Finite Group Databasebeta

← #16809594

Subgroups — #16809594

Order 3328.

1744 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131779C213yesmaximal, complemented
2#13131778C213yesmaximal, complemented
3#13131768C211yesmaximal, characteristic, complemented
4#13131767C213yesmaximal, complemented
5#13131745C213yesmaximal, complemented
6#13131730C211yesmaximal, characteristic, complemented
7#13131729C211yesmaximal, characteristic, complemented
8#13131668C213yesmaximal, complemented
9#13131667C213yesmaximal, complemented
10#13131646C213yesmaximal, complemented
11#41×#1057C211yesmaximal, characteristic, complemented
12Q8×#6118C211yesmaximal, characteristic, complemented
13Q8×#6122C211yesmaximal, characteristic, complemented
14#13131624C213yesmaximal, complemented
15#13128452C211yesmaximal, characteristic
16C13×#548C411yescharacteristic
17#11719536C411yescharacteristic
18#41×Dic13C2211yescharacteristic
19Q8×C22⋊D13C411yescharacteristic
20C2×Q8×Dic13C2211yescharacteristic
21#11719385C2213yes—
22#11719376C413yes—
23#11719344C413yes—
24#11719327C2213yes—
25#11719316C413yes—
26#11719305C2213yes—
27C4×Q8×D13C2211yescharacteristic
28#11719274C411yescharacteristic
29#11719246C413yes—
30C4×#6129C2213yes—
31#11719158C2213yes—
32#11719158C2213yes—
33Q8×#1057C2213yes—
34Q8×#1057C2211yescharacteristic
35Q8×#1057C2211yescharacteristic
36Q8×#1057C2211yescharacteristic
37Q8×#1057C2211yescharacteristic
38Q8×#1057C2213yes—
39#11719145C2216yes—
40#11719145C2213yes—
41#11719145C2213yes—
42#11719144C2213yes—
43#11719144C2213yes—
44D4×#1057C2213yes—
45D4×#1057C2213yes—
46#11719129C2213yes—
47#11719129C2213yes—
48#11719125C2213yes—
49C4×#6122C2213yes—
50#11719119C2213yes—
51#11719119C2213yes—
52#11719119C2213yes—
53C2×C4×#1057C2213yes—
54#11719080C2213yes—
55#11719080C2213yes—
56#11719078C2213yes—
57#11719078C2213yes—
58#11719074C2213yes—
59#11719074C2216yes—
60#11719074C2213yes—
61#11719068C2216yes—
62#11719068C2216yes—
63#11719067C2216yes—
64#11719066C2216yes—
65#11719066C2211yescharacteristic
66#11719066C2213yes—
67#11719064C2213yes—
68#11719064C2213yes—
69#11719062C2216yes—
70#11719052C2213yes—
71#11719051C2213yes—
72#11719049C2213yes—
73C4×#6118C2213yes—
74C2×C13×#41C2×C411yescharacteristic
75C22×Q8×C13C2×C411yescharacteristic
76C2×Q8×D13C2×C411yescharacteristic
77C2×#6129C2×C413yes—
78C2×#6122C2311yescharacteristic
79C2×#6122C2316yes—
80C2×#6122C2313yes—
81C22×#1057C2313yes—
82C22×#1057C2313yes—
83C2×#6118C2311yescharacteristic
84C2×#6118C2313yes—
85C13×#124C2×C413yes—
86C13×C22⋊Q8C2×C413yes—
87C13×#121C2×C413yes—
88C4×Q8×C13C2×C411yescharacteristic
89C4×D4×C13C2×C413yes—
90#88200C2×C413yes—
91Q8×Dic13C2×C411yescharacteristic
92Q8×Dic13C2×C413yes—
