Finite Group Databasebeta

← #16799727

Subgroups — #16799727

Order 3328.

710 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130910C211yesmaximal, characteristic
2#13130910C211yesmaximal, characteristic
3#13130906C211yesmaximal, characteristic
4#13130906C211yesmaximal, characteristic
5#13130896C211yesmaximal, characteristic, complemented
6#13130893C211yesmaximal, characteristic, complemented
7#13130892C211yesmaximal, characteristic, complemented
8#13130889C211yesmaximal, characteristic, complemented
9#13130624C211yesmaximal, characteristic, complemented
10#13130624C211yesmaximal, characteristic, complemented
11#13130562C211yesmaximal, characteristic
12C4×C22⋊#1057C211yesmaximal, characteristic
13#13130555C211yesmaximal, characteristic, complemented
14#13130493C211yesmaximal, characteristic, complemented
15#13117231C211yesmaximal, characteristic
16C22×C4×Dic13C2211yescharacteristic
17C2×C22⋊#1057C2211yescharacteristic
18C2×C22⋊#1057C2211yescharacteristic
19C2×C22⋊#1057C2211yescharacteristic
20C2×C22⋊#1057C2211yescharacteristic
21C2×#88112C2211yescharacteristic
22C2×#88112C2211yescharacteristic
23C2×#88110C2211yescharacteristic
24C2×#88110C2211yescharacteristic
25C2×#88110C2211yescharacteristic
26C2×#88110C2211yescharacteristic
27C2×C4⋊#1057C2211yescharacteristic
28C2×C4⋊#1057C2211yescharacteristic
29C2×C4×#1057C2211yescharacteristic
30C2×C4×#1057C2211yescharacteristic
31C2×C4×#1057C2211yescharacteristic
32C2×C4×#1057C2211yescharacteristic
33C13×#380C411yescharacteristic
34#11718873C411yescharacteristic
35#11718638C411yescharacteristic
36#11718638C411yescharacteristic
37C4⋊C4×Dic13C2211yescharacteristic
38C4⋊C4×Dic13C2211yescharacteristic
39#11718604C411yescharacteristic
40#11718604C411yescharacteristic
41C22⋊C4×Dic13C2211yescharacteristic
42C22⋊C4×Dic13C2211yescharacteristic
43#11718312C411yescharacteristic
44#11718312C411yescharacteristic
45#11718309C2211yescharacteristic
46#11718309C2211yescharacteristic
47#11718290C2211yescharacteristic
48#11718290C2211yescharacteristic
49#11718290C2211yescharacteristic
50#11718290C2211yescharacteristic
51#11718290C2211yescharacteristic
52#11718290C2211yescharacteristic
53#11718290C2211yescharacteristic
54#11718290C2211yescharacteristic
55#11718290C2211yescharacteristic
56#11718290C2211yescharacteristic
57#11718290C2211yescharacteristic
58#11718290C2211yescharacteristic
59C23×C4×C13C2×C411yescharacteristic
60C23×Dic13C2×C411yescharacteristic
61C23×Dic13C2311yescharacteristic
62C22×#1057C2311yescharacteristic
63C22×#1057C2311yescharacteristic
64C22×#1057C2311yescharacteristic
65C22×#1057C2311yescharacteristic
66C22×#1057C2311yescharacteristic
67C22×#1057C2311yescharacteristic
68C22×#1057C2311yescharacteristic
69C22×#1057C2311yescharacteristic
70C2×C13×C4⋊C4C2×C411yescharacteristic
71C2×C13×C4⋊C4C2×C411yescharacteristic
72C2×C13×C22⋊C4C2×C411yescharacteristic
73C2×C13×C22⋊C4C2×C411yescharacteristic
74C2×C22⋊Dic13C2×C411yescharacteristic
75C2×C22⋊Dic13C2×C411yescharacteristic
76C2×C4⋊Dic13C2×C411yescharacteristic
77C2×C4⋊Dic13C2×C411yescharacteristic
78C2×C4×Dic13—22no—
79C2×C4×Dic13—22no—
80C2×C4×Dic13C2×C411yescharacteristic
