Finite Group Databasebeta

← #27547353

Subgroups — #27547353

Order 13568.

1990 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811154C211yesmaximal, characteristic
2#20277865C212yesmaximal, complemented
3#20277858C212yesmaximal, complemented
4#20277837C212yesmaximal, complemented
5#20277833C212yesmaximal, complemented
6#20277687C212yesmaximal, complemented
7#20277653C212yesmaximal, complemented
8#20277597C212yesmaximal, complemented
9#20277569C212yesmaximal, complemented
10#20277524C212yesmaximal, complemented
11#20277515C212yesmaximal, complemented
12#20277482C211yesmaximal, characteristic
13#20277471C211yesmaximal, characteristic, complemented
14#20277468C211yesmaximal, characteristic, complemented
15#20277364C212yesmaximal, complemented
16#20277341C212yesmaximal, complemented
17#20277109C211yesmaximal, characteristic, complemented
18#20277106C211yesmaximal, characteristic, complemented
19C53×#2333C211yesmaximal, characteristic
20#16811154C4116yescomplemented
21C2×#13133210C2212yes—
22C2×#13133208C2211yescharacteristic
23C2×#13133204C2211yescharacteristic
24C2×#13133198C2212yes—
25C2×#13133196C2211yescharacteristic
26C2×#13133182C2211yescharacteristic
27C2×D4×Dic53C2211yescharacteristic
28C2×D4×Dic53C2212yes—
29C2×#13133173C2212yes—
30C22×C4×Dic53C2211yescharacteristic
31#16810527C2212yes—
32#16810527C2212yes—
33#16810526C2212yes—
34#16810520C2212yes—
35#16810520C2212yes—
36#16810518C2212yes—
37#16810518C2212yes—
38#16810517C2212yes—
39#16810517C2212yes—
40#16810517C2212yes—
41#16810517C2212yes—
42#16810517C2212yes—
43#16810516C2212yes—
44#16810511C2212yes—
45#16810511C2212yes—
46#16810511C2212yes—
47#16810511C2212yes—
48#16810511C2212yes—
49#16810509C2212yes—
50#16810508C2212yes—
51#16810508C2212yes—
52#16810507C2212yes—
53#16810507C2212yes—
54#16810507C2212yes—
55#16810506C2212yes—
56#16810506C2212yes—
57#16810505C2212yes—
58#16810505C2212yes—
59#16810505C2212yes—
60#16810503C2212yes—
61#16810503C2212yes—
62#16810496C2212yes—
63#16810496C2212yes—
64#16810495C2212yes—
65#16810495C2212yes—
66#16810490C2212yes—
67#16810490C2212yes—
68#16810490C2212yes—
69#16810488C2212yes—
70#16810487C2212yes—
71#16810487C2212yes—
72#16810486C2211yescharacteristic
73#16810484C2212yes—
74#16810484C2212yes—
75#16810481C2212yes—
76#16810481C2211yescharacteristic
77#16810481C2212yes—
78#16810481C2211yescharacteristic
79C4⋊C4×Dic53C2212yes—
80C4×#11719919C2212yes—
81C4×#11719919C2211yescharacteristic
82C4×#11719919C2212yes—
83C4×#11719919C2211yescharacteristic
84C4×C4⋊Dic53C2212yes—
85#16810474C2212yes—
86#16810474C2212yes—
87C22⋊C4×Dic53C2212yes—
88C22⋊C4×Dic53C2212yes—
89C22⋊C4×Dic53C2212yes—
90C22⋊C4×Dic53C2211yescharacteristic
91C22⋊C4×Dic53C2211yescharacteristic
92C4×C22⋊Dic53C2212yes—
93C4×C22⋊Dic53C2211yescharacteristic
94#16810469C2211yescharacteristic
95#16810469C2211yescharacteristic
96#16810468C2212yes—
97#16810468C2212yes—
98C2×#13133124C2212yes—
99C2×#121×C53C2211yescharacteristic
100C53×#390C2212yes—
