Finite Group Databasebeta

← #27399858

Subgroups — #27399858

Order 13568.

1650 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133242C211yesmaximal, characteristic
2C2×#16810733C211yesmaximal, characteristic, complemented
3C2×C4×#11719922C211yesmaximal, characteristic, complemented
4C22⋊C4×D212C211yesmaximal, characteristic, complemented
5#20275599C211yesmaximal, characteristic, complemented
6#20275572C211yesmaximal, characteristic, complemented
7#20275063C211yesmaximal, characteristic, complemented
8#20275063C211yesmaximal, characteristic, complemented
9#20275052C211yesmaximal, characteristic, complemented
10#20275052C211yesmaximal, characteristic, complemented
11#20274746C211yesmaximal, characteristic, complemented
12#20274655C211yesmaximal, characteristic, complemented
13#20274645C211yesmaximal, characteristic, complemented
14#20274499C211yesmaximal, characteristic, complemented
15C53×#2339C211yesmaximal, characteristic, complemented
16C23×D212C2211yescharacteristic
17C2×#13133242—24no—
18C2×#13133242—24no—
19C2×#13133242C418yescomplemented
20C22×#11719924C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22C22×#11719922C2211yescharacteristic
23C22×#11719922C2211yescharacteristic
24C22×#11719917C2211yescharacteristic
25C2×C4×D212C2211yescharacteristic
26C2×C4×D212C2211yescharacteristic
27C2×C22⋊C4×D53—21no—
28#16810733—24no—
29C4×#11719922—24no—
30C2×#13133150C2211yescharacteristic, complemented
31C2×#13133148C2211yescharacteristic, complemented
32C2×#13133141C2211yescharacteristic, complemented
33C2×#13133141C2211yescharacteristic, complemented
34C2×#13133138C2211yescharacteristic, complemented
35C2×#13133138C2211yescharacteristic, complemented
36C2×#13133137C2211yescharacteristic
37C2×#13133137C2211yescharacteristic
38C2×#13133137C2211yescharacteristic
39C2×#13133137C2211yescharacteristic
40C2×C22⋊#88322C2211yescharacteristic
41C2×#13133128C2211yescharacteristic, complemented
42C2×C4×#88322C2211yescharacteristic, complemented
43#16810525C2211yescharacteristic
44#16810525C2211yescharacteristic
45#16810501—21no—
46#16810501—21no—
47#16810483C2211yescharacteristic
48#16810478—21no—
49#16810385C2211yescharacteristic, complemented
50#16810385C2211yescharacteristic, complemented
51#16810378C2211yescharacteristic, complemented
52#16810378C2211yescharacteristic, complemented
53C22×#41×C53C2211yescharacteristic
54C2×C4×D4×C53C2211yescharacteristic, complemented
55C2×C4×D4×C53C2211yescharacteristic, complemented
56C53×#391C2211yescharacteristic, complemented
57C53×#391C2211yescharacteristic, complemented
58C53×#386—21no—
59C53×#386—21no—
60C53×#381—21no—
61C53×#380C2211yescharacteristic
62C4×C22⋊C4×C53C2211yescharacteristic
63C2×#95×C53—21no—
64C24×D53—21no—
65C22×D212—22no—
66C22×D212—22no—
67C22×D212—21no—
68C22×D212—22no—
69C22×D212—41no—