93Q8×Dic13C2×C411yescharacteristic
94Q8×Dic13C2311yescharacteristic
95Q8×Dic13C2313yes—
96#88198C2×C413yes—
97#88192C2×C413yes—
98#88190C2×C413yes—
99#88189C2×C416yes—
100D4×Dic13C2×C413yes—
101D4×Dic13C2313yes—
102D4×Dic13C2313yes—
103C4×C22⋊D13C2×C413yes—
104C4×C22⋊D13C2×C413yes—
105#88180C2×C413yes—
106C2×C4⋊Dic13C2×C413yes—
107#88178C2×C413yes—
108#88178C2×C413yes—
109C2×C4×Dic13C2313yes—
110C2×C4×Dic13C2313yes—
111#88146C2×C413yes—
112C4⋊C4×D13C2×C413yes—
113#88144C2×C413yes—
114#88143C2×C416yes—
115#88142C2×C413yes—
116#88141C2313yes—
117#88141C2313yes—
118#88137C2×C416yes—
119#88135C2311yescharacteristic
120#88135C2313yes—
121#88133C2×C416yes—
122#88133C2×C416yes—
123#88132C2×C416yes—
124#88131C2×C413yes—
125#88131C2×C413yes—
126#88131C2316yes—
127C42×D13C2313yes—
128#88124C2×C413yes—
129C4×Dic26C2×C413yes—
130C4×Dic26C2×C413yes—
131C22⋊#1057C2313yes—
132C22⋊#1057C2313yes—
133C22⋊#1057C2316yes—
134C22⋊#1057C2311yescharacteristic
135C22⋊#1057C2313yes—
136#88112C2313yes—
137#88112C2313yes—
138#88112C2316yes—
139#88112C2313yes—
140#88112C2311yescharacteristic
141#88111C2311yescharacteristic
142#88111C2313yes—
143#88110C2313yes—
144#88110C2313yes—
145#88110C2313yes—
146#88110C2313yes—
147C4⋊#1057C2313yes—
148C4⋊#1057C2313yes—
149C4⋊#1057C2316yes—
150C4⋊#1057C2313yes—
151C4⋊#1057C2313yes—
152C4⋊#1057C2313yes—
153C4⋊#1057C2313yes—
154C4×#1057C2313yes—
155C4×#1057C2313yes—
156C4×#1057C2313yes—
157C4×#1057C2313yes—
158C4×#1057C2316yes—
159C4×#1057C2316yes—
160C4×#1057C2313yes—
161C4×#1057C2311yescharacteristic
162#60345—131nomaximal, Sylow
163C13×#41—24no—
164C2×Q8×C13—24no—
165C2×Q8×C13C22×C413yes—
166C2×Q8×C13C22×C411yescharacteristic
167C2×D4×C13C22×C413yes—
168C2×D4×C13C22×C413yes—
169C22×C4×C13C22×C413yes—
170C22×C4×C13C22×C413yes—
171C2×C22⋊D13C22×C411yescharacteristic
172C2×C22⋊D13C22×C413yes—
173C22×Dic13C22×C413yes—
174C22×Dic13C22×C413yes—
175C22×Dic13C2413yes—
176C22×Dic13C2411yescharacteristic
177Q8×D13—24no—
178#6129—46no—
179C2×C4×D13C22×C413yes—
180C2×C4×D13C22×C413yes—
181C2×C4×D13C2411yescharacteristic
182C2×Dic26C22×C413yes—
183C2×Dic26C22×C413yes—
184#6122—22no—
185#6122—43no—
186#6122—46no—
187C2×#1057—26no—
188C2×#1057—43no—
189C2×#1057C2413yes—
190C2×#1057C2411yescharacteristic
191C2×#1057C2413yes—
192C2×#1057C2411yescharacteristic
193C2×#1057C2413yes—
194C2×#1057C2411yescharacteristic
195C2×#1057C2413yes—
196C2×#1057C2411yescharacteristic
197#6118—22no—
198#6118—43no—
199C13×C4⋊C4C22×C413yes—
200C13×C4⋊C4C22×C413yes—
201C13×C22⋊C4C22×C411yescharacteristic
202C13×C22⋊C4C22×C413yes—
203C13×C22⋊C4C22×C416yes—
204C42×C13C22×C413yes—
205C22⋊Dic13C22×C413yes—
206C22⋊Dic13C22×C413yes—
