Finite Group Databasebeta

← #15873118

Subgroups — #15873118

Order 3328.

670 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#13117234C211yesmaximal, characteristic
2#13115452C211yesmaximal, characteristic
3#13115446C211yesmaximal, characteristic
4#13115445C211yesmaximal, characteristic
5#13115439C211yesmaximal, characteristic
6#13115401C211yesmaximal, characteristic, complemented
7#13115399C211yesmaximal, characteristic, complemented
8#13115394C211yesmaximal, characteristic, complemented
9#13115392C211yesmaximal, characteristic, complemented
10#13114989C211yesmaximal, characteristic, complemented
11#13114955C211yesmaximal, characteristic, complemented
12#13114816C211yesmaximal, characteristic
13#13114695C211yesmaximal, characteristic, complemented
14#13114695C211yesmaximal, characteristic, complemented
15C13×#1797C211yesmaximal, characteristic
16C22×C42×C13C2211yescharacteristic
17C2×C13×C4⋊C8C2211yescharacteristic
18C2×C13×C4⋊C8C2211yescharacteristic
19C2×C13×C22⋊C8C2211yescharacteristic
20C2×C13×C22⋊C8C2211yescharacteristic
21#11718873C411yescharacteristic
22#11718873C411yescharacteristic
23#11718872C411yescharacteristic
24#11718872C411yescharacteristic
25C4×C22⋊Dic13C2211yescharacteristic
26C4×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊#1055C2211yescharacteristic
28C2×C22⋊#1055C2211yescharacteristic
29C2×#88055C2211yescharacteristic
30C2×#88055C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×#88054C2211yescharacteristic
33C2×#88054C2211yescharacteristic
34C2×#88054C2211yescharacteristic
35C2×C8×Dic13C2211yescharacteristic
36C2×C8×Dic13C2211yescharacteristic
37#11718598C411yescharacteristic
38#11718598C411yescharacteristic
39#11718597C411yescharacteristic
40#11718597C411yescharacteristic
41C4×C4⋊Dic13C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43#11718593C2211yescharacteristic
44#11718593C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4⋊#1055C2211yescharacteristic
47C13×#336C2211yescharacteristic
48C13×#336C2211yescharacteristic
49#11718142C2211yescharacteristic
50#11718142C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C23×C4×C13C2×C411yescharacteristic
60C23×C4×C13C2×C411yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C2×C42×C13—22no—
67C2×C42×C13—22no—
68C2×C42×C13C2×C411yescharacteristic
69C2×C42×C13C2×C411yescharacteristic
70C2×C42×C13C2311yescharacteristic
71C2×C42×C13C2311yescharacteristic
72C2×C22⋊Dic13C2×C411yescharacteristic
73C2×C22⋊Dic13C2×C411yescharacteristic
74C2×C22⋊Dic13C2×C411yescharacteristic
75C2×C22⋊Dic13C2×C411yescharacteristic
76C2×C4⋊Dic13C2×C411yescharacteristic
77C2×C4⋊Dic13C2×C411yescharacteristic
78C2×C4⋊Dic13C2×C411yescharacteristic
79C2×C4⋊Dic13C2×C411yescharacteristic
80C2×C4×Dic13C2311yescharacteristic
81C2×C4×Dic13C2311yescharacteristic
82C2×C4×Dic13C2311yescharacteristic
83C2×C4×Dic13C2311yescharacteristic
84C22×#1055C2311yescharacteristic
85C22×#1055C2311yescharacteristic
86C22×#1055C2311yescharacteristic
87C22×#1055C2311yescharacteristic
88C13×C4⋊C8—22no—
89C13×C4⋊C8—22no—
90C13×C22⋊C8—41no—
91C13×C22⋊C8—41no—
92#88071C2×C411yescharacteristic
93#88071C2×C411yescharacteristic
94#88071C2×C411yescharacteristic
95#88071C2×C411yescharacteristic
96#88071C2×C411yescharacteristic
97#88071C2×C411yescharacteristic
98#88071C2×C411yescharacteristic
99#88071C2×C411yescharacteristic
100#88071C2×C411yescharacteristic
101#88071C2×C411yescharacteristic
102#88071C2×C411yescharacteristic
103#88071C2×C411yescharacteristic
104#88071C2×C411yescharacteristic
105#88071C2×C411yescharacteristic
106#88071C2×C411yescharacteristic
107#88071C2×C411yescharacteristic
108C22⋊#1055—41no—
109C22⋊#1055—41no—
110#88055—41no—
111#88055—41no—
112#88054—41no—
113#88054—41no—
114#88054—41no—
115#88054—41no—
116C8×Dic13—41no—
