Finite Group Databasebeta

← #27399686

Subgroups — #27399686

Order 13568.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811269C211yesmaximal, characteristic
2C2×#16810701C211yesmaximal, characteristic, complemented
3C2×#16810622C211yesmaximal, characteristic, complemented
4C2×#16810627C211yesmaximal, characteristic, complemented
5#20275647C211yesmaximal, characteristic, complemented
6#20275524C211yesmaximal, characteristic, complemented
7#20275151C211yesmaximal, characteristic, complemented
8#20275146C211yesmaximal, characteristic, complemented
9#20275032C211yesmaximal, characteristic, complemented
10#20275027C211yesmaximal, characteristic, complemented
11#20274722C211yesmaximal, characteristic, complemented
12#20274653C211yesmaximal, characteristic, complemented
13#20274645C211yesmaximal, characteristic, complemented
14C4×#13133137C211yesmaximal, characteristic, complemented
15C53×#2352C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C23×D212C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19C22×#11719917C2211yescharacteristic, 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#16810701—24no—
31C2×C4⋊#88322C2211yescharacteristic, complemented
32#16810627—24no—
33#16810622—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×C4×#88322C2211yescharacteristic, complemented
49#16810385C2211yescharacteristic, complemented
50#16810385C2211yescharacteristic, complemented
51#16810385C2211yescharacteristic, complemented
52#16810385C2211yescharacteristic, complemented
53C2×C4×D4×C53C2211yescharacteristic
54C2×#117×C53C2211yescharacteristic
55C22×C4⋊C4×C53C2211yescharacteristic, complemented
56C53×#388—21no—
57C53×#387—21no—
58C53×#386—21no—
59C53×#382C2211yescharacteristic, complemented
60C53×#380C2211yescharacteristic
61C53×#380C2211yescharacteristic, complemented
62C4×C4⋊C4×C53C2211yescharacteristic, complemented
63C4×C22⋊C4×C53—21no—
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×C414yescomplemented
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—22no—
88C2×#11719917—22no—
89C2×#11719917—41no—
90C2×#11719917—41no—
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C22×#88322C2311yescharacteristic
95#13133205—22no—
96#13133205C2×C414yescomplemented
97#13133202—28no—
98#13133196—22no—
99#13133196C2×C414yescomplemented
100#13133191—22no—
101#13133191C2×C414yes—
102#13133190—28no—
103#13133185—28no—
104C4×D212—22no—
105C4×D212C2×C414yescomplemented
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—
129C4×#88322—22no—
130C22×D4×C53D411yescharacteristic
131C23×C4×C53—21no—
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134C4×D4×C53C2×C414yes—
135C4×D4×C53D414yes—
136#117×C53—22no—
137#117×C53—41no—
138C2×C4⋊C4×C53—21no—
139C2×C4⋊C4×C53—22no—
140C2×C4⋊C4×C53—41no—
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×C53D411yescharacteristic
150C2×C22⋊C4×C53D411yescharacteristic
151C2×C42×C53—21no—
152C2×C42×C53—21no—
153C2×C42×C53C2311yescharacteristic
154#95×C53—21no—
155#95×C53—21no—
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×C53—42no—
186C22×C4×C53—42no—
187C22×C4×C53—81no—
188C22×C4×C53C22×C412yes—
189C22×C4×C53C22×C412yes—
