Finite Group Databasebeta

← #15903971

Subgroups — #15903971

Order 3328.

780 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718724C211yesmaximal, characteristic, complemented
2C2×#11718679C211yesmaximal, characteristic
3#13117791C211yesmaximal, characteristic, complemented
4#13116255C211yesmaximal, characteristic, complemented
5#13116245C211yesmaximal, characteristic, complemented
6#13116153C211yesmaximal, characteristic
7#13116153C211yesmaximal, characteristic
8#13115806C211yesmaximal, characteristic, complemented
9#13115602C211yesmaximal, characteristic, complemented
10#13115592C211yesmaximal, characteristic, complemented
11#13115560C211yesmaximal, characteristic, complemented
12#13115460C211yesmaximal, characteristic
13#13115453C211yesmaximal, characteristic
14#13114836C211yesmaximal, characteristic
15C13×#2566C211yesmaximal, characteristic
16C2×C13×#125C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C22×#6105C2211yescharacteristic
19C2×C4×Dic26C2211yescharacteristic
20C13×#396—21no—
21C13×#396—21no—
22C13×#390C2211yescharacteristic
23C13×#390C2211yescharacteristic
24C13×#385—21no—
25C13×#385—21no—
26C13×#384C2211yescharacteristic
27C13×#382C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32#11718724—24no—
33#11718679—24no—
34#11718638—21no—
35C4⋊C4×Dic13—21no—
36C2×#88050C2211yescharacteristic
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42#11718596C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44C4×C4⋊Dic13C2211yescharacteristic
45#11718590C2211yescharacteristic
46#11718590C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51#11718316—21no—
52#11718316—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C22×Dic26C2311yescharacteristic
64C13×#125—22no—
65C13×#125—22no—
66C4×D4×C13—22no—
67C4×D4×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⋊C4D411yescharacteristic
73C2×C13×C4⋊C4D411yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×#6105—22no—
86C2×#6105—22no—
87C2×#6105—22no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×#6101—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C4×Dic26—22no—
102C4×Dic26D414yes—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95D411yescharacteristic
106C13×#95D411yescharacteristic
107#88072—22no—
108#88072—22no—
109#88072—22no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88050—22no—
117#88050—22no—
118#88050—22no—
119#88048—22no—
120#88047—22no—
121#88047—22no—
122C4⋊#1055—22no—
123C4⋊#1055—22no—
124C4⋊#1055—22no—
125#88043—22no—
126#24689—131nomaximal, Sylow
127C24×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13#4112yes—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—42no—
138C22×C4×C13—81no—
139C22×C4×C13—81no—
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2411yescharacteristic
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26C2×D412yes—
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—81no—
168C13×C4⋊C4—81no—
169C13×C22⋊C4—42no—
170C13×C22⋊C4—42no—
171C13×C22⋊C4—42no—
172C13×C22⋊C4—81no—
173C13×C22⋊C4—81no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13C2×D412yes—
179C42×C13#4112yes—
180#6105—28no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—42no—
187C4⋊Dic13—81no—
188C4⋊Dic13C2×D412yes—
189#6101—24no—
190C4×Dic13—24no—
191C4×Dic13—81no—
192C4×Dic13—81no—
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—21no—
203C2×#1055—21no—
204C2×#1055#4112yes—
205C2×#479—131no—
206C2×#440—131no—
207#2566D1311yescharacteristic
208#2355—131no—
209#2074—131no—
210#2072—131no—
211#2055—131no—
212#2055—131no—
213#1992—131no—
214#1949—131no—
215#1947—131no—
216#1940—131no—
217#1926—131no—
218#1925—131no—
219#1802—131no—
220C23×C13—22no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13C22×D411yescharacteristic
228D4×C13—22no—
229D4×C13—22no—
230D4×C13—41no—
231D4×C13—41no—
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—21no—
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—21no—
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—84no—
257C2×C4×C13#12112yes—
258C2×C4×C13#12112yes—
259C2×C4×C13#13712yes—
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—22no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278Dic26—22no—
279Dic26—22no—
280Dic26—41no—
281Dic26—41no—
282#1055—22no—
283#1055—41no—
284#1055—41no—
285#1055—41no—
286C22×SD16—131no—
287C2×#125C2×D1311yescharacteristic
288C2×C4×Q8—131no—
289C2×C4×D4C2×D1311yescharacteristic
290#479—264no—
291#440—264no—
292C2×#107—131no—
293C2×#107—131no—
294C2×#106—131no—
295C2×C4⋊C8—131no—
296C2×C4⋊C8—131no—
297C2×C4⋊C8—131no—
298C2×#103—131no—
299C2×#103—131no—
300C2×#103—131no—
301C2×#102—131no—
302C2×#102—131no—
303C2×#102—131no—
304C2×#97—131no—
305#396—21no—
306#396—21no—
307#391—131no—
308#391—131no—
309#390C2×D1311yescharacteristic
310#390C2×D1311yescharacteristic
311#387—261no—
312#387—261no—
313#385—21no—
314#385—21no—
315#384—131no—
316#384C2×D1311yescharacteristic
317#382—261no—
318#382C2×D1311yescharacteristic
319C4×C4⋊C4—131no—
320C4×C4⋊C4—131no—
321C4×C4⋊C4—261no—
322C4×C4⋊C4C2×D1311yescharacteristic
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#336—131no—
330#336—131no—
331C22×C13—42no—
332C22×C13—42no—
333C22×C13—42no—
334C22×C13—81no—
335C22×C13—81no—
336C22×C13—81no—
337C22×C13—81no—
338C22×C13C2×#12111yescharacteristic