117C8×Dic13—41no—
118C4⋊#1055—22no—
119C4⋊#1055—22no—
120#21928—131nomaximal, Sylow
121C24×C13C22×C411yescharacteristic
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—41no—
133C22×C4×C13—41no—
134C22×C4×C13C22×C411yescharacteristic
135C22×C4×C13C22×C411yescharacteristic
136C22×C4×C13C22×C411yescharacteristic
137C22×C4×C13C22×C411yescharacteristic
138C22×C4×C13C22×C411yescharacteristic
139C22×C4×C13C2411yescharacteristic
140C22×Dic13C22×C411yescharacteristic
141C22×Dic13C22×C411yescharacteristic
142C22×Dic13C22×C411yescharacteristic
143C22×Dic13C22×C411yescharacteristic
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C411yescharacteristic
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C42×C13—22no—
161C42×C13—22no—
162C42×C13—21no—
163C42×C13—21no—
164C42×C13#4112yes—
165C42×C13#4112yes—
166C22⋊Dic13—22no—
167C22⋊Dic13—22no—
168C22⋊Dic13—41no—
169C22⋊Dic13—41no—
170C4⋊Dic13—22no—
171C4⋊Dic13—22no—
172C4⋊Dic13—41no—
173C4⋊Dic13—41no—
174C4×Dic13—21no—
175C4×Dic13—21no—
176C4×Dic13—21no—
177C4×Dic13—21no—
178C4×Dic13—21no—
179C4×Dic13—21no—
180C4×Dic13—21no—
181C4×Dic13—21no—
182C2×#1055—21no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
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#1843—131no—
204#1832—131no—
205#1797—131no—
206#1797D1311yescharacteristic
207#1768—131no—
208#1768—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—44no—
230C2×C4×C13—44no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13#11712yes—
236C2×C4×C13#11712yes—
237C2×C4×C13#13112yes—
238C2×C4×C13C2×#4111yescharacteristic
239C2×C4×C13C2×#4111yescharacteristic
240C2×C4×C13H(5,𝔽2)11yescharacteristic
241C2×C4×C13H(5,𝔽2)11yescharacteristic
242C2×C4×C132−1+411yescharacteristic
243C2×C4×C132−1+411yescharacteristic
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—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C8×C13—41no—
269C8×C13—41no—
270C8×C13—41no—
271C8×C13—41no—
272#1055—41no—
273#1055—41no—
274#1055—41no—
275#1055—41no—
276C22×C42C2×D1311yescharacteristic
277C2×C4⋊C8—131no—
278C2×C4⋊C8—131no—
279C2×C4⋊C8—131no—
280C2×C4⋊C8—131no—
281C2×C4⋊C8—131no—
282C2×C4⋊C8—131no—
283C2×C4⋊C8C2×D1311yescharacteristic
284C2×C4⋊C8C2×D1311yescharacteristic
285C2×C22⋊C8—131no—
286C2×C22⋊C8—131no—
287C2×C22⋊C8C2×D1311yescharacteristic
288C2×C22⋊C8C2×D1311yescharacteristic
289C2×#97—131no—
290C2×#97—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—131no—
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#336C2×D1311yescharacteristic
318#336C2×D1311yescharacteristic
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×C13#52011yescharacteristic
328C22×C13#52011yescharacteristic
329C22×C13C2×#13111yescharacteristic
330C22×C13C2×#13111yescharacteristic
331C22×C13#56811yescharacteristic
332C22×C13#56811yescharacteristic
333C4×C13—22no—
334C4×C13—22no—
335C4×C13—22no—
336C4×C13—41no—
337C4×C13—41no—
338C4×C13#54011yescharacteristic
339C4×C13#54111yescharacteristic
340C4×C13#54211yescharacteristic
341C4×C13#54211yescharacteristic
342Dic13—41no—
343Dic13—41no—
344Dic13—41no—
345Dic13—41no—
346Dic13—41no—
347Dic13—41no—
348Dic13—41no—
349Dic13—41no—
350C23×C4C4×D1311yescharacteristic
351C23×C4C4×D1311yescharacteristic
352C23×C4C22×D1311yescharacteristic
353C22×C8—131no—
354C22×C8—131no—
355C22×C8—131no—
356C22×C8—131no—
357C22×C8C22×D1311yescharacteristic
358C22×C8C22×D1311yescharacteristic
359C22×C8C22×D1311yescharacteristic
360C22×C8C22×D1311yescharacteristic
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C22⋊C4—131no—
366C2×C22⋊C4—131no—
367C2×C22⋊C4—131no—
368C2×C22⋊C4—131no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—131no—
372C2×C42—131no—
373C2×C42—131no—
374C2×C42—131no—
375C2×C42C4×D1311yescharacteristic
376C2×C42C4×D1311yescharacteristic
377C2×C42C22×D1311yescharacteristic