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D412yes—
195C22×C4×C53C2×D412yes—
196C22×C4×C53C2411yescharacteristic
197C2×C22⋊D53—24no—
198C2×C22⋊D53—24no—
199C2×C22⋊D53—42no—
200C2×C22⋊D53—42no—
201C2×C22⋊D53—81no—
202C2×C22⋊D53—81no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205#11719945—28no—
206#11719945—44no—
207#11719945—44no—
208#11719945—44no—
209C2×D212—21no—
210C2×D212—21no—
211C2×D212—21no—
212C2×D212—21no—
213C2×D212—21no—
214C2×D212—21no—
215C2×D212—21no—
216C2×D212—28no—
217C2×D212—24no—
218C2×D212—21no—
219C2×D212—44no—
220C2×D212—44no—
221C2×D212—44no—
222C2×D212—42no—
223C2×D212—42no—
224C2×D212C22×C412yes—
225C2×D212C22×C412yes—
226C2×D212C2×D412yes—
227C2×D212#4112yes—
228C2×C4×D53—24no—
229C2×C4×D53—24no—
230C2×C4×D53—42no—
231C2×C4×D53—42no—
232C2×C4×D53—81no—
233C2×C4×D53—81no—
234C2×Dic106—21no—
235C2×Dic106—21no—
236C2×Dic106—21no—
237C2×Dic106—21no—
238C2×Dic106—21no—
239C2×Dic106C22×C412yes—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53—21no—
244C4⋊C4×C53—21no—
245C4⋊C4×C53—21no—
246C4⋊C4×C53—21no—
247C4⋊C4×C53—42no—
248C4⋊C4×C53C22⋊C414yes—
249C4⋊C4×C53C2×D412yes—
250C22⋊C4×C53—42no—
251C22⋊C4×C53—42no—
252C22⋊C4×C53—81no—
253C22⋊C4×C53C22⋊C414yes—
254C22⋊C4×C53C22⋊C414yes—
255C42×C53—42no—
256C42×C53—81no—
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—
268#11719917—44no—
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—21no—
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×C53—84no—
347C2×C4×C53C2×C22⋊C412yes—
348C2×C4×C53C2×C22⋊C412yes—
349C2×C4×C53C2×C22⋊C412yes—
350C2×C4×C53C2×C22⋊C412yes—
351C2×C4×C53C23×C411yescharacteristic
352C2×C4×C53C22×D411yescharacteristic
353C2×C4×C53C22×D411yescharacteristic
354C2×C4×C53C2×#4111yescharacteristic
355C2×C4×C53H(5,𝔽2)11yescharacteristic
356C2×C4×C53H(5,𝔽2)11yescharacteristic
357C22⋊D53—48no—
358C22⋊D53—84no—
359C2×Dic53—22no—
360C2×Dic53—22no—
361C2×Dic53—41no—
362C2×Dic53—41no—
363C2×Dic53—41no—
364C2×Dic53—41no—
365D212—22no—
366D212—22no—
367D212—22no—
368D212—22no—
369D212—22no—
370D212—48no—
371D212—41no—
372D212—41no—
373D212C4×D414yes—
374C4×D53—48no—
375C4×D53—84no—
376Dic106—22no—
377Dic106—22no—
378Dic106—41no—
379Dic106—41no—
380#88322—22no—
381#88322—41no—
382#88322—41no—
383#88322—41no—
384#22427—531nomaximal, Sylow
385C22×C53—22no—
386C22×C53—22no—
387C22×C53—22no—
388C22×C53—22no—
389C22×C53—22no—
390C22×C53—22no—
391C22×C53—41no—
392C22×C53—41no—
393C22×C53—41no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53—41no—
397C22×C53—41no—
398C22×C53—41no—
399C22×C53C22×C22⋊C411yescharacteristic
400C22×C53D4211yescharacteristic
401C22×C53#54611yescharacteristic
402C22×C53#57511yescharacteristic
403C22×C53#57511yescharacteristic
404C22×C53#57611yescharacteristic
405C22×C53#57711yescharacteristic
406C2×D53—24no—
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—42no—
416C2×D53—816no—
417C2×D53—81no—
418C2×D53—81no—
419C2×D53—81no—
420C2×D53—81no—
421C4×C53—22no—
422C4×C53—22no—
423C4×C53—22no—
424C4×C53—22no—
425C4×C53—42no—
426C4×C53—81no—
427C4×C53—81no—
428C4×C53—81no—
429C4×C53C2×C4×D411yescharacteristic
430C4×C53#51811yescharacteristic