70C22×D212—41no—
71C22×D212C2×C414yescomplemented
72C22×D212C2311yescharacteristic
73C22×D212C2311yescharacteristic
74C22×C4×D53—21no—
75C22×C4×D53—21no—
76#13133242—232no—
77C2×#11719924—22no—
78C2×#11719924—22no—
79C2×#11719924—22no—
80C2×#11719924—22no—
81C2×#11719924C2×C414yescomplemented
82C2×#11719924C2×C414yescomplemented
83C2×#11719922—22no—
84C2×#11719922—22no—
85C2×#11719922C2×C414yes—
86C2×#11719922C2×C414yescomplemented
87C2×#11719922D414yes—
88C2×#11719922D414yes—
89C2×#11719917—22no—
90C2×#11719917—22no—
91C2×#11719917C2×C414yescomplemented
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C22×#88322C2311yescharacteristic
95C22×#88322C2311yescharacteristic
96C4×D212—22no—
97C4×D212—22no—
98C4×D212—41no—
99C4×D212—41no—
100C2×C4⋊Dic53C2311yescharacteristic
101C2×C4⋊Dic53C2311yescharacteristic
102C2×C22⋊Dic53—21no—
103C2×#11719921—21no—
104C2×#11719921—21no—
105C2×#11719921—21no—
106C2×#11719921—21no—
107C2×#11719921—21no—
108C2×#11719921—21no—
109C22⋊C4×D53—44no—
110#13133150—22no—
111#13133148—22no—
112#13133141—41no—
113#13133141—41no—
114#13133138—22no—
115#13133138—22no—
116#13133137—22no—
117#13133137—22no—
118#13133137—41no—
119#13133137—41no—
120C22⋊#88322—22no—
121#13133128—22no—
122C4×#88322—22no—
123#13133124—21no—
124C2×#41×C53—22no—
125C2×#41×C53—22no—
126C2×#41×C53—22no—
127C2×#41×C53—41no—
128C2×#41×C53—41no—
129C2×#41×C53C2×C414yescomplemented
130C22×Q8×C53C2311yescharacteristic
131C22×D4×C53—21no—
132C22×D4×C53C2311yescharacteristic
133C23×C4×C53—21no—
134C23×C4×C53—21no—
135C23×C4×C53—21no—
136C23×C4×C53C2311yescharacteristic
137C4×D4×C53—22no—
138C4×D4×C53—22no—
139C4×D4×C53—41no—
140C4×D4×C53—41no—
141C2×C4⋊C4×C53C2311yescharacteristic
142C2×C4⋊C4×C53C2311yescharacteristic
143C2×C22⋊C4×C53—21no—
144C2×C22⋊C4×C53—21no—
145C2×C22⋊C4×C53—21no—
146C2×C22⋊C4×C53D411yescharacteristic
147C2×C22⋊C4×C53D411yescharacteristic
148C2×C42×C53C2311yescharacteristic
149C2×C42×C53C2311yescharacteristic
150#95×C53—21no—
151#95×C53—21no—
152#95×C53—21no—
153#95×C53—21no—
154#95×C53—21no—
155#95×C53D411yescharacteristic
156#95×C53D411yescharacteristic
157C24×C53—21no—
158C24×C53C2×D411yescharacteristic
159C23×D53—21no—
160C23×D53—21no—
161C23×D53—24no—
162C23×D53—42no—
163C23×D53—42no—
164C23×D53—42no—
165C23×D53—42no—
166C23×D53—81no—
167C23×D53—81no—
168#41×C53—28no—
169#41×C53—44no—
170#41×C53—44no—
171#41×C53—44no—
172C2×Q8×C53—21no—
173C2×Q8×C53—21no—
174C2×Q8×C53—21no—
175C2×Q8×C53—21no—
176C2×Q8×C53—21no—
177C2×Q8×C53C22×C412yes—
178C2×D4×C53—24no—
179C2×D4×C53—21no—
180C2×D4×C53—21no—
181C2×D4×C53—21no—
182C2×D4×C53—42no—
183C2×D4×C53—42no—
184C2×D4×C53C22×C412yes—
185C2×D4×C53C2×D412yes—
186C2×D4×C53C2×D412yes—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—24no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—42no—
