Finite Group Databasebeta

← #27418262

Subgroups — #27418262

Order 13568.

1090 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811313C211yesmaximal, characteristic
2C2×#16810930C211yesmaximal, characteristic, complemented
3C2×#16810728C211yesmaximal, characteristic, complemented
4#20275918C211yesmaximal, characteristic, complemented
5#20275911C211yesmaximal, characteristic, complemented
6#20275723C211yesmaximal, characteristic, complemented
7#20275723C211yesmaximal, characteristic, complemented
8#20275683C211yesmaximal, characteristic, complemented
9#20275514C211yesmaximal, characteristic
10#20275028C211yesmaximal, characteristic, complemented
11#20275023C211yesmaximal, characteristic, complemented
12#20274912C211yesmaximal, characteristic, complemented
13#20274907C211yesmaximal, characteristic, complemented
14#20274717C211yesmaximal, characteristic, complemented
15C53×#2538C211yesmaximal, characteristic
16C22×#11719925C2211yescharacteristic
17#16811313—24no—
18#16811313—24no—
19C2×#13133210—21no—
20C2×#13133209C2211yescharacteristic
21C2×#13133207—21no—
22C2×#13133198—21no—
23C2×#13133196C2211yescharacteristic
24C2×#13133196C2211yescharacteristic
25C2×C4×Dic106C2211yescharacteristic
26C2×#13133176C2211yescharacteristic
27C2×#13133173—21no—
28C22×C4⋊Dic53C2211yescharacteristic
29#16810930—24no—
30#16810728—24no—
31C2×#13133150C2211yescharacteristic
32C2×#13133148C2211yescharacteristic
33C2×#13133148C2211yescharacteristic
34C2×C4⋊#88322C2211yescharacteristic
35C2×#13133141C2211yescharacteristic
36C2×#13133141C2211yescharacteristic
37C2×#13133141C2211yescharacteristic
38C2×#13133140C2211yescharacteristic
39C2×#13133140C2211yescharacteristic
40C2×#13133140C2211yescharacteristic
41C2×C22⋊#88322C2211yescharacteristic
42C2×C22⋊#88322C2211yescharacteristic
43C2×C22⋊#88322C2211yescharacteristic
44C2×C22⋊#88322C2211yescharacteristic
45C2×#13133128C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52C2×C22⋊Q8×C53C2211yescharacteristic
53C2×C22⋊Q8×C53C2211yescharacteristic
54C2×C4×Q8×C53C2211yescharacteristic
55C2×C4×D4×C53C2211yescharacteristic
56C53×#396—21no—
57C53×#396—21no—
58C53×#390—21no—
59C53×#389—21no—
60C53×#384C2211yescharacteristic
61C53×#380C2211yescharacteristic
62C53×#380C2211yescharacteristic
63C22×Dic106C2311yescharacteristic
64C23×Dic53—21no—
65C2×#11719925—22no—
66C2×#11719925—22no—
67C2×#11719925—22no—
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71C22×#88322C2311yescharacteristic
72#13133210—28no—
73#13133209—22no—
74#13133209D414yes—
75#13133207—28no—
76#13133198—28no—
77#13133196—22no—
78#13133196—22no—
79#13133196—22no—
80#13133196—22no—
81C4×Dic106—22no—
82C4×Dic106D414yes—
83#13133176—22no—
84#13133176—22no—
85#13133173—28no—
86C2×C4⋊Dic53—22no—
87C2×C4⋊Dic53—22no—
88C2×C4⋊Dic53—21no—
89C2×C4⋊Dic53C2311yescharacteristic
90C2×C4⋊Dic53C2311yescharacteristic
91C2×C4⋊Dic53C2311yescharacteristic
92C2×#11719919—21no—
93C2×#11719919—21no—
94C2×#11719919—21no—
