Finite Group Databasebeta

← #15848431

Subgroups — #15848431

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125997C211yesmaximal, characteristic, complemented
2#13124998C211yesmaximal, characteristic
3#13124907C211yesmaximal, characteristic
4#13114294C211yesmaximal, characteristic, complemented
5#13114287C211yesmaximal, characteristic, complemented
6#13114266C211yesmaximal, characteristic, complemented
7#13114259C211yesmaximal, characteristic, complemented
8#13114230C211yesmaximal, characteristic, complemented
9#13114225C211yesmaximal, characteristic, complemented
10#13114218C211yesmaximal, characteristic, complemented
11#13114211C211yesmaximal, characteristic, complemented
12#13113616C211yesmaximal, characteristic, complemented
13#13113534C211yesmaximal, characteristic, complemented
14#13113494C211yesmaximal, characteristic, complemented
15C13×#2988C211yesmaximal, characteristic
16C4×C13×#41C2211yescharacteristic
17#11719175C2211yescharacteristic
18#11719175C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C8×Q8×C13C2211yescharacteristic
21C8×D4×C13—21no—
22C8×D4×C13—21no—
23C8×D4×C13C2211yescharacteristic
24C8×D4×C13C2211yescharacteristic
25C13×#431—21no—
26C13×#431C2211yescharacteristic
27C2×C13×C4⋊C8—21no—
28C2×C13×C4⋊C8C2211yescharacteristic
29#11718900—21no—
30#11718900—21no—
31#11718692C2211yescharacteristic
32#11718692C2211yescharacteristic
33#11718691—21no—
34C4×#6107—21no—
35#11718682C2211yescharacteristic
36#11718681C2211yescharacteristic
37#11718680C2211yescharacteristic
38#11718680C2211yescharacteristic
39#11718679—21no—
40C4×#6105—21no—
41#11718669C2211yescharacteristic
42#11718668C2211yescharacteristic
43#11718657—21no—
44#11718657—21no—
45#11718587C2211yescharacteristic
46#11718586C2211yescharacteristic
47#11718490—21no—
48#11718490—21no—
49#11718384—21no—
50#11718384—21no—
51#11718343C2211yescharacteristic
52#11718342C2211yescharacteristic
53#11718342C2211yescharacteristic
54#11718341C2211yescharacteristic
55#11718078C2211yescharacteristic
56#11718078C2211yescharacteristic
57#11718078C2211yescharacteristic
58#11718078C2211yescharacteristic
59#11718074C2211yescharacteristic
60#11718074C2211yescharacteristic
61#11718073C2211yescharacteristic
62#11718073C2211yescharacteristic
63#11718050C2211yescharacteristic
64#11718050C2211yescharacteristic
65#11718049C2211yescharacteristic
66#11718049C2211yescharacteristic
67C2×C13×#41D411yescharacteristic
68C22×C8×C13—21no—
69C22×C8×C13—21no—
70C22×C8×C13—21no—
71C4×Q8×C13D411yescharacteristic
72C4×Q8×C13C2311yescharacteristic
73C4×D4×C13—21no—
74C4×D4×C13—21no—
75C4×D4×C13D411yescharacteristic
76C4×D4×C13C2311yescharacteristic
77C13×#117—21no—
78C13×#117D411yescharacteristic
79C2×C42×C13—21no—
80C2×C42×C13C2311yescharacteristic
81C2×#6107—21no—
82C2×#6107—21no—
83C2×#6105—21no—
84C2×#6105—21no—
85#88180—21no—
86#88180—21no—
87#88178—21no—
88#88178—21no—
89#88178—21no—
90#88178—21no—
91#88124—21no—
92#88124—21no—
93#88123C2311yescharacteristic
94#88123C2311yescharacteristic
95#88123C2311yescharacteristic
96#88123C2311yescharacteristic