196C22×C4×C53—42no—
197C22×C4×C53—42no—
198C22×C4×C53—42no—
199C22×C4×C53—42no—
200C22×C4×C53—42no—
201C22×C4×C53—81no—
202C22×C4×C53—81no—
203C22×C4×C53C22×C412yes—
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53#4112yes—
210C22×C4×C53C2411yescharacteristic
211C22×Dic53—21no—
212C22×Dic53—21no—
213C2×D212—21no—
214C2×D212—21no—
215C2×D212—21no—
216C2×D212—21no—
217C2×D212—21no—
218C2×D212—21no—
219C2×D212—21no—
220C2×D212—28no—
221C2×D212—24no—
222C2×D212—21no—
223C2×D212—44no—
224C2×D212—44no—
225C2×D212—44no—
226C2×D212—42no—
227C2×D212—42no—
228C2×D212C22×C412yes—
229C2×D212C22×C412yes—
230C2×D212C2×D412yes—
231C2×D212C2×D412yes—
232C2×C4×D53—42no—
233C2×C4×D53—42no—
234C2×C4×D53—42no—
235C2×C4×D53—42no—
236C2×C4×D53—81no—
237C2×C4×D53—81no—
238C4⋊C4×C53—21no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—21no—
242C22⋊C4×C53—22no—
243C22⋊C4×C53—41no—
244C22⋊C4×C53—42no—
245C22⋊C4×C53—42no—
246C22⋊C4×C53—81no—
247C42×C53—21no—
248C42×C53—21no—
249C42×C53—21no—
250C42×C53—21no—
251C22⋊Dic53—42no—
252#11719924—28no—
253#11719924—28no—
254#11719922—28no—
255#11719922C22⋊C4116yescomplemented
256#11719921—42no—
257#11719921—42no—
258#11719921—42no—
259#11719921—42no—
260#11719921—81no—
261#11719921—81no—
262C4⋊Dic53—21no—
263C4⋊Dic53—21no—
264C4⋊Dic53—21no—
265C4⋊Dic53—21no—
266#11719917—28no—
267C2×#88322—21no—
268C2×#88322—21no—
269C2×#88322—21no—
270C2×#88322—21no—
271C2×#88322—21no—
272C2×#88322—21no—
273C2×#88322—21no—
274C2×#88322—21no—
275C2×#88322C22×C412yes—
276C2×#88322C22×C412yes—
277C2×#88322C2×D412yes—
278C2×#88322C2×D412yes—
279C23×C53—22no—
280C23×C53—21no—
281C23×C53—21no—
282C23×C53—22no—
283C23×C53—22no—
284C23×C53—21no—
285C23×C53—21no—
286C23×C53—21no—
287C23×C53—21no—
288C23×C53—41no—
289C23×C53—41no—
290C23×C53—41no—
291C23×C53—41no—
292C23×C53C4×D412yes—
293C23×C53C22×D411yescharacteristic
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—48no—
299C22×D53—41no—
300C22×D53—41no—
301C22×D53—41no—
302C22×D53—41no—
303C22×D53—48no—
304C22×D53—41no—
305C22×D53—41no—
306C22×D53—41no—
307C22×D53—41no—
308C22×D53—41no—
309C22×D53—41no—
310C22×D53—84no—
311C22×D53—84no—
312C22×D53—84no—
313C22×D53—84no—
314C22×D53—84no—
315Q8×C53—22no—
316Q8×C53—22no—
317Q8×C53—41no—
318Q8×C53—41no—
319D4×C53—22no—
320D4×C53—22no—
321D4×C53—22no—
322D4×C53—48no—
323D4×C53C2×C22⋊C414yescomplemented
324C2×C4×C53—21no—
325C2×C4×C53—21no—
326C2×C4×C53—21no—
327C2×C4×C53—21no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—21no—
334C2×C4×C53—21no—
335C2×C4×C53—21no—
336C2×C4×C53—21no—
337C2×C4×C53—21no—
338C2×C4×C53—21no—
339C2×C4×C53—21no—
340C2×C4×C53—21no—
341C2×C4×C53—21no—
342C2×C4×C53—48no—
343C2×C4×C53—41no—
344C2×C4×C53—41no—
345C2×C4×C53—41no—
346C2×C4×C53—41no—
347C2×C4×C53—41no—
348C2×C4×C53—41no—
349C2×C4×C53—41no—
350C2×C4×C53—41no—
