Finite Group Databasebeta

← #27549951

Subgroups — #27549951

Order 13568.

2016 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811376C211yesmaximal, characteristic
2#20277878C212yesmaximal, complemented
3#20277850C211yesmaximal, characteristic
4#20277842C212yesmaximal, complemented
5#20277833C212yesmaximal, complemented
6#20277824C211yesmaximal, characteristic
7#20277817C212yesmaximal, complemented
8#20277768C212yesmaximal, complemented
9#20277715C212yesmaximal, complemented
10#20277491C212yesmaximal, complemented
11#20277488C212yesmaximal, complemented
12#20277472C212yesmaximal, complemented
13#20277460C212yesmaximal, complemented
14#20277453C212yesmaximal, complemented
15#20277425C211yesmaximal, characteristic
16#20277389C211yesmaximal, characteristic
17#20277243C212yesmaximal, complemented
18#123×Dic53C211yesmaximal, characteristic
19C53×#2376C211yesmaximal, characteristic
20#16811376C4116yescomplemented
21C2×#13133216C2212yes—
22C2×#13133210C2212yes—
23C2×#13133210C2212yes—
24C2×#13133207C2212yes—
25C2×#13133204C2211yescharacteristic
26C2×#13133198C2211yescharacteristic
27C2×#13133196C2212yes—
28C2×#13133194C2212yes—
29C2×#13133182C2211yescharacteristic
30C2×#13133182C2212yes—
31C2×D4×Dic53C2211yescharacteristic
32C22×#11719919C2211yescharacteristic
33C22×C4×Dic53C2211yescharacteristic
34#16810529C2211yescharacteristic
35#16810528C2212yes—
36#16810527C2212yes—
37#16810527C2212yes—
38#16810527C2212yes—
39#16810520C2212yes—
40#16810519C2212yes—
41#16810519C2212yes—
42#16810518C2212yes—
43#16810518C2212yes—
44#16810518C2212yes—
45#16810518C2212yes—
46#16810517C2212yes—
47#16810517C2212yes—
48#16810517C2212yes—
49#16810517C2212yes—
50#16810517C2212yes—
51#16810516C2212yes—
52#16810511C2212yes—
53#16810511C2212yes—
54#16810510C2212yes—
55#16810510C2212yes—
56#16810509C2212yes—
57#16810508C2212yes—
58#16810507C2212yes—
59#16810506C2212yes—
60#16810506C2212yes—
61#16810506C2212yes—
62#16810505C2212yes—
63#16810505C2212yes—
64#16810505C2212yes—
65#16810505C2212yes—
66#16810504C2212yes—
67#16810504C2212yes—
68#16810504C2212yes—
69#16810503C2211yescharacteristic
70#16810498C2211yescharacteristic
71#16810496C2211yescharacteristic
72#16810495C2212yes—
73#16810495C2212yes—
74#16810495C2212yes—
75#16810492C2211yescharacteristic
76#16810487C2212yes—
77#16810486C2211yescharacteristic
78#16810484C2211yescharacteristic
79C4⋊C4×Dic53C2212yes—
80C4⋊C4×Dic53C2212yes—
81C4⋊C4×Dic53C2212yes—
82C4×#11719919C2212yes—
83C4×#11719919C2212yes—
84C4×#11719919C2212yes—
85C4×C4⋊Dic53C2212yes—
86#16810474C2212yes—
87#16810474C2212yes—
88#16810474C2212yes—
89C22⋊C4×Dic53C2212yes—
90C22⋊C4×Dic53C2211yescharacteristic
91C22⋊C4×Dic53C2212yes—
92C22⋊C4×Dic53C2212yes—
93C22⋊C4×Dic53C2212yes—
94C22⋊C4×Dic53C2211yescharacteristic
95C4×C22⋊Dic53C2212yes—
96#16810469C2211yescharacteristic
97#16810468C2212yes—
