Finite Group Databasebeta

← #15833557

Subgroups — #15833557

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#13125438C211yesmaximal, characteristic
2#13123986C211yesmaximal, characteristic
3#13123927C211yesmaximal, characteristic, complemented
4#13113744C211yesmaximal, characteristic, complemented
5#13113739C211yesmaximal, characteristic, complemented
6#13113730C211yesmaximal, characteristic, complemented
7#13113729C211yesmaximal, characteristic, complemented
8#13113653C211yesmaximal, characteristic, complemented
9#13113648C211yesmaximal, characteristic, complemented
10C8×Dic52C211yesmaximal, characteristic, complemented
11#13113600C211yesmaximal, characteristic, complemented
12#13113293C211yesmaximal, characteristic
13#13113289C211yesmaximal, characteristic, complemented
14C8×#6094C211yesmaximal, characteristic, complemented
15C8×C13×SD16C211yesmaximal, characteristic, complemented
16#11719283C2211yescharacteristic
17#11719262C2211yescharacteristic
18C8×Q8×C13C2211yescharacteristic
19C4×C13×SD16C2211yescharacteristic
20C8×D4×C13C2211yescharacteristic
21#11718835C411yescharacteristic
22#11718828C411yescharacteristic
23#11718772—21no—
24#11718763—21no—
25C4×#6107C2211yescharacteristic
26#11718685C2211yescharacteristic
27C4×#6105C2211yescharacteristic
28#11718673C2211yescharacteristic
29#11718529C411yescharacteristic
30#11718517C411yescharacteristic
31#11718501—21no—
32#11718498C2211yescharacteristic
33#11718496C2211yescharacteristic
34#11718492C2211yescharacteristic
35#11718492C2211yescharacteristic
36#11718489—21no—
37#11718477C411yescharacteristic
38#11718458C411yescharacteristic
39#11718441C411yescharacteristic
40#11718426C411yescharacteristic
41#11718390—21no—
42#11718381—21no—
43C4×Dic52C2211yescharacteristic
44#11718351—21no—
45C4×#6094C2211yescharacteristic
46#11718346C2211yescharacteristic
47C4×C8×D13C2211yescharacteristic
48#11718340—21no—
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#334C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C82×C13C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718050C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718047C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×SD16C2×C411yescharacteristic
68C22×C8×C13—21no—
69C4×Q8×C13C2311yescharacteristic
70C4×D4×C13C2311yescharacteristic
71#88200C2×C411yescharacteristic
72#88198C2×C411yescharacteristic
73C2×#6107C2×C411yescharacteristic
74#88192C2×C411yescharacteristic
75#88190C2×C411yescharacteristic
76C2×#6105C2×C411yescharacteristic
77C4×C22⋊D13—21no—
78#88180—21no—
79C2×#6099—21no—
80C2×Dic52C2×C411yescharacteristic
81C2×#6094—21no—
82C2×#6094C2×C411yescharacteristic
83C2×#6094C2×C411yescharacteristic
84C2×C8×D13—21no—
85#88151C2×C411yescharacteristic
86#88151C2×C411yescharacteristic
87#88150—21no—
88#88144C2×C411yescharacteristic
89#88143—21no—
90#88142C2×C411yescharacteristic
91#88137—21no—
92#88133—21no—
93#88126—21no—
94C42×D13C2311yescharacteristic
95C4×Dic26—21no—
96C4×Dic26C2311yescharacteristic
97C4×Dic26C2311yescharacteristic
98C13×#106C2×C411yescharacteristic
99C13×C4⋊C8—21no—
100C13×C4⋊C8C2311yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×#103C2×C411yescharacteristic
103C13×#102C2×C411yescharacteristic
104C13×C22⋊C8—21no—
105C4×C8×C13—21no—
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109#88075C2×C411yescharacteristic
110#88072C2×C411yescharacteristic
111C22⋊#1055—21no—
112#88060—21no—
113#88060D411yescharacteristic
114#88060D411yescharacteristic
115#88058C2×C411yescharacteristic
116#88056C2×C411yescharacteristic
117#88056C2×C411yescharacteristic
118#88055—21no—
119#88055—21no—
120#88055—21no—
121#88055C2×C411yescharacteristic
122#88055C2×C411yescharacteristic
123#88054—21no—
124#88054—21no—
125#88054—21no—
126#88054—21no—
127#88054—21no—
128#88054D411yescharacteristic
129#88054D411yescharacteristic
130C8×Dic13—21no—
131C8×Dic13—21no—
132C8×Dic13—21no—
133#88050C2×C411yescharacteristic
134#88050C2×C411yescharacteristic
135#88048C2×C411yescharacteristic
136#88047C2×C411yescharacteristic
137C4⋊#1055—21no—
