Finite Group Databasebeta

← #27399641

Subgroups — #27399641

Order 13568.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811269C211yesmaximal, characteristic
2C2×#16810695C211yesmaximal, characteristic, complemented
3C2×#16810627C211yesmaximal, characteristic, complemented
4C2×#16810617C211yesmaximal, characteristic, complemented
5#20275647C211yesmaximal, characteristic, complemented
6#20275529C211yesmaximal, characteristic, complemented
7#20275146C211yesmaximal, characteristic, complemented
8#20275141C211yesmaximal, characteristic, complemented
9#20275037C211yesmaximal, characteristic, complemented
10#20275027C211yesmaximal, characteristic, complemented
11#20274712C211yesmaximal, characteristic, complemented
12#20274653C211yesmaximal, characteristic, complemented
13#20274645C211yesmaximal, characteristic, complemented
14#20274543C211yesmaximal, characteristic, complemented
15C53×#2354C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C23×D212C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19C23×#88322C2211yescharacteristic, complemented
20#16811269—24no—
21#16811269C418yescomplemented
22C2×#13133205C2211yescharacteristic
23C2×#13133202—21no—
24C2×#13133196C2211yescharacteristic
25C2×#13133191C2211yescharacteristic
26C2×#13133190—21no—
27C2×#13133185—21no—
28C2×C4×D212C2211yescharacteristic
29C2×C22⋊C4×D53—21no—
30#16810695—24no—
31C2×C4⋊#88322C2211yescharacteristic, complemented
32#16810627—24no—
33#16810617—24no—
34C2×#13133140C2211yescharacteristic, complemented
35C2×#13133140C2211yescharacteristic, complemented
36C2×#13133140C2211yescharacteristic, complemented
37C2×#13133140C2211yescharacteristic, complemented
38C2×#13133137C2211yescharacteristic
39C2×#13133137C2211yescharacteristic
40C2×#13133137C2211yescharacteristic
41C2×#13133137C2211yescharacteristic
42C2×#13133137C2211yescharacteristic
43C2×#13133137C2211yescharacteristic
44C2×#13133137C2211yescharacteristic
45C2×#13133137C2211yescharacteristic
46C2×C22⋊#88322C2211yescharacteristic
47C2×C22⋊#88322C2211yescharacteristic, complemented
48C2×#13133128C2211yescharacteristic, complemented
49#16810385C2211yescharacteristic, complemented
50#16810385C2211yescharacteristic, complemented
51#16810385C2211yescharacteristic, complemented
52#16810385C2211yescharacteristic, complemented
53C2×C4×D4×C53C2211yescharacteristic
54C2×#117×C53C2211yescharacteristic
55C2×#117×C53C2211yescharacteristic, complemented
56C53×#390—21no—
57C53×#388—21no—
58C53×#388—21no—
59C53×#384C2211yescharacteristic, complemented
60C53×#380C2211yescharacteristic
61C53×#380C2211yescharacteristic, complemented
62C4×C4⋊C4×C53—21no—
63C4×C4⋊C4×C53C2211yescharacteristic, complemented
64C24×D53—21no—
65C2×#11719945—22no—
66C2×#11719945—22no—
67C2×#11719945—22no—
68C2×#11719945—41no—
69C2×#11719945—41no—
70C2×#11719945C2×C414yes—
71C22×Dic106C2311yescharacteristic
72C22×D212—22no—
73C22×D212—22no—
74C22×D212—22no—
75C22×D212—21no—
76C22×D212—41no—
77C22×D212—41no—
78C22×D212C2×C414yes—
79C22×D212C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C22×C4×D53—21no—
84C22×C4×D53—21no—
85C2×#11719917—22no—
86C2×#11719917—22no—
87C2×#11719917—41no—
88C22×#88322—22no—
89C22×#88322—22no—
