Finite Group Databasebeta

← #15833646

Subgroups — #15833646

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125402C211yesmaximal, characteristic
2#13123814C211yesmaximal, characteristic, complemented
3#13123813C211yesmaximal, characteristic, complemented
4#13113689C211yesmaximal, characteristic, complemented
5#13113686C211yesmaximal, characteristic, complemented
6#13113678C211yesmaximal, characteristic, complemented
7#13113674C211yesmaximal, characteristic, complemented
8#13113673C211yesmaximal, characteristic, complemented
9#13113663C211yesmaximal, characteristic, complemented
10#13113662C211yesmaximal, characteristic, complemented
11#13113596C211yesmaximal, characteristic, complemented
12#13113295C211yesmaximal, characteristic, complemented
13#13113293C211yesmaximal, characteristic, complemented
14D13×#322C211yesmaximal, characteristic, complemented
15C13×#1583C211yesmaximal, characteristic, complemented
16#11719285C2211yescharacteristic
17#11719262C2211yescharacteristic
18C8×Q8×C13C2211yescharacteristic
19C4×C13×SD16C2211yescharacteristic
20C13×#436C2211yescharacteristic
21#11718832C411yescharacteristic
22#11718829C411yescharacteristic
23#11718788—21no—
24#11718783—21no—
25C4×#6107C2211yescharacteristic
26#11718685C2211yescharacteristic
27C4×#6104C2211yescharacteristic
28D4×#1055C2211yescharacteristic
29#11718525C411yescharacteristic
30#11718519C411yescharacteristic
31#11718501—21no—
32#11718499C2211yescharacteristic
33#11718497—21no—
34#11718496C2211yescharacteristic
35#11718496C2211yescharacteristic
36#11718491C2211yescharacteristic
37#11718474C411yescharacteristic
38#11718461C411yescharacteristic
39#11718436C411yescharacteristic
40#11718429C411yescharacteristic
41#11718386—21no—
42#11718381—21no—
43C4×#6095C2211yescharacteristic
44#11718350—21no—
45C8×D52—21no—
46C8×D52C2211yescharacteristic
47C4×C8×D13C2211yescharacteristic
48C4×C8×D13C2211yescharacteristic
49C4×C8×D13C2211yescharacteristic
50#11718340C2211yescharacteristic
51C13×#334C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718071C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718049C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718047C2211yescharacteristic
65#11718046C2211yescharacteristic
66#11718046C2211yescharacteristic
67C2×C13×SD16C2×C411yescharacteristic
68C2×C13×M16—21no—
69C4×Q8×C13C2311yescharacteristic
70C4×D4×C13C2311yescharacteristic
71#88201C2×C411yescharacteristic
72#88200C2×C411yescharacteristic
73C2×#6107C2×C411yescharacteristic
74#88192C2×C411yescharacteristic
75#88190C2×C411yescharacteristic
76C2×#6104C2×C411yescharacteristic
77C4×C22⋊D13—21no—
78#88180—21no—
79C22×#1055—21no—
80C2×#6095C2×C411yescharacteristic
81C2×#6094—21no—
82C2×C8×D13—21no—
83C2×C8×D13—21no—
84C2×C8×D13C2×C411yescharacteristic
85C2×C8×D13C2×C411yescharacteristic
86C2×C8×D13D411yescharacteristic
87C2×C8×D13D411yescharacteristic
88#88152—21no—
89#88151C2×C411yescharacteristic
90#88149C2×C411yescharacteristic
91#88148—21no—
92#88144C2×C411yescharacteristic
93#88144C2×C411yescharacteristic
94#88137—21no—
95#88133—21no—
96C4×D52—21no—
97C4×D52C2311yescharacteristic
98#88126—21no—
99C42×D13C2311yescharacteristic
100C4×Dic26C2311yescharacteristic
101C13×#106C2×C411yescharacteristic
102C13×C4⋊C8—21no—