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140#88043—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17969—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×D4×C13C22×C411yescharacteristic
147C22×C4×C13—21no—
148C2×C22⋊D13—21no—
149C2×C4×D13C22×C411yescharacteristic
150C2×C4×D13C2×D411yescharacteristic
151C2×C4×D13#4111yescharacteristic
152C2×Dic26—21no—
153C2×Dic26C22×C411yescharacteristic
154C2×Dic26C22×C411yescharacteristic
155C13×SD16—22no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—81no—
160C2×C8×C13C22×C411yescharacteristic
161C2×C8×C13C22×C411yescharacteristic
162C2×C8×C13C2×D411yescharacteristic
163C2×C8×C13C2×D411yescharacteristic
164C13×C4⋊C4—21no—
165C13×C4⋊C4C22×C411yescharacteristic
166C13×C4⋊C4C22×C411yescharacteristic
167C13×C22⋊C4—21no—
168C42×C13—21no—
169C42×C13C2411yescharacteristic
170C22⋊Dic13—21no—
171C22⋊Dic13—21no—
172C22⋊Dic13—21no—
173#6107—22no—
174#6105—22no—
175#6103—21no—
176#6103—21no—
177#6103—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13C22×C411yescharacteristic
182C4⋊Dic13C22×C411yescharacteristic
183#6101—21no—
184#6101—21no—
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13C22×C411yescharacteristic
193C4×Dic13C2×D411yescharacteristic
194C4×Dic13#4111yescharacteristic
195#6099—81no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055C22×C411yescharacteristic
200C2×#1055C22×C411yescharacteristic
201C2×#1055C2×D411yescharacteristic
202C2×#1055C2×D411yescharacteristic
203Dic52—22no—
204#6094—22no—
205#6094—22no—
206#6094—81no—
207C8×D13—42no—
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×SD16D1311yescharacteristic, complemented
219#1569—131no—
220#1494—131no—
221#1493—131no—
222C8×M16—131no—
223C23×C13—21no—
224C22×D13C4×D411yescharacteristic
225Q8×C13—21no—
226Q8×C13—21no—
227D4×C13—21no—
228D4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13C23×C411yescharacteristic
235C2×C4×C13C22×D411yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C22⋊D13—81no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13C4×D411yescharacteristic
243C2×Dic13C4×D411yescharacteristic
244C2×Dic13C4×D411yescharacteristic
245C4×D13—21no—
246C4×D13—21no—
247C4×D13—21no—
248C4×D13—21no—
249C4×D13—41no—
250Dic26—21no—
251Dic26—21no—
252Dic26—21no—
253Dic26—21no—
254Dic26—81no—
255C8×C13—22no—
256C8×C13—21no—
257C8×C13—21no—
258C8×C13—21no—
259C8×C13—41no—
260C8×C13—41no—
261C8×C13#13112yes—
262#1055—21no—
263#1055—21no—
264#1055—21no—
265#1055—41no—
266#1055—41no—
267#1055—41no—
268#1055#13112yes—
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×Q8C2×D1311yescharacteristic
287C4×Q16—131no—
288C4×Q16—131no—
289C4×SD16—131no—
290C4×SD16C2×D1311yescharacteristic
291#436—131no—
292#436—261no—
293#435—261no—
294C8×D4C2×D1311yescharacteristic
295#433—261no—
296#433—261no—
297#433—261no—
298#432—131no—
299#431—131no—
300#424—261no—
301#423—131no—
302C4×M16—131no—
303C2×C4×C8—131no—
304#335—131no—
305#335—131no—
306#334—131no—
307#334C2×D1311yescharacteristic
308Q8⋊C8—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8C2×D1311yescharacteristic
314D4⋊C8—131no—
315D4⋊C8C2×D1311yescharacteristic
316#322—131no—
317#322—131no—
318C82—131no—
319C82C2×D1311yescharacteristic
320C22×C13—41no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13C2×C4×D411yescharacteristic
324C2×D13—21no—
325C2×D13—21no—
326C2×D13—21no—
327C4×C13—21no—
328C4×C13—41no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13C2×#13111yescharacteristic
332C4×C13C2×#13111yescharacteristic
333C4×C13#57711yescharacteristic
334C4×C13#57811yescharacteristic
335Dic13—21no—
336Dic13—21no—
337Dic13—21no—
338Dic13—41no—
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342C2×Q16—131no—
343C2×Q16—131no—
344C2×SD16—131no—
345C2×SD16C4×D1311yescharacteristic
346C2×M16—131no—
347C2×M16—131no—
348C2×M16—261no—
349C2×M16—261no—
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—261no—
367C4×Q8C22×D1311yescharacteristic
368C4×D4—261no—
369C4×D4C22×D1311yescharacteristic
370#117—261no—
371#117—261no—
372C2×C42—131no—