90C22×#88322—41no—
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C22×#88322C2311yescharacteristic
95#13133205—22no—
96#13133205C2×C414yes—
97#13133202—28no—
98#13133196—22no—
99#13133196C2×C414yes—
100#13133191—22no—
101#13133191C2×C414yes—
102#13133190—28no—
103#13133185—28no—
104C4×D212—22no—
105C4×D212C2×C414yes—
106C2×C4⋊Dic53C2311yescharacteristic
107C2×#11719919—21no—
108C2×C22⋊Dic53—21no—
109C2×#11719921—21no—
110C2×#11719921—21no—
111C2×#11719921—21no—
112C2×#11719921—21no—
113C22⋊C4×D53—28no—
114C4⋊#88322—22no—
115#13133140—22no—
116#13133140—22no—
117#13133140—41no—
118#13133140—41no—
119#13133137—22no—
120#13133137—22no—
121#13133137—22no—
122#13133137—22no—
123#13133137—22no—
124#13133137—41no—
125#13133137—41no—
126#13133137D414yescomplemented
127C22⋊#88322—22no—
128C22⋊#88322—22no—
129#13133128—22no—
130C22×D4×C53D411yescharacteristic
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C4×D4×C53C2×C414yes—
134C4×D4×C53D414yes—
135#117×C53—22no—
136#117×C53—22no—
137#117×C53—41no—
138#117×C53—41no—
139C2×C4⋊C4×C53—21no—
140C2×C4⋊C4×C53—21no—
141C2×C4⋊C4×C53D411yescharacteristic
142C2×C4⋊C4×C53C2311yescharacteristic
143C2×C4⋊C4×C53C2311yescharacteristic
144C2×C4⋊C4×C53C2311yescharacteristic
145C2×C4⋊C4×C53C2311yescharacteristic
146C2×C22⋊C4×C53—21no—
147C2×C22⋊C4×C53—21no—
148C2×C22⋊C4×C53—21no—
149C2×C22⋊C4×C53—21no—
150C2×C22⋊C4×C53D411yescharacteristic
151C2×C22⋊C4×C53D411yescharacteristic
152C2×C42×C53—21no—
153C2×C42×C53—21no—
154C2×C42×C53—21no—
155C2×C42×C53C2311yescharacteristic
156#95×C53—21no—
157#95×C53—21no—
158#95×C53—21no—
159C24×C53C2×D411yescharacteristic
160C24×C53C2×D411yescharacteristic
161C23×D53—21no—
162C23×D53—21no—
163C23×D53—24no—
164C23×D53—42no—
165C23×D53—42no—
166C23×D53—42no—
167C23×D53—42no—
168C23×D53—81no—
169C23×D53—81no—
170C2×D4×C53—41no—
171C2×D4×C53—41no—
172C2×D4×C53C22⋊C414yes—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53C22×C412yes—
186C22×C4×C53C22×C412yes—
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D412yes—
192C22×C4×C53C2×D412yes—
193C22×C4×C53C2411yescharacteristic
194C2×C22⋊D53—24no—
195C2×C22⋊D53—24no—
196C2×C22⋊D53—42no—
197C2×C22⋊D53—42no—
198C2×C22⋊D53—81no—
199C2×C22⋊D53—81no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202#11719945—28no—
203#11719945—44no—
204#11719945—44no—
205#11719945—44no—
206C2×D212—21no—
207C2×D212—21no—
208C2×D212—21no—
209C2×D212—21no—
210C2×D212—21no—
211C2×D212—21no—
212C2×D212—21no—
213C2×D212—28no—
214C2×D212—24no—
215C2×D212—21no—
216C2×D212—44no—
217C2×D212—44no—
218C2×D212—44no—
219C2×D212—42no—
220C2×D212—42no—
221C2×D212C22×C412yes—
222C2×D212C22×C412yes—
223C2×D212C2×D412yes—
224C2×D212#4112yes—
225C2×C4×D53—24no—
226C2×C4×D53—24no—
227C2×C4×D53—42no—
228C2×C4×D53—42no—
229C2×C4×D53—81no—
230C2×C4×D53—81no—
231C2×Dic106—21no—
232C2×Dic106—21no—
233C2×Dic106—21no—
234C2×Dic106—21no—
235C2×Dic106—21no—
236C2×Dic106C22×C412yes—
237C4⋊C4×C53—21no—
238C4⋊C4×C53—21no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53—21no—
244C4⋊C4×C53—42no—
245C4⋊C4×C53—81no—
246C4⋊C4×C53C22⋊C414yes—
247C4⋊C4×C53C2×D412yes—
248C22⋊C4×C53—42no—
249C22⋊C4×C53—42no—
250C22⋊C4×C53—81no—