101C53×#388C2212yes—
102C53×#387C2212yes—
103C53×#386C2212yes—
104C53×#386C2212yes—
105C53×#381C2211yescharacteristic
106C4×C22⋊C4×C53C2212yes—
107C4×C22⋊C4×C53C2211yescharacteristic
108C22×Dic106C2311yescharacteristic
109C23×Dic53C2312yes—
110C23×Dic53C2311yescharacteristic
111C23×Dic53C2311yescharacteristic
112C23×Dic53C2312yes—
113#13133210C2×C4116yescomplemented
114#13133208C2×C418yescomplemented
115#13133204C2×C418yes—
116#13133198C2×C4116yescomplemented
117#13133196C2×C418yescomplemented
118#13133182C2×C418yescomplemented
119D4×Dic53C2×C418yes—
120D4×Dic53C2×C4116yescomplemented
121#13133173C2×C4116yescomplemented
122C2×C4⋊Dic53C2312yes—
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2312yes—
125C2×#11719919C2312yes—
126C2×#11719919C2312yes—
127C2×#11719919C2312yes—
128C2×#11719919C2312yes—
129C2×#11719919C2312yes—
130C2×#11719919C2312yes—
131C2×#11719919C2312yes—
132C2×#11719919C2312yes—
133C2×#11719919C2312yes—
134C2×#11719919C2312yes—
135C2×#11719919C2312yes—
136C2×C22⋊Dic53C2312yes—
137C2×C22⋊Dic53C2312yes—
138C2×C22⋊Dic53C2312yes—
139C2×C22⋊Dic53C2311yescharacteristic
140C2×C22⋊Dic53C2312yes—
141C2×C22⋊Dic53C2311yescharacteristic
142C2×C22⋊Dic53C2312yes—
143C2×C22⋊Dic53C2312yes—
144C2×C22⋊Dic53C2312yes—
145C2×C22⋊Dic53C2312yes—
146C2×C4×Dic53C2×C418yescomplemented
147C2×C4×Dic53C2312yes—
148C2×C4×Dic53C2311yescharacteristic
149C2×C4×Dic53C2312yes—
150C2×C4×Dic53C2312yes—
151C2×C4×Dic53C2312yes—
152C2×C4×Dic53C2312yes—
153C2×C4×Dic53C2312yes—
154C2×C4×Dic53C2312yes—
155C2×C4×Dic53C2311yescharacteristic
156C2×C4×Dic53C2311yescharacteristic
157C2×C4×Dic53C2311yescharacteristic
158C2×C4×Dic53C2311yescharacteristic
159C2×C4×Dic53C2311yescharacteristic
160C2×C4×Dic53C2312yes—
161#13133124C2312yes—
162#13133124C2312yes—
163#13133124C2312yes—
164#13133124C2312yes—
165#13133124C2312yes—
166#13133124C2312yes—
167#13133124C2312yes—
168#13133124C2312yes—
169#13133124C2312yes—
170#13133124C2312yes—
171#13133124C2312yes—
172#13133124C2312yes—
173#13133124C2312yes—
174#13133124C2312yes—
175#13133124C2312yes—
176#13133124C2312yes—
177#13133124C2312yes—
178#13133124C2312yes—
179#13133124C2312yes—
180#13133124C2312yes—
181#13133124C2312yes—
182#13133124C2312yes—
183#13133124C2312yes—
184C22×D4×C53C2311yescharacteristic
185C22×D4×C53C2312yes—
186C23×C4×C53C2312yes—
187C23×C4×C53C2311yescharacteristic
188#121×C53C2×C418yes—
189C2×C4⋊C4×C53C2312yes—
190C2×C4⋊C4×C53C2311yescharacteristic
191C2×C22⋊C4×C53C2312yes—
192C2×C22⋊C4×C53C2311yescharacteristic
193C2×C22⋊C4×C53C2312yes—
194C2×C22⋊C4×C53C2312yes—
195C2×C22⋊C4×C53C2311yescharacteristic
196C2×C22⋊C4×C53C2312yes—
197C2×C22⋊C4×C53C2312yes—
198C2×C42×C53C2311yescharacteristic
199C2×C42×C53C2312yes—
200C2×C42×C53C2311yescharacteristic
201#95×C53C2312yes—
202#95×C53C2312yes—
203#95×C53C2312yes—
204#95×C53C2312yes—
205#95×C53C2312yes—
206C24×C53C2412yes—
207C24×C53C2411yescharacteristic
208C2×D4×C53—41no—
209C2×D4×C53—41no—
210C2×D4×C53—42no—
211C2×D4×C53—42no—
