Subgroups — #27366579

Order 13568.

620 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	#20285301	C₂	1	1	yes	maximal, characteristic, complemented
2	#20284787	C₂	1	2	yes	maximal
3	C₈×#11719945	C₂	1	1	yes	maximal, characteristic
4	#20274146	C₂	1	2	yes	maximal, complemented
5	#20274139	C₂	1	2	yes	maximal, complemented
6	#20274110	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274105	C₂	1	1	yes	maximal, characteristic, complemented
8	#20274086	C₂	1	1	yes	maximal, characteristic, complemented
9	#20274081	C₂	1	1	yes	maximal, characteristic, complemented
10	#20273379	C₂	1	2	yes	maximal, complemented
11	C₅₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811180	C₂²	1	2	yes	—
13	C₄×#11719945	C₂²	1	1	yes	characteristic
14	#16811028	C₂²	1	1	yes	characteristic
15	#16811003	C₂²	1	1	yes	characteristic
16	#16810974	C₂²	1	2	yes	—
17	#16810965	—	2	2	no	—
18	#16810909	C₂²	1	2	yes	—
19	#16810904	C₂²	1	2	yes	—
20	#16810864	—	2	1	no	—
21	#16810864	—	2	1	no	—
22	#16810834	C₂²	1	2	yes	—
23	#16810829	C₂²	1	2	yes	—
24	#16810787	—	2	2	no	—
25	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
26	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
27	C₄×Dic₂₁₂	—	2	2	no	—
28	C₄×Dic₂₁₂	—	2	1	no	—
29	C₄×Dic₂₁₂	—	2	1	no	—
30	C₄×#11719913	—	2	2	no	—
31	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
32	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
33	C₈×C₂²⋊D₅₃	—	2	1	no	—
34	C₈×C₂²⋊D₅₃	—	2	1	no	—
35	#16810676	C₂²	1	1	yes	characteristic
36	#16810674	—	2	1	no	—
37	C₄×C₈×D₅₃	—	2	1	no	—
38	#16810370	C₂²	1	2	yes	—
39	#16810370	C₂²	1	2	yes	—
40	#16810368	C₂²	1	2	yes	—
41	#16810368	C₂²	1	2	yes	—
42	C₅₃×#431	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
44	C₅₃×#335	C₂²	1	1	yes	characteristic
45	C₅₃×#335	C₂²	1	1	yes	characteristic
46	C₅₃×#334	C₂²	1	2	yes	—
47	C₂×#11719945	D₄	1	1	yes	characteristic
48	C₂×Dic₂₁₂	—	2	1	no	—
49	C₂×Dic₂₁₂	—	2	1	no	—
50	C₂×Dic₂₁₂	—	2	2	no	—
51	C₂×#11719913	—	2	2	no	—
52	C₂×C₈×D₅₃	—	2	1	no	—
53	C₂×C₈×D₅₃	—	2	1	no	—
54	#13133217	C₂³	1	2	yes	—
55	#13133217	C₂³	1	2	yes	—
56	#13133209	—	2	2	no	—
57	#13133196	—	2	2	no	—
58	#13133196	—	2	2	no	—
59	C₄×Dic₁₀₆	—	2	2	no	—
60	C₄×Dic₁₀₆	—	2	2	no	—
61	C₄×Dic₁₀₆	D₄	1	1	yes	characteristic
62	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
63	C₄×D₂₁₂	D₄	1	1	yes	characteristic
64	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
65	C₄×C₂²⋊D₅₃	—	2	1	no	—
66	C₄×C₂²⋊D₅₃	—	2	1	no	—
67	#13133176	—	2	2	no	—
68	#13133176	D₄	1	1	yes	characteristic
69	#13133174	—	2	1	no	—
70	C₄²×D₅₃	—	2	1	no	—
71	#13133151	—	2	1	no	—
