Finite Group Databasebeta

← #16795168

Subgroups — #16795168

Order 3328.

592 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131767C211yesmaximal, characteristic
2#13131761C211yesmaximal, characteristic
3#13130412C211yesmaximal, characteristic, complemented
4#13130412C211yesmaximal, characteristic, complemented
5#13130408C211yesmaximal, characteristic, complemented
6#13130407C211yesmaximal, characteristic, complemented
7#13130404C211yesmaximal, characteristic, complemented
8#13130403C211yesmaximal, characteristic, complemented
9#13130402C211yesmaximal, characteristic, complemented
10#13130400C211yesmaximal, characteristic, complemented
11#13130390C211yesmaximal, characteristic, complemented
12#13130389C211yesmaximal, characteristic, complemented
13#13130388C211yesmaximal, characteristic, complemented
14#13130385C211yesmaximal, characteristic, complemented
15#13123796C211yesmaximal, characteristic
16C4×#6129C2211yescharacteristic
17#11719145—21no—
18#11719144—21no—
19#11719130C2211yescharacteristic
20#11719129C2211yescharacteristic
21#11719129C2211yescharacteristic
22#11719129C2211yescharacteristic
23#11719119C2211yescharacteristic
24#11719119C2211yescharacteristic
25#11719119C2211yescharacteristic
26C2×C4⋊#1057C2211yescharacteristic
27#11719078—21no—
28#11719074—21no—
29#11719066—21no—
30#11719066—21no—
31#11719065—21no—
32#11719063—21no—
33#11719054C2211yescharacteristic
34#11719052C2211yescharacteristic
35#11719051C2211yescharacteristic
36D13⋊(C4⋊C8)C2211yescharacteristic
37C13×#435C411yescharacteristic
38#11718789C411yescharacteristic
39M16×Dic13C2211yescharacteristic
40#11718772C411yescharacteristic
41C2×C8×Dic13C2211yescharacteristic
42#11718672C411yescharacteristic
43#11718494C2211yescharacteristic
44#11718489C411yescharacteristic
45#11718391C411yescharacteristic
46#11718390C411yescharacteristic
47#11718379C2211yescharacteristic
48#11718379C2211yescharacteristic
49#11718368C2211yescharacteristic
50#11718362C411yescharacteristic
51#11718256C2211yescharacteristic
52#11718256C2211yescharacteristic
53#11718256C2211yescharacteristic
54#11718256C2211yescharacteristic
55#11718255C2211yescharacteristic
56#11718255C2211yescharacteristic
57#11718255C2211yescharacteristic
58#11718255C2211yescharacteristic
59#11718255C2211yescharacteristic
60#11718255C2211yescharacteristic
61#11718254C2211yescharacteristic
62#11718254C2211yescharacteristic
63#11718253C2211yescharacteristic
64#11718253C2211yescharacteristic
65#11718253C2211yescharacteristic
66#11718253C2211yescharacteristic
67C2×#6129Q811yescharacteristic
68C2×#6122—21no—
69C2×#6122—21no—
70C2×#6122—21no—
71C22×#1057—21no—
72C2×#6118—21no—
73C2×D13⋊C8—21no—
74C2×C13×M16C2×C411yescharacteristic
75C22×C8×C13C2×C411yescharacteristic
76C4×D4×C13C2×C411yescharacteristic
77D4×Dic13D411yescharacteristic
78C4×C22⋊D13C2×C411yescharacteristic
79C4×C22⋊D13C2×C411yescharacteristic
80C2×C4×Dic13C2311yescharacteristic
81C2×C4×Dic13C2311yescharacteristic
82C2×#6099C2×C411yescharacteristic
83C22×#1055C2×C411yescharacteristic
84C2×#6094C2×C411yescharacteristic
85C2×#6094C2×C411yescharacteristic
86#88146Q811yescharacteristic
87#88141D411yescharacteristic
88#88135D411yescharacteristic
89#88135D411yescharacteristic
90#88131Q811yescharacteristic
91#88131Q811yescharacteristic
92C42×D13C2311yescharacteristic
93C4×Dic26C2×C411yescharacteristic
94C22⋊#1057—21no—
95C22⋊#1057—21no—
96C22⋊#1057—21no—
97C22⋊#1057—21no—
98#88112—21no—
99#88112—21no—
100#88112—21no—
101#88112—21no—
