Finite Group Databasebeta

← #27351613

Subgroups — #27351613

Order 13568.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288747C211yesmaximal, characteristic
2#20283750C211yesmaximal, characteristic, complemented
3#20273290C211yesmaximal, characteristic, complemented
4#20273282C211yesmaximal, characteristic, complemented
5#20273274C211yesmaximal, characteristic, complemented
6#20273269C211yesmaximal, characteristic, complemented
7#20273261C211yesmaximal, characteristic, complemented
8#20273256C211yesmaximal, characteristic, complemented
9#20273251C211yesmaximal, characteristic, complemented
10#20273243C211yesmaximal, characteristic, complemented
11#20273230C211yesmaximal, characteristic, complemented
12#20273217C211yesmaximal, characteristic, complemented
13#20273204C211yesmaximal, characteristic, complemented
14C2×#16810356C211yesmaximal, characteristic, complemented
15C53×#2318C211yesmaximal, characteristic, complemented
16#16811338C411yescharacteristic, complemented
17#16811330C411yescharacteristic, complemented
18#16811321—21no—
19#16811319C411yescharacteristic, complemented
20#16811319C411yescharacteristic, complemented
21#16811294C411yescharacteristic, complemented
22#16811269C411yescharacteristic, complemented
23#16811269C411yescharacteristic, complemented
24#16811263—21no—
25#16811263—21no—
26D4×D212C411yescharacteristic, complemented
27D4×C22⋊D53—21no—
28#16811224—21no—
29#16811206—21no—
30#16811206—21no—
31#16811173C2211yescharacteristic
32#16811157C2211yescharacteristic
33#16811134C2211yescharacteristic
34#16811134C2211yescharacteristic
35C2×#13133191C2211yescharacteristic
36C2×#13133191C2211yescharacteristic
37#16811095—21no—
38#16810701—21no—
39#16810695—21no—
40#16810695—21no—
41D4×#88322—21no—
42#16810680C2211yescharacteristic, complemented
43#16810676C2211yescharacteristic, complemented
44#16810587C2211yescharacteristic, complemented
45#16810587C2211yescharacteristic, complemented
46C2×C22⋊#88322C2211yescharacteristic, complemented
47C2×C22⋊#88322C2211yescharacteristic, complemented
48#16810359C2211yescharacteristic, complemented
49#16810359C2211yescharacteristic, complemented
50#16810359C2211yescharacteristic, complemented
51#16810359C2211yescharacteristic, complemented
52#16810356C2211yescharacteristic
53#16810356C2211yescharacteristic
54#16810356C2211yescharacteristic
55#16810356C2211yescharacteristic
56#16810356C2211yescharacteristic, complemented
57#16810356C2211yescharacteristic, complemented
58#16810356C2211yescharacteristic, complemented
59#16810356C2211yescharacteristic, complemented
60#16810356C2211yescharacteristic, complemented
61#16810356C2211yescharacteristic, complemented
62#16810356C2211yescharacteristic, complemented
63#16810356C2211yescharacteristic, complemented
64C2×C4×D4×C53C2211yescharacteristic
65C53×#388—21no—
66C53×#387—21no—
67C53×#386—21no—
68C53×#385—21no—
69C53×#383C2211yescharacteristic, complemented
70C53×#382C2211yescharacteristic, complemented
71C53×#381C2211yescharacteristic, complemented
72C53×#380C2211yescharacteristic, complemented
73C4×C22⋊C4×C53C2211yescharacteristic, complemented