72	#13133151	—	2	1	no	—
73	#13133151	—	2	2	no	—
74	#13133149	—	2	2	no	—
75	C₄⋊#88322	C₂³	1	1	yes	characteristic
76	C₄⋊#88322	C₂³	1	1	yes	characteristic
77	#13133146	—	2	1	no	—
78	#13133146	—	2	1	no	—
79	#13133142	—	2	2	no	—
80	#13133142	—	2	2	no	—
81	#13133142	—	2	2	no	—
82	#13133142	—	2	2	no	—
83	#13133142	—	2	2	no	—
84	#13133139	—	2	2	no	—
85	C₂²⋊#88322	—	2	1	no	—
86	#13133129	—	2	1	no	—
87	#13133129	—	2	1	no	—
88	C₄×#88322	—	2	1	no	—
89	C₈×Dic₅₃	—	2	1	no	—
90	C₈×Dic₅₃	—	2	1	no	—
91	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
92	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
95	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
96	C₂²⋊C₈×C₅₃	—	2	2	no	—
97	C₄×C₈×C₅₃	—	2	2	no	—
98	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
99	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
105	C₂×C₂²⋊D₅₃	—	2	1	no	—
106	#11719945	—	2	2	no	—
107	#11719945	—	2	2	no	—
108	C₂×D₂₁₂	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₅₃	—	2	1	no	—
110	C₂×C₄×D₅₃	—	2	1	no	—
111	C₂×C₄×D₅₃	—	2	1	no	—
112	C₂×Dic₁₀₆	—	2	2	no	—
113	C₂×Dic₁₀₆	—	2	2	no	—
114	C₂×Dic₁₀₆	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₅₃	—	2	2	no	—
116	C₂×C₈×C₅₃	—	2	2	no	—
117	C₂×C₈×C₅₃	—	2	2	no	—
118	C₂×C₈×C₅₃	—	4	1	no	—
119	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₅₃	#41	1	1	yes	characteristic
126	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
127	C₂²⋊Dic₅₃	—	2	1	no	—
128	C₂²⋊Dic₅₃	—	4	2	no	—
129	#11719921	—	2	1	no	—
130	#11719921	—	2	1	no	—
131	C₄⋊Dic₅₃	—	2	2	no	—
132	C₄⋊Dic₅₃	—	2	2	no	—
133	C₄⋊Dic₅₃	—	2	2	no	—
134	C₄⋊Dic₅₃	—	2	2	no	—
135	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
136	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
137	#11719919	—	2	1	no	—
138	#11719919	—	2	1	no	—
139	#11719919	—	4	2	no	—
140	#11719919	—	4	2	no	—
141	C₄×Dic₅₃	—	2	1	no	—
142	C₄×Dic₅₃	—	2	1	no	—
143	C₄×Dic₅₃	—	2	1	no	—
144	C₄×Dic₅₃	—	4	2	no	—
145	C₂×#88322	—	2	1	no	—
146	C₂×#88322	—	2	1	no	—
147	Dic₂₁₂	—	4	2	no	—
148	Dic₂₁₂	—	4	4	no	—
149	Dic₂₁₂	—	4	2	no	—
150	#11719913	—	4	4	no	—
151	C₈×D₅₃	—	4	2	no	—
152	C₈×D₅₃	—	4	2	no	—
153	C₂³×C₅₃	#121	1	1	yes	characteristic
154	C₂²×D₅₃	—	2	1	no	—
155	C₂×C₄×C₅₃	—	2	1	no	—
156	C₂×C₄×C₅₃	—	2	1	no	—
157	C₂×C₄×C₅₃	—	2	1	no	—
158	C₂×C₄×C₅₃	—	2	1	no	—
159	C₂×C₄×C₅₃	—	2	2	no	—
160	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
161	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
162	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
166	C₂²⋊D₅₃	—	2	4	no	—
167	C₂×Dic₅₃	—	2	1	no	—
168	C₂×Dic₅₃	—	2	1	no	—
