Finite Group Databasebeta

← #15833537

Subgroups — #15833537

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125438C211yesmaximal, characteristic
2#13123808C211yesmaximal, characteristic
3#13123765C211yesmaximal, characteristic, complemented
4#13113732C211yesmaximal, characteristic, complemented
5#13113730C211yesmaximal, characteristic, complemented
6#13113729C211yesmaximal, characteristic, complemented
7#13113727C211yesmaximal, characteristic, complemented
8#13113656C211yesmaximal, characteristic, complemented
9#13113653C211yesmaximal, characteristic, complemented
10#13113648C211yesmaximal, characteristic, complemented
11#13113602C211yesmaximal, characteristic, complemented
12#13113307C211yesmaximal, characteristic, complemented
13#13113298C211yesmaximal, characteristic
14#13113115C211yesmaximal, characteristic, complemented
15C13×SD16⋊C8C211yesmaximal, characteristic, complemented
16#11719283C2211yescharacteristic
17#11719262C2211yescharacteristic
18C8×Q8×C13C2211yescharacteristic
19C4×C13×SD16C2211yescharacteristic
20C8×D4×C13C2211yescharacteristic
21#11718835C411yescharacteristic
22#11718828C411yescharacteristic
23C8×C22⋊D13—21no—
24#11718762—21no—
25C4×#6107C2211yescharacteristic
26#11718685C2211yescharacteristic
27C4×#6105C2211yescharacteristic
28#11718673C2211yescharacteristic
29#11718529C411yescharacteristic
30#11718517C411yescharacteristic
31#11718500—21no—
32#11718498C2211yescharacteristic
33#11718496C2211yescharacteristic
34#11718492C2211yescharacteristic
35#11718492C2211yescharacteristic
36#11718489—21no—
37#11718477C411yescharacteristic
38#11718458C411yescharacteristic
39#11718441C411yescharacteristic
40#11718426C411yescharacteristic
41#11718389—21no—
42#11718381—21no—
43C4×Dic52C2211yescharacteristic
44#11718350—21no—
45C4×#6094C2211yescharacteristic
46#11718346C2211yescharacteristic
47C4×C8×D13C2211yescharacteristic
48C8×Dic26—21no—
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#335C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718049C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
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×D13D411yescharacteristic
85C2×C8×D13D411yescharacteristic
86#88151C2×C411yescharacteristic
87#88151C2×C411yescharacteristic
88#88150—21no—
89#88144C2×C411yescharacteristic
90#88143—21no—
91#88142C2×C411yescharacteristic
92#88137—21no—
93#88133—21no—
94#88126—21no—
95C42×D13C2311yescharacteristic
96C4×Dic26—21no—
97C4×Dic26C2311yescharacteristic
98C4×Dic26C2311yescharacteristic
99C13×#106C2×C411yescharacteristic
100C13×C4⋊C8—21no—
101C13×C4⋊C8C2311yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×#103C2×C411yescharacteristic
104C13×#102C2×C411yescharacteristic
105C13×C22⋊C8—21no—
106C4×C8×C13—21no—
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110#88075C2×C411yescharacteristic
111#88072C2×C411yescharacteristic
112C22⋊#1055—21no—
113#88060—21no—
114#88060—21no—
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#88054—21no—
129C8×Dic13—21no—
130C8×Dic13—21no—
131C8×Dic13D411yescharacteristic
132C8×Dic13D411yescharacteristic
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#17967—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—42no—
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—42no—
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—42no—
207C8×D13—22no—
208C8×D13—41no—
209#3172—131no—
210#2966—131no—
