Finite Group Databasebeta

← #15834867

Subgroups — #15834867

Order 3328.

612 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#13125431C211yesmaximal, characteristic
2#13123998C211yesmaximal, characteristic, complemented
3#13123902C211yesmaximal, characteristic, complemented
4#13113740C211yesmaximal, characteristic, complemented
5#13113722C211yesmaximal, characteristic, complemented
6#13113716C211yesmaximal, characteristic, complemented
7#13113702C211yesmaximal, characteristic, complemented
8#13113674C211yesmaximal, characteristic, complemented
9#13113667C211yesmaximal, characteristic, complemented
10#13113661C211yesmaximal, characteristic, complemented
11C8×#6095C211yesmaximal, characteristic, complemented
12#13113588C211yesmaximal, characteristic, complemented
13#13113245C211yesmaximal, characteristic, complemented
14#13113236C211yesmaximal, characteristic, complemented
15C13×#1453C211yesmaximal, characteristic, complemented
16#11719184C2211yescharacteristic
17#11719182C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C4×C13×M16C2211yescharacteristic
21#11718796C411yescharacteristic
22#11718796C411yescharacteristic
23#11718795C411yescharacteristic
24#11718795C411yescharacteristic
25#11718586C2211yescharacteristic
26C2×C4⋊#1055C2211yescharacteristic
27#11718501—21no—
28#11718500—21no—
29#11718499—21no—
30#11718495—21no—
31#11718391—21no—
32#11718388—21no—
33#11718388—21no—
34#11718386—21no—
35#11718375C411yescharacteristic
36#11718374C411yescharacteristic
37#11718373C411yescharacteristic
38#11718363C411yescharacteristic
39C4×D104C2211yescharacteristic
40C4×D104C2211yescharacteristic
41C4×#6095C2211yescharacteristic
42C4×#6095C2211yescharacteristic
43#11718349C2211yescharacteristic
44#11718349C2211yescharacteristic
45#11718349C2211yescharacteristic
46C8×D52C2211yescharacteristic
47C8×D52C2211yescharacteristic
48C8×D52C2211yescharacteristic
49#11718340C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#322C2211yescharacteristic
52C13×#322C2211yescharacteristic
53C13×#322C2211yescharacteristic
54C82×C13C2211yescharacteristic
55#11718051C2211yescharacteristic
56#11718051C2211yescharacteristic
57#11718051C2211yescharacteristic
58#11718051C2211yescharacteristic
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718050C2211yescharacteristic
62#11718050C2211yescharacteristic
63#11718049C2211yescharacteristic
64#11718049C2211yescharacteristic
65#11718048C2211yescharacteristic
66#11718048C2211yescharacteristic
67C2×#6127—21no—
68C2×C13×M16C2×C411yescharacteristic
69C2×C13×M16C2×C411yescharacteristic
70C2×C42×C13C2311yescharacteristic
71#88184—21no—
72#88184C2×C411yescharacteristic
73#88184C2×C411yescharacteristic
74#88184C2×C411yescharacteristic
75#88183—21no—
76C4×C22⋊D13—21no—
77#88178C2×C411yescharacteristic
78C22×#1055—21no—
79C2×D104C2×C411yescharacteristic
80C2×D104C2×C411yescharacteristic
81C2×#6095C2×C411yescharacteristic
82C2×#6095C2×C411yescharacteristic
83C2×#6094—21no—
84C2×#6094—21no—
85C2×#6094—21no—
86C2×C8×D13—21no—
87C2×C8×D13—21no—
88C2×C8×D13—21no—
89#88130—21no—
90#88129—21no—
91#88129C2×C411yescharacteristic
92#88128C2×C411yescharacteristic
93C4×D52—21no—
94C4×D52C2311yescharacteristic
95C4×D52C2311yescharacteristic
96C4×D52C2311yescharacteristic
97#88126—21no—
98#88124C2×C411yescharacteristic
99#88123C2×C411yescharacteristic
100C4×Dic26C2311yescharacteristic
101C13×C4⋊C8—21no—
102C13×C4⋊C8D411yescharacteristic
103C13×C4⋊C8D411yescharacteristic
104C13×C22⋊C8—21no—
