Finite Group Databasebeta

← #27351621

Subgroups — #27351621

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#20277348C211yesmaximal, characteristic, complemented
3#20273293C211yesmaximal, characteristic, complemented
4#20273284C211yesmaximal, characteristic, complemented
5#20273276C211yesmaximal, characteristic, complemented
6#20273272C211yesmaximal, characteristic, complemented
7#20273263C211yesmaximal, characteristic, complemented
8#20273259C211yesmaximal, characteristic, complemented
9#20273254C211yesmaximal, characteristic, complemented
10#20273245C211yesmaximal, characteristic, complemented
11#20273232C211yesmaximal, characteristic, complemented
12#20273220C211yesmaximal, characteristic, complemented
13#20273207C211yesmaximal, characteristic, complemented
14C2×#16810358C211yesmaximal, characteristic, complemented
15C53×#2974C211yesmaximal, 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#16810516—21no—
39#16810509—21no—
40#16810503—21no—
41#16810498—21no—
42#16810491C2211yescharacteristic, complemented
43#16810489C2211yescharacteristic, complemented
44#16810486C2211yescharacteristic, complemented
45#16810483C2211yescharacteristic, complemented
46C4×C22⋊Dic53C2211yescharacteristic, complemented
47C2×#13133124C2211yescharacteristic, complemented
48#16810361C2211yescharacteristic, complemented
49#16810361C2211yescharacteristic, complemented
50#16810361C2211yescharacteristic, complemented
51#16810361C2211yescharacteristic, complemented
52#16810358C2211yescharacteristic
53#16810358C2211yescharacteristic
54#16810358C2211yescharacteristic
55#16810358C2211yescharacteristic
56#16810358C2211yescharacteristic, complemented
57#16810358C2211yescharacteristic, complemented
58#16810358C2211yescharacteristic, complemented
59#16810358C2211yescharacteristic, complemented
60#16810358C2211yescharacteristic, complemented
61#16810358C2211yescharacteristic, complemented
62#16810358C2211yescharacteristic, complemented
63#16810358C2211yescharacteristic, complemented
64C2×C4×D4×C53C2211yescharacteristic
65C53×#436—21no—
66C53×#435—21no—
67C53×#435—21no—
68C8×D4×C53—21no—
69C53×#432C2211yescharacteristic, complemented
70C53×#431C2211yescharacteristic, complemented
71C53×#407C2211yescharacteristic, complemented
72C53×#407C2211yescharacteristic, complemented
73C2×C22⋊C8×C53C2211yescharacteristic, complemented
74C2×C22⋊C8×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—
83C23×Dic53—21no—
84#13133217C2×C411yescharacteristic, complemented
85#13133214C2×C411yescharacteristic, complemented
86#13133213—21no—
87#13133212—21no—
88#13133212—21no—
89#13133211—21no—
90#13133209C2×C411yescharacteristic, complemented
91#13133208—21no—
92#13133205—21no—
93#13133205C2×C411yescharacteristic, complemented
94#13133203—21no—
95#13133203—21no—
96#13133202—21no—
97#13133202—21no—
98#13133200—21no—
99#13133200—21no—
100#13133200—21no—
101#13133199—21no—
102#13133199—21no—
103#13133196C2×C411yescharacteristic
104#13133196C2×C411yescharacteristic, complemented
105#13133196C2311yescharacteristic
106#13133194—21no—
107#13133194—21no—
108#13133192—21no—
109#13133191—21no—
110#13133191—21no—
111#13133191—21no—
112#13133191—21no—
113#13133191—21no—
114#13133191C2×C411yescharacteristic
115#13133191C2×C411yescharacteristic
