Finite Group Databasebeta

← #15833615

Subgroups — #15833615

Order 3328.

592 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125400C211yesmaximal, characteristic
2#13123987C211yesmaximal, characteristic, complemented
3#13113748C211yesmaximal, characteristic, complemented
4#13113743C211yesmaximal, characteristic, complemented
5#13113726C211yesmaximal, characteristic, complemented
6#13113724C211yesmaximal, characteristic, complemented
7#13113658C211yesmaximal, characteristic, complemented
8#13113653C211yesmaximal, characteristic, complemented
9C8×#6106C211yesmaximal, characteristic, complemented
10C8×#6105C211yesmaximal, characteristic, complemented
11#13113591C211yesmaximal, characteristic, complemented
12#13113301C211yesmaximal, characteristic, complemented
13#13113299C211yesmaximal, characteristic, complemented
14#13113120C211yesmaximal, characteristic, complemented
15C13×#2993C211yesmaximal, characteristic, complemented
16C13×#529C2211yescharacteristic
17#11719184C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C13×#436—21no—
21C13×#436C2211yescharacteristic
22C13×#435—21no—
23C8×D4×C13C2211yescharacteristic
24C13×#433—21no—
25C13×#431C2211yescharacteristic
26C13×#424—21no—
27C13×#423C2211yescharacteristic
28#11718729C411yescharacteristic
29#11718725C411yescharacteristic
30#11718720C411yescharacteristic
31#11718717C411yescharacteristic
32#11718712C411yescharacteristic
33#11718709C411yescharacteristic
34#11718702C411yescharacteristic
35#11718699C411yescharacteristic
36C4×#6107C2211yescharacteristic
37C4×#6106C2211yescharacteristic
38C4×#6105C2211yescharacteristic
39C4×#6104C2211yescharacteristic
40#11718586C2211yescharacteristic
41#11718585C2211yescharacteristic
42C2×C4×#1055C2211yescharacteristic
43#11718501—21no—
44#11718500—21no—
45#11718390—21no—
46#11718389—21no—
47#11718349C2211yescharacteristic
48C8×D52C2211yescharacteristic
49#11718340C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718072C2211yescharacteristic
62#11718072C2211yescharacteristic
63#11718046C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×M16—21no—
68C2×C13×M16—21no—
69C22×C8×C13—21no—
70C13×#126—21no—
71C13×#125C2×C411yescharacteristic
72C13×#124C2×C411yescharacteristic
73C13×#123—21no—
74C13×C22⋊Q8C2×C411yescharacteristic
75C13×#121C2×C411yescharacteristic
76C4×Q8×C13C2311yescharacteristic
77C4×D4×C13—21no—
78C4×D4×C13C2311yescharacteristic
79C13×#117—21no—
80C2×C42×C13C2311yescharacteristic
81C2×#6107C2×C411yescharacteristic
82C2×#6106C2×C411yescharacteristic
83C2×#6105C2×C411yescharacteristic
84C2×#6104C2×C411yescharacteristic
85#88184C2×C411yescharacteristic
86#88183—21no—
87C4×C22⋊D13—21no—
88#88178C2×C411yescharacteristic
89C2×#6099—21no—
90C22×#1055C2×C411yescharacteristic
91C22×#1055C2×C411yescharacteristic
92C2×#6094—21no—
93C2×C8×D13—21no—
94#88130—21no—
95#88129C2×C411yescharacteristic
96C4×D52C2311yescharacteristic
97#88126—21no—
98#88124C2×C411yescharacteristic
99C4×Dic26C2311yescharacteristic
100C13×C4⋊C8—21no—
101C13×C4⋊C8—21no—
102C13×C4⋊C8—21no—
103C13×C4⋊C8D411yescharacteristic
104C13×C4⋊C8D411yescharacteristic
105C13×C4⋊C8C2311yescharacteristic
106C13×C4⋊C8C2311yescharacteristic
107C13×C22⋊C8—21no—
