Finite Group Databasebeta

← #15834289

Subgroups — #15834289

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124863C211yesmaximal, characteristic
2#13123926C211yesmaximal, characteristic, complemented
3#13123903C211yesmaximal, characteristic
4#13113735C211yesmaximal, characteristic, complemented
5#13113729C211yesmaximal, characteristic, complemented
6#13113717C211yesmaximal, characteristic, complemented
7#13113690C211yesmaximal, characteristic, complemented
8#13113682C211yesmaximal, characteristic, complemented
9#13113669C211yesmaximal, characteristic, complemented
10#13113645C211yesmaximal, characteristic, complemented
11#13113639C211yesmaximal, characteristic, complemented
12#13113617C211yesmaximal, characteristic, complemented
13#13113232C211yesmaximal, characteristic, complemented
14#13113136C211yesmaximal, characteristic, complemented
15C13×#1496C211yesmaximal, characteristic
16C13×#532C2211yescharacteristic
17C2×C4×Dic26C2211yescharacteristic
18C13×#432C2211yescharacteristic
19C13×#431C2211yescharacteristic
20#11718895—21no—
21#11718895—21no—
22#11718755C411yescharacteristic
23#11718755C411yescharacteristic
24#11718736C411yescharacteristic
25#11718736C411yescharacteristic
26#11718701C411yescharacteristic
27#11718701C411yescharacteristic
28#11718695C411yescharacteristic
29#11718695C411yescharacteristic
30C4×#6105C2211yescharacteristic
31C4×#6105C2211yescharacteristic
32C4×#6105C2211yescharacteristic
33C4×#6105C2211yescharacteristic
34#11718673—21no—
35#11718673C2211yescharacteristic
36#11718673C2211yescharacteristic
37D4×#1055—21no—
38D4×#1055C2211yescharacteristic
39D4×#1055C2211yescharacteristic
40#11718586C2211yescharacteristic
41#11718586C2211yescharacteristic
42#11718586C2211yescharacteristic
43#11718492C2211yescharacteristic
44#11718492C2211yescharacteristic
45#11718491C2211yescharacteristic
46#11718491C2211yescharacteristic
47#11718380—21no—
48#11718379—21no—
49#11718362—21no—
50#11718362—21no—
51C13×D4⋊C8C2211yescharacteristic
52C13×D4⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×D4⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718048C2211yescharacteristic
60#11718048C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41—21no—
68C22×Dic26C2×C411yescharacteristic
69C13×C4⋊Q8C2×C411yescharacteristic
70C13×#127C2×C411yescharacteristic
71C13×#124—21no—
72C13×#121—21no—
73C13×#121C2×C411yescharacteristic
74C13×#121C2×C411yescharacteristic
75C4×D4×C13—21no—
76C4×D4×C13C2311yescharacteristic
77C4×D4×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×#6105C2×C411yescharacteristic
80C2×#6105C2×C411yescharacteristic
81C2×#6105C2×C411yescharacteristic
82C2×#6105C2×C411yescharacteristic
83C2×C4⋊Dic13C2×C411yescharacteristic
84C2×#6101—21no—
85C2×C4×Dic13—21no—
86C2×#6099—21no—
87C2×#6099—21no—
88C22×#1055—21no—
89C22×#1055—21no—
90C4×Dic26—21no—
91C4×Dic26—21no—
92C4×Dic26C2×C411yescharacteristic
93C4×Dic26C2×C411yescharacteristic
94C4×Dic26C2311yescharacteristic
95C4×Dic26C2311yescharacteristic
96C13×C4⋊C8—21no—
97C13×C4⋊C8C2311yescharacteristic
98C13×C4⋊C8C2311yescharacteristic
99C13×C22⋊C8—21no—
100C13×C22⋊C8—21no—
101C13×#97—21no—
102C4×C8×C13C2311yescharacteristic
