Finite Group Databasebeta

← #15875254

Subgroups — #15875254

Order 3328.

628 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
1#13124618C211yesmaximal, characteristic
2#13123777C211yesmaximal, characteristic, complemented
3#13123488C211yesmaximal, characteristic
4#13115611C211yesmaximal, characteristic, complemented
5#13115588C211yesmaximal, characteristic, complemented
6#13115583C211yesmaximal, characteristic, complemented
7#13115548C211yesmaximal, characteristic
8#13115541C211yesmaximal, characteristic
9#13115482C211yesmaximal, characteristic
10#13115482C211yesmaximal, characteristic
11#13115433C211yesmaximal, characteristic, complemented
12#13115433C211yesmaximal, characteristic, complemented
13#13114857C211yesmaximal, characteristic
14#13114711C211yesmaximal, characteristic, complemented
15C13×#1986C211yesmaximal, characteristic, complemented
16C13×#533C2211yescharacteristic
17C4×#6127C2211yescharacteristic
18C4×C13×M16C2211yescharacteristic
19C4×C13×C4⋊C4C2211yescharacteristic
20#11718790C2211yescharacteristic
21#11718790C2211yescharacteristic
22C2×#88062C2211yescharacteristic
23C2×#88062C2211yescharacteristic
24#11718780C2211yescharacteristic
25#11718780C2211yescharacteristic
26#11718755C411yescharacteristic, complemented
27#11718752C411yescharacteristic, complemented
28#11718748C411yescharacteristic, complemented
29#11718745C411yescharacteristic, complemented
30#11718727C411yescharacteristic, complemented
31#11718727C411yescharacteristic, complemented
32#11718724C411yescharacteristic, complemented
33#11718724C411yescharacteristic, complemented
34#11718685—21no—
35#11718685—21no—
36#11718685—21no—
37#11718685—21no—
38#11718663C2211yescharacteristic
39#11718663C2211yescharacteristic
40#11718660C2211yescharacteristic
41#11718660C2211yescharacteristic
42#11718659C2211yescharacteristic
43#11718659C2211yescharacteristic
44#11718658C2211yescharacteristic
45#11718658C2211yescharacteristic
46C2×#88045C2211yescharacteristic
47C2×#88045C2211yescharacteristic
48#11718585C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51C2×#88043C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
53#11718366—21no—
54#11718366—21no—
55#11718351—21no—
56#11718351—21no—
57C13×#339C2211yescharacteristic
58C13×#339C2211yescharacteristic
59C13×#339C2211yescharacteristic
60C13×#339C2211yescharacteristic
61#11718150C2211yescharacteristic
62#11718150C2211yescharacteristic
63#11718116C2211yescharacteristic
64#11718116C2211yescharacteristic
65#11718115C2211yescharacteristic
66#11718115C2211yescharacteristic
67C2×#6127C2311yescharacteristic
68C2×C13×M16C2311yescharacteristic
69C2×C13×M16C2311yescharacteristic
70C13×C4⋊Q8C2×C411yescharacteristic
71C13×C4⋊Q8C2×C411yescharacteristic
72C13×#125C2×C411yescharacteristic
73C13×#125C2×C411yescharacteristic
74C13×C22⋊Q8—21no—
75C13×C22⋊Q8—21no—
76C4×Q8×C13—21no—
77C4×Q8×C13—21no—
78C13×#117C2311yescharacteristic
79C13×#117C2311yescharacteristic
80C2×C13×C4⋊C4—21no—
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C4×C22⋊D13—21no—
85C4×C22⋊D13—21no—
86#88180C2311yescharacteristic
87C2×#6099C2311yescharacteristic
88C2×#6099C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C4×D52C2×C411yescharacteristic
94C4×D52C2×C411yescharacteristic
95#88126—21no—
96C42×D13—21no—
97C4×Dic26C2×C411yescharacteristic
98C4×Dic26C2×C411yescharacteristic
99C13×#97—21no—
100C4×C8×C13—21no—
101C13×#95—21no—
102#88062—41no—
103#88062—41no—
104#88060—21no—
105#88060—21no—
106#88060—21no—
107#88060—21no—
108#88054—21no—
109#88054—21no—