207C22⋊Dic13C22×C416yes—
208C22⋊Dic13C22×C416yes—
209#6103C22×C413yes—
210#6103C22×C411yescharacteristic
211C4⋊Dic13C22×C413yes—
212C4⋊Dic13C22×C413yes—
213C4⋊Dic13C22×C413yes—
214C4⋊Dic13C22×C413yes—
215C4⋊Dic13C22×C416yes—
216#6101C22×C411yescharacteristic
217#6101C22×C413yes—
218#6101C22×C416yes—
219#6101C22×C416yes—
220#6101C22×C413yes—
221#6101C22×C413yes—
222#6101C22×C416yes—
223C4×Dic13C22×C413yes—
224C4×Dic13C22×C413yes—
225C4×Dic13C22×C413yes—
226C4×Dic13C22×C413yes—
227C4×Dic13C22×C413yes—
228C4×Dic13C2413yes—
229C4×Dic13C2411yescharacteristic
230C4×Dic13C2413yes—
231C4×Dic13C2413yes—
232#3482—131no—
233#2993—133no—
234#2993—133no—
235#2991—133no—
236#2991—131no—
237#2986—133no—
238#2982—131no—
239#2982—131no—
240#2969—133no—
241#2969—133no—
242#2965—133no—
243C8×#41—131no—
244Q8×M16—131no—
245Q8×M16—131no—
246#2960—133no—
247C23×C13C23×C413yes—
248C23×C13C23×C411yescharacteristic
249C22×D13C23×C411yescharacteristic
250Q8×C13—26no—
251Q8×C13#13114yes—
252D4×C13—26no—
253D4×C13—43no—
254C2×C4×C13—26no—
255C2×C4×C13—26no—
256C2×C4×C13C23×C411yescharacteristic
257C2×C4×C13C23×C411yescharacteristic
258C2×C4×C13C23×C413yes—
259C2×C4×C13C23×C413yes—
260C2×C4×C13C23×C413yes—
261C22⋊D13—22no—
262C22⋊D13—43no—
263C2×Dic13—26no—
264C2×Dic13—23no—
265C2×Dic13—21no—
266C2×Dic13—23no—
267C2×Dic13—21no—
268C2×Dic13—43no—
269C2×Dic13C23×C411yescharacteristic
270C2×Dic13C23×C413yes—
271C2×Dic13C23×C413yes—
272C2×Dic13C23×C413yes—
273C2×Dic13C23×C413yes—
274C2×Dic13C23×C411yescharacteristic
275C2×Dic13C2511yescharacteristic
276C4×D13—26no—
277C4×D13—21no—
278C4×D13—21no—
279C4×D13—43no—
280Dic26—26no—
281Dic26—26no—
282#1057—21no—
283#1057—23no—
284#1057—21no—
285#1057—23no—
286#1057—23no—
287#1057—21no—
288#1057—23no—
289#10572−1+412yes—
290#557—131no—
291#556—133no—
292#552—133no—
293#552—133no—
294D4×Q8—131no—
295#548—131no—
296#548#26111yescharacteristic
297#547—133no—
298#533—133no—
299#529—133no—
300#529—133no—
301C4×#41—131no—
302C4×#41—133no—
303C2×C4×Q8—131no—
304C2×C4×Q8—131no—
305#446—133no—
306#446—133no—
307#446—133no—
308#446—133no—
309#446—133no—
310#446—133no—
311C8×Q8—133no—
312C8×Q8—136no—
313C8×Q8—133no—
314C8×Q8—131no—
315C8×Q8—131no—
316C8×Q8—131no—
317C8×Q8—131no—
318C8×Q8—133no—
319C8×Q8—133no—
320#436—131no—
321#436—133no—
322#436—136no—
323#436—133no—
324#436—133no—
325#436—136no—
326#435—133no—
327#435—133no—
328#435—133no—
329#435—133no—
330C8×D4—133no—
331C8×D4—133no—
332#433—136no—
333#433—136no—
334#431—133no—
335#431—133no—
336#431—133no—
337#431—133no—
338#431—133no—
339#431—133no—
340#424—136no—
341#423—133no—
342#423—133no—
343#423—133no—
344#405—136no—
345C4×M16—133no—
346C4×M16—133no—
347C2×C4×C8—133no—