102#88111—21no—
103#88111—21no—
104#88110—21no—
105#88110—21no—
106C4⋊#1057—21no—
107C4⋊#1057—21no—
108C4⋊#1057C2311yescharacteristic
109C4⋊#1057C2311yescharacteristic
110C4⋊#1057C2311yescharacteristic
111C4⋊#1057C2311yescharacteristic
112C4⋊#1057C2311yescharacteristic
113C4⋊#1057C2311yescharacteristic
114C4⋊#1057C2311yescharacteristic
115C4⋊#1057C2311yescharacteristic
116C4×#1057—21no—
117C4×#1057—21no—
118C4×#1057—21no—
119C4×#1057—21no—
120C13×C4⋊C8C2×C411yescharacteristic
121C13×C22⋊C8C2×C411yescharacteristic
122C13×C22⋊C8C2×C411yescharacteristic
123C13×#97C2×C411yescharacteristic
124C22⋊#1055C2×C411yescharacteristic
125C22⋊#1055C2×C411yescharacteristic
126#88060C2×C411yescharacteristic
127#88060C2×C411yescharacteristic
128#88055C2×C411yescharacteristic
129#88055C2×C411yescharacteristic
130#88054C2×C411yescharacteristic
131#88054C2×C411yescharacteristic
132#88054C2×C411yescharacteristic
133#88054C2×C411yescharacteristic
134C8×Dic13C2×C411yescharacteristic
135C8×Dic13C2×C411yescharacteristic
136C8×Dic13C2311yescharacteristic
137C8×Dic13C2311yescharacteristic
138C8×Dic13C2311yescharacteristic
139C8×Dic13C2311yescharacteristic
140C4⋊#1055C2×C411yescharacteristic
141#88043C2×C411yescharacteristic
142#17841—131nomaximal, Sylow
143C2×D4×C13C4⋊C411yescharacteristic
144C22×C4×C13C22×C411yescharacteristic
145C22×C4×C13C22×C411yescharacteristic
146C2×C22⋊D13C4⋊C411yescharacteristic
147C2×C22⋊D13C4⋊C411yescharacteristic
148C22×Dic13C2×D411yescharacteristic
149C22×Dic13C2×D411yescharacteristic
150C22×Dic13C2×Q811yescharacteristic
151C22×Dic13C2×Q811yescharacteristic
152#6129—42no—
153C2×C4×D13C22×C411yescharacteristic
154C2×C4×D13C2×D411yescharacteristic
155C2×C4×D13C2×Q811yescharacteristic
156C2×Dic26C4⋊C411yescharacteristic
157#6122—81no—
158#6122—81no—
159#6122—81no—
160C2×#1057—21no—
161C2×#1057—21no—
162C2×#1057—21no—
163C2×#1057—21no—
164C2×#1057—21no—
165C2×#1057—21no—
166C2×#1057—21no—
167C2×#1057—21no—
168C2×#1057—81no—
169#6118—81no—
170D13⋊C8—81no—
171C13×M16—41no—
172C2×C8×C13—41no—
173C2×C8×C13C22×C411yescharacteristic
174C2×C8×C13C22×C411yescharacteristic
175C2×C8×C13C22×C411yescharacteristic
176C2×C8×C13C22×C411yescharacteristic
177C13×C4⋊C4C4⋊C411yescharacteristic
178C13×C22⋊C4C4⋊C411yescharacteristic
179C13×C22⋊C4C4⋊C411yescharacteristic
180C42×C13C22×C411yescharacteristic
181C22⋊Dic13C4⋊C411yescharacteristic
182C22⋊Dic13C4⋊C411yescharacteristic
183#6103C4⋊C411yescharacteristic
184#6103C4⋊C411yescharacteristic
185C4⋊Dic13C4⋊C411yescharacteristic
186#6101C4⋊C411yescharacteristic
187#6101C4⋊C411yescharacteristic
188#6101C4⋊C411yescharacteristic
189#6101C4⋊C411yescharacteristic
190C4×Dic13C22×C411yescharacteristic
191C4×Dic13C22×C411yescharacteristic
192C4×Dic13C2×D411yescharacteristic
193C4×Dic13C2×D411yescharacteristic
194C4×Dic13C2×D411yescharacteristic
195C4×Dic13C2×Q811yescharacteristic
196C4×Dic13C2×Q811yescharacteristic
197C4×Dic13C2×Q811yescharacteristic
198C4×Dic13C2411yescharacteristic
199#6099—22no—
200C2×#1055—22no—
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205#6094—22no—
206#6094—41no—
207#2991—131no—
208#2990—131no—
209#2965—131no—
210#1574—131no—
211#1574—131no—
212#1572—131no—
213#1572—131no—
214#1570—131no—
215#1570—131no—
216#1569—131no—
217#1569—131no—
218#1566—131no—
219#1565—131no—
220#1565—131no—
221#1564—131no—
222C23×C13C2×C4⋊C411yescharacteristic
223C23×C13C2×C4⋊C411yescharacteristic
224C22×D13C2×C4⋊C411yescharacteristic