110#88054—21no—
111#88054—21no—
112#88050C2×C411yescharacteristic
113#88050C2×C411yescharacteristic
114#88050C2×C411yescharacteristic
115#88050C2×C411yescharacteristic
116#88049C2×C411yescharacteristic
117#88049C2×C411yescharacteristic
118#88049C2×C411yescharacteristic
119#88049C2×C411yescharacteristic
120#88048C2×C411yescharacteristic
121#88048C2×C411yescharacteristic
122#88048C2×C411yescharacteristic
123#88048C2×C411yescharacteristic
124#88047C2×C411yescharacteristic
125#88047C2×C411yescharacteristic
126#88047C2×C411yescharacteristic
127#88047C2×C411yescharacteristic
128#88045—41no—
129#88045—41no—
130C4⋊#1055—21no—
131C4⋊#1055—21no—
132C4⋊#1055—21no—
133C4⋊#1055—21no—
134C4⋊#1055—21no—
135C4⋊#1055—21no—
136C4⋊#1055C2×C411yescharacteristic
137C4⋊#1055C2×C411yescharacteristic
138C4⋊#1055C2×C411yescharacteristic
139C4⋊#1055C2×C411yescharacteristic
140#88043—21no—
141#88043—21no—
142#88043—41no—
143#88043D411yescharacteristic
144#88043D411yescharacteristic
145#88043D411yescharacteristic
146#88043D411yescharacteristic
147C4×#1055—21no—
148C4×#1055—21no—
149C4×#1055—41no—
150#22132—131nomaximal, Sylow
151C2×Q8×C13—21no—
152C2×Q8×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13#4111yescharacteristic
156C22×C4×C13#4111yescharacteristic
157C22×C4×C13C2411yescharacteristic
158C2×C22⋊D13—21no—
159#6127—21no—
160#6127—21no—
161#6127—21no—
162#6127—21no—
163C2×D52C22×C411yescharacteristic
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×C4×D13—21no—
167C2×Dic26C22×C411yescharacteristic
168C13×M16—21no—
169C13×M16—21no—
170C13×M16—21no—
171C13×M16—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—42no—
181C13×C4⋊C4C22×C411yescharacteristic
182C13×C4⋊C4C22×C411yescharacteristic
183C13×C4⋊C4C22×C411yescharacteristic
184C13×C4⋊C4C22×C411yescharacteristic
185C13×C22⋊C4—21no—
186C13×C22⋊C4—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13—21no—
192C42×C13—21no—
193C42×C13C22×C411yescharacteristic
194C42×C13C22×C411yescharacteristic
195C42×C13C2×D411yescharacteristic
196C42×C13C2×D411yescharacteristic
197C22⋊Dic13—21no—
198#6103—21no—
199#6103—21no—
200C4⋊Dic13C22×C411yescharacteristic
201C4⋊Dic13C22×C411yescharacteristic
202#6101—21no—
203#6101—21no—
204C4×Dic13—21no—
205C4×Dic13—21no—
206C4×Dic13—21no—
207#6099—21no—
208#6099—21no—
209#6099—21no—
210#6099—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055C22×C411yescharacteristic
222C2×#1055C22×C411yescharacteristic
223C2×#1055C22×C411yescharacteristic
224C2×#1055C22×C411yescharacteristic
225C2×#1055C2×D411yescharacteristic
226C2×#1055C2×D411yescharacteristic
227C2×#1055C2×D411yescharacteristic
228C2×#1055C2×D411yescharacteristic
229#3076—131no—
230#2961—131no—
231#2923—131no—
232#1986D1311yescharacteristic, complemented
233#1950—131no—
234#1946—131no—
235#1945—131no—
236#1938—131no—
237#1937—131no—
238#1929—131no—
239#1929—131no—
240#1922—131no—
241#1922—131no—
242#1806—131no—
243#1771—131no—
244C23×C13C2×#4111yescharacteristic
245C22×D13—21no—
246Q8×C13—81no—
247Q8×C13—81no—
248C2×C4×C13—22no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13C4×D411yescharacteristic
261C2×C4×C13C4×D411yescharacteristic
262C2×C4×C13C4×D411yescharacteristic
263C2×C4×C13C4×D411yescharacteristic
264C2×C4×C13C23×C411yescharacteristic
265C2×C4×C13C22×D411yescharacteristic
266C2×C4×C13H(5,𝔽2)11yescharacteristic
267C2×C4×C132−1+411yescharacteristic
268C2×C4×C132−1+411yescharacteristic
269C2×C4×C132−1+411yescharacteristic
270C22⋊D13—41no—
271C22⋊D13—41no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—21no—
