Finite Group Databasebeta

← #27350367

Subgroups — #27350367

Order 13568.

1060 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283750C212yesmaximal, complemented
2#20273084C212yesmaximal, complemented
3#20273079C212yesmaximal, complemented
4#20273063C212yesmaximal, complemented
5#20273053C211yesmaximal, characteristic, complemented
6#20273049C211yesmaximal, characteristic, complemented
7#20273042C211yesmaximal, characteristic, complemented
8#20273033C211yesmaximal, characteristic, complemented
9#20273029C211yesmaximal, characteristic, complemented
10C2×#16810347C211yesmaximal, characteristic, complemented
11C2×C53×#551C211yesmaximal, characteristic
12#16810701—22no—
13#16810695—22no—
14#16810695—22no—
15D4×#88322—22no—
16#16810680C2212yescomplemented
17#16810676C2212yescomplemented
18#16810587C2212yes—
19#16810587C2212yescomplemented
20C2×C22⋊#88322C2212yes—
21C2×C22⋊#88322C2212yescomplemented
22#16810349C2212yescomplemented
23#16810349C2212yescomplemented
24#16810349C2212yescomplemented
25#16810349C2212yescomplemented
26#16810347C2211yescharacteristic
27#16810347C2211yescharacteristic
28#16810347C2212yes—
29#16810347C2211yescharacteristic
30#16810347C2211yescharacteristic
31#16810347C2212yes—
32C53×#551—22no—
33C53×#551—22no—
34C53×#551—22no—
35C53×#551—22no—
36C2×#126×C53C411yescharacteristic
37C2×#126×C53C2211yescharacteristic
38C2×#124×C53C411yescharacteristic
39C2×#123×C53C411yescharacteristic
40C2×#123×C53C411yescharacteristic
41C2×#123×C53C2211yescharacteristic
42C2×C22⋊Q8×C53C411yescharacteristic
43C2×C22⋊Q8×C53C2211yescharacteristic
44C2×#120×C53C411yescharacteristic
45C2×C4×D4×C53C2211yescharacteristic
46C2×C4×D4×C53C2211yescharacteristic
47C2×#117×C53C411yescharacteristic
48C2×#117×C53C2211yescharacteristic
49C22×C22⋊C4×C53C411yescharacteristic
50C22×C22⋊C4×C53C2211yescharacteristic
51C2×#11719917—22no—
52C2×#11719917—22no—
53C22×#88322—22no—
54C22×#88322—22no—
55C4⋊#88322—22no—
56C4⋊#88322—22no—
57C22⋊#88322—22no—
58C22⋊#88322—22no—
59C22⋊#88322—22no—
60C22⋊#88322—22no—
61C22⋊#88322C2312yes—
62C22⋊#88322C2312yes—
63C22⋊#88322C2312yes—
64C22⋊#88322C2312yes—
65#13133128—22no—
66C4×#88322—22no—
67C25×C53C2×C411yescharacteristic
68C22×Q8×C53C2×C411yescharacteristic
69C22×D4×C53C2×C411yescharacteristic
70C22×D4×C53C2×C411yescharacteristic
71C22×D4×C53C2×C411yescharacteristic
72C23×C4×C53C2×C411yescharacteristic
73C23×C4×C53C2×C411yescharacteristic
74C23×C4×C53C2×C411yescharacteristic
75C23×C4×C53C2311yescharacteristic
76C23×C4×C53C2311yescharacteristic
77#126×C53—22no—
78#126×C53—22no—
79#126×C53—22no—
80#126×C53—22no—
81#124×C53—22no—
82#124×C53—22no—
83#123×C53—22no—
84#123×C53—22no—
85#123×C53—22no—
86#123×C53—22no—
87#123×C53—22no—
88#123×C53—22no—
89C22⋊Q8×C53—22no—