431C4×C53D4211yescharacteristic
432C4×C53#54611yescharacteristic
433Dic53—42no—
434Dic53—42no—
435C2×#546—531no—
436C2×#436—531no—
437C2×#417—531no—
438C2×#418—531no—
439#2352D5311yescharacteristic, complemented
440#1983—531no—
441#1958—531no—
442#1895—531no—
443#1894—531no—
444#1874—531no—
445#1873—531no—
446#1804—531no—
447#1788—531no—
448#1786—531no—
449C4×#102—531no—
450C2×C53—42no—
451C2×C53—42no—
452C2×C53D4×C22⋊C411yescharacteristic
453C2×C53#289611yescharacteristic
454C2×C53#289711yescharacteristic
455C2×C53#327311yescharacteristic
456C2×C53#327511yescharacteristic
457C2×C53#332211yescharacteristic
458C2×C53#332311yescharacteristic
459D53—44no—
460D53—82no—
461C22×#41—531no—
462C23×D4—531no—
463C22×M16—531no—
464C22×M16—531no—
465#546—538no—
466#546—1064no—
467C2×#124—531no—
468C2×#123—1061no—
469C2×C22⋊Q8—531no—
470C2×#121—531no—
471C2×#121—1061no—
472C2×#120—1061no—
473C2×C4×D4—531no—
474C2×C4×D4C2×D5311yescharacteristic
475C2×#117C2×D5311yescharacteristic
476C22×C4⋊C4C2×D5311yescharacteristic, complemented
477C22×C22⋊C4—1061no—
478#436—1064no—
479C2×C4⋊C8—531no—
480#418—1064no—
481#417—1064no—
482C2×#103—531no—
483C2×#103—531no—
484C2×#103—531no—
485C2×#103—531no—
486C2×#102—531no—
487C2×#102—531no—
488C2×#102—531no—
489C2×#102—531no—
490C2×#102—531no—
491C2×#102—531no—
492C2×#102—531no—
493C2×#102—531no—
494C2×C22⋊C8—531no—
495C2×C22⋊C8—531no—
496C2×C4×C8—531no—
497#388—21no—
498#387—21no—
499#386—21no—
500#382C2×D5311yescharacteristic, complemented
501#380C2×D5311yescharacteristic
502#380C2×D5311yescharacteristic, complemented
503C4×C4⋊C4C2×D5311yescharacteristic, complemented
504C4×C22⋊C4—21no—
505#340—531no—
506#340—531no—
507#340—531no—
508#340—531no—
509C53#2242711yescharacteristic, complemented, Sylow
510C25—1061no—
511C2×#41—534no—
512C2×#41—1062no—
513C2×#41—1062no—
514C2×#41—1062no—
515C2×#41—2121no—
516C2×#41—2121no—
517C22×Q8—531no—
518C22×D4—534no—
519C22×D4—531no—
520C22×D4—531no—
521C22×D4—1062no—
522C22×D4—1062no—
523C22×D4—1061no—
524C22×D4—1061no—
525C22×D4—1062no—
526C22×D4—1061no—
527C22×D4—2121no—
528C22×D4—2121no—
529C22×D4C22⋊D5311yescharacteristic
530C23×C4—21no—
531C23×C4—1061no—
532C23×C4—1061no—
533C23×C4C22×D5311yescharacteristic
534C23×C4C22×D5311yescharacteristic
535C2×M16—1062no—
536C2×M16—1062no—
537C2×M16—1062no—
538C2×M16—1062no—
539C2×M16—2121no—
540C2×M16—2121no—
541C22×C8—531no—
542C22×C8—531no—
543C22×C8—531no—
544C22×C8—531no—
545#124—534no—
546#124—1062no—
547#123—1068no—
548C22⋊Q8—534no—
549C22⋊Q8—1062no—
550#121—534no—
551#121—1062no—
552#121—1068no—
553#120—1068no—
554C4×D4—534no—
555C4×D4—1062no—
556C4×D4C4×D5314yes—
557C4×D4D21214yes—
558#117—22no—
559#117—41no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—531no—
564C2×C4⋊C4—1061no—
565C2×C4⋊C4C22⋊D5311yescharacteristic
566C2×C4⋊C4C22×D5311yescharacteristic
567C2×C4⋊C4C22×D5311yescharacteristic
568C2×C4⋊C4C22×D5311yescharacteristic
569C2×C4⋊C4C22×D5311yescharacteristic
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×C42C22×D5311yescharacteristic
584C4⋊C8—1062no—
585#103—1062no—
586#103—1062no—
587#103—2121no—
588#103—2121no—
589#102—534no—