103C4×C8×C13C2311yescharacteristic
104#88072C2×C411yescharacteristic
105#88072C2×C411yescharacteristic
106#88072C2×C411yescharacteristic
107#88072C2×C411yescharacteristic
108C22⋊#1055—21no—
109C22⋊#1055—21no—
110C22⋊#1055—21no—
111C22⋊#1055—21no—
112C22⋊#1055—21no—
113C22⋊#1055C2×C411yescharacteristic
114C22⋊#1055C2×C411yescharacteristic
115C22⋊#1055D411yescharacteristic
116C22⋊#1055D411yescharacteristic
117#88055—21no—
118#88055—21no—
119#88054—21no—
120#88054—21no—
121#88054—21no—
122#88054—21no—
123C8×Dic13—21no—
124C8×Dic13—21no—
125#88050C2×C411yescharacteristic
126#88050C2×C411yescharacteristic
127#88050C2×C411yescharacteristic
128#88050C2×C411yescharacteristic
129#88048C2×C411yescharacteristic
130#88048C2×C411yescharacteristic
131#88048C2×C411yescharacteristic
132#88048C2×C411yescharacteristic
133C4⋊#1055C2×C411yescharacteristic
134C4⋊#1055C2×C411yescharacteristic
135C4⋊#1055D411yescharacteristic
136C4⋊#1055D411yescharacteristic
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18030—131nomaximal, Sylow
145C13×#41—81no—
146C13×#41—81no—
147C2×Q8×C13—21no—
148C2×D4×C13—21no—
149C2×D4×C13—21no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13C22×C411yescharacteristic
153C2×D4×C13C22×C411yescharacteristic
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13C22×C411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13#4111yescharacteristic
159C22×Dic13—21no—
160C22×Dic13—21no—
161C2×Dic26—22no—
162C2×Dic26—21no—
163C2×Dic26—41no—
164C2×Dic26C22×C411yescharacteristic
165C2×Dic26C22×C411yescharacteristic
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4C22×C411yescharacteristic
172C13×C4⋊C4C22×C411yescharacteristic
173C13×C22⋊C4—21no—
174C13×C22⋊C4—21no—
175C13×C22⋊C4—21no—
176C13×C22⋊C4—21no—
177C42×C13C22×C411yescharacteristic
178C42×C13C2×D411yescharacteristic
179C42×C13#4111yescharacteristic
180C42×C13C2411yescharacteristic
181#6105—22no—
182#6105—22no—
183#6105—41no—
184#6105—41no—
185C4⋊Dic13—21no—
186C4⋊Dic13C22×C411yescharacteristic
187C4⋊Dic13C22×C411yescharacteristic
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196#6099—81no—
197#6099—81no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—81no—
201C2×#1055—81no—
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208C2×#1055C2×D411yescharacteristic
209C2×#1055C2×D411yescharacteristic
210#3103—131no—
211#2984—131no—
212#2979—131no—
213#1592—131no—
214#1590—131no—
215#1588—131no—
216#1585—131no—
217#1583—131no—
218#1582—131no—
219SD16⋊C8—131no—
220C8×SD16—131no—
221#1572—131no—
222#1496D1311yescharacteristic
223#1479—131no—
224#1454—131no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13C4×D411yescharacteristic
228Q8×C13—81no—
229D4×C13—21no—
230D4×C13—21no—
231D4×C13—21no—
232D4×C13—21no—
233D4×C13—42no—
234D4×C13—81no—
235D4×C13—81no—
236D4×C13—81no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13C4×D411yescharacteristic
249C2×C4×C13C4×D411yescharacteristic
250C2×C4×C13C4×D411yescharacteristic
251C2×C4×C13C23×C411yescharacteristic
252C2×C4×C13C22×D411yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260Dic26—21no—
261Dic26—21no—
262Dic26—21no—
263Dic26—42no—
264Dic26#13112yes—
265C8×C13—41no—
266C8×C13—41no—