74C2×#95×C53C2211yescharacteristic, complemented
75C2×#11719945—21no—
76C2×#11719945C2×C411yescharacteristic
77C2×#11719945C2×C411yescharacteristic, complemented
78C22×D212C2×C411yescharacteristic
79C22×D212C2×C411yescharacteristic, complemented
80C22×C22⋊D53—21no—
81C22×C22⋊D53—21no—
82C2×D4×D53—21no—
83C2×#11719917—21no—
84C2×#11719917—21no—
85C22×#88322—21no—
86C22×#88322—21no—
87#13133217C2×C411yescharacteristic, complemented
88#13133214C2×C411yescharacteristic, complemented
89#13133213—21no—
90#13133212—21no—
91#13133212—21no—
92#13133211—21no—
93#13133209C2×C411yescharacteristic, complemented
94#13133208—21no—
95#13133205—21no—
96#13133205C2×C411yescharacteristic, complemented
97#13133203—21no—
98#13133203—21no—
99#13133202—21no—
100#13133202—21no—
101#13133200—21no—
102#13133200—21no—
103#13133200—21no—
104#13133199—21no—
105#13133199—21no—
106#13133196C2×C411yescharacteristic
107#13133196C2×C411yescharacteristic, complemented
108#13133196C2311yescharacteristic
109#13133194—21no—
110#13133194—21no—
111#13133192—21no—
112#13133191—21no—
113#13133191—21no—
114#13133191—21no—
115#13133191—21no—
116#13133191—21no—
117#13133191C2×C411yescharacteristic
118#13133191C2×C411yescharacteristic
119#13133191C2×C411yescharacteristic
120#13133191C2×C411yescharacteristic, complemented
121#13133191C2×C411yescharacteristic, complemented
122#13133191C2×C411yescharacteristic, complemented
123#13133191C2311yescharacteristic
124#13133191C2311yescharacteristic
125#13133191C2311yescharacteristic
126#13133190—21no—
127#13133190—21no—
128#13133190—21no—
129#13133190—21no—
130#13133189—21no—
131#13133189—21no—
132#13133188—21no—
133#13133187—21no—
134#13133187—21no—
135#13133186—21no—
136#13133186—21no—
137#13133185—21no—
138#13133185—21no—
139C4×Dic106C2×C411yescharacteristic, complemented
140C4×D212—21no—
141C4×D212C2×C411yescharacteristic, complemented
142C4×D212C2×C411yescharacteristic, complemented
143C4×D212C2×C411yescharacteristic, complemented
144D4×Dic53—21no—
145#13133179—21no—
146C4×C22⋊D53—21no—
147C4×C22⋊D53—21no—
148C4×C22⋊D53—21no—
149C4×C22⋊D53—21no—
150C4×C22⋊D53—21no—
151#13133177—21no—
152#13133177—21no—
153#13133176C2×C411yescharacteristic
154#13133176C2×C411yescharacteristic, complemented
155#13133175—21no—
156#13133174—21no—
157C2×C4⋊Dic53C2×C411yescharacteristic
158C2×C4⋊Dic53C2×C411yescharacteristic, complemented
159C2×#11719921—21no—
160C2×#11719921—21no—
161C22⋊C4×D53—21no—
162C22⋊C4×D53—21no—
163C4⋊#88322—21no—
164C4⋊#88322—21no—
165C22⋊#88322—21no—
166C22⋊#88322—21no—
167C22⋊#88322—21no—
168C22⋊#88322—21no—
169C22⋊#88322C2311yescharacteristic
170C22⋊#88322C2311yescharacteristic
171C22⋊#88322C2311yescharacteristic
172C22⋊#88322C2311yescharacteristic
173#13133128—21no—
174C4×#88322—21no—
175C22×D4×C53D411yescharacteristic
176C23×C4×C53—21no—
177C23×C4×C53C2311yescharacteristic
178C23×C4×C53C2311yescharacteristic
179C4×D4×C53C2×C411yescharacteristic
180C4×D4×C53C2×C411yescharacteristic
181C4×D4×C53C2×C411yescharacteristic
182C4×D4×C53C2×C411yescharacteristic
183C4×D4×C53D411yescharacteristic
184C4×D4×C53D411yescharacteristic