351C2×C4×C53—84no—
352C2×C4×C53—84no—
353C2×C4×C53C4×D412yes—
354C2×C4×C53AGL(1,ℤ/8)12yescomplemented
355C2×C4×C53C23×C411yescharacteristic
356C2×C4×C53C22×D411yescharacteristic
357C2×C4×C53C22×D411yescharacteristic
358C2×C4×C53C2×#4111yescharacteristic
359C2×C4×C53H(5,𝔽2)11yescharacteristic
360C2×C4×C53H(5,𝔽2)11yescharacteristic
361C2×Dic53—41no—
362C2×Dic53—41no—
363C2×Dic53—41no—
364C2×Dic53—41no—
365C2×Dic53—41no—
366C2×Dic53—41no—
367D212—22no—
368D212—22no—
369D212—22no—
370D212—22no—
371D212—22no—
372D212—48no—
373D212—41no—
374D212—41no—
375D212C2×C22⋊C414yes—
376C4×D53—84no—
377C4×D53—84no—
378#88322—22no—
379#88322—41no—
380#88322—41no—
381#88322C2×C22⋊C414yescomplemented
382#22442—531nomaximal, Sylow
383C22×C53—22no—
384C22×C53—24no—
385C22×C53—22no—
386C22×C53—22no—
387C22×C53—42no—
388C22×C53—42no—
389C22×C53—42no—
390C22×C53—41no—
391C22×C53—41no—
392C22×C53—42no—
393C22×C53—41no—
394C22×C53—42no—
395C22×C53—42no—
396C22×C53—41no—
397C22×C53C2×C4×D411yescharacteristic
398C22×C53D4211yescharacteristic
399C22×C53D4211yescharacteristic
400C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C53#57511yescharacteristic
402C22×C53#57611yescharacteristic
403C22×C53#57711yescharacteristic
404C2×D53—24no—
405C2×D53—42no—
406C2×D53—42no—
407C2×D53—42no—
408C2×D53—42no—
409C2×D53—42no—
410C2×D53—42no—
411C2×D53—42no—
412C2×D53—42no—
413C2×D53—42no—
414C2×D53—816no—
415C2×D53—81no—
416C2×D53—81no—
417C2×D53—81no—
418C2×D53—81no—
419C4×C53—22no—
420C4×C53—22no—
421C4×C53—42no—
422C4×C53—41no—
423C4×C53—41no—
424C4×C53—41no—
425C4×C53—81no—
426C4×C53—81no—
427C4×C53C22×C22⋊C411yescharacteristic
428C4×C53#51811yescharacteristic
429C4×C53#54611yescharacteristic
430C4×C53#54611yescharacteristic
431Dic53—81no—
432Dic53—81no—
433C22×AGL(1,ℤ/8)—531no—
434C2×#442—531no—
435C2×C4×D8—531no—
436#2339D5311yescharacteristic, complemented
437D4×C22⋊C4—531no—
438#1973—531no—
439#1968—531no—
440#1879—531no—
441#1879—531no—
442#1877—531no—
443#1877—531no—
444#1809—531no—
445#1788—531no—
446#1786—531no—
447#1753—531no—
448C2×C53—42no—
449C2×C53—44no—
450C2×C53D4×C22⋊C411yescharacteristic
451C2×C53C4×AGL(1,ℤ/8)11yescharacteristic
452C2×C53#294611yescharacteristic
453C2×C53#326411yescharacteristic
454C2×C53#326711yescharacteristic
455C2×C53#327211yescharacteristic
456C2×C53#327311yescharacteristic
457D53—44no—
458D53—82no—
459C22×#41C2×D5311yescharacteristic
460C23×D4—531no—
461C2×AGL(1,ℤ/8)—538no—
462C2×AGL(1,ℤ/8)—1064no—
463C2×AGL(1,ℤ/8)—1064no—
464C22×SD16—531no—
465C22×SD16—531no—
466C22×D8—531no—
467C22×D8—531no—
468C22×M16—531no—
469C2×C4×D4—531no—
470C2×C4×D4—531no—
471C2×C4×D4C2×D5311yescharacteristic, complemented
472C2×C4×D4C2×D5311yescharacteristic, complemented
473C22×C22⋊C4—1061no—
474#442—1064no—
475C4×D8—1064no—
476C2×#107—531no—
477C2×#106—531no—
