Finite Group Databasebeta

← #15833562

Subgroups — #15833562

Order 3328.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125442C211yesmaximal, characteristic
2#13123981C211yesmaximal, characteristic
3#13123933C211yesmaximal, characteristic, complemented
4#13113744C211yesmaximal, characteristic, complemented
5#13113737C211yesmaximal, characteristic, complemented
6#13113732C211yesmaximal, characteristic, complemented
7#13113725C211yesmaximal, characteristic, complemented
8#13113654C211yesmaximal, characteristic, complemented
9#13113647C211yesmaximal, characteristic, complemented
10#13113642C211yesmaximal, characteristic, complemented
11#13113635C211yesmaximal, characteristic, complemented
12#13113294C211yesmaximal, characteristic
13#13113290C211yesmaximal, characteristic, complemented
14M16×#1055C211yesmaximal, characteristic, complemented
15C13×#1569C211yesmaximal, characteristic, complemented
16#11719184C2211yescharacteristic
17#11719175C2211yescharacteristic
18C13×#432C2211yescharacteristic
19C13×#423C2211yescharacteristic
20C4×C13×M16C2211yescharacteristic
21#11718798C411yescharacteristic
22#11718798C411yescharacteristic
23#11718795C411yescharacteristic
24#11718795C411yescharacteristic
25#11718789—21no—
26#11718788—21no—
27#11718586C2211yescharacteristic
28C2×C4×#1055C2211yescharacteristic
29#11718501—21no—
30#11718500—21no—
31#11718499C2211yescharacteristic
32#11718495C2211yescharacteristic
33#11718492C2211yescharacteristic
34#11718492C2211yescharacteristic
35#11718492C2211yescharacteristic
36#11718491C2211yescharacteristic
37#11718491C2211yescharacteristic
38#11718491C2211yescharacteristic
39#11718381—21no—
40#11718381—21no—
41#11718376C411yescharacteristic
42#11718375C411yescharacteristic
43#11718364C411yescharacteristic
44#11718363C411yescharacteristic
45#11718362—21no—
46#11718362—21no—
47C4×Dic52C2211yescharacteristic
48C4×Dic52C2211yescharacteristic
49C4×#6095C2211yescharacteristic
50C4×#6095C2211yescharacteristic
51C13×#335C2211yescharacteristic
52C13×#335C2211yescharacteristic
53C13×#334C2211yescharacteristic
54C13×#334C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718076C2211yescharacteristic
60#11718076C2211yescharacteristic
61#11718075C2211yescharacteristic
62#11718075C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718047C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×M16—21no—
68C2×C13×M16C2×C411yescharacteristic
69C2×C13×M16C2×C411yescharacteristic
70C2×C42×C13C2311yescharacteristic
71#88184C2×C411yescharacteristic
72#88183—21no—
73C4×C22⋊D13—21no—
74#88180—21no—
75#88178—21no—
76#88178C2×C411yescharacteristic
77#88178C2×C411yescharacteristic
78#88178C2×C411yescharacteristic
79C22×#1055—21no—
80C2×Dic52C2×C411yescharacteristic
81C2×Dic52C2×C411yescharacteristic
82C2×#6095C2×C411yescharacteristic
83C2×#6095C2×C411yescharacteristic
84C2×#6094—21no—
85C2×C8×D13—21no—
86#88130—21no—
87#88129C2×C411yescharacteristic
88C4×D52C2311yescharacteristic
89#88126—21no—
90#88124—21no—
91#88124C2×C411yescharacteristic
92#88123C2×C411yescharacteristic
93#88123C2×C411yescharacteristic
94C4×Dic26—21no—
95C4×Dic26C2311yescharacteristic
96C4×Dic26C2311yescharacteristic