378C2×C42C22×D1311yescharacteristic
379C4⋊C8—22no—
380C4⋊C8—22no—
381C4⋊C8—262no—
382C4⋊C8—262no—
383C4⋊C8—521no—
384C4⋊C8—521no—
385C4⋊C8—521no—
386C4⋊C8—521no—
387C22⋊C8—41no—
388C22⋊C8—41no—
389C22⋊C8—521no—
390C22⋊C8—521no—
391#97—521no—
392#97—521no—
393C4×C8—521no—
394C4×C8—521no—
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#95—131no—
410#95—131no—
411C2×C13—42no—
412C2×C13#231411yescharacteristic
413C2×C13#292411yescharacteristic
414C2×C13#292411yescharacteristic
415C2×C13#299211yescharacteristic
416C2×C13#299311yescharacteristic
417C2×C13#299411yescharacteristic
418C2×C13#299511yescharacteristic
419C24C2×C4×D1311yescharacteristic
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—131no—
433C22×C4—131no—
434C22×C4—131no—
435C22×C4—131no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4C2×C4×D1311yescharacteristic
441C22×C4C2×C4×D1311yescharacteristic
442C22×C4C2×C4×D1311yescharacteristic
443C22×C4C2×C4×D1311yescharacteristic
444C22×C4C2×C4×D1311yescharacteristic
445C22×C4C23×D1311yescharacteristic
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
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—262no—
471C4⋊C4—262no—
472C4⋊C4—521no—
473C4⋊C4—521no—
474C22⋊C4—262no—
475C22⋊C4—262no—
476C22⋊C4—521no—
477C22⋊C4—521no—
478C42—22no—
479C42—22no—
480C42—21no—
481C42—21no—
482C42—261no—
483C42—261no—
484C42—261no—
485C42—261no—
486C42—261no—
487C42—261no—
488C42—261no—
489C42—261no—
490C42#612912yes—
491C42#612912yes—
492C13#2192811yescharacteristic, complemented, Sylow
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23#8816112yes—
500C23C22×C4×D1311yescharacteristic
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—44no—
514C2×C4—44no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—261no—
520C2×C4—261no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—261no—
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#8813112yes—
544C2×C4#8813112yes—
545C2×C4#8815512yes—
546C2×C4C2×#612911yescharacteristic
547C2×C4C2×#612911yescharacteristic
548C2×C4#8825111yescharacteristic
549C2×C4#8825411yescharacteristic
550C2×C4#8825611yescharacteristic
551C2×C4#8825711yescharacteristic
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—521no—
557C8—521no—
558C8—521no—
559C8—521no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22C2×#8813111yescharacteristic
568C22#1171920911yescharacteristic
569C22#1171922811yescharacteristic
570C22C2×#8815511yescharacteristic
571C22C2×#8816111yescharacteristic
572C22#1171945011yescharacteristic
573C22#1171945011yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—41no—
579C4—521no—
580C4—521no—
581C4—521no—
582C4—521no—
583C4—521no—
584C4—521no—
585C4—521no—
586C4—521no—
587C4#1171930811yescharacteristic
588C4#1171932411yescharacteristic
589C4#1171933011yescharacteristic
590C4#1171934811yescharacteristic
591C2—42no—
592C2#1311744311yescharacteristic
593C2#1312349011yescharacteristic
594C2#1312349611yescharacteristic
595C2#1312397711yescharacteristic
596C2#1312398711yescharacteristic
597C2#1312399211yescharacteristic
598C2#1312400311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1797C2
prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenter#1797D13
hypocenterC13#21928
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
6. #13115401C2semidirect
7. #13115399C2semidirect
8. #13115394C2semidirect
9. #13115392C2semidirect
10. #13114989C2semidirect
11. #13114955C2semidirect
13. #13114695C2semidirect
14. #13114695C2semidirect
492. C13#21928semidirect

Maximal subgroups

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

subgroupindex
#131172342
#131154522
#131154462
#131154452
#131154392
#131154012
#131153992
#131153942
#131153922
#131149892
#131149552
#131148162
#131146952
C13×#17972
#2192813