103C13×C4⋊C8C2311yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C13×#103C2×C411yescharacteristic
106C13×#102C2×C411yescharacteristic
107C13×C22⋊C8—21no—
108C4×C8×C13—21no—
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112#88075C2×C411yescharacteristic
113#88072C2×C411yescharacteristic
114C22⋊#1055—21no—
115#88061C2×C411yescharacteristic
116#88060—21no—
117#88060—21no—
118#88060—21no—
119#88060—21no—
120#88057C2×C411yescharacteristic
121#88056C2×C411yescharacteristic
122#88055—21no—
123#88055—21no—
124#88055—21no—
125#88054—21no—
126#88054—21no—
127C8×Dic13—21no—
128C8×Dic13—21no—
129C8×Dic13C2×C411yescharacteristic
130C8×Dic13C2×C411yescharacteristic
131C8×Dic13D411yescharacteristic
132C8×Dic13D411yescharacteristic
133#88050C2×C411yescharacteristic
134#88049C2×C411yescharacteristic
135#88047C2×C411yescharacteristic
136#88047C2×C411yescharacteristic
137C4⋊#1055—21no—
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140#88043—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17978—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×D4×C13C22×C411yescharacteristic
147C22×C4×C13—21no—
148C2×C22⋊D13—21no—
149C2×D52—21no—
150C2×D52C22×C411yescharacteristic
151C2×C4×D13—21no—
152C2×C4×D13C22×C411yescharacteristic
153C2×C4×D13C2×D411yescharacteristic
154C2×C4×D13#4111yescharacteristic
155C2×Dic26C22×C411yescharacteristic
156C13×SD16—41no—
157C13×M16—42no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13C22×C411yescharacteristic
162C2×C8×C13C22×C411yescharacteristic
163C2×C8×C13C2×D411yescharacteristic
164C2×C8×C13C2×D411yescharacteristic
165C13×C4⋊C4—21no—
166C13×C4⋊C4C22×C411yescharacteristic
167C13×C4⋊C4C22×C411yescharacteristic
168C13×C22⋊C4—21no—
169C42×C13—21no—
170C42×C13C2411yescharacteristic
171C22⋊Dic13—21no—
172C22⋊Dic13—21no—
173C22⋊Dic13—21no—
174#6107—41no—
175#6104—41no—
176#6103—21no—
177#6103—21no—
178#6103—21no—
179#6103—21no—
180#6103—21no—
181#6103—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13C22×C411yescharacteristic
186C4⋊Dic13C22×C411yescharacteristic
187#6101—21no—
188#6101—21no—
189#6101—21no—
190#6101—21no—
191C4×Dic13—21no—
192C4×Dic13C22×C411yescharacteristic
193C4×Dic13C2×D411yescharacteristic
194C4×Dic13#4111yescharacteristic
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—42no—
199C2×#1055C22×C411yescharacteristic
200C2×#1055C22×C411yescharacteristic
201C2×#1055C2×D411yescharacteristic
202C2×#1055C2×D411yescharacteristic
203#6095—41no—
204#6094—42no—
205C8×D13—22no—
206C8×D13—22no—
207C8×D13—41no—
208C8×D13—41no—
209C8×D13—42no—
210C8×D13—42no—
211#3168—131no—
212#2966—131no—
213#2966—131no—
214#1584—131no—
215#1584—131no—
216#1583—131no—
217#1583D1311yescharacteristic, complemented
218#1582—131no—
219#1582—131no—
220#1581—131no—
221#1581—131no—
222#1568—131no—
223#1494—131no—
224#1494—131no—
225C2×#322—131no—
226C23×C13—21no—
227C22×D13—21no—
228C22×D13C4×D411yescharacteristic
229Q8×C13—21no—
230Q8×C13—21no—
231D4×C13—21no—
232D4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13C23×C411yescharacteristic
239C2×C4×C13C22×D411yescharacteristic
240C2×C4×C13C2×#4111yescharacteristic
241C22⋊D13—42no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13C4×D411yescharacteristic
246C2×Dic13C4×D411yescharacteristic
247C2×Dic13C4×D411yescharacteristic
248D52—21no—
249D52—21no—
250D52—42no—
251C4×D13—22no—
