Finite Group Databasebeta

← #15926845

Subgroups — #15926845

Order 3328.

740 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118554C211yesmaximal, characteristic
2#13117863C211yesmaximal, characteristic
3#13116408C211yesmaximal, characteristic, complemented
4#13116340C211yesmaximal, characteristic, complemented
5#13116218C211yesmaximal, characteristic, complemented
6#13115986C211yesmaximal, characteristic, complemented
7#13115792C211yesmaximal, characteristic, complemented
8#13115426C211yesmaximal, characteristic, complemented
9#13115269C211yesmaximal, characteristic
10#13115143C211yesmaximal, characteristic
11#13115091C211yesmaximal, characteristic, complemented
12#13115035C211yesmaximal, characteristic
13#13115019C211yesmaximal, characteristic
14#13114850C211yesmaximal, characteristic, complemented
15C13×#1736C211yesmaximal, characteristic
16C22×C13×M16C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88178C2211yescharacteristic
20C2×#88144C2211yescharacteristic
21C2×#88141C2211yescharacteristic
22#11718873—21no—
23#11718873C2211yescharacteristic
24#11718871—21no—
25C4×C22⋊Dic13C2211yescharacteristic
26C2×C22⋊#1055C2211yescharacteristic
27C2×#88056C2211yescharacteristic
28C2×#88056C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31#11718647—21no—
32#11718646C2211yescharacteristic
33#11718645—21no—
34#11718638C2211yescharacteristic
35C4⋊C4×Dic13C2211yescharacteristic
36#11718635C2211yescharacteristic
37#11718634C2211yescharacteristic
38#11718634C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43#11718606—21no—
44#11718605—21no—
45#11718594—21no—
46C4×#6101—21no—
47C13×#340C2211yescharacteristic
48C13×#340C2211yescharacteristic
49C13×#340C2211yescharacteristic
50C13×#340C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59C23×C4×C13—21no—
60C23×C4×C13C2311yescharacteristic
61C22×Dic26C2311yescharacteristic
62C2×C13×M16—22no—
63C2×C13×M16—41no—
64C2×C13×M16—41no—
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C13×#117—22no—
68C13×#117—41no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—41no—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C22⋊C4—21no—
77C2×C42×C13—21no—
78C2×C22⋊Dic13—21no—
79C2×C22⋊Dic13—21no—
80C2×C22⋊Dic13D411yescharacteristic
81C2×C22⋊Dic13D411yescharacteristic
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87#88178—22no—
88#88178Q814yes—
89C2×#6101—21no—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13C2311yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100#88144—22no—
101#88144—41no—
102#88141—22no—
103#88141—41no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071D411yescharacteristic
114#88071D411yescharacteristic
115C22⋊#1055—22no—
116#88056—41no—
117#88056—41no—
118#88054—41no—
119#88054—41no—
120#88050—22no—
121#88050—41no—
122#88048—41no—
123#88047—22no—
124#26433—131nomaximal, Sylow
125C24×C13C2×D411yescharacteristic
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—21no—
133C22×C4×C13—21no—
134C22×C4×C13—42no—
135C22×C4×C13—42no—
136C22×C4×C13—81no—
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×Q812yes—
139C22×C4×C13#4112yes—
140C22×C4×C13C2411yescharacteristic
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13C2×D411yescharacteristic
146C22×Dic13C2×D411yescharacteristic
147C22×Dic13C2×D411yescharacteristic
148C22×Dic13C2×D411yescharacteristic
149C2×Dic26—21no—
150C2×Dic26—21no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26C2×Q812yes—
155C13×M16—44no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—42no—
169C13×C4⋊C4#4112yes—
170C13×C4⋊C4#4112yes—