97C4×Dic26—21no—
98C4×Dic26—21no—
99C4×Dic26—21no—
100C4×Dic26—21no—
101C13×C4⋊C8—21no—
102C13×C4⋊C8—21no—
103C13×C4⋊C8—21no—
104C13×C4⋊C8D411yescharacteristic
105C13×C4⋊C8D411yescharacteristic
106C13×C4⋊C8C2311yescharacteristic
107C13×C4⋊C8C2311yescharacteristic
108C13×C22⋊C8—21no—
109C13×C22⋊C8—21no—
110C13×C22⋊C8D411yescharacteristic
111C13×C22⋊C8D411yescharacteristic
112C4×C8×C13—21no—
113C4×C8×C13—21no—
114C4×C8×C13C2311yescharacteristic
115C4×C8×C13C2311yescharacteristic
116#88075—21no—
117#88075—21no—
118#88072—21no—
119#88072—21no—
120C22⋊#1055—21no—
121C22⋊#1055—21no—
122#88058—21no—
123#88058—21no—
124#88057—21no—
125#88057—21no—
126#88056—21no—
127#88056—21no—
128#88056—21no—
129#88056—21no—
130#88050—21no—
131#88050—21no—
132#88050—21no—
133#88050—21no—
134#88048—21no—
135#88048—21no—
136#88047—21no—
137#88047—21no—
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142#88043—21no—
143C4×#1055—21no—
144#19418—131nomaximal, Sylow
145C13×#41—22no—
146C13×#41—22no—
147C2×Q8×C13C2×D411yescharacteristic
148C2×D4×C13—21no—
149C2×D4×C13C2×D411yescharacteristic
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13#4111yescharacteristic
156C2×Dic26—21no—
157C2×Dic26—21no—
158C2×Dic26—21no—
159C2×Dic26—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—81no—
163C2×C8×C13—81no—
164C2×C8×C13—81no—
165C2×C8×C13C2×D411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C2×C8×C13C2×D411yescharacteristic
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4C2×D411yescharacteristic
172C13×C4⋊C4C2×D411yescharacteristic
173C13×C22⋊C4—21no—
174C13×C22⋊C4—21no—
175C13×C22⋊C4—21no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13C2×D411yescharacteristic
180C42×C13C2×D411yescharacteristic
181C42×C13#4111yescharacteristic
182C42×C13C2411yescharacteristic
183C22⋊Dic13—41no—
184C22⋊Dic13—41no—
185#6107—42no—
186#6107—42no—
187#6105—42no—
188#6105—42no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197#6101—41no—
198#6101—41no—
199#6101—41no—
200#6101—41no—
201C4×Dic13—41no—
202C4×Dic13—41no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207#3231—131no—
208#3116—131no—
209#3107—131no—
210#2988D1311yescharacteristic
211#1684—131no—
212#1683—131no—
213#1680—131no—
214#1679—131no—
215#1674—131no—
216#1673—131no—
217#1672—131no—
218#1671—131no—
219#1572—131no—
220#1552—131no—
221#1542—131no—
222C23×C13—21no—
223C23×C13#12111yescharacteristic
224Q8×C13—21no—
225Q8×C13#13512yes—
226D4×C13—24no—
227D4×C13—21no—
228D4×C13#13512yes—
229C2×C4×C13—24no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—81no—
241C2×C4×C13#12111yescharacteristic
242C2×C4×C13#12111yescharacteristic
243C2×C4×C13#12111yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×Dic13—41no—
248C2×Dic13—41no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251Dic26—41no—
252Dic26—41no—
253Dic26—41no—
254Dic26—41no—
255Dic26—41no—
256Dic26—41no—
257Dic26—81no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—41no—
263C8×C13—41no—
264#1055—41no—
265#1055—41no—
266#1055—41no—
267#1055—41no—
268#533—131no—