252C4×D13—21no—
253C4×D13—21no—
254C4×D13—21no—
255C4×D13—21no—
256C4×D13—41no—
257C4×D13—41no—
258Dic26—21no—
259Dic26—21no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—21no—
263C8×C13—41no—
264C8×C13—41no—
265C8×C13—41no—
266C8×C13#13512yes—
267#1055—21no—
268#1055—21no—
269#1055—21no—
270#1055—41no—
271#1055—41no—
272#1055—41no—
273#1055#13512yes—
274#529—131no—
275#529—131no—
276#499—131no—
277#495—131no—
278#488—131no—
279#488—131no—
280#467—131no—
281#466—131no—
282#465—131no—
283#465—131no—
284#446—131no—
285#446—131no—
286C8×Q8—131no—
287C8×Q8C2×D1311yescharacteristic
288C4×Q16—131no—
289C4×SD16—131no—
290C4×SD16C2×D1311yescharacteristic
291C4×D8—131no—
292#436—131no—
293#436C2×D1311yescharacteristic
294#435—261no—
295#435—261no—
296C8×D4—131no—
297C8×D4—131no—
298C8×D4—261no—
299C8×D4—261no—
300#433—261no—
301#433—261no—
302#432—131no—
303#432—131no—
304#405—261no—
305#405—261no—
306C2×C4×C8—131no—
307C2×C4×C8—131no—
308C2×C4×C8—131no—
309#335—131no—
310#335—131no—
311#334—131no—
312#334C2×D1311yescharacteristic
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316Q8⋊C8C2×D1311yescharacteristic
317D4⋊C8—131no—
318D4⋊C8—131no—
319D4⋊C8—131no—
320D4⋊C8C2×D1311yescharacteristic
321#322—131no—
322#322—131no—
323#322—131no—
324#322C2×D1311yescharacteristic
325C22×C13—41no—
326C22×C13—41no—
327C22×C13—41no—
328C22×C13C2×C4×D411yescharacteristic
329C2×D13—21no—
330C2×D13—21no—
331C2×D13—41no—
332C2×D13—41no—
333C2×D13—41no—
334C2×D13#44412yes—
335C4×C13—21no—
336C4×C13—41no—
337C4×C13—41no—
338C4×C13—41no—
339C4×C13#56811yescharacteristic
340C4×C13#56811yescharacteristic
341C4×C13C2×#13511yescharacteristic
342C4×C13C2×#13511yescharacteristic
343Dic13—21no—
344Dic13—21no—
345Dic13—21no—
346Dic13—41no—
347Dic13—41no—
348Dic13—41no—
349C2×Q16—131no—
350C2×SD16—131no—
351C2×SD16C4×D1311yescharacteristic
352C2×D8—131no—
353C2×M16—21no—
354C2×M16—261no—
355C22×C8—131no—
356C22×C8—131no—
357C22×C8—131no—
358C22×C8—131no—
359C22×C8—261no—
360C22×C8—261no—
361C22×C8—261no—
362#126—261no—
363#126—261no—
364#125—131no—
365#125—131no—
366#124—131no—
367#124—131no—
368#123—261no—
369#123—261no—
370C22⋊Q8—131no—
371C22⋊Q8—131no—
372#121—131no—
373#121—131no—
374C4×Q8—131no—
375C4×Q8C22×D1311yescharacteristic
376C4×D4—131no—
377C4×D4—261no—
378C4×D4—261no—
379C4×D4C22×D1311yescharacteristic
380#117—261no—
381#117—261no—
382C2×C42—131no—
383#107—131no—
384#107—131no—
385#106—131no—
386#106C4×D1311yescharacteristic
387C4⋊C8—21no—
388C4⋊C8—131no—
389C4⋊C8—131no—
390C4⋊C8—261no—
391C4⋊C8—261no—
392C4⋊C8—261no—
393C4⋊C8C22×D1311yescharacteristic
394C4⋊C8C22×D1311yescharacteristic
395#103—131no—
396#103—131no—
397#103—131no—
398#103C4×D1311yescharacteristic
399#102—131no—
400#102—131no—
401#102—131no—
402#102C4×D1311yescharacteristic
403C22⋊C8—21no—
404C22⋊C8—261no—
405C22⋊C8—261no—
406C22⋊C8—261no—
407C22⋊C8—261no—
408C22⋊C8—261no—
409#97—261no—
410#97—261no—
411#97—261no—
412#97—261no—
413C4×C8—21no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—131no—
417C4×C8—131no—
418C4×C8—131no—
419C4×C8—131no—
420C4×C8—131no—
421C4×C8—261no—
422C4×C8—261no—
423C4×C8C22×D1311yescharacteristic
424C4×C8C22×D1311yescharacteristic
425C4×C8C22×D1311yescharacteristic
426C2×C13—81no—
427C2×C13#293211yescharacteristic
428C2×C13C4×#13511yescharacteristic