212C2×D4×C53C22×C414yes—
213C2×D4×C53C22×C418yes—
214C22×C4×C53—41no—
215C22×C4×C53—41no—
216C22×C4×C53—42no—
217C22×C4×C53—42no—
218C22×C4×C53—42no—
219C22×C4×C53C22×C414yes—
220C22×C4×C53C2412yes—
221C22×C4×C53C2412yes—
222C22×C4×C53C2412yes—
223C22×C4×C53C2412yes—
224C22×C4×C53C2411yescharacteristic
225C22×C4×C53C2411yescharacteristic
226C22×C4×C53C2412yes—
227C22×Dic53—42no—
228C22×Dic53—42no—
229C22×Dic53—42no—
230C22×Dic53—42no—
231C22×Dic53—42no—
232C22×Dic53—42no—
233C22×Dic53—42no—
234C22×Dic53C22×C414yes—
235C22×Dic53C22×C414yes—
236C22×Dic53C22×C418yes—
237C22×Dic53C2412yes—
238C22×Dic53C2412yes—
239C22×Dic53C2412yes—
240C22×Dic53C2412yes—
241C22×Dic53C2411yescharacteristic
242C22×Dic53C2411yescharacteristic
243C22×Dic53C2412yes—
244C22×Dic53C2411yescharacteristic
245C22×Dic53C2411yescharacteristic
246C22×Dic53C2412yes—
247C2×Dic106—41no—
248C2×Dic106—41no—
249C2×Dic106C22×C414yes—
250C4⋊C4×C53—42no—
251C4⋊C4×C53C22×C414yes—
252C22⋊C4×C53—41no—
253C22⋊C4×C53—42no—
254C22⋊C4×C53—42no—
255C22⋊C4×C53—42no—
256C22⋊C4×C53—42no—
257C22⋊C4×C53—41no—
258C22⋊C4×C53C22×C418yes—
259C42×C53—41no—
260C42×C53—41no—
261C42×C53—42no—
262C22⋊Dic53—41no—
263C22⋊Dic53—42no—
264C22⋊Dic53—42no—
265C22⋊Dic53—42no—
266C22⋊Dic53—42no—
267C22⋊Dic53—41no—
268C22⋊Dic53C22×C418yes—
269C22⋊Dic53C22×C418yes—
270C22⋊Dic53C22×C418yes—
271C22⋊Dic53C22×C418yes—
272C4⋊Dic53—42no—
273C4⋊Dic53C22×C414yes—
274C4⋊Dic53C22×C418yes—
275#11719919—42no—
276#11719919—42no—
277#11719919—42no—
278#11719919—42no—
279#11719919—42no—
280#11719919—42no—
281#11719919—42no—
282#11719919—42no—
283#11719919C22×C418yes—
284#11719919C22×C418yes—
285#11719919C22×C418yes—
286C4×Dic53—42no—
287C4×Dic53—42no—
288C4×Dic53—42no—
289C4×Dic53—42no—
290C4×Dic53—42no—
291C4×Dic53—42no—
292C4×Dic53—41no—
293C4×Dic53—42no—
294C4×Dic53—41no—
295C4×Dic53C22×C414yes—
296C4×Dic53C22×C414yes—
297C4×Dic53C22×C414yes—
298C4×Dic53C22×C414yes—
299C4×Dic53C22×C418yes—
300C23×C53—22no—
301C23×C53—22no—
302C23×C53—22no—
303C23×C53—22no—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—21no—
308C23×C53—21no—
309C23×C53—22no—
310C23×C53C23×C412yes—
311C23×C53C23×C414yes—
312C23×C53C2511yescharacteristic
313D4×C53—44no—
314D4×C53—48no—
315C2×C4×C53—21no—
316C2×C4×C53—21no—
317C2×C4×C53—21no—
318C2×C4×C53—21no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—44no—
334C2×C4×C53—84no—
335C2×C4×C53C23×C412yes—
336C2×C4×C53C23×C412yes—
337C2×C4×C53C23×C414yes—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—22no—
347C2×Dic53—22no—
348C2×Dic53—22no—
349C2×Dic53—22no—
350C2×Dic53—22no—
351C2×Dic53—22no—
352C2×Dic53—22no—
353C2×Dic53—22no—
354C2×Dic53—22no—
355C2×Dic53—22no—
356C2×Dic53—22no—
357C2×Dic53—22no—
358C2×Dic53—44no—
359C2×Dic53—48no—
360C2×Dic53—44no—
361C2×Dic53—84no—
362C2×Dic53C23×C414yes—
363C2×Dic53C23×C412yes—
364C2×Dic53C23×C412yes—
365C2×Dic53C23×C412yes—
366C2×Dic53C23×C412yes—
367C2×Dic53C23×C414yes—
368Dic106—44no—
369#34400—531nomaximal, Sylow
370C22×C53—22no—