171C13×C22⋊C4—42no—
172C42×C13—42no—
173C22⋊Dic13—24no—
174C22⋊Dic13—41no—
175C22⋊Dic13—41no—
176C22⋊Dic13—42no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—42no—
183C4⋊Dic13—81no—
184C4⋊Dic13C2×Q812yes—
185#6101—24no—
186#6101—42no—
187#6101—42no—
188#6101—42no—
189#6101—81no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—42no—
195C4×Dic13—42no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202#2442—131no—
203#2362—131no—
204#2101—131no—
205#2088—131no—
206#2066—131no—
207#2026—131no—
208#1989—131no—
209#1921—131no—
210#1894—131no—
211#1872—131no—
212#1863—131no—
213#1854—131no—
214#1851—131no—
215#1805—131no—
216#1736D1311yescharacteristic
217C23×C13—21no—
218C23×C13—21no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13C22⋊Q812yes—
224C23×C13C22×D411yescharacteristic
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—84no—
244C2×C4×C13C22⋊Q812yes—
245C2×C4×C13C22×Q811yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13H(5,𝔽2)11yescharacteristic
250C2×C4×C13H(5,𝔽2)11yescharacteristic
251C2×Dic13—22no—
252C2×Dic13—22no—
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—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275Dic26—22no—
276Dic26—22no—
277Dic26—41no—
278Dic26—41no—
279C8×C13—41no—
280C8×C13—41no—
281#1055—41no—
282#1055—41no—
283C22×M16C2×D1311yescharacteristic
284C2×#125—131no—
285C2×C22⋊Q8—131no—
286C2×C4×Q8—131no—
287C2×#117C2×D1311yescharacteristic
288C22×C4⋊C4C2×D1311yescharacteristic
289C2×#107—131no—
290C2×#106—131no—
291C2×C4⋊C8—131no—
292C2×C4⋊C8—131no—
293C2×#103—131no—
294C2×#103—131no—
295C2×#103—131no—
296C2×#103—131no—
297C2×C22⋊C8—131no—
298#400—261no—
299#398—261no—
300#391—131no—
301#389—131no—
302#389—131no—
303#389—131no—
304#388—261no—
305#388—261no—
306#387—261no—
307#385—261no—
308#382—131no—
309#380—131no—
310#380—261no—
311C4×C4⋊C4—131no—
312C4×C4⋊C4—261no—
313C4×C22⋊C4—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340C2×D1311yescharacteristic
321#340C2×D1311yescharacteristic
322#340C2×D1311yescharacteristic
323#340C2×D1311yescharacteristic
324#336—131no—
325#336—131no—
326C22×C13—22no—
327C22×C13—22no—
328C22×C13—22no—
329C22×C13—41no—
330C22×C13—41no—
331C22×C13—41no—
332C22×C13—41no—
333C22×C13C2×C22⋊Q811yescharacteristic
334C22×C13#54611yescharacteristic
335C22×C13#54611yescharacteristic
336C22×C13#57511yescharacteristic
337C22×C13#57511yescharacteristic
338C22×C13#57711yescharacteristic
339C22×C13#57811yescharacteristic
340C4×C13—22no—
341C4×C13—42no—
342C4×C13—42no—
343C4×C13—81no—
344C4×C13—81no—
345C4×C13#52911yescharacteristic
346C4×C13#53811yescharacteristic
347C4×C13#55411yescharacteristic
348C4×C13#55411yescharacteristic
349Dic13—42no—
350Dic13—42no—
351Dic13—41no—
352Dic13—41no—
353Dic13—41no—
354Dic13—41no—
355Dic13—81no—
356Dic13—81no—
357C22×Q8—131no—
358C23×C4—21no—
359C23×C4C22×D1311yescharacteristic
360C2×M16—22no—
361C2×M16—41no—
362C2×M16—41no—
363C22×C8—131no—
364C22×C8—131no—
365C22×C8C22×D1311yescharacteristic
366C22×C8C22×D1311yescharacteristic
367#125—262no—
368#125—521no—
369C22⋊Q8—134no—
370C22⋊Q8—262no—
371C4×Q8—262no—
372C4×Q8—521no—
373#117—22no—
374#117—41no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—41no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C4⋊C4C22×D1311yescharacteristic
390C2×C4⋊C4C22×D1311yescharacteristic
391C2×C4⋊C4C22×D1311yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—131no—
394C2×C22⋊C4—131no—
395C2×C22⋊C4—261no—
396C2×C22⋊C4—261no—
397C2×C42—21no—
398C2×C42—131no—
399C2×C42—131no—
400C2×C42—261no—
401C2×C42—261no—
402#107—262no—