95C2×#11719919—21no—
96C2×#11719919—21no—
97C2×C22⋊Dic53—21no—
98C2×C22⋊Dic53—21no—
99C2×C22⋊Dic53—21no—
100C2×C4×Dic53—21no—
101C2×C4×Dic53—21no—
102#13133150—22no—
103#13133148—22no—
104#13133148—22no—
105C4⋊#88322—22no—
106#13133141—22no—
107#13133141—22no—
108#13133141—22no—
109#13133140—22no—
110#13133140—41no—
111#13133140—41no—
112C22⋊#88322—22no—
113C22⋊#88322—22no—
114C22⋊#88322—41no—
115C22⋊#88322—41no—
116#13133128—22no—
117C22×Q8×C53C2311yescharacteristic
118C22×D4×C53D411yescharacteristic
119C23×C4×C53C2311yescharacteristic
120C23×C4×C53C2311yescharacteristic
121C22⋊Q8×C53—22no—
122C22⋊Q8×C53—22no—
123C22⋊Q8×C53—41no—
124C22⋊Q8×C53—41no—
125C4×Q8×C53—22no—
126C4×Q8×C53—22no—
127C4×D4×C53—22no—
128C4×D4×C53—22no—
129C2×C4⋊C4×C53—21no—
130C2×C4⋊C4×C53—21no—
131C2×C4⋊C4×C53—21no—
132C2×C4⋊C4×C53—21no—
133C2×C4⋊C4×C53—21no—
134C2×C4⋊C4×C53D411yescharacteristic
135C2×C4⋊C4×C53C2311yescharacteristic
136C2×C4⋊C4×C53C2311yescharacteristic
137C2×C4⋊C4×C53C2311yescharacteristic
138C2×C22⋊C4×C53—21no—
139C2×C22⋊C4×C53—21no—
140C2×C22⋊C4×C53—21no—
141C2×C22⋊C4×C53—21no—
142C2×C22⋊C4×C53D411yescharacteristic
143C2×C22⋊C4×C53D411yescharacteristic
144C2×C42×C53—21no—
145C2×C42×C53C2311yescharacteristic
146#95×C53—21no—
147#95×C53—21no—
148C24×C53C2×D411yescharacteristic
149C24×C53C2×D411yescharacteristic
150C2×Q8×C53—21no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53—21no—
154C2×Q8×C53—21no—
155C2×Q8×C53#4112yes—
156C2×D4×C53—22no—
157C2×D4×C53—22no—
158C2×D4×C53—41no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53C2×D411yescharacteristic
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2411yescharacteristic
180C22×Dic53—24no—
181C22×Dic53—21no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C22×Dic53—21no—
185C22×Dic53—42no—
186C22×Dic53—42no—
187C2×Dic106—21no—
188C2×Dic106—21no—
189C2×Dic106—21no—
190C2×Dic106—21no—
191C2×Dic106—21no—
192C2×Dic106C2×D412yes—
193C4⋊C4×C53—22no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—21no—
197C4⋊C4×C53—21no—
198C4⋊C4×C53—21no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53—42no—
201C4⋊C4×C53—42no—
202C4⋊C4×C53—42no—
203C4⋊C4×C53—42no—
204C4⋊C4×C53—81no—
205C22⋊C4×C53—22no—
206C22⋊C4×C53—22no—
207C22⋊C4×C53—42no—
208C22⋊C4×C53—42no—
209C22⋊C4×C53—81no—
210C22⋊C4×C53—81no—
211C42×C53—42no—
212C42×C53C2×D412yes—
213C42×C53C2×D412yes—
214C22⋊Dic53—24no—
215C22⋊Dic53—24no—
216C22⋊Dic53—24no—
217#11719925—28no—
218C4⋊Dic53—24no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53C2×D412yes—
223C4⋊Dic53C2×D412yes—
224C4⋊Dic53C2×D412yes—
225#11719919—24no—
226#11719919—24no—
227#11719919—24no—
228#11719919—24no—
229#11719919—24no—
230C4×Dic53—24no—
231C4×Dic53—24no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322—21no—
240C2×#88322—21no—
241C2×#88322—21no—
242C2×#88322—21no—
243C2×#88322#4112yes—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53—21no—
256C23×C53—21no—
257C23×C53#13712yes—