97C4×Dic26C2311yescharacteristic
98C13×C4⋊C8—21no—
99C13×C4⋊C8C2311yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×C22⋊C8—21no—
104C13×#97—21no—
105C13×#97C2×C411yescharacteristic
106C13×#97C2×C411yescharacteristic
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109C22⋊#1055D411yescharacteristic
110C22⋊#1055D411yescharacteristic
111#88061C2×C411yescharacteristic
112#88061C2×C411yescharacteristic
113#88060—21no—
114#88060—21no—
115#88058C2×C411yescharacteristic
116#88058C2×C411yescharacteristic
117#88057C2×C411yescharacteristic
118#88057C2×C411yescharacteristic
119#88056C2×C411yescharacteristic
120#88056C2×C411yescharacteristic
121#88056C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88056C2×C411yescharacteristic
124#88056C2×C411yescharacteristic
125#88055—21no—
126#88055—21no—
127#88055—21no—
128#88054—21no—
129#88054—21no—
130#88054—21no—
131#88054—21no—
132#88054—21no—
133#88054—21no—
134C8×Dic13—21no—
135C8×Dic13—21no—
136C8×Dic13—21no—
137C4⋊#1055D411yescharacteristic
138C4⋊#1055D411yescharacteristic
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17969—131nomaximal, Sylow
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13#4111yescharacteristic
148C2×C22⋊D13—21no—
149C2×D52C22×C411yescharacteristic
150C2×C4×D13—21no—
151C2×Dic26—21no—
152C2×Dic26C22×C411yescharacteristic
153C2×Dic26C22×C411yescharacteristic
154C2×Dic26C22×C411yescharacteristic
155C13×M16—22no—
156C13×M16—22no—
157C13×M16—81no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13C22×C411yescharacteristic
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C22×C411yescharacteristic
166C42×C13C22×C411yescharacteristic
167C42×C13C2×D411yescharacteristic
168C42×C13#4111yescharacteristic
169C42×C13C2411yescharacteristic
170C22⋊Dic13—21no—
171C22⋊Dic13—21no—
172C22⋊Dic13—21no—
173#6103—21no—
174#6103—21no—
175#6103—21no—
176#6103—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13C22×C411yescharacteristic
181C4⋊Dic13C22×C411yescharacteristic
182C4⋊Dic13C22×C411yescharacteristic
183C4⋊Dic13C22×C411yescharacteristic
184#6101—21no—
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—42no—
198C2×#1055C2×D411yescharacteristic
199C2×#1055C2×D411yescharacteristic
200C2×#1055C2×D411yescharacteristic
201C2×#1055C2×D411yescharacteristic
202Dic52—22no—
203Dic52—22no—
204#6095—22no—
205#6095—22no—
206#6094—81no—
207C8×D13—81no—
208#3172—131no—
209#2993—131no—
210#2985—131no—
211#1593—131no—
212#1592—131no—
213#1591—131no—
214#1590—131no—
215#1579—131no—
216SD16⋊C8—131no—
217C8×Q16—131no—
218C8×SD16—131no—
219#1569D1311yescharacteristic, complemented
220#1494—131no—
221#1493—131no—
222C8×M16—131no—
223C23×C13C4×D411yescharacteristic
224C22×D13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—41no—
230C2×C4×C13C4×D411yescharacteristic
231C2×C4×C13C4×D411yescharacteristic
232C2×C4×C13C4×D411yescharacteristic
233C2×C4×C13C23×C411yescharacteristic
234C2×C4×C13C22×D411yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C22⋊D13—81no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244D52—21no—
245D52—21no—
246C4×D13—41no—
247C4×D13—41no—
248Dic26—21no—
249Dic26—21no—
250Dic26—21no—
251Dic26—21no—
252Dic26—21no—
253Dic26—21no—