90C22⋊Q8×C53—22no—
91C22⋊Q8×C53—22no—
92C22⋊Q8×C53—22no—
93#120×C53—22no—
94#120×C53—22no—
95C4×D4×C53—22no—
96C4×D4×C53—22no—
97C4×D4×C53D412yes—
98C4×D4×C53D412yes—
99C4×D4×C53D412yes—
100C4×D4×C53D412yes—
101#117×C53—21no—
102#117×C53—21no—
103#117×C53—21no—
104#117×C53—21no—
105#117×C53—22no—
106#117×C53—22no—
107C2×C4⋊C4×C53C2×C411yescharacteristic
108C2×C4⋊C4×C53C2×C411yescharacteristic
109C2×C4⋊C4×C53C2×C411yescharacteristic
110C2×C4⋊C4×C53C2×C411yescharacteristic
111C2×C4⋊C4×C53C2×C411yescharacteristic
112C2×C4⋊C4×C53C2×C411yescharacteristic
113C2×C4⋊C4×C53C2311yescharacteristic
114C2×C4⋊C4×C53C2311yescharacteristic
115C2×C22⋊C4×C53—21no—
116C2×C22⋊C4×C53—21no—
117C2×C22⋊C4×C53—21no—
118C2×C22⋊C4×C53—21no—
119C2×C22⋊C4×C53—22no—
120C2×C22⋊C4×C53—22no—
121C2×C22⋊C4×C53C2×C411yescharacteristic
122C2×C22⋊C4×C53C2×C411yescharacteristic
123C2×C22⋊C4×C53C2×C411yescharacteristic
124C2×C22⋊C4×C53C2×C411yescharacteristic
125C2×C22⋊C4×C53C2×C411yescharacteristic
126C2×C22⋊C4×C53C2×C411yescharacteristic
127C2×C22⋊C4×C53C2×C411yescharacteristic
128C2×C22⋊C4×C53C2×C411yescharacteristic
129C2×C22⋊C4×C53C2×C411yescharacteristic
130C2×C22⋊C4×C53C2×C411yescharacteristic
131C2×C22⋊C4×C53C2×C411yescharacteristic
132C2×C22⋊C4×C53C2×C411yescharacteristic
133C2×C22⋊C4×C53C2311yescharacteristic
134C2×C22⋊C4×C53C2311yescharacteristic
135C2×C42×C53C2×C411yescharacteristic
136C2×C42×C53C2×C411yescharacteristic
137C2×C42×C53C2311yescharacteristic
138C24×C53—21no—
139C24×C53—21no—
140C24×C53—22no—
141C24×C53—41no—
142C24×C53—42no—
143C24×C53—81no—
144C24×C53C22×C411yescharacteristic
145C24×C53C22×C411yescharacteristic
146C24×C53C22×C411yescharacteristic
147C24×C53C22×C411yescharacteristic
148C2×Q8×C53—22no—
149C2×Q8×C53—81no—
150C2×D4×C53—22no—
151C2×D4×C53—22no—
152C2×D4×C53—22no—
153C2×D4×C53—41no—
154C2×D4×C53—42no—
155C2×D4×C53—81no—
156C2×D4×C53C22⋊C412yes—
157C2×D4×C53C22⋊C412yes—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—22no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—41no—
166C22×C4×C53—42no—
167C22×C4×C53—81no—
168C22×C4×C53—81no—
169C22×C4×C53—81no—
170C22×C4×C53C22×C411yescharacteristic
171C22×C4×C53C22×C411yescharacteristic
172C22×C4×C53C22×C411yescharacteristic
173C22×C4×C53C22×C411yescharacteristic
174C22×C4×C53C22×C411yescharacteristic
175C22×C4×C53C22×C411yescharacteristic
176C22×C4×C53C22×C411yescharacteristic
177C22×C4×C53C22×C411yescharacteristic
178C22×C4×C53C22×C411yescharacteristic
179C22×C4×C53C22×C411yescharacteristic
180C22×C4×C53C2×D412yes—
181C22×C4×C53C2×D412yes—
182C22×C4×C53C2×D412yes—
183C22×C4×C53C2×D412yes—
184C22×C4×C53C2411yescharacteristic
185C4⋊C4×C53—21no—
186C4⋊C4×C53—21no—
187C4⋊C4×C53—22no—
188C4⋊C4×C53—21no—
189C4⋊C4×C53—21no—
190C4⋊C4×C53—22no—
191C4⋊C4×C53—22no—