105C13×C22⋊C8D411yescharacteristic
106C13×C22⋊C8D411yescharacteristic
107C13×#97C2×C411yescharacteristic
108C13×#97C2×C411yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114C4×C8×C13C2311yescharacteristic
115C22⋊#1055—21no—
116#88061C2×C411yescharacteristic
117#88061C2×C411yescharacteristic
118#88061C2×C411yescharacteristic
119#88061C2×C411yescharacteristic
120#88061C2×C411yescharacteristic
121#88061C2×C411yescharacteristic
122#88060—21no—
123#88060—21no—
124#88060—21no—
125#88060—21no—
126#88060—21no—
127#88060—21no—
128#88058C2×C411yescharacteristic
129#88058C2×C411yescharacteristic
130#88057C2×C411yescharacteristic
131#88057C2×C411yescharacteristic
132#88056C2×C411yescharacteristic
133#88056C2×C411yescharacteristic
134#88055—21no—
135#88054—21no—
136#88054—21no—
137C8×Dic13—21no—
138C4⋊#1055—21no—
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142C4⋊#1055C2311yescharacteristic
143C4×#1055—21no—
144#18082—131nomaximal, Sylow
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13#4111yescharacteristic
148C2×C22⋊D13—21no—
149C2×C22⋊D13—21no—
150C2×C22⋊D13—21no—
151#6127—81no—
152#6127—81no—
153C2×D52—21no—
154C2×D52—21no—
155C2×D52C22×C411yescharacteristic
156C2×D52C22×C411yescharacteristic
157C2×D52C22×C411yescharacteristic
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×Dic26—21no—
162C2×Dic26C22×C411yescharacteristic
163C13×M16—22no—
164C13×M16—41no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13C22×C411yescharacteristic
168C2×C8×C13C22×C411yescharacteristic
169C2×C8×C13C22×C411yescharacteristic
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C2×D411yescharacteristic
172C2×C8×C13C2×D411yescharacteristic
173C2×C8×C13C2×D411yescharacteristic
174C2×C8×C13C2×D411yescharacteristic
175C42×C13C22×C411yescharacteristic
176C42×C13C2×D411yescharacteristic
177C42×C13#4111yescharacteristic
178C42×C13C2411yescharacteristic
179C22⋊Dic13—21no—
180#6103—21no—
181#6103—21no—
182#6103—21no—
183#6103—21no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187#6103—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13C22×C411yescharacteristic
190C4⋊Dic13C22×C411yescharacteristic
191C4⋊Dic13C22×C411yescharacteristic
192C4⋊Dic13C22×C411yescharacteristic
193#6101—21no—
194#6101—21no—
195#6101—21no—
196#6101—21no—
197C4×Dic13—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—81no—
203D104—22no—
204D104—41no—
205#6095—22no—
206#6095—41no—
207#6094—81no—
208#6094—81no—
209#6094—81no—
210C8×D13—81no—
211C8×D13—81no—
212C8×D13—81no—
213#3171—131no—
214#2994—131no—
215#2979—131no—
216#1592—131no—
217#1589—131no—
218#1588—131no—
219#1586—131no—
220#1582—131no—
221#1581—131no—
222#1580—131no—
223C8×SD16—131no—
224#1565—131no—
225#1482—131no—
226#1480—131no—
227#1453D1311yescharacteristic, complemented
228C23×C13C4×D411yescharacteristic
229C22×D13—21no—
230C22×D13—21no—
231C22×D13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—41no—
237C2×C4×C13C4×D411yescharacteristic
238C2×C4×C13C4×D411yescharacteristic
239C2×C4×C13C4×D411yescharacteristic
240C2×C4×C13C23×C411yescharacteristic
241C2×C4×C13C22×D411yescharacteristic
242C2×C4×C13C2×#4111yescharacteristic
243C22⋊D13—42no—
244C22⋊D13—81no—
245C22⋊D13—81no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251D52—21no—
252D52—21no—
253D52—21no—
254D52—21no—
255D52—21no—
256D52—21no—
257D52—42no—
258D52—81no—
259C4×D13—41no—
260C4×D13—41no—
261C4×D13—41no—
262C4×D13—41no—
263C4×D13—41no—
264C4×D13—41no—
265Dic26—21no—
266Dic26—21no—
267Dic26—81no—
268C8×C13—21no—
