Finite Group Databasebeta

← #15904191

Subgroups — #15904191

Order 3328.

784 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718490C211yesmaximal, characteristic, complemented
2#13123146C211yesmaximal, characteristic
3C4×#88178C211yesmaximal, characteristic
4#13116269C211yesmaximal, characteristic
5#13116264C211yesmaximal, characteristic
6#13116040C211yesmaximal, characteristic
7#13116033C211yesmaximal, characteristic
8#13115791C211yesmaximal, characteristic, complemented
9#13115606C211yesmaximal, characteristic, complemented
10#13115579C211yesmaximal, characteristic, complemented
11#13115574C211yesmaximal, characteristic, complemented
12#13115526C211yesmaximal, characteristic, complemented
13#13115526C211yesmaximal, characteristic, complemented
14#13114852C211yesmaximal, characteristic, complemented
15C2×C13×#432C211yesmaximal, characteristic
16C22×C42×C13C2211yescharacteristic
17C2×#88178C2211yescharacteristic
18C2×#88124C2211yescharacteristic
19C2×C4×Dic26C2211yescharacteristic
20C13×#432—24no—
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C2×C13×C22⋊C8C2211yescharacteristic
25C2×C13×#97C2211yescharacteristic
26C2×C13×#97C2211yescharacteristic
27#11718873C2211yescharacteristic
28#11718873C2211yescharacteristic
29#11718873C2211yescharacteristic
30#11718871—21no—
31#11718871—21no—
32#11718871—21no—
33C4×C22⋊Dic13—21no—
34C2×#88058C2211yescharacteristic
35C2×#88058C2211yescharacteristic
36C2×#88057C2211yescharacteristic
37C2×#88057C2211yescharacteristic
38C2×#88056C2211yescharacteristic
39C2×#88056C2211yescharacteristic
40C2×#88056C2211yescharacteristic
41C2×#88056C2211yescharacteristic
42#11718597C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44#11718594—21no—
45#11718594—21no—
46#11718594—21no—
47C4×#6101—21no—
48#11718590C2211yescharacteristic
49#11718589C2211yescharacteristic
50#11718589C2211yescharacteristic
51#11718589C2211yescharacteristic
52#11718490—24no—
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60#11718143C2211yescharacteristic
61C23×C4×C13D411yescharacteristic
62C23×C4×C13D411yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C22×Dic26C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C2×C42×C13—22no—
70C2×C42×C13—22no—
71C2×C42×C13D411yescharacteristic
72C2×C42×C13D411yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×C22⋊Dic13—21no—
76C2×C22⋊Dic13—21no—
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13—21no—
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86#88178—22no—
87#88178—22no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97#88124—22no—
98#88124—22no—
99C4×Dic26—22no—
100C4×Dic26—22no—
101C13×C4⋊C8—22no—
102C13×C4⋊C8D414yes—
103C13×C22⋊C8—22no—
104C13×C22⋊C8—22no—
105C13×#97—22no—
106C13×#97—22no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88058—22no—
119#88058—22no—
120#88057—22no—
121#88057—22no—
122#88056—22no—
123#88056—22no—
124#88056—22no—
125#88056—22no—
126#24707—131nomaximal, Sylow
127C24×C13C2×D411yescharacteristic
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—41no—
138C22×C4×C13—41no—
139C22×C4×C13—41no—
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2411yescharacteristic
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26—21no—
157C2×Dic26—21no—
158C2×Dic26—21no—
159C2×Dic26#4112yes—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13C2×D412yes—
171C2×C8×C13C2×D412yes—
172C42×C13—22no—
173C42×C13—22no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13C2×D412yes—
177C42×C13#4112yes—
178C22⋊Dic13—24no—
179C22⋊Dic13—42no—
180C22⋊Dic13—42no—
181C22⋊Dic13—42no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13#4112yes—