590#102—1062no—
591#102—1062no—
592#102—1062no—
593#102—1062no—
594#102—1062no—
595#102—2121no—
596#102—2121no—
597C22⋊C8—1062no—
598C22⋊C8—1062no—
599C4×C8—1062no—
600#95—21no—
601#95—21no—
602#95—21no—
603#95—21no—
604#95—21no—
605C24—1061no—
606C24—1064no—
607C24—1061no—
608C24—4241no—
609C24—4241no—
610C24—2122no—
611C24—2122no—
612C24—2122no—
613C24—2122no—
614C24C2×C22⋊D5311yescharacteristic
615C24C2×C22⋊D5311yescharacteristic
616#41—1068no—
617#41—2124no—
618#41—2124no—
619#41—2124no—
620C2×Q8—532no—
621C2×Q8—1061no—
622C2×Q8—1061no—
623C2×Q8—1061no—
624C2×Q8—1061no—
625C2×Q8—1061no—
626C2×D4—41no—
627C2×D4—41no—
628C2×D4—532no—
629C2×D4—532no—
630C2×D4—532no—
631C2×D4—532no—
632C2×D4—1068no—
633C2×D4—1064no—
634C2×D4—1064no—
635C2×D4—1064no—
636C2×D4—1061no—
637C2×D4—1061no—
638C2×D4—1061no—
639C2×D4—1061no—
640C2×D4—1061no—
641C2×D4—1061no—
642C2×D4—1061no—
643C2×D4—1061no—
644C2×D4—4241no—
645C2×D4—4241no—
646C2×D4—2124no—
647C2×D4—2124no—
648C2×D4—2124no—
649C2×D4—2122no—
650C2×D4—2122no—
651C2×D4—2122no—
652C2×D4—2122no—
653C2×D4#1171992114yes—
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—21no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—81no—
669C22×C4—1061no—
670C22×C4—1061no—
671C22×C4—1064no—
672C22×C4—1064no—
673C22×C4—4241no—
674C22×C4—4241no—
675C22×C4—2122no—
676C22×C4—2122no—
677C22×C4C2×C4×D5312yes—
678C22×C4C2×C4×D5312yes—
679C22×C4C2×D21212yes—
680C22×C4C2×D21212yes—
681C22×C4C2×C22⋊D5311yescharacteristic
682C22×C4C2×C22⋊D5311yescharacteristic
683C22×C4C2×C22⋊D5311yescharacteristic
684C22×C4C2×C22⋊D5311yescharacteristic
685C22×C4C23×D5311yescharacteristic
686M16—2124no—
687M16—2124no—
688C2×C8—532no—
689C2×C8—1061no—
690C2×C8—1061no—
691C2×C8—1061no—
692C2×C8—1061no—
693C2×C8—1061no—
694C2×C8—1061no—
695C2×C8—1061no—
696C2×C8—1061no—
697C2×C8—1061no—
698C2×C8—1061no—
699C2×C8—1061no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—42no—
708C4⋊C4—532no—
709C4⋊C4—1064no—
710C4⋊C4—1061no—
711C4⋊C4#1171992114yes—
712C4⋊C4D4×D5312yes—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—81no—
716C22⋊C4—1064no—
717C22⋊C4—1064no—
718C22⋊C4—1064no—
719C22⋊C4—1064no—
720C22⋊C4—1064no—
721C22⋊C4#1171992114yes—
722C22⋊C4#1171992114yes—
723C42—42no—
724C42—81no—
725C42C2×C4×D5312yes—
726C42C2×D21212yes—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—1062no—
740C23—1062no—
741C23—1062no—
742C23—1062no—
743C23—4244no—
744C23—4244no—
745C23—4244no—
746C23—4244no—
747C23—4244no—
748C23—2128no—
749C23—2128no—
750C23—2121no—
751C23—2121no—
752C23—2121no—
753C23—2121no—
754C23—2121no—
755C23—2121no—
756C23—2121no—
757C23—2121no—
758C23—2121no—
759C23—2121no—
760C23C2×#1171992112yes—
761C23C2×#1171992112yes—
762C23C22×C22⋊D5311yescharacteristic
763Q8—1062no—
764Q8—1062no—
765Q8—2121no—
766Q8—2121no—
767D4—44no—
768D4—534no—
769D4—1062no—
770D4—1062no—
771D4—1062no—
772D4—1062no—
773D4—1062no—
774D4—4244no—
775D4—2128no—
776D4—2128no—
777D4—2121no—
778D4—2121no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
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—22no—
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—41no—