269C8×C13—21no—
270C8×C13—21no—
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—21no—
274C8×C13—21no—
275C8×C13—41no—
276C8×C13—41no—
277C8×C13#13112yes—
278#1055—41no—
279#1055—41no—
280#1055—41no—
281#1055—41no—
282#532—131no—
283#529—131no—
284#501—131no—
285#496—131no—
286#490—131no—
287#489—131no—
288#469—131no—
289#469—131no—
290#468—131no—
291#468—131no—
292#446—131no—
293C8×Q8—131no—
294C4×SD16—131no—
295C4×SD16—131no—
296C4×D8—131no—
297C4×D8—131no—
298#436—131no—
299#436—131no—
300#436—131no—
301#436—261no—
302#435—261no—
303C8×D4—131no—
304C8×D4—131no—
305C8×D4—131no—
306C8×D4—261no—
307C8×D4—261no—
308#433—261no—
309#431—131no—
310#431C2×D1311yescharacteristic
311#431C2×D1311yescharacteristic
312#424—261no—
313C2×C4⋊C8—131no—
314#408—261no—
315#408—261no—
316C4×M16C2×D1311yescharacteristic
317#335—131no—
318#335—131no—
319#334—131no—
320#334—131no—
321Q8⋊C8—131no—
322Q8⋊C8—131no—
323D4⋊C8—131no—
324D4⋊C8—131no—
325D4⋊C8—131no—
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329#322C2×D1311yescharacteristic
330#322C2×D1311yescharacteristic
331#322C2×D1311yescharacteristic
332C82C2×D1311yescharacteristic
333C22×C13—21no—
334C22×C13—21no—
335C22×C13—21no—
336C22×C13C2×C4×D411yescharacteristic
337C2×D13—41no—
338C2×D13—41no—
339C2×D13—41no—
340C2×D13—41no—
341C2×D13—41no—
342C2×D13—41no—
343C2×D13—41no—
344C2×D13—41no—
345C2×D13—41no—
346C4×C13—21no—
347C4×C13—21no—
348C4×C13—21no—
349C4×C13—21no—
350C4×C13C2×#13111yescharacteristic
351C4×C13#56811yescharacteristic
352C4×C13#57611yescharacteristic
353C4×C13#57711yescharacteristic
354Dic13—41no—
355Dic13—41no—
356Dic13—41no—
357Dic13—41no—
358Dic13—41no—
359C2×#41—261no—
360C2×SD16—131no—
361C2×SD16—131no—
362C2×D8—131no—
363C2×D8—131no—
364C2×M16—261no—
365C2×M16—261no—
366C2×M16—261no—
367C2×M16C4×D1311yescharacteristic
368C2×M16C4×D1311yescharacteristic
369C22×C8—261no—
370C22×C8—261no—
371C22×C8—261no—
372C22×C8—261no—
373C4⋊Q8—131no—
374#127—131no—
375#126—261no—
376#125—131no—
377#124—131no—
378#124—261no—
379#123—261no—
380C22⋊Q8—131no—
381#121—131no—
382#121—131no—
383#121—131no—
384#121—261no—
385C4×Q8—131no—
386C4×D4—131no—
387C4×D4—131no—
388C4×D4—131no—
389C4×D4—261no—
390C4×D4—261no—
391#117—261no—
392C2×C42C22×D1311yescharacteristic
393#107—131no—
394#107—131no—
395#106—131no—
396#106—131no—
397C4⋊C8—21no—
398C4⋊C8—131no—
399C4⋊C8—131no—
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—261no—
403C4⋊C8—261no—
404C4⋊C8—261no—
405C4⋊C8D5211yescharacteristic
406C4⋊C8D5211yescharacteristic
407#103—131no—
408#103—131no—
409#102—131no—
410#102—131no—
411#102—131no—
412#102—131no—
413#102—131no—
414#102—131no—
415C22⋊C8—21no—
416C22⋊C8—261no—
417C22⋊C8—261no—
418C22⋊C8—261no—
419C22⋊C8—261no—
420C22⋊C8—261no—
421C22⋊C8—261no—
422C22⋊C8—261no—
423C22⋊C8D5211yescharacteristic
424C22⋊C8D5211yescharacteristic
425#97—261no—
426#97C4×D1311yescharacteristic
427#97C4×D1311yescharacteristic
428C4×C8—261no—
429C4×C8—261no—
430C4×C8C22×D1311yescharacteristic
431C4×C8C22×D1311yescharacteristic
432C4×C8C22×D1311yescharacteristic
433C4×C8C22×D1311yescharacteristic
434C4×C8C22×D1311yescharacteristic
435C4×C8C22×D1311yescharacteristic
436C2×C13—41no—
437C2×C13#293511yescharacteristic
438C2×C13#294611yescharacteristic
439C2×C13#295511yescharacteristic
440D13—81no—
441D13—81no—
442D13—81no—
443#41—1041no—
444#41—1041no—
445C2×Q8—131no—
446C2×Q8—261no—
447C2×D4—131no—
448C2×D4—131no—
449C2×D4—131no—
450C2×D4—261no—
451C2×D4—261no—
452C2×D4—261no—
