Finite Group Databasebeta

← #15833568

Subgroups — #15833568

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#13123987C211yesmaximal, characteristic
3#13123930C211yesmaximal, characteristic, complemented
4#13113746C211yesmaximal, characteristic, complemented
5#13113740C211yesmaximal, characteristic, complemented
6#13113734C211yesmaximal, characteristic, complemented
7#13113728C211yesmaximal, characteristic, complemented
8#13113656C211yesmaximal, characteristic, complemented
9#13113650C211yesmaximal, characteristic, complemented
10C8×Dic52C211yesmaximal, characteristic, complemented
11C8×#6095C211yesmaximal, characteristic, complemented
12#13113603C211yesmaximal, characteristic, complemented
13#13113297C211yesmaximal, characteristic
14#13113292C211yesmaximal, characteristic, complemented
15C8×C13×M16C211yesmaximal, characteristic, complemented
16#11719184C2211yescharacteristic
17#11719175C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C4×C13×M16C2211yescharacteristic
20C2×C4×C8×C13C2211yescharacteristic
21#11718798C411yescharacteristic
22#11718798C411yescharacteristic
23#11718795C411yescharacteristic
24#11718795C411yescharacteristic
25#11718587C2211yescharacteristic
26#11718585C2211yescharacteristic
27#11718501—21no—
28#11718500—21no—
29#11718489—21no—
30#11718489—21no—
31#11718390—21no—
32#11718389—21no—
33#11718381—21no—
34#11718381—21no—
35#11718376C411yescharacteristic
36#11718375C411yescharacteristic
37#11718364C411yescharacteristic
38#11718363C411yescharacteristic
39C4×Dic52C2211yescharacteristic
40C4×Dic52C2211yescharacteristic
41C4×#6095C2211yescharacteristic
42C4×#6095C2211yescharacteristic
43#11718349C2211yescharacteristic
44C8×D52C2211yescharacteristic
45#11718340C2211yescharacteristic
46#11718340C2211yescharacteristic
47#11718340C2211yescharacteristic
48C8×Dic26C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#322C2211yescharacteristic
52C13×#322C2211yescharacteristic
53C82×C13C2211yescharacteristic
54C82×C13C2211yescharacteristic
55#11718051C2211yescharacteristic
56#11718051C2211yescharacteristic
57#11718050C2211yescharacteristic
58#11718050C2211yescharacteristic
59#11718049C2211yescharacteristic
60#11718049C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718048C2211yescharacteristic
65#11718048C2211yescharacteristic
66#11718048C2211yescharacteristic
67C2×C13×M16C2×C411yescharacteristic
68C2×C13×M16C2×C411yescharacteristic
69C22×C8×C13—21no—
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
79C2×#6099—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⋊C8D411yescharacteristic
99C13×C4⋊C8D411yescharacteristic
100C13×C22⋊C8D411yescharacteristic
101C13×C22⋊C8D411yescharacteristic
102C13×#97C2×C411yescharacteristic
103C13×#97C2×C411yescharacteristic
104C4×C8×C13—21no—
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111C22⋊#1055—21no—
112#88061C2×C411yescharacteristic
113#88061C2×C411yescharacteristic
114#88060—21no—
115#88060—21no—
116#88058C2×C411yescharacteristic
117#88058C2×C411yescharacteristic
118#88057C2×C411yescharacteristic
119#88057C2×C411yescharacteristic
120#88056C2×C411yescharacteristic
121#88056C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88056C2×C411yescharacteristic
124#88056C2×C411yescharacteristic
125#88056C2×C411yescharacteristic
126#88055—21no—
127#88055—21no—
128#88055—21no—
129#88054—21no—
130#88054—21no—
131#88054—21no—
132#88054—21no—
133#88054—21no—
134#88054—21no—
135C8×Dic13—21no—
136C8×Dic13—21no—
137C8×Dic13—21no—
138C4⋊#1055—21no—
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142C4⋊#1055C2311yescharacteristic
143#88043—21no—
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—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—42no—
160C2×C8×C13C22×C411yescharacteristic
161C2×C8×C13C22×C411yescharacteristic
162C2×C8×C13C22×C411yescharacteristic
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C2×D411yescharacteristic
165C2×C8×C13C2×D411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C42×C13C22×C411yescharacteristic
169C42×C13C2×D411yescharacteristic
170C42×C13#4111yescharacteristic
171C42×C13C2411yescharacteristic
172C22⋊Dic13—21no—
173C22⋊Dic13—21no—
174C22⋊Dic13—21no—
175#6103—21no—
176#6103—21no—
177#6103—21no—
178#6103—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13C22×C411yescharacteristic
183C4⋊Dic13C22×C411yescharacteristic
184C4⋊Dic13C22×C411yescharacteristic
185C4⋊Dic13C22×C411yescharacteristic
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192#6101—21no—