81C2×C4×Dic13C2×C411yescharacteristic
82C2×C4×Dic13C2311yescharacteristic
83C2×C4×Dic13C2311yescharacteristic
84C2×C4×Dic13C2311yescharacteristic
85C2×C4×Dic13C2311yescharacteristic
86C2×C4×Dic13C2311yescharacteristic
87C2×C4×Dic13C2311yescharacteristic
88C22⋊#1057—22no—
89C22⋊#1057—22no—
90C22⋊#1057—22no—
91C22⋊#1057—22no—
92#88112—22no—
93#88112—22no—
94#88110—22no—
95#88110—22no—
96#88110—22no—
97#88110—22no—
98C4⋊#1057—22no—
99C4⋊#1057—22no—
100C4×#1057—22no—
101C4×#1057—22no—
102C4×#1057—22no—
103C4×#1057—22no—
104C13×#95C2×C411yescharacteristic
105C13×#95C2×C411yescharacteristic
106#88071C2×C411yescharacteristic
107#88071C2×C411yescharacteristic
108#88071C2×C411yescharacteristic
109#88071C2×C411yescharacteristic
110#88071C2×C411yescharacteristic
111#88071C2×C411yescharacteristic
112#88071C2×C411yescharacteristic
113#88071C2×C411yescharacteristic
114#88071C2×C411yescharacteristic
115#88071C2×C411yescharacteristic
116#88071C2×C411yescharacteristic
117#88071C2×C411yescharacteristic
118#88071C2×C411yescharacteristic
119#88071C2×C411yescharacteristic
120#21437—131nomaximal, Sylow
121C24×C13C22×C411yescharacteristic
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—41no—
125C22×C4×C13C22×C411yescharacteristic
126C22×C4×C13C22×C411yescharacteristic
127C22×C4×C13C22×C411yescharacteristic
128C22×C4×C13C22×C411yescharacteristic
129C22×C4×C13C22×C411yescharacteristic
130C22×C4×C13C22×C411yescharacteristic
131C22×Dic13—22no—
132C22×Dic13—22no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—41no—
140C22×Dic13C22×C411yescharacteristic
141C22×Dic13C22×C411yescharacteristic
142C22×Dic13C22×C411yescharacteristic
143C22×Dic13C22×C411yescharacteristic
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C2411yescharacteristic
148C2×#1057—21no—
149C2×#1057—21no—
150C2×#1057—21no—
151C2×#1057—21no—
152C2×#1057—21no—
153C2×#1057—21no—
154C2×#1057—21no—
155C2×#1057—21no—
156C2×#1057—21no—
157C2×#1057—21no—
158C2×#1057—21no—
159C2×#1057—21no—
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#4112yes—
169C2×#1057#4112yes—
170C2×#1057#4112yes—
171C2×#1057#4112yes—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—41no—
174C13×C22⋊C4—41no—
175C13×C22⋊C4—41no—
176C22⋊Dic13—22no—
177C22⋊Dic13—22no—
178C4⋊Dic13—22no—
179C4⋊Dic13—41no—
180C4×Dic13—22no—
181C4×Dic13—22no—
182C4×Dic13—21no—
183C4×Dic13—21no—
184C4×Dic13—21no—
185C4×Dic13—21no—
186C4×Dic13—21no—
187C4×Dic13—21no—
188C4×Dic13—21no—
189C4×Dic13—21no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13#4112yes—
193C4×Dic13#4112yes—
194#2283—131no—
195#1924—131no—
196#1924—131no—
197#1923—131no—
198#1923—131no—
199#1917—131no—
200#1917—131no—
201#1916—131no—
202#1916—131no—
203#1768—131no—
204#1768—131no—
205#1749—131no—
206C4×C22⋊C8—131no—
207#1746—131no—
208#1726—131no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13#13112yes—
216C23×C13C23×C411yescharacteristic
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—44no—
234C2×C4×C13#11712yes—
235C2×C4×C13#13112yes—
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—44no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13#11712yes—
262C2×Dic13C2×#4111yescharacteristic