251C22⋊C4×C53—81no—
252C22⋊C4×C53C22⋊C414yes—
253C22⋊C4×C53C22⋊C414yes—
254C42×C53—42no—
255C42×C53—42no—
256C42×C53—42no—
257C42×C53C22×C412yes—
258C42×C53C2×D412yes—
259C22⋊Dic53—24no—
260#11719921—24no—
261#11719921—24no—
262#11719921—24no—
263#11719921—24no—
264C4⋊Dic53—21no—
265C4⋊Dic53C22×C412yes—
266#11719919—24no—
267#11719917—44no—
268C2×#88322—21no—
269C2×#88322—21no—
270C2×#88322—21no—
271C2×#88322—21no—
272C2×#88322—21no—
273C2×#88322—21no—
274C2×#88322—21no—
275C2×#88322—21no—
276C2×#88322—21no—
277C2×#88322—21no—
278C2×#88322—21no—
279C2×#88322—44no—
280C2×#88322C2×D412yes—
281C23×C53—21no—
282C23×C53—21no—
283C23×C53—21no—
284C23×C53—21no—
285C23×C53—21no—
286C23×C53—21no—
287C23×C53—21no—
288C23×C53—21no—
289C23×C53—21no—
290C23×C53—21no—
291C23×C53—21no—
292C23×C53—21no—
293C23×C53C2×C22⋊C412yes—
294C23×C53C2×C22⋊C412yes—
295C23×C53C22×D411yescharacteristic
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—48no—
301C22×D53—41no—
302C22×D53—41no—
303C22×D53—41no—
304C22×D53—41no—
305C22×D53—48no—
306C22×D53—41no—
307C22×D53—41no—
308C22×D53—41no—
309C22×D53—41no—
310C22×D53—41no—
311C22×D53—41no—
312C22×D53—84no—
313C22×D53—84no—
314C22×D53—84no—
315C22×D53—84no—
316C22×D53—84no—
317D4×C53—44no—
318C2×C4×C53—21no—
319C2×C4×C53—21no—
320C2×C4×C53—21no—
321C2×C4×C53—21no—
322C2×C4×C53—21no—
323C2×C4×C53—21no—
324C2×C4×C53—21no—
325C2×C4×C53—21no—
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—22no—
334C2×C4×C53—22no—
335C2×C4×C53—41no—
336C2×C4×C53—41no—
337C2×C4×C53—41no—
338C2×C4×C53—41no—
339C2×C4×C53—41no—
340C2×C4×C53—41no—
341C2×C4×C53—41no—
342C2×C4×C53—41no—
343C2×C4×C53—41no—
344C2×C4×C53—41no—
345C2×C4×C53—41no—
346C2×C4×C53C2×C22⋊C412yes—
347C2×C4×C53C2×C22⋊C412yes—
348C2×C4×C53C2×C22⋊C412yes—
349C2×C4×C53C2×C22⋊C412yes—
350C2×C4×C53C23×C411yescharacteristic
351C2×C4×C53C22×D411yescharacteristic
352C2×C4×C53C22×D411yescharacteristic
353C2×C4×C53C2×#4111yescharacteristic
354C2×C4×C53H(5,𝔽2)11yescharacteristic
355C2×C4×C53H(5,𝔽2)11yescharacteristic
356C22⋊D53—48no—
357C22⋊D53—84no—
358C2×Dic53—22no—
359C2×Dic53—22no—
360C2×Dic53—41no—
361C2×Dic53—41no—
362C2×Dic53—41no—
363C2×Dic53—41no—
364D212—22no—
365D212—22no—
366D212—22no—
367D212—22no—
368D212—22no—
369D212—48no—
370D212—41no—
371D212—41no—
372D212C4×D414yes—
373C4×D53—48no—
374C4×D53—84no—
375Dic106—22no—
376Dic106—22no—
377Dic106—41no—
378Dic106—41no—
379#88322—22no—
380#88322—41no—
381#88322—41no—
382#88322—41no—
383#22424—531nomaximal, Sylow
384C22×C53—22no—
385C22×C53—22no—
386C22×C53—22no—
387C22×C53—22no—
388C22×C53—22no—
389C22×C53—22no—
390C22×C53—41no—
391C22×C53—41no—
392C22×C53—41no—
393C22×C53—41no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53—41no—
397C22×C53—41no—
398C22×C53C22×C22⋊C411yescharacteristic
399C22×C53D4211yescharacteristic
400C22×C53#54611yescharacteristic
401C22×C53#57511yescharacteristic
402C22×C53#57511yescharacteristic
403C22×C53#57611yescharacteristic
404C22×C53#57711yescharacteristic
405C2×D53—24no—
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—42no—
415C2×D53—816no—
416C2×D53—81no—
417C2×D53—81no—
418C2×D53—81no—
419C2×D53—81no—
420C4×C53—22no—
421C4×C53—22no—
422C4×C53—22no—
