Finite Group Databasebeta

← #27404465

Subgroups — #27404465

Order 13568.

1134 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810785C211yesmaximal, characteristic
2C2×#16810723C211yesmaximal, characteristic, complemented
3C2×#16810624C211yesmaximal, characteristic
4#20277718C211yesmaximal, characteristic, complemented
5#20275575C211yesmaximal, characteristic, complemented
6#20275408C211yesmaximal, characteristic, complemented
7#20275353C211yesmaximal, characteristic, complemented
8#20275146C211yesmaximal, characteristic, complemented
9#20275059C211yesmaximal, characteristic, complemented
10#20275049C211yesmaximal, characteristic, complemented
11#20274962C211yesmaximal, characteristic, complemented
12#20274902C211yesmaximal, characteristic, complemented
13C4×#13133138C211yesmaximal, characteristic, complemented
14#20274499C211yesmaximal, characteristic, complemented
15C53×#2339C211yesmaximal, characteristic
16C22×#11719925C2211yescharacteristic
17C22×#11719923C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19C2×#13133196C2211yescharacteristic
20C2×C4×Dic106C2211yescharacteristic
21C22×C4⋊Dic53C2211yescharacteristic
22#16810785C418yescomplemented
23#16810723—24no—
24C2×#13133150C2211yescharacteristic
25C2×#13133150C2211yescharacteristic
26#16810624—24no—
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133141C2211yescharacteristic
30C2×#13133140C2211yescharacteristic
31C2×#13133140C2211yescharacteristic
32C2×#13133138C2211yescharacteristic
33C2×#13133138C2211yescharacteristic
34C2×#13133138C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36C2×#13133128C2211yescharacteristic
37C2×C4×#88322C2211yescharacteristic
38#16810529C2211yescharacteristic
39#16810521C2211yescharacteristic
40#16810520—21no—
41#16810510—21no—
42#16810495—21no—
43C4×C4⋊Dic53C2211yescharacteristic
44C22⋊C4×Dic53—21no—
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810378C2211yescharacteristic
51C22×#41×C53C2211yescharacteristic
52C2×C4×D4×C53C2211yescharacteristic
53C2×C4×D4×C53C2211yescharacteristic
54C53×#391C2211yescharacteristic
55C53×#391C2211yescharacteristic
56C53×#386—21no—
57C53×#386—21no—
58C53×#381—21no—
59C53×#380C2211yescharacteristic
60C4×C22⋊C4×C53C2211yescharacteristic
61C2×#95×C53—21no—
62C22×Dic106C2311yescharacteristic
63C23×Dic53—21no—
64C2×#11719925—41no—
65C2×#11719925—41no—
66C2×#11719925C2×C414yescomplemented
67C2×#11719923—22no—
68C2×#11719923—22no—
69C2×#11719923C2×C414yescomplemented
70C2×#11719917—22no—
71C2×#11719917—22no—
72C2×#11719917—41no—
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76C22×#88322C2311yescharacteristic
77#13133196—22no—
78#13133196C2×C414yescomplemented
79C4×Dic106—22no—
80C4×Dic106—41no—
81C2×C4⋊Dic53—21no—
82C2×C4⋊Dic53—22no—
83C2×C4⋊Dic53—41no—
84C2×C4⋊Dic53C2311yescharacteristic
85C2×C4⋊Dic53C2311yescharacteristic
86C2×C4⋊Dic53C2311yescharacteristic
87C2×#11719919—21no—
88C2×#11719919—21no—
89C2×#11719919—21no—
90C2×C22⋊Dic53—21no—
91C2×C4×Dic53—21no—
92C2×C4×Dic53—21no—
93#13133150—22no—
94#13133150—41no—
95#13133141—22no—
96#13133141—22no—
97#13133141C2×C414yescomplemented