108C13×C22⋊C8—21no—
109C13×C22⋊C8D411yescharacteristic
110C13×C22⋊C8D411yescharacteristic
111C13×#97—21no—
112C4×C8×C13—21no—
113C4×C8×C13C2311yescharacteristic
114C4×C8×C13C2311yescharacteristic
115#88075C2×C411yescharacteristic
116#88075C2×C411yescharacteristic
117#88072C2×C411yescharacteristic
118#88072C2×C411yescharacteristic
119C22⋊#1055—21no—
120#88060—21no—
121#88060—21no—
122#88055—21no—
123#88054—21no—
124#88054—21no—
125C8×Dic13—21no—
126#88050C2×C411yescharacteristic
127#88050C2×C411yescharacteristic
128#88049C2×C411yescharacteristic
129#88049C2×C411yescharacteristic
130#88048C2×C411yescharacteristic
131#88048C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134C4⋊#1055—21no—
135C4⋊#1055—21no—
136C4⋊#1055C2311yescharacteristic
137C4⋊#1055C2311yescharacteristic
138C4×#1055C2×C411yescharacteristic
139C4×#1055C2×C411yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17974—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×D4×C13—21no—
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13#4111yescharacteristic
152C2×C22⋊D13—21no—
153C2×D52C22×C411yescharacteristic
154C2×C4×D13—21no—
155C2×Dic26C22×C411yescharacteristic
156C13×M16—81no—
157C13×M16—81no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—81no—
161C2×C8×C13C2×D411yescharacteristic
162C2×C8×C13C2×D411yescharacteristic
163C2×C8×C13C2×D411yescharacteristic
164C2×C8×C13C2×D411yescharacteristic
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4C22×C411yescharacteristic
170C13×C4⋊C4C22×C411yescharacteristic
171C13×C22⋊C4—21no—
172C13×C22⋊C4—21no—
173C13×C22⋊C4—21no—
174C13×C22⋊C4—21no—
175C13×C22⋊C4—21no—
176C42×C13—21no—
177C42×C13C22×C411yescharacteristic
178C42×C13C2×D411yescharacteristic
179C42×C13#4111yescharacteristic
180C42×C13C2411yescharacteristic
181C22⋊Dic13—21no—
182#6107—22no—
183#6106—22no—
184#6105—22no—
185#6104—22no—
186#6103—21no—
187#6103—21no—
188#6103—21no—
189#6103—21no—
190C4⋊Dic13C22×C411yescharacteristic
191C4⋊Dic13C22×C411yescharacteristic
192#6101—21no—
193#6101—21no—
194#6101—21no—
195#6101—21no—
196C4×Dic13—21no—
197#6099—81no—
198C2×#1055—22no—
199C2×#1055—22no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208#6094—81no—
209C8×D13—81no—
210#3168—131no—
211#2993—131no—
212#2993D1311yescharacteristic, complemented
213#1594—131no—
214#1593—131no—
215#1590—131no—
216#1590—131no—
217#1580—131no—
218#1579—131no—
219C8×SD16—131no—
220C8×SD16—131no—
221#1566—131no—
222#1495—131no—
223#1495—131no—
224#1450—131no—
225C23×C13—21no—
226C23×C13C4×D411yescharacteristic
227C22×D13—21no—
228Q8×C13—21no—
229Q8×C13—21no—
230D4×C13—21no—
231D4×C13—21no—
232D4×C13—81no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13C4×D411yescharacteristic
246C2×C4×C13C23×C411yescharacteristic
247C2×C4×C13C22×D411yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C22⋊D13—81no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253D52—21no—
254D52—21no—
255C4×D13—41no—
256C4×D13—41no—
257Dic26—21no—
258Dic26—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—21no—
263C8×C13—41no—
264C8×C13—41no—
265#1055—21no—
266#1055—21no—
267#1055—41no—
268#1055—41no—
269#1055—41no—
270#1055—41no—
271#1055#13112yes—