185C4×D4×C53D411yescharacteristic
186C4×D4×C53D411yescharacteristic
187C2×C4⋊C4×C53—21no—
188C2×C4⋊C4×C53—21no—
189C2×C4⋊C4×C53D411yescharacteristic
190C2×C22⋊C4×C53—21no—
191C2×C22⋊C4×C53—21no—
192C2×C22⋊C4×C53—21no—
193C2×C22⋊C4×C53D411yescharacteristic
194C2×C22⋊C4×C53D411yescharacteristic
195C2×C42×C53—21no—
196C2×C42×C53C2311yescharacteristic
197#95×C53—21no—
198#95×C53—21no—
199#95×C53—21no—
200#95×C53—21no—
201#95×C53—21no—
202#95×C53C2311yescharacteristic
203#95×C53C2311yescharacteristic
204#95×C53C2311yescharacteristic
205#95×C53C2311yescharacteristic
206C24×C53C2×D411yescharacteristic
207C24×C53C2×D411yescharacteristic
208C23×D53—21no—
209C23×D53—21no—
210C2×D4×C53—42no—
211C2×D4×C53C22⋊C411yescharacteristic
212C2×D4×C53C22⋊C411yescharacteristic
213C2×D4×C53C22⋊C411yescharacteristic
214C2×D4×C53C22⋊C411yescharacteristic
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—42no—
220C22×C4×C53—81no—
221C22×C4×C53—81no—
222C22×C4×C53—81no—
223C22×C4×C53—81no—
224C22×C4×C53C22×C411yescharacteristic
225C22×C4×C53C22×C411yescharacteristic
226C22×C4×C53C22×C411yescharacteristic
227C22×C4×C53C22×C411yescharacteristic
228C22×C4×C53C2×D411yescharacteristic
229C22×C4×C53C2×D411yescharacteristic
230C22×C4×C53C2×D411yescharacteristic
231C22×C4×C53C2×D411yescharacteristic
232C22×C4×C53C2×D411yescharacteristic
233C22×C4×C53C2×D411yescharacteristic
234C22×C4×C53C2×D411yescharacteristic
235C22×C4×C53C2×D411yescharacteristic
236C22×C4×C53C2411yescharacteristic
237C2×C22⋊D53—21no—
238C2×C22⋊D53—21no—
239C2×C22⋊D53—21no—
240C2×C22⋊D53—21no—
241C2×C22⋊D53—21no—
242C2×C22⋊D53—21no—
243C2×C22⋊D53—21no—
244C2×C22⋊D53—21no—
245C2×C22⋊D53—21no—
246C2×C22⋊D53—21no—
247C2×C22⋊D53—21no—
248C2×C22⋊D53—81no—
249C2×C22⋊D53—81no—
250C2×C22⋊D53—81no—
251C2×C22⋊D53—81no—
252C22×Dic53—21no—
253C22×Dic53—21no—
254D4×D53—44no—
255#11719945—81no—
256#11719945—81no—
257#11719945—81no—
258#11719945—81no—
259C2×D212—21no—
260C2×D212—21no—
261C2×D212—21no—
262C2×D212—21no—
263C2×D212—81no—
264C2×D212—81no—
265C2×D212C22×C411yescharacteristic
266C2×D212C22×C411yescharacteristic
267C2×D212C22×C411yescharacteristic
268C2×C4×D53—21no—
269C2×C4×D53—21no—
270C2×C4×D53—21no—
271C2×C4×D53—21no—
272C2×C4×D53—21no—
273C2×Dic106—21no—
274C2×Dic106C22×C411yescharacteristic
275C4⋊C4×C53—81no—
276C4⋊C4×C53—81no—
277C4⋊C4×C53C22⋊C411yescharacteristic
278C4⋊C4×C53C22⋊C411yescharacteristic
279C4⋊C4×C53C22⋊C411yescharacteristic
280C4⋊C4×C53C22⋊C411yescharacteristic
281C22⋊C4×C53—42no—
282C22⋊C4×C53—81no—
283C22⋊C4×C53—81no—
284C22⋊C4×C53C22⋊C411yescharacteristic
285C22⋊C4×C53C22⋊C411yescharacteristic
286C22⋊C4×C53C22⋊C411yescharacteristic
287C22⋊C4×C53C22⋊C411yescharacteristic
288C22⋊C4×C53C22⋊C411yescharacteristic
289C22⋊C4×C53C22⋊C411yescharacteristic
290C22⋊C4×C53C22⋊C411yescharacteristic
291C22⋊C4×C53C22⋊C411yescharacteristic
292C42×C53—81no—
293C42×C53C22×C411yescharacteristic
294C42×C53C22×C411yescharacteristic
295C42×C53C2×D411yescharacteristic
296C42×C53C2×D411yescharacteristic
297C22⋊Dic53—21no—
298C22⋊Dic53—21no—
299C22⋊Dic53—21no—
300C22⋊Dic53—21no—