258C23×C53C22×D411yescharacteristic
259Q8×C53—22no—
260Q8×C53—22no—
261Q8×C53—41no—
262Q8×C53—41no—
263D4×C53—44no—
264C2×C4×C53—21no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—21no—
269C2×C4×C53—21no—
270C2×C4×C53—21no—
271C2×C4×C53—21no—
272C2×C4×C53—22no—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
275C2×C4×C53—41no—
276C2×C4×C53—41no—
277C2×C4×C53—41no—
278C2×C4×C53—41no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—41no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53#12012yes—
295C2×C4×C53#12012yes—
296C2×C4×C53C22×D411yescharacteristic
297C2×C4×C53C22×D411yescharacteristic
298C2×C4×C53C2×#4111yescharacteristic
299C2×C4×C53C2×#4111yescharacteristic
300C2×C4×C53H(5,𝔽2)11yescharacteristic
301C2×C4×C532−1+411yescharacteristic
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—48no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315Dic106—22no—
316Dic106—22no—
317Dic106—41no—
318Dic106—41no—
319#88322—22no—
320#88322—41no—
321#88322—41no—
322#88322—41no—
323#24139—531nomaximal, Sylow
324C22×C53—22no—
325C22×C53—22no—
326C22×C53—22no—
327C22×C53—41no—
328C22×C53—41no—
329C22×C53—41no—
330C22×C53—41no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53—41no—
334C22×C53—41no—
335C22×C53—41no—
336C22×C53—41no—
337C22×C53—41no—
338C22×C53C2×#12011yescharacteristic
339C22×C53#54611yescharacteristic
340C22×C53#54711yescharacteristic
341C22×C53C2×#13711yescharacteristic
342C22×C53#57511yescharacteristic
343C22×C53#57711yescharacteristic
344C22×C53#57811yescharacteristic
345C4×C53—22no—
346C4×C53—22no—
347C4×C53—41no—
348C4×C53—41no—
349C4×C53—42no—
350C4×C53—81no—
351C4×C53—81no—
352C4×C53—81no—
353C4×C53#52511yescharacteristic
354C4×C53#53711yescharacteristic
355C4×C53#54811yescharacteristic
356C4×C53#55011yescharacteristic
357Dic53—42no—
358Dic53—42no—
359Dic53—42no—
360Dic53—42no—
361C2×#552—531no—
362C2×#479—531no—
363C2×#441—531no—
364#2538D5311yescharacteristic
365#2036—531no—
366#2035—531no—
367#2001—531no—
368#2001—531no—
369#1992—531no—
370#1955—531no—
371#1873—531no—
372#1872—531no—
373#1854—531no—
374#1853—531no—
375#1803—531no—
376C2×C53—42no—
377C2×C53—81no—
378C2×C53#240711yescharacteristic
379C2×C53#300711yescharacteristic
380C2×C53#301311yescharacteristic
381C2×C53#331211yescharacteristic
382C2×C53#331711yescharacteristic
383C2×C53#334411yescharacteristic
384C2×C53#334911yescharacteristic
385C22×Q16—531no—
386#552—1064no—
387#552—1064no—
388C2×#126—1061no—
389C2×#125—531no—
390C2×#125—1061no—
391C2×#123—1061no—
392C2×C22⋊Q8—531no—
393C2×C22⋊Q8—531no—
394C2×C22⋊Q8C2×D5311yescharacteristic
395C2×C22⋊Q8C2×D5311yescharacteristic
396C2×C4×Q8—531no—
397C2×C4×Q8C2×D5311yescharacteristic
398C2×C4×D4C2×D5311yescharacteristic
399C2×#117—531no—
400C2×#117—1061no—
401C22×C4⋊C4—531no—
402#479—1064no—
403#441—1064no—
404C2×#107—531no—
405C2×#106—531no—
406C2×#106—531no—
407C2×C4⋊C8—531no—
408C2×#103—531no—
409C2×#103—531no—
410C2×#103—531no—
