Finite Group Databasebeta

← #15935766

Subgroups — #15935766

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#13119254C211yesmaximal, characteristic
2#13117867C211yesmaximal, characteristic
3#13116247C211yesmaximal, characteristic, complemented
4#13116229C211yesmaximal, characteristic, complemented
5#13116036C211yesmaximal, characteristic
6#13115591C211yesmaximal, characteristic, complemented
7#13115570C211yesmaximal, characteristic, complemented
8#13115445C211yesmaximal, characteristic
9#13115420C211yesmaximal, characteristic, complemented
10#13115410C211yesmaximal, characteristic, complemented
11#13115106C211yesmaximal, characteristic, complemented
12#13115037C211yesmaximal, characteristic
13#13114928C211yesmaximal, characteristic
14#103×Dic13C211yesmaximal, characteristic, complemented
15C13×#2036C211yesmaximal, characteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×Q8×Dic13C2211yescharacteristic
18C2×#88180C2211yescharacteristic
19C2×#88133—21no—
20C2×C13×#107C2211yescharacteristic
21C2×C13×#103C2211yescharacteristic
22C2×C13×#103C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C13×#380C2211yescharacteristic
25#11718891C2211yescharacteristic
26C2×#88075C2211yescharacteristic
27C2×#88075C2211yescharacteristic
28#11718873C2211yescharacteristic
29C4×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31C2×#88058C2211yescharacteristic
32C2×#88057C2211yescharacteristic
33C2×#88054C2211yescharacteristic
34C2×C8×Dic13C2211yescharacteristic
35#11718646C2211yescharacteristic
36#11718646C2211yescharacteristic
37#11718642—21no—
38#11718637C2211yescharacteristic
39C4⋊C4×Dic13—21no—
40C4⋊C4×Dic13C2211yescharacteristic
41C4⋊C4×Dic13C2211yescharacteristic
42#11718634C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718613—21no—
45#11718612—21no—
46#11718612—21no—
47#11718319—21no—
48#11718316—21no—
49C13×#340C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C13×C22⋊Q8—22no—
64C13×C22⋊Q8—22no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—21no—
71C2×C22⋊Dic13—21no—
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13D411yescharacteristic
74C2×C22⋊Dic13D411yescharacteristic
75Q8×Dic13—22no—
76Q8×Dic13—41no—
77#88180—22no—
78#88180—41no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×#6101—21no—
87C2×#6101—21no—
88C2×#6101—21no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13C2311yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97#88133—44no—
98C13×#107—22no—
99C13×#103—22no—
100C13×#103—22no—
101C13×C22⋊C8—22no—
102C13×#95—21no—
103#88075—22no—
104#88075—41no—
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#88071D411yescharacteristic
114#88071D411yescharacteristic
115C22⋊#1055—41no—
116#88058—41no—
117#88057—22no—
118#88054—22no—
119C8×Dic13—41no—
120#88047—22no—
121#27043—131nomaximal, Sylow
122C24×C13C2×D411yescharacteristic
123C2×Q8×C13—21no—
124C2×Q8×C13—21no—
125C2×Q8×C13—21no—
126C2×Q8×C13—21no—
127C2×Q8×C13—21no—
128C2×Q8×C13#4112yes—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2411yescharacteristic
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13C2×D411yescharacteristic
146C22×Dic13C2×D411yescharacteristic
147C22×Dic13C2×D411yescharacteristic
148C22×Dic13C2×D411yescharacteristic
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13#4112yes—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4#4112yes—
162C13×C22⋊C4—24no—
163C13×C22⋊C4—42no—
164C22⋊Dic13—22no—
165C22⋊Dic13—22no—
166C22⋊Dic13—42no—
167C22⋊Dic13—42no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—42no—
176C4⋊Dic13—42no—
177C4⋊Dic13—42no—
178C4⋊Dic13#4112yes—
179#6101—42no—
180#6101—42no—
181#6101—42no—
182C4×Dic13—21no—
183C4×Dic13—21no—
184C4×Dic13—21no—
185C4×Dic13—21no—
186C4×Dic13—42no—
187C4×Dic13—42no—
188C4×Dic13—42no—
189C4×Dic13—42no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196#2496—131no—
197#2362—131no—
198#2072—131no—
199#2068—131no—
200#2036—131no—
201#2036D1311yescharacteristic
202#1947—131no—
203#1942—131no—
204#1923—131no—
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
219Q8×C13—22no—
220Q8×C13—22no—
221Q8×C13—41no—
222Q8×C13—41no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13C2×#4111yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C13H(5,𝔽2)11yescharacteristic
247C2×C4×C132−1+411yescharacteristic
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—22no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
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—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13#13512yes—
271C2×Dic13AGL(1,ℤ/8)12yes—
272C8×C13—22no—
273C8×C13—41no—
274#1055—41no—
275#1055—41no—
276C2×#126—261no—
277C2×C22⋊Q8C2×D1311yescharacteristic
278C2×C4×Q8—131no—
279C2×#117—131no—
280C2×#107—131no—
281C2×#107—131no—
282C2×#107C2×D1311yescharacteristic
283C2×#106—131no—
284C2×C4⋊C8—131no—
285C2×#103—131no—
286C2×#103—131no—
287C2×#103C2×D1311yescharacteristic