272#1055#13112yes—
273#529—131no—
274#529C2×D1311yescharacteristic
275#499—131no—
276#495—131no—
277#488—131no—
278#488—131no—
279#467—131no—
280#466—131no—
281#465—131no—
282#465—131no—
283#446—131no—
284#446C2×D1311yescharacteristic
285C8×Q8—131no—
286C8×Q8C2×D1311yescharacteristic
287C4×Q16—131no—
288C4×SD16—131no—
289C4×SD16—131no—
290C4×D8—131no—
291#436—21no—
292#436—131no—
293#436—261no—
294#436C2×D1311yescharacteristic
295#435—21no—
296#435—261no—
297C8×D4—131no—
298C8×D4C2×D1311yescharacteristic
299#433—21no—
300#433—261no—
301#431—131no—
302#431C2×D1311yescharacteristic
303#424—21no—
304#424—261no—
305#423—131no—
306#423C2×D1311yescharacteristic
307C2×C4×C8—131no—
308#334—131no—
309#334—131no—
310#334—131no—
311#334—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316D4⋊C8—131no—
317D4⋊C8—131no—
318D4⋊C8—131no—
319D4⋊C8—131no—
320#322—131no—
321#322—131no—
322C82—131no—
323C82—131no—
324C22×C13—21no—
325C22×C13—21no—
326C22×C13—21no—
327C22×C13—41no—
328C22×C13—41no—
329C22×C13—41no—
330C22×C13C2×C4×D411yescharacteristic
331C2×D13—41no—
332C2×D13—41no—
333C2×D13—41no—
334C4×C13—21no—
335C4×C13—21no—
336C4×C13—21no—
337C4×C13—21no—
338C4×C13—41no—
339C4×C13—41no—
340C4×C13—41no—
341C4×C13C2×#13111yescharacteristic
342C4×C13C2×#13111yescharacteristic
343C4×C13#57711yescharacteristic
344C4×C13#57711yescharacteristic
345Dic13—41no—
346Dic13—41no—
347Dic13—41no—
348C2×Q16—131no—
349C2×SD16—131no—
350C2×SD16—131no—
351C2×D8—131no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—261no—
355C2×M16—261no—
356C22×C8—21no—
357C22×C8—131no—
358C22×C8—131no—
359C22×C8—261no—
360#126—21no—
361#126—261no—
362#125—131no—
363#125C4×D1311yescharacteristic
364#124—131no—
365#124C4×D1311yescharacteristic
366#123—21no—
367#123—261no—
368C22⋊Q8—131no—
369C22⋊Q8C4×D1311yescharacteristic
370#121—131no—
371#121C4×D1311yescharacteristic
372C4×Q8—131no—
373C4×Q8C22×D1311yescharacteristic
374C4×D4—21no—
375C4×D4—131no—
376C4×D4—261no—
377C4×D4C22×D1311yescharacteristic
378#117—21no—
379#117—261no—
380C2×C42C22×D1311yescharacteristic
381#107—131no—
382#107—131no—
383#106—131no—
384#106—131no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—131no—
389C4⋊C8—131no—
390C4⋊C8—261no—
391C4⋊C8—261no—
392C4⋊C8—261no—
393C4⋊C8—261no—
394C4⋊C8C22⋊D1311yescharacteristic
395C4⋊C8C22⋊D1311yescharacteristic
396C4⋊C8C22×D1311yescharacteristic
397C4⋊C8C22×D1311yescharacteristic
398#103—131no—
399#103—131no—
400#103—131no—
401#103—131no—
402#102—131no—
403#102—131no—
404#102—131no—
405#102—131no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—261no—
409C22⋊C8—261no—
410C22⋊C8—261no—
411C22⋊C8C22⋊D1311yescharacteristic
412C22⋊C8C22⋊D1311yescharacteristic
413#97—21no—
414#97—261no—
415C4×C8—21no—
416C4×C8—131no—
417C4×C8—131no—
418C4×C8—131no—
419C4×C8—131no—
420C4×C8—131no—
421C4×C8—131no—
422C4×C8—261no—
423C4×C8C22×D1311yescharacteristic
424C4×C8C22×D1311yescharacteristic
425C2×C13—41no—
426C2×C13—81no—
427C2×C13#293111yescharacteristic
428C2×C13#295211yescharacteristic
429C2×C13#295711yescharacteristic
430D13—81no—
431C2×Q8—131no—
432C2×Q8C2×C4×D1311yescharacteristic
433C2×D4—21no—
434C2×D4—131no—
435C2×D4—261no—
436C2×D4C2×C4×D1311yescharacteristic
