Finite Group Databasebeta

← #15834324

Subgroups — #15834324

Order 3328.

598 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124848C211yesmaximal, characteristic
2#13123965C211yesmaximal, characteristic, complemented
3#13113736C211yesmaximal, characteristic, complemented
4#13113719C211yesmaximal, characteristic, complemented
5#13113714C211yesmaximal, characteristic, complemented
6#13113712C211yesmaximal, characteristic, complemented
7#13113684C211yesmaximal, characteristic, complemented
8#13113665C211yesmaximal, characteristic, complemented
9#13113648C211yesmaximal, characteristic, complemented
10C8×#6107C211yesmaximal, characteristic, complemented
11#13113610C211yesmaximal, characteristic, complemented
12#13113301C211yesmaximal, characteristic, complemented
13#13113221C211yesmaximal, characteristic, complemented
14#13113136C211yesmaximal, characteristic, complemented
15C13×#2994C211yesmaximal, characteristic, complemented
16C13×#529C2211yescharacteristic
17C4×#6127C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C13×#436C2211yescharacteristic
21C13×#435—21no—
22C8×D4×C13—21no—
23C8×D4×C13C2211yescharacteristic
24C13×#433—21no—
25C13×#431C2211yescharacteristic
26C13×#424—21no—
27C2×C13×C4⋊C8C2211yescharacteristic
28#11718727C411yescharacteristic
29#11718724C411yescharacteristic
30#11718718C411yescharacteristic
31#11718715C411yescharacteristic
32#11718708C411yescharacteristic
33#11718706C411yescharacteristic
34#11718698C411yescharacteristic
35#11718696C411yescharacteristic
36C4×#6107C2211yescharacteristic
37C4×#6106C2211yescharacteristic
38C4×#6105C2211yescharacteristic
39C4×#6104C2211yescharacteristic
40#11718586C2211yescharacteristic
41#11718586C2211yescharacteristic
42#11718585C2211yescharacteristic
43#11718498—21no—
44#11718494—21no—
45#11718390—21no—
46#11718390—21no—
47#11718349C2211yescharacteristic
48#11718349C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718071C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718071C2211yescharacteristic
62#11718071C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×#6127C2×C411yescharacteristic
68C2×C13×M16—21no—
69C22×C8×C13—21no—
70C22×C8×C13—21no—
71C13×#126—21no—
72C13×#125C2×C411yescharacteristic
73C13×#124C2×C411yescharacteristic
74C13×#123—21no—
75C13×C22⋊Q8C2×C411yescharacteristic
76C13×#121C2×C411yescharacteristic
77C4×Q8×C13C2311yescharacteristic
78C4×D4×C13—21no—
79C4×D4×C13C2311yescharacteristic
80C13×#117—21no—
81C2×C42×C13C2311yescharacteristic
82C2×#6107C2×C411yescharacteristic
83C2×#6106C2×C411yescharacteristic
84C2×#6105C2×C411yescharacteristic
85C2×#6104C2×C411yescharacteristic
86C4×C22⋊D13—21no—
87C4×C22⋊D13—21no—
88#88180C2×C411yescharacteristic
89C2×#6099—21no—
90C2×#6094—21no—
91C2×#6094—21no—
92C4×D52C2×C411yescharacteristic
93C4×D52C2311yescharacteristic
94#88126—21no—
95C42×D13—21no—
96C4×Dic26C2×C411yescharacteristic
97C4×Dic26C2311yescharacteristic
98C13×C4⋊C8—21no—
99C13×C4⋊C8—21no—
100C13×C4⋊C8—21no—
101C13×C4⋊C8D411yescharacteristic
102C13×C4⋊C8D411yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C13×C22⋊C8—21no—
106C13×C22⋊C8—21no—
107C13×C22⋊C8D411yescharacteristic
108C13×C22⋊C8D411yescharacteristic
109C13×#97—21no—
110C4×C8×C13—21no—
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113#88075C2×C411yescharacteristic
114#88075C2×C411yescharacteristic
115#88072C2×C411yescharacteristic
116#88072C2×C411yescharacteristic
117C22⋊#1055—21no—
118C22⋊#1055C2×C411yescharacteristic
119C22⋊#1055C2×C411yescharacteristic
120#88060—21no—
121#88060—21no—
122#88054—21no—
123#88054—21no—
124C8×Dic13—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⋊#1055C2×C411yescharacteristic
137C4⋊#1055C2×C411yescharacteristic
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18033—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—
153#6127—22no—
154#6127—41no—
155C2×D52C22×C411yescharacteristic
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×Dic26C22×C411yescharacteristic