193#6101—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197#6099—81no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
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#1569—131no—
220#1494—131no—
221#1493—131no—
222C8×M16D1311yescharacteristic, complemented
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—22no—
256C8×C13—21no—
257C8×C13—21no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—41no—
263C8×C13#13112yes—
264C8×C13#13112yes—
265#1055—41no—
266#1055—41no—
267#1055—41no—
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#432—131no—
299#431C2×D1311yescharacteristic
300#424—261no—
301#423—131no—
302C4×M16C2×D1311yescharacteristic
303C2×C4×C8C2×D1311yescharacteristic
304#335—131no—
305#335—131no—
306#334—131no—
307#334—131no—
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#322C2×D1311yescharacteristic
317#322C2×D1311yescharacteristic
318C82C2×D1311yescharacteristic
319C82C2×D1311yescharacteristic
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—261no—
347C2×M16—261no—
348C2×M16C4×D1311yescharacteristic
349C2×M16C4×D1311yescharacteristic
350C22×C8—21no—
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—131no—
378C4⋊C8—131no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—261no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8D5211yescharacteristic
389C4⋊C8D5211yescharacteristic
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—261no—
399C22⋊C8—261no—
400C22⋊C8—261no—
401C22⋊C8D5211yescharacteristic
402C22⋊C8D5211yescharacteristic
403#97—261no—
404#97—261no—
405#97—261no—
406#97—261no—
407#97C4×D1311yescharacteristic
408#97C4×D1311yescharacteristic
409C4×C8—21no—
410C4×C8—261no—
411C4×C8—261no—
412C4×C8—261no—
413C4×C8C22×D1311yescharacteristic
414C4×C8C22×D1311yescharacteristic
415C4×C8C22×D1311yescharacteristic
416C4×C8C22×D1311yescharacteristic
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×C4C2×D5211yescharacteristic
433C22×C4#612711yescharacteristic
434Q16—262no—
435Q16—262no—
436SD16—262no—
437SD16—262no—
438M16—22no—
439M16—22no—
440M16—1041no—
441M16—1041no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—42no—
445C2×C8—261no—
446C2×C8—261no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—1041no—
450C2×C8C2×C4×D1311yescharacteristic
451C2×C8C2×C4×D1311yescharacteristic
452C2×C8C2×C4×D1311yescharacteristic
453C2×C8C2×C4×D1311yescharacteristic
454C2×C8C2×D5211yescharacteristic
455C2×C8C2×D5211yescharacteristic
456C2×C8C2×D5211yescharacteristic
457C2×C8C2×D5211yescharacteristic
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
484C42C2×D5211yescharacteristic
485C42#612711yescharacteristic
486C42C23×D1311yescharacteristic
487C13#1796911yescharacteristic, complemented, Sylow
488C23—261no—
489C23C4×D5211yescharacteristic
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×C4C4×D5211yescharacteristic
515C2×C4C4×D5211yescharacteristic
516C2×C4C4×D5211yescharacteristic
517C2×C4C22×C4×D1311yescharacteristic
518C2×C4C22×D5211yescharacteristic
519C2×C4C2×#612711yescharacteristic
520C8—22no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—521no—
529C8—521no—
530C8—521no—
531C8—521no—
532C8#8815512yes—
533C8#8815512yes—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—521no—
538C22—521no—
539C22—521no—
540C22C2×C4×D5211yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—521no—
546C4—521no—
547C4—521no—
548C4—521no—
549C4—521no—
550C4—521no—
551C4—521no—
552C4C2×#8815511yescharacteristic
553C4C2×#8815511yescharacteristic
554C4#1171945611yescharacteristic
555C4#1171945811yescharacteristic
556C2—41no—
557C2—1041no—
558C2#1312354911yescharacteristic
559C2#1312368111yescharacteristic
560C2#1312374711yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC8×C13×M16C2
socleC22×C13C2×C4×D4
prime radical#88184C2×C4
cosocleC42×C13C24
hypercenterC8×M16D13
hypocenterC13#17969
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
3. #13123930C2semidirect
4. #13113746C2semidirect
5. #13113740C2semidirect
6. #13113734C2semidirect
7. #13113728C2semidirect
8. #13113656C2semidirect
9. #13113650C2semidirect
10. C8×Dic52C2semidirect
11. C8×#6095C2semidirect
12. #13113603C2semidirect
14. #13113292C2semidirect
15. C8×C13×M16C2semidirect
222. C8×M16D13semidirect
487. C13#17969semidirect

Maximal subgroups

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

subgroupindex
#131254422
#131239872
#131239302
#131137462
#131137402
#131137342
#131137282
#131136562
#131136502
C8×Dic522
C8×#60952
#131136032
#131132972
#131132922
C8×C13×M162
#1796913