269#533—131no—
270C4×#41C2×D1311yescharacteristic
271#500—131no—
272#498—131no—
273#487—131no—
274#487—131no—
275#485—261no—
276#485—261no—
277#485—261no—
278#485—261no—
279#479—261no—
280#479—261no—
281#477—131no—
282#476—131no—
283#475—131no—
284#474—131no—
285#462—131no—
286#462—131no—
287#461—131no—
288#461—131no—
289#452—261no—
290#452—261no—
291C8×Q8C2×D1311yescharacteristic
292C8×Q8C2×D1311yescharacteristic
293#441—261no—
294#440—261no—
295C4×Q16—261no—
296C4×SD16—261no—
297C8×D4—21no—
298C8×D4—21no—
299C8×D4C2×D1311yescharacteristic
300C8×D4C2×D1311yescharacteristic
301#432—131no—
302#431—21no—
303#431—131no—
304#431C2×D1311yescharacteristic
305C2×C4⋊C8—21no—
306C2×C4⋊C8C2×D1311yescharacteristic
307#335—131no—
308#335—131no—
309#334—131no—
310#334—131no—
311#333—131no—
312#333—131no—
313#332—131no—
314#332—131no—
315#332—131no—
316#332—131no—
317#332—131no—
318#332—131no—
319C22×C13—21no—
320C22×C13—21no—
321C22×C13—22no—
322C22×C13—21no—
323C22×C13—41no—
324C22×C13—41no—
325C22×C13C2×#12111yescharacteristic
326C4×C13—21no—
327C4×C13—21no—
328C4×C13—22no—
329C4×C13—21no—
330C4×C13—21no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13C2×#13511yescharacteristic
334C4×C13C2×#13511yescharacteristic
335C4×C13#57711yescharacteristic
336C4×C13#57811yescharacteristic
337Dic13—81no—
338Dic13—81no—
339Dic13—81no—
340Dic13—81no—
341C2×#41D5211yescharacteristic
342C2×Q16—261no—
343C2×Q16—261no—
344C2×SD16—261no—
345C2×SD16—261no—
346C22×C8—21no—
347C22×C8—21no—
348C22×C8—21no—
349C4⋊Q8—131no—
350C4⋊Q8—131no—
351C4⋊Q8—131no—
352C4⋊Q8—131no—
353#125—261no—
354#125—261no—
355C22⋊Q8—261no—
356C22⋊Q8—261no—
357C22⋊Q8—261no—
358C22⋊Q8—261no—
359C4×Q8—261no—
360C4×Q8—261no—
361C4×Q8—261no—
362C4×Q8—261no—
363C4×Q8D5211yescharacteristic
364C4×Q8C22×D1311yescharacteristic
365C4×D4—21no—
366C4×D4—21no—
367C4×D4D5211yescharacteristic
368C4×D4C22×D1311yescharacteristic
369#117—21no—
370#117—261no—
371#117—261no—
372#117D5211yescharacteristic
373C2×C42—21no—
374C2×C42C22×D1311yescharacteristic
375#107—261no—
376#107—261no—
377#107—261no—
378#107—261no—
379#106—261no—
380#106—261no—
381#106—261no—
382#106—261no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—131no—
387C4⋊C8—131no—
388C4⋊C8—131no—
389C4⋊C8—131no—
390C4⋊C8C22⋊D1311yescharacteristic
391C4⋊C8C22⋊D1311yescharacteristic
392C4⋊C8C22×D1311yescharacteristic
393C4⋊C8C22×D1311yescharacteristic
394#103—261no—
395#103—261no—
396#103—261no—
397#103—261no—
398#103—261no—
399#103—261no—
400#103—261no—
401#103—261no—
402#103—261no—
403#103—261no—
404#102—261no—
405#102—261no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—261no—
409C22⋊C8—261no—
410C22⋊C8C22⋊D1311yescharacteristic
411C22⋊C8C22⋊D1311yescharacteristic
412#97—261no—
413C4×C8—21no—
414C4×C8—21no—
415C4×C8—261no—
416C4×C8C22×D1311yescharacteristic
417C4×C8C22×D1311yescharacteristic
418C2×C13—41no—
419C2×C13—42no—
420C2×C13#304611yescharacteristic
421C2×C13#305011yescharacteristic
422C2×C13#306911yescharacteristic
423#41—22no—
424#41—22no—
425C2×Q8—261no—
426C2×Q8—261no—
