Finite Group Databasebeta

← #27351624

Subgroups — #27351624

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#20288742C211yesmaximal, characteristic
2#20283752C211yesmaximal, characteristic, complemented
3#20277346C211yesmaximal, characteristic, complemented
4#20273290C211yesmaximal, characteristic, complemented
5#20273281C211yesmaximal, characteristic, complemented
6#20273275C211yesmaximal, characteristic, complemented
7#20273268C211yesmaximal, characteristic, complemented
8#20273255C211yesmaximal, characteristic, complemented
9#20273254C211yesmaximal, characteristic, complemented
10#20273242C211yesmaximal, characteristic, complemented
11#20273229C211yesmaximal, characteristic, complemented
12#20273216C211yesmaximal, characteristic, complemented
13#20273203C211yesmaximal, characteristic, complemented
14#327×D53C211yesmaximal, characteristic, complemented
15C53×#1514C211yesmaximal, characteristic, complemented
16#16811339C411yescharacteristic, complemented
17#16811334C411yescharacteristic, complemented
18#16811325—21no—
19#16811323C411yescharacteristic, complemented
20#16811323C411yescharacteristic, complemented
21#16811293C411yescharacteristic, complemented
22#16811268C411yescharacteristic, complemented
23#16811268C411yescharacteristic, complemented
24#16811261—21no—
25#16811261—21no—
26#16811258C411yescharacteristic, complemented
27#16811257—21no—
28#16811224—21no—
29#16811207—21no—
30#16811207—21no—
31#16811157C2211yescharacteristic
32#16811133C2211yescharacteristic
33#16811133C2211yescharacteristic
34#121×D53C2211yescharacteristic
35#121×D53C2211yescharacteristic
36#16811095—21no—
37C2×C4×D212C2211yescharacteristic
38#16810700—21no—
39#16810696—21no—
40#16810696—21no—
41#16810688—21no—
42#16810676C2211yescharacteristic, complemented
43#16810585C2211yescharacteristic, complemented
44#16810585C2211yescharacteristic, complemented
45C22⋊C8×D53C2211yescharacteristic, complemented
46C22⋊C8×D53C2211yescharacteristic, complemented
47#16810515—21no—
48#16810506—21no—
49#16810501—21no—
50#16810497—21no—
51#16810489C2211yescharacteristic, complemented
52#16810485C2211yescharacteristic, complemented
53#16810482C2211yescharacteristic, complemented
54#16810470C2211yescharacteristic, complemented
55#95×D53C2211yescharacteristic, complemented
56#16810361C2211yescharacteristic, complemented
57#16810361C2211yescharacteristic, complemented
58#16810359C2211yescharacteristic, complemented
59#16810359C2211yescharacteristic, complemented
60#16810358C2211yescharacteristic
61#16810358C2211yescharacteristic
62#16810357C2211yescharacteristic, complemented
63#16810357C2211yescharacteristic, complemented
64#16810357C2211yescharacteristic, complemented
65#16810357C2211yescharacteristic, complemented
66#16810356C2211yescharacteristic
67#16810356C2211yescharacteristic
68C53×#532C2211yescharacteristic
69C53×#432C2211yescharacteristic, complemented