288C2×#103C2×D1311yescharacteristic
289C2×C22⋊C8—131no—
290C2×C22⋊C8C2×D1311yescharacteristic
291C2×C4×C8—131no—
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#380C2×D1311yescharacteristic
305C4×C4⋊C4—131no—
306C4×C4⋊C4—131no—
307C4×C4⋊C4—261no—
308C4×C22⋊C4—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340C2×D1311yescharacteristic
317#336—131no—
318#336—131no—
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—42no—
334C4×C13—41no—
335C4×C13—42no—
336C4×C13—81no—
337C4×C13—81no—
338C4×C13#52911yescharacteristic
339C4×C13#53911yescharacteristic
340C4×C13#55311yescharacteristic
341C4×C13#55611yescharacteristic
342Dic13—22no—
343Dic13—22no—
344Dic13—41no—
345Dic13—41no—
346Dic13—42no—
347Dic13—81no—
348Dic13—81no—
349Dic13—81no—
350C22×Q8C22×D1311yescharacteristic
351C23×C4C22×D1311yescharacteristic
352C22×C8—131no—
353C22×C8—131no—
354C22×C8C22×D1311yescharacteristic
355C22×C8C22×D1311yescharacteristic
356#126—524no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C4×Q8—262no—
360C4×Q8—521no—
361#117—262no—
362#117—521no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C4⋊C4C22×D1311yescharacteristic
376C2×C4⋊C4C22×D1311yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—131no—
380C2×C22⋊C4—131no—
381C2×C22⋊C4—261no—
382C2×C22⋊C4—261no—
383C2×C42—131no—
384C2×C42—131no—
385C2×C42—261no—
386C2×C42—261no—
387C2×C42—261no—
388C2×C42—261no—
389#107—22no—
390#107—262no—
391#107—521no—
392#106—262no—
393C4⋊C8—262no—
394#103—22no—
395#103—22no—
396#103—262no—
397#103—521no—
398C22⋊C8—22no—
399C22⋊C8—521no—
400C4×C8—521no—
401#95—21no—
402#95—131no—
403#95—131no—
404#95—261no—
405#95—261no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95—261no—
410#95—261no—
411#95—261no—
412C2×C13—81no—
413C2×C13#246611yescharacteristic
414C2×C13#310611yescharacteristic
415C2×C13#312711yescharacteristic
416C2×C13#330211yescharacteristic
417C2×C13#330811yescharacteristic
418C2×C13#333611yescharacteristic
419C2×C13#335311yescharacteristic
420C24D4×D1311yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8#612912yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4—131no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4D4×D1311yescharacteristic
446C22×C4C23×D1311yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8#612912yes—
459C4⋊C4—24no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—132no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—522no—
474C4⋊C4—522no—
475C4⋊C4—522no—
476C4⋊C4—522no—
477C4⋊C4—522no—
478C4⋊C4—522no—
479C4⋊C4#612912yes—
480C22⋊C4—24no—
481C22⋊C4—42no—
482C22⋊C4—262no—
483C22⋊C4—262no—
484C22⋊C4—522no—
485C22⋊C4—522no—
486C42—261no—
487C42—261no—
488C42—261no—
489C42—261no—
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—
502C23C2×D4×D1311yescharacteristic
503Q8—22no—
504Q8—22no—
505Q8—41no—
506Q8—41no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—132no—
527C2×C4—132no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—262no—
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—521no—
549C2×C4—521no—
550C2×C4C2×#612911yescharacteristic
551C2×C4C2×#612911yescharacteristic
552C2×C4C2×#612911yescharacteristic
553C2×C4#41×D1311yescharacteristic
554C2×C4#8825611yescharacteristic
555C2×C4#8825711yescharacteristic
556C8—22no—
557C8—41no—
558C8—521no—
559C8—521no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22#1171929111yescharacteristic
568C22#1171931611yescharacteristic
569C22#1171935911yescharacteristic
570C22#1171947111yescharacteristic
571C22D13×#13511yescharacteristic
572C22D13×AGL(1,ℤ/8)11yescharacteristic
573C22#1171948411yescharacteristic
574C4—42no—
575C4—41no—
576C4—42no—
577C4—81no—
578C4—81no—
579C4—262no—
580C4—262no—
581C4—521no—
582C4—522no—
583C4—521no—
584C4—1041no—
585C4—1041no—
586C4—1041no—
587C4#1171930511yescharacteristic
588C4#1171932311yescharacteristic
589C4#1171937011yescharacteristic
590C4#1171937611yescharacteristic
591C2—81no—
592C2#1311886711yescharacteristic
593C2#1312488911yescharacteristic
594C2#1312513011yescharacteristic
595C2#1312675111yescharacteristic
596C2#1312683011yescharacteristic
597C2#1312719911yescharacteristic
598C2#1312741511yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2036C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2036D13
hypocenterC13#27043
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2036

Complements

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

NH ≅ G/Ntype
3. #13116247C2semidirect
4. #13116229C2semidirect
6. #13115591C2semidirect
7. #13115570C2semidirect
9. #13115420C2semidirect
10. #13115410C2semidirect
11. #13115106C2semidirect
14. #103×Dic13C2semidirect
494. C13#27043semidirect

Maximal subgroups

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

subgroupindex
#131192542
#131178672
#131162472
#131162292
#131160362
#131155912
#131155702
#131154452
#131154202
#131154102
#131151062
#131150372
#131149282
#103×Dic132
C13×#20362
#2704313