275D52—21no—
276D52—21no—
277C4×D13—41no—
278C4×D13—41no—
279C4×D13—81no—
280C4×D13—81no—
281Dic26—21no—
282Dic26—21no—
283C8×C13—41no—
284C8×C13—41no—
285#1055—21no—
286#1055—21no—
287#1055—21no—
288#1055—21no—
289#1055—21no—
290#1055—21no—
291#1055—21no—
292#1055—21no—
293#1055—41no—
294#1055—41no—
295#533C2×D1311yescharacteristic
296C4×#41—131no—
297#479—131no—
298#479—131no—
299#478—131no—
300#478—131no—
301#477—131no—
302#476—131no—
303#475—131no—
304#474—131no—
305#446—261no—
306#446—261no—
307#446—261no—
308#446—261no—
309#433—261no—
310#433—261no—
311#432—261no—
312#432—261no—
313C2×#108—131no—
314C2×#108—131no—
315#427—131no—
316#427—131no—
317#424—131no—
318#424—131no—
319#424—131no—
320#424—131no—
321#423—131no—
322C2×C4⋊C8—131no—
323C2×#104—131no—
324C2×#104—131no—
325#416—131no—
326#416—131no—
327#408—131no—
328#408—131no—
329#405—131no—
330#405—131no—
331C4×M16C2×D1311yescharacteristic
332C2×#97—131no—
333C2×#97—131no—
334C2×C4×C8—131no—
335C4×C4⋊C4C2×D1311yescharacteristic
336#341—131no—
337#341—131no—
338#339—131no—
339#339—131no—
340#339C2×D1311yescharacteristic
341#339C2×D1311yescharacteristic
342#339C2×D1311yescharacteristic
343#339C2×D1311yescharacteristic
344#336—131no—
345#336—131no—
346C22×C13—21no—
347C22×C13—21no—
348C22×C13C2×C4×D411yescharacteristic
349C22×C13#54111yescharacteristic
350C22×C13#54211yescharacteristic
351C2×D13—41no—
352C2×D13—41no—
353C2×D13—41no—
354C4×C13—21no—
355C4×C13—21no—
356C4×C13—21no—
357C4×C13—21no—
358C4×C13—42no—
359C4×C13—41no—
360C4×C13—41no—
361C4×C13—41no—
362C4×C13—41no—
363C4×C13—81no—
364C4×C13#51911yescharacteristic
365C4×C13#52011yescharacteristic
366C4×C13#53611yescharacteristic
367C4×C13#53711yescharacteristic
368Dic13—41no—
369Dic13—41no—
370Dic13—41no—
371C2×#41—131no—
372C2×M16—131no—
373C2×M16—131no—
374C2×M16C22×D1311yescharacteristic
375C2×M16C22×D1311yescharacteristic
376C22×C8—131no—
377C22×C8—131no—
378C22×C8—131no—
379C22×C8—131no—
380C4⋊Q8C4×D1311yescharacteristic
381C4⋊Q8C4×D1311yescharacteristic
382#125C4×D1311yescharacteristic
383#125C4×D1311yescharacteristic
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—131no—
389C4×Q8—131no—
390C4×D4—131no—
391C4×D4—131no—
392C4×D4—261no—
393C4×D4—261no—
394#117—131no—
395#117—261no—
396#117C22×D1311yescharacteristic
397#117C22×D1311yescharacteristic
398C2×C4⋊C4—21no—
399C2×C42—261no—
400C2×C42C22×D1311yescharacteristic
401C2×C42C22×D1311yescharacteristic
402C2×C42C22×D1311yescharacteristic
403#108—521no—
404#108—521no—
405#107—131no—
406#107—131no—
407#107—131no—
408#107—131no—
409#106—131no—
410#106—131no—
411#106—131no—
412#106—131no—
413C4⋊C8—131no—
414C4⋊C8—131no—
415C4⋊C8—131no—
416C4⋊C8—131no—
417C4⋊C8—261no—
418C4⋊C8—261no—
419C4⋊C8—261no—
420C4⋊C8—261no—
421C4⋊C8—261no—
422C4⋊C8—261no—
423C4⋊C8—261no—
424C4⋊C8—261no—
425C4⋊C8—261no—
426C4⋊C8—261no—
427#104—521no—
428#104—521no—
429#103—131no—
430#103—131no—
431#103—131no—
432#103—131no—
433#102—131no—
434#102—131no—
435#102—131no—
436#102—131no—
437C22⋊C8—261no—
438C22⋊C8—261no—
439C22⋊C8—261no—
440C22⋊C8—261no—
441#97—21no—
442#97—131no—
443#97—131no—
444#97—131no—
445#97—131no—
446#97—261no—
447#97—261no—
448#97—521no—
449C4×C8—21no—
450C4×C8—261no—
451C4×C8—261no—
452C4×C8—521no—
453#95—21no—
454C2×C13—21no—
455C2×C13—21no—
456C2×C13#232311yescharacteristic
457C2×C13#295611yescharacteristic
458C2×C13#295711yescharacteristic
459D13—81no—
460#41—261no—
461#41—261no—
462#41—261no—
463#41—261no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—131no—
