Finite Group Databasebeta

← #15873121

Subgroups — #15873121

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#13117232C211yesmaximal, characteristic
2#13115449C211yesmaximal, characteristic
3#13115448C211yesmaximal, characteristic
4#13115443C211yesmaximal, characteristic
5#13115440C211yesmaximal, characteristic
6#13115401C211yesmaximal, characteristic, complemented
7#13115395C211yesmaximal, characteristic, complemented
8#13115392C211yesmaximal, characteristic, complemented
9#13114989C211yesmaximal, characteristic, complemented
10#13114954C211yesmaximal, characteristic, complemented
11#13114815C211yesmaximal, characteristic
12#13114815C211yesmaximal, characteristic
13#13114696C211yesmaximal, characteristic, complemented
14#13114692C211yesmaximal, characteristic, complemented
15C13×#1917C211yesmaximal, characteristic, complemented
16C2×C42×D13C2211yescharacteristic
17C2×C13×C4⋊C8C2211yescharacteristic
18C2×C13×#97C2211yescharacteristic
19C4×C13×C4⋊C4C2211yescharacteristic
20C2×#88060C2211yescharacteristic
21C2×#88060C2211yescharacteristic
22C2×#88060C2211yescharacteristic
23C2×#88060C2211yescharacteristic
24C2×#88055C2211yescharacteristic
25C2×#88054C2211yescharacteristic
26C2×#88054C2211yescharacteristic
27C2×#88054C2211yescharacteristic
28C2×#88054C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31C2×C8×Dic13C2211yescharacteristic
32#11718648C411yescharacteristic
33#11718648C411yescharacteristic
34#11718638C411yescharacteristic
35#11718638C411yescharacteristic
36C4×#6103C2211yescharacteristic
37C4×#6103C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39#11718593C2211yescharacteristic
40#11718593C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4×#1055C2211yescharacteristic
43#11718325C411yescharacteristic
44#11718325C411yescharacteristic
45#11718312C411yescharacteristic
46#11718312C411yescharacteristic
47C13×#336C2211yescharacteristic
48C13×#336C2211yescharacteristic
49C13×#336C2211yescharacteristic
50C13×#336C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×C4×D13C2×C411yescharacteristic
60C22×C4×D13C2×C411yescharacteristic
61C22×C4×D13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C2×C13×C4⋊C4C2×C411yescharacteristic
67C2×C13×C4⋊C4C2×C411yescharacteristic
68C2×C42×C13C2311yescharacteristic
69C2×C42×C13C2311yescharacteristic
70C2×C42×C13C2311yescharacteristic
71C2×#6103C2×C411yescharacteristic
72C2×#6103C2×C411yescharacteristic
73C2×#6103C2×C411yescharacteristic
74C2×#6103C2×C411yescharacteristic
75C2×C4⋊Dic13C2×C411yescharacteristic
76C2×C4⋊Dic13C2×C411yescharacteristic
77C2×C4×Dic13C2×C411yescharacteristic
78C2×C4×Dic13C2×C411yescharacteristic
79C2×C4×Dic13C2311yescharacteristic
80C2×C4×Dic13C2311yescharacteristic
81C2×C4×Dic13C2311yescharacteristic
82C22×#1055C2311yescharacteristic
83C22×#1055C2311yescharacteristic
84C22×#1055C2311yescharacteristic
85C22×#1055C2311yescharacteristic
86C42×D13—22no—
87C42×D13—22no—
88C13×C4⋊C8—41no—
89C13×#97—41no—
90C13×#95C2×C411yescharacteristic
91C13×#95C2×C411yescharacteristic
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#88060—41no—
107#88060—41no—
108#88060—41no—
109#88060—41no—
110#88055—41no—
111#88054—22no—
112#88054—22no—
113#88054—22no—
114#88054—22no—
115#88054—41no—
116#88054—41no—
117C8×Dic13—41no—
118C4⋊#1055—41no—
119C4×#1055—41no—
120#21928—131nomaximal, Sylow
121C23×D13C22×C411yescharacteristic
122C22×C4×C13C22×C411yescharacteristic
123C22×C4×C13C22×C411yescharacteristic
124C22×C4×C13C22×C411yescharacteristic
125C22×C4×C13C22×C411yescharacteristic
126C22×C4×C13C22×C411yescharacteristic
127C22×C4×C13C22×C411yescharacteristic