98#13133140—22no—
99#13133140—41no—
100#13133138—22no—
101#13133138C2×C414yescomplemented
102#13133138D414yes—
103C22⋊#88322C2×C414yescomplemented
104#13133128—22no—
105C4×#88322—41no—
106#13133124—21no—
107#13133124—21no—
108#13133124—21no—
109#13133124—21no—
110C2×#41×C53—22no—
111C2×#41×C53—22no—
112C2×#41×C53—22no—
113C2×#41×C53—41no—
114C2×#41×C53—41no—
115C2×#41×C53C2×C414yes—
116C22×Q8×C53C2311yescharacteristic
117C22×D4×C53—21no—
118C22×D4×C53C2311yescharacteristic
119C23×C4×C53—21no—
120C23×C4×C53—21no—
121C23×C4×C53—21no—
122C23×C4×C53C2311yescharacteristic
123C4×D4×C53—22no—
124C4×D4×C53—22no—
125C4×D4×C53—41no—
126C4×D4×C53—41no—
127C2×C4⋊C4×C53C2311yescharacteristic
128C2×C4⋊C4×C53C2311yescharacteristic
129C2×C22⋊C4×C53—21no—
130C2×C22⋊C4×C53—21no—
131C2×C22⋊C4×C53—21no—
132C2×C22⋊C4×C53D411yescharacteristic
133C2×C22⋊C4×C53D411yescharacteristic
134C2×C42×C53C2311yescharacteristic
135C2×C42×C53C2311yescharacteristic
136#95×C53—21no—
137#95×C53—21no—
138#95×C53—21no—
139#95×C53—21no—
140#95×C53—21no—
141#95×C53D411yescharacteristic
142#95×C53D411yescharacteristic
143C24×C53—21no—
144C24×C53C2×D411yescharacteristic
145#41×C53—28no—
146#41×C53—44no—
147#41×C53—44no—
148#41×C53—44no—
149C2×Q8×C53—21no—
150C2×Q8×C53—21no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53—21no—
154C2×Q8×C53C22×C412yes—
155C2×D4×C53—24no—
156C2×D4×C53—21no—
157C2×D4×C53—21no—
158C2×D4×C53—21no—
159C2×D4×C53—42no—
160C2×D4×C53—42no—
161C2×D4×C53C22×C412yes—
162C2×D4×C53C2×D412yes—
163C2×D4×C53#4112yes—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—24no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—42no—
173C22×C4×C53—42no—
174C22×C4×C53—42no—
175C22×C4×C53—42no—
176C22×C4×C53—42no—
177C22×C4×C53—42no—
178C22×C4×C53—81no—
179C22×C4×C53—81no—
180C22×C4×C53C22×C412yes—
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53#4112yes—
187C22×C4×C53C2411yescharacteristic
188C22×Dic53—21no—
189C22×Dic53—21no—
190C22×Dic53—21no—
191C22×Dic53—21no—
192C22×Dic53—42no—
193C22×Dic53—42no—
194C22×Dic53—81no—
195C2×Dic106—21no—
196C2×Dic106—21no—
197C2×Dic106—21no—
198C2×Dic106—21no—
199C2×Dic106—21no—
200C2×Dic106C22×C412yes—
201C4⋊C4×C53—21no—
202C4⋊C4×C53—21no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—21no—
205C22⋊C4×C53—22no—
206C22⋊C4×C53—41no—
207C22⋊C4×C53—42no—
208C22⋊C4×C53—42no—
209C22⋊C4×C53—81no—
210C42×C53—21no—
211C42×C53—21no—
212C42×C53—21no—
213C42×C53—21no—
214C22⋊Dic53—24no—
215#11719925—44no—
216#11719923—28no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53—42no—
222C4⋊Dic53C22×C412yes—
223C4⋊Dic53C2×D412yes—
224#11719919—24no—
225#11719919—42no—
226#11719919—81no—
227C4×Dic53—42no—
228C4×Dic53—81no—
229#11719917—44no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322C22×C412yes—
240C2×#88322C22×C412yes—
241C2×#88322C2×D412yes—
242C23×C53—22no—
243C23×C53—21no—
244C23×C53—22no—
245C23×C53—21no—
246C23×C53—22no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53C4×D412yes—
256C23×C53C22×D411yescharacteristic
257Q8×C53—22no—
258Q8×C53—22no—
259Q8×C53—41no—
260Q8×C53—41no—
261D4×C53—22no—