196#6101—24no—
197#6101—42no—
198#6101—42no—
199#6101—42no—
200#6101—42no—
201#6101—42no—
202#6101—42no—
203C4×Dic13—42no—
204C4×Dic13—42no—
205C2×#479—131no—
206C2×#432D1311yescharacteristic
207#2851—131no—
208C4×C22⋊Q8—131no—
209#2077—131no—
210#2076—131no—
211#2036—131no—
212#2035—131no—
213#1989—131no—
214#1949—131no—
215#1944—131no—
216#1943—131no—
217#1935—131no—
218#1935—131no—
219#1805—131no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13#13712yes—
227C23×C13C22×D411yescharacteristic
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—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—44no—
242C2×C4×C13—44no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13#12112yes—
248C2×C4×C13#12112yes—
249C2×C4×C13C22×D411yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C132−1+411yescharacteristic
254C2×C4×C132−1+411yescharacteristic
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
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—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279Dic26—22no—
280Dic26—22no—
281Dic26—41no—
282Dic26—41no—
283C8×C13—22no—
284C8×C13—22no—
285C8×C13—41no—
286C8×C13—41no—
287C2×#125—131no—
288C2×C22⋊Q8—131no—
289C2×C4×Q8—131no—
290C22×C42C2×D1311yescharacteristic
291#479—264no—
292#432—24no—
293C2×#107—131no—
294C2×#107—131no—
295C2×#106—131no—
296C2×#106—131no—
297C2×C4⋊C8C2×D1311yescharacteristic
298C2×C4⋊C8C2×D1311yescharacteristic
299C2×#103—131no—
300C2×#103—131no—
301C2×#103—131no—
302C2×#103—131no—
303C2×C22⋊C8C2×D1311yescharacteristic
304C2×C22⋊C8C2×D1311yescharacteristic
305C2×#97C2×D1311yescharacteristic
306C2×#97C2×D1311yescharacteristic
307#391—131no—
308#389—131no—
309#389—131no—
310#389—131no—
311#387—261no—
312#387—261no—
313#387—261no—
314#385—261no—
315#385—261no—
316#385—261no—
317#382—131no—
318#380—131no—
319#380—131no—
320#380—131no—
321C4×C4⋊C4—131no—
322C4×C4⋊C4—261no—
323C4×C22⋊C4—261no—
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332C22×C13—22no—
333C22×C13—22no—
334C22×C13—22no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13C2×#12111yescharacteristic
340C22×C13#52511yescharacteristic
341C22×C13#53611yescharacteristic
342C22×C13C2×#13711yescharacteristic
343C22×C13#57511yescharacteristic
344C22×C13#57511yescharacteristic
345C22×C13#57511yescharacteristic
346C4×C13—22no—
347C4×C13—22no—
348C4×C13—41no—
349C4×C13—41no—
350C4×C13—41no—
351C4×C13#54711yescharacteristic
352C4×C13#54811yescharacteristic
353C4×C13#55211yescharacteristic
354C4×C13#55611yescharacteristic
355Dic13—42no—
356Dic13—42no—
357Dic13—81no—
358Dic13—81no—
359Dic13—81no—
360Dic13—81no—
361Dic13—81no—
362Dic13—81no—
363C22×Q8—131no—
364C23×C4D5211yescharacteristic
365C23×C4D5211yescharacteristic
366C23×C4C22×D1311yescharacteristic
367C22×C8C22×D1311yescharacteristic
368C22×C8C22×D1311yescharacteristic
369C22×C8C22×D1311yescharacteristic
370C22×C8C22×D1311yescharacteristic
371#125—262no—
372#125—262no—
373C22⋊Q8—262no—
374C22⋊Q8—262no—
375C4×Q8—262no—
376C4×Q8—262no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—261no—
390C2×C4⋊C4—261no—
391C2×C22⋊C4—261no—
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C22⋊C4—261no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—261no—
398C2×C42—261no—
399C2×C42D5211yescharacteristic
400C2×C42D5211yescharacteristic
401C2×C42C22×D1311yescharacteristic
402C2×C42C22×D1311yescharacteristic
403#107—262no—
404#107—262no—
405#106—262no—
406#106—262no—
407C4⋊C8—22no—
408C4⋊C8C22⋊D1314yes—
409#103—262no—
410#103—262no—
411#103—262no—
412#103—262no—
413C22⋊C8—22no—
414C22⋊C8—22no—
415#97—22no—