225D4×C13—41no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13C2×C4⋊C411yescharacteristic
231C2×C4×C13C2×C4⋊C411yescharacteristic
232C2×C4×C13C2×C4⋊C411yescharacteristic
233C2×C4×C13C2×C4⋊C411yescharacteristic
234C2×C4×C13C23×C411yescharacteristic
235C22⋊D13—22no—
236C22⋊D13—41no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—22no—
242C2×Dic13—41no—
243C2×Dic13C2×C4⋊C411yescharacteristic
244C2×Dic13C2×C4⋊C411yescharacteristic
245C2×Dic13C2×C4⋊C411yescharacteristic
246C2×Dic13C2×C4⋊C411yescharacteristic
247C2×Dic13C2×C4⋊C411yescharacteristic
248C2×Dic13C22×D411yescharacteristic
249C2×Dic13C22×Q811yescharacteristic
250C4×D13—21no—
251C4×D13—21no—
252C4×D13—21no—
253C4×D13—21no—
254C4×D13—41no—
255Dic26—22no—
256#1057—41no—
257#1057—41no—
258#1057—41no—
259#1057—41no—
260#1057—41no—
261#1057—41no—
262#1057—41no—
263#1057—41no—
264C8×C13—21no—
265C8×C13—21no—
266C8×C13—21no—
267C8×C13—21no—
268#1055—21no—
269#1055—21no—
270#1055—21no—
271#1055#13112yes—
272C4×#41—131no—
273#446—131no—
274#446—131no—
275#446—261no—
276C8×Q8—261no—
277#436—131no—
278#436—131no—
279#436—261no—
280#436—261no—
281#436—261no—
282#435—131no—
283#435—131no—
284#435—131no—
285#435—261no—
286#435—261no—
287#435#26111yescharacteristic
288C8×D4—261no—
289#432—131no—
290#432—131no—
291#431—131no—
292#431—131no—
293#431—131no—
294#431—131no—
295#431—131no—
296#431—131no—
297#431—131no—
298#423—131no—
299#423—131no—
300#423—131no—
301#423—131no—
302C2×C4⋊C8—131no—
303C2×C4⋊C8—131no—
304C4×M16—131no—
305C4×M16—131no—
306C2×C4×C8—131no—
307#335—131no—
308#335—131no—
309#335—131no—
310#335—131no—
311#335—131no—
312#335—131no—
313#334—131no—
314#334—131no—
315#334—131no—
316#334—131no—
317#334—131no—
318#334—131no—
319#334—131no—
320#334—131no—
321#334—131no—
322#334—131no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—21no—
326C22×C13—21no—
327C22×C13—21no—
328C22×C13—21no—
329C22×C13C22×C4⋊C411yescharacteristic
330C2×D13—21no—
331C2×D13—21no—
332C2×D13—21no—
333C4×C13—21no—
334C4×C13—21no—
335C4×C13—21no—
336C4×C13—21no—
337C4×C13C2×#13111yescharacteristic
338C4×C13#56811yescharacteristic
339Dic13—21no—
340Dic13—21no—
341Dic13—21no—
342Dic13—21no—
343Dic13—21no—
344Dic13#43012yes—
345Dic13#57711yescharacteristic
346Dic13#57711yescharacteristic
347C2×#41—131no—
348C2×M16—131no—
349C2×M16—131no—
350C2×M16—131no—
351C2×M16—261no—
352C2×M16—261no—
353C2×M16—261no—
354C2×M16—261no—
355C2×M16C2×#26111yescharacteristic
356C22×C8—131no—
357C22×C8—261no—
358C22×C8—261no—
359C22×C8C2×#26111yescharacteristic
360C4×Q8—131no—
361C4×Q8—131no—
362C4×D4—131no—
363C4×D4—131no—
364C4×D4—131no—
365C4×D4—131no—
366C4×D4—131no—
367C4×D4C2×#26111yescharacteristic
368#117—131no—
369#117—131no—
370#117—131no—
371C2×C42—131no—
372C2×C42—131no—
373C2×C42—131no—
374C4⋊C8—131no—
375C4⋊C8—131no—
376C4⋊C8—131no—
377C4⋊C8—131no—
378C4⋊C8—131no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—131no—
384C4⋊C8—131no—
385C4⋊C8—131no—
386C4⋊C8—131no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391C4⋊C8—261no—
392C4⋊C8—261no—
393C4⋊C8C2×#26111yescharacteristic
394C22⋊C8—131no—
395C22⋊C8—131no—
396C22⋊C8—131no—
397C22⋊C8—131no—
398C22⋊C8—261no—
399C22⋊C8—261no—
400C22⋊C8—261no—
401C22⋊C8—261no—
402C22⋊C8—261no—
403C22⋊C8—261no—
404C22⋊C8C2×#26111yescharacteristic
405C22⋊C8C2×#26111yescharacteristic
406#97—131no—
407#97—131no—
408#97—131no—
409#97—261no—
410#97—261no—
411#97C2×#26111yescharacteristic
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—131no—
417C4×C8—131no—