98#16810468C2212yes—
99C2×#123×C53C2211yescharacteristic
100C53×#390C2211yescharacteristic
101C53×#389C2212yes—
102C53×#388C2212yes—
103C53×#388C2212yes—
104C53×#387C2212yes—
105C53×#386C2211yescharacteristic
106C53×#385C2212yes—
107C53×#380C2212yes—
108C22×Dic106C2312yes—
109C22×Dic106C2311yescharacteristic
110C23×Dic53C2311yescharacteristic
111C23×Dic53C2311yescharacteristic
112C23×Dic53C2311yescharacteristic
113C23×Dic53C2311yescharacteristic
114#13133216C2×C4116yescomplemented
115#13133210C2×C4116yescomplemented
116#13133210C2×C4116yescomplemented
117#13133207C2×C4116yescomplemented
118#13133204C2×C418yes—
119#13133198C2×C418yes—
120#13133196C2×C4116yescomplemented
121#13133194C2×C4116yescomplemented
122#13133182—44no—
123#13133182—42no—
124D4×Dic53—42no—
125C2×C4⋊Dic53C2312yes—
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2312yes—
128C2×C4⋊Dic53C2312yes—
129C2×#11719919—42no—
130C2×#11719919C2312yes—
131C2×#11719919C2312yes—
132C2×#11719919C2312yes—
133C2×#11719919C2312yes—
134C2×#11719919C2312yes—
135C2×#11719919C2312yes—
136C2×#11719919C2312yes—
137C2×#11719919C2312yes—
138C2×#11719919C2312yes—
139C2×#11719919C2312yes—
140C2×#11719919C2312yes—
141C2×#11719919C2312yes—
142C2×#11719919C2312yes—
143C2×C22⋊Dic53C2312yes—
144C2×C22⋊Dic53C2311yescharacteristic
145C2×C22⋊Dic53C2311yescharacteristic
146C2×C22⋊Dic53C2311yescharacteristic
147C2×C22⋊Dic53C2311yescharacteristic
148C2×C22⋊Dic53C2312yes—
149C2×C22⋊Dic53C2312yes—
150C2×C22⋊Dic53C2312yes—
151C2×C4×Dic53—42no—
152C2×C4×Dic53C2312yes—
153C2×C4×Dic53C2311yescharacteristic
154C2×C4×Dic53C2312yes—
155C2×C4×Dic53C2312yes—
156C2×C4×Dic53C2312yes—
157C2×C4×Dic53C2312yes—
158C2×C4×Dic53C2312yes—
159C2×C4×Dic53C2312yes—
160C2×C4×Dic53C2312yes—
161C2×C4×Dic53C2312yes—
162C2×C4×Dic53C2312yes—
163C2×C4×Dic53C2312yes—
164C2×C4×Dic53C2311yescharacteristic
165C2×C4×Dic53C2312yes—
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—
184#13133124C2312yes—
185#13133124C2312yes—
186#13133124C2312yes—
187C22×D4×C53C2311yescharacteristic
188C23×C4×C53C2311yescharacteristic
189C23×C4×C53C2311yescharacteristic
190#123×C53C2×C418yes—
191C2×C4⋊C4×C53C2311yescharacteristic
192C2×C4⋊C4×C53C2312yes—
193C2×C4⋊C4×C53C2312yes—
194C2×C4⋊C4×C53C2312yes—
195C2×C4⋊C4×C53C2312yes—
196C2×C22⋊C4×C53C2312yes—
197C2×C22⋊C4×C53C2312yes—
198C2×C22⋊C4×C53C2312yes—
199C2×C22⋊C4×C53C2311yescharacteristic
200C2×C22⋊C4×C53C2311yescharacteristic
201C2×C22⋊C4×C53C2312yes—
202C2×C42×C53C2312yes—
203C2×C42×C53C2311yescharacteristic
204#95×C53C2312yes—
205#95×C53C2312yes—
206#95×C53C2312yes—
207#95×C53C2312yes—
208#95×C53C2312yes—
209C24×C53C2411yescharacteristic
210C24×C53C2411yescharacteristic
211C2×D4×C53—41no—
212C2×D4×C53—41no—
213C2×D4×C53C22×C414yes—
214C22×C4×C53—41no—
215C22×C4×C53—41no—
216C22×C4×C53—42no—
217C22×C4×C53—41no—