416#97—22no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95—261no—
424#95—261no—
425#95—261no—
426#95—261no—
427#95—261no—
428C2×C13—42no—
429C2×C13#241511yescharacteristic
430C2×C13#305411yescharacteristic
431C2×C13#305611yescharacteristic
432C2×C13#311111yescharacteristic
433C2×C13#311711yescharacteristic
434C2×C13#323611yescharacteristic
435C2×C13#324011yescharacteristic
436C24C2×D5211yescharacteristic
437C2×Q8—132no—
438C2×Q8—261no—
439C2×Q8—261no—
440C2×Q8—261no—
441C2×Q8—261no—
442C2×Q8—261no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4C2×D5211yescharacteristic
464C22×C4C2×D5211yescharacteristic
465C22×C4C2×D5211yescharacteristic
466C22×C4C2×D5211yescharacteristic
467C22×C4C2×D5211yescharacteristic
468C22×C4C23×D1311yescharacteristic
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8C2×C22⋊D1312yes—
480C2×C8C2×C22⋊D1312yes—
481C4⋊C4—132no—
482C4⋊C4—264no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—522no—
497C4⋊C4—522no—
498C4⋊C4—522no—
499C4⋊C4—522no—
500C4⋊C4—522no—
501C4⋊C4—522no—
502C22⋊C4—264no—
503C22⋊C4—522no—
504C22⋊C4—522no—
505C22⋊C4—522no—
506C42—22no—
507C42—22no—
508C42—21no—
509C42—21no—
510C42—522no—
511C42—522no—
512C42#612712yes—
513C42C2×C22⋊D1312yes—
514C13#2470711yescharacteristic, complemented, Sylow
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23#8816312yes—
522C23C22×D5211yescharacteristic
523Q8—262no—
524Q8—262no—
525Q8—521no—
526Q8—521no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
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—44no—
541C2×C4—44no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—262no—
547C2×C4—262no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
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—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4#8818412yes—
571C2×C4#8818412yes—
572C2×C4C2×#612711yescharacteristic
573C2×C4#41×D1311yescharacteristic
574C2×C4#41×D1311yescharacteristic
575C2×C4#8825711yescharacteristic
576C2×C4#8825711yescharacteristic
577C2×C4C22×C22⋊D1311yescharacteristic
578C8—22no—
579C8—22no—
580C8—41no—
581C8—41no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22#1171922911yescharacteristic
590C22#1171923111yescharacteristic
591C22C2×#8816311yescharacteristic
592C22#1171945311yescharacteristic
593C22#1171945311yescharacteristic
594C22#1171945311yescharacteristic
595C22C2×#8818411yescharacteristic
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—522no—
602C4—522no—
603C4—1041no—
604C4—1041no—
605C4—1041no—
606C4—1041no—
607C4—1041no—
608C4—1041no—
609C4#1171923411yescharacteristic
610C4#1171923811yescharacteristic
611C4#1171952911yescharacteristic
612C4#1171953611yescharacteristic
613C2—42no—
614C2#1311825911yescharacteristic
615C2#1312444511yescharacteristic
616C2#1312446611yescharacteristic
617C2#1312494711yescharacteristic
618C2#1312500911yescharacteristic
619C2#1312604411yescharacteristic
620C2#1312607811yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#432C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC2×#432D13
hypocenterC13#24707
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
1. C2×#11718490C2semidirect
8. #13115791C2semidirect
9. #13115606C2semidirect
10. #13115579C2semidirect
11. #13115574C2semidirect
12. #13115526C2semidirect
13. #13115526C2semidirect
14. #13114852C2semidirect
514. C13#24707semidirect

Maximal subgroups

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

subgroupindex
C2×#117184902
#131231462
C4×#881782
#131162692
#131162642
#131160402
#131160332
#131157912
#131156062
#131155792
#131155742
#131155262
#131148522
C2×C13×#4322
#2470713