Finite Group Databasebeta

← #15935769

Subgroups — #15935769

Order 3328.

706 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119258C211yesmaximal, characteristic
2#13117861C211yesmaximal, characteristic
3#13116246C211yesmaximal, characteristic, complemented
4#13116230C211yesmaximal, characteristic, complemented
5#13116040C211yesmaximal, characteristic
6#13116040C211yesmaximal, characteristic
7#13115595C211yesmaximal, characteristic, complemented
8#13115569C211yesmaximal, characteristic, complemented
9#13115422C211yesmaximal, characteristic, complemented
10#13115408C211yesmaximal, characteristic, complemented
11#13115107C211yesmaximal, characteristic, complemented
12#13115037C211yesmaximal, characteristic
13#13114932C211yesmaximal, characteristic
14C4×#88056C211yesmaximal, characteristic, complemented
15C13×#1923C211yesmaximal, characteristic
16C2×#88180C2211yescharacteristic
17C2×#88178C2211yescharacteristic
18C2×#88133—21no—
19C2×C4×Dic26C2211yescharacteristic
20C2×C13×C4⋊C8C2211yescharacteristic
21C2×C13×C22⋊C8C2211yescharacteristic
22C2×C13×C22⋊C8C2211yescharacteristic
23C2×C4×C8×C13C2211yescharacteristic
24C4×C13×C22⋊C4C2211yescharacteristic
25#11718873C2211yescharacteristic
26#11718873C2211yescharacteristic
27C2×#88058C2211yescharacteristic
28C2×#88058C2211yescharacteristic
29C2×#88058C2211yescharacteristic
30C2×#88057C2211yescharacteristic
31C2×#88056C2211yescharacteristic
32C2×#88056C2211yescharacteristic
33C2×#88056C2211yescharacteristic
34C2×#88056C2211yescharacteristic
35#11718614—21no—
36#11718606—21no—
37#11718605—21no—
38#11718596C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40C4×C4⋊Dic13C2211yescharacteristic
41#11718590C2211yescharacteristic
42#11718589C2211yescharacteristic
43#11718589C2211yescharacteristic
44#11718589C2211yescharacteristic
45#11718320—21no—
46#11718314—21no—
47#11718313—21no—
48#11718310—21no—
49C13×#336C2211yescharacteristic
50C13×#336C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C22×Dic26C2311yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C2×C13×C22⋊C4D411yescharacteristic
66C2×C13×C22⋊C4D411yescharacteristic
67C2×C42×C13C2311yescharacteristic
68C2×C42×C13C2311yescharacteristic
69C2×C22⋊Dic13—21no—
70C2×C22⋊Dic13—21no—
71C2×C22⋊Dic13—21no—
72C2×C22⋊Dic13—21no—
73#88180—22no—
74#88180—41no—
75C2×C4⋊Dic13—21no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84#88178—22no—
85#88178—22no—
86C2×#6101—21no—
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95#88133—44no—
96C4×Dic26—22no—
97C4×Dic26—41no—
98C13×C4⋊C8—22no—
99C13×C22⋊C8—22no—
100C13×C22⋊C8—41no—
101C4×C8×C13—41no—
102C13×#95D411yescharacteristic
103C13×#95D411yescharacteristic
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88058—22no—
114#88058—22no—
115#88058—41no—
116#88057—22no—
117#88056—22no—
118#88056—22no—
119#88056—22no—
120#88056—41no—
121#27043—131nomaximal, Sylow
122C24×C13C2×D411yescharacteristic
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2411yescharacteristic
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C2×Dic26—21no—
144C2×Dic26—21no—
145C2×Dic26—21no—
146C2×Dic26—21no—
147C2×Dic26—21no—
148C2×Dic26#4112yes—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13#4112yes—
161C13×C22⋊C4—22no—
162C13×C22⋊C4—22no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—21no—
167C22⋊Dic13—24no—
168C22⋊Dic13—42no—
169C22⋊Dic13—42no—
170C22⋊Dic13—42no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—42no—
184C4⋊Dic13—42no—