371C22×C53—24no—
372C22×C53—22no—
373C22×C53—22no—
374C22×C53—24no—
375C22×C53—24no—
376C22×C53—42no—
377C22×C53—42no—
378C22×C53—42no—
379C22×C53—42no—
380C22×C53—42no—
381C22×C53—42no—
382C22×C53C24×C411yescharacteristic
383C22×C53#58511yescharacteristic
384C22×C53#58512yes—
385C22×C53#58511yescharacteristic
386C22×C53#58512yes—
387C4×C53—22no—
388C4×C53—22no—
389C4×C53—24no—
390C4×C53—42no—
391C4×C53—42no—
392C4×C53—42no—
393C4×C53—42no—
394Dic53—24no—
395Dic53—22no—
396Dic53—22no—
397Dic53—22no—
398Dic53—22no—
399Dic53—24no—
400Dic53—42no—
401Dic53—42no—
402Dic53—42no—
403Dic53—42no—
404C2×#529—531no—
405#2376—532no—
406#2376—532no—
407#2373—532no—
408#2373—532no—
409#2357—532no—
410#2353—532no—
411#2346—532no—
412#2343—532no—
413#2337—532no—
414#2336—532no—
415#2333—531no—
416#2333D5311yescharacteristic
417#2332—531no—
418#2332—531no—
419#2320—532no—
420#2318—532no—
421#2283—531no—
422#2283—531no—
423C2×C53—42no—
424C2×C53—44no—
425C2×C53#342811yescharacteristic
426C2×C53#342811yescharacteristic
427C2×C53#342811yescharacteristic
428C2×C53#356612yes—
429C2×C53#356612yes—
430#529—5316no—
431C2×#126—532no—
432C2×#125—531no—
433C2×#124—531no—
434C2×#123—532no—
435C2×C22⋊Q8—531no—
436C2×#121C2×D5311yescharacteristic
437C2×C4×Q8—531no—
438C2×C4×D4—531no—
439C2×C4×D4—532no—
440C2×#117—532no—
441C22×C42—531no—
442#391—532no—
443#391—532no—
444#390—532no—
445#390C2×D5312yes—
446#389—532no—
447#389—532no—
448#389—532no—
449#389—532no—
450#388—532no—
451#388—532no—
452#388—532no—
453#388—532no—
454#388—532no—
455#388—532no—
456#388—532no—
457#388—532no—
458#388—532no—
459#388—532no—
460#388—532no—
461#388C2×D5312yes—
462#387—532no—
463#387—532no—
464#387—532no—
465#387—532no—
466#387—532no—
467#387—532no—
468#387—532no—
469#387—532no—
470#387—532no—
471#387—532no—
472#387—532no—
473#387C2×D5312yes—
474#386—532no—
475#386—532no—
476#386C2×D5312yes—
477#386C2×D5312yes—
478#385—532no—
479#385—532no—
480#385—532no—
481#385—532no—
482#383—532no—
483#383—532no—
484#383—532no—
485#382—532no—
486#382—532no—
487#382—532no—
488#381—531no—
489#381—532no—
490#381—532no—
491#381C2×D5311yescharacteristic
492#380—532no—
493#380—532no—
494#380—531no—
495#380—531no—
496C4×C4⋊C4—532no—
497C4×C4⋊C4—532no—
498C4×C4⋊C4—532no—
499C4×C4⋊C4—532no—
500C4×C4⋊C4—531no—
501C4×C4⋊C4—531no—
502C4×C4⋊C4—532no—
503C4×C4⋊C4—532no—
504C4×C22⋊C4—531no—
505C4×C22⋊C4—532no—
506C4×C22⋊C4—532no—
507C4×C22⋊C4—532no—
508C4×C22⋊C4—532no—
509C4×C22⋊C4—531no—
510C4×C22⋊C4—531no—
511C4×C22⋊C4C2×D5311yescharacteristic
512C4×C22⋊C4C2×D5312yes—
513#376—531no—
514#376—531no—
515#376—532no—
516#376—532no—
517C2×#95—532no—
518C53#3440011yescharacteristic, complemented, Sylow
519C22×Q8—531no—
520C22×D4C22×D5312yes—
521C22×D4C22×D5311yescharacteristic
522C23×C4—532no—
523C23×C4—531no—
524C23×C4—531no—
525C23×C4—532no—
526C23×C4C22×D5312yes—
527C23×C4C22×D5311yescharacteristic
528#126—5316no—
529#125—538no—
530#124—538no—
531#123—5316no—
532C22⋊Q8—538no—
533#121C4×D5318yes—