160C13×M16—81no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—81no—
164C2×C8×C13—81no—
165C2×C8×C13C2×D411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C2×C8×C13C2×D411yescharacteristic
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4C22×C411yescharacteristic
174C13×C4⋊C4C22×C411yescharacteristic
175C13×C22⋊C4—21no—
176C13×C22⋊C4—21no—
177C13×C22⋊C4—21no—
178C13×C22⋊C4—21no—
179C13×C22⋊C4—21no—
180C42×C13—21no—
181C42×C13C22×C411yescharacteristic
182C42×C13C2×D411yescharacteristic
183C42×C13#4111yescharacteristic
184C42×C13C2411yescharacteristic
185C22⋊Dic13—21no—
186#6107—22no—
187#6106—41no—
188#6105—22no—
189#6104—41no—
190#6103—21no—
191#6103—21no—
192C4⋊Dic13C22×C411yescharacteristic
193C4⋊Dic13C22×C411yescharacteristic
194#6101—21no—
195#6101—21no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199#6099—81no—
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—
209#6094—81no—
210#3102—131no—
211#2994D1311yescharacteristic, complemented
212#2991—131no—
213#1592—131no—
214#1589—131no—
215#1588—131no—
216#1588—131no—
217#1584—131no—
218#1581—131no—
219SD16⋊C8—131no—
220C8×Q16—131no—
221#1571—131no—
222#1495—131no—
223#1477—131no—
224#1454—131no—
225C23×C13—21no—
226C23×C13C4×D411yescharacteristic
227C22×D13—21no—
228Q8×C13—21no—
229Q8×C13—21no—
230D4×C13—21no—
231D4×C13—21no—
232D4×C13—42no—
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—42no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253D52—21no—
254D52—21no—
255C4×D13—42no—
256C4×D13—42no—
257C4×D13—41no—
258C4×D13—41no—
259Dic26—21no—
260Dic26#13112yes—
261C8×C13—21no—
262C8×C13—21no—
263C8×C13—21no—
264C8×C13—21no—
265C8×C13—41no—
266C8×C13—41no—
267#1055—21no—
268#1055—21no—
269#1055—21no—
270#1055—21no—
271#1055—41no—
272#1055—41no—
273#1055—41no—
274#1055—41no—
275#529C2×D1311yescharacteristic
276C4×#41—131no—
277#485—131no—
278#482—131no—
279#479—131no—
280#478—131no—
281#464—131no—
282#463—131no—
283#452—131no—
284#449—131no—
285#446C2×D1311yescharacteristic
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8C2×D1311yescharacteristic
289C4×Q16—131no—
290C4×SD16—131no—
291C4×SD16—131no—
292C4×D8—131no—
293#436—131no—
294#436—131no—
295#436—261no—
296#436—261no—
297#436C2×D1311yescharacteristic
298#435—21no—
299C8×D4—21no—
300C8×D4C2×D1311yescharacteristic
301#433—21no—
302#431—131no—
303#431—131no—
304#431—261no—
305#431C2×D1311yescharacteristic
306#424—21no—
307#423—131no—
308#423—261no—
309C2×C4⋊C8C2×D1311yescharacteristic
310#335—131no—
311#335—131no—
312#335—131no—
313#335—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316Q8⋊C8—131no—
317Q8⋊C8—131no—
318D4⋊C8—131no—
319D4⋊C8—131no—
320D4⋊C8—131no—
321D4⋊C8—131no—
322#322—131no—
323#322—131no—
324#322—131no—
325C82—131no—
326C22×C13—21no—
327C22×C13—21no—
328C22×C13—21no—
329C22×C13—41no—
330C22×C13—41no—
331C22×C13—41no—
332C22×C13C2×C4×D411yescharacteristic
333C2×D13—41no—
334C2×D13—41no—
335C2×D13—41no—
336C4×C13—21no—
337C4×C13—21no—
338C4×C13—21no—
339C4×C13—21no—
340C4×C13—41no—
341C4×C13—41no—
342C4×C13—41no—
343C4×C13C2×#13111yescharacteristic
344C4×C13#56811yescharacteristic
345C4×C13#57611yescharacteristic
346C4×C13#57811yescharacteristic
347Dic13—22no—
348Dic13—41no—
349Dic13—41no—
350C2×#41—131no—
351C2×Q16—131no—
352C2×SD16—131no—
353C2×SD16—131no—
354C2×D8—131no—
355C2×M16—21no—
356C2×M16—261no—
357C2×M16—261no—
358C2×M16—261no—
359C22×C8—21no—
360C22×C8—21no—
361#126—21no—
362#125C4×D1311yescharacteristic
363#124C4×D1311yescharacteristic
364#123—21no—
365C22⋊Q8C4×D1311yescharacteristic
366#121C4×D1311yescharacteristic
367C4×Q8—131no—
368C4×Q8—131no—
369C4×Q8C22×D1311yescharacteristic
370C4×D4—21no—
371C4×D4—131no—
372C4×D4—131no—
373C4×D4—261no—
374C4×D4—261no—
375C4×D4C22×D1311yescharacteristic
376#117—21no—
377#117—131no—
378#117—261no—
379C2×C42—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—131no—
391C4⋊C8—131no—
392C4⋊C8—261no—
393C4⋊C8—261no—