301C22⋊Dic53—21no—
302#11719921—21no—
303#11719921—21no—
304#11719921—21no—
305#11719921—21no—
306#11719921—21no—
307#11719921—21no—
308#11719921—21no—
309#11719921—21no—
310#11719921—21no—
311#11719921—21no—
312#11719921—21no—
313#11719921—21no—
314#11719921—21no—
315#11719921—21no—
316C4⋊Dic53—21no—
317C4⋊Dic53—21no—
318C4⋊Dic53—21no—
319C4⋊Dic53C22×C411yescharacteristic
320C4⋊Dic53C22×C411yescharacteristic
321C4⋊Dic53C22×C411yescharacteristic
322C4⋊Dic53C22×C411yescharacteristic
323#11719919—21no—
324#11719919—21no—
325#11719919—21no—
326#11719919—21no—
327#11719919—21no—
328#11719919—21no—
329C4×Dic53—21no—
330C4×Dic53—21no—
331C4×Dic53—21no—
332#11719917—81no—
333#11719917—81no—
334C2×#88322—21no—
335C2×#88322—21no—
336C2×#88322—21no—
337C2×#88322—21no—
338C2×#88322—81no—
339C2×#88322—81no—
340C23×C53—21no—
341C23×C53—21no—
342C23×C53—22no—
343C23×C53—21no—
344C23×C53—21no—
345C23×C53—41no—
346C23×C53—41no—
347C23×C53—41no—
348C23×C53C2×C22⋊C411yescharacteristic
349C23×C53C2×C22⋊C411yescharacteristic
350C23×C53C2×C22⋊C411yescharacteristic
351C23×C53C2×C22⋊C411yescharacteristic
352C23×C53C22×D411yescharacteristic
353C22×D53—21no—
354C22×D53—21no—
355C22×D53—21no—
356C22×D53—42no—
357C22×D53—42no—
358C22×D53—81no—
359C22×D53—81no—
360C22×D53—81no—
361C22×D53—81no—
362D4×C53—22no—
363D4×C53—22no—
364D4×C53—41no—
365D4×C53—41no—
366C2×C4×C53—21no—
367C2×C4×C53—21no—
368C2×C4×C53—41no—
369C2×C4×C53—41no—
370C2×C4×C53—41no—
371C2×C4×C53—41no—
372C2×C4×C53—41no—
373C2×C4×C53—41no—
374C2×C4×C53—41no—
375C2×C4×C53—41no—
376C2×C4×C53—41no—
377C2×C4×C53—41no—
378C2×C4×C53—41no—
379C2×C4×C53—41no—
380C2×C4×C53—41no—
381C2×C4×C53—41no—
382C2×C4×C53—41no—
383C2×C4×C53—41no—
384C2×C4×C53—41no—
385C2×C4×C53—41no—
386C2×C4×C53—41no—
387C2×C4×C53—41no—
388C2×C4×C53—41no—
389C2×C4×C53—41no—
390C2×C4×C53—41no—
391C2×C4×C53—41no—
392C2×C4×C53—84no—
393C2×C4×C53C2×C22⋊C411yescharacteristic
394C2×C4×C53C2×C22⋊C411yescharacteristic
395C2×C4×C53C2×C22⋊C411yescharacteristic
396C2×C4×C53C2×C22⋊C411yescharacteristic
397C2×C4×C53C2×C22⋊C411yescharacteristic
398C2×C4×C53C2×C22⋊C411yescharacteristic
399C2×C4×C53C2×C22⋊C411yescharacteristic
400C2×C4×C53C2×C22⋊C411yescharacteristic
401C2×C4×C53C23×C411yescharacteristic
402C2×C4×C53C22×D411yescharacteristic
403C22⋊D53—42no—
404C22⋊D53—41no—
405C22⋊D53—41no—
406C22⋊D53—41no—
407C22⋊D53—41no—
408C22⋊D53—41no—
409C22⋊D53—41no—
410C22⋊D53—42no—
411C22⋊D53—81no—
412C22⋊D53—81no—
413C22⋊D53—81no—
414C22⋊D53—81no—
415C22⋊D53—81no—
416C22⋊D53—81no—
417C2×Dic53—21no—
418C2×Dic53—21no—
419C2×Dic53—21no—
420C2×Dic53—21no—
421C2×Dic53—21no—
422C2×Dic53—81no—
423C2×Dic53—81no—
424D212—41no—
425D212—41no—
426D212—41no—
427D212—42no—
428D212—81no—
429D212—81no—
430D212—81no—
431C4×D53—42no—
432C4×D53—81no—
433C4×D53—81no—
434C4×D53—81no—
435C4×D53—81no—
436Dic106—41no—
437Dic106—81no—
438#88322—41no—
439#88322—41no—
440#88322—41no—
441#88322—41no—
442#17597—531nomaximal, Sylow
443C22×C53—21no—
444C22×C53—21no—
445C22×C53—21no—
446C22×C53—21no—
447C22×C53—21no—
448C22×C53—21no—
449C22×C53—21no—
450C22×C53—21no—
451C22×C53—21no—