467C2×D4—131no—
468C2×D4—261no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4#612911yescharacteristic
475C22×C4#612911yescharacteristic
476C22×C4C23×D1311yescharacteristic
477M16—21no—
478M16—21no—
479M16—21no—
480M16—21no—
481M16—261no—
482M16—261no—
483M16—261no—
484M16—261no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—131no—
488C2×C8—131no—
489C2×C8—131no—
490C2×C8—131no—
491C2×C8—131no—
492C2×C8—131no—
493C2×C8—131no—
494C2×C8—131no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—261no—
503C2×C8—261no—
504C2×C8—261no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—42no—
512C4⋊C4—131no—
513C4⋊C4—131no—
514C4⋊C4—261no—
515C4⋊C4—261no—
516C4⋊C4C2×C4×D1311yescharacteristic
517C4⋊C4C2×C4×D1311yescharacteristic
518C4⋊C4C2×C4×D1311yescharacteristic
519C4⋊C4C2×C4×D1311yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—261no—
523C22⋊C4—261no—
524C22⋊C4—261no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—261no—
532C42—261no—
533C42—261no—
534C42C2×C4×D1311yescharacteristic
535C42C2×C4×D1311yescharacteristic
536C42D4×D1311yescharacteristic
537C42D4×D1311yescharacteristic
538C13#2213211yescharacteristic, complemented, Sylow
539C23—261no—
540C23C2×#612911yescharacteristic
541Q8—81no—
542Q8—81no—
543Q8—261no—
544Q8—261no—
545D4—261no—
546D4—261no—
547D4—521no—
548D4—521no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—261no—
562C2×C4—261no—
563C2×C4—261no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—1041no—
567C2×C4—1041no—
568C2×C4#8813511yescharacteristic
569C2×C4#8813511yescharacteristic
570C2×C4#8813511yescharacteristic
571C2×C4#8813511yescharacteristic
572C2×C4C22×C4×D1311yescharacteristic
573C2×C4C2×D4×D1311yescharacteristic
574C2×C4#8825411yescharacteristic
575C2×C4#8825411yescharacteristic
576C2×C4#8825611yescharacteristic
577C2×C4#8825711yescharacteristic
578C8—41no—
579C8—41no—
580C8—261no—
581C8—261no—
582C8—261no—
583C8—261no—
584C8—261no—
585C8—261no—
586C8—261no—
587C8—261no—
588C8—521no—
589C8—521no—
590C22—21no—
591C22—21no—
592C22—521no—
593C22—521no—
594C22—521no—
595C22C2×#8813511yescharacteristic
596C22#1171938711yescharacteristic
597C22#1171943611yescharacteristic
598C4—21no—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—42no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—81no—
608C4—521no—
609C4—521no—
610C4—521no—
611C4#1171927711yescharacteristic
612C4#1171927911yescharacteristic
613C4#1171933311yescharacteristic
614C4#1171933411yescharacteristic
615C2—21no—
616C2—21no—
617C2—1041no—
618C2#1311752111yescharacteristic
619C2#1312374211yescharacteristic
620C2#1312374911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1986C2
socleC22×C13C2×C4×D4
prime radicalC2×#6127C23
cosocleC22×C4×C13C24
hypercenter#1986D13
hypocenterC13#22132
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
2. #13123777C2semidirect
4. #13115611C2semidirect
5. #13115588C2semidirect
6. #13115583C2semidirect
11. #13115433C2semidirect
12. #13115433C2semidirect
14. #13114711C2semidirect
15. C13×#1986C2semidirect
26. #11718755C4semidirect
27. #11718752C4semidirect
28. #11718748C4semidirect
29. #11718745C4semidirect
30. #11718727C4semidirect
31. #11718727C4semidirect
32. #11718724C4semidirect
33. #11718724C4semidirect
232. #1986D13semidirect
538. C13#22132semidirect

Maximal subgroups

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

subgroupindex
#131246182
#131237772
#131234882
#131156112
#131155882
#131155832
#131155482
#131155412
#131154822
#131154332
#131148572
#131147112
C13×#19862
#2213213