211#2960—131no—
212#1591—131no—
213#1591—131no—
214#1590—131no—
215#1590—131no—
216#1579—131no—
217#1579—131no—
218SD16⋊C8—131no—
219SD16⋊C8D1311yescharacteristic, complemented
220#1569—131no—
221#1497—131no—
222#1495—131no—
223C8×M16—131no—
224C23×C13—21no—
225C22×D13C4×D411yescharacteristic
226Q8×C13—21no—
227Q8×C13—21no—
228D4×C13—21no—
229D4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13C23×C411yescharacteristic
236C2×C4×C13C22×D411yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C22⋊D13—42no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13C4×D411yescharacteristic
244C2×Dic13C4×D411yescharacteristic
245C2×Dic13C4×D411yescharacteristic
246C4×D13—21no—
247C4×D13—21no—
248C4×D13—21no—
249C4×D13—21no—
250C4×D13—41no—
251Dic26—21no—
252Dic26—21no—
253Dic26—21no—
254Dic26—21no—
255Dic26—42no—
256C8×C13—21no—
257C8×C13—21no—
258C8×C13—21no—
259C8×C13—41no—
260C8×C13—41no—
261C8×C13—41no—
262C8×C13#13112yes—
263#1055—21no—
264#1055—21no—
265#1055—41no—
266#1055—41no—
267#1055—41no—
268#1055#13112yes—
269#1055#13712yes—
270#533—131no—
271#529—131no—
272#501—131no—
273#497—131no—
274#491—131no—
275#489—131no—
276#470—131no—
277#470—131no—
278#468—131no—
279#468—131no—
280#446—131no—
281#446—131no—
282#446—131no—
283#446—261no—
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8—261no—
287C8×Q8C2×D1311yescharacteristic
288C4×Q16—131no—
289C4×Q16—131no—
290C4×SD16—131no—
291C4×SD16C2×D1311yescharacteristic
292#436—131no—
293#435—261no—
294C8×D4—261no—
295C8×D4C2×D1311yescharacteristic
296#433—261no—
297#432—131no—
298#431—131no—
299#424—261no—
300#423—131no—
301#405—261no—
302#405—261no—
303C4×M16—131no—
304C2×C4×C8—131no—
305#335—131no—
306#335C2×D1311yescharacteristic
307#334—131no—
308#334—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8C2×D1311yescharacteristic
315D4⋊C8—131no—
316D4⋊C8C2×D1311yescharacteristic
317#322—131no—
318#322C2×D1311yescharacteristic
319C82—131no—
320C82—131no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13C2×C4×D411yescharacteristic
325C2×D13—21no—
326C2×D13—21no—
327C2×D13—21no—
328C4×C13—21no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13C2×#13111yescharacteristic
333C4×C13C2×#13111yescharacteristic
334C4×C13C2×#13711yescharacteristic
335C4×C13#57511yescharacteristic
336Dic13—21no—
337Dic13—21no—
338Dic13—21no—
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343C2×Q16—131no—
344C2×Q16—131no—
345C2×SD16—131no—
346C2×SD16C4×D1311yescharacteristic
347C2×M16—131no—
348C2×M16—131no—
349C2×M16—261no—
350C2×M16—261no—
351C22×C8—21no—
352C22×C8—131no—
353C22×C8—131no—
354C4⋊Q8—131no—
355C4⋊Q8—131no—
356#126—261no—
357#125—131no—
358#125—261no—
359#124—131no—
360#123—261no—
361C22⋊Q8—131no—
362C22⋊Q8—131no—
363C22⋊Q8—131no—
364C22⋊Q8—261no—
365#121—131no—
366C4×Q8—131no—
367C4×Q8—131no—
368C4×Q8—261no—
369C4×Q8C22×D1311yescharacteristic
370C4×D4—261no—
371C4×D4C22×D1311yescharacteristic
372#117—261no—
373#117—261no—
374C2×C42—131no—
375#107—131no—
376#107—131no—
377#106—131no—
378#106C4×D1311yescharacteristic
379C4⋊C8—21no—
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⋊C8—261no—
389C4⋊C8C22×D1311yescharacteristic
390C4⋊C8C22×D1311yescharacteristic
391#103—131no—
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#103C4×D1311yescharacteristic
397#102—131no—
398#102C4×D1311yescharacteristic
399C22⋊C8—21no—
400C22⋊C8—261no—