411C2×#103—531no—
412C2×#103—531no—
413C2×#103—531no—
414C2×C22⋊C8—531no—
415C2×C22⋊C8—531no—
416C2×C22⋊C8—531no—
417C2×C22⋊C8—531no—
418C2×#97—531no—
419#396—21no—
420#396—21no—
421#390—21no—
422#389—21no—
423#384C2×D5311yescharacteristic
424#380C2×D5311yescharacteristic
425#380C2×D5311yescharacteristic
426#340—531no—
427#340—531no—
428#340—531no—
429#340—531no—
430#340—531no—
431#340—531no—
432C53#2413911yescharacteristic, complemented, Sylow
433C22×Q8—531no—
434C22×Q8C22×D5311yescharacteristic
435C22×D4C22⋊D5311yescharacteristic
436C23×C4—1061no—
437C23×C4C22×D5311yescharacteristic
438C23×C4C22×D5311yescharacteristic
439C2×Q16—1062no—
440C2×Q16—1062no—
441C2×Q16—1062no—
442C22×C8—531no—
443C22×C8—531no—
444C22×C8—531no—
445C22×C8—531no—
446#126—1068no—
447#125—534no—
448#125—1068no—
449#125—1062no—
450#123—1068no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453C22⋊Q8—41no—
454C22⋊Q8—41no—
455C22⋊Q8—1062no—
456C22⋊Q8—1062no—
457C22⋊Q8—1062no—
458C22⋊Q8—1062no—
459C4×Q8—22no—
460C4×Q8—22no—
461C4×Q8—534no—
462C4×Q8—1062no—
463C4×D4—22no—
464C4×D4—22no—
465#117—1068no—
466#117—1062no—
467#117—1062no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—531no—
474C2×C4⋊C4—531no—
475C2×C4⋊C4—531no—
476C2×C4⋊C4—1062no—
477C2×C4⋊C4—1062no—
478C2×C4⋊C4—1061no—
479C2×C4⋊C4—1061no—
480C2×C4⋊C4—1061no—
481C2×C4⋊C4—1061no—
482C2×C4⋊C4—1061no—
483C2×C4⋊C4—1061no—
484C2×C4⋊C4C22⋊D5311yescharacteristic
485C2×C4⋊C4C22×D5311yescharacteristic
486C2×C4⋊C4C22×D5311yescharacteristic
487C2×C4⋊C4C22×D5311yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—1061no—
493C2×C22⋊C4—1061no—
494C2×C22⋊C4—1061no—
495C2×C22⋊C4C22⋊D5311yescharacteristic
496C2×C22⋊C4C22⋊D5311yescharacteristic
497C2×C42—21no—
498C2×C42—1061no—
499C2×C42—1061no—
500C2×C42C22×D5311yescharacteristic
501#107—1062no—
502#106—1062no—
503#106—1062no—
504C4⋊C8—1062no—
505#103—1062no—
506#103—1062no—
507#103—1062no—
508#103—1062no—
509#103—2121no—
510#103—2121no—
511C22⋊C8—1062no—
512C22⋊C8—1062no—
513C22⋊C8—2121no—
514C22⋊C8—2121no—
515#97—1062no—
516#95—21no—
517#95—21no—
518C24C2×C22⋊D5311yescharacteristic
519C24C2×C22⋊D5311yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—532no—
526C2×Q8—1061no—
527C2×Q8—1061no—
528C2×Q8—1061no—
529C2×Q8—1061no—
530C2×Q8—1061no—
531C2×Q8#1171994712yes—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—41no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—1064no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—2122no—
557C22×C4—2122no—
558C22×C4C2×C22⋊D5311yescharacteristic
559C22×C4C2×C22⋊D5311yescharacteristic
560C22×C4C2×C22⋊D5311yescharacteristic
561C22×C4C2×C22⋊D5311yescharacteristic
562C22×C4C23×D5311yescharacteristic
563Q16—1068no—
564C2×C8—532no—
565C2×C8—1061no—
566C2×C8—1061no—
567C2×C8—1061no—
568C2×C8—1061no—
569C2×C8—1061no—
570C2×C8—1061no—
571C2×C8—1061no—
572C2×C8—1061no—
573C2×C8—1061no—
574C2×C8—1061no—
575C2×C8—1061no—
576C4⋊C4—22no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—81no—