267C8×C13—41no—
268C8×C13—41no—
269#1055—21no—
270#1055—21no—
271#1055—21no—
272#1055—21no—
273#1055—21no—
274#1055—21no—
275#1055—21no—
276#1055—21no—
277#1055—41no—
278#1055—41no—
279#532C2×D1311yescharacteristic
280C2×C4×Q8—131no—
281#481—131no—
282#481—131no—
283#475—131no—
284#475—131no—
285#460—131no—
286#460—131no—
287#448—131no—
288#448—131no—
289#446—131no—
290#446—131no—
291#446—261no—
292#446—261no—
293C8×Q8—131no—
294C8×Q8—131no—
295C4×SD16—131no—
296C4×SD16—131no—
297C4×SD16—131no—
298C4×SD16—131no—
299#436—131no—
300#436—131no—
301#436—261no—
302C8×D4—131no—
303C8×D4—131no—
304C8×D4—261no—
305#432—261no—
306#432C2×D1311yescharacteristic
307#431—131no—
308#431—131no—
309#431—131no—
310#431—261no—
311#431C2×D1311yescharacteristic
312#408—261no—
313#408—261no—
314#335—131no—
315#335—131no—
316#334—131no—
317#334—131no—
318Q8⋊C8—131no—
319Q8⋊C8—131no—
320Q8⋊C8—131no—
321Q8⋊C8—131no—
322D4⋊C8C2×D1311yescharacteristic
323D4⋊C8C2×D1311yescharacteristic
324D4⋊C8C2×D1311yescharacteristic
325D4⋊C8C2×D1311yescharacteristic
326#322—131no—
327#322—131no—
328#322—131no—
329C82—131no—
330C22×C13—21no—
331C22×C13—21no—
332C22×C13—21no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13C2×C4×D411yescharacteristic
340C4×C13—21no—
341C4×C13—21no—
342C4×C13—21no—
343C4×C13—21no—
344C4×C13—41no—
345C4×C13—41no—
346C4×C13C2×#13111yescharacteristic
347C4×C13#56811yescharacteristic
348C4×C13#57711yescharacteristic
349C4×C13#57711yescharacteristic
350Dic13—22no—
351Dic13—41no—
352Dic13—41no—
353Dic13—41no—
354C2×#41—21no—
355C22×Q8—131no—
356C2×SD16—131no—
357C2×SD16—131no—
358C2×SD16—131no—
359C2×SD16—131no—
360C2×M16—261no—
361C2×M16—261no—
362C22×C8—261no—
363C22×C8—261no—
364C4⋊Q8C4×D1311yescharacteristic
365#127C4×D1311yescharacteristic
366#124—21no—
367#121—21no—
368#121C4×D1311yescharacteristic
369#121C4×D1311yescharacteristic
370C4×Q8—131no—
371C4×Q8—131no—
372C4×Q8—131no—
373C4×Q8—131no—
374C4×Q8—261no—
375C4×Q8—261no—
376C4×D4—21no—
377C4×D4C22×D1311yescharacteristic
378C4×D4C22×D1311yescharacteristic
379C2×C4⋊C4—131no—
380C2×C4⋊C4—261no—
381C2×C42—261no—
382C2×C42C22×D1311yescharacteristic
383#106—131no—
384#106—131no—
385#106—131no—
386#106—131no—
387C4⋊C8—21no—
388C4⋊C8—131no—
389C4⋊C8—131no—
390C4⋊C8—131no—
391C4⋊C8—131no—
392C4⋊C8—131no—
393C4⋊C8—131no—
394C4⋊C8—261no—
395C4⋊C8—261no—
396C4⋊C8—261no—
397C4⋊C8—261no—
398C4⋊C8C22×D1311yescharacteristic
399C4⋊C8C22×D1311yescharacteristic
400#103—131no—
401#103—131no—
402#103—131no—
403#103—131no—
404#102—131no—
405#102—131no—
406#102—131no—
407#102—131no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—131no—
411C22⋊C8—131no—
412C22⋊C8—131no—
413C22⋊C8—131no—
414C22⋊C8—261no—
415C22⋊C8—261no—
416C22⋊C8—261no—
417C22⋊C8—261no—
418C22⋊C8—261no—
419#97—21no—
420#97—261no—
421#97—261no—
422C4×C8—131no—
423C4×C8—131no—
424C4×C8—131no—
425C4×C8—131no—
426C4×C8—261no—
427C4×C8—261no—
428C4×C8—261no—
429C4×C8C22×D1311yescharacteristic
430C4×C8C22×D1311yescharacteristic
431C2×C13—41no—
432C2×C13—81no—
433C2×C13—81no—
434C2×C13#293311yescharacteristic
435C2×C13#294911yescharacteristic
436C2×C13#295511yescharacteristic
437#41—81no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—131no—