437C22×C4—21no—
438C22×C4—261no—
439C22×C4C2×C4×D1311yescharacteristic
440C22×C4#612711yescharacteristic
441C22×C4C2×C22⋊D1311yescharacteristic
442Q16—262no—
443SD16—262no—
444SD16—262no—
445D8—262no—
446M16—81no—
447M16—81no—
448M16—1041no—
449M16—1041no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—81no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—131no—
456C2×C8—131no—
457C2×C8—262no—
458C2×C8—262no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—1041no—
464C2×C8C2×C22⋊D1311yescharacteristic
465C2×C8C2×C22⋊D1311yescharacteristic
466C2×C8C2×C22⋊D1311yescharacteristic
467C2×C8C2×C22⋊D1311yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—131no—
473C4⋊C4—131no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4C2×C4×D1311yescharacteristic
479C4⋊C4C2×C4×D1311yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—261no—
486C22⋊C4—261no—
487C22⋊C4—261no—
488C22⋊C4—261no—
489C22⋊C4—261no—
490C42—21no—
491C42—261no—
492C42C2×C4×D1311yescharacteristic
493C42#612711yescharacteristic
494C42C2×C22⋊D1311yescharacteristic
495C42C23×D1311yescharacteristic
496C13#1797411yescharacteristic, complemented, Sylow
497C23—21no—
498C23—261no—
499C23C4×C22⋊D1311yescharacteristic
500Q8—21no—
501Q8—21no—
502Q8—261no—
503Q8—261no—
504D4—21no—
505D4—21no—
506D4—81no—
507D4—261no—
508D4—261no—
509D4—1041no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—261no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—521no—
524C2×C4—521no—
525C2×C4C4×C22⋊D1311yescharacteristic
526C2×C4C4×C22⋊D1311yescharacteristic
527C2×C4C4×C22⋊D1311yescharacteristic
528C2×C4C22×C4×D1311yescharacteristic
529C2×C4C2×#612711yescharacteristic
530C2×C4C22×C22⋊D1311yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—132no—
538C8—132no—
539C8—261no—
540C8—261no—
541C8—521no—
542C8—521no—
543C8—521no—
544C8—521no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—521no—
552C22—521no—
553C22—521no—
554C22C2×C4×C22⋊D1311yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—521no—
563C4—521no—
564C4—521no—
565C4D13×#13111yescharacteristic
566C4D13×#13111yescharacteristic
567C4#1171954111yescharacteristic
568C4#1171954211yescharacteristic
569C2—41no—
570C2—81no—
571C2—1041no—
572C2#1312354611yescharacteristic
573C2#1312371711yescharacteristic
574C2#1312375111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2993C2
socleC22×C13C2×C4×D4
prime radical#11718699C4
cosocleC42×C13C24
hypercenter#2993D13
hypocenterC13#17974
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #13123987C2semidirect
3. #13113748C2semidirect
4. #13113743C2semidirect
5. #13113726C2semidirect
6. #13113724C2semidirect
7. #13113658C2semidirect
8. #13113653C2semidirect
9. C8×#6106C2semidirect
10. C8×#6105C2semidirect
11. #13113591C2semidirect
12. #13113301C2semidirect
13. #13113299C2semidirect
14. #13113120C2semidirect
15. C13×#2993C2semidirect
212. #2993D13semidirect
496. C13#17974semidirect

Maximal subgroups

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

subgroupindex
#131254002
#131239872
#131137482
#131137432
#131137262
#131137242
#131136582
#131136532
C8×#61062
C8×#61052
#131135912
#131133012
#131132992
#131131202
C13×#29932
#1797413