70C53×#383C2211yescharacteristic, complemented
71C53×#327C2211yescharacteristic, complemented
72C53×#327C2211yescharacteristic, complemented
73C53×#327C2211yescharacteristic, complemented
74C53×#327C2211yescharacteristic, complemented
75C2×#11719947C2×C411yescharacteristic
76C2×#11719947C2×C411yescharacteristic, complemented
77C22×D212D411yescharacteristic
78C2×D4×D53—21no—
79C2×D4×D53—21no—
80C2×D4×D53—21no—
81C2×D4×D53C2×C411yescharacteristic
82C2×D4×D53C2×C411yescharacteristic, complemented
83C22×C4×D53—21no—
84C22×C4×D53C2311yescharacteristic
85C22×C4×D53C2311yescharacteristic
86C2×#11719912—21no—
87C2×#11719912—21no—
88C2×C8×D53—21no—
89C2×C8×D53—21no—
90#13133213—21no—
91#13133211—21no—
92#13133210—21no—
93#13133210—21no—
94#13133209C2×C411yescharacteristic, complemented
95#13133208—21no—
96#13133206—21no—
97#13133206—21no—
98#13133205C2×C411yescharacteristic, complemented
99#13133201—21no—
100#13133201—21no—
101#13133200—21no—
102#13133200—21no—
103#13133200—21no—
104#13133199—21no—
105#13133199—21no—
106#13133197C2×C411yescharacteristic
107#13133197C2×C411yescharacteristic, complemented
108#13133196C2311yescharacteristic
109#13133193—21no—
110#13133193—21no—
111#13133192—21no—
112#13133192C2×C411yescharacteristic
113#13133192C2×C411yescharacteristic, complemented
114#13133191—21no—
115#13133191—21no—
116#13133191C2311yescharacteristic
117#13133190—21no—
118#13133190—21no—
119#13133190—21no—
120#13133190—21no—
121#13133189—21no—
122#13133189—21no—
123#13133189—21no—
124#13133189—21no—
125#13133188—21no—
126#13133188C2×C411yescharacteristic
127#13133188C2×C411yescharacteristic
128#13133188C2×C411yescharacteristic, complemented
129#13133188C2×C411yescharacteristic, complemented
130#13133187—21no—
131#13133187—21no—
132#13133185—21no—
133#13133185—21no—
134#13133185—21no—
135#13133185—21no—
136C4×Dic106C2×C411yescharacteristic, complemented
137C4×D212C2×C411yescharacteristic
138C4×D212C2×C411yescharacteristic
139C4×D212C2×C411yescharacteristic
140C4×D212C2×C411yescharacteristic
141C4×D212C2×C411yescharacteristic, complemented
142C4×D212D411yescharacteristic
143C4×D212D411yescharacteristic
144C4×D212D411yescharacteristic
145C4×D212D411yescharacteristic
146D4×Dic53—21no—
147D4×Dic53—21no—
148D4×Dic53—21no—
149#13133179—21no—
150C4×C22⋊D53—21no—
151C4×C22⋊D53—21no—
152C4×C22⋊D53—21no—
153#13133177—21no—
154#13133177—21no—
155#13133175—21no—
156#13133175C2×C411yescharacteristic
157#13133175C2×C411yescharacteristic, complemented
158#13133174—21no—
159C2×C4⋊Dic53—21no—
160C2×C4⋊Dic53D411yescharacteristic
161C2×#11719919—21no—
162C4⋊C4×D53C2×C411yescharacteristic
163C4⋊C4×D53C2×C411yescharacteristic, complemented
164C2×#11719921—21no—
165C2×#11719921—21no—
166C2×#11719921—21no—
167C2×#11719921—21no—
168C2×#11719921—21no—
169C2×#11719921D411yescharacteristic
170C2×#11719921D411yescharacteristic
171C22⋊C4×D53—21no—
