Finite Group Databasebeta

← #15903926

Subgroups — #15903926

Order 3328.

778 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718727C211yesmaximal, characteristic
2C2×C4×#6106C211yesmaximal, characteristic
3#13117807C211yesmaximal, characteristic
4#13116250C211yesmaximal, characteristic
5#13116240C211yesmaximal, characteristic
6#13116151C211yesmaximal, characteristic
7#13116151C211yesmaximal, characteristic
8#13115802C211yesmaximal, characteristic, complemented
9#13115602C211yesmaximal, characteristic, complemented
10#13115597C211yesmaximal, characteristic, complemented
11#13115555C211yesmaximal, characteristic, complemented
12#13115474C211yesmaximal, characteristic, complemented
13#13115467C211yesmaximal, characteristic, complemented
14#13114851C211yesmaximal, characteristic, complemented
15C13×#2565C211yesmaximal, characteristic, complemented
16C2×C13×#125C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C22×#6106C2211yescharacteristic
19C2×C4×D52C2211yescharacteristic
20C13×#398—21no—
21C13×#398—21no—
22C13×#391C2211yescharacteristic
23C13×#391C2211yescharacteristic
24C13×#387—21no—
25C13×#387—21no—
26C13×#384C2211yescharacteristic
27C13×#382C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C2×#88075C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32#11718727—24no—
33C4×#6106—24no—
34#11718651—21no—
35#11718651—21no—
36C2×#88049C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42#11718600C2211yescharacteristic
43#11718600C2211yescharacteristic
44#11718597C2211yescharacteristic
45C4×C4⋊Dic13C2211yescharacteristic
46C4×C4⋊Dic13C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51#11718327—21no—
52#11718325—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13C2311yescharacteristic
62C22×D52C2311yescharacteristic
63C22×C4×D13—21no—
64C13×#125—22no—
65C13×#125—22no—
66C4×Q8×C13—22no—
67C4×Q8×C13—22no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4D411yescharacteristic
74C2×C13×C4⋊C4D411yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C42×C13—21no—
79C2×C42×C13C2311yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×#6106—22no—
83C2×#6106—22no—
84C2×#6106—22no—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×#6103—21no—
88C2×#6103—21no—
89C2×#6103—21no—
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C4×D52—22no—
100C4×D52D414yes—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95D411yescharacteristic
108C13×#95D411yescharacteristic
109#88075—22no—
110#88075—22no—
111#88075—22no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88049—22no—
117#88049—22no—
118#88049—22no—
119#88048—22no—
120#88048—22no—
121#88047—22no—
122C4⋊#1055—22no—
123C4⋊#1055—22no—
124C4⋊#1055—22no—
125C4×#1055—22no—
126#24686—131nomaximal, Sylow
127C23×D13—21no—
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13—21no—
132C2×Q8×C13—21no—
133C2×Q8×C13#4112yes—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2411yescharacteristic
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C2×D52—21no—
149C2×D52—21no—
150C2×D52—21no—
151C2×D52—21no—
152C2×D52—21no—
153C2×D52C2×D412yes—
154C2×C4×D13—24no—
155C2×C4×D13—81no—
156C2×C4×D13—81no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—41no—
165C13×C4⋊C4—42no—
166C13×C4⋊C4—42no—
167C13×C4⋊C4—42no—
168C13×C4⋊C4—42no—
169C13×C4⋊C4—42no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—42no—
175C42×C13C2×D412yes—
176C42×C13#4112yes—
177#6106—28no—
178#6103—24no—
179#6103—42no—
180#6103—42no—
181#6103—81no—
182#6103—81no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13C2×D412yes—
189C4×Dic13—81no—
190C4×Dic13—81no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055#4112yes—
203C2×#478—131no—
