Finite Group Databasebeta

← #15936170

Subgroups — #15936170

Order 3328.

740 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119444C211yesmaximal, characteristic, complemented
2#13116357C211yesmaximal, characteristic
3#13116153C211yesmaximal, characteristic
4#13116072C211yesmaximal, characteristic
5#13115930C211yesmaximal, characteristic
6#13115696C211yesmaximal, characteristic, complemented
7#13115470C211yesmaximal, characteristic, complemented
8#13115467C211yesmaximal, characteristic, complemented
9#13115428C211yesmaximal, characteristic, complemented
10#13115395C211yesmaximal, characteristic, complemented
11#13115177C211yesmaximal, characteristic, complemented
12#13115170C211yesmaximal, characteristic
13#13114851C211yesmaximal, characteristic, complemented
14C4×#88072C211yesmaximal, characteristic
15C13×#2367C211yesmaximal, characteristic
16C2×C13×#124C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C22×#6107C2211yescharacteristic
20C22×#6105C2211yescharacteristic
21C13×#391C2211yescharacteristic
22C13×#390C2211yescharacteristic
23C13×#388—21no—
24C13×#388—21no—
25C13×#385—21no—
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C22⋊C4—21no—
29C2×#88075C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35#11718643—21no—
36#11718639—21no—
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41#11718597C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43#11718590C2211yescharacteristic
44#11718590C2211yescharacteristic
45#11718590C2211yescharacteristic
46#11718589C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×C4×#1055C2211yescharacteristic
49C13⋊#401—21no—
50#11718312—21no—
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C22×Dic26C2311yescharacteristic
63C13×#124—22no—
64C13×#124—22no—
65C4×Q8×C13—22no—
66C4×Q8×C13—41no—
67C4×D4×C13—22no—
68C4×D4×C13—41no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4D411yescharacteristic
71C2×C13×C4⋊C4D411yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C42×C13—21no—
80C2×C42×C13—21no—
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×#6107—22no—
85C2×#6107—22no—
86C2×#6107—41no—
87C2×#6105—22no—
88C2×#6105—41no—
89C2×#6105—41no—
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×#6101—21no—
94C2×C4×Dic13—21no—
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95D411yescharacteristic
103C13×#95D411yescharacteristic
104#88075—22no—
105#88075—41no—
106#88075—41no—
107#88072—22no—
108#88072—22no—
109#88072—41no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88050—22no—
121#88050—41no—
122#88048—41no—
123#88047—22no—
124C4⋊#1055—41no—
125C4×#1055—41no—
126#27070—131nomaximal, Sylow
127C24×C13—21no—
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13—21no—
132C2×Q8×C13—21no—
133C2×Q8×C13#4112yes—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13#4112yes—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—42no—
144C22×C4×C13—42no—
145C22×C4×C13—81no—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2411yescharacteristic
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C2×Dic26—21no—
158C2×Dic26—21no—
159C2×Dic26—21no—
160C2×Dic26—21no—
161C2×Dic26—21no—
162C2×Dic26—21no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—41no—
168C13×C4⋊C4—42no—
169C13×C4⋊C4#4112yes—
170C13×C22⋊C4—24no—
171C13×C22⋊C4—24no—
172C13×C22⋊C4—42no—
173C13×C22⋊C4—42no—
174C13×C22⋊C4—81no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—42no—
182C42×C13—81no—
183#6107—44no—
184#6105—44no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191#6101—42no—
192C4×Dic13—42no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055#4112yes—
205#2514—131no—