172C22⋊C4×D53—21no—
173C2×C4×Dic53—21no—
174C4⋊#88322—21no—
175C22⋊#88322C2311yescharacteristic
176C22⋊#88322C2311yescharacteristic
177#13133129—21no—
178#13133129—21no—
179#13133129—21no—
180#13133129—21no—
181C4×#88322—21no—
182#13133124—21no—
183#13133124—21no—
184#13133124—21no—
185#13133124C2311yescharacteristic
186#13133124C2311yescharacteristic
187C2×#41×C53—21no—
188C4⋊Q8×C53C2×C411yescharacteristic, complemented
189#127×C53C2×C411yescharacteristic, complemented
190#124×C53—21no—
191#121×C53—21no—
192#121×C53C2311yescharacteristic
193#121×C53C2311yescharacteristic
194C4×D4×C53—21no—
195C4×D4×C53C2×C411yescharacteristic, complemented
196C4×D4×C53C2×C411yescharacteristic, complemented
197C2×C42×C53C2311yescharacteristic
198C4⋊C8×C53—21no—
199C22⋊C8×C53C2311yescharacteristic
200C22⋊C8×C53C2311yescharacteristic
201#97×C53—21no—
202#95×C53—21no—
203#95×C53—21no—
204#95×C53C2311yescharacteristic
205#95×C53C2311yescharacteristic
206C23×D53—21no—
207C23×D53—21no—
208C23×D53C2×D411yescharacteristic
209C23×D53C2×D411yescharacteristic
210#41×C53—81no—
211#41×C53—81no—
212C2×Q8×C53—21no—
213C2×D4×C53—21no—
214C2×D4×C53—21no—
215C2×D4×C53—21no—
216C2×D4×C53—21no—
217C2×D4×C53C22×C411yescharacteristic
218C2×D4×C53C22×C411yescharacteristic
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53C2×D411yescharacteristic
224C22×C4×C53C2×D411yescharacteristic
225C22×C4×C53C2411yescharacteristic
226C2×C22⋊D53—21no—
227C2×C22⋊D53—21no—
228C2×C22⋊D53—21no—
229C2×C22⋊D53—21no—
230C2×C22⋊D53—21no—
231C2×C22⋊D53—21no—
232C2×C22⋊D53—21no—
233C2×C22⋊D53—21no—
234C2×C22⋊D53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53C2×D411yescharacteristic
240C22×Dic53C2×D411yescharacteristic
241#11719947—81no—
242#11719947—81no—
243D4×D53—44no—
244D4×D53—81no—
245D4×D53—81no—
246D4×D53—81no—
247D4×D53—81no—
248D4×D53—81no—
249D4×D53—81no—
250C2×D212—21no—
251C2×D212—21no—
252C2×D212—42no—
253C2×D212C22⋊C411yescharacteristic
254C2×D212C22⋊C411yescharacteristic
255C2×D212C22⋊C411yescharacteristic
256C2×D212C22⋊C411yescharacteristic
257C2×D212C22×C411yescharacteristic
258C2×C4×D53—21no—
259C2×C4×D53—21no—
260C2×C4×D53—21no—
261C2×C4×D53—42no—
262C2×C4×D53—81no—
263C2×C4×D53—81no—
264C2×C4×D53—81no—
265C2×C4×D53—81no—
266C2×C4×D53C22×C411yescharacteristic
267C2×C4×D53C22×C411yescharacteristic
268C2×C4×D53C22×C411yescharacteristic
269C2×C4×D53C22×C411yescharacteristic
270C2×C4×D53C2×D411yescharacteristic
271C2×C4×D53C2×D411yescharacteristic
272C2×C4×D53C2×D411yescharacteristic
273C2×C4×D53C2×D411yescharacteristic
274C2×Dic106C22×C411yescharacteristic
275C2×C8×C53—21no—
276C2×C8×C53—21no—
277C4⋊C4×C53—21no—
278C4⋊C4×C53C22×C411yescharacteristic
279C4⋊C4×C53C22×C411yescharacteristic
280C22⋊C4×C53—21no—
281C22⋊C4×C53—21no—
282C22⋊C4×C53—21no—
283C22⋊C4×C53—21no—
284C42×C53C22×C411yescharacteristic
285C42×C53C22×C411yescharacteristic