452C22×C53—21no—
453C22×C53—21no—
454C22×C53—21no—
455C22×C53—21no—
456C22×C53—42no—
457C22×C53—42no—
458C22×C53—81no—
459C22×C53—81no—
460C22×C53#42112yes—
461C22×C53C22×C22⋊C411yescharacteristic
462C22×C53#57611yescharacteristic
463C22×C53#57711yescharacteristic
464C2×D53—41no—
465C2×D53—41no—
466C2×D53—41no—
467C2×D53—41no—
468C2×D53—41no—
469C2×D53—41no—
470C2×D53—41no—
471C2×D53—41no—
472C2×D53—41no—
473C2×D53—162no—
474C2×D53—162no—
475C4×C53—21no—
476C4×C53—21no—
477C4×C53—21no—
478C4×C53—21no—
479C4×C53—21no—
480C4×C53—21no—
481C4×C53—21no—
482C4×C53—21no—
483C4×C53—21no—
484C4×C53—21no—
485C4×C53—81no—
486C4×C53—81no—
487C4×C53—81no—
488C4×C53—81no—
489Dic53—41no—
490Dic53—41no—
491Dic53—41no—
492Dic53—41no—
493Dic53—41no—
494#3519—531no—
495#2974—531no—
496#2318D5311yescharacteristic, complemented
497#1521—531no—
498#1519—531no—
499#1517—531no—
500#1516—531no—
501#1514—531no—
502#1513—531no—
503#1512—531no—
504#1510—531no—
505#1507—531no—
506#1504—531no—
507#1501—531no—
508C2×#327—531no—
509C2×C53—21no—
510C2×C53—21no—
511C2×C53—22no—
512C2×C53—41no—
513C2×C53—41no—
514C2×C53—41no—
515C2×C53#288311yescharacteristic
516C2×C53#289711yescharacteristic
517C2×C53C2×#42111yescharacteristic
518D53—81no—
519D53—81no—
520D53—81no—
521#555—531no—
522#554—531no—
523#553—531no—
524#553—531no—
525#553—1061no—
526#550—531no—
527#546—531no—
528#546—531no—
529#546—1061no—
530#546—1061no—
531D42—531no—
532D42—1061no—
533#540—1061no—
534#538—1061no—
535#538—1061no—
536#532—531no—
537#529—531no—
538#525—531no—
539#525—531no—
540C2×#121—531no—
541C2×#121—531no—
542#518—1061no—
543C2×C4×D4C2×D5311yescharacteristic
544#436—1061no—
545#435—1061no—
546#435—1061no—
547C8×D4—1061no—
548#432—531no—
549#431—531no—
550#407—531no—
551#407—531no—
552C2×C22⋊C8—531no—
553C2×C22⋊C8—531no—
554#388—21no—
555#387—21no—
556#386—21no—
557#385—21no—
558#383C2×D5311yescharacteristic, complemented
559#382C2×D5311yescharacteristic, complemented
560#381C2×D5311yescharacteristic, complemented
561#380C2×D5311yescharacteristic, complemented
562C4×C22⋊C4C2×D5311yescharacteristic, complemented
563C2×#95C2×D5311yescharacteristic, complemented
564#328—531no—
565#328—531no—
566#328—531no—
567#328—531no—
568#327—531no—
569#327—531no—
570#327—531no—
571#327—531no—
572#327—531no—
573#327—531no—
574#327—531no—
575#327—531no—
576#327—531no—
577#327—531no—
578#327—531no—
579#327—531no—
580C53#1759711yescharacteristic, complemented, Sylow
581C2×#41—531no—
582C2×#41—531no—
583C2×#41—1061no—
584C22×D4—531no—
585C22×D4—531no—
586C22×D4—1061no—
587C22×D4—1061no—
588C22×D4—1061no—
589C22×D4C22⋊D5311yescharacteristic
590C23×C4—21no—
591C23×C4C22×D5311yescharacteristic
592C23×C4C22×D5311yescharacteristic
593C2×M16—1061no—
594C2×M16—1061no—
595C22×C8—1061no—
596C22×C8—1061no—
597C4⋊Q8—531no—
598#127—531no—
599#127—1061no—
600#126—1061no—
601#126—1061no—
602#126—1061no—
603#125—531no—
604#125—1061no—
605#124—531no—
606#124—1061no—
607#124—1061no—
608#124—1061no—
609#123—1061no—
610#123—1061no—
611#123—1061no—
612#123—1061no—
613#123—1061no—
614#123—1061no—
615#123—1061no—
616C22⋊Q8—531no—