192C4⋊C4×C53—22no—
193C4⋊C4×C53—22no—
194C4⋊C4×C53C22⋊C412yes—
195C4⋊C4×C53C22⋊C412yes—
196C22⋊C4×C53—21no—
197C22⋊C4×C53—21no—
198C22⋊C4×C53—21no—
199C22⋊C4×C53—21no—
200C22⋊C4×C53—22no—
201C22⋊C4×C53—22no—
202C22⋊C4×C53—22no—
203C22⋊C4×C53—21no—
204C22⋊C4×C53—21no—
205C22⋊C4×C53—21no—
206C22⋊C4×C53—21no—
207C22⋊C4×C53—22no—
208C22⋊C4×C53—22no—
209C22⋊C4×C53—22no—
210C22⋊C4×C53—22no—
211C22⋊C4×C53—22no—
212C22⋊C4×C53C22⋊C411yescharacteristic
213C22⋊C4×C53C22⋊C411yescharacteristic
214C22⋊C4×C53C22⋊C411yescharacteristic
215C22⋊C4×C53C22⋊C411yescharacteristic
216C22⋊C4×C53C22⋊C412yes—
217C22⋊C4×C53C22⋊C412yes—
218C42×C53—21no—
219C42×C53—21no—
220C42×C53—21no—
221C42×C53—21no—
222C42×C53C2×D412yes—
223C42×C53C2×D412yes—
224#11719917—82no—
225#11719917—82no—
226C2×#88322—22no—
227C2×#88322—22no—
228C2×#88322—22no—
229C2×#88322—22no—
230C2×#88322—82no—
231C2×#88322—82no—
232C23×C53—21no—
233C23×C53—21no—
234C23×C53—21no—
235C23×C53—21no—
236C23×C53—22no—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—41no—
243C23×C53—41no—
244C23×C53—41no—
245C23×C53—42no—
246C23×C53—42no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—42no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—42no—
253C23×C53—81no—
254C23×C53—81no—
255C23×C53—84no—
256C23×C53—84no—
257C23×C53C2×C22⋊C411yescharacteristic
258C23×C53C2×C22⋊C412yes—
259C23×C53C2×C22⋊C411yescharacteristic
260C23×C53#13112yes—
261C23×C53C23×C411yescharacteristic
262Q8×C53—82no—
263D4×C53—24no—
264D4×C53—42no—
265D4×C53—44no—
266D4×C53—82no—
267C2×C4×C53—21no—
268C2×C4×C53—21no—
269C2×C4×C53—21no—
270C2×C4×C53—21no—
271C2×C4×C53—21no—
272C2×C4×C53—21no—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—42no—
283C2×C4×C53—42no—
284C2×C4×C53—42no—
285C2×C4×C53—42no—
286C2×C4×C53—41no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53—42no—
290C2×C4×C53—42no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53—81no—
296C2×C4×C53—81no—
297C2×C4×C53C2×C22⋊C411yescharacteristic
298C2×C4×C53C2×C22⋊C411yescharacteristic
299C2×C4×C53C2×C22⋊C411yescharacteristic
300C2×C4×C53C2×C22⋊C411yescharacteristic
301C2×C4×C53C2×C22⋊C412yes—
302C2×C4×C53C2×C22⋊C412yes—
303C2×C4×C53C22×D412yes—
304#88322—42no—
305#88322—42no—
306#88322—42no—
307#88322—42no—
308#17422—531nomaximal, Sylow
309C22×C53—21no—
310C22×C53—21no—
311C22×C53—21no—
312C22×C53—21no—
313C22×C53—22no—
314C22×C53—22no—
315C22×C53—21no—
316C22×C53—22no—
317C22×C53—21no—
318C22×C53—21no—
319C22×C53—22no—
320C22×C53—42no—
321C22×C53—42no—
322C22×C53—42no—
323C22×C53—42no—
324C22×C53—41no—
325C22×C53—41no—
326C22×C53—41no—
327C22×C53—41no—
328C22×C53—41no—
329C22×C53—81no—
330C22×C53—81no—
331C22×C53—84no—
332C22×C53—81no—
333C22×C53—81no—
334C22×C53—84no—
335C22×C53#41312yes—