262D4×C53—22no—
263D4×C53—22no—
264D4×C53—48no—
265D4×C53C4×D414yes—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—21no—
269C2×C4×C53—21no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53—21no—
282C2×C4×C53—21no—
283C2×C4×C53—21no—
284C2×C4×C53—48no—
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—84no—
294C2×C4×C53—84no—
295C2×C4×C53C4×D412yes—
296C2×C4×C53#13712yes—
297C2×C4×C53C23×C411yescharacteristic
298C2×C4×C53C22×D411yescharacteristic
299C2×C4×C53C2×#4111yescharacteristic
300C2×C4×C53C2×#4111yescharacteristic
301C2×C4×C53H(5,𝔽2)11yescharacteristic
302C2×C4×C53H(5,𝔽2)11yescharacteristic
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—84no—
316Dic106—22no—
317Dic106—22no—
318Dic106—41no—
319Dic106—41no—
320#88322—22no—
321#88322—22no—
322#88322—22no—
323#88322—41no—
324#22862—531nomaximal, Sylow
325C22×C53—22no—
326C22×C53—24no—
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—42no—
330C22×C53—42no—
331C22×C53—41no—
332C22×C53—42no—
333C22×C53—41no—
334C22×C53—42no—
335C22×C53—42no—
336C22×C53—41no—
337C22×C53—41no—
338C22×C53—42no—
339C22×C53C2×C4×D411yescharacteristic
340C22×C53D4211yescharacteristic
341C22×C53#54611yescharacteristic
342C22×C53C2×#13711yescharacteristic
343C22×C53#57511yescharacteristic
344C22×C53#57611yescharacteristic
345C22×C53#57811yescharacteristic
346C4×C53—22no—
347C4×C53—22no—
348C4×C53—42no—
349C4×C53—41no—
350C4×C53—41no—
351C4×C53—41no—
352C4×C53—81no—
353C4×C53—81no—
354C4×C53C2×C4×D411yescharacteristic
355C4×C53#51811yescharacteristic
356C4×C53#54611yescharacteristic
357C4×C53#55111yescharacteristic
358Dic53—42no—
359Dic53—42no—
360Dic53—42no—
361Dic53—81no—
362C2×#452—531no—
363C2×#440—531no—
364C2×#417—531no—
365#2360—531no—
366#2339D5311yescharacteristic
367#1969—531no—
368#1935—531no—
369#1928—531no—
370#1894—531no—
371#1878—531no—
372#1877—531no—
373#1862—531no—
374#1852—531no—
375C4×#102—531no—
376#1753—531no—
377C2×C53—42no—
378C2×C53—44no—
379C2×C53#235811yescharacteristic
380C2×C53C4×#13711yescharacteristic
381C2×C53#295111yescharacteristic
382C2×C53#327311yescharacteristic
383C2×C53#327611yescharacteristic
384C2×C53#331411yescharacteristic
385C2×C53#331511yescharacteristic
386C22×#41C2×D5311yescharacteristic
387C22×Q16—531no—
388C22×SD16—531no—
389C22×M16—531no—
390C2×C22⋊Q8—531no—
391C2×C4×Q8—531no—
392C2×C4×D4C2×D5311yescharacteristic
393C2×C4×D4C2×D5311yescharacteristic
394C22×C4⋊C4—531no—
395#452—538no—
396#440—1064no—
397C2×#107—531no—
398C2×#107—531no—
399#417—1064no—
400C2×#103—531no—
401C2×#103—531no—
402C2×#103—531no—
403C2×#103—531no—
404C2×#103—531no—
405C2×#102—531no—
406C2×#102—531no—
407C2×#102—531no—
408C2×C22⋊C8—531no—
409C2×#97—531no—
410C2×C4×C8—531no—
411#391—531no—
412#391C2×D5311yescharacteristic
413#391C2×D5311yescharacteristic
414#389—531no—
415#389—1061no—
416#387—1061no—
417#386—21no—
418#386—21no—
419#385—1061no—
420#381—21no—
421#380C2×D5311yescharacteristic
422C4×C4⋊C4—531no—
423C4×C22⋊C4—1061no—
424C4×C22⋊C4C2×D5311yescharacteristic
425C2×#95—21no—
426#340—531no—
427#340—531no—
428#340—531no—
429#340—531no—