617C22⋊Q8—531no—
618C22⋊Q8—531no—
619C22⋊Q8—1061no—
620C22⋊Q8—1061no—
621#121—531no—
622#121—531no—
623#121—531no—
624#121—531no—
625#121—531no—
626#121—531no—
627#121—531no—
628#121—531no—
629#121—531no—
630#121—1061no—
631#121—1061no—
632#121—1061no—
633#121—1061no—
634#121—1061no—
635#121—1061no—
636#121—1061no—
637#121—1061no—
638#121—1061no—
639#121—1061no—
640#121—1061no—
641#121—1061no—
642#121—1061no—
643#120—1061no—
644#120—1061no—
645#120—1061no—
646#120—1061no—
647#120—1061no—
648#120—1061no—
649C4×Q8—531no—
650C4×D4—531no—
651C4×D4—531no—
652C4×D4—531no—
653C4×D4—1061no—
654C4×D4—1061no—
655C4×D4—1061no—
656C4×D4—1061no—
657C4×D4—1061no—
658C4×D4—1061no—
659C4×D4—1061no—
660C4×D4—1061no—
661C4×D4—1061no—
662C4×D4—1061no—
663C4×D4C4×D5311yescharacteristic
664C4×D4C4×D5311yescharacteristic
665C4×D4C4×D5311yescharacteristic
666C4×D4C4×D5311yescharacteristic
667C4×D4D21211yescharacteristic
668C4×D4D21211yescharacteristic
669C4×D4D21211yescharacteristic
670C4×D4D21211yescharacteristic
671#117—531no—
672#117—531no—
673#117—1061no—
674#117—1061no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—531no—
678C2×C4⋊C4—531no—
679C2×C4⋊C4C22⋊D5311yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—1061no—
684C2×C22⋊C4—1061no—
685C2×C22⋊C4—1061no—
686C2×C22⋊C4—1061no—
687C2×C22⋊C4C22⋊D5311yescharacteristic
688C2×C22⋊C4C22⋊D5311yescharacteristic
689C2×C42—21no—
690C2×C42C22×D5311yescharacteristic
691C4⋊C8—1061no—
692C4⋊C8—1061no—
693C22⋊C8—531no—
694C22⋊C8—531no—
695C22⋊C8—531no—
696C22⋊C8—531no—
697C22⋊C8—1061no—
698C22⋊C8—1061no—
699C22⋊C8—1061no—
700C22⋊C8—1061no—
701#97—1061no—
702C4×C8—1061no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95C22×D5311yescharacteristic
709#95C22×D5311yescharacteristic
710#95C22×D5311yescharacteristic
711#95C22×D5311yescharacteristic
712C24—1061no—
713C24—1061no—
714C24C2×C22⋊D5311yescharacteristic
715C24C2×C22⋊D5311yescharacteristic
716#41—4241no—
717#41—4241no—
718#41—4241no—
719#41—4241no—
720C2×Q8—531no—
721C2×Q8—1061no—
722C2×D4—42no—
723C2×D4—531no—
724C2×D4—531no—
725C2×D4—531no—
726C2×D4—1061no—
727C2×D4—1061no—
728C2×D4—1061no—
729C2×D4—1061no—
730C2×D4—1061no—
731C2×D4—1061no—
732C2×D4—1061no—
733C2×D4—1061no—
734C2×D4—1061no—
735C2×D4—1061no—
736C2×D4—1061no—
737C2×D4—1061no—
738C2×D4—1061no—
739C2×D4—1061no—
740C2×D4—1061no—
741C2×D4—4241no—
742C2×D4—4241no—
743C2×D4—4241no—
744C2×D4—4241no—
745C2×D4—4241no—
746C2×D4—4241no—
747C2×D4—2124no—
748C2×D4#1171992111yescharacteristic
749C2×D4#1171992111yescharacteristic
750C2×D4#1171992111yescharacteristic
751C2×D4#1171992111yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—42no—
757C22×C4—81no—
758C22×C4—81no—
759C22×C4—81no—
760C22×C4—81no—
761C22×C4—1061no—
762C22×C4—1061no—
763C22×C4—1061no—
764C22×C4—1061no—
765C22×C4—1061no—
766C22×C4—1061no—
767C22×C4—1061no—
768C22×C4C2×C4×D5311yescharacteristic
769C22×C4C2×C4×D5311yescharacteristic
770C22×C4C2×C4×D5311yescharacteristic
771C22×C4C2×C4×D5311yescharacteristic
772C22×C4C2×D21211yescharacteristic
773C22×C4C2×D21211yescharacteristic
774C22×C4C2×D21211yescharacteristic