336C22×C53C22×C22⋊C411yescharacteristic
337C22×C53C2×#13111yescharacteristic
338C22×C53#56811yescharacteristic
339C4×C53—21no—
340C4×C53—21no—
341C4×C53—22no—
342C4×C53—21no—
343C4×C53—21no—
344C4×C53—22no—
345C4×C53—22no—
346C4×C53—41no—
347C4×C53—41no—
348C4×C53—41no—
349C4×C53—41no—
350C4×C53—41no—
351C4×C53—41no—
352C2×#551D5311yescharacteristic
353#2974—532no—
354#1473—532no—
355#1472—532no—
356#1468—532no—
357#1465—531no—
358#1464—531no—
359#1462—531no—
360#1459—531no—
361#1458—531no—
362C2×#323—531no—
363C2×C53—21no—
364C2×C53—21no—
365C2×C53—22no—
366C2×C53—41no—
367C2×C53—42no—
368C2×C53—42no—
369C2×C53—81no—
370C2×C53#288011yescharacteristic
371C2×C53#288311yescharacteristic
372C2×C53C2×#41311yescharacteristic
373#551—22no—
374#551—22no—
375#551—22no—
376#551—22no—
377C2×#126Dic5311yescharacteristic
378C2×#126C2×D5311yescharacteristic
379C2×#124Dic5311yescharacteristic
380C2×#123Dic5311yescharacteristic
381C2×#123Dic5311yescharacteristic
382C2×#123C2×D5311yescharacteristic
383C2×C22⋊Q8Dic5311yescharacteristic
384C2×C22⋊Q8C2×D5311yescharacteristic
385C2×#120Dic5311yescharacteristic
386C2×C4×D4C2×D5311yescharacteristic
387C2×C4×D4C2×D5311yescharacteristic
388C2×#117Dic5311yescharacteristic
389C2×#117C2×D5311yescharacteristic
390C22×C22⋊C4Dic5311yescharacteristic
391C22×C22⋊C4C2×D5311yescharacteristic
392#436—1062no—
393#435—1062no—
394#435—1062no—
395C8×D4—1062no—
396#432—532no—
397#431—532no—
398#407—532no—
399#407—532no—
400C2×C22⋊C8—532no—
401C2×C22⋊C8—532no—
402#324—532no—
403#324—532no—
404#324—532no—
405#324—532no—
406#323—531no—
407#323—531no—
408#323—532no—
409#323—531no—
410#323—531no—
411#323—532no—
412C53#1742211yescharacteristic, complemented, Sylow
413C25C2×Dic5311yescharacteristic
414C22×Q8C2×Dic5311yescharacteristic
415C22×D4C2×Dic5311yescharacteristic
416C22×D4C2×Dic5311yescharacteristic
417C22×D4C2×Dic5311yescharacteristic
418C23×C4C2×Dic5311yescharacteristic
419C23×C4C2×Dic5311yescharacteristic
420C23×C4C2×Dic5311yescharacteristic
421C23×C4C22×D5311yescharacteristic
422C23×C4C22×D5311yescharacteristic
423C2×M16—1062no—
424C2×M16—1062no—
425C22×C8—1062no—
426C22×C8—1062no—
427#126—22no—
428#126—22no—
429#126—22no—
430#126—22no—
431#124—22no—
432#124—22no—
433#123—22no—
434#123—22no—
435#123—22no—
436#123—22no—
437#123—22no—
438#123—22no—
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441C22⋊Q8—22no—
442C22⋊Q8—22no—
443#120—22no—
444#120—22no—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4C22⋊D5312yes—
448C4×D4C22⋊D5312yes—
449C4×D4C22⋊D5312yes—
450C4×D4C22⋊D5312yes—
451#117—21no—
452#117—21no—
453#117—21no—
454#117—21no—
455#117—22no—
456#117—22no—
457C2×C4⋊C4C2×Dic5311yescharacteristic
458C2×C4⋊C4C2×Dic5311yescharacteristic
459C2×C4⋊C4C2×Dic5311yescharacteristic