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—131no—
414C4×C8—131no—
415C4×C8—261no—
416C4×C8—261no—
417C4×C8C22×D1311yescharacteristic
418C4×C8C22×D1311yescharacteristic
419C4×C8C22×D1311yescharacteristic
420C2×C13—81no—
421C2×C13#293111yescharacteristic
422C2×C13C4×#13711yescharacteristic
423C2×C13#295511yescharacteristic
424D13—41no—
425C2×Q8—131no—
426C2×Q8—131no—
427C2×Q8—261no—
428C2×Q8C2×C4×D1311yescharacteristic
429C2×D4—261no—
430C2×D4C2×C4×D1311yescharacteristic
431C22×C4—21no—
432C22×C4—131no—
433C22×C4—131no—
434C22×C4—131no—
435Q16—262no—
436Q16—262no—
437SD16—22no—
438SD16—262no—
439M16—262no—
440M16—262no—
441M16—522no—
442M16—522no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—42no—
447C2×C8—131no—
448C2×C8—131no—
449C2×C8—131no—
450C2×C8—131no—
451C2×C8—262no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—521no—
456C2×C8C2×C4×D1311yescharacteristic
457C2×C8C2×C4×D1311yescharacteristic
458C2×C8D4×D1311yescharacteristic
459C2×C8D4×D1311yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—131no—
462C4⋊C4—131no—
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—
473C4⋊C4C2×C4×D1311yescharacteristic
474C4⋊C4C2×C4×D1311yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—261no—
477C22⋊C4—261no—
478C22⋊C4—261no—
479C22⋊C4—261no—
480C22⋊C4—261no—
481C22⋊C4—261no—
482C42—21no—
483C42—131no—
484C42—131no—
485C42—131no—
486C42—261no—
487C42—261no—
488C42C23×D1311yescharacteristic
489C13#1796711yescharacteristic, complemented, Sylow
490C23—21no—
491C23—131no—
492Q8—21no—
493Q8—21no—
494Q8—261no—
495Q8—261no—
496Q8—261no—
497Q8—261no—
498Q8—522no—
499D4—21no—
500D4—21no—
501D4—522no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—131no—
508C2×C4—131no—
509C2×C4—131no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—521no—
519C2×C4C22×C4×D1311yescharacteristic
520C2×C4C2×D4×D1311yescharacteristic
521C2×C4#41×D1311yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—132no—
529C8—132no—
530C8—261no—
531C8—261no—
532C8—521no—
533C8—521no—
534C8—521no—
535C8#8815512yes—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—261no—
540C22—261no—
541C22—261no—
542C22C4×D4×D1311yescharacteristic
543C4—21no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—261no—
548C4—261no—
549C4—261no—
550C4—521no—
551C4—521no—
552C4—521no—
553C4—521no—
554C4C2×#8815511yescharacteristic
555C4D13×#13111yescharacteristic
556C4#1171947811yescharacteristic
557C4D13×#13711yescharacteristic
558C2—81no—
559C2—521no—
560C2#1312354311yescharacteristic
561C2#1312365811yescharacteristic
562C2#1312373611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×SD16⋊C8C2
socleC22×C13C2×C4×D4
prime radical#88192C2×C4
cosocleC42×C13C24
hypercenterSD16⋊C8D13
hypocenterC13#17967
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
3. #13123765C2semidirect
4. #13113732C2semidirect
5. #13113730C2semidirect
6. #13113729C2semidirect
7. #13113727C2semidirect
8. #13113656C2semidirect
9. #13113653C2semidirect
10. #13113648C2semidirect
11. #13113602C2semidirect
12. #13113307C2semidirect
14. #13113115C2semidirect
15. C13×SD16⋊C8C2semidirect
219. SD16⋊C8D13semidirect
489. C13#17967semidirect

Maximal subgroups

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

subgroupindex
#131254382
#131238082
#131237652
#131137322
#131137302
#131137292
#131137272
#131136562
#131136532
#131136482
#131136022
#131133072
#131132982
#131131152
C13×SD16⋊C82
#1796713