429C2×C13C2×#44411yescharacteristic
430D13—22no—
431D13—81no—
432C2×Q8—131no—
433C2×Q8C2×C4×D1311yescharacteristic
434C2×D4—131no—
435C2×D4—261no—
436C2×D4—261no—
437C2×D4C2×C4×D1311yescharacteristic
438C22×C4—21no—
439C22×C4—131no—
440C22×C4—131no—
441C22×C4—131no—
442C22×C4—261no—
443Q16—521no—
444SD16—41no—
445SD16—521no—
446D8—521no—
447M16—42no—
448M16—522no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—131no—
456C2×C8—262no—
457C2×C8—262no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—521no—
462C2×C8—521no—
463C2×C8—522no—
464C2×C8—522no—
465C2×C8—522no—
466C2×C8C2×C4×D1311yescharacteristic
467C2×C8C2×C4×D1311yescharacteristic
468C2×C8D4×D1311yescharacteristic
469C2×C8D4×D1311yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—131no—
472C4⋊C4—131no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4C2×C4×D1311yescharacteristic
481C4⋊C4C2×C4×D1311yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—261no—
484C22⋊C4—261no—
485C22⋊C4—261no—
486C22⋊C4—261no—
487C22⋊C4—261no—
488C22⋊C4—261no—
489C22⋊C4—261no—
490C22⋊C4—261no—
491C22⋊C4—261no—
492C42—21no—
493C42—131no—
494C42—131no—
495C42—131no—
496C42—261no—
497C42C23×D1311yescharacteristic
498C13#1797811yescharacteristic, complemented, Sylow
499C23—21no—
500C23—131no—
501C23—261no—
502Q8—21no—
503Q8—21no—
504Q8—261no—
505Q8—261no—
506D4—21no—
507D4—21no—
508D4—261no—
509D4—261no—
510D4—522no—
511D4—522no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—131no—
518C2×C4—131no—
519C2×C4—131no—
520C2×C4—262no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4C22×C4×D1311yescharacteristic
531C2×C4C2×D4×D1311yescharacteristic
532C2×C4#41×D1311yescharacteristic
533C8—21no—
534C8—21no—
535C8—21no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—132no—
540C8—261no—
541C8—261no—
542C8—261no—
543C8—521no—
544C8—521no—
545C8—521no—
546C8#8817012yes—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—132no—
551C22—261no—
552C22—261no—
553C22—521no—
554C22—521no—
555C22—521no—
556C22C4×D4×D1311yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—261no—
562C4—261no—
563C4—261no—
564C4—521no—
565C4—521no—
566C4—521no—
567C4#1171945011yescharacteristic
568C4#1171945511yescharacteristic
569C4C2×#8817011yescharacteristic
570C4D13×#13511yescharacteristic
571C2—81no—
572C2—262no—
573C2—1041no—
574C2#1312355011yescharacteristic
575C2C4×#8817011yescharacteristic
576C2D13×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1583C2
socleC22×C13C2×C4×D4
prime radical#11718436C4
cosocleC42×C13C24
hypercenter#1583D13
hypocenterC13#17978
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
2. #13123814C2semidirect
3. #13123813C2semidirect
4. #13113689C2semidirect
5. #13113686C2semidirect
6. #13113678C2semidirect
7. #13113674C2semidirect
8. #13113673C2semidirect
9. #13113663C2semidirect
10. #13113662C2semidirect
11. #13113596C2semidirect
12. #13113295C2semidirect
13. #13113293C2semidirect
14. D13×#322C2semidirect
15. C13×#1583C2semidirect
217. #1583D13semidirect
498. C13#17978semidirect

Maximal subgroups

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

subgroupindex
#131254022
#131238142
#131238132
#131136892
#131136862
#131136782
#131136742
#131136732
#131136632
#131136622
#131135962
#131132952
#131132932
D13×#3222
C13×#15832
#1797813