185C4⋊Dic13#4112yes—
186C4⋊Dic13#4112yes—
187#6101—24no—
188#6101—42no—
189#6101—42no—
190#6101—42no—
191#6101—42no—
192C4×Dic13—42no—
193C4×Dic13—42no—
194C4×Dic13—42no—
195C4×Dic13—42no—
196#2496—131no—
197#2362—131no—
198#2072—131no—
199#2068—131no—
200#2036—131no—
201#2036—131no—
202#1947—131no—
203#1942—131no—
204#1923D1311yescharacteristic
205#1920—131no—
206#1918—131no—
207#1865—131no—
208#1854—131no—
209#1825—131no—
210C4×#103—131no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13—21no—
218C23×C13C22×D411yescharacteristic
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13#13512yes—
237C2×C4×C13AGL(1,ℤ/8)12yes—
238C2×C4×C13C2×#4111yescharacteristic
239C2×C4×C13C2×#4111yescharacteristic
240C2×C4×C13C2×#4111yescharacteristic
241C2×C4×C13C2×#4111yescharacteristic
242C2×C4×C13H(5,𝔽2)11yescharacteristic
243C2×C4×C132−1+411yescharacteristic
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—41no—
248C2×Dic13—41no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268Dic26—22no—
269Dic26—22no—
270Dic26—41no—
271Dic26—41no—
272C8×C13—22no—
273C8×C13—41no—
274C8×C13—41no—
275C8×C13—41no—
276C2×#126—261no—
277C2×C22⋊Q8—131no—
278C2×C4×Q8—131no—
279C2×#117—131no—
280C2×#107—131no—
281C2×#107—131no—
282C2×#107—131no—
283C2×#106—131no—
284C2×C4⋊C8C2×D1311yescharacteristic
285C2×#103—131no—
286C2×#103—131no—
287C2×#103—131no—
288C2×#103—131no—
289C2×C22⋊C8C2×D1311yescharacteristic
290C2×C22⋊C8C2×D1311yescharacteristic
291C2×C4×C8C2×D1311yescharacteristic
292#400—261no—
293#397—261no—
294#391—131no—
295#389—131no—
296#389—131no—
297#389—131no—
298#388—261no—
299#388—261no—
300#387—261no—
301#387—261no—
302#384—131no—
303#380—131no—
304#380—131no—
305C4×C4⋊C4—131no—
306C4×C4⋊C4—131no—
307C4×C4⋊C4—261no—
308C4×C22⋊C4C2×D1311yescharacteristic
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#336C2×D1311yescharacteristic
318#336C2×D1311yescharacteristic
319C22×C13—41no—
320C22×C13—41no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13—41no—
325C22×C13—41no—
326C22×C13#52511yescharacteristic
327C22×C13#54611yescharacteristic
328C22×C13#54711yescharacteristic
329C22×C13C2×#13511yescharacteristic
330C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C13#57811yescharacteristic
332C22×C13#57811yescharacteristic
333C4×C13—22no—
334C4×C13—22no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13—41no—
338C4×C13#52911yescharacteristic
339C4×C13#53911yescharacteristic
340C4×C13#55311yescharacteristic
341C4×C13#55611yescharacteristic
342Dic13—42no—
343Dic13—42no—
344Dic13—42no—
345Dic13—81no—
346Dic13—81no—
347Dic13—81no—
348Dic13—81no—
349Dic13—81no—
350C22×Q8—131no—
351C23×C4C22×D1311yescharacteristic
352C22×C8C22×D1311yescharacteristic
353C22×C8C22×D1311yescharacteristic
354C22×C8C22×D1311yescharacteristic
355C22×C8C22×D1311yescharacteristic
356#126—524no—
357C22⋊Q8—262no—
358C22⋊Q8—262no—
359C4×Q8—262no—
360C4×Q8—521no—
361#117—262no—
362#117—521no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C22⋊C4—261no—
378C2×C22⋊C4—261no—
379C2×C22⋊C4—261no—
380C2×C22⋊C4—261no—
381C2×C22⋊C4D5211yescharacteristic
382C2×C22⋊C4D5211yescharacteristic
383C2×C42—261no—
384C2×C42—261no—
385C2×C42—261no—
386C2×C42—261no—
387C2×C42C22×D1311yescharacteristic
388C2×C42C22×D1311yescharacteristic
389#107—262no—
390#107—262no—
391#107—521no—
392#106—262no—
393C4⋊C8—22no—
394#103—262no—
395#103—262no—
396#103—262no—
397#103—521no—
398C22⋊C8—22no—
399C22⋊C8—41no—
400C4×C8—41no—
401#95—261no—