441C2×Q8—131no—
442C2×Q8—262no—
443C2×Q8—261no—
444C2×Q8—521no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4C2×C4×D1311yescharacteristic
450C2×D4C2×C4×D1311yescharacteristic
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4C2×C4×D1311yescharacteristic
456C22×C4D4×D1311yescharacteristic
457C22×C4#612911yescharacteristic
458SD16—262no—
459SD16—262no—
460SD16—521no—
461SD16—521no—
462M16—1041no—
463M16—1041no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—131no—
469C2×C8—131no—
470C2×C8—131no—
471C2×C8—131no—
472C2×C8—131no—
473C2×C8—131no—
474C2×C8—131no—
475C2×C8—131no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—1041no—
479C2×C8—1041no—
480C4⋊C4—21no—
481C4⋊C4—131no—
482C4⋊C4—131no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4C2×C4×D1311yescharacteristic
489C4⋊C4C2×C4×D1311yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C42—261no—
495C42—261no—
496C42—261no—
497C42—261no—
498C42C2×C4×D1311yescharacteristic
499C42D4×D1311yescharacteristic
500C42#612911yescharacteristic
501C42C23×D1311yescharacteristic
502C13#1803011yescharacteristic, complemented, Sylow
503C23—21no—
504C23—21no—
505C23#8813511yescharacteristic
506Q8—81no—
507Q8—132no—
508Q8—261no—
509Q8—261no—
510Q8—261no—
511Q8—522no—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—42no—
517D4—81no—
518D4—81no—
519D4—81no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—522no—
536C2×C4—522no—
537C2×C4#8813511yescharacteristic
538C2×C4#8813511yescharacteristic
539C2×C4#8813511yescharacteristic
540C2×C4C22×C4×D1311yescharacteristic
541C2×C4C2×D4×D1311yescharacteristic
542C2×C4C2×#612911yescharacteristic
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—261no—
548C8—261no—
549C8—261no—
550C8—261no—
551C8—261no—
552C8—261no—
553C8—261no—
554C8—261no—
555C8—521no—
556C8—521no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22C2×#8813511yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—41no—
572C4—41no—
573C4—262no—
574C4—521no—
575C4—521no—
576C4—521no—
577C4D13×#13111yescharacteristic
578C4#1171945511yescharacteristic
579C4#1171948011yescharacteristic
580C4#1171948011yescharacteristic
581C2—41no—
582C2—81no—
583C2—81no—
584C2#1312356611yescharacteristic
585C2#1312369811yescharacteristic
586C2#1312373511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1496C2
socleC22×C13C2×C4×D4
prime radicalC13×#532C22
cosocleC42×C13C24
hypercenter#1496D13
hypocenterC13#18030
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1496

Complements

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

NH ≅ G/Ntype
2. #13123926C2semidirect
4. #13113735C2semidirect
5. #13113729C2semidirect
6. #13113717C2semidirect
7. #13113690C2semidirect
8. #13113682C2semidirect
9. #13113669C2semidirect
10. #13113645C2semidirect
11. #13113639C2semidirect
12. #13113617C2semidirect
13. #13113232C2semidirect
14. #13113136C2semidirect
502. C13#18030semidirect

Maximal subgroups

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

subgroupindex
#131248632
#131239262
#131239032
#131137352
#131137292
#131137172
#131136902
#131136822
#131136692
#131136452
#131136392
#131136172
#131132322
#131131362
C13×#14962
#1803013