286C42×C53C2×D411yescharacteristic
287C42×C53C2×D411yescharacteristic
288C22⋊Dic53—21no—
289C22⋊Dic53—21no—
290C22⋊Dic53—21no—
291C22⋊Dic53—21no—
292C22⋊Dic53—21no—
293#11719921—21no—
294#11719921—21no—
295#11719921—21no—
296#11719921—21no—
297#11719921—21no—
298#11719921—21no—
299#11719921—21no—
300#11719921—21no—
301#11719921—21no—
302#11719921—21no—
303#11719921—42no—
304#11719921—81no—
305#11719921—81no—
306#11719921C22⋊C411yescharacteristic
307#11719921C22⋊C411yescharacteristic
308#11719921C22⋊C411yescharacteristic
309#11719921C22⋊C411yescharacteristic
310#11719921C22⋊C411yescharacteristic
311#11719921C22⋊C411yescharacteristic
312#11719921C22⋊C411yescharacteristic
313#11719921C22⋊C411yescharacteristic
314C4⋊Dic53—21no—
315C4⋊Dic53—21no—
316C4⋊Dic53—81no—
317C4⋊Dic53C22⋊C411yescharacteristic
318C4⋊Dic53C22⋊C411yescharacteristic
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—
329#11719919—81no—
330C4×Dic53—21no—
331C4×Dic53—21no—
332C4×Dic53—21no—
333C4×Dic53—81no—
334C2×#88322—21no—
335C2×#88322—21no—
336#11719912—81no—
337#11719912—81no—
338C8×D53—81no—
339C8×D53—81no—
340C23×C53—21no—
341C23×C53—21no—
342C23×C53C22×D411yescharacteristic
343C22×D53—21no—
344C22×D53—21no—
345C22×D53—21no—
346C22×D53—21no—
347C22×D53—22no—
348C22×D53—21no—
349C22×D53—41no—
350C22×D53—41no—
351C22×D53—41no—
352C22×D53—42no—
353C22×D53—42no—
354C22×D53—81no—
355C22×D53—81no—
356C22×D53—81no—
357C22×D53—81no—
358C22×D53C2×C22⋊C411yescharacteristic
359C22×D53C2×C22⋊C411yescharacteristic
360C22×D53C2×C22⋊C411yescharacteristic
361C22×D53C2×C22⋊C411yescharacteristic
362Q8×C53—81no—
363D4×C53—41no—
364D4×C53—41no—
365D4×C53—42no—
366D4×C53—41no—
367D4×C53—41no—
368D4×C53—41no—
369D4×C53—41no—
370D4×C53—81no—
371C2×C4×C53—21no—
372C2×C4×C53—21no—
373C2×C4×C53—21no—
374C2×C4×C53—21no—
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—81no—
384C2×C4×C53—81no—
385C2×C4×C53C2×C22⋊C411yescharacteristic
386C2×C4×C53C2×C22⋊C411yescharacteristic
387C2×C4×C53C2×C22⋊C411yescharacteristic
388C2×C4×C53C2×C22⋊C411yescharacteristic
389C2×C4×C53C23×C411yescharacteristic
390C2×C4×C53C22×D411yescharacteristic
391C22⋊D53—42no—
392C22⋊D53—41no—
393C22⋊D53—41no—
394C22⋊D53—42no—
395C22⋊D53—81no—
396C22⋊D53—81no—
397C22⋊D53—81no—
398C22⋊D53—81no—
399C22⋊D53—81no—
400C22⋊D53—81no—
401C2×Dic53—21no—
402C2×Dic53—21no—
403C2×Dic53—21no—
404C2×Dic53—41no—
405C2×Dic53—41no—
406C2×Dic53—41no—
407C2×Dic53—41no—
408C2×Dic53—41no—
409C2×Dic53—41no—
410C2×Dic53—41no—
411C2×Dic53—41no—
412C2×Dic53—81no—
413C2×Dic53—81no—
414C2×Dic53C2×C22⋊C411yescharacteristic
415C2×Dic53C2×C22⋊C411yescharacteristic
416C2×Dic53C2×C22⋊C411yescharacteristic
417C2×Dic53C2×C22⋊C411yescharacteristic
418D212—22no—
419D212—22no—
420D212—41no—
421D212—41no—
422D212—41no—
423D212—81no—
424D212—81no—
425C4×D53—41no—
426C4×D53—41no—
427C4×D53—41no—
428C4×D53—41no—
429C4×D53—41no—
430C4×D53—41no—