263C2×Dic13C2×#4111yescharacteristic
264C2×Dic13C2×#4111yescharacteristic
265C2×Dic13C2×#4111yescharacteristic
266C2×Dic13C2×#4111yescharacteristic
267C2×Dic13C2×#4111yescharacteristic
268#1057—22no—
269#1057—22no—
270#1057—22no—
271#1057—22no—
272#1057—41no—
273#1057—41no—
274#1057—41no—
275#1057—41no—
276C22×C42—131no—
277C2×C4⋊C8—131no—
278C2×C4⋊C8—131no—
279C2×C4⋊C8—131no—
280C2×C4⋊C8—131no—
281C2×C22⋊C8—131no—
282C2×C22⋊C8—131no—
283C2×C22⋊C8—131no—
284C2×C22⋊C8—131no—
285C2×#97—131no—
286C2×#97—131no—
287C2×#97—131no—
288C2×#97—131no—
289C2×C4×C8—131no—
290C2×C4×C8—131no—
291C2×C4×C8—131no—
292C2×C4×C8—131no—
293#383—131no—
294#383—131no—
295#382—131no—
296#382—131no—
297#381—131no—
298#381—131no—
299#380—131no—
300#380#26111yescharacteristic
301C4×C4⋊C4—131no—
302C4×C4⋊C4—131no—
303C4×C22⋊C4—131no—
304C4×C22⋊C4—131no—
305#376—131no—
306#376—131no—
307#336—131no—
308#336—131no—
309#336—131no—
310#336—131no—
311#336—131no—
312#336—131no—
313#336—131no—
314#336—131no—
315#336—131no—
316#336—131no—
317#336—131no—
318#336—131no—
319C22×C13—22no—
320C22×C13—22no—
321C22×C13—22no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13—41no—
325C22×C13—41no—
326C22×C13C2×#11711yescharacteristic
327C22×C13C4×#4111yescharacteristic
328C22×C13C4×#4111yescharacteristic
329C22×C13C2×#13111yescharacteristic
330C22×C13C2×#13111yescharacteristic
331C22×C13#56811yescharacteristic
332C22×C13#56811yescharacteristic
333C4×C13—22no—
334C4×C13—22no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13—41no—
338C4×C13—41no—
339Dic13—22no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343Dic13—41no—
344Dic13—41no—
345Dic13—41no—
346Dic13#52911yescharacteristic
347Dic13#52911yescharacteristic
348Dic13#52911yescharacteristic
349Dic13#52911yescharacteristic
350C23×C4—131no—
351C23×C4—131no—
352C23×C4C2×#26111yescharacteristic
353C22×C8—131no—
354C22×C8—131no—
355C22×C8—131no—
356C22×C8—131no—
357C22×C8—131no—
358C22×C8—131no—
359C22×C8—131no—
360C22×C8—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4C2×#26111yescharacteristic
364C2×C4⋊C4C2×#26111yescharacteristic
365C2×C22⋊C4—131no—
366C2×C22⋊C4—131no—
367C2×C22⋊C4C2×#26111yescharacteristic
368C2×C22⋊C4C2×#26111yescharacteristic
369C2×C42—131no—
370C2×C42—131no—
371C2×C42—131no—
372C2×C42—131no—
373C2×C42—131no—
374C2×C42—131no—
375C2×C42—131no—
376C2×C42—131no—
377C2×C42—262no—
378C2×C42—262no—
379C4⋊C8—262no—
380C4⋊C8—262no—
381C4⋊C8—262no—
382C4⋊C8—262no—
383C22⋊C8—262no—
384C22⋊C8—262no—
385C22⋊C8—262no—
386C22⋊C8—262no—
387#97—262no—
388#97—262no—
389#97—262no—
390#97—262no—
391C4×C8—262no—
392C4×C8—262no—
393C4×C8—262no—
394C4×C8—262no—
395#95—131no—
396#95—131no—
397#95—131no—
398#95—131no—
399#95—131no—
400#95—131no—
401#95—131no—
402#95—131no—
403#95—131no—
404#95—131no—
405#95—131no—
406#95—131no—
407#95—131no—
408#95—131no—
409#95C2×#26111yescharacteristic
410#95C2×#26111yescharacteristic
411C2×C13—42no—
412C2×C13#229811yescharacteristic
413C2×C13#292411yescharacteristic
414C2×C13#292411yescharacteristic
415C2×C13#296611yescharacteristic
416C2×C13#296711yescharacteristic
417C2×C13#296811yescharacteristic
418C2×C13#296911yescharacteristic