775C22×C4C2×D21211yescharacteristic
776C22×C4C2×C22⋊D5311yescharacteristic
777C22×C4C2×C22⋊D5311yescharacteristic
778C22×C4C2×C22⋊D5311yescharacteristic
779C22×C4C2×C22⋊D5311yescharacteristic
780C22×C4C23×D5311yescharacteristic
781M16—4241no—
782M16—4241no—
783C2×C8—1061no—
784C2×C8—1061no—
785C2×C8—1061no—
786C2×C8—1061no—
787C2×C8—4241no—
788C2×C8—4241no—
789C4⋊C4—81no—
790C4⋊C4—81no—
791C4⋊C4—531no—
792C4⋊C4—531no—
793C4⋊C4—531no—
794C4⋊C4—531no—
795C4⋊C4—1061no—
796C4⋊C4—1061no—
797C4⋊C4—1061no—
798C4⋊C4—1061no—
799C4⋊C4—1061no—
800C4⋊C4—1061no—
801C4⋊C4—1061no—
802C4⋊C4—1061no—
803C4⋊C4—1061no—
804C4⋊C4#1171992111yescharacteristic
805C4⋊C4#1171992111yescharacteristic
806C4⋊C4#1171992111yescharacteristic
807C4⋊C4#1171992111yescharacteristic
808C22⋊C4—42no—
809C22⋊C4—81no—
810C22⋊C4—81no—
811C22⋊C4—1061no—
812C22⋊C4—1061no—
813C22⋊C4—1061no—
814C22⋊C4—1061no—
815C22⋊C4—1061no—
816C22⋊C4—1061no—
817C22⋊C4—1061no—
818C22⋊C4—1061no—
819C22⋊C4—1061no—
820C22⋊C4—1061no—
821C22⋊C4—1061no—
822C22⋊C4—1061no—
823C22⋊C4—1061no—
824C22⋊C4—1061no—
825C22⋊C4—1061no—
826C22⋊C4—1061no—
827C22⋊C4—1061no—
828C22⋊C4—1061no—
829C22⋊C4—1061no—
830C22⋊C4#1171992111yescharacteristic
831C22⋊C4#1171992111yescharacteristic
832C22⋊C4#1171992111yescharacteristic
833C22⋊C4#1171992111yescharacteristic
834C22⋊C4#1171992111yescharacteristic
835C22⋊C4#1171992111yescharacteristic
836C22⋊C4#1171992111yescharacteristic
837C22⋊C4#1171992111yescharacteristic
838C42—81no—
839C42—1061no—
840C42—1061no—
841C42—1061no—
842C42C2×C4×D5311yescharacteristic
843C42C2×C4×D5311yescharacteristic
844C42C2×D21211yescharacteristic
845C42C2×D21211yescharacteristic
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—1061no—
855C23—1061no—
856C23—1061no—
857C23—4241no—
858C23—4241no—
859C23—4241no—
860C23—4241no—
861C23—2122no—
862C23—2122no—
863C23C2×#1171992111yescharacteristic
864C23C2×#1171992111yescharacteristic
865C23C2×#1171992111yescharacteristic
866C23C2×#1171992111yescharacteristic
867C23C22×C22⋊D5311yescharacteristic
868Q8—4241no—
869Q8—2121no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—4241no—
875D4—4241no—
876D4—4241no—
877D4—4241no—
878D4—4241no—
879D4—4241no—
880D4—4241no—
881D4—4241no—
882D4—4241no—
883D4—2121no—
884D4—2121no—
885D4—2121no—
886D4—2122no—
887D4—2122no—
888D4—2122no—
889D4—2121no—
890D4—2121no—
891D4—2121no—
892D4—2121no—
893D4—2121no—
894D4—2121no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—84no—
922C2×C4—1061no—
923C2×C4—1061no—
924C2×C4—1061no—
925C2×C4—1061no—
926C2×C4—1061no—
927C2×C4—4241no—
928C2×C4—4241no—
929C2×C4—4241no—
930C2×C4—4241no—
931C2×C4—4241no—
932C2×C4—4241no—
933C2×C4—2122no—
934C2×C4C2×#1171992111yescharacteristic
935C2×C4C2×#1171992111yescharacteristic
936C2×C4C2×#1171992111yescharacteristic
937C2×C4C2×#1171992111yescharacteristic
938C2×C4C2×#1171992111yescharacteristic
939C2×C4C2×#1171992111yescharacteristic
940C2×C4C2×#1171992111yescharacteristic
941C2×C4C2×#1171992111yescharacteristic
942C2×C4C22×C4×D5311yescharacteristic
943C2×C4C22×D21211yescharacteristic
944C8—2121no—
945C8—2121no—
946C8—2121no—