394C4⋊C8—261no—
395C4⋊C8—261no—
396C4⋊C8C22⋊D1311yescharacteristic
397C4⋊C8C22⋊D1311yescharacteristic
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—261no—
413C22⋊C8—261no—
414C22⋊C8—261no—
415C22⋊C8C22⋊D1311yescharacteristic
416C22⋊C8C22⋊D1311yescharacteristic
417#97—21no—
418C4×C8—21no—
419C4×C8—131no—
420C4×C8—131no—
421C4×C8—131no—
422C4×C8—131no—
423C4×C8—261no—
424C4×C8—261no—
425C4×C8C22×D1311yescharacteristic
426C4×C8C22×D1311yescharacteristic
427C2×C13—41no—
428C2×C13—81no—
429C2×C13#293311yescharacteristic
430C2×C13#295111yescharacteristic
431C2×C13#295511yescharacteristic
432D13—81no—
433#41—262no—
434#41—521no—
435C2×Q8—131no—
436C2×Q8C2×C4×D1311yescharacteristic
437C2×D4—21no—
438C2×D4—131no—
439C2×D4—261no—
440C2×D4C2×C4×D1311yescharacteristic
441C22×C4—21no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4C2×C4×D1311yescharacteristic
446C22×C4#612711yescharacteristic
447C22×C4C2×C22⋊D1311yescharacteristic
448Q16—262no—
449SD16—262no—
450SD16—521no—
451D8—521no—
452M16—81no—
453M16—1041no—
454M16—1041no—
455M16—1041no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—81no—
459C2×C8—81no—
460C2×C8—131no—
461C2×C8—131no—
462C2×C8—131no—
463C2×C8—131no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8C2×C22⋊D1311yescharacteristic
469C2×C8C2×C22⋊D1311yescharacteristic
470C2×C8C2×C22⋊D1311yescharacteristic
471C2×C8C2×C22⋊D1311yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—131no—
477C4⋊C4—131no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4C2×C4×D1311yescharacteristic
481C4⋊C4C2×C4×D1311yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—261no—
488C22⋊C4—261no—
489C22⋊C4—261no—
490C42—21no—
491C42—261no—
492C42—261no—
493C42—261no—
494C42C2×C4×D1311yescharacteristic
495C42#612711yescharacteristic
496C42C2×C22⋊D1311yescharacteristic
497C42C23×D1311yescharacteristic
498C13#1803311yescharacteristic, complemented, Sylow
499C23—21no—
500C23—261no—
501C23C4×C22⋊D1311yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—132no—
505Q8—261no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—261no—
510D4—261no—
511D4—522no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—522no—
526C2×C4—522no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4C4×C22⋊D1311yescharacteristic
530C2×C4C4×C22⋊D1311yescharacteristic
531C2×C4C4×C22⋊D1311yescharacteristic
532C2×C4C22×C4×D1311yescharacteristic
533C2×C4C2×#612711yescharacteristic
534C2×C4C22×C22⋊D1311yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—261no—
542C8—261no—
543C8—261no—
544C8—261no—
545C8—521no—
546C8—521no—
547C8—521no—
548C8—521no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—521no—
556C22—521no—
557C22—521no—
558C22C2×C4×C22⋊D1311yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—262no—
567C4—521no—
568C4—521no—
569C4D13×#13111yescharacteristic
570C4#1171945511yescharacteristic
571C4#1171954011yescharacteristic
572C4#1171954311yescharacteristic
573C2—41no—
574C2—81no—
575C2—1041no—
576C2#1312355811yescharacteristic
577C2#1312370911yescharacteristic
578C2#1312373711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2994C2
socleC22×C13C2×C4×D4
prime radical#11718698C4
cosocleC42×C13C24
hypercenter#2994D13
hypocenterC13#18033
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. #13123965C2semidirect
3. #13113736C2semidirect
4. #13113719C2semidirect
5. #13113714C2semidirect
6. #13113712C2semidirect
7. #13113684C2semidirect
8. #13113665C2semidirect
9. #13113648C2semidirect
10. C8×#6107C2semidirect
11. #13113610C2semidirect
12. #13113301C2semidirect
13. #13113221C2semidirect
14. #13113136C2semidirect
15. C13×#2994C2semidirect
211. #2994D13semidirect
498. C13#18033semidirect

Maximal subgroups

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

subgroupindex
#131248482
#131239652
#131137362
#131137192
#131137142
#131137122
#131136842
#131136652
#131136482
C8×#61072
#131136102
#131133012
#131132212
#131131362
C13×#29942
#1803313