254Dic26—81no—
255C8×C13—21no—
256C8×C13—21no—
257C8×C13—41no—
258C8×C13—41no—
259C8×C13—41no—
260C8×C13—41no—
261C8×C13#13112yes—
262C8×C13#13112yes—
263#1055—22no—
264#1055—21no—
265#1055—21no—
266#1055—21no—
267#1055—21no—
268#1055—41no—
269#533—131no—
270#529—131no—
271#501—131no—
272#497—131no—
273#491—131no—
274#489—131no—
275#470—131no—
276#470—131no—
277#468—131no—
278#468—131no—
279#446—131no—
280#446—131no—
281#446—131no—
282#446—261no—
283#446—261no—
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8—131no—
287C4×Q16—131no—
288C4×Q16—131no—
289C4×SD16—131no—
290C4×SD16—131no—
291#436—131no—
292#436—261no—
293#435—261no—
294C8×D4—131no—
295#433—261no—
296#433—261no—
297#433—261no—
298#432C2×D1311yescharacteristic
299#431—131no—
300#424—261no—
301#423C2×D1311yescharacteristic
302C4×M16C2×D1311yescharacteristic
303C2×C4×C8—131no—
304#335C2×D1311yescharacteristic
305#335C2×D1311yescharacteristic
306#334C2×D1311yescharacteristic
307#334C2×D1311yescharacteristic
308Q8⋊C8—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314D4⋊C8—131no—
315D4⋊C8—131no—
316#322—131no—
317#322—131no—
318C82—131no—
319C82—131no—
320C22×C13—21no—
321C22×C13—21no—
322C22×C13—21no—
323C22×C13C2×C4×D411yescharacteristic
324C2×D13—41no—
325C2×D13—41no—
326C2×D13—41no—
327C4×C13—21no—
328C4×C13—21no—
329C4×C13—21no—
330C4×C13—21no—
331C4×C13C2×#13111yescharacteristic
332C4×C13C2×#13111yescharacteristic
333C4×C13#57711yescharacteristic
334C4×C13#57811yescharacteristic
335Dic13—41no—
336Dic13—41no—
337Dic13—41no—
338Dic13—41no—
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342C2×Q16—131no—
343C2×Q16—131no—
344C2×SD16—131no—
345C2×SD16—131no—
346C2×M16—21no—
347C2×M16—261no—
348C2×M16C4×D1311yescharacteristic
349C2×M16C4×D1311yescharacteristic
350C22×C8—261no—
351C22×C8—261no—
352C4⋊Q8—131no—
353C4⋊Q8—131no—
354#126—261no—
355#125—131no—
356#125—261no—
357#124—131no—
358#123—261no—
359C22⋊Q8—131no—
360C22⋊Q8—131no—
361C22⋊Q8—131no—
362C22⋊Q8—261no—
363#121—131no—
364C4×Q8—131no—
365C4×Q8—131no—
366C4×Q8—131no—
367C4×Q8—261no—
368C4×D4—131no—
369C4×D4—261no—
370#117—261no—
371#117—261no—
372C2×C42C22×D1311yescharacteristic
373#107—131no—
374#107—131no—
375#106—131no—
376#106—131no—
377C4⋊C8—21no—
378C4⋊C8—131no—
379C4⋊C8—131no—
380C4⋊C8—261no—
381C4⋊C8—261no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8C22×D1311yescharacteristic
387C4⋊C8C22×D1311yescharacteristic
388C4⋊C8C22×D1311yescharacteristic
389C4⋊C8C22×D1311yescharacteristic
390#103—131no—
391#103—131no—
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#102—131no—
397#102—131no—
398C22⋊C8—21no—
399C22⋊C8—131no—
400C22⋊C8—131no—
401C22⋊C8—261no—
402C22⋊C8—261no—
403#97—21no—
404#97—261no—
405#97—261no—
406#97—261no—
407#97C4×D1311yescharacteristic
408#97C4×D1311yescharacteristic
409C4×C8—131no—
410C4×C8—131no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—261no—
414C4×C8—261no—
415C4×C8—261no—
416C4×C8—261no—
417C4×C8C22×D1311yescharacteristic
418C4×C8C22×D1311yescharacteristic
419C2×C13—41no—
420C2×C13#293111yescharacteristic
421C2×C13#294711yescharacteristic
422C2×C13#295611yescharacteristic
423D13—81no—
424C2×Q8—131no—
425C2×Q8—131no—