431C4×D53—41no—
432C4×D53—41no—
433C4×D53—42no—
434C4×D53—81no—
435C4×D53—81no—
436C4×D53—84no—
437Dic106—41no—
438C8×C53—41no—
439C8×C53—41no—
440#88322—41no—
441#88322—41no—
442#17597—531nomaximal, Sylow
443C22×C53—21no—
444C22×C53—21no—
445C22×C53—41no—
446C22×C53—41no—
447C22×C53—41no—
448C22×C53—41no—
449C22×C53—41no—
450C22×C53—41no—
451C22×C53C22×C22⋊C411yescharacteristic
452C22×C53#57611yescharacteristic
453C22×C53#57711yescharacteristic
454C2×D53—21no—
455C2×D53—21no—
456C2×D53—21no—
457C2×D53—21no—
458C2×D53—21no—
459C2×D53—21no—
460C2×D53—21no—
461C2×D53—21no—
462C2×D53—21no—
463C2×D53—21no—
464C2×D53—21no—
465C2×D53—42no—
466C2×D53—42no—
467C2×D53—41no—
468C2×D53—41no—
469C2×D53—41no—
470C2×D53—81no—
471C2×D53—81no—
472C2×D53—162no—
473C2×D53—162no—
474C2×D53#42112yes—
475C4×C53—21no—
476C4×C53—21no—
477C4×C53—21no—
478C4×C53—21no—
479C4×C53—21no—
480C4×C53—21no—
481C4×C53—41no—
482C4×C53—41no—
483C4×C53—81no—
484C4×C53—81no—
485Dic53—21no—
486Dic53—21no—
487Dic53—21no—
488Dic53—21no—
489Dic53—41no—
490Dic53—41no—
491Dic53—41no—
492Dic53—81no—
493Dic53—81no—
494#3519—531no—
495#2974—531no—
496#2318—531no—
497#1521—531no—
498#1519—531no—
499#1517—531no—
500#1516—531no—
501#1514D5311yescharacteristic, complemented
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—81no—
512C2×C53—81no—
513C2×C53#288311yescharacteristic
514C2×C53#289711yescharacteristic
515C2×C53C2×#42111yescharacteristic
516D53—22no—
517D53—41no—
518D53—41no—
519D53—41no—
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#532C2×D5311yescharacteristic
537#529—531no—
538#525—531no—
539#525—531no—
540C2×#121—531no—
541C2×#121—531no—
542#518—1061no—
543C2×C4×D4—531no—
544#436—1061no—
545#435—1061no—
546#435—1061no—
547C8×D4—1061no—
548#432C2×D5311yescharacteristic, complemented
549#431—531no—
550#407—531no—
551#407—531no—
552C2×C22⋊C8—531no—
553C2×C22⋊C8—531no—
554#388—1061no—
555#387—1061no—
556#386—1061no—
557#385—1061no—
558#383C2×D5311yescharacteristic, complemented
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#327C2×D5311yescharacteristic, complemented
577#327C2×D5311yescharacteristic, complemented
578#327C2×D5311yescharacteristic, complemented
579#327C2×D5311yescharacteristic, complemented
580C53#1759711yescharacteristic, complemented, Sylow
581C2×#41—21no—
582C2×#41—531no—
583C2×#41—531no—
584C22×D4—531no—
585C22×D4—531no—
586C22×D4—531no—
587C22×D4—1061no—
588C22×D4—1061no—
589C22×D4—1061no—
590C23×C4—531no—
591C23×C4—531no—
592C23×C4—1061no—
593C2×M16—1061no—
594C2×M16—1061no—
595C22×C8—1061no—
596C22×C8—1061no—
597C4⋊Q8C4×D5311yescharacteristic, complemented
598#127—1061no—
599#127C4×D5311yescharacteristic, complemented
600#126—1061no—
601#126—1061no—
602#126—1061no—
603#125—531no—
604#125—1061no—
605#124—21no—
606#124—531no—
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—21no—
622#121—531no—
623#121—531no—
624#121—531no—