430#336—531no—
431#336—531no—
432C53#2286211yescharacteristic, complemented, Sylow
433C2×#41—22no—
434C2×#41—22no—
435C2×#41—22no—
436C2×#41—41no—
437C2×#41—41no—
438C2×#41C4×D5314yes—
439C22×Q8—531no—
440C22×Q8C22×D5311yescharacteristic
441C22×D4—21no—
442C22×D4C22×D5311yescharacteristic
443C23×C4—21no—
444C23×C4—21no—
445C23×C4—21no—
446C23×C4—1061no—
447C23×C4C22×D5311yescharacteristic
448C2×Q16—534no—
449C2×Q16—2121no—
450C2×Q16—2121no—
451C2×SD16—534no—
452C2×SD16—1062no—
453C2×SD16—1062no—
454C2×M16—1062no—
455C2×M16—1062no—
456C2×M16—2121no—
457C22×C8—531no—
458C22×C8—531no—
459C22×C8—531no—
460C22×C8—531no—
461C22⋊Q8—534no—
462C22⋊Q8—1062no—
463C4×Q8—1062no—
464C4×Q8—2121no—
465C4×D4—22no—
466C4×D4—22no—
467C4×D4—41no—
468C4×D4—41no—
469C2×C4⋊C4—531no—
470C2×C4⋊C4—531no—
471C2×C4⋊C4—531no—
472C2×C4⋊C4—1062no—
473C2×C4⋊C4—1061no—
474C2×C4⋊C4—1061no—
475C2×C4⋊C4—1061no—
476C2×C4⋊C4—1061no—
477C2×C4⋊C4—2121no—
478C2×C4⋊C4C22×D5311yescharacteristic
479C2×C4⋊C4C22×D5311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—1061no—
484C2×C22⋊C4C22⋊D5311yescharacteristic
485C2×C22⋊C4C22⋊D5311yescharacteristic
486C2×C42—1061no—
487C2×C42—1061no—
488C2×C42C22×D5311yescharacteristic
489C2×C42C22×D5311yescharacteristic
490#107—1062no—
491#107—2121no—
492#103—534no—
493#103—1062no—
494#103—1062no—
495#103—1062no—
496#103—2121no—
497#102—534no—
498#102—534no—
499#102—1062no—
500C22⋊C8—534no—
501#97—1062no—
502C4×C8—2121no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—1061no—
509#95—1061no—
510#95—1061no—
511#95—1061no—
512#95C22⋊D5311yescharacteristic
513#95C22⋊D5311yescharacteristic
514C24—21no—
515C24C2×C22⋊D5311yescharacteristic
516#41—28no—
517#41—44no—
518#41—44no—
519#41—44no—
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×Q8C2×C4×D5312yes—
532C2×D4—24no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4C2×C4×D5312yes—
539C2×D4D4×D5312yes—
540C2×D4#1171994712yes—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—24no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—1061no—
558C22×C4—1061no—
559C22×C4—1061no—
560C22×C4—1061no—
561C22×C4—4241no—
562C22×C4—2122no—
563C22×C4—2122no—
564C22×C4C2×C4×D5312yes—
565C22×C4#1171994512yes—
566C22×C4C2×C22⋊D5311yescharacteristic
567C22×C4C2×C22⋊D5311yescharacteristic
568C22×C4C2×C22⋊D5311yescharacteristic
569C22×C4C2×C22⋊D5311yescharacteristic
570C22×C4C2×C22⋊D5311yescharacteristic
571C22×C4C23×D5311yescharacteristic
572Q16—2124no—
573SD16—1068no—
574M16—2124no—
575C2×C8—532no—
576C2×C8—532no—
577C2×C8—532no—
578C2×C8—1061no—
579C2×C8—1061no—
580C2×C8—1061no—
581C2×C8—1061no—
582C2×C8—1061no—
583C2×C8—1061no—
584C2×C8—1061no—
585C2×C8—1061no—
586C2×C8—1061no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—532no—
592C4⋊C4—532no—
593C4⋊C4—1064no—
594C4⋊C4—1061no—
595C4⋊C4—1061no—
596C4⋊C4—1061no—
597C4⋊C4—1061no—
598C4⋊C4—4241no—
599C4⋊C4—2122no—
600C4⋊C4—2122no—
601C22⋊C4—22no—
602C22⋊C4—41no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—81no—
606C22⋊C4—1064no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—4241no—
612C42—2122no—
613C23—22no—
614C23—21no—