423C4×C53—22no—
424C4×C53—42no—
425C4×C53—81no—
426C4×C53—81no—
427C4×C53—81no—
428C4×C53C2×C4×D411yescharacteristic
429C4×C53#51811yescharacteristic
430C4×C53D4211yescharacteristic
431C4×C53#54611yescharacteristic
432Dic53—42no—
433Dic53—42no—
434C2×#546—531no—
435C2×#435—531no—
436C2×#418—531no—
437C2×#416—531no—
438#2354D5311yescharacteristic, complemented
439#1983—531no—
440#1959—531no—
441#1894—531no—
442#1893—531no—
443#1875—531no—
444#1873—531no—
445#1802—531no—
446#1788—531no—
447#1786—531no—
448#1762—531no—
449C2×C53—42no—
450C2×C53—42no—
451C2×C53D4×C22⋊C411yescharacteristic
452C2×C53#289611yescharacteristic
453C2×C53#289711yescharacteristic
454C2×C53#326711yescharacteristic
455C2×C53#326811yescharacteristic
456C2×C53#331111yescharacteristic
457C2×C53#331911yescharacteristic
458D53—44no—
459D53—82no—
460C22×#41—531no—
461C23×D4—531no—
462C22×M16—531no—
463C23×C8—531no—
464#546—538no—
465#546—1064no—
466C2×#124—531no—
467C2×#123—1061no—
468C2×C22⋊Q8—531no—
469C2×#121—531no—
470C2×#121—1061no—
471C2×#120—1061no—
472C2×C4×D4—531no—
473C2×C4×D4C2×D5311yescharacteristic
474C2×#117C2×D5311yescharacteristic
475C2×#117C2×D5311yescharacteristic, complemented
476C22×C22⋊C4—1061no—
477#435—1064no—
478C2×C4⋊C8—531no—
479#418—1064no—
480#416—1064no—
481C2×#103—531no—
482C2×#103—531no—
483C2×#103—531no—
484C2×#103—531no—
485C2×#102—531no—
486C2×#102—531no—
487C2×#102—531no—
488C2×#102—531no—
489C2×#102—531no—
490C2×#102—531no—
491C2×#102—531no—
492C2×#102—531no—
493C2×C22⋊C8—531no—
494C2×C22⋊C8—531no—
495C2×#97—531no—
496#390—21no—
497#388—21no—
498#388—21no—
499#384C2×D5311yescharacteristic, complemented
500#380C2×D5311yescharacteristic
501#380C2×D5311yescharacteristic, complemented
502C4×C4⋊C4—21no—
503C4×C4⋊C4C2×D5311yescharacteristic, complemented
504#340—531no—
505#340—531no—
506#340—531no—
507#340—531no—
508C53#2242411yescharacteristic, complemented, Sylow
509C25—1061no—
510C2×#41—534no—
511C2×#41—1062no—
512C2×#41—1062no—
513C2×#41—1062no—
514C2×#41—2121no—
515C2×#41—2121no—
516C22×Q8—531no—
517C22×D4—534no—
518C22×D4—531no—
519C22×D4—531no—
520C22×D4—1062no—
521C22×D4—1062no—
522C22×D4—1061no—
523C22×D4—1061no—
524C22×D4—1062no—
525C22×D4—1061no—
526C22×D4—2121no—
527C22×D4—2121no—
528C22×D4C22⋊D5311yescharacteristic
529C23×C4—1061no—
530C23×C4—1061no—
531C23×C4C22×D5311yescharacteristic
532C23×C4C22×D5311yescharacteristic
533C2×M16—1062no—
534C2×M16—1062no—
535C2×M16—2121no—
536C22×C8—531no—
537C22×C8—531no—
538C22×C8—531no—
539C22×C8—531no—
540C22×C8—1062no—
541C22×C8—1062no—
542C22×C8—2121no—
543#124—534no—
544#124—1062no—
545#123—1068no—
546C22⋊Q8—534no—
547C22⋊Q8—1062no—
548#121—534no—
549#121—1062no—
550#121—1068no—
551#120—1068no—
552C4×D4—534no—
553C4×D4—1062no—
554C4×D4C4×D5314yes—
555C4×D4D21214yes—
556#117—22no—
557#117—22no—
558#117—41no—
559#117—41no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—531no—
563C2×C4⋊C4—1061no—
564C2×C4⋊C4C22⋊D5311yescharacteristic
565C2×C4⋊C4C22×D5311yescharacteristic
566C2×C4⋊C4C22×D5311yescharacteristic
567C2×C4⋊C4C22×D5311yescharacteristic
568C2×C4⋊C4C22×D5311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1061no—
576C2×C22⋊C4—1061no—
577C2×C22⋊C4—1061no—