625#121—531no—
626#121—531no—
627#121—531no—
628#121—531no—
629#121—1061no—
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#121C22×D5311yescharacteristic
642#121C22×D5311yescharacteristic
643#120—1061no—
644#120—1061no—
645#120—1061no—
646#120—1061no—
647#120—1061no—
648#120—1061no—
649C4×Q8—531no—
650C4×D4—21no—
651C4×D4—531no—
652C4×D4—531no—
653C4×D4—531no—
654C4×D4—531no—
655C4×D4—531no—
656C4×D4—531no—
657C4×D4—531no—
658C4×D4—531no—
659C4×D4—531no—
660C4×D4—1061no—
661C4×D4—1061no—
662C4×D4—1061no—
663C4×D4—1061no—
664C4×D4—1061no—
665C4×D4—1061no—
666C4×D4—1061no—
667C4×D4—1061no—
668C4×D4—1061no—
669C4×D4C4×D5311yescharacteristic, complemented
670C4×D4C4×D5311yescharacteristic, complemented
671#117—531no—
672#117—531no—
673#117—1061no—
674#117—1061no—
675C2×C4⋊C4—531no—
676C2×C4⋊C4—531no—
677C2×C4⋊C4—531no—
678C2×C4⋊C4—1061no—
679C2×C4⋊C4—1061no—
680C2×C22⋊C4—531no—
681C2×C22⋊C4—531no—
682C2×C22⋊C4—1061no—
683C2×C22⋊C4—1061no—
684C2×C22⋊C4—1061no—
685C2×C22⋊C4—1061no—
686C2×C22⋊C4—1061no—
687C2×C22⋊C4—1061no—
688C2×C22⋊C4—1061no—
689C2×C42—1061no—
690C2×C42C22×D5311yescharacteristic
691C4⋊C8—21no—
692C4⋊C8—1061no—
693C22⋊C8—531no—
694C22⋊C8—531no—
695C22⋊C8—1061no—
696C22⋊C8—1061no—
697C22⋊C8—1061no—
698C22⋊C8—1061no—
699C22⋊C8C22×D5311yescharacteristic
700C22⋊C8C22×D5311yescharacteristic
701#97—21no—
702C4×C8—1061no—
703#95—21no—
704#95—21no—
705#95—531no—
706#95—531no—
707#95—1061no—
708#95—1061no—
709#95—1061no—
710#95C22×D5311yescharacteristic
711#95C22×D5311yescharacteristic
712C24—531no—
713C24—531no—
714C24—1061no—
715C24—1061no—
716#41—81no—
717#41—81no—
718#41—4241no—
719#41—4241no—
720C2×Q8—21no—
721C2×Q8—531no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—531no—
727C2×D4—531no—
728C2×D4—531no—
729C2×D4—531no—
730C2×D4—531no—
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—1061no—
742C2×D4—4241no—
743C2×D4—4241no—
744C2×D4—4241no—
745C2×D4—4241no—
746C2×D4—4241no—
747C2×D4—4241no—
748C2×D4—2122no—
749C2×D4—2124no—
750C2×D4C2×C4×D5311yescharacteristic
751C2×D4C2×C4×D5311yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—531no—
757C22×C4—531no—
758C22×C4—531no—
759C22×C4—531no—
760C22×C4—531no—
761C22×C4—531no—
762C22×C4—531no—
763C22×C4—531no—
764C22×C4—531no—
765C22×C4—531no—
766C22×C4—1061no—
767C22×C4—1061no—
768C22×C4—1061no—
769C22×C4—1061no—
770C22×C4—1061no—
771C22×C4—1061no—
772C22×C4—1061no—
773C22×C4—4241no—
774C22×C4—4241no—
775C22×C4—4241no—
776C22×C4—4241no—
777C22×C4—2122no—
778C22×C4D4×D5311yescharacteristic
779C22×C4D4×D5311yescharacteristic
780C22×C4C23×D5311yescharacteristic
781M16—4241no—
782M16—4241no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—1061no—
786C2×C8—1061no—
787C2×C8—4241no—
788C2×C8—4241no—
789C4⋊C4—21no—
790C4⋊C4—531no—
791C4⋊C4—531no—
792C4⋊C4—531no—
793C4⋊C4—531no—
794C4⋊C4—531no—
795C4⋊C4—531no—
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—4241no—