807C2×C4—84no—
808C2×C4—1062no—
809C2×C4—1062no—
810C2×C4—4244no—
811C2×C4—2128no—
812C2×C4—2121no—
813C2×C4—2121no—
814C2×C4—2121no—
815C2×C4—2121no—
816C2×C4C2×#1171992112yes—
817C2×C4C2×#1171992112yes—
818C2×C4C2×#1171992112yes—
819C2×C4C2×#1171992112yes—
820C2×C4C22×C4×D5311yescharacteristic
821C2×C4C2×D4×D5311yescharacteristic
822C2×C4C22×D21211yescharacteristic
823C2×C4#41×D5311yescharacteristic
824C2×C4#1313326211yescharacteristic
825C2×C4#1313326311yescharacteristic
826C8—1062no—
827C8—2121no—
828C8—2121no—
829C8—2121no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—1064no—
845C22—42416no—
846C22—4241no—
847C22—4241no—
848C22—4241no—
849C22—4241no—
850C22—2122no—
851C22—2122no—
852C22—2122no—
853C22—2122no—
854C22—2122no—
855C22—2122no—
856C22—2122no—
857C22—2122no—
858C22—2122no—
859C22C22×#1171992111yescharacteristic
860C22D4×C22⋊D5311yescharacteristic
861C22#1681126111yescharacteristic
862C22#1681142111yescharacteristic
863C22#1681142111yescharacteristic
864C22#1681142611yescharacteristic
865C22#1681143111yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—2122no—
875C4—2122no—
876C4C4×D4×D5311yescharacteristic
877C4#1681109511yescharacteristic
878C4D4×D21211yescharacteristic
879C4#1681126811yescharacteristic
880C2—42no—
881C2—42no—
882C2—4242no—
883C2—2124no—
884C2D4×#1171992111yescharacteristic
885C2#2028323211yescharacteristic
886C2#2028323811yescharacteristic
887C2#2028632211yescharacteristic
888C2#2028634711yescharacteristic
889C2#2028691011yescharacteristic
890C2#2028692511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2352C2
socleC23×C53C22×D4
prime radicalC2×#16811269C2
cosocleC22×C4×C53C24
hypercenter#2352D53
hypocenterC53#22427
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#16810701C2semidirect
3. C2×#16810622C2semidirect
4. C2×#16810627C2semidirect
5. #20275647C2semidirect
6. #20275524C2semidirect
7. #20275151C2semidirect
8. #20275146C2semidirect
9. #20275032C2semidirect
10. #20275027C2semidirect
11. #20274722C2semidirect
12. #20274653C2semidirect
13. #20274645C2semidirect
14. C4×#13133137C2semidirect
15. C53×#2352C2semidirect
19. C22×#11719917C22semidirect
21. #16811269C4semidirect
31. C2×C4⋊#88322C22semidirect
34. C2×#13133140C22semidirect
35. C2×#13133140C22semidirect
36. C2×#13133140C22semidirect
37. C2×#13133140C22semidirect
47. C2×C22⋊#88322C22semidirect
48. C2×C4×#88322C22semidirect
49. #16810385C22semidirect
50. #16810385C22semidirect
51. #16810385C22semidirect
52. #16810385C22semidirect
55. C22×C4⋊C4×C53C22semidirect
59. C53×#382C22semidirect
61. C53×#380C22semidirect
62. C4×C4⋊C4×C53C22semidirect
78. C22×D212C2×C4semidirect
96. #13133205C2×C4semidirect
99. #13133196C2×C4semidirect
105. C4×D212C2×C4semidirect
126. #13133137D4semidirect
439. #2352D53semidirect
476. C22×C4⋊C4C2×D53semidirect
500. #382C2×D53semidirect
502. #380C2×D53semidirect
503. C4×C4⋊C4C2×D53semidirect
509. C53#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#168112692
C2×#168107012
C2×#168106222
C2×#168106272
#202756472
#202755242
#202751512
#202751462
#202750322
#202750272
#202747222
#202746532
#202746452
C4×#131331372
C53×#23522
#2242753