218C22×C4×C53C22×C414yes—
219C22×C4×C53C2412yes—
220C22×C4×C53C2412yes—
221C22×C4×C53C2412yes—
222C22×C4×C53C2412yes—
223C22×C4×C53C2412yes—
224C22×C4×C53C2411yescharacteristic
225C22×C4×C53C2412yes—
226C22×Dic53—22no—
227C22×Dic53—24no—
228C22×Dic53—22no—
229C22×Dic53—41no—
230C22×Dic53—41no—
231C22×Dic53—41no—
232C22×Dic53—42no—
233C22×Dic53—42no—
234C22×Dic53C22×C414yes—
235C22×Dic53C2412yes—
236C22×Dic53C2411yescharacteristic
237C22×Dic53C2411yescharacteristic
238C22×Dic53C2411yescharacteristic
239C22×Dic53C2412yes—
240C22×Dic53C2412yes—
241C22×Dic53C2412yes—
242C22×Dic53C2412yes—
243C22×Dic53C2411yescharacteristic
244C22×Dic53C2412yes—
245C2×Dic106—41no—
246C2×Dic106—42no—
247C2×Dic106—41no—
248C2×Dic106—42no—
249C2×Dic106C22×C418yes—
250C2×Dic106C22×C414yes—
251C4⋊C4×C53—42no—
252C4⋊C4×C53—42no—
253C4⋊C4×C53—42no—
254C4⋊C4×C53—41no—
255C4⋊C4×C53C22×C418yes—
256C22⋊C4×C53—42no—
257C22⋊C4×C53—42no—
258C22⋊C4×C53—42no—
259C22⋊C4×C53—41no—
260C22⋊C4×C53C22×C418yes—
261C22⋊C4×C53C22×C414yes—
262C42×C53—41no—
263C42×C53—42no—
264C22⋊Dic53—24no—
265C22⋊Dic53—41no—
266C22⋊Dic53—41no—
267C22⋊Dic53—41no—
268C22⋊Dic53C22×C418yes—
269C22⋊Dic53C22×C418yes—
270C22⋊Dic53C22×C418yes—
271C22⋊Dic53C22×C414yes—
272C4⋊Dic53—24no—
273C4⋊Dic53—41no—
274C4⋊Dic53C22×C418yes—
275C4⋊Dic53C22×C418yes—
276#11719919—24no—
277#11719919—24no—
278#11719919—42no—
279#11719919—42no—
280#11719919—42no—
281#11719919—42no—
282#11719919—42no—
283#11719919—42no—
284#11719919C22×C418yes—
285#11719919C22×C418yes—
286#11719919C22×C418yes—
287#11719919C22×C418yes—
288#11719919C22×C418yes—
289C4×Dic53—24no—
290C4×Dic53—22no—
291C4×Dic53—24no—
292C4×Dic53—24no—
293C4×Dic53—42no—
294C4×Dic53—42no—
295C4×Dic53—42no—
296C4×Dic53—42no—
297C4×Dic53—42no—
298C4×Dic53—42no—
299C4×Dic53—42no—
300C4×Dic53—42no—
301C4×Dic53C22×C414yes—
302C4×Dic53C22×C418yes—
303C23×C53—21no—
304C23×C53—21no—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—22no—
308C23×C53—21no—
309C23×C53—22no—
310C23×C53—21no—
311C23×C53C23×C412yes—
312C23×C53C23×C412yes—
313C23×C53C2511yescharacteristic
314D4×C53—44no—
315C2×C4×C53—22no—
316C2×C4×C53—21no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—21no—
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—82no—
335C2×C4×C53C23×C414yes—
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—21no—
350C2×Dic53—21no—
351C2×Dic53—21no—
352C2×Dic53—22no—
353C2×Dic53—22no—
354C2×Dic53—22no—
355C2×Dic53—22no—
356C2×Dic53—22no—
357C2×Dic53—22no—
358C2×Dic53—44no—
359C2×Dic53—44no—
360C2×Dic53—44no—
361C2×Dic53—82no—
362C2×Dic53C23×C414yes—
363C2×Dic53C23×C414yes—
364C2×Dic53C23×C414yes—
365C2×Dic53C23×C414yes—
366C2×Dic53H(5,𝔽2)12yes—
367C2×Dic532−1+414yes—
368Dic106—44no—
369Dic106—48no—
370#34514—531nomaximal, Sylow
371C22×C53—22no—
372C22×C53—22no—
373C22×C53—24no—
374C22×C53—24no—
375C22×C53—41no—