427C2×Q8—261no—
428C2×Q8—261no—
429C2×Q8C2×D5211yescharacteristic
430C2×D4—21no—
431C2×D4C2×D5211yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4C2×D5211yescharacteristic
436C22×C4#612711yescharacteristic
437C22×C4C2×C22⋊D1311yescharacteristic
438Q16—522no—
439Q16—522no—
440SD16—522no—
441SD16—522no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—81no—
445C2×C8—81no—
446C2×C8—81no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—261no—
451C2×C8C2×C22⋊D1311yescharacteristic
452C2×C8C2×C22⋊D1311yescharacteristic
453C2×C8C2×C22⋊D1311yescharacteristic
454C2×C8C2×C22⋊D1311yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—521no—
466C4⋊C4—521no—
467C4⋊C4—521no—
468C4⋊C4—521no—
469C4⋊C4C2×D5211yescharacteristic
470C4⋊C4C2×D5211yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—521no—
475C22⋊C4—521no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—521no—
480C42—521no—
481C42C2×D5211yescharacteristic
482C42#612711yescharacteristic
483C42C2×C22⋊D1311yescharacteristic
484C42C23×D1311yescharacteristic
485C13#1941811yescharacteristic, complemented, Sylow
486C23—21no—
487C23#8818411yescharacteristic
488Q8—21no—
489Q8—521no—
490Q8—521no—
491Q8—521no—
492Q8—521no—
493Q8—521no—
494Q8—521no—
495Q8—1041no—
496Q8#8815812yes—
497D4—24no—
498D4—21no—
499D4#8815812yes—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—81no—
512C2×C4—521no—
513C2×C4—521no—
514C2×C4—521no—
515C2×C4—521no—
516C2×C4#8818411yescharacteristic
517C2×C4#8818411yescharacteristic
518C2×C4#8818411yescharacteristic
519C2×C4C22×D5211yescharacteristic
520C2×C4C2×#612711yescharacteristic
521C2×C4C22×C22⋊D1311yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—521no—
529C8—521no—
530C8—521no—
531C8—521no—
532C22—21no—
533C22—21no—
534C22—22no—
535C22—21no—
536C22—41no—
537C22—41no—
538C22C2×#8818411yescharacteristic
539C4—21no—
540C4—21no—
541C4—22no—
542C4—21no—
543C4—21no—
544C4—41no—
545C4—41no—
546C4—1041no—
547C4—1041no—
548C4—1041no—
549C4—1041no—
550C4C2×#8815811yescharacteristic
551C4C2×#8815811yescharacteristic
552C4#1171954111yescharacteristic
553C4#1171954311yescharacteristic
554C2—41no—
555C2—42no—
556C2#1312438611yescharacteristic
557C2#1312441711yescharacteristic
558C2#1312457311yescharacteristic
subgroupG/H
centerC22C2×#88184
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#2988C2
socleC22×C13C2×#121
prime radicalC2×C13×#41D4
hypercenter#2988D13
hypocenterC13#19418
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #13125997C2semidirect
4. #13114294C2semidirect
5. #13114287C2semidirect
6. #13114266C2semidirect
7. #13114259C2semidirect
8. #13114230C2semidirect
9. #13114225C2semidirect
10. #13114218C2semidirect
11. #13114211C2semidirect
12. #13113616C2semidirect
13. #13113534C2semidirect
14. #13113494C2semidirect
485. C13#19418semidirect

Maximal subgroups

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

subgroupindex
#131259972
#131249982
#131249072
#131142942
#131142872
#131142662
#131142592
#131142302
#131142252
#131142182
#131142112
#131136162
#131135342
#131134942
C13×#29882
#1941813