169	C₂×Dic₅₃	—	2	1	no	—
170	C₂×Dic₅₃	—	4	2	no	—
171	C₂×Dic₅₃	—	4	2	no	—
172	D₂₁₂	—	2	1	no	—
173	D₂₁₂	#135	1	2	yes	—
174	C₄×D₅₃	—	2	4	no	—
175	C₄×D₅₃	—	4	1	no	—
176	C₄×D₅₃	—	4	1	no	—
177	C₄×D₅₃	—	4	2	no	—
178	Dic₁₀₆	—	2	1	no	—
179	Dic₁₀₆	—	4	2	no	—
180	Dic₁₀₆	—	4	2	no	—
181	Dic₁₀₆	—	4	2	no	—
182	Dic₁₀₆	—	4	2	no	—
183	Dic₁₀₆	#135	1	2	yes	—
184	C₈×C₅₃	—	2	1	no	—
185	C₈×C₅₃	—	2	1	no	—
186	C₈×C₅₃	—	2	1	no	—
187	C₈×C₅₃	—	4	2	no	—
188	C₈×C₅₃	—	4	2	no	—
189	C₈×C₅₃	#135	1	2	yes	—
190	#88322	—	4	1	no	—
191	#88322	—	4	1	no	—
192	#19129	—	53	1	no	maximal, Sylow
193	C₂²×C₅₃	—	2	1	no	—
194	C₂²×C₅₃	—	2	1	no	—
195	C₂²×C₅₃	—	2	1	no	—
196	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
197	C₂×D₅₃	—	2	2	no	—
198	C₂×D₅₃	—	4	1	no	—
199	C₂×D₅₃	—	4	1	no	—
200	C₄×C₅₃	—	2	1	no	—
201	C₄×C₅₃	—	2	1	no	—
202	C₄×C₅₃	—	2	1	no	—
203	C₄×C₅₃	#473	1	2	yes	—
204	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
205	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
206	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
207	C₄×C₅₃	#575	1	1	yes	characteristic
208	Dic₅₃	—	2	2	no	—
209	Dic₅₃	—	4	1	no	—
210	Dic₅₃	—	4	1	no	—
211	Dic₅₃	—	8	2	no	—
212	Dic₅₃	—	8	2	no	—
213	#3170	—	53	1	no	—
214	#3107	—	53	2	no	—
215	C₈×#41	—	53	1	no	—
216	#1680	—	53	2	no	—
217	#1679	—	53	2	no	—
218	#1674	—	53	1	no	—
219	#1673	—	53	1	no	—
220	#1670	—	53	1	no	—
221	#1669	—	53	1	no	—
222	#1564	D₅₃	1	1	yes	characteristic, complemented
223	#1544	—	53	2	no	—
224	C₂×C₅₃	—	4	1	no	—
225	C₂×C₅₃	#3035	1	1	yes	characteristic
226	C₂×C₅₃	#3050	1	1	yes	characteristic
227	C₂×C₅₃	C₂×#473	1	1	yes	characteristic
228	D₅₃	—	4	2	no	—
229	#533	—	53	2	no	—
230	C₄×#41	—	53	1	no	—
231	#500	—	53	1	no	—
232	#494	—	53	1	no	—
233	#487	—	53	2	no	—
234	#485	—	106	2	no	—
235	#475	—	53	2	no	—
236	#474	—	53	2	no	—
237	#467	—	106	1	no	—
238	#467	—	106	1	no	—
239	#462	—	53	2	no	—
240	#461	—	53	2	no	—
241	#452	—	106	2	no	—
242	C₈×Q₈	—	53	1	no	—
243	C₈×Q₈	—	53	1	no	—
244	C₄×Q₁₆	—	106	2	no	—
245	C₄×Q₁₆	—	106	1	no	—
246	C₄×Q₁₆	—	106	1	no	—
247	C₄×SD₁₆	—	106	2	no	—
248	C₈×D₄	—	53	1	no	—
249	C₈×D₄	—	53	1	no	—
250	C₈×D₄	—	106	1	no	—
251	C₈×D₄	—	106	1	no	—
252	#431	—	53	1	no	—
253	#431	—	106	1	no	—
254	#431	C₂×D₅₃	1	2	yes	—
255	C₂×C₄×C₈	—	106	1	no	—
256	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
257	#335	C₂×D₅₃	1	1	yes	characteristic
258	#335	C₂×D₅₃	1	1	yes	characteristic
259	#334	C₂×D₅₃	1	2	yes	—
260	#332	—	53	2	no	—
261	#332	—	53	2	no	—
262	#332	—	53	2	no	—
263	#332	—	53	2	no	—
264	C₅₃	#19129	1	1	yes	characteristic, complemented, Sylow
265	C₂×#41	—	53	1	no	—