116#13133191C2×C411yescharacteristic
117#13133191C2×C411yescharacteristic, complemented
118#13133191C2×C411yescharacteristic, complemented
119#13133191C2×C411yescharacteristic, complemented
120#13133191C2311yescharacteristic
121#13133191C2311yescharacteristic
122#13133191C2311yescharacteristic
123#13133190—21no—
124#13133190—21no—
125#13133190—21no—
126#13133190—21no—
127#13133189—21no—
128#13133189—21no—
129#13133188—21no—
130#13133187—21no—
131#13133187—21no—
132#13133186—21no—
133#13133186—21no—
134#13133185—21no—
135#13133185—21no—
136C4×Dic106C2×C411yescharacteristic, complemented
137C4×D212—21no—
138C4×D212C2×C411yescharacteristic, complemented
139C4×D212C2×C411yescharacteristic, complemented
140C4×D212C2×C411yescharacteristic, complemented
141D4×Dic53—21no—
142#13133179—21no—
143C4×C22⋊D53—21no—
144C4×C22⋊D53—21no—
145C4×C22⋊D53—21no—
146C4×C22⋊D53—21no—
147C4×C22⋊D53—21no—
148#13133177—21no—
149#13133177—21no—
150#13133176C2×C411yescharacteristic
151#13133176C2×C411yescharacteristic, complemented
152#13133175—21no—
153#13133174—21no—
154C2×C4⋊Dic53—21no—
155C2×C4⋊Dic53—21no—
156C2×C4⋊Dic53C2×C411yescharacteristic
157C2×C4⋊Dic53C2×C411yescharacteristic, complemented
158C2×C22⋊Dic53—21no—
159C2×C22⋊Dic53—21no—
160C2×C22⋊Dic53—21no—
161C2×#11719921—21no—
162C2×#11719921—21no—
163C22⋊C4×D53—21no—
164C22⋊C4×D53—21no—
165C2×C4×Dic53—21no—
166#13133124—21no—
167#13133124—21no—
168#13133124—21no—
169#13133124—21no—
170#13133124—21no—
171#13133124C2311yescharacteristic
172#13133124C2311yescharacteristic
173#13133124C2311yescharacteristic
174#13133124C2311yescharacteristic
175C22×D4×C53D411yescharacteristic
176C23×C4×C53C2311yescharacteristic
177C23×C4×C53C2311yescharacteristic
178C2×M16×C53—21no—
179C2×M16×C53—21no—
180C22×C8×C53—21no—
181C22×C8×C53—21no—
182C4×D4×C53C2×C411yescharacteristic
183C4×D4×C53C2×C411yescharacteristic
184C4×D4×C53C2×C411yescharacteristic
185C4×D4×C53C2×C411yescharacteristic
186C4×D4×C53D411yescharacteristic
187C4×D4×C53D411yescharacteristic
188C4×D4×C53D411yescharacteristic
189C4×D4×C53D411yescharacteristic
190C2×C4⋊C4×C53D411yescharacteristic
191C2×C22⋊C4×C53D411yescharacteristic
192C2×C22⋊C4×C53D411yescharacteristic
193C2×C42×C53C2311yescharacteristic
194C4⋊C8×C53—21no—
195C4⋊C8×C53—21no—
196C22⋊C8×C53—21no—
197C22⋊C8×C53—21no—
198C22⋊C8×C53—21no—
199C22⋊C8×C53—21no—
200C22⋊C8×C53C2311yescharacteristic
201C22⋊C8×C53C2311yescharacteristic
202C22⋊C8×C53C2311yescharacteristic
203C22⋊C8×C53C2311yescharacteristic
204#97×C53—21no—
205C4×C8×C53—21no—
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—81no—
216C22×C4×C53—81no—
217C22×C4×C53C22×C411yescharacteristic
218C22×C4×C53C22×C411yescharacteristic
219C22×C4×C53C22×C411yescharacteristic
220C22×C4×C53C22×C411yescharacteristic
221C22×C4×C53C2×D411yescharacteristic
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53C2×D411yescharacteristic
224C22×C4×C53C2×D411yescharacteristic
225C22×C4×C53C2×D411yescharacteristic
226C22×C4×C53C2×D411yescharacteristic
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53C2×D411yescharacteristic
229C22×C4×C53C2411yescharacteristic
230C2×C22⋊D53—21no—
231C2×C22⋊D53—21no—
232C2×C22⋊D53—21no—
233C2×C22⋊D53—21no—
234C2×C22⋊D53—21no—
235C2×C22⋊D53—21no—
236C2×C22⋊D53—21no—
237C2×C22⋊D53—21no—