206#2367D1311yescharacteristic
207#2092—131no—
208#2055—131no—
209#2042—131no—
210#2015—131no—
211#1969—131no—
212#1927—131no—
213#1927—131no—
214#1921—131no—
215#1916—131no—
216#1878—131no—
217#1877—131no—
218#1805—131no—
219C4×#102—131no—
220C23×C13—22no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13C22×D411yescharacteristic
228Q8×C13—22no—
229Q8×C13—22no—
230Q8×C13—41no—
231Q8×C13—41no—
232D4×C13—22no—
233D4×C13—22no—
234D4×C13—41no—
235D4×C13—41no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—22no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—22no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—84no—
263C2×C4×C13#13512yes—
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13C2×#4111yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×C4×C13H(5,𝔽2)11yescharacteristic
269C2×C4×C13H(5,𝔽2)11yescharacteristic
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282Dic26—41no—
283Dic26—41no—
284Dic26—41no—
285Dic26—41no—
286#1055—22no—
287#1055—41no—
288#1055—41no—
289#1055—41no—
290C22×Q16—131no—
291C22×SD16—131no—
292C2×#124C2×D1311yescharacteristic
293C2×C4×Q8C2×D1311yescharacteristic
294C2×C4×D4C2×D1311yescharacteristic
295C2×#107—131no—
296C2×#106—131no—
297C2×C4⋊C8—131no—
298C2×#103—131no—
299C2×#103—131no—
300C2×#103—131no—
301C2×#103—131no—
302C2×#103—131no—
303C2×#102—131no—
304C2×#102—131no—
305C2×#102—131no—
306C2×C4×C8—131no—
307#401—261no—
308#400—261no—
309#391—131no—
310#391—131no—
311#391—131no—
312#391C2×D1311yescharacteristic
313#390C2×D1311yescharacteristic
314#389—131no—
315#388—21no—
316#388—21no—
317#387—261no—
318#385—21no—
319#383—261no—
320#382—131no—
321C4×C4⋊C4—131no—
322C4×C4⋊C4C2×D1311yescharacteristic
323C4×C4⋊C4C2×D1311yescharacteristic
324C4×C22⋊C4—21no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#336—131no—
330#336—131no—
331#336—131no—
332#336—131no—
333C22×C13—42no—
334C22×C13—42no—
335C22×C13—42no—
336C22×C13—81no—
337C22×C13—81no—
338C22×C13—81no—
339C22×C13—81no—
340C22×C13#52511yescharacteristic
341C22×C13#54611yescharacteristic
342C22×C13#55011yescharacteristic
343C22×C13C2×#13511yescharacteristic
344C22×C13#57511yescharacteristic
345C22×C13#57711yescharacteristic
346C22×C13#57811yescharacteristic
347C4×C13—22no—
348C4×C13—41no—
349C4×C13—41no—
350C4×C13—42no—
351C4×C13—41no—
352C4×C13—42no—
353C4×C13—41no—
354C4×C13—41no—
355C4×C13—81no—
356C4×C13#52911yescharacteristic
357C4×C13#53811yescharacteristic
358C4×C13#55111yescharacteristic
359C4×C13#55311yescharacteristic
360Dic13—81no—
361Dic13—81no—
362Dic13—81no—
363Dic13—81no—
364C22×Q8—131no—
365C22×Q8C22×D1311yescharacteristic
366C22×D4C22×D1311yescharacteristic
367C23×C4—21no—
368C2×Q16—262no—
369C2×Q16—262no—
370C2×Q16—521no—
371C2×SD16—262no—
372C2×SD16—521no—
373C2×SD16—521no—
374C22×C8—131no—
375C22×C8—131no—
376C22×C8—131no—
377C22×C8—131no—
378#124—22no—
379#124—22no—
380C4×Q8—22no—
381C4×Q8—41no—
382C4×D4—22no—
383C4×D4—41no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4C22⋊D1311yescharacteristic
390C2×C4⋊C4C22⋊D1311yescharacteristic
391C2×C4⋊C4C22×D1311yescharacteristic
392C2×C4⋊C4C22×D1311yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—261no—
401C2×C42C22×D1311yescharacteristic
402C2×C42C22×D1311yescharacteristic
403C2×C42C22×D1311yescharacteristic
404#107—262no—
405#106—521no—
406C4⋊C8—521no—
407#103—262no—
408#103—262no—
409#103—521no—
410#103—521no—
411#103—521no—
412#102—262no—
413#102—262no—
414#102—521no—
415C4×C8—521no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—261no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95—261no—
424#95—261no—
425#95—261no—
426#95—261no—
427#95—261no—