615C23—22no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—22no—
621C23—21no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23C4×C22⋊D5312yes—
627C23C22×C22⋊D5311yescharacteristic
628Q8—22no—
629Q8—22no—
630Q8—41no—
631Q8—41no—
632Q8—1062no—
633Q8—1062no—
634Q8—2121no—
635Q8—2121no—
636D4—22no—
637D4—22no—
638D4—22no—
639D4—48no—
640D4#1313317714yes—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—48no—
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—84no—
669C2×C4—84no—
670C2×C4—1062no—
671C2×C4—1062no—
672C2×C4—1062no—
673C2×C4—4244no—
674C2×C4—2121no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4—2121no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4—2121no—
682C2×C4—2121no—
683C2×C4C4×C22⋊D5312yes—
684C2×C4#1313324712yes—
685C2×C4C22×C4×D5311yescharacteristic
686C2×C4C2×D4×D5311yescharacteristic
687C2×C4C2×#1171994711yescharacteristic
688C2×C4C2×#1171994511yescharacteristic
689C2×C4#1313326211yescharacteristic
690C2×C4#1313326211yescharacteristic
691C8—1062no—
692C8—1062no—
693C8—1062no—
694C8—2121no—
695C22—22no—
696C22—22no—
697C22—24no—
698C22—22no—
699C22—42no—
700C22—41no—
701C22—41no—
702C22—42no—
703C22—42no—
704C22—41no—
705C22—42no—
706C22—41no—
707C22—42no—
708C22—42no—
709C22C2×C4×C22⋊D5311yescharacteristic
710C22D4×C22⋊D5311yescharacteristic
711C22#1681126711yescharacteristic
712C22C2×#1313324711yescharacteristic
713C22#1681142111yescharacteristic
714C22#1681142611yescharacteristic
715C22#1681143811yescharacteristic
716C4—22no—
717C4—22no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—42no—
722C4—81no—
723C4—81no—
724C4—4241no—
725C4—2122no—
726C4—2122no—
727C4—2122no—
728C4C2×#1313317711yescharacteristic
729C4#1681109611yescharacteristic
730C4#1681126311yescharacteristic
731C4#1681129911yescharacteristic
732C2—42no—
733C2—44no—
734C2#2027769411yescharacteristic
735C2C4×#1313324711yescharacteristic
736C2#2028358811yescharacteristic
737C2#2028632211yescharacteristic
738C2#2028635711yescharacteristic
739C2#2028679611yescharacteristic
740C2#2028681111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2339C2
socleC23×C53C22×D4
prime radicalC22×#41×C53C22
cosocleC22×C4×C53C24
hypercenter#2339D53
hypocenterC53#22862
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. C2×#16810723C2semidirect
4. #20277718C2semidirect
5. #20275575C2semidirect
6. #20275408C2semidirect
7. #20275353C2semidirect
8. #20275146C2semidirect
9. #20275059C2semidirect
10. #20275049C2semidirect
11. #20274962C2semidirect
12. #20274902C2semidirect
13. C4×#13133138C2semidirect
14. #20274499C2semidirect
22. #16810785C4semidirect
66. C2×#11719925C2×C4semidirect
69. C2×#11719923C2×C4semidirect
78. #13133196C2×C4semidirect
97. #13133141C2×C4semidirect
101. #13133138C2×C4semidirect
103. C22⋊#88322C2×C4semidirect
432. C53#22862semidirect

Maximal subgroups

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

subgroupindex
C2×#168107852
C2×#168107232
C2×#168106242
#202777182
#202755752
#202754082
#202753532
#202751462
#202750592
#202750492
#202749622
#202749022
C4×#131331382
#202744992
C53×#23392
#2286253