402#95—261no—
403#95—261no—
404#95—261no—
405#95—261no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95—261no—
410#95D5211yescharacteristic
411#95D5211yescharacteristic
412C2×C13—81no—
413C2×C13#246611yescharacteristic
414C2×C13#310611yescharacteristic
415C2×C13#312711yescharacteristic
416C2×C13#330211yescharacteristic
417C2×C13#330811yescharacteristic
418C2×C13#333611yescharacteristic
419C2×C13#335311yescharacteristic
420C24C2×D5211yescharacteristic
421C2×Q8—132no—
422C2×Q8—261no—
423C2×Q8—261no—
424C2×Q8—261no—
425C2×Q8—261no—
426C2×Q8—261no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—261no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4C2×D5211yescharacteristic
442C22×C4C2×D5211yescharacteristic
443C22×C4C2×D5211yescharacteristic
444C22×C4C2×D5211yescharacteristic
445C22×C4C2×D5211yescharacteristic
446C22×C4C23×D1311yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8#612912yes—
459C4⋊C4—132no—
460C4⋊C4—132no—
461C4⋊C4—264no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—522no—
475C4⋊C4—522no—
476C4⋊C4—522no—
477C4⋊C4—522no—
478C4⋊C4—522no—
479C4⋊C4—522no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—264no—
483C22⋊C4—522no—
484C22⋊C4—522no—
485C22⋊C4—522no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—522no—
491C42—522no—
492C42—522no—
493C42—522no—
494C13#2704311yescharacteristic, complemented, Sylow
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23C22×D5211yescharacteristic
503Q8—262no—
504Q8—262no—
505Q8—521no—
506Q8—521no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—262no—
525C2×C4—262no—
526C2×C4—262no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4#8815812yes—
549C2×C4#8816212yes—
550C2×C4C2×#612911yescharacteristic
551C2×C4#8825111yescharacteristic
552C2×C4#41×D1311yescharacteristic
553C2×C4#41×D1311yescharacteristic
554C2×C4#41×D1311yescharacteristic
555C2×C4#8825711yescharacteristic
556C8—22no—
557C8—41no—
558C8—41no—
559C8—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22#1171922911yescharacteristic
568C22#1171925911yescharacteristic
569C22#1171926011yescharacteristic
570C22C2×#8815811yescharacteristic
571C22C2×#8816211yescharacteristic
572C22#1171945811yescharacteristic
573C22#1171945811yescharacteristic
574C4—22no—
575C4—22no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—522no—
580C4—522no—
581C4—522no—
582C4—1041no—
583C4—1041no—
584C4—1041no—
585C4—1041no—
586C4—1041no—
587C4#1171930611yescharacteristic
588C4#1171936511yescharacteristic
589C4#1171938511yescharacteristic
590C4#1171940711yescharacteristic
591C2—81no—
592C2#1311887011yescharacteristic
593C2#1312489711yescharacteristic
594C2#1312513711yescharacteristic
595C2#1312675411yescharacteristic
596C2#1312682911yescharacteristic
597C2#1312720511yescharacteristic
598C2#1312742111yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1923C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1923D13
hypocenterC13#27043
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
3. #13116246C2semidirect
4. #13116230C2semidirect
7. #13115595C2semidirect
8. #13115569C2semidirect
9. #13115422C2semidirect
10. #13115408C2semidirect
11. #13115107C2semidirect
14. C4×#88056C2semidirect
494. C13#27043semidirect

Maximal subgroups

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

subgroupindex
#131192582
#131178612
#131162462
#131162302
#131160402
#131155952
#131155692
#131154222
#131154082
#131151072
#131150372
#131149322
C4×#880562
C13×#19232
#2704313