128C22×C4×C13C2411yescharacteristic
129C22×Dic13C22×C411yescharacteristic
130C22×Dic13C22×C411yescharacteristic
131C22×Dic13C22×C411yescharacteristic
132C22×Dic13C22×C411yescharacteristic
133C22×Dic13C22×C411yescharacteristic
134C22×Dic13C22×C411yescharacteristic
135C22×Dic13C22×C411yescharacteristic
136C2×C4×D13—22no—
137C2×C4×D13—22no—
138C2×C4×D13—21no—
139C2×C4×D13—21no—
140C2×C4×D13—21no—
141C2×C4×D13—21no—
142C2×C4×D13—21no—
143C2×C4×D13—21no—
144C2×C4×D13—22no—
145C2×C4×D13—22no—
146C2×C4×D13—41no—
147C2×C4×D13—41no—
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—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—41no—
162C42×C13—21no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—21no—
167C42×C13—21no—
168#6103—22no—
169#6103—22no—
170#6103—41no—
171#6103—41no—
172C4⋊Dic13—22no—
173C4⋊Dic13—41no—
174C4×Dic13—21no—
175C4×Dic13—21no—
176C4×Dic13—21no—
177C4×Dic13—21no—
178C4×Dic13—22no—
179C4×Dic13—22no—
180C4×Dic13#4112yes—
181C4×Dic13#4112yes—
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#1917D1311yescharacteristic, complemented
201#1916—131no—
202#1916—131no—
203#1843—131no—
204#1832—131no—
205#1797—131no—
206#1797—131no—
207#1768—131no—
208#1768—131no—
209C23×C13C23×C411yescharacteristic
210C22×D13—21no—
211C22×D13—21no—
212C22×D13—21no—
213C22×D13—21no—
214C22×D13—21no—
215C22×D13—21no—
216C22×D13#13112yes—
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—21no—
234C2×C4×C13#13112yes—
235C2×C4×C13C2×#4111yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C2×C4×C13H(5,𝔽2)11yescharacteristic
238C2×C4×C13H(5,𝔽2)11yescharacteristic
239C2×C4×C132−1+411yescharacteristic
240C2×C4×C132−1+411yescharacteristic
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—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13#11712yes—
261C2×Dic13#11712yes—
262C4×D13—44no—
263C4×D13—44no—
264C4×D13—41no—
265C4×D13—41no—
266C4×D13—41no—
267C4×D13—41no—
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×C42—131no—
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⋊C8—131no—
284C2×C4⋊C8C2×D1311yescharacteristic
285C2×C22⋊C8—131no—
286C2×C22⋊C8—131no—
287C2×C22⋊C8—131no—
288C2×C22⋊C8—131no—
289C2×#97—131no—
290C2×#97C2×D1311yescharacteristic
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⋊C4C2×D1311yescharacteristic
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#336C2×D1311yescharacteristic
316#336C2×D1311yescharacteristic
317#336C2×D1311yescharacteristic
318#336C2×D1311yescharacteristic
319C22×C13C2×#11711yescharacteristic
320C22×C13#52011yescharacteristic
321C22×C13#52011yescharacteristic
322C22×C13C2×#13111yescharacteristic
323C22×C13C2×#13111yescharacteristic
324C22×C13#56811yescharacteristic
325C22×C13#56811yescharacteristic
326C2×D13—22no—
327C2×D13—22no—
328C2×D13—22no—
329C2×D13—41no—
330C2×D13—41no—
331C2×D13—41no—
332C2×D13—41no—
333C4×C13—22no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13—41no—
338C4×C13—41no—
339C4×C13#54011yescharacteristic
340C4×C13#54111yescharacteristic
341C4×C13#54211yescharacteristic
342C4×C13#54211yescharacteristic
343Dic13—22no—
344Dic13—22no—
345Dic13—41no—
346Dic13—41no—
347Dic13—41no—
348Dic13—41no—
349Dic13—41no—
350C23×C4—131no—
351C23×C4—131no—
352C23×C4—131no—
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⋊C4C4×D1311yescharacteristic
364C2×C4⋊C4C4×D1311yescharacteristic
365C2×C22⋊C4—131no—
366C2×C22⋊C4—131no—
367C2×C22⋊C4—131no—
368C2×C22⋊C4—131no—
369C2×C42—131no—
370C2×C42—131no—
371C2×C42—131no—
372C2×C42—131no—
373C2×C42—131no—
374C2×C42—262no—
375C2×C42—262no—
376C2×C42C22×D1311yescharacteristic
377C2×C42C22×D1311yescharacteristic