376C22×C53—41no—
377C22×C53—41no—
378C22×C53—41no—
379C22×C53—42no—
380C22×C53—42no—
381C22×C53C24×C411yescharacteristic
382C22×C53C2×H(5,𝔽2)11yescharacteristic
383C22×C53C2×2−1+412yes—
384C22×C53#58511yescharacteristic
385C22×C53#58512yes—
386C4×C53—24no—
387C4×C53—22no—
388C4×C53—24no—
389C4×C53—42no—
390C4×C53—42no—
391C4×C53—42no—
392C4×C53—42no—
393Dic53—24no—
394Dic53—24no—
395Dic53—24no—
396Dic53—24no—
397Dic53—22no—
398Dic53—24no—
399Dic53—41no—
400Dic53—41no—
401Dic53—41no—
402Dic53—42no—
403C2×#563—531no—
404#2378—532no—
405#2376D5311yescharacteristic
406#2374—531no—
407#2373—532no—
408#2373—532no—
409#2372—531no—
410#2371—532no—
411#2365—532no—
412#2360—532no—
413#2334—532no—
414#2334—532no—
415#2332—532no—
416#2331—532no—
417#2330—532no—
418#2326—531no—
419#2322—531no—
420C4×C22⋊Q8—532no—
421C4×#123—531no—
422C2×C53—42no—
423C2×C53—42no—
424C2×C53C4×H(5,𝔽2)11yescharacteristic
425C2×C53C4×2−1+412yes—
426C2×C53#353311yescharacteristic
427C2×C53#353811yescharacteristic
428C2×C53#356512yes—
429#563—5316no—
430C2×C4⋊Q8—532no—
431C2×#126—532no—
432C2×#126—532no—
433C2×#125—532no—
434C2×#124—531no—
435C2×#123—531no—
436C2×#123C2×D5311yescharacteristic
437C2×C22⋊Q8—532no—
438C2×C22⋊Q8—532no—
439C2×C4×Q8—531no—
440C2×C4×Q8—532no—
441C2×C4×D4—531no—
442C22×C4⋊C4—531no—
443C22×C42—531no—
444#391—532no—
445#391—531no—
446#391—532no—
447#391—532no—
448#391—532no—
449#390C2×D5311yescharacteristic
450#389—532no—
451#389—532no—
452#389—532no—
453#389—532no—
454#389—532no—
455#389—532no—
456#389—532no—
457#389C2×D5312yes—
458#388—532no—
459#388—532no—
460#388—532no—
461#388—532no—
462#388—532no—
463#388—532no—
464#388—532no—
465#388—532no—
466#388C2×D5312yes—
467#388C2×D5312yes—
468#387—532no—
469#387—532no—
470#387—532no—
471#387—532no—
472#387—532no—
473#387—532no—
474#387—532no—
475#387—532no—
476#387—532no—
477#387—532no—
478#387—532no—
479#387—532no—
480#387—532no—
481#387—532no—
482#387—532no—
483#387C2×D5312yes—
484#386—531no—
485#386C2×D5311yescharacteristic
486#385—531no—
487#385—531no—
488#385—532no—
489#385—532no—
490#385—532no—
491#385C2×D5312yes—
492#384—531no—
493#382—532no—
494#381—531no—
495#381—531no—
496#380C2×D5312yes—
497C4×C4⋊C4—532no—
498C4×C4⋊C4—532no—
499C4×C4⋊C4—532no—
500C4×C4⋊C4—532no—
501C4×C4⋊C4—532no—
502C4×C4⋊C4—532no—
503C4×C4⋊C4—532no—
504C4×C4⋊C4—532no—
505C4×C4⋊C4—532no—
506C4×C4⋊C4—532no—
507C4×C22⋊C4—532no—
508C4×C22⋊C4—531no—
509C4×C22⋊C4—532no—
510C4×C22⋊C4—531no—
511C4×C22⋊C4—532no—
512C4×C22⋊C4—532no—
513C4×C22⋊C4—532no—
514#376—531no—
515#376—532no—
516#376—532no—
517C53#3451411yescharacteristic, complemented, Sylow
518C22×Q8—532no—
519C22×Q8—531no—
520C22×D4C22×D5311yescharacteristic
521C23×C4—531no—
522C23×C4—531no—
523C23×C4—531no—
524C23×C4—531no—
525C23×C4C22×D5311yescharacteristic
526C23×C4C22×D5311yescharacteristic
527C4⋊Q8—5316no—