460C2×C4⋊C4C2×Dic5311yescharacteristic
461C2×C4⋊C4C2×Dic5311yescharacteristic
462C2×C4⋊C4C2×Dic5311yescharacteristic
463C2×C4⋊C4C22×D5311yescharacteristic
464C2×C4⋊C4C22×D5311yescharacteristic
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4C2×Dic5311yescharacteristic
472C2×C22⋊C4C2×Dic5311yescharacteristic
473C2×C22⋊C4C2×Dic5311yescharacteristic
474C2×C22⋊C4C2×Dic5311yescharacteristic
475C2×C22⋊C4C2×Dic5311yescharacteristic
476C2×C22⋊C4C2×Dic5311yescharacteristic
477C2×C22⋊C4C2×Dic5311yescharacteristic
478C2×C22⋊C4C2×Dic5311yescharacteristic
479C2×C22⋊C4C2×Dic5311yescharacteristic
480C2×C22⋊C4C2×Dic5311yescharacteristic
481C2×C22⋊C4C2×Dic5311yescharacteristic
482C2×C22⋊C4C2×Dic5311yescharacteristic
483C2×C22⋊C4C22×D5311yescharacteristic
484C2×C22⋊C4C22×D5311yescharacteristic
485C2×C42C2×Dic5311yescharacteristic
486C2×C42C2×Dic5311yescharacteristic
487C2×C42C22×D5311yescharacteristic
488C4⋊C8—1062no—
489C4⋊C8—1062no—
490C22⋊C8—532no—
491C22⋊C8—532no—
492C22⋊C8—532no—
493C22⋊C8—532no—
494C22⋊C8—1062no—
495C22⋊C8—1062no—
496C22⋊C8—1062no—
497C22⋊C8—1062no—
498#97—1062no—
499C4×C8—1062no—
500C24—21no—
501C24—21no—
502C24—22no—
503C24—41no—
504C24—42no—
505C24—81no—
506C24C22×Dic5311yescharacteristic
507C24C22×Dic5311yescharacteristic
508C24C22×Dic5311yescharacteristic
509C24C22×Dic5311yescharacteristic
510C2×Q8—22no—
511C2×Q8—81no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—41no—
516C2×D4—42no—
517C2×D4—81no—
518C2×D4C22⋊Dic5312yes—
519C2×D4C22⋊Dic5312yes—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—41no—
528C22×C4—42no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4C22×Dic5311yescharacteristic
533C22×C4C22×Dic5311yescharacteristic
534C22×C4C22×Dic5311yescharacteristic
535C22×C4C22×Dic5311yescharacteristic
536C22×C4C22×Dic5311yescharacteristic
537C22×C4C22×Dic5311yescharacteristic
538C22×C4C22×Dic5311yescharacteristic
539C22×C4C22×Dic5311yescharacteristic
540C22×C4C22×Dic5311yescharacteristic
541C22×C4C22×Dic5311yescharacteristic
542C22×C4C2×C22⋊D5312yes—
543C22×C4C2×C22⋊D5312yes—
544C22×C4C2×C22⋊D5312yes—
545C22×C4C2×C22⋊D5312yes—
546C22×C4C23×D5311yescharacteristic
547M16—4242no—
548M16—4242no—
549C2×C8—1062no—
550C2×C8—1062no—
551C2×C8—1062no—
552C2×C8—1062no—
553C2×C8—4242no—
554C2×C8—4242no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—22no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4C22⋊Dic5312yes—
565C4⋊C4C22⋊Dic5312yes—
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—21no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C22⋊C4—22no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4C22⋊Dic5311yescharacteristic
583C22⋊C4C22⋊Dic5311yescharacteristic
584C22⋊C4C22⋊Dic5311yescharacteristic
585C22⋊C4C22⋊Dic5311yescharacteristic
586C22⋊C4C22⋊Dic5312yes—