204C2×C4×SD16—131no—
205#2565D1311yescharacteristic, complemented
206#2357—131no—
207#2073—131no—
208#2071—131no—
209#2055—131no—
210#2055—131no—
211#1991—131no—
212#1949—131no—
213#1948—131no—
214#1939—131no—
215#1928—131no—
216#1927—131no—
217#1805—131no—
218C23×C13C22×D411yescharacteristic
219C22×D13—22no—
220C22×D13—41no—
221C22×D13—41no—
222C22×D13—41no—
223C22×D13—41no—
224C22×D13—41no—
225C22×D13—41no—
226Q8×C13—22no—
227Q8×C13—22no—
228Q8×C13—41no—
229Q8×C13—41no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—22no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13#12112yes—
258C2×C4×C13#12112yes—
259C2×C4×C13#13512yes—
260C2×C4×C13C22×D411yescharacteristic
261C2×C4×C13C2×#4111yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C132−1+411yescharacteristic
265C2×C4×C132−1+411yescharacteristic
266C2×Dic13—22no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275D52—22no—
276D52—22no—
277D52—41no—
278D52—41no—
279C4×D13—84no—
280#1055—22no—
281#1055—41no—
282#1055—41no—
283#1055—41no—
284C22×SD16—131no—
285C2×#125C2×D1311yescharacteristic
286C2×C4×Q8C2×D1311yescharacteristic
287C2×C4×D4—131no—
288#478—264no—
289C4×SD16—264no—
290C2×#107—131no—
291C2×#106—131no—
292C2×#106—131no—
293C2×C4⋊C8—131no—
294C2×C4⋊C8—131no—
295C2×C4⋊C8—131no—
296C2×#103—131no—
297C2×#103—131no—
298C2×#103—131no—
299C2×#102—131no—
300C2×#102—131no—
301C2×#102—131no—
302C2×C4×C8—131no—
303#398—21no—
304#398—21no—
305#391C2×D1311yescharacteristic
306#391C2×D1311yescharacteristic
307#390—131no—
308#390—131no—
309#388—261no—
310#388—261no—
311#387—21no—
312#387—21no—
313#384C2×D1311yescharacteristic
314#382—131no—
315#382C2×D1311yescharacteristic
316#381—261no—
317C4×C4⋊C4—131no—
318C4×C4⋊C4—131no—
319C4×C4⋊C4C2×D1311yescharacteristic
320C4×C22⋊C4—261no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#336—131no—
328#336—131no—
329C22×C13C2×#12111yescharacteristic
330C22×C13#54711yescharacteristic
331C22×C13#54811yescharacteristic
332C22×C13C2×#13511yescharacteristic
333C22×C13#57511yescharacteristic
334C22×C13#57711yescharacteristic
335C22×C13#57711yescharacteristic
336C2×D13—42no—
337C2×D13—42no—
338C2×D13—42no—
339C2×D13—81no—
340C2×D13—81no—
341C2×D13—81no—
342C2×D13—81no—
343C4×C13—22no—
344C4×C13—22no—
345C4×C13—22no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13—41no—
349C4×C13—42no—
350C4×C13—81no—
351C4×C13—81no—
352C4×C13—81no—
353C4×C13#52511yescharacteristic
354C4×C13#53611yescharacteristic
355C4×C13#55211yescharacteristic
356C4×C13#55611yescharacteristic
357Dic13—42no—
358Dic13—81no—
359Dic13—81no—
360C22×Q8C22×D1311yescharacteristic
361C22×D4—131no—
362C23×C4—261no—
363C2×SD16—262no—
364C2×SD16—262no—
365C2×SD16—262no—
366C22×C8—131no—
367C22×C8—131no—
368C22×C8—131no—
369C22×C8—131no—
370#125—22no—
371#125—22no—
372C4×Q8—22no—
373C4×Q8—22no—
374C4×D4—134no—
375C4×D4—262no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4C22⋊D1311yescharacteristic
385C2×C4⋊C4C22⋊D1311yescharacteristic
386C2×C4⋊C4C22×D1311yescharacteristic
387C2×C4⋊C4C22×D1311yescharacteristic
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C22⋊C4—261no—
390C2×C22⋊C4—261no—
391C2×C22⋊C4—261no—
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C42—21no—
395C2×C42—261no—
396C2×C42—261no—
397C2×C42C22×D1311yescharacteristic
398C2×C42C22×D1311yescharacteristic
399C2×C42C22×D1311yescharacteristic
400#107—262no—
401#106—262no—
402#106—262no—
403C4⋊C8—262no—
404C4⋊C8—262no—
405C4⋊C8—262no—
406#103—262no—
407#103—262no—
408#103—262no—
409#102—262no—
410#102—262no—
411#102—262no—
412C4×C8—262no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—261no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95C22⋊D1311yescharacteristic