478C2×#103—531no—
479C2×#103—531no—
480C2×#102—531no—
481C2×#102—531no—
482C2×#102—531no—
483C2×#102—531no—
484C2×#102—531no—
485C2×#102—531no—
486C2×C22⋊C8—531no—
487C2×#97—531no—
488C2×C4×C8—531no—
489#391C2×D5311yescharacteristic, complemented
490#391C2×D5311yescharacteristic, complemented
491#390—531no—
492#390—531no—
493#386—21no—
494#386—21no—
495#386—1061no—
496#386—1061no—
497#381—21no—
498#380—531no—
499#380C2×D5311yescharacteristic
500#379—1061no—
501C4×C22⋊C4C2×D5311yescharacteristic
502C2×#95—21no—
503#340—531no—
504#340—531no—
505#336—531no—
506#336—531no—
507C53#2244211yescharacteristic, complemented, Sylow
508C25—1061no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41C4×D5314yescomplemented
515C22×Q8C22×D5311yescharacteristic
516C22×D4—21no—
517C22×D4—534no—
518C22×D4—531no—
519C22×D4—531no—
520C22×D4—1062no—
521C22×D4—1062no—
522C22×D4—1062no—
523C22×D4—1061no—
524C22×D4—2121no—
525C22×D4—2121no—
526C22×D4C22×D5311yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—1061no—
531C23×C4—1061no—
532C23×C4C22×D5311yescharacteristic
533AGL(1,ℤ/8)—10632no—
534C2×SD16—534no—
535C2×SD16—534no—
536C2×SD16—1062no—
537C2×SD16—1062no—
538C2×SD16—1062no—
539C2×SD16—1062no—
540C2×D8—534no—
541C2×D8—534no—
542C2×D8—534no—
543C2×D8—534no—
544C2×D8—1062no—
545C2×D8—1062no—
546C2×M16—534no—
547C2×M16—1062no—
548C2×M16—1062no—
549C22×C8—531no—
550C22×C8—531no—
551C22×C8—531no—
552C22×C8—531no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—41no—
556C4×D4—41no—
557C4×D4—1062no—
558C4×D4—1062no—
559C4×D4—2121no—
560C4×D4—2121no—
561C2×C4⋊C4—531no—
562C2×C4⋊C4—531no—
563C2×C4⋊C4C22×D5311yescharacteristic
564C2×C4⋊C4C22×D5311yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C22⋊C4—1061no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—2124no—
576C2×C22⋊C4C22⋊D5311yescharacteristic
577C2×C22⋊C4C22⋊D5311yescharacteristic
578C2×C42C22×D5311yescharacteristic
579C2×C42C22×D5311yescharacteristic
580#107—1062no—
581#106—1062no—
582#103—2121no—
583#103—2121no—
584#102—1062no—
585#102—1062no—
586#102—1062no—
587#102—1062no—
588#102—2121no—
589#102—2121no—
590C22⋊C8—1062no—
591#97—1062no—
592C4×C8—1062no—
593#95—21no—
594#95—21no—
595#95—21no—
596#95—21no—
597#95—21no—
598#95—1061no—
599#95C22⋊D5311yescharacteristic
600#95C22⋊D5311yescharacteristic
601C24—21no—
602C24—1061no—
603C24—1064no—
604C24—1061no—
605C24—4241no—
606C24—4241no—
607C24—2122no—
608C24—2122no—
609C24—2122no—
610C24—2122no—
611C24C2×C22⋊D5311yescharacteristic
612#41—28no—
613#41—44no—
614#41—44no—
615#41—44no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8C2×C4×D5312yes—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—532no—
629C2×D4—532no—
630C2×D4—532no—
631C2×D4—532no—
632C2×D4—1068no—
633C2×D4—1064no—
634C2×D4—1061no—
635C2×D4—1061no—
636C2×D4—1061no—
637C2×D4—1061no—