534C4×Q8—538no—
535C4×D4—538no—
536C4×D4—5316no—
537#117—5316no—
538C2×C4⋊C4—532no—
539C2×C4⋊C4—532no—
540C2×C4⋊C4—531no—
541C2×C4⋊C4—532no—
542C2×C4⋊C4—532no—
543C2×C4⋊C4—532no—
544C2×C4⋊C4—532no—
545C2×C4⋊C4—532no—
546C2×C4⋊C4—532no—
547C2×C4⋊C4—532no—
548C2×C4⋊C4—532no—
549C2×C4⋊C4—532no—
550C2×C4⋊C4—532no—
551C2×C4⋊C4—532no—
552C2×C4⋊C4C22×D5312yes—
553C2×C4⋊C4C22×D5311yescharacteristic
554C2×C22⋊C4—532no—
555C2×C22⋊C4—532no—
556C2×C22⋊C4—532no—
557C2×C22⋊C4—532no—
558C2×C22⋊C4—531no—
559C2×C22⋊C4—532no—
560C2×C22⋊C4—531no—
561C2×C22⋊C4—532no—
562C2×C22⋊C4—532no—
563C2×C22⋊C4—532no—
564C2×C22⋊C4C22×D5311yescharacteristic
565C2×C22⋊C4C22×D5311yescharacteristic
566C2×C22⋊C4C22×D5312yes—
567C2×C22⋊C4C22×D5312yes—
568C2×C22⋊C4C22×D5312yes—
569C2×C22⋊C4C22×D5312yes—
570C2×C22⋊C4C22×D5312yes—
571C2×C42—538no—
572C2×C42—531no—
573C2×C42—532no—
574C2×C42—531no—
575C2×C42—531no—
576C2×C42—531no—
577C2×C42—532no—
578C2×C42—531no—
579C2×C42—532no—
580C2×C42—531no—
581C2×C42—532no—
582C2×C42—532no—
583C2×C42—532no—
584C2×C42—532no—
585C2×C42—532no—
586C2×C42C22×D5311yescharacteristic
587C2×C42C22×D5311yescharacteristic
588C2×C42C22×D5312yes—
589#95—532no—
590#95—532no—
591#95—532no—
592#95—532no—
593#95—532no—
594#95—532no—
595#95—532no—
596#95—532no—
597#95—532no—
598#95—532no—
599#95—532no—
600#95—532no—
601#95—532no—
602#95—532no—
603#95—532no—
604#95—532no—
605#95—532no—
606#95—532no—
607#95—532no—
608#95—532no—
609#95—532no—
610#95—532no—
611#95—532no—
612#95C22×D5312yes—
613#95C22×D5312yes—
614#95C22×D5312yes—
615#95C22×D5312yes—
616#95C22×D5312yes—
617C24C23×D5311yescharacteristic
618C24C23×D5312yes—
619C2×Q8—534no—
620C2×Q8—2121no—
621C2×Q8—2121no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4C2×C4×D5318yes—
627C2×D4C2×C4×D5314yes—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—531no—
634C22×C4—531no—
635C22×C4—532no—
636C22×C4—531no—
637C22×C4—531no—
638C22×C4—532no—
639C22×C4—534no—
640C22×C4—534no—
641C22×C4—538no—
642C22×C4—532no—
643C22×C4—532no—
644C22×C4—532no—
645C22×C4—532no—
646C22×C4—2122no—
647C22×C4—2122no—
648C22×C4—2122no—
649C22×C4—2122no—
650C22×C4—2122no—
651C22×C4—2122no—
652C22×C4—2122no—
653C22×C4C2×C4×D5314yes—
654C22×C4C23×D5312yes—
655C22×C4C23×D5312yes—
656C22×C4C23×D5312yes—
657C22×C4C23×D5312yes—
658C22×C4C23×D5311yescharacteristic
659C22×C4C23×D5311yescharacteristic
660C22×C4C23×D5312yes—
661C4⋊C4—42no—
662C4⋊C4—538no—
663C4⋊C4—538no—
664C4⋊C4—534no—
665C4⋊C4—538no—
666C4⋊C4—538no—
667C4⋊C4—2122no—
668C4⋊C4—2122no—
669C4⋊C4—2122no—
670C4⋊C4—2122no—
671C4⋊C4—2122no—
672C4⋊C4—2122no—
673C4⋊C4—2122no—
674C4⋊C4—2122no—
675C4⋊C4—2122no—
676C4⋊C4C2×C4×D5314yes—
677C22⋊C4—42no—
678C22⋊C4—41no—
679C22⋊C4—41no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—538no—
684C22⋊C4—538no—
685C22⋊C4—538no—
686C22⋊C4—538no—
687C22⋊C4—2122no—
688C22⋊C4—2121no—
689C22⋊C4—2121no—
690C22⋊C4—2122no—
691C22⋊C4—2122no—
692C22⋊C4—2122no—
693C22⋊C4C2×C4×D5318yes—
694C42—41no—
695C42—41no—