238C2×C22⋊D53—21no—
239C2×C22⋊D53—21no—
240C2×C22⋊D53—21no—
241C2×C22⋊D53—81no—
242C2×C22⋊D53—81no—
243C2×C22⋊D53—81no—
244C2×C22⋊D53—81no—
245C22×Dic53—21no—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—21no—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—42no—
252C22×Dic53—81no—
253C22×Dic53—81no—
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
275M16×C53—81no—
276M16×C53—81no—
277C2×C8×C53—21no—
278C2×C8×C53—21no—
279C2×C8×C53—21no—
280C2×C8×C53—21no—
281C2×C8×C53—81no—
282C2×C8×C53—81no—
283C4⋊C4×C53C22⋊C411yescharacteristic
284C4⋊C4×C53C22⋊C411yescharacteristic
285C4⋊C4×C53C22⋊C411yescharacteristic
286C4⋊C4×C53C22⋊C411yescharacteristic
287C22⋊C4×C53C22⋊C411yescharacteristic
288C22⋊C4×C53C22⋊C411yescharacteristic
289C22⋊C4×C53C22⋊C411yescharacteristic
290C22⋊C4×C53C22⋊C411yescharacteristic
291C22⋊C4×C53C22⋊C411yescharacteristic
292C22⋊C4×C53C22⋊C411yescharacteristic
293C22⋊C4×C53C22⋊C411yescharacteristic
294C22⋊C4×C53C22⋊C411yescharacteristic
295C42×C53C22×C411yescharacteristic
296C42×C53C22×C411yescharacteristic
297C42×C53C2×D411yescharacteristic
298C42×C53C2×D411yescharacteristic
299C22⋊Dic53—21no—
300C22⋊Dic53—21no—
301C22⋊Dic53—21no—
302C22⋊Dic53—21no—
303C22⋊Dic53—21no—
304C22⋊Dic53—42no—
305C22⋊Dic53—81no—
306C22⋊Dic53—81no—
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—
316#11719921—21no—
317#11719921—21no—
318#11719921—21no—
319#11719921—21no—
320#11719921—21no—
321C4⋊Dic53—21no—
322C4⋊Dic53—21no—
323C4⋊Dic53—21no—
324C4⋊Dic53—81no—
325C4⋊Dic53—81no—
326C4⋊Dic53C22×C411yescharacteristic
327C4⋊Dic53C22×C411yescharacteristic
328C4⋊Dic53C22×C411yescharacteristic
329C4⋊Dic53C22×C411yescharacteristic
330#11719919—21no—
331#11719919—21no—
332#11719919—21no—
333#11719919—21no—
334#11719919—21no—
335#11719919—21no—
336C4×Dic53—21no—
337C4×Dic53—21no—
338C4×Dic53—21no—
339C4×Dic53—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×C53C2×C22⋊C411yescharacteristic
381C2×C4×C53C2×C22⋊C411yescharacteristic
382C2×C4×C53C2×C22⋊C411yescharacteristic
383C2×C4×C53C2×C22⋊C411yescharacteristic
384C2×C4×C53C2×C22⋊C411yescharacteristic
385C2×C4×C53C2×C22⋊C411yescharacteristic
386C2×C4×C53C2×C22⋊C411yescharacteristic
387C2×C4×C53C2×C22⋊C411yescharacteristic
388C2×C4×C53C23×C411yescharacteristic
389C2×C4×C53C22×D411yescharacteristic
390C22⋊D53—42no—
391C22⋊D53—41no—
392C22⋊D53—41no—
393C22⋊D53—41no—
394C22⋊D53—41no—
395C22⋊D53—41no—
396C22⋊D53—41no—
397C22⋊D53—42no—
398C22⋊D53—81no—
399C22⋊D53—81no—
400C22⋊D53—81no—
401C22⋊D53—81no—
402C22⋊D53—81no—
403C22⋊D53—81no—
404C2×Dic53—21no—
405C2×Dic53—21no—
406C2×Dic53—21no—
407C2×Dic53—21no—
408C2×Dic53—21no—
409C2×Dic53—41no—
410C2×Dic53—41no—
411C2×Dic53—41no—
412C2×Dic53—41no—
413C2×Dic53—41no—
414C2×Dic53—41no—
415C2×Dic53—41no—
416C2×Dic53—41no—
417C2×Dic53—41no—
418C2×Dic53—41no—
419C2×Dic53—41no—
420C2×Dic53—41no—
421C2×Dic53—81no—
422C2×Dic53—81no—
423C2×Dic53—84no—
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—
438C8×C53—41no—
439C8×C53—41no—
440C8×C53—41no—
441C8×C53—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—
485Dic53—41no—
486Dic53—41no—
487Dic53—41no—
488Dic53—41no—
489Dic53—41no—
490Dic53—81no—
491Dic53—81no—
492Dic53—81no—
493Dic53—81no—
494#3519—531no—
495#2974D5311yescharacteristic, complemented
496#2318—531no—