266	C₂×Q₁₆	—	106	2	no	—
267	C₂×Q₁₆	—	106	1	no	—
268	C₂×Q₁₆	—	106	1	no	—
269	C₂×SD₁₆	—	106	2	no	—
270	C₂²×C₈	—	106	1	no	—
271	C₂²×C₈	—	106	1	no	—
272	C₂²×C₈	D₂₁₂	1	1	yes	characteristic
273	C₂²×C₈	D₂₁₂	1	1	yes	characteristic
274	C₄⋊Q₈	—	53	2	no	—
275	C₄⋊Q₈	—	53	2	no	—
276	#125	—	106	2	no	—
277	C₂²⋊Q₈	—	106	2	no	—
278	C₂²⋊Q₈	—	106	2	no	—
279	C₄×Q₈	—	53	1	no	—
280	C₄×Q₈	—	53	1	no	—
281	C₄×Q₈	—	106	2	no	—
282	C₄×Q₈	—	106	2	no	—
283	C₄×D₄	—	53	1	no	—
284	C₄×D₄	—	53	1	no	—
285	C₄×D₄	—	106	1	no	—
286	C₄×D₄	—	106	1	no	—
287	#117	—	53	1	no	—
288	#117	—	106	1	no	—
289	#117	—	106	2	no	—
290	C₂×C₄²	—	106	1	no	—
291	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
292	#107	—	106	2	no	—
293	#107	—	106	1	no	—
294	#107	—	106	1	no	—
295	#106	—	106	2	no	—
296	C₄⋊C₈	—	53	1	no	—
297	C₄⋊C₈	—	53	1	no	—
298	C₄⋊C₈	—	106	1	no	—
299	C₄⋊C₈	—	106	1	no	—
300	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
301	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
302	#103	—	106	2	no	—
303	#103	—	106	2	no	—
304	#103	—	106	2	no	—
305	#103	—	106	2	no	—
306	#103	—	106	2	no	—
307	#102	—	106	2	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	C₂²⋊C₈	—	106	1	no	—
310	C₂²⋊C₈	—	106	1	no	—
311	C₂²⋊C₈	—	106	1	no	—
312	C₄×C₈	—	2	2	no	—
313	C₄×C₈	—	106	1	no	—
314	C₄×C₈	—	106	1	no	—
315	C₄×C₈	—	106	1	no	—
316	C₄×C₈	D₂₁₂	1	1	yes	characteristic
317	C₄×C₈	D₂₁₂	1	1	yes	characteristic
318	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
320	#41	—	106	2	no	—
321	#41	—	106	2	no	—
322	C₂×Q₈	—	53	1	no	—
323	C₂×Q₈	—	106	2	no	—
324	C₂×Q₈	—	106	2	no	—
325	C₂×D₄	—	53	1	no	—
326	C₂×D₄	—	106	1	no	—
327	C₂²×C₄	—	106	1	no	—
328	C₂²×C₄	—	106	1	no	—
329	C₂²×C₄	—	106	1	no	—
330	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
331	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
332	C₂²×C₄	#11719949	1	1	yes	characteristic
333	Q₁₆	—	212	2	no	—
334	Q₁₆	—	212	4	no	—
335	Q₁₆	—	212	2	no	—
336	SD₁₆	—	212	4	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	106	1	no	—
342	C₂×C₈	—	106	1	no	—
343	C₂×C₈	—	212	2	no	—
344	C₂×C₈	—	212	2	no	—
345	C₂×C₈	C₂×D₂₁₂	1	1	yes	characteristic
346	C₂×C₈	C₂×D₂₁₂	1	1	yes	characteristic
347	C₂×C₈	C₂×D₂₁₂	1	1	yes	characteristic
348	C₂×C₈	C₂×D₂₁₂	1	1	yes	characteristic
349	C₄⋊C₄	—	53	1	no	—
350	C₄⋊C₄	—	53	1	no	—
351	C₄⋊C₄	—	106	1	no	—
352	C₄⋊C₄	—	106	1	no	—
353	C₄⋊C₄	—	106	2	no	—
354	C₄⋊C₄	—	106	2	no	—
355	C₄⋊C₄	—	106	2	no	—
356	C₄⋊C₄	—	106	2	no	—
357	C₄⋊C₄	—	212	2	no	—
358	C₄⋊C₄	—	212	2	no	—
359	C₂²⋊C₄	—	106	1	no	—
360	C₂²⋊C₄	—	106	1	no	—
361	C₂²⋊C₄	—	106	1	no	—
362	C₂²⋊C₄	—	212	2	no	—