348C22×C13—23no—
349C22×C13—21no—
350C22×C13—21no—
351C22×C13—23no—
352C22×C13—23no—
353C22×C13—21no—
354C22×C13C24×C411yescharacteristic
355C2×D13—21no—
356C2×D13—21no—
357C2×D13—21no—
358C4×C13—21no—
359C4×C13—21no—
360C4×C13—23no—
361C4×C13—23no—
362C4×C13C2×#13116yes—
363Dic13—23no—
364Dic13—21no—
365Dic13—23no—
366Dic13—23no—
367Dic13—23no—
368Dic13#56812yes—
369Dic13C2×2−1+411yescharacteristic
370Dic13#58511yescharacteristic
371C2×#41—133no—
372C2×#41C2×#26111yescharacteristic
373C22×Q8—131no—
374C22×Q8C2×#26111yescharacteristic
375C2×M16—131no—
376C2×M16—131no—
377C2×M16—133no—
378C2×M16—133no—
379C2×M16—136no—
380C22×C8—133no—
381C22×C8—133no—
382C4⋊Q8—133no—
383C4⋊Q8—133no—
384#126—136no—
385#126—136no—
386#125—133no—
387#125—136no—
388#125—133no—
389#124—133no—
390#124C2×#26113yes—
391#123—136no—
392#123—136no—
393C22⋊Q8—133no—
394C22⋊Q8—133no—
395C22⋊Q8—133no—
396C22⋊Q8—136no—
397C22⋊Q8C2×#26113yes—
398#121—133no—
399#121C2×#26113yes—
400C4×Q8—131no—
401C4×Q8—133no—
402C4×Q8—131no—
403C4×Q8—133no—
404C4×Q8—131no—
405C4×Q8—133no—
406C4×Q8—133no—
407C4×Q8—133no—
408C4×Q8—133no—
409C4×Q8C2×#26111yescharacteristic
410C4×D4—133no—
411C4×D4—133no—
412C4×D4—133no—
413C4×D4—133no—
414C4×D4—133no—
415C4×D4—131no—
416C4×D4—133no—
417C4×D4C2×#26113yes—
418#117—133no—
419#117—133no—
420#117—133no—
421#117—133no—
422#117—136no—
423C2×C4⋊C4—133no—
424C2×C4⋊C4—133no—
425C2×C42—133no—
426C2×C42—133no—
427C2×C42—133no—
428C4⋊C8—133no—
429C4⋊C8—133no—
430C4⋊C8—133no—
431C4⋊C8—136no—
432C4⋊C8—133no—
433C4⋊C8—133no—
434C4⋊C8—133no—
435C4⋊C8—133no—
436C4⋊C8—136no—
437C4⋊C8—133no—
438C4⋊C8—131no—
439C4⋊C8—133no—
440C22⋊C8—131no—
441C22⋊C8—133no—
442C22⋊C8—131no—
443C22⋊C8—133no—
444C22⋊C8—136no—
445C22⋊C8—133no—
446C22⋊C8—133no—
447#97—133no—
448#97—133no—
449#97—133no—
450#97—133no—
451C4×C8—131no—
452C4×C8—133no—
453C4×C8—133no—
454C4×C8—133no—
455C4×C8—133no—
456C4×C8—133no—
457C4×C8—136no—
458C4×C8—136no—
459C2×C13—41no—
460C2×C13—43no—
461C2×C13C4×2−1+411yescharacteristic
462C2×C13C22×#13111yescharacteristic
463C2×C13C2×#56811yescharacteristic
464D13—41no—
465#41—24no—
466#41—526no—
467C2×Q8—24no—
468C2×Q8—133no—
469C2×Q8—133no—
470C2×Q8—264no—
471C2×Q8C22×#26113yes—
472C2×Q8C22×#26111yescharacteristic
473C2×D4—131no—
474C2×D4—133no—
475C2×D4C22×#26113yes—
476C2×D4C22×#26113yes—
477C22×C4—131no—
478C22×C4—133no—
479C22×C4—133no—
480C22×C4—133no—
481C22×C4—131no—
482C22×C4—133no—
483C22×C4—133no—
484C22×C4C22×#26113yes—
485C22×C4C22×#26113yes—
486M16—262no—
487M16—262no—
488M16—523no—
489M16—523no—
490M16—526no—
491C2×C8—131no—
492C2×C8—133no—
493C2×C8—131no—
494C2×C8—131no—
495C2×C8—131no—
496C2×C8—133no—
497C2×C8—133no—