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—21no—
545#435—21no—
546#435—21no—
547C8×D4—21no—
548#432C2×D5311yescharacteristic, complemented
549#431C2×D5311yescharacteristic, complemented
550#407C2×D5311yescharacteristic, complemented
551#407C2×D5311yescharacteristic, complemented
552C2×C22⋊C8C2×D5311yescharacteristic, complemented
553C2×C22⋊C8C2×D5311yescharacteristic, complemented
554#388—1061no—
555#387—1061no—
556#386—1061no—
557#385—1061no—
558#383—531no—
559#382—531no—
560#381—531no—
561#380—531no—
562C4×C22⋊C4—531no—
563C2×#95—531no—
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×D4D21211yescharacteristic
590C23×C4—1061no—
591C23×C4C22×D5311yescharacteristic
592C23×C4C22×D5311yescharacteristic
593C2×M16—21no—
594C2×M16—21no—
595C22×C8—21no—
596C22×C8—21no—
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×D4C22⋊D5311yescharacteristic
668C4×D4C22⋊D5311yescharacteristic
669C4×D4C22⋊D5311yescharacteristic
670C4×D4C22⋊D5311yescharacteristic
671#117—531no—
672#117—531no—
673#117—1061no—
674#117—1061no—
675C2×C4⋊C4—531no—
676C2×C4⋊C4—531no—
677C2×C4⋊C4—1061no—
678C2×C4⋊C4—1061no—
679C2×C4⋊C4D21211yescharacteristic
680C2×C22⋊C4—1061no—
681C2×C22⋊C4—1061no—
682C2×C22⋊C4—1061no—
683C2×C22⋊C4—1061no—
684C2×C22⋊C4—1061no—
685C2×C22⋊C4—1061no—
686C2×C22⋊C4—1061no—
687C2×C22⋊C4D21211yescharacteristic
688C2×C22⋊C4D21211yescharacteristic
689C2×C42—1061no—
690C2×C42C22×D5311yescharacteristic
691C4⋊C8—21no—
692C4⋊C8—21no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696C22⋊C8—21no—
697C22⋊C8C22×D5311yescharacteristic
698C22⋊C8C22×D5311yescharacteristic
699C22⋊C8C22×D5311yescharacteristic
700C22⋊C8C22×D5311yescharacteristic
701#97—21no—
702C4×C8—21no—
703#95—531no—
704#95—531no—
705#95—531no—
706#95—531no—
707#95—1061no—
708#95—1061no—
709#95—1061no—
710#95—1061no—
711#95—1061no—
712C24—1061no—
713C24—1061no—
714C24C2×D21211yescharacteristic
715C24C2×D21211yescharacteristic
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—81no—
753C22×C4—81no—
754C22×C4—1061no—
755C22×C4—1061no—
756C22×C4—1061no—
757C22×C4—1061no—
758C22×C4—1061no—
759C22×C4—1061no—
760C22×C4—1061no—
761C22×C4—1061no—
762C22×C4—1061no—
763C22×C4—1061no—
764C22×C4—1061no—
765C22×C4—4241no—
766C22×C4—4241no—
767C22×C4—2122no—
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—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C2×C8—81no—
789C4⋊C4—531no—
790C4⋊C4—531no—
791C4⋊C4—531no—
792C4⋊C4—531no—
793C4⋊C4—1061no—
794C4⋊C4—1061no—
795C4⋊C4—1061no—
796C4⋊C4—1061no—
797C4⋊C4—1061no—
798C4⋊C4—1061no—
799C4⋊C4—1061no—
800C4⋊C4—1061no—
801C4⋊C4—1061no—
802C4⋊C4—4241no—
803C4⋊C4—4241no—
804C4⋊C4#1171992111yescharacteristic
805C4⋊C4#1171992111yescharacteristic
806C4⋊C4#1171992111yescharacteristic
807C4⋊C4#1171992111yescharacteristic
808C22⋊C4—1061no—
809C22⋊C4—1061no—
810C22⋊C4—1061no—
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—4241no—
828C22⋊C4—4241no—
829C22⋊C4—2122no—
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—1061no—
839C42—1061no—
840C42—1061no—
841C42—4241no—
842C42C2×C4×D5311yescharacteristic
843C42C2×C4×D5311yescharacteristic
844C42C2×C22⋊D5311yescharacteristic
845C42C2×C22⋊D5311yescharacteristic
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×D21211yescharacteristic