453C2×D4—261no—
454C2×D4—261no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4C2×C4×D1311yescharacteristic
459C22×C4C2×D5211yescharacteristic
460C22×C4#612711yescharacteristic
461SD16—262no—
462SD16—521no—
463D8—262no—
464D8—521no—
465M16—22no—
466M16—41no—
467M16—1041no—
468M16—1041no—
469M16—1041no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—1041no—
477C2×C8—1041no—
478C2×C8—1041no—
479C2×C8—1041no—
480C2×C8C2×C4×D1311yescharacteristic
481C2×C8C2×C4×D1311yescharacteristic
482C2×C8C2×C4×D1311yescharacteristic
483C2×C8C2×C4×D1311yescharacteristic
484C2×C8C2×D5211yescharacteristic
485C2×C8C2×D5211yescharacteristic
486C2×C8C2×D5211yescharacteristic
487C2×C8C2×D5211yescharacteristic
488C4⋊C4—131no—
489C4⋊C4—131no—
490C4⋊C4—131no—
491C4⋊C4—131no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C22⋊C4—261no—
498C22⋊C4—261no—
499C22⋊C4—261no—
500C22⋊C4—261no—
501C22⋊C4—261no—
502C22⋊C4—261no—
503C22⋊C4—261no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C42—261no—
507C42C2×C4×D1311yescharacteristic
508C42C2×D5211yescharacteristic
509C42#612711yescharacteristic
510C42C23×D1311yescharacteristic
511C13#1808211yescharacteristic, complemented, Sylow
512C23—261no—
513C23—261no—
514C23—261no—
515C23C4×D5211yescharacteristic
516Q8—261no—
517Q8—261no—
518Q8—1041no—
519D4—261no—
520D4—261no—
521D4—261no—
522D4—261no—
523D4—261no—
524D4—261no—
525D4—522no—
526D4—522no—
527D4—1041no—
528D4—1041no—
529D4—1041no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4C4×D5211yescharacteristic
547C2×C4C4×D5211yescharacteristic
548C2×C4C4×D5211yescharacteristic
549C2×C4C22×C4×D1311yescharacteristic
550C2×C4C22×D5211yescharacteristic
551C2×C4C2×#612711yescharacteristic
552C8—21no—
553C8—21no—
554C8—21no—
555C8—21no—
556C8—21no—
557C8—21no—
558C8—21no—
559C8—41no—
560C8—41no—
561C8—521no—
562C8—521no—
563C8—521no—
564C8—521no—
565C8#8816112yes—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—521no—
570C22—521no—
571C22—521no—
572C22—521no—
573C22—521no—
574C22—521no—
575C22—521no—
576C22—521no—
577C22—521no—
578C22C2×C4×D5211yescharacteristic
579C4—21no—
580C4—21no—
581C4—21no—
582C4—21no—
583C4—521no—
584C4—521no—
585C4—521no—
586C4—521no—
587C4—521no—
588C4C2×#8816111yescharacteristic
589C4#1171945011yescharacteristic
590C4#1171945611yescharacteristic
591C4#1171945711yescharacteristic
592C2—41no—
593C2—1041no—
594C2—1041no—
595C2—1041no—
596C2#1312358211yescharacteristic
597C2#1312367011yescharacteristic
598C2#1312374011yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1453C2
socleC22×C13C2×C4×D4
prime radical#13125431C2
cosocleC42×C13C24
hypercenter#1453D13
hypocenterC13#18082
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1453

Complements

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

NH ≅ G/Ntype
2. #13123998C2semidirect
3. #13123902C2semidirect
4. #13113740C2semidirect
5. #13113722C2semidirect
6. #13113716C2semidirect
7. #13113702C2semidirect
8. #13113674C2semidirect
9. #13113667C2semidirect
10. #13113661C2semidirect
11. C8×#6095C2semidirect
12. #13113588C2semidirect
13. #13113245C2semidirect
14. #13113236C2semidirect
15. C13×#1453C2semidirect
227. #1453D13semidirect
511. C13#18082semidirect

Maximal subgroups

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

subgroupindex
#131254312
#131239982
#131239022
#131137402
#131137222
#131137162
#131137022
#131136742
#131136672
#131136612
C8×#60952
#131135882
#131132452
#131132362
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