419C24C22×#26111yescharacteristic
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—41no—
423C22×C4—131no—
424C22×C4—131no—
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—131no—
428C22×C4—131no—
429C22×C4—131no—
430C22×C4—131no—
431C22×C4—261no—
432C22×C4—261no—
433C22×C4—261no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4—262no—
438C22×C4—262no—
439C22×C4—521no—
440C22×C4C22×#26111yescharacteristic
441C22×C4C22×#26111yescharacteristic
442C22×C4C22×#26111yescharacteristic
443C22×C4C22×#26111yescharacteristic
444C22×C4C22×#26111yescharacteristic
445C22×C4C22×#26111yescharacteristic
446C2×C8—132no—
447C2×C8—132no—
448C2×C8—132no—
449C2×C8—132no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
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—261no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C4⋊C4—22no—
471C4⋊C4—41no—
472C4⋊C4—262no—
473C4⋊C4—521no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—262no—
477C22⋊C4—262no—
478C42—132no—
479C42—132no—
480C42—261no—
481C42—261no—
482C42—261no—
483C42—261no—
484C42—261no—
485C42—261no—
486C42—261no—
487C42—261no—
488C42—261no—
489C42—261no—
490C42—262no—
491C42—262no—
492C13#2143711yescharacteristic, complemented, Sylow
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23#8824012yes—
500C23C23×#26111yescharacteristic
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—44no—
518C2×C4—131no—
519C2×C4—131no—
520C2×C4—131no—
521C2×C4—131no—
522C2×C4—131no—
523C2×C4—131no—
524C2×C4—132no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—524no—
550C2×C4#8823712yes—
551C2×C4#8823812yes—
552C8—262no—
553C8—262no—
554C8—262no—
555C8—262no—
556C8—521no—
557C8—521no—
558C8—521no—
559C8—521no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22C2×#8823711yescharacteristic
568C22C2×#8823811yescharacteristic
569C22#1171962111yescharacteristic
570C22#1171962111yescharacteristic
571C22C2×#8824011yescharacteristic
572C22#41×#26111yescharacteristic
573C22#41×#26111yescharacteristic
574C4—22no—
575C4—22no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—131no—
581C4—131no—
582C4—131no—
583C4—131no—
584C4—262no—
585C4—521no—
586C4—521no—
587C4—521no—
588C4—521no—
589C4—521no—
590C4—521no—
591C2—42no—
592C2#1313129811yescharacteristic
593C2#1313152511yescharacteristic
594C2#1313152711yescharacteristic
595C2#1313165211yescharacteristic
596C2#1313165511yescharacteristic
597C2#1313166411yescharacteristic
598C2#1313166711yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutator, socleC23×C13C23×C4
FittingC13×#380C4
prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenter#380#261
hypocenterC13#21437
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
5. #13130896C2semidirect
6. #13130893C2semidirect
7. #13130892C2semidirect
8. #13130889C2semidirect
9. #13130624C2semidirect
10. #13130624C2semidirect
13. #13130555C2semidirect
14. #13130493C2semidirect
492. C13#21437semidirect

Maximal subgroups

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

subgroupindex
#131309102
#131309062
#131308962
#131308932
#131308922
#131308892
#131306242
#131305622
C4×C22⋊#10572
#131305552
#131304932
#131172312
#2143713