578C2×C22⋊C4—1068no—
579C2×C22⋊C4C22⋊D5311yescharacteristic
580C2×C22⋊C4C22⋊D5311yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42—21no—
584C2×C42C22×D5311yescharacteristic
585C4⋊C8—1062no—
586#103—1062no—
587#103—1062no—
588#103—2121no—
589#103—2121no—
590#102—534no—
591#102—1062no—
592#102—1062no—
593#102—1062no—
594#102—1062no—
595#102—1062no—
596#102—2121no—
597#102—2121no—
598C22⋊C8—1062no—
599C22⋊C8—1062no—
600#97—1062no—
601#95—21no—
602#95—21no—
603#95—21no—
604C24—1061no—
605C24—1064no—
606C24—1061no—
607C24—4241no—
608C24—4241no—
609C24—2122no—
610C24—2122no—
611C24—2122no—
612C24—2122no—
613C24C2×C22⋊D5311yescharacteristic
614C24C2×C22⋊D5311yescharacteristic
615#41—1068no—
616#41—2124no—
617#41—2124no—
618#41—2124no—
619C2×Q8—532no—
620C2×Q8—1061no—
621C2×Q8—1061no—
622C2×Q8—1061no—
623C2×Q8—1061no—
624C2×Q8—1061no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—532no—
628C2×D4—532no—
629C2×D4—532no—
630C2×D4—532no—
631C2×D4—1068no—
632C2×D4—1064no—
633C2×D4—1064no—
634C2×D4—1064no—
635C2×D4—1061no—
636C2×D4—1061no—
637C2×D4—1061no—
638C2×D4—1061no—
639C2×D4—1061no—
640C2×D4—1061no—
641C2×D4—1061no—
642C2×D4—1061no—
643C2×D4—4241no—
644C2×D4—4241no—
645C2×D4—2124no—
646C2×D4—2124no—
647C2×D4—2124no—
648C2×D4—2122no—
649C2×D4—2122no—
650C2×D4—2122no—
651C2×D4—2122no—
652C2×D4#1171992114yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—1061no—
666C22×C4—1061no—
667C22×C4—1064no—
668C22×C4—1064no—
669C22×C4—4241no—
670C22×C4—4241no—
671C22×C4—2122no—
672C22×C4—2122no—
673C22×C4C2×C4×D5312yes—
674C22×C4C2×C4×D5312yes—
675C22×C4C2×D21212yes—
676C22×C4C2×D21212yes—
677C22×C4C2×C22⋊D5311yescharacteristic
678C22×C4C2×C22⋊D5311yescharacteristic
679C22×C4C2×C22⋊D5311yescharacteristic
680C22×C4C2×C22⋊D5311yescharacteristic
681C22×C4C23×D5311yescharacteristic
682M16—2124no—
683C2×C8—532no—
684C2×C8—1061no—
685C2×C8—1061no—
686C2×C8—1061no—
687C2×C8—1061no—
688C2×C8—1061no—
689C2×C8—1061no—
690C2×C8—1061no—
691C2×C8—1061no—
692C2×C8—1061no—
693C2×C8—1061no—
694C2×C8—1061no—
695C2×C8—2124no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—42no—
704C4⋊C4—81no—
705C4⋊C4—532no—
706C4⋊C4—1064no—
707C4⋊C4—1061no—
708C4⋊C4#1171992114yes—
709C4⋊C4D4×D5312yes—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C22⋊C4—1064no—
715C22⋊C4—1064no—
716C22⋊C4—1064no—
717C22⋊C4—1064no—
718C22⋊C4—1064no—
719C22⋊C4#1171992114yes—
720C22⋊C4#1171992114yes—
721C42—42no—
722C42—42no—
723C42—42no—
724C42C2×C4×D5312yes—
725C42C2×D21212yes—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—1062no—
739C23—1062no—
740C23—1062no—
741C23—1062no—
742C23—4244no—
743C23—4244no—
744C23—4244no—
745C23—4244no—
746C23—4244no—
747C23—2128no—
748C23—2128no—
749C23—2121no—
750C23—2121no—
751C23—2121no—
752C23—2121no—
753C23—2121no—
754C23—2121no—
755C23—2121no—
756C23—2121no—
757C23—2121no—
758C23—2121no—
759C23C2×#1171992112yes—
760C23C2×#1171992112yes—
761C23C22×C22⋊D5311yescharacteristic
762Q8—1062no—
763Q8—1062no—
764Q8—2121no—
765Q8—2121no—
766D4—44no—
767D4—534no—
768D4—1062no—
769D4—1062no—
770D4—1062no—
771D4—1062no—
772D4—1062no—
773D4—4244no—
774D4—2128no—
775D4—2128no—
776D4—2121no—