426C2×Q8—131no—
427C2×Q8—261no—
428C2×D4—131no—
429C2×D4—261no—
430C22×C4—261no—
431C22×C4C2×C4×D1311yescharacteristic
432C22×C4D4×D1311yescharacteristic
433C22×C4#613111yescharacteristic
434Q16—262no—
435Q16—262no—
436SD16—262no—
437SD16—262no—
438M16—22no—
439M16—22no—
440M16—81no—
441M16—1041no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—131no—
447C2×C8—131no—
448C2×C8—131no—
449C2×C8—131no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—522no—
453C2×C8—1041no—
454C2×C8C2×C4×D1311yescharacteristic
455C2×C8C2×C4×D1311yescharacteristic
456C2×C8C2×C4×D1311yescharacteristic
457C2×C8C2×C4×D1311yescharacteristic
458C4⋊C4—131no—
459C4⋊C4—131no—
460C4⋊C4—131no—
461C4⋊C4—131no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C22⋊C4—261no—
474C22⋊C4—261no—
475C22⋊C4—261no—
476C22⋊C4—261no—
477C22⋊C4—261no—
478C22⋊C4—261no—
479C22⋊C4—261no—
480C42—261no—
481C42—261no—
482C42—261no—
483C42C2×C4×D1311yescharacteristic
484C42D4×D1311yescharacteristic
485C42#613111yescharacteristic
486C42C23×D1311yescharacteristic
487C13#1796911yescharacteristic, complemented, Sylow
488C23—261no—
489C23#8814711yescharacteristic
490Q8—261no—
491Q8—261no—
492Q8—261no—
493Q8—261no—
494Q8—261no—
495Q8—261no—
496Q8—1041no—
497D4—261no—
498D4—261no—
499D4—1041no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—261no—
506C2×C4—261no—
507C2×C4—261no—
508C2×C4—261no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—521no—
513C2×C4—521no—
514C2×C4#8814711yescharacteristic
515C2×C4#8814711yescharacteristic
516C2×C4#8814711yescharacteristic
517C2×C4C22×C4×D1311yescharacteristic
518C2×C4C2×D4×D1311yescharacteristic
519C2×C4C2×#613111yescharacteristic
520C8—21no—
521C8—21no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—262no—
527C8—261no—
528C8—261no—
529C8—261no—
530C8—261no—
531C8—521no—
532C8#8816112yes—
533C8#8816112yes—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—521no—
538C22—521no—
539C22—521no—
540C22C2×#8814711yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—521no—
546C4—521no—
547C4—521no—
548C4—521no—
549C4—521no—
550C4—521no—
551C4—521no—
552C4C2×#8816111yescharacteristic
553C4C2×#8816111yescharacteristic
554C4#1171948011yescharacteristic
555C4#1171948411yescharacteristic
556C2—41no—
557C2—1041no—
558C2#1312354711yescharacteristic
559C2#1312367711yescharacteristic
560C2#1312374511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1569C2
socleC22×C13C2×C4×D4
prime radical#88184C2×C4
cosocleC42×C13C24
hypercenter#1569D13
hypocenterC13#17969
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
3. #13123933C2semidirect
4. #13113744C2semidirect
5. #13113737C2semidirect
6. #13113732C2semidirect
7. #13113725C2semidirect
8. #13113654C2semidirect
9. #13113647C2semidirect
10. #13113642C2semidirect
11. #13113635C2semidirect
13. #13113290C2semidirect
14. M16×#1055C2semidirect
15. C13×#1569C2semidirect
219. #1569D13semidirect
487. C13#17969semidirect

Maximal subgroups

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

subgroupindex
#131254422
#131239812
#131239332
#131137442
#131137372
#131137322
#131137252
#131136542
#131136472
#131136422
#131136352
#131132942
#131132902
M16×#10552
C13×#15692
#1796913