428#95—261no—
429#95C22⋊D1311yescharacteristic
430#95C22⋊D1311yescharacteristic
431C2×C13—82no—
432C2×C13#246711yescharacteristic
433C2×C13#310211yescharacteristic
434C2×C13#312011yescharacteristic
435C2×C13#329611yescharacteristic
436C2×C13#331311yescharacteristic
437C2×C13#339311yescharacteristic
438C2×C13#340111yescharacteristic
439C24—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—261no—
446C2×Q8—261no—
447C2×Q8—261no—
448C2×Q8—261no—
449C2×Q8—261no—
450C2×Q8—261no—
451C2×Q8#612712yes—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4#612712yes—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—81no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4C2×C22⋊D1311yescharacteristic
469C22×C4C2×C22⋊D1311yescharacteristic
470C22×C4C2×C22⋊D1311yescharacteristic
471C22×C4C2×C22⋊D1311yescharacteristic
472C22×C4C2×C22⋊D1311yescharacteristic
473C22×C4C2×C22⋊D1311yescharacteristic
474C22×C4C23×D1311yescharacteristic
475Q16—524no—
476SD16—524no—
477C2×C8—132no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—41no—
494C4⋊C4—42no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4—261no—
500C4⋊C4—261no—
501C4⋊C4—522no—
502C4⋊C4#612912yes—
503C22⋊C4—24no—
504C22⋊C4—24no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—81no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—42no—
515C42—81no—
516C42—522no—
517C13#2707011yescharacteristic, complemented, Sylow
518C23—22no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23C22×C22⋊D1311yescharacteristic
526Q8—22no—
527Q8—22no—
528Q8—41no—
529Q8—41no—
530Q8—521no—
531Q8—521no—
532Q8—521no—
533Q8—521no—
534D4—22no—
535D4—22no—
536D4—41no—
537D4—41no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—84no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4#8820412yes—
578C2×C4C2×#612711yescharacteristic
579C2×C4C2×#612711yescharacteristic
580C2×C4C2×#612911yescharacteristic
581C2×C4#8825111yescharacteristic
582C2×C4#41×D1311yescharacteristic
583C2×C4#8825611yescharacteristic
584C8—262no—
585C8—521no—
586C8—521no—
587C8—521no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22#1171949611yescharacteristic
596C22#1171951111yescharacteristic
597C22C2×#8820411yescharacteristic
598C22#1171952711yescharacteristic
599C22#1171953911yescharacteristic
600C22#1171954111yescharacteristic
601C22#1171954311yescharacteristic
602C4—22no—
603C4—41no—
604C4—42no—
605C4—42no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—1041no—
612C4—1041no—
613C4—1041no—
614C4—1041no—
615C4#1171924311yescharacteristic
616C4#1171926111yescharacteristic
617C4#1171926511yescharacteristic
618C4#1171927011yescharacteristic
619C2—82no—
620C2#1311888111yescharacteristic
621C2#1312485411yescharacteristic
622C2#1312505011yescharacteristic
623C2#1312667111yescharacteristic
624C2#1312690211yescharacteristic
625C2#1312782011yescharacteristic
626C2#1312789611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2367C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenter#2367D13
hypocenterC13#27070
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2367

Complements

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

NH ≅ G/Ntype
1. #13119444C2semidirect
6. #13115696C2semidirect
7. #13115470C2semidirect
8. #13115467C2semidirect
9. #13115428C2semidirect
10. #13115395C2semidirect
11. #13115177C2semidirect
13. #13114851C2semidirect
517. C13#27070semidirect

Maximal subgroups

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

subgroupindex
#131194442
#131163572
#131161532
#131160722
#131159302
#131156962
#131154702
#131154672
#131154282
#131153952
#131151772
#131151702
#131148512
C4×#880722
C13×#23672
#2707013