528#126—5316no—
529#126—5316no—
530#125—5316no—
531#124—538no—
532#123—538no—
533#123C4×D5318yes—
534C22⋊Q8—5316no—
535C22⋊Q8—5316no—
536C4×Q8—2124no—
537C4×Q8—2122no—
538C4×D4—2122no—
539C2×C4⋊C4—532no—
540C2×C4⋊C4—532no—
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—531no—
551C2×C4⋊C4—532no—
552C2×C4⋊C4—532no—
553C2×C4⋊C4—532no—
554C2×C4⋊C4—532no—
555C2×C4⋊C4—532no—
556C2×C4⋊C4—2122no—
557C2×C4⋊C4C22×D5312yes—
558C2×C4⋊C4C22×D5311yescharacteristic
559C2×C4⋊C4C22×D5312yes—
560C2×C4⋊C4C22×D5312yes—
561C2×C4⋊C4C22×D5312yes—
562C2×C22⋊C4—532no—
563C2×C22⋊C4—532no—
564C2×C22⋊C4—532no—
565C2×C22⋊C4—531no—
566C2×C22⋊C4—532no—
567C2×C22⋊C4—531no—
568C2×C22⋊C4—531no—
569C2×C22⋊C4—531no—
570C2×C22⋊C4C22×D5312yes—
571C2×C22⋊C4C22×D5312yes—
572C2×C22⋊C4C22×D5311yescharacteristic
573C2×C22⋊C4C22×D5312yes—
574C2×C22⋊C4C22×D5312yes—
575C2×C22⋊C4C22×D5311yescharacteristic
576C2×C42—531no—
577C2×C42—532no—
578C2×C42—531no—
579C2×C42—532no—
580C2×C42—532no—
581C2×C42—532no—
582C2×C42—532no—
583C2×C42—532no—
584C2×C42—532no—
585C2×C42—532no—
586C2×C42—532no—
587C2×C42—532no—
588C2×C42—532no—
589C2×C42—532no—
590C2×C42—2122no—
591C2×C42C22×D5311yescharacteristic
592C2×C42C22×D5312yes—
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#95—532no—
613#95—532no—
614#95C22×D5312yes—
615#95C22×D5312yes—
616#95C22×D5312yes—
617#95C22×D5312yes—
618#95C22×D5312yes—
619C24C23×D5311yescharacteristic
620C24C23×D5311yescharacteristic
621C2×Q8—538no—
622C2×Q8—534no—
623C2×Q8—2122no—
624C2×Q8—2121no—
625C2×Q8—2121no—
626C2×Q8—2122no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4C2×C4×D5314yes—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—42no—
634C22×C4—532no—
635C22×C4—531no—
636C22×C4—532no—
637C22×C4—532no—
638C22×C4—532no—
639C22×C4—532no—
640C22×C4—534no—
641C22×C4—531no—
642C22×C4—532no—
643C22×C4—531no—
644C22×C4—531no—
645C22×C4—1062no—
646C22×C4—1062no—
647C22×C4—1064no—
648C22×C4—2122no—
649C22×C4—2121no—
650C22×C4—2121no—
651C22×C4—2122no—
652C22×C4—2121no—
653C22×C4C2×C4×D5314yes—
654C22×C4C23×D5312yes—
655C22×C4C23×D5312yes—
656C22×C4C23×D5312yes—
657C22×C4C23×D5312yes—
658C22×C4C23×D5312yes—
659C22×C4C23×D5311yescharacteristic
660C22×C4C23×D5312yes—
661C4⋊C4—42no—
662C4⋊C4—41no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—538no—
666C4⋊C4—538no—
667C4⋊C4—538no—
668C4⋊C4—538no—
669C4⋊C4—538no—
670C4⋊C4—538no—
671C4⋊C4—538no—
672C4⋊C4—1064no—
673C4⋊C4—1064no—
674C4⋊C4—1064no—
675C4⋊C4—2122no—
676C4⋊C4—2121no—
677C4⋊C4—2122no—
678C4⋊C4—2122no—
679C4⋊C4—2122no—
680C4⋊C4—2122no—
681C4⋊C4—2122no—
682C4⋊C4C2×C4×D5318yes—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—41no—
687C22⋊C4—538no—
688C22⋊C4—538no—
689C22⋊C4—538no—
690C22⋊C4—534no—
691C22⋊C4—1064no—
692C22⋊C4—2121no—
693C22⋊C4—2121no—
694C22⋊C4—2121no—
695C22⋊C4C2×C4×D5318yes—
696C22⋊C4C2×C4×D5314yes—