638C2×D4—1061no—
639C2×D4—1061no—
640C2×D4—1061no—
641C2×D4—1061no—
642C2×D4—2124no—
643C2×D4—2124no—
644C2×D4—2124no—
645C2×D4—2122no—
646C2×D4—2122no—
647C2×D4C2×C4×D5312yes—
648C2×D4D4×D5312yes—
649C2×D4D4×D5312yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—81no—
665C22×C4—81no—
666C22×C4—1061no—
667C22×C4—1061no—
668C22×C4—4241no—
669C22×C4—4241no—
670C22×C4—2122no—
671C22×C4—2122no—
672C22×C4—2122no—
673C22×C4—2122no—
674C22×C4C2×C4×D5312yes—
675C22×C4#1171994512yes—
676C22×C4C2×C22⋊D5311yescharacteristic
677C22×C4C2×C22⋊D5311yescharacteristic
678C22×C4C2×C22⋊D5311yescharacteristic
679C22×C4C2×C22⋊D5311yescharacteristic
680C22×C4C2×C22⋊D5311yescharacteristic
681C22×C4C23×D5311yescharacteristic
682SD16—1068no—
683SD16—1068no—
684D8—5316no—
685D8—1068no—
686M16—1068no—
687C2×C8—532no—
688C2×C8—532no—
689C2×C8—532no—
690C2×C8—532no—
691C2×C8—1061no—
692C2×C8—1061no—
693C2×C8—1061no—
694C2×C8—1061no—
695C2×C8—1061no—
696C2×C8—1061no—
697C2×C8—1061no—
698C2×C8—1061no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—1061no—
704C4⋊C4—1061no—
705C4⋊C4—1061no—
706C4⋊C4—1061no—
707C22⋊C4—22no—
708C22⋊C4—41no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—81no—
712C22⋊C4—4241no—
713C22⋊C4—4241no—
714C22⋊C4—2122no—
715C22⋊C4—2122no—
716C22⋊C4—2122no—
717C22⋊C4—2122no—
718C22⋊C4—2122no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—1062no—
737C23—1062no—
738C23—1062no—
739C23—1062no—
740C23—4244no—
741C23—4244no—
742C23—4244no—
743C23—4244no—
744C23—4244no—
745C23—2128no—
746C23—2128no—
747C23—2121no—
748C23—2121no—
749C23—2121no—
750C23—2121no—
751C23—2121no—
752C23—2121no—
753C23—2121no—
754C23—2121no—
755C23—2121no—
756C23—2121no—
757C23C4×C22⋊D5312yes—
758C23C22×C22⋊D5311yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—41no—
762Q8—41no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—48no—
767D4—534no—
768D4—1062no—
769D4—1062no—
770D4—1062no—
771D4—1062no—
772D4—1062no—
773D4—2128no—
774D4—2121no—
775D4—2121no—
776D4C22⋊C4×D5314yescomplemented
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—84no—
805C2×C4—84no—
806C2×C4—4244no—
807C2×C4—4244no—
808C2×C4—2121no—
809C2×C4—2121no—
810C2×C4—2121no—
811C2×C4—2121no—
812C2×C4—2121no—
813C2×C4—2121no—
814C2×C4C4×C22⋊D5312yes—
815C2×C4#1313324212yescomplemented
816C2×C4C22×C4×D5311yescharacteristic
817C2×C4C2×D4×D5311yescharacteristic
818C2×C4C2×D4×D5311yescharacteristic
819C2×C4C2×#1171994511yescharacteristic
820C2×C4#1313326211yescharacteristic
821C2×C4#1313326211yescharacteristic
822C8—534no—
823C8—1062no—
824C8—2121no—
825C8—2121no—
826C22—22no—
827C22—24no—
828C22—22no—
829C22—22no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—41no—
840C22—1064no—
841C22—42416no—
842C22—4241no—
843C22—4241no—
844C22—4241no—
845C22—4241no—
846C22—2122no—
847C22—2122no—