805C4⋊C4—4241no—
806C4⋊C4C2×C4×D5311yescharacteristic
807C4⋊C4C2×C4×D5311yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—531no—
813C22⋊C4—531no—
814C22⋊C4—531no—
815C22⋊C4—531no—
816C22⋊C4—531no—
817C22⋊C4—531no—
818C22⋊C4—531no—
819C22⋊C4—531no—
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—1061no—
831C22⋊C4—1061no—
832C22⋊C4—1061no—
833C22⋊C4—1061no—
834C22⋊C4—1061no—
835C22⋊C4—4241no—
836C22⋊C4—4241no—
837C22⋊C4—2122no—
838C42—1061no—
839C42—1061no—
840C42—1061no—
841C42—4241no—
842C42C2×C4×D5311yescharacteristic
843C42C2×C4×D5311yescharacteristic
844C42D4×D5311yescharacteristic
845C42D4×D5311yescharacteristic
846C23—21no—
847C23—21no—
848C23—531no—
849C23—531no—
850C23—531no—
851C23—531no—
852C23—1062no—
853C23—1061no—
854C23—1061no—
855C23—1061no—
856C23—1061no—
857C23—1061no—
858C23—4241no—
859C23—4241no—
860C23—4241no—
861C23—4241no—
862C23—2121no—
863C23—2121no—
864C23—2121no—
865C23—2122no—
866C23—2122no—
867C23C2×D4×D5311yescharacteristic
868Q8—81no—
869Q8—2121no—
870D4—41no—
871D4—41no—
872D4—42no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—81no—
878D4—1062no—
879D4—1062no—
880D4—4241no—
881D4—4241no—
882D4—4241no—
883D4—4241no—
884D4—4241no—
885D4—4241no—
886D4—4241no—
887D4—4241no—
888D4—2121no—
889D4—2121no—
890D4—2121no—
891D4—2122no—
892D4—2122no—
893D4—2121no—
894D4—2121no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
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—81no—
908C2×C4—81no—
909C2×C4—531no—
910C2×C4—531no—
911C2×C4—531no—
912C2×C4—531no—
913C2×C4—1061no—
914C2×C4—1061no—
915C2×C4—1061no—
916C2×C4—4241no—
917C2×C4—4241no—
918C2×C4—4244no—
919C2×C4—4241no—
920C2×C4—4241no—
921C2×C4—2121no—
922C2×C4—2121no—
923C2×C4—2121no—
924C2×C4—2121no—
925C2×C4—2121no—
926C2×C4—2121no—
927C2×C4—2121no—
928C2×C4—2121no—
929C2×C4—2122no—
930C2×C4—2121no—
931C2×C4—2121no—
932C2×C4—2121no—
933C2×C4—2121no—
934C2×C4—2121no—
935C2×C4—2121no—
936C2×C4—2121no—
937C2×C4—2121no—
938C2×C4C22⋊C4×D5311yescharacteristic
939C2×C4C22⋊C4×D5311yescharacteristic
940C2×C4C22⋊C4×D5311yescharacteristic
941C2×C4C22⋊C4×D5311yescharacteristic
942C2×C4C22×C4×D5311yescharacteristic
943C2×C4C2×D4×D5311yescharacteristic
944C8—41no—
945C8—41no—
946C8—2121no—
947C8—2121no—
948C22—21no—
949C22—21no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—532no—
957C22—8482no—
958C22—8482no—
959C22—1061no—
960C22—1061no—
961C22—1061no—
962C22—1061no—
963C22—1061no—
964C22—1061no—
965C22—1061no—
966C22—1061no—
967C22—1061no—
968C22—1061no—
969C22—1061no—
970C22—4241no—
971C22—4241no—
972C22—2122no—
973C22—2122no—
974C22—2121no—
975C22—2121no—
976C22—2121no—
977C22C2×C22⋊C4×D5311yescharacteristic
978C22#1681142711yescharacteristic
979C22#1681143311yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—41no—
987C4—41no—
988C4—81no—
989C4—81no—
990C4—1061no—
991C4—1061no—