697C42—42no—
698C42—41no—
699C42—534no—
700C42—538no—
701C42—1064no—
702C42—1062no—
703C42—1064no—
704C42—1064no—
705C42—2122no—
706C42—2122no—
707C42—2122no—
708C42—2122no—
709C42—2122no—
710C42—2122no—
711C42—2122no—
712C42—2122no—
713C23—21no—
714C23—21no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—21no—
720C23—21no—
721C23C22×C4×D5312yes—
722C23C22×C4×D5312yes—
723C23C24×D5311yescharacteristic
724Q8—2128no—
725Q8—2124no—
726D4—44no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—22no—
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—82no—
747C2×C4—534no—
748C2×C4—534no—
749C2×C4—534no—
750C2×C4—534no—
751C2×C4—532no—
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—1061no—
765C2×C4—1061no—
766C2×C4—1061no—
767C2×C4—1062no—
768C2×C4—1062no—
769C2×C4—1062no—
770C2×C4—1062no—
771C2×C4—1062no—
772C2×C4—1062no—
773C2×C4—4242no—
774C2×C4—2124no—
775C2×C4—2124no—
776C2×C4—2124no—
777C2×C4C22×C4×D5314yes—
778C2×C4C22×C4×D5312yes—
779C2×C4C22×C4×D5314yes—
780C22—22no—
781C22—22no—
782C22—24no—
783C22—24no—
784C22—42no—
785C22—42no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22C23×C4×D5311yescharacteristic
791C22H(5,𝔽2)×D5311yescharacteristic
792C222−1+4×D5312yes—
793C22#1681145811yescharacteristic
794C22#1681145812yes—
795C4—24no—
796C4—22no—
797C4—24no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—1062no—
803C4—1064no—
804C4—1064no—
805C4—1064no—
806C4—1064no—
807C4—1064no—
808C4—2122no—
809C4—2121no—
810C4—2121no—
811C4—2121no—
812C2—42no—
813C2—42no—
814C2#2028791911yescharacteristic
815C2#2028792612yes—
816C2#2028888411yescharacteristic
817C2#2028895911yescharacteristic
818C2#2028934912yes—
subgroupG/H
center, FrattiniC23C24×D53
commutatorC22×C53C24×C4
FittingC53×#2376C2
socle, cosocleC23×C53C25
prime radicalC22×D4×C53C23
hypercenter#2376D53
hypocenterC53#34514
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ #2376

Complements

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

NH ≅ G/Ntype
2. #20277878C2semidirect
4. #20277842C2semidirect
5. #20277833C2semidirect
7. #20277817C2semidirect
8. #20277768C2semidirect
9. #20277715C2semidirect
10. #20277491C2semidirect
11. #20277488C2semidirect
12. #20277472C2semidirect
13. #20277460C2semidirect
14. #20277453C2semidirect
17. #20277243C2semidirect
20. #16811376C4semidirect
114. #13133216C2×C4semidirect
115. #13133210C2×C4semidirect
116. #13133210C2×C4semidirect
117. #13133207C2×C4semidirect
120. #13133196C2×C4semidirect
121. #13133194C2×C4semidirect
517. C53#34514semidirect

Maximal subgroups

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

subgroupindex
C2×#168113762
#202778782
#202778502
#202778422
#202778332
#202778242
#202778172
#202777682
#202777152
#202774912
#202774882
#202774722
#202774602
#202774532
#202774252
#202773892
#202772432
#123×Dic532
C53×#23762
#3451453