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—1061no—
910C2×C4—1061no—
911C2×C4—1061no—
912C2×C4—1061no—
913C2×C4—1061no—
914C2×C4—4241no—
915C2×C4—4241no—
916C2×C4—4241no—
917C2×C4—4241no—
918C2×C4—4244no—
919C2×C4—4241no—
920C2×C4—4241no—
921C2×C4—2122no—
922C2×C4—2121no—
923C2×C4—2121no—
924C2×C4—2121no—
925C2×C4—2121no—
926C2×C4—2121no—
927C2×C4—2121no—
928C2×C4—2121no—
929C2×C4—2121no—
930C2×C4—2121no—
931C2×C4—2121no—
932C2×C4—2121no—
933C2×C4—2121no—
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×C22⋊D5311yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
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#1681063912yes—
977C22C22×#1171992111yescharacteristic
978C22#1681142811yescharacteristic
979C22#1681143511yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—4241no—
991C4—4241no—
992C4—4241no—
993C4—4241no—
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#2028324211yescharacteristic
1010C2C2×#1681063911yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2974C2
socleC22×C53C22×C22⋊C4
prime radical#20288747C2
cosocleC22×C4×C53C24
hypercenter#2974D53
hypocenterC53#17597
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #20277348C2semidirect
3. #20273293C2semidirect
4. #20273284C2semidirect
5. #20273276C2semidirect
6. #20273272C2semidirect
7. #20273263C2semidirect
8. #20273259C2semidirect
9. #20273254C2semidirect
10. #20273245C2semidirect
11. #20273232C2semidirect
12. #20273220C2semidirect
13. #20273207C2semidirect
14. C2×#16810358C2semidirect
15. C53×#2974C2semidirect
16. #16811338C4semidirect
17. #16811330C4semidirect
19. #16811319C4semidirect
20. #16811319C4semidirect
21. #16811294C4semidirect
22. #16811269C4semidirect
23. #16811269C4semidirect
26. D4×D212C4semidirect
42. #16810491C22semidirect
43. #16810489C22semidirect
44. #16810486C22semidirect
45. #16810483C22semidirect
46. C4×C22⋊Dic53C22semidirect
47. C2×#13133124C22semidirect
48. #16810361C22semidirect
49. #16810361C22semidirect
50. #16810361C22semidirect
51. #16810361C22semidirect
56. #16810358C22semidirect
57. #16810358C22semidirect
58. #16810358C22semidirect
59. #16810358C22semidirect
60. #16810358C22semidirect
61. #16810358C22semidirect
62. #16810358C22semidirect
63. #16810358C22semidirect
69. C53×#432C22semidirect
70. C53×#431C22semidirect
71. C53×#407C22semidirect
72. C53×#407C22semidirect
73. C2×C22⋊C8×C53C22semidirect
74. C2×C22⋊C8×C53C22semidirect
77. C2×#11719945C2×C4semidirect
79. C22×D212C2×C4semidirect
84. #13133217C2×C4semidirect
85. #13133214C2×C4semidirect
90. #13133209C2×C4semidirect
93. #13133205C2×C4semidirect
104. #13133196C2×C4semidirect
117. #13133191C2×C4semidirect
118. #13133191C2×C4semidirect
119. #13133191C2×C4semidirect
136. C4×Dic106C2×C4semidirect
138. C4×D212C2×C4semidirect
139. C4×D212C2×C4semidirect
140. C4×D212C2×C4semidirect
151. #13133176C2×C4semidirect
157. C2×C4⋊Dic53C2×C4semidirect
495. #2974D53semidirect
548. #432C2×D53semidirect
549. #431C2×D53semidirect
550. #407C2×D53semidirect
551. #407C2×D53semidirect
552. C2×C22⋊C8C2×D53semidirect
553. C2×C22⋊C8C2×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
#202773482
#202732932
#202732842
#202732762
#202732722
#202732632
#202732592
#202732542
#202732452
#202732322
#202732202
#202732072
C2×#168103582
C53×#29742
#1759753