Finite Group Databasebeta

← #15834700

Subgroups — #15834700

Order 3328.

600 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#13123841C211yesmaximal, characteristic, complemented
3#13123834C211yesmaximal, characteristic, complemented
4#13113730C211yesmaximal, characteristic, complemented
5#13113718C211yesmaximal, characteristic, complemented
6#13113682C211yesmaximal, characteristic, complemented
7#13113676C211yesmaximal, characteristic, complemented
8#13113675C211yesmaximal, characteristic, complemented
9#13113669C211yesmaximal, characteristic, complemented
10#13113640C211yesmaximal, characteristic, complemented
11#13113628C211yesmaximal, characteristic, complemented
12#13113582C211yesmaximal, characteristic, complemented
13#13113245C211yesmaximal, characteristic, complemented
14#13113117C211yesmaximal, characteristic, complemented
15C13×#1482C211yesmaximal, characteristic, complemented
16C13×#529C2211yescharacteristic
17#11719184C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20#11718729C411yescharacteristic
21#11718725C411yescharacteristic
22#11718720C411yescharacteristic
23#11718717C411yescharacteristic
24#11718712C411yescharacteristic
25#11718709C411yescharacteristic
26#11718702C411yescharacteristic
27#11718699C411yescharacteristic
28C4×#6107C2211yescharacteristic
29C4×#6106C2211yescharacteristic
30#11718685C2211yescharacteristic
31Q8×#1055C2211yescharacteristic
32C4×#6105C2211yescharacteristic
33C4×#6104C2211yescharacteristic
34#11718673—21no—
35#11718673C2211yescharacteristic
36#11718672—21no—
37D4×#1055C2211yescharacteristic
38#11718661—21no—
39#11718658—21no—
40#11718586C2211yescharacteristic
41C4×#6099C2211yescharacteristic
42C2×C4×#1055C2211yescharacteristic
43#11718499C2211yescharacteristic
44#11718495C2211yescharacteristic
45#11718492C2211yescharacteristic
46#11718491C2211yescharacteristic
47#11718390—21no—
48#11718389—21no—
49#11718351—21no—
50#11718350—21no—
51C13×Q8⋊C8C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×D4⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718046C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C13×#126—21no—
68C13×#125C2×C411yescharacteristic
69C13×#124C2×C411yescharacteristic
70C13×#123—21no—
71C13×C22⋊Q8C2×C411yescharacteristic
72C13×#121C2×C411yescharacteristic
73C4×Q8×C13C2311yescharacteristic
74C4×D4×C13—21no—
75C4×D4×C13C2311yescharacteristic
76C13×#117—21no—
77C2×C42×C13C2311yescharacteristic
78C2×#6107C2×C411yescharacteristic
79C2×#6106C2×C411yescharacteristic
80C2×#6105C2×C411yescharacteristic
81C2×#6104C2×C411yescharacteristic
82#88184C2×C411yescharacteristic
83#88183—21no—
84C4×C22⋊D13—21no—
85#88178C2×C411yescharacteristic
86C2×#6099—21no—
87C2×#6099D411yescharacteristic
88C2×#6099D411yescharacteristic
89C22×#1055—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⋊C8C2311yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×C22⋊C8—21no—
104C13×C22⋊C8—21no—
105C4×C8×C13—21no—
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108#88075C2×C411yescharacteristic
109#88075C2×C411yescharacteristic
110#88072C2×C411yescharacteristic
111#88072C2×C411yescharacteristic
112C22⋊#1055—21no—
113C22⋊#1055—21no—
114C22⋊#1055—21no—
115#88060—21no—
116#88060—21no—
117#88055—21no—
118#88054—21no—
119#88054—21no—
120C8×Dic13—21no—
121#88050C2×C411yescharacteristic