777D4—2121no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—41no—
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—41no—
805C2×C4—41no—
806C2×C4—1062no—
807C2×C4—1062no—
808C2×C4—4244no—
809C2×C4—2128no—
810C2×C4—2121no—
811C2×C4—2121no—
812C2×C4—2121no—
813C2×C4—2121no—
814C2×C4C2×#1171992112yes—
815C2×C4C2×#1171992112yes—
816C2×C4C2×#1171992112yes—
817C2×C4C2×#1171992112yes—
818C2×C4C22×C4×D5311yescharacteristic
819C2×C4C2×D4×D5311yescharacteristic
820C2×C4C22×D21211yescharacteristic
821C2×C4#41×D5311yescharacteristic
822C2×C4#1313326211yescharacteristic
823C2×C4#1313326311yescharacteristic
824C8—1062no—
825C8—2121no—
826C8—2121no—
827C8—2121no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—1064no—
843C22—42416no—
844C22—4241no—
845C22—4241no—
846C22—4241no—
847C22—4241no—
848C22—2122no—
849C22—2122no—
850C22—2122no—
851C22—2122no—
852C22—2122no—
853C22—2122no—
854C22—2122no—
855C22—2122no—
856C22—2122no—
857C22C22×#1171992111yescharacteristic
858C22D4×C22⋊D5311yescharacteristic
859C22#1681126111yescharacteristic
860C22#1681142111yescharacteristic
861C22#1681142111yescharacteristic
862C22#1681142611yescharacteristic
863C22#1681143111yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4—2122no—
873C4—2122no—
874C4C4×D4×D5311yescharacteristic
875C4#1681109511yescharacteristic
876C4D4×D21211yescharacteristic
877C4#1681126811yescharacteristic
878C2—42no—
879C2—42no—
880C2—4242no—
881C2—2124no—
882C2D4×#1171992111yescharacteristic
883C2#2028323211yescharacteristic
884C2#2028323811yescharacteristic
885C2#2028624111yescharacteristic
886C2#2028625611yescharacteristic
887C2#2028674511yescharacteristic
888C2#2028686511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2354C2
socleC23×C53C22×D4
prime radicalC2×#16811269C2
cosocleC22×C4×C53C24
hypercenter#2354D53
hypocenterC53#22424
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. C2×#16810695C2semidirect
3. C2×#16810627C2semidirect
4. C2×#16810617C2semidirect
5. #20275647C2semidirect
6. #20275529C2semidirect
7. #20275146C2semidirect
8. #20275141C2semidirect
9. #20275037C2semidirect
10. #20275027C2semidirect
11. #20274712C2semidirect
12. #20274653C2semidirect
13. #20274645C2semidirect
14. #20274543C2semidirect
15. C53×#2354C2semidirect
19. C23×#88322C22semidirect
21. #16811269C4semidirect
31. C2×C4⋊#88322C22semidirect
34. C2×#13133140C22semidirect
35. C2×#13133140C22semidirect
36. C2×#13133140C22semidirect
37. C2×#13133140C22semidirect
47. C2×C22⋊#88322C22semidirect
48. C2×#13133128C22semidirect
49. #16810385C22semidirect
50. #16810385C22semidirect
51. #16810385C22semidirect
52. #16810385C22semidirect
55. C2×#117×C53C22semidirect
59. C53×#384C22semidirect
61. C53×#380C22semidirect
63. C4×C4⋊C4×C53C22semidirect
126. #13133137D4semidirect
438. #2354D53semidirect
475. C2×#117C2×D53semidirect
499. #384C2×D53semidirect
501. #380C2×D53semidirect
503. C4×C4⋊C4C2×D53semidirect
508. C53#22424semidirect

Maximal subgroups

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

subgroupindex
C2×#168112692
C2×#168106952
C2×#168106272
C2×#168106172
#202756472
#202755292
#202751462
#202751412
#202750372
#202750272
#202747122
#202746532
#202746452
#202745432
C53×#23542
#2242453