498C2×C8—133no—
499C2×C8—266no—
500C2×C8—523no—
501C4⋊C4—133no—
502C4⋊C4—133no—
503C4⋊C4—136no—
504C4⋊C4—136no—
505C4⋊C4—131no—
506C4⋊C4—133no—
507C4⋊C4—133no—
508C4⋊C4—133no—
509C4⋊C4—133no—
510C4⋊C4—133no—
511C4⋊C4—136no—
512C4⋊C4—136no—
513C4⋊C4C22×#26113yes—
514C4⋊C4C22×#26113yes—
515C22⋊C4—133no—
516C22⋊C4—136no—
517C22⋊C4—133no—
518C22⋊C4—136no—
519C22⋊C4—131no—
520C22⋊C4—133no—
521C22⋊C4C22×#26111yescharacteristic
522C22⋊C4C22×#26113yes—
523C22⋊C4C22×#26116yes—
524C42—131no—
525C42—133no—
526C42—133no—
527C42—133no—
528C42—133no—
529C42—133no—
530C42—133no—
531C42—133no—
532C42—133no—
533C42C22×#26113yes—
534C13#6034511yescharacteristic, complemented, Sylow
535C23—131no—
536C23C23×#26113yes—
537C23C23×#26111yescharacteristic
538Q8—26no—
539Q8—266no—
540Q8—266no—
541Q8#8823814yes—
542D4—26no—
543D4—43no—
544D4—262no—
545D4—523no—
546C2×C4—26no—
547C2×C4—26no—
548C2×C4—131no—
549C2×C4—131no—
550C2×C4—131no—
551C2×C4—133no—
552C2×C4—133no—
553C2×C4—133no—
554C2×C4—133no—
555C2×C4—261no—
556C2×C4—261no—
557C2×C4—263no—
558C2×C4—263no—
559C2×C4—261no—
560C2×C4—261no—
561C2×C4—266no—
562C2×C4—266no—
563C2×C4—523no—
564C2×C4—523no—
565C2×C4C23×#26111yescharacteristic
566C2×C4C23×#26111yescharacteristic
567C2×C4C23×#26113yes—
568C2×C4C23×#26113yes—
569C2×C4C23×#26113yes—
570C8—132no—
571C8—263no—
572C8—261no—
573C8—263no—
574C8—261no—
575C8—261no—
576C8—263no—
577C8—263no—
578C22—23no—
579C22—21no—
580C22—21no—
581C22—23no—
582C22—23no—
583C22—21no—
584C22—261no—
585C22—261no—
586C22—261no—
587C22C24×#26111yescharacteristic
588C4—21no—
589C4—21no—
590C4—23no—
591C4—23no—
592C4—131no—
593C4—131no—
594C4—132no—
595C4—261no—
596C4—263no—
597C4—263no—
598C4—263no—
599C4—263no—
600C4C2×#8823816yes—
601C2—41no—
602C2—43no—
603C2—521no—
604C22−1+4×#26111yescharacteristic
605C2C22×#8823811yescharacteristic
606C2D13⋊#56811yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#548C4
prime radical#13128452C2
cosocleC2×Dic13C25
hypercenter#548#261
hypocenterC13#60345
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #13131779C2semidirect
2. #13131778C2semidirect
3. #13131768C2semidirect
4. #13131767C2semidirect
5. #13131745C2semidirect
6. #13131730C2semidirect
7. #13131729C2semidirect
8. #13131668C2semidirect
9. #13131667C2semidirect
10. #13131646C2semidirect
11. #41×#1057C2semidirect
12. Q8×#6118C2semidirect
13. Q8×#6122C2semidirect
14. #13131624C2semidirect
534. C13#60345semidirect

Maximal subgroups

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

subgroupindex
#131317792
#131317782
#131317682
#131317672
#131317452
#131317302
#131317292
#131316682
#131316672
#131316462
#41×#10572
Q8×#61182
Q8×#61222
#131316242
#131284522
#6034513