992C4—1061no—
993C4—1061no—
994C4—4241no—
995C4—4241no—
996C4—2121no—
997C4—2121no—
998C4—2121no—
999C2—21no—
1000C2—21no—
1001C2—81no—
1002C2—81no—
1003C2—1062no—
1004C2—4241no—
1005C2—2121no—
1006C2—2121no—
1007C2—2121no—
1008C2#2028317411yescharacteristic
1009C2#2028324011yescharacteristic
1010C2#421×D5311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1514C2
socleC22×C53C22×C22⋊C4
prime radical#20288742C2
cosocleC22×C4×C53C24
hypercenter#1514D53
hypocenterC53#17597
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1514

Complements

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

NH ≅ G/Ntype
2. #20283752C2semidirect
3. #20277346C2semidirect
4. #20273290C2semidirect
5. #20273281C2semidirect
6. #20273275C2semidirect
7. #20273268C2semidirect
8. #20273255C2semidirect
9. #20273254C2semidirect
10. #20273242C2semidirect
11. #20273229C2semidirect
12. #20273216C2semidirect
13. #20273203C2semidirect
14. #327×D53C2semidirect
15. C53×#1514C2semidirect
16. #16811339C4semidirect
17. #16811334C4semidirect
19. #16811323C4semidirect
20. #16811323C4semidirect
21. #16811293C4semidirect
22. #16811268C4semidirect
23. #16811268C4semidirect
26. #16811258C4semidirect
42. #16810676C22semidirect
43. #16810585C22semidirect
44. #16810585C22semidirect
45. C22⋊C8×D53C22semidirect
46. C22⋊C8×D53C22semidirect
51. #16810489C22semidirect
52. #16810485C22semidirect
53. #16810482C22semidirect
54. #16810470C22semidirect
55. #95×D53C22semidirect
56. #16810361C22semidirect
57. #16810361C22semidirect
58. #16810359C22semidirect
59. #16810359C22semidirect
62. #16810357C22semidirect
63. #16810357C22semidirect
64. #16810357C22semidirect
65. #16810357C22semidirect
69. C53×#432C22semidirect
70. C53×#383C22semidirect
71. C53×#327C22semidirect
72. C53×#327C22semidirect
73. C53×#327C22semidirect
74. C53×#327C22semidirect
76. C2×#11719947C2×C4semidirect
82. C2×D4×D53C2×C4semidirect
94. #13133209C2×C4semidirect
98. #13133205C2×C4semidirect
107. #13133197C2×C4semidirect
113. #13133192C2×C4semidirect
128. #13133188C2×C4semidirect
129. #13133188C2×C4semidirect
136. C4×Dic106C2×C4semidirect
141. C4×D212C2×C4semidirect
157. #13133175C2×C4semidirect
163. C4⋊C4×D53C2×C4semidirect
188. C4⋊Q8×C53C2×C4semidirect
189. #127×C53C2×C4semidirect
195. C4×D4×C53C2×C4semidirect
196. C4×D4×C53C2×C4semidirect
501. #1514D53semidirect
548. #432C2×D53semidirect
558. #383C2×D53semidirect
576. #327C2×D53semidirect
577. #327C2×D53semidirect
578. #327C2×D53semidirect
579. #327C2×D53semidirect
580. C53#17597semidirect
597. C4⋊Q8C4×D53semidirect
599. #127C4×D53semidirect
669. C4×D4C4×D53semidirect
670. C4×D4C4×D53semidirect

Maximal subgroups

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

subgroupindex
#202887422
#202837522
#202773462
#202732902
#202732812
#202732752
#202732682
#202732552
#202732542
#202732422
#202732292
#202732162
#202732032
#327×D532
C53×#15142
#1759753