848C22—2122no—
849C22—2122no—
850C22—2122no—
851C22—2122no—
852C22—2122no—
853C22—2122no—
854C22—2122no—
855C22C2×C4×C22⋊D5311yescharacteristic
856C22D4×C22⋊D5311yescharacteristic
857C22D4×C22⋊D5311yescharacteristic
858C22C2×#1313324211yescharacteristic
859C22#1681142111yescharacteristic
860C22#1681142611yescharacteristic
861C22#1681143111yescharacteristic
862C4—22no—
863C4—22no—
864C4—42no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—81no—
869C4—81no—
870C4—4241no—
871C4—4241no—
872C4C2×C22⋊C4×D5311yescharacteristic
873C4#1681109611yescharacteristic
874C4#1681126311yescharacteristic
875C4#1681126311yescharacteristic
876C2—42no—
877C2—44no—
878C2—4242no—
879C2—2124no—
880C2C22⋊C4×C22⋊D5311yescharacteristic
881C2C4×#1313324211yescharacteristic
882C2#2028354311yescharacteristic
883C2#2028619611yescharacteristic
884C2#2028624111yescharacteristic
885C2#2028631511yescharacteristic
886C2#2028632211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2339C2
socleC23×C53C22×D4
prime radicalC22×#13133242C2
cosocleC22×C4×C53C24
hypercenter#2339D53
hypocenterC53#22442
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×#16810733C2semidirect
3. C2×C4×#11719922C2semidirect
4. C22⋊C4×D212C2semidirect
5. #20275599C2semidirect
6. #20275572C2semidirect
7. #20275063C2semidirect
8. #20275063C2semidirect
9. #20275052C2semidirect
10. #20275052C2semidirect
11. #20274746C2semidirect
12. #20274655C2semidirect
13. #20274645C2semidirect
14. #20274499C2semidirect
15. C53×#2339C2semidirect
19. C2×#13133242C4semidirect
30. C2×#13133150C22semidirect
31. C2×#13133148C22semidirect
32. C2×#13133141C22semidirect
33. C2×#13133141C22semidirect
34. C2×#13133138C22semidirect
35. C2×#13133138C22semidirect
41. C2×#13133128C22semidirect
42. C2×C4×#88322C22semidirect
49. #16810385C22semidirect
50. #16810385C22semidirect
51. #16810378C22semidirect
52. #16810378C22semidirect
54. C2×C4×D4×C53C22semidirect
55. C2×C4×D4×C53C22semidirect
56. C53×#391C22semidirect
57. C53×#391C22semidirect
71. C22×D212C2×C4semidirect
81. C2×#11719924C2×C4semidirect
82. C2×#11719924C2×C4semidirect
86. C2×#11719922C2×C4semidirect
91. C2×#11719917C2×C4semidirect
129. C2×#41×C53C2×C4semidirect
255. #11719922C22⋊C4semidirect
323. D4×C53C2×C22⋊C4semidirect
354. C2×C4×C53AGL(1,ℤ/8)semidirect
381. #88322C2×C22⋊C4semidirect
436. #2339D53semidirect
471. C2×C4×D4C2×D53semidirect
472. C2×C4×D4C2×D53semidirect
489. #391C2×D53semidirect
490. #391C2×D53semidirect
507. C53#22442semidirect
514. C2×#41C4×D53semidirect
776. D4C22⋊C4×D53semidirect
815. C2×C4#13133242semidirect

Maximal subgroups

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

subgroupindex
C22×#131332422
C2×#168107332
C2×C4×#117199222
C22⋊C4×D2122
#202755992
#202755722
#202750632
#202750522
#202747462
#202746552
#202746452
#202744992
C53×#23392
#2244253