	no	—
294	#108	—	2	1	no	—
295	#108	—	2	1	no	—
296	#108	—	53	2	no	—
297	#108	—	53	2	no	—
298	#108	—	106	4	no	—
299	#108	—	106	2	no	—
300	#108	—	106	2	no	—
301	#108	—	106	1	no	—
302	#108	—	106	1	no	—
303	#108	C₄×D₅₃	1	2	yes	—
304	#108	C₄×D₅₃	1	2	yes	—
305	#107	—	106	1	no	—
306	#106	—	106	1	no	—
307	C₄⋊C₈	—	212	2	no	—
308	#104	—	53	4	no	—
309	#104	—	53	4	no	—
310	#104	—	106	4	no	—
311	#104	—	106	4	no	—
312	#97	—	2	1	no	—
313	#97	—	106	1	no	—
314	C₄×C₈	—	2	1	no	—
315	C₄×C₈	—	53	1	no	—
316	C₄×C₈	—	53	1	no	—
317	C₄×C₈	—	53	1	no	—
318	C₄×C₈	—	53	1	no	—
319	C₄×C₈	—	106	1	no	—
320	#41	—	53	4	no	—
321	#41	—	53	4	no	—
322	#41	—	106	2	no	—
323	#41	—	106	2	no	—
324	C₂×Q₈	—	53	2	no	—
325	C₂×D₄	—	53	2	no	—
326	C₂×D₄	—	106	2	no	—
327	C₂²×C₄	—	106	2	no	—
328	C₂²×C₄	—	106	1	no	—
329	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
330	Q₁₆	—	53	2	no	—
331	Q₁₆	—	53	2	no	—
332	SD₁₆	—	53	4	no	—
333	SD₁₆	—	53	4	no	—
334	D₈	—	53	2	no	—
335	D₈	—	53	2	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	—	2	1	no	—
338	M₁₆	—	2	2	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	53	2	no	—
341	M₁₆	—	106	4	no	—
342	M₁₆	—	106	4	no	—
343	M₁₆	—	106	1	no	—
344	M₁₆	—	106	2	no	—
345	M₁₆	—	106	2	no	—
346	M₁₆	—	212	4	no	—
347	M₁₆	—	212	4	no	—
348	M₁₆	C₂×C₄×D₅₃	1	4	yes	—
349	M₁₆	D₄×D₅₃	1	2	yes	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	53	1	no	—
354	C₂×C₈	—	53	1	no	—
355	C₂×C₈	—	53	1	no	—
356	C₂×C₈	—	53	1	no	—
357	C₂×C₈	—	53	1	no	—
358	C₂×C₈	—	53	1	no	—
359	C₂×C₈	—	106	4	no	—
360	C₂×C₈	—	106	4	no	—
361	C₂×C₈	—	106	1	no	—
362	C₂×C₈	—	106	2	no	—
363	C₂×C₈	—	212	4	no	—
364	C₂×C₈	—	212	4	no	—
365	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
367	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
368	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
369	C₂×C₈	Q₈×D₅₃	1	1	yes	characteristic
370	C₂×C₈	Q₈×D₅₃	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	106	1	no	—
373	C₂²⋊C₄	—	2	1	no	—
374	C₂²⋊C₄	—	106	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	53	1	no	—
377	C₄²	—	53	1	no	—
378	C₄²	—	106	1	no	—
379	C₄²	—	106	1	no	—
380	C₂³	—	106	2	no	—
381	C₂³	#13133265	1	1	yes	characteristic
382	Q₈	—	53	4	no	—
383	Q₈	—	106	2	no	—
384	D₄	—	53	4	no	—
385	D₄	—	106	4	no	—
386	D₄	—	106	4	no	—
387	D₄	—	106	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	106	2	no	—
390	C₂×C₄	—	106	1	no	—
391	C₂×C₄	—	106	4	no	—
392	C₂×C₄	—	106	4	no	—
393	C₂×C₄	—	106	1	no	—
394	C₂×C₄	—	212	2	no	—
395	C₂×C₄	—	212	1	no	—
396	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
397	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
398	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
399	C₂×C₄	C₂×Q₈×D₅₃	1	1	yes	characteristic
400	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
401	C₂×C₄	#13133263	1	1	yes	characteristic
402	C₈	—	2	4	no	—
403	C₈	—	2	2	no	—
404	C₈	—	4	2	no	—
405	C₈	—	53	1	no	—
406	C₈	—	53	1	no	—
407	C₈	—	53	1	no	—
408	C₈	—	53	1	no	—
409	C₈	—	106	2	no	—
410	C₈	—	212	2	no	—
411	C₈	C₄⋊C₄×D₅₃	1	1	yes	characteristic
412	C₈	C₄⋊C₄×D₅₃	1	1	yes	characteristic
413	C₈	C₄⋊C₄×D₅₃	1	1	yes	characteristic
414	C₈	C₄⋊C₄×D₅₃	1	1	yes	characteristic
415	C₂²	—	4	1	no	—
416	C₂²	—	106	4	no	—
417	C₂²	—	424	2	no	—
418	C₂²	#16811105	1	1	yes	characteristic
419	C₂²	#16811275	1	1	yes	characteristic
420	C₂²	#16811288	1	1	yes	characteristic
421	C₄	—	8	1	no	—
422	C₄	—	106	2	no	—
423	C₄	—	106	4	no	—
424	C₄	—	424	1	no	—
425	C₄	—	212	1	no	—
426	C₄	C₂×C₄⋊C₄×D₅₃	1	1	yes	characteristic
427	C₄	C₄×D₄×D₅₃	1	1	yes	characteristic
428	C₄	#16811257	1	1	yes	characteristic
429	C₄	#16811329	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	212	4	no	—
434	C₂	#20277616	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16811257
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1953	C₂
socle	C₂×C₅₃	D₄×C₄⋊C₄
prime radical	C₂×#13133239	C₂²
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1953	D₅₃
hypocenter	C₅₃	#22694
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1953

Complements

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

N	H ≅ G/N	type
4. #20283325	C₂	semidirect
5. #20275506	C₂	semidirect
6. #20274958	C₂	semidirect
7. #20274952	C₂	semidirect
8. #20274885	C₂	semidirect
9. #20274768	C₂	semidirect
10. #20274595	C₂	semidirect
11. C₅₃×#1953	C₂	semidirect
20. #16810739	C₄	semidirect
21. #16810739	C₄	semidirect
22. #16810739	C₄	semidirect
23. #16810739	C₄	semidirect
218. #1953	D₅₃	semidirect
262. C₅₃	#22694	semidirect

Maximal subgroups

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

subgroup	index
#20283633	2
#20283631	2
C₂×#16810739	2
#20283325	2
#20275506	2
#20274958	2
#20274952	2
#20274885	2
#20274768	2
#20274595	2
C₅₃×#1953	2
#22694	53