418C4×C8—261no—
419C4×C8—261no—
420C4×C8—261no—
421C4×C8—261no—
422C2×C13—41no—
423C2×C13—41no—
424C2×C13#290611yescharacteristic
425C2×C13#291211yescharacteristic
426C2×C13C2×#43011yescharacteristic
427D13—41no—
428#41—522no—
429C2×Q8—131no—
430C2×D4—131no—
431C2×D4—131no—
432C2×D4C4⋊#26111yescharacteristic
433C22×C4—131no—
434C22×C4—131no—
435C22×C4—131no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4C22×#26111yescharacteristic
441C22×C4C22×#26111yescharacteristic
442M16—41no—
443M16—262no—
444M16—262no—
445M16—521no—
446M16—1041no—
447M16—1041no—
448M16—1041no—
449M16—1041no—
450C2×C8—41no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—262no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—1041no—
465C2×C8—1041no—
466C2×C8C22×#26111yescharacteristic
467C2×C8C22×#26111yescharacteristic
468C2×C8C22×#26111yescharacteristic
469C2×C8C22×#26111yescharacteristic
470C4⋊C4—131no—
471C4⋊C4—131no—
472C4⋊C4—131no—
473C4⋊C4—131no—
474C4⋊C4—131no—
475C4⋊C4C4⋊#26111yescharacteristic
476C22⋊C4—131no—
477C22⋊C4—131no—
478C22⋊C4—131no—
479C22⋊C4—131no—
480C22⋊C4C4⋊#26111yescharacteristic
481C22⋊C4C4⋊#26111yescharacteristic
482C42—131no—
483C42—131no—
484C42—131no—
485C42—131no—
486C42—131no—
487C42—131no—
488C42—131no—
489C42—131no—
490C42—131no—
491C42C22×#26111yescharacteristic
492C13#1784111yescharacteristic, complemented, Sylow
493C23—131no—
494C23C2×C4⋊#26111yescharacteristic
495C23C2×C4⋊#26111yescharacteristic
496Q8—262no—
497D4—41no—
498D4—262no—
499D4—521no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—131no—
505C2×C4—131no—
506C2×C4—131no—
507C2×C4—131no—
508C2×C4—131no—
509C2×C4—131no—
510C2×C4—131no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—262no—
518C2×C4—261no—
519C2×C4—261no—
520C2×C4—521no—
521C2×C4—521no—
522C2×C4C2×C4⋊#26111yescharacteristic
523C2×C4C2×C4⋊#26111yescharacteristic
524C2×C4C2×C4⋊#26111yescharacteristic
525C2×C4C2×C4⋊#26111yescharacteristic
526C2×C4C23×#26111yescharacteristic
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—132no—
532C8—261no—
533C8—261no—
534C8—261no—
535C8—521no—
536C8—521no—
537C8—521no—
538C8—521no—
539C8—521no—
540C8—521no—
541C8—521no—
542C8—521no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—261no—
550C22—261no—
551C22—261no—
552C22C22×C4⋊#26111yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—131no—
558C4—131no—
559C4—132no—
560C4—261no—
561C4—261no—
562C4—261no—
563C4—261no—
564C4—261no—
565C4#1171962111yescharacteristic
566C4D13⋊#13111yescharacteristic
567C2—41no—
568C2—41no—
569C2—521no—
570C2#1313148311yescharacteristic
571C2#1313149011yescharacteristic
572C2D13⋊#43011yescharacteristic
subgroupG/H
centerC22C22×C4⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#435C4
socleC22×C13C22×C4⋊C4
prime radicalC2×#6129Q8
cosocleC4×Dic13C24
hypercenter#435#261
hypocenterC13#17841
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
3. #13130412C2semidirect
4. #13130412C2semidirect
5. #13130408C2semidirect
6. #13130407C2semidirect
7. #13130404C2semidirect
8. #13130403C2semidirect
9. #13130402C2semidirect
10. #13130400C2semidirect
11. #13130390C2semidirect
12. #13130389C2semidirect
13. #13130388C2semidirect
14. #13130385C2semidirect
492. C13#17841semidirect

Maximal subgroups

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

subgroupindex
#131317672
#131317612
#131304122
#131304082
#131304072
#131304042
#131304032
#131304022
#131304002
#131303902
#131303892
#131303882
#131303852
#131237962
#1784113