122#88050C2×C411yescharacteristic
123#88049C2×C411yescharacteristic
124#88049C2×C411yescharacteristic
125#88048C2×C411yescharacteristic
126#88048C2×C411yescharacteristic
127#88047C2×C411yescharacteristic
128#88047C2×C411yescharacteristic
129C4⋊#1055—21no—
130C4⋊#1055—21no—
131C4⋊#1055C2311yescharacteristic
132C4⋊#1055C2311yescharacteristic
133#88043—21no—
134#88043D411yescharacteristic
135#88043D411yescharacteristic
136C4×#1055—21no—
137C4×#1055—21no—
138C4×#1055C2×C411yescharacteristic
139C4×#1055C2×C411yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18069—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
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4C22×C411yescharacteristic
165C13×C4⋊C4C22×C411yescharacteristic
166C13×C22⋊C4—21no—
167C13×C22⋊C4—21no—
168C13×C22⋊C4—21no—
169C13×C22⋊C4—21no—
170C13×C22⋊C4—21no—
171C42×C13—21no—
172C42×C13C22×C411yescharacteristic
173C42×C13C2×D411yescharacteristic
174C42×C13#4111yescharacteristic
175C42×C13C2411yescharacteristic
176C22⋊Dic13—21no—
177#6107—22no—
178#6106—41no—
179#6105—41no—
180#6104—22no—
181#6103—21no—
182#6103—21no—
183#6103—21no—
184#6103—21no—
185C4⋊Dic13C22×C411yescharacteristic
186C4⋊Dic13C22×C411yescharacteristic
187#6101—21no—
188#6101—21no—
189#6101—21no—
190#6101—21no—
191C4×Dic13—21no—
192#6099—22no—
193#6099—22no—
194#6099—42no—
195C2×#1055—22no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—41no—
199C2×#1055—42no—
200C2×#1055C22×C411yescharacteristic
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208#6094—42no—
209C8×D13—42no—
210#3168—131no—
211#2969—131no—
212#2969—131no—
213#1591—131no—
214#1589—131no—
215#1583—131no—
216#1583—131no—
217#1582—131no—
218#1582—131no—
219C8×Q16—131no—
220C8×D8—131no—
221#1564—131no—
222#1482—131no—
223#1482D1311yescharacteristic, complemented
224C8×M16—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—41no—
260C8×C13—41no—
261C8×C13—41no—
262C8×C13—41no—
263#1055—21no—
264#1055—21no—
265#1055—21no—
266#1055—21no—
267#1055—21no—
268#1055—41no—
269#1055—41no—
270#1055#13112yes—
271#1055#13512yes—
272#1055#13512yes—
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#446—131no—
285C8×Q8—131no—
286C8×Q8—131no—
287C4×Q16—131no—
288C4×SD16—131no—
289C4×SD16—131no—
290C4×D8—131no—
291#436—131no—
292#436—131no—
293#436—261no—
294#436—261no—
295#435—261no—
296#435—261no—
297C8×D4—131no—
298C8×D4—131no—
299#433—261no—
300#433—261no—
301#431—131no—
302#431C2×D1311yescharacteristic
303#431C2×D1311yescharacteristic
304#405—261no—
305#405—261no—
306C4×M16—131no—
307C2×C4×C8—131no—
308#335—131no—
309#335—131no—
310#334—131no—
311#334—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8C2×D1311yescharacteristic
315Q8⋊C8C2×D1311yescharacteristic
316D4⋊C8—131no—
317D4⋊C8—131no—
318D4⋊C8C2×D1311yescharacteristic
319D4⋊C8C2×D1311yescharacteristic
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×C13#56811yescharacteristic
343C4×C13C2×#13511yescharacteristic
344C4×C13C2×#13511yescharacteristic
345Dic13—41no—
346Dic13—41no—
347Dic13—41no—
348C2×Q16—131no—
349C2×SD16—131no—
350C2×SD16—131no—
351C2×D8—131no—
352C2×M16—131no—
353C2×M16—131no—
354C2×M16—261no—
355C2×M16—261no—
356C22×C8—131no—
357C22×C8—131no—
358C22×C8—261no—
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—131no—