378C2×C42C22×D1311yescharacteristic
379C4⋊C8—41no—
380C4⋊C8—262no—
381C4⋊C8—262no—
382C4⋊C8—262no—
383C4⋊C8—262no—
384C4⋊C8—521no—
385C4⋊C8—521no—
386C4⋊C8—521no—
387C22⋊C8—521no—
388C22⋊C8—521no—
389C22⋊C8—521no—
390C22⋊C8—521no—
391#97—41no—
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#95C4×D1311yescharacteristic
410#95C4×D1311yescharacteristic
411C2×C13#231411yescharacteristic
412C2×C13#292411yescharacteristic
413C2×C13#292411yescharacteristic
414C2×C13#299211yescharacteristic
415C2×C13#299311yescharacteristic
416C2×C13#299411yescharacteristic
417C2×C13#299511yescharacteristic
418D13—42no—
419C24—131no—
420C22×C4—131no—
421C22×C4—131no—
422C22×C4—131no—
423C22×C4—131no—
424C22×C4—131no—
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—262no—
428C22×C4—262no—
429C22×C4—262no—
430C22×C4—262no—
431C22×C4—261no—
432C22×C4—261no—
433C22×C4—261no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4—521no—
438C22×C4—521no—
439C22×C4C2×C4×D1311yescharacteristic
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—22no—
471C4⋊C4—41no—
472C4⋊C4—262no—
473C4⋊C4—521no—
474C22⋊C4—262no—
475C22⋊C4—262no—
476C22⋊C4—521no—
477C22⋊C4—521no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—132no—
485C42—132no—
486C42—262no—
487C42—262no—
488C42—261no—
489C42—261no—
490C42—261no—
491C42—261no—
492C13#2192811yescharacteristic, complemented, Sylow
493C23—132no—
494C23—261no—
495C23—261no—
496C23—261no—
497C23—261no—
498C23—261no—
499C23—261no—
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—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—132no—
519C2×C4—132no—
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—524no—
540C2×C4—524no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4#8816112yes—
546C2×C4#8825111yescharacteristic
547C2×C4#8825411yescharacteristic
548C2×C4#41×D1311yescharacteristic
549C2×C4#41×D1311yescharacteristic
550C2×C4#8825611yescharacteristic
551C2×C4#8825711yescharacteristic
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—521no—
557C8—521no—
558C8—521no—
559C8—521no—
560C22—262no—
561C22—262no—
562C22—262no—
563C22—521no—
564C22—521no—
565C22—521no—
566C22—521no—
567C22D13×#11711yescharacteristic
568C22#1171925111yescharacteristic
569C22#1171927911yescharacteristic
570C22C2×#8816111yescharacteristic
571C22#1171945011yescharacteristic
572C22D13×#13111yescharacteristic
573C22#1171945511yescharacteristic
574C4—22no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—262no—
581C4—262no—
582C4—521no—
583C4—521no—
584C4—521no—
585C4—521no—
586C4—521no—
587C4#1171934511yescharacteristic
588C4#1171936811yescharacteristic
589C4#1171940111yescharacteristic
590C4#1171941511yescharacteristic
591C2—522no—
592C2#1311744211yescharacteristic
593C2#1312349211yescharacteristic
594C2#1312349511yescharacteristic
595C2#1312397411yescharacteristic
596C2#1312398811yescharacteristic
597C2#1312399711yescharacteristic
598C2#1312400211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1917C2
prime radicalC23×D13C22×C4
cosocleC22×C4×C13C24
hypercenter#1917D13
hypocenterC13#21928
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
6. #13115401C2semidirect
7. #13115395C2semidirect
8. #13115392C2semidirect
9. #13114989C2semidirect
10. #13114954C2semidirect
13. #13114696C2semidirect
14. #13114692C2semidirect
15. C13×#1917C2semidirect
200. #1917D13semidirect
492. C13#21928semidirect

Maximal subgroups

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

subgroupindex
#131172322
#131154492
#131154482
#131154432
#131154402
#131154012
#131153952
#131153922
#131149892
#131149542
#131148152
#131146962
#131146922
C13×#19172
#2192813