947C8—2121no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—81no—
964C22—81no—
965C22—8482no—
966C22—8482no—
967C22—2121no—
968C22—2121no—
969C22—2121no—
970C22—2121no—
971C22—2121no—
972C22—2121no—
973C22—2121no—
974C22—2121no—
975C22—2121no—
976C22#1681064112yes—
977C22C22×#1171992111yescharacteristic
978C22#1681142611yescharacteristic
979C22#1681143111yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—81no—
991C4—81no—
992C4—81no—
993C4—81no—
994C4—2121no—
995C4—2121no—
996C4—2121no—
997C4—2121no—
998C4—2121no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—4241no—
1006C2—4241no—
1007C2—4241no—
1008C2#2028317511yescharacteristic
1009C2#2028323811yescharacteristic
1010C2C2×#1681064111yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2318C2
socleC22×C53C22×C22⋊C4
prime radical#20288747C2
cosocleC22×C4×C53C24
hypercenter#2318D53
hypocenterC53#17597
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #20283750C2semidirect
3. #20273290C2semidirect
4. #20273282C2semidirect
5. #20273274C2semidirect
6. #20273269C2semidirect
7. #20273261C2semidirect
8. #20273256C2semidirect
9. #20273251C2semidirect
10. #20273243C2semidirect
11. #20273230C2semidirect
12. #20273217C2semidirect
13. #20273204C2semidirect
14. C2×#16810356C2semidirect
15. C53×#2318C2semidirect
16. #16811338C4semidirect
17. #16811330C4semidirect
19. #16811319C4semidirect
20. #16811319C4semidirect
21. #16811294C4semidirect
22. #16811269C4semidirect
23. #16811269C4semidirect
26. D4×D212C4semidirect
42. #16810680C22semidirect
43. #16810676C22semidirect
44. #16810587C22semidirect
45. #16810587C22semidirect
46. C2×C22⋊#88322C22semidirect
47. C2×C22⋊#88322C22semidirect
48. #16810359C22semidirect
49. #16810359C22semidirect
50. #16810359C22semidirect
51. #16810359C22semidirect
56. #16810356C22semidirect
57. #16810356C22semidirect
58. #16810356C22semidirect
59. #16810356C22semidirect
60. #16810356C22semidirect
61. #16810356C22semidirect
62. #16810356C22semidirect
63. #16810356C22semidirect
69. C53×#383C22semidirect
70. C53×#382C22semidirect
71. C53×#381C22semidirect
72. C53×#380C22semidirect
73. C4×C22⋊C4×C53C22semidirect
74. C2×#95×C53C22semidirect
77. C2×#11719945C2×C4semidirect
79. C22×D212C2×C4semidirect
87. #13133217C2×C4semidirect
88. #13133214C2×C4semidirect
93. #13133209C2×C4semidirect
96. #13133205C2×C4semidirect
107. #13133196C2×C4semidirect
120. #13133191C2×C4semidirect
121. #13133191C2×C4semidirect
122. #13133191C2×C4semidirect
139. C4×Dic106C2×C4semidirect
141. C4×D212C2×C4semidirect
142. C4×D212C2×C4semidirect
143. C4×D212C2×C4semidirect
154. #13133176C2×C4semidirect
158. C2×C4⋊Dic53C2×C4semidirect
496. #2318D53semidirect
558. #383C2×D53semidirect
559. #382C2×D53semidirect
560. #381C2×D53semidirect
561. #380C2×D53semidirect
562. C4×C22⋊C4C2×D53semidirect
563. C2×#95C2×D53semidirect
580. C53#17597semidirect

Maximal subgroups

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

subgroupindex
#202887472
#202837502
#202732902
#202732822
#202732742
#202732692
#202732612
#202732562
#202732512
#202732432
#202732302
#202732172
#202732042
C2×#168103562
C53×#23182
#1759753