696C42—42no—
697C42—534no—
698C42—534no—
699C42—534no—
700C42—534no—
701C42—538no—
702C42—2121no—
703C42—2121no—
704C42—2122no—
705C42—2122no—
706C42—2122no—
707C42—2122no—
708C42—2122no—
709C42—2122no—
710C42—2122no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23C22×C4×D5314yes—
722C23C22×C4×D5312yes—
723C23C24×D5311yescharacteristic
724Q8—2124no—
725D4—44no—
726D4—48no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—44no—
746C2×C4—84no—
747C2×C4—532no—
748C2×C4—532no—
749C2×C4—532no—
750C2×C4—532no—
751C2×C4—534no—
752C2×C4—534no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—1062no—
758C2×C4—1062no—
759C2×C4—1062no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—1062no—
766C2×C4—1062no—
767C2×C4—1062no—
768C2×C4—1062no—
769C2×C4—1062no—
770C2×C4—1062no—
771C2×C4—1062no—
772C2×C4—1062no—
773C2×C4—4244no—
774C2×C4—2124no—
775C2×C4—2124no—
776C2×C4—2128no—
777C2×C4C22×C4×D5312yes—
778C2×C4C22×C4×D5312yes—
779C2×C4C22×C4×D5314yes—
780C22—22no—
781C22—22no—
782C22—24no—
783C22—24no—
784C22—22no—
785C22—24no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22C23×C4×D5311yescharacteristic
793C22#1681145811yescharacteristic
794C22#1681145812yes—
795C22#1681145811yescharacteristic
796C22#1681145912yes—
797C4—22no—
798C4—22no—
799C4—24no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—1062no—
805C4—1062no—
806C4—1064no—
807C4—1062no—
808C4—1062no—
809C4—1064no—
810C4—2122no—
811C4—2122no—
812C4—2122no—
813C4—2122no—
814C2—42no—
815C2—44no—
816C2#2028791311yescharacteristic
817C2#2028791311yescharacteristic
818C2#2028791411yescharacteristic
819C2#2028937912yes—
820C2#2028938712yes—
subgroupG/H
center, FrattiniC23C24×D53
commutatorC22×C53C24×C4
FittingC53×#2333C2
socle, cosocleC23×C53C25
prime radicalC2×#121×C53C22
hypercenter#2333D53
hypocenterC53#34400
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ #2333

Complements

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

NH ≅ G/Ntype
2. #20277865C2semidirect
3. #20277858C2semidirect
4. #20277837C2semidirect
5. #20277833C2semidirect
6. #20277687C2semidirect
7. #20277653C2semidirect
8. #20277597C2semidirect
9. #20277569C2semidirect
10. #20277524C2semidirect
11. #20277515C2semidirect
13. #20277471C2semidirect
14. #20277468C2semidirect
15. #20277364C2semidirect
16. #20277341C2semidirect
17. #20277109C2semidirect
18. #20277106C2semidirect
20. #16811154C4semidirect
113. #13133210C2×C4semidirect
114. #13133208C2×C4semidirect
116. #13133198C2×C4semidirect
117. #13133196C2×C4semidirect
118. #13133182C2×C4semidirect
120. D4×Dic53C2×C4semidirect
121. #13133173C2×C4semidirect
146. C2×C4×Dic53C2×C4semidirect
518. C53#34400semidirect

Maximal subgroups

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

subgroupindex
C2×#168111542
#202778652
#202778582
#202778372
#202778332
#202776872
#202776532
#202775972
#202775692
#202775242
#202775152
#202774822
#202774712
#202774682
#202773642
#202773412
#202771092
#202771062
C53×#23332
#3440053