403#106—521no—
404C4⋊C8—521no—
405C4⋊C8—521no—
406#103—262no—
407#103—521no—
408#103—521no—
409#103—521no—
410C22⋊C8—262no—
411#95—131no—
412#95—131no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95—261no—
421#95—261no—
422C2×C13—42no—
423C2×C13#245011yescharacteristic
424C2×C13#308011yescharacteristic
425C2×C13#308211yescharacteristic
426C2×C13#330711yescharacteristic
427C2×C13#331111yescharacteristic
428C2×C13#332711yescharacteristic
429C2×C13#332711yescharacteristic
430C24D4×D1311yescharacteristic
431C2×Q8—132no—
432C2×Q8—261no—
433C2×Q8—261no—
434C2×Q8—261no—
435C2×Q8—261no—
436C2×Q8—261no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—81no—
448C22×C4—131no—
449C22×C4—131no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4#612712yes—
457C22×C4D4×D1311yescharacteristic
458C22×C4Q8×D1312yes—
459C22×C4C23×D1311yescharacteristic
460M16—44no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—42no—
480C4⋊C4—132no—
481C4⋊C4—264no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—522no—
488C4⋊C4—522no—
489C4⋊C4—522no—
490C4⋊C4—522no—
491C4⋊C4—1041no—
492C4⋊C4—1041no—
493C4⋊C4#612712yes—
494C4⋊C4#612712yes—
495C22⋊C4—42no—
496C22⋊C4—264no—
497C22⋊C4—521no—
498C22⋊C4—521no—
499C22⋊C4—522no—
500C42—42no—
501C42—261no—
502C42—261no—
503C42—261no—
504C42—261no—
505C42—522no—
506C42—522no—
507C13#2643311yescharacteristic, complemented, Sylow
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23#8815012yes—
515C23C2×D4×D1311yescharacteristic
516Q8—262no—
517Q8—262no—
518Q8—521no—
519Q8—521no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—84no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—261no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—261no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4#8815012yes—
564C2×C4C2×#612711yescharacteristic
565C2×C4C2×#612711yescharacteristic
566C2×C4C2×#612711yescharacteristic
567C2×C4#8825111yescharacteristic
568C2×C4#8825111yescharacteristic
569C2×C4C2×Q8×D1311yescharacteristic
570C8—41no—
571C8—41no—
572C8—521no—
573C8—521no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22#1171919511yescharacteristic
582C22#1171919511yescharacteristic
583C22C2×#8815011yescharacteristic
584C22#1171947811yescharacteristic
585C22#1171948011yescharacteristic
586C22#1171948211yescharacteristic
587C22#1171948411yescharacteristic
588C4—22no—
589C4—42no—
590C4—42no—
591C4—81no—
592C4—81no—
593C4—522no—
594C4—521no—
595C4—521no—
596C4—521no—
597C4—522no—
598C4—521no—
599C4—1041no—
600C4—1041no—
601C4#1171918411yescharacteristic
602C4#1171919911yescharacteristic
603C4#1171921611yescharacteristic
604C4#1171921611yescharacteristic
605C2—42no—
606C2#1311866011yescharacteristic
607C2#1312465711yescharacteristic
608C2#1312467611yescharacteristic
609C2#1312681311yescharacteristic
610C2#1312687311yescharacteristic
611C2#1312710011yescharacteristic
612C2#1312710511yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1736C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1736D13
hypocenterC13#26433
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
3. #13116408C2semidirect
4. #13116340C2semidirect
5. #13116218C2semidirect
6. #13115986C2semidirect
7. #13115792C2semidirect
8. #13115426C2semidirect
11. #13115091C2semidirect
14. #13114850C2semidirect
507. C13#26433semidirect

Maximal subgroups

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

subgroupindex
#131185542
#131178632
#131164082
#131163402
#131162182
#131159862
#131157922
#131154262
#131152692
#131151432
#131150912
#131150352
#131150192
#131148502
C13×#17362
#2643313