387C4⋊C8—131no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391C4⋊C8—261no—
392C4⋊C8C22×D1311yescharacteristic
393C4⋊C8C22×D1311yescharacteristic
394#103—131no—
395#103—131no—
396#103—131no—
397#103—131no—
398#102—131no—
399#102—131no—
400#102—131no—
401#102—131no—
402C22⋊C8—21no—
403C22⋊C8—21no—
404C22⋊C8—261no—
405C22⋊C8—261no—
406C22⋊C8—261no—
407C22⋊C8—261no—
408C22⋊C8—261no—
409#97—131no—
410#97—131no—
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—261no—
421C4×C8—261no—
422C4×C8—261no—
423C4×C8C22×D1311yescharacteristic
424C4×C8C22×D1311yescharacteristic
425C2×C13—41no—
426C2×C13—81no—
427C2×C13#293511yescharacteristic
428C2×C13C4×#13511yescharacteristic
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×C4D4×D1311yescharacteristic
441C22×C4#612911yescharacteristic
442Q16—262no—
443SD16—521no—
444SD16—521no—
445D8—262no—
446M16—262no—
447M16—262no—
448M16—522no—
449M16—522no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—131no—
455C2×C8—131no—
456C2×C8—131no—
457C2×C8—131no—
458C2×C8—131no—
459C2×C8—131no—
460C2×C8—131no—
461C2×C8—131no—
462C2×C8—262no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—522no—
466C2×C8—522no—
467C2×C8—521no—
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
493C42D4×D1311yescharacteristic
494C42#612911yescharacteristic
495C42C23×D1311yescharacteristic
496C13#1806911yescharacteristic, complemented, Sylow
497C23—21no—
498C23—261no—
499C23#8813511yescharacteristic
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×C4#8813511yescharacteristic
526C2×C4#8813511yescharacteristic
527C2×C4#8813511yescharacteristic
528C2×C4C22×C4×D1311yescharacteristic
529C2×C4C2×D4×D1311yescharacteristic
530C2×C4C2×#612911yescharacteristic
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—132no—
536C8—132no—
537C8—132no—
538C8—261no—
539C8—261no—
540C8—261no—
541C8—261no—
542C8—261no—
543C8—521no—
544C8—521no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—521no—
552C22—521no—
553C22—521no—
554C22C2×#8813511yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—521no—
563C4—521no—
564C4—521no—
565C4D13×#13111yescharacteristic
566C4#1171945511yescharacteristic
567C4D13×#13511yescharacteristic
568C4D13×#13511yescharacteristic
569C2—41no—
570C2—81no—
571C2—1041no—
572C2#1312357611yescharacteristic
573C2#1312360411yescharacteristic
574C2#1312374911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1482C2
socleC22×C13C2×C4×D4
prime radical#11718699C4
cosocleC42×C13C24
hypercenter#1482D13
hypocenterC13#18069
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1482

Complements

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

NH ≅ G/Ntype
2. #13123841C2semidirect
3. #13123834C2semidirect
4. #13113730C2semidirect
5. #13113718C2semidirect
6. #13113682C2semidirect
7. #13113676C2semidirect
8. #13113675C2semidirect
9. #13113669C2semidirect
10. #13113640C2semidirect
11. #13113628C2semidirect
12. #13113582C2semidirect
13. #13113245C2semidirect
14. #13113117C2semidirect
15. C13×#1482C2semidirect
223. #1482D13semidirect
496. C13#18069semidirect

Maximal subgroups

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

subgroupindex
#131254002
#131238412
#131238342
#131137302
#131137182
#131136822
#131136762
#131136752
#131136692
#131136402
#131136282
#131135822
#131132452
#131131172
C13×#14822
#1806913