339C22×C13#54711yescharacteristic
340C22×C13#54811yescharacteristic
341C22×C13C2×#13711yescharacteristic
342C22×C13#57511yescharacteristic
343C22×C13#57611yescharacteristic
344C22×C13#57711yescharacteristic
345C4×C13—22no—
346C4×C13—22no—
347C4×C13—22no—
348C4×C13—41no—
349C4×C13—41no—
350C4×C13—41no—
351C4×C13—81no—
352C4×C13—81no—
353C4×C13—81no—
354C4×C13#52511yescharacteristic
355C4×C13#53611yescharacteristic
356C4×C13#55211yescharacteristic
357C4×C13#55611yescharacteristic
358Dic13—42no—
359Dic13—42no—
360Dic13—81no—
361Dic13—81no—
362C22×Q8—131no—
363C22×D4C22×D1311yescharacteristic
364C23×C4—21no—
365C2×SD16—262no—
366C2×SD16—262no—
367C2×SD16—262no—
368C22×C8—131no—
369C22×C8—131no—
370C22×C8—131no—
371C22×C8—131no—
372#125—22no—
373#125—22no—
374C4×Q8—134no—
375C4×Q8—262no—
376C4×D4—22no—
377C4×D4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—131no—
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×C4⋊C4C22×D1311yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C42—261no—
399C2×C42—261no—
400C2×C42—261no—
401C2×C42C22×D1311yescharacteristic
402C2×C42C22×D1311yescharacteristic
403C2×C42C22×D1311yescharacteristic
404#107—262no—
405#107—262no—
406#106—262no—
407C4⋊C8—262no—
408C4⋊C8—262no—
409C4⋊C8—262no—
410#103—262no—
411#103—262no—
412#103—262no—
413#102—262no—
414#102—262no—
415#102—262no—
416#97—262no—
417#95—21no—
418#95—21no—
419#95—261no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95—261no—
424#95—261no—
425#95C22⋊D1311yescharacteristic
426#95C22⋊D1311yescharacteristic
427C2×C13—82no—
428C2×C13#241511yescharacteristic
429C2×C13#303711yescharacteristic
430C2×C13#304511yescharacteristic
431C2×C13#334611yescharacteristic
432C2×C13#335011yescharacteristic
433C2×C13#337011yescharacteristic
434C2×C13#337211yescharacteristic
435C24—21no—
436C2×Q8—132no—
437C2×Q8—261no—
438C2×Q8—261no—
439C2×Q8—261no—
440C2×Q8—261no—
441C2×Q8—261no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4#613112yes—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—42no—
452C22×C4—81no—
453C22×C4—81no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4C2×C22⋊D1311yescharacteristic
459C22×C4C2×C22⋊D1311yescharacteristic
460C22×C4C2×C22⋊D1311yescharacteristic
461C22×C4C2×C22⋊D1311yescharacteristic
462C22×C4C2×C22⋊D1311yescharacteristic
463C22×C4C2×C22⋊D1311yescharacteristic
464C22×C4C23×D1311yescharacteristic
465SD16—268no—
466C2×C8—132no—
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—
476C2×C8—261no—
477C2×C8—261no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—41no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—81no—
489C4⋊C4—81no—
490C4⋊C4—132no—
491C4⋊C4—264no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—522no—
498C4⋊C4—1041no—
499C22⋊C4—42no—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C22⋊C4—81no—
503C22⋊C4—81no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—264no—
509C42—1041no—
510C42—1041no—
511C42D4×D1312yes—
512C42#612912yes—
513C13#2468911yescharacteristic, complemented, Sylow
514C23—22no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C22×C22⋊D1311yescharacteristic
522Q8—262no—
523Q8—262no—
524Q8—521no—
525Q8—521no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
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—21no—
543C2×C4—21no—
544C2×C4—21no—
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—41no—
554C2×C4—84no—
555C2×C4—262no—
556C2×C4—262no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4#8819212yes—
568C2×C4#8819212yes—
569C2×C4#8820512yes—
570C2×C4C2×D4×D1311yescharacteristic
571C2×C4C2×#612911yescharacteristic
572C2×C4C2×#613111yescharacteristic
573C2×C4#8825411yescharacteristic
574C2×C4#41×D1311yescharacteristic
575C2×C4#8825711yescharacteristic
576C8—262no—
577C8—521no—
578C8—521no—
579C8—521no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22C2×#8819211yescharacteristic
588C22#1171952211yescharacteristic
589C22#1171952711yescharacteristic
590C22C2×#8820511yescharacteristic
591C22#1171952911yescharacteristic
592C22#1171954011yescharacteristic
593C22#1171954111yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4—522no—
604C4—522no—
605C4—1041no—
606C4—1041no—
607C4#1171933211yescharacteristic
608C4#1171933311yescharacteristic
609C4#1171934611yescharacteristic
610C4#1171934711yescharacteristic
611C2—82no—
612C2#1311826111yescharacteristic
613C2#1312430411yescharacteristic
614C2#1312437111yescharacteristic
615C2#1312732111yescharacteristic
616C2#1312737511yescharacteristic
617C2#1312758911yescharacteristic
618C2#1312761711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2566C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenter#2566D13
hypocenterC13#24689
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2566

Complements

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

NH ≅ G/Ntype
1. C2×#11718724C2semidirect
3. #13117791C2semidirect
4. #13116255C2semidirect
5. #13116245C2semidirect
8. #13115806C2semidirect
9. #13115602C2semidirect
10. #13115592C2semidirect
11. #13115560C2semidirect
513. C13#24689semidirect

Maximal subgroups

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

subgroupindex
C2×#117187242
C2×#117186792
#131177912
#131162552
#131162452
#131161532
#131158062
#131156022
#131155922
#131155602
#131154602
#131154532
#131148362
C13×#25662
#2468913