588C4⋊C4—532no—
589C4⋊C4—532no—
590C4⋊C4—532no—
591C4⋊C4—1064no—
592C4⋊C4—1064no—
593C4⋊C4—1064no—
594C4⋊C4—1064no—
595C4⋊C4—1064no—
596C4⋊C4—1064no—
597C4⋊C4—1061no—
598C4⋊C4—1061no—
599C4⋊C4—1061no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—1064no—
607C22⋊C4—1064no—
608C22⋊C4—1064no—
609C42—42no—
610C42—1064no—
611C42—1064no—
612C42D4×D5312yes—
613C42D4×D5312yes—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23#1313324812yes—
628C23C22×C22⋊D5311yescharacteristic
629Q8—22no—
630Q8—22no—
631Q8—41no—
632Q8—41no—
633Q8—1062no—
634Q8—1062no—
635Q8—2121no—
636Q8—2121no—
637D4—44no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—1062no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1062no—
672C2×C4—2128no—
673C2×C4—2121no—
674C2×C4—2121no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4—2121no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4#1313318512yes—
682C2×C4#1313318512yes—
683C2×C4C2×D4×D5311yescharacteristic
684C2×C4C2×D4×D5311yescharacteristic
685C2×C4#41×D5311yescharacteristic
686C2×C4C2×#1171994711yescharacteristic
687C2×C4#1313326211yescharacteristic
688C2×C4#1313326411yescharacteristic
689C8—1062no—
690C8—2121no—
691C8—2121no—
692C8—2121no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22C2×#1313318511yescharacteristic
708C22#1681126711yescharacteristic
709C22#1681127211yescharacteristic
710C22C2×#1313324811yescharacteristic
711C22#1681142111yescharacteristic
712C22#1681143411yescharacteristic
713C22#1681143811yescharacteristic
714C4—22no—
715C4—22no—
716C4—41no—
717C4—41no—
718C4—42no—
719C4—81no—
720C4—81no—
721C4—81no—
722C4—2122no—
723C4—2122no—
724C4—2122no—
725C4—2122no—
726C4#1681113311yescharacteristic
727C4#1681120211yescharacteristic
728C4#1681127911yescharacteristic
729C4#1681129111yescharacteristic
730C2—42no—
731C2—81no—
732C2#2027805611yescharacteristic
733C2#2028397311yescharacteristic
734C2#2028402711yescharacteristic
735C2#2028676611yescharacteristic
736C2#2028684111yescharacteristic
737C2#2028716411yescharacteristic
738C2#2028723911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC53×#2538C2
socleC23×C53C22×D4
prime radicalC22×D4×C53D4
hypercenter#2538D53
hypocenterC53#24139
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

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

NH ≅ G/Ntype
2. C2×#16810930C2semidirect
3. C2×#16810728C2semidirect
4. #20275918C2semidirect
5. #20275911C2semidirect
6. #20275723C2semidirect
7. #20275723C2semidirect
8. #20275683C2semidirect
10. #20275028C2semidirect
11. #20275023C2semidirect
12. #20274912C2semidirect
13. #20274907C2semidirect
14. #20274717C2semidirect
432. C53#24139semidirect

Maximal subgroups

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

subgroupindex
C2×#168113132
C2×#168109302
C2×#168107282
#202759182
#202759112
#202757232
#202756832
#202755142
#202750282
#202750232
#202749122
#202749072
#202747172
C53×#25382
#2413953