373#107—131no—
374#107—131no—
375#106—131no—
376#106C4×D1311yescharacteristic
377C4⋊C8—21no—
378C4⋊C8—131no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—131no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8C22×D1311yescharacteristic
389C4⋊C8C22×D1311yescharacteristic
390#103—131no—
391#103—131no—
392#103—131no—
393#103—131no—
394#103—131no—
395#103C4×D1311yescharacteristic
396#102—131no—
397#102C4×D1311yescharacteristic
398C22⋊C8—21no—
399C22⋊C8—131no—
400C22⋊C8—131no—
401C22⋊C8—261no—
402C22⋊C8—261no—
403#97—131no—
404#97—131no—
405#97—261no—
406#97—261no—
407#97—261no—
408#97—261no—
409C4×C8—21no—
410C4×C8—131no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—261no—
414C4×C8—261no—
415C4×C8—261no—
416C4×C8C22×D1311yescharacteristic
417C4×C8C22×D1311yescharacteristic
418C4×C8C22×D1311yescharacteristic
419C2×C13—81no—
420C2×C13#293111yescharacteristic
421C2×C13#294711yescharacteristic
422C2×C13#295611yescharacteristic
423D13—41no—
424C2×Q8—131no—
425C2×Q8—131no—
426C2×Q8—261no—
427C2×Q8C2×C4×D1311yescharacteristic
428C2×D4—261no—
429C2×D4C2×C4×D1311yescharacteristic
430C22×C4—21no—
431C22×C4—131no—
432C22×C4—131no—
433C22×C4—131no—
434Q16—262no—
435Q16—262no—
436SD16—22no—
437SD16—262no—
438M16—262no—
439M16—262no—
440M16—1041no—
441M16—1041no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—81no—
446C2×C8—131no—
447C2×C8—131no—
448C2×C8—131no—
449C2×C8—131no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—522no—
454C2×C8C2×C4×D1311yescharacteristic
455C2×C8C2×C4×D1311yescharacteristic
456C2×C8D4×D1311yescharacteristic
457C2×C8D4×D1311yescharacteristic
458C4⋊C4—21no—
459C4⋊C4—131no—
460C4⋊C4—131no—
461C4⋊C4—261no—
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⋊C4C2×C4×D1311yescharacteristic
472C4⋊C4C2×C4×D1311yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—261no—
475C22⋊C4—261no—
476C22⋊C4—261no—
477C22⋊C4—261no—
478C22⋊C4—261no—
479C22⋊C4—261no—
480C42—21no—
481C42—131no—
482C42—131no—
483C42—131no—
484C42—261no—
485C42—261no—
486C42C23×D1311yescharacteristic
487C13#1796911yescharacteristic, complemented, Sylow
488C23—21no—
489C23—131no—
490Q8—21no—
491Q8—21no—
492Q8—261no—
493Q8—261no—
494Q8—261no—
495Q8—261no—
496Q8—1041no—
497D4—21no—
498D4—21no—
499D4—1041no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—131no—
506C2×C4—131no—
507C2×C4—131no—
508C2×C4—261no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—521no—
517C2×C4C22×C4×D1311yescharacteristic
518C2×C4C2×D4×D1311yescharacteristic
519C2×C4#41×D1311yescharacteristic
520C8—22no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—132no—
527C8—261no—
528C8—261no—
529C8—261no—
530C8—521no—
531C8—521no—
532C8—521no—
533C8#8815512yes—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—261no—
538C22—261no—
539C22—261no—
540C22C4×D4×D1311yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—261no—
546C4—261no—
547C4—261no—
548C4—521no—
549C4—521no—
550C4—521no—
551C4—521no—
552C4C2×#8815511yescharacteristic
553C4D13×#13111yescharacteristic
554C4#1171946711yescharacteristic
555C4#1171947611yescharacteristic
556C2—81no—
557C2—521no—
558C2#1312354311yescharacteristic
559C2#1312367211yescharacteristic
560C2#1312374111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC8×C13×SD16C2
socleC22×C13C2×C4×D4
prime radical#88192C2×C4
cosocleC42×C13C24
hypercenterC8×SD16D13
hypocenterC13#17969
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
3. #13123927C2semidirect
4. #13113744C2semidirect
5. #13113739C2semidirect
6. #13113730C2semidirect
7. #13113729C2semidirect
8. #13113653C2semidirect
9. #13113648C2semidirect
10. C8×Dic52C2semidirect
11. #13113600C2semidirect
13. #13113289C2semidirect
14. C8×#6094C2semidirect
15. C8×C13×SD16C2semidirect
218. C8×SD16D13semidirect
487. C13#17969semidirect

Maximal subgroups

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

subgroupindex
#131254382
#131239862
#131239272
#131137442
#131137392
#131137302
#131137292
#131136532
#131136482
C8×Dic522
#131136002
#131132932
#131132892
C8×#60942
C8×C13×SD162
#1796913