587C22⋊C4C22⋊Dic5312yes—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42C2×C22⋊D5312yes—
593C42C2×C22⋊D5312yes—
594C23—21no—
595C23—22no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—42no—
608C23—42no—
609C23—41no—
610C23—41no—
611C23—42no—
612C23—41no—
613C23—41no—
614C23—42no—
615C23—81no—
616C23—81no—
617C23—84no—
618C23—84no—
619C23C2×C22⋊Dic5311yescharacteristic
620C23C2×C22⋊Dic5312yes—
621C23C2×C22⋊Dic5311yescharacteristic
622C23#1313322412yes—
623C23C23×Dic5311yescharacteristic
624Q8—82no—
625D4—24no—
626D4—42no—
627D4—44no—
628D4—82no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—81no—
658C2×C4—81no—
659C2×C4C2×C22⋊Dic5311yescharacteristic
660C2×C4C2×C22⋊Dic5311yescharacteristic
661C2×C4C2×C22⋊Dic5311yescharacteristic
662C2×C4C2×C22⋊Dic5311yescharacteristic
663C2×C4C2×C22⋊Dic5312yes—
664C2×C4C2×C22⋊Dic5312yes—
665C2×C4C22×C22⋊D5312yes—
666C8—2122no—
667C8—2122no—
668C8—2122no—
669C8—2122no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—22no—
675C22—22no—
676C22—21no—
677C22—22no—
678C22—21no—
679C22—21no—
680C22—22no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—81no—
691C22—81no—
692C22—84no—
693C22—81no—
694C22—81no—
695C22—84no—
696C22#1681060712yes—
697C22C22×C22⋊Dic5311yescharacteristic
698C22C2×#1313322411yescharacteristic
699C22#1681139011yescharacteristic
700C4—21no—
701C4—21no—
702C4—22no—
703C4—21no—
704C4—21no—
705C4—22no—
706C4—22no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C2—21no—
714C2—21no—
715C2—22no—
716C2—41no—
717C2—42no—
718C2—42no—
719C2—81no—
720C2#2028316411yescharacteristic
721C2#2028317611yescharacteristic
722C2C2×#1681060711yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic53
commutatorC23×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#551C2
socleC22×C53C22×C22⋊C4
prime radicalC2×#120×C53C4
cosocleC22×C4×C53C24
hypercenterC2×#551D53
hypocenterC53#17422
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#551

Complements

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

NH ≅ G/Ntype
1. #20283750C2semidirect
2. #20273084C2semidirect
3. #20273079C2semidirect
4. #20273063C2semidirect
5. #20273053C2semidirect
6. #20273049C2semidirect
7. #20273042C2semidirect
8. #20273033C2semidirect
9. #20273029C2semidirect
10. C2×#16810347C2semidirect
16. #16810680C22semidirect
17. #16810676C22semidirect
19. #16810587C22semidirect
21. C2×C22⋊#88322C22semidirect
22. #16810349C22semidirect
23. #16810349C22semidirect
24. #16810349C22semidirect
25. #16810349C22semidirect
412. C53#17422semidirect

Maximal subgroups

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

subgroupindex
#202837502
#202730842
#202730792
#202730632
#202730532
#202730492
#202730422
#202730332
#202730292
C2×#168103472
C2×C53×#5512
#1742253