363	C₄²	—	106	1	no	—
364	C₄²	—	106	1	no	—
365	C₄²	—	106	1	no	—
366	C₄²	—	212	2	no	—
367	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
368	C₄²	D₄×D₅₃	1	1	yes	characteristic
369	C₄²	#11719949	1	1	yes	characteristic
370	C₄²	C₂³×D₅₃	1	1	yes	characteristic
371	C₂³	—	106	1	no	—
372	C₂³	#13133192	1	1	yes	characteristic
373	Q₈	—	53	2	no	—
374	Q₈	—	106	1	no	—
375	Q₈	—	212	2	no	—
376	Q₈	—	212	2	no	—
377	Q₈	—	212	2	no	—
378	Q₈	—	212	2	no	—
379	D₄	—	53	2	no	—
380	D₄	—	106	4	no	—
381	D₄	—	106	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	106	4	no	—
388	C₂×C₄	—	106	1	no	—
389	C₂×C₄	—	106	1	no	—
390	C₂×C₄	—	106	1	no	—
391	C₂×C₄	—	212	2	no	—
392	C₂×C₄	—	212	2	no	—
393	C₂×C₄	—	212	1	no	—
394	C₂×C₄	—	212	2	no	—
395	C₂×C₄	—	212	1	no	—
396	C₂×C₄	#13133192	1	1	yes	characteristic
397	C₂×C₄	#13133192	1	1	yes	characteristic
398	C₂×C₄	#13133192	1	1	yes	characteristic
399	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
401	C₂×C₄	C₂×#11719949	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	4	2	no	—
406	C₈	—	4	2	no	—
407	C₈	—	212	1	no	—
408	C₈	—	212	1	no	—
409	C₈	#13133239	1	2	yes	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	106	2	no	—
414	C₂²	—	212	1	no	—
415	C₂²	—	212	1	no	—
416	C₂²	C₂×#13133192	1	1	yes	characteristic
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	106	2	no	—
421	C₄	—	424	2	no	—
422	C₄	—	424	2	no	—
423	C₄	—	212	1	no	—
424	C₄	—	212	1	no	—
425	C₄	#16810899	1	2	yes	—
426	C₄	#135×D₅₃	1	1	yes	characteristic
427	C₄	#135×D₅₃	1	1	yes	characteristic
428	C₄	C₂×#13133239	1	1	yes	characteristic
429	C₄	#16811423	1	1	yes	characteristic
430	C₂	—	4	1	no	—
431	C₂	—	212	2	no	—
432	C₂	#20284172	1	1	yes	characteristic
433	C₂	#20284297	1	1	yes	characteristic
434	C₂	C₂×#16810899	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13133192
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1564	C₂
socle	C₂²×C₅₃	C₂×#121
prime radical	C₂×#11719945	D₄
hypercenter	#1564	D₅₃
hypocenter	C₅₃	#19129
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
1. #20285301	C₂	semidirect
4. #20274146	C₂	semidirect
5. #20274139	C₂	semidirect
6. #20274110	C₂	semidirect
7. #20274105	C₂	semidirect
8. #20274086	C₂	semidirect
9. #20274081	C₂	semidirect
10. #20273379	C₂	semidirect
11. C₅₃×#1564	C₂	semidirect
222. #1564	D₅₃	semidirect
264. C₅₃	#19129	semidirect

Maximal subgroups

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

subgroup	index
#20285301	2
#20284787	2
C₈×#11719945	2
#20274146	2
#20274139	2
#20274110	2
#20274105	2
#20274086	2
#20274081	2
#20273379	2
C₅₃×#1564	2
#19129	53