424#95C22⋊D1311yescharacteristic
425C2×C13#241511yescharacteristic
426C2×C13#303511yescharacteristic
427C2×C13#304211yescharacteristic
428C2×C13#333711yescharacteristic
429C2×C13#335111yescharacteristic
430C2×C13#336511yescharacteristic
431C2×C13#337111yescharacteristic
432D13—82no—
433C24—261no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8#613112yes—
440C2×D4—132no—
441C2×D4—261no—
442C2×D4—261no—
443C2×D4—261no—
444C2×D4—261no—
445C2×D4—261no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—261no—
451C22×C4—264no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—1041no—
455C22×C4—1041no—
456C22×C4C2×C22⋊D1311yescharacteristic
457C22×C4C2×C22⋊D1311yescharacteristic
458C22×C4C2×C22⋊D1311yescharacteristic
459C22×C4C2×C22⋊D1311yescharacteristic
460C22×C4C2×C22⋊D1311yescharacteristic
461C22×C4C2×C22⋊D1311yescharacteristic
462C22×C4C23×D1311yescharacteristic
463SD16—268no—
464C2×C8—132no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—132no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C22⋊C4—264no—
496C22⋊C4—522no—
497C22⋊C4—522no—
498C22⋊C4—1041no—
499C22⋊C4—1041no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—42no—
505C42—1041no—
506C42—1041no—
507C42D4×D1312yes—
508C42#612912yes—
509C13#2468611yescharacteristic, complemented, Sylow
510C23—262no—
511C23—521no—
512C23—521no—
513C23—521no—
514C23—521no—
515C23—521no—
516C23—521no—
517C23C22×C22⋊D1311yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522D4—262no—
523D4—262no—
524D4—521no—
525D4—521no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—262no—
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—1044no—
563C2×C4#8819212yes—
564C2×C4#8819212yes—
565C2×C4#8820412yes—
566C2×C4C2×D4×D1311yescharacteristic
567C2×C4C2×#612911yescharacteristic
568C2×C4C2×#613111yescharacteristic
569C2×C4#8825411yescharacteristic
570C2×C4#41×D1311yescharacteristic
571C2×C4#8825711yescharacteristic
572C8—262no—
573C8—521no—
574C8—521no—
575C8—521no—
576C22—522no—
577C22—522no—
578C22—522no—
579C22—1041no—
580C22—1041no—
581C22—1041no—
582C22—1041no—
583C22C2×#8819211yescharacteristic
584C22#1171952211yescharacteristic
585C22C2×#8820411yescharacteristic
586C22#1171952711yescharacteristic
587C22#1171952911yescharacteristic
588C22#1171954211yescharacteristic
589C22#1171954211yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—41no—
594C4—42no—
595C4—41no—
596C4—41no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—522no—
601C4—1041no—
602C4—1041no—
603C4#1171933211yescharacteristic
604C4#1171933311yescharacteristic
605C4#1171934611yescharacteristic
606C4#1171934711yescharacteristic
607C2—1042no—
608C2#1311826111yescharacteristic
609C2#1312428511yescharacteristic
610C2#1312434411yescharacteristic
611C2#1312721511yescharacteristic
612C2#1312739611yescharacteristic
613C2#1312753211yescharacteristic
614C2#1312760411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2565C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2565D13
hypocenterC13#24686
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2565

Complements

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

NH ≅ G/Ntype
8. #13115802C2semidirect
9. #13115602C2semidirect
10. #13115597C2semidirect
11. #13115555C2semidirect
12. #13115474C2semidirect
13. #13115467C2semidirect
14. #13114851C2semidirect
15. C13×#2565C2semidirect
205. #2565D13semidirect
509. C13#24686semidirect

Maximal subgroups

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

subgroupindex
C2×#117187272
C2×C4×#61062
#131178072
#131162502
#131162402
#131161512
#131158022
#131156022
#131155972
#131155552
#131154742
#131154672
#131148512
C13×#25652
#2468613