Finite Group Databasebeta

← #15833949

Subgroups — #15833949

Order 3328.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124883C211yesmaximal, characteristic
2#13123834C211yesmaximal, characteristic, complemented
3D4×#6099C211yesmaximal, characteristic, complemented
4#13113747C211yesmaximal, characteristic, complemented
5#13113729C211yesmaximal, characteristic, complemented
6#13113717C211yesmaximal, characteristic, complemented
7#13113697C211yesmaximal, characteristic, complemented
8#13113669C211yesmaximal, characteristic, complemented
9#13113668C211yesmaximal, characteristic, complemented
10#13113645C211yesmaximal, characteristic, complemented
11#13113628C211yesmaximal, characteristic, complemented
12#13113624C211yesmaximal, characteristic, complemented
13#13113302C211yesmaximal, characteristic, complemented
14#13113131C211yesmaximal, characteristic, complemented
15C13×#1478C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17C22×#6099—21no—
18#11719184C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C13×#431C2211yescharacteristic
21#11718879C411yescharacteristic
22#11718878C411yescharacteristic
23#11718868—21no—
24C4×#6105C2211yescharacteristic
25C4×#6105C2211yescharacteristic
26#11718677C411yescharacteristic
27#11718677C411yescharacteristic
28C4×#6104C2211yescharacteristic
29C4×#6104C2211yescharacteristic
30#11718673C2211yescharacteristic
31#11718673C2211yescharacteristic
32#11718672—21no—
33#11718672—21no—
34D4×#1055C2211yescharacteristic
35D4×#1055C2211yescharacteristic
36#11718670C411yescharacteristic
37#11718670C411yescharacteristic
38#11718631C411yescharacteristic
39#11718629C411yescharacteristic
40#11718586C2211yescharacteristic
41#11718585C2211yescharacteristic
42C4×#6099C2211yescharacteristic
43#11718499C2211yescharacteristic, complemented
44#11718495C2211yescharacteristic, complemented
45#11718492C2211yescharacteristic, complemented
46#11718491C2211yescharacteristic, complemented
47#11718390—21no—
48#11718389—21no—
49#11718351—21no—
50#11718350—21no—
51C13×D4⋊C8C2211yescharacteristic
52C13×D4⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×D4⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic, complemented
56#11718072C2211yescharacteristic, complemented
57#11718071C2211yescharacteristic, complemented
58#11718071C2211yescharacteristic, complemented
59#11718051C2211yescharacteristic, complemented
60#11718051C2211yescharacteristic, complemented
61#11718048C2211yescharacteristic, complemented
62#11718048C2211yescharacteristic, complemented
63#11718047C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C22×D4×C13C2×C411yescharacteristic
68C23×C4×C13—21no—
69C4×D4×C13—21no—
70C4×D4×C13—21no—
71C4×D4×C13C2×C411yescharacteristic
72C4×D4×C13C2×C411yescharacteristic
73C4×D4×C13C2311yescharacteristic
74C4×D4×C13C2311yescharacteristic
75C2×C13×C4⋊C4C2×C411yescharacteristic
76C2×C13×C22⋊C4—21no—
77C2×C42×C13C2311yescharacteristic
78C2×#6105C2×C411yescharacteristic
79C2×#6105C2×C411yescharacteristic
80C2×#6104C2×C411yescharacteristic
81C2×#6104C2×C411yescharacteristic
82#88184C2×C411yescharacteristic
83#88183—21no—
84C4×C22⋊D13—21no—
85#88178C2×C411yescharacteristic
86C2×#6099—21no—
87C2×#6099—21no—
88C2×#6099—21no—
89C2×#6099—44no—
90C2×#6099D411yescharacteristic
91C2×#6099D411yescharacteristic
92C22×#1055—21no—
93C22×#1055—21no—
94C2×#6094—21no—
95C2×C8×D13—21no—
96#88130—21no—
97#88129C2×C411yescharacteristic
98C4×D52C2311yescharacteristic
99#88126—21no—
100#88124C2×C411yescharacteristic
101C4×Dic26C2311yescharacteristic
102C13×C4⋊C8—21no—
103C13×C4⋊C8C2311yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C13×C22⋊C8—21no—
106C13×C22⋊C8—21no—
107C4×C8×C13—21no—
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110#88072C2×C411yescharacteristic
111#88072C2×C411yescharacteristic
112#88072C2×C411yescharacteristic
113#88072C2×C411yescharacteristic
114C22⋊#1055—21no—
115C22⋊#1055—21no—
116C22⋊#1055—21no—
117C22⋊#1055—21no—
118C22⋊#1055C2×C411yescharacteristic
119C22⋊#1055C2×C411yescharacteristic
120#88060—21no—
121#88060—21no—
122#88055—21no—
123#88054—21no—
124#88054—21no—
125C8×Dic13—21no—
126#88050C2×C411yescharacteristic
127#88050C2×C411yescharacteristic
128#88049C2×C411yescharacteristic
129#88049C2×C411yescharacteristic
130#88048C2×C411yescharacteristic
131#88048C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134C4⋊#1055—21no—
135C4⋊#1055C2×C411yescharacteristic
136C4⋊#1055C2×C411yescharacteristic
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139#88043D411yescharacteristic
140#88043D411yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#18006—131nomaximal, Sylow
146C24×C13—21no—
147C2×D4×C13—22no—
148C2×D4×C13—21no—
149C2×D4×C13—41no—
150C2×D4×C13C22×C411yescharacteristic
151C2×D4×C13C22×C411yescharacteristic
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—42no—
158C22×C4×C13—42no—
159C22×C4×C13C22×C411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13#4111yescharacteristic
162C2×C22⋊D13—21no—
163C2×D52C22×C411yescharacteristic
164C2×C4×D13—21no—
165C2×Dic26C22×C411yescharacteristic
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4C22×C411yescharacteristic
172C13×C4⋊C4C22×C411yescharacteristic
173C13×C22⋊C4—21no—
174C13×C22⋊C4—21no—
175C13×C22⋊C4—21no—
176C13×C22⋊C4—21no—
177C42×C13C22×C411yescharacteristic
178C42×C13C2×D411yescharacteristic
179C42×C13#4111yescharacteristic
180C42×C13C2411yescharacteristic
181C22⋊Dic13—21no—
182#6105—22no—
183#6105—41no—
184#6104—22no—
185#6104—41no—
186#6103—21no—
187#6103—21no—
188#6103—21no—
189#6103—21no—
190C4⋊Dic13C22×C411yescharacteristic
191C4⋊Dic13C22×C411yescharacteristic
192#6101—21no—
193#6101—21no—
194#6101—21no—
195#6101—21no—
196C4×Dic13—21no—
197#6099—22no—
198#6099—41no—
199#6099—42no—
200#6099—42no—
201#6099—42no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—42no—
205C2×#1055—42no—
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209C2×#1055C22×C411yescharacteristic
210C2×#1055C2×D411yescharacteristic
211C2×#1055C2×D411yescharacteristic
212C2×#1055C2×D411yescharacteristic
213C2×#1055C2×D411yescharacteristic
214#6094—42no—
215C8×D13—42no—
216#3105—131no—
217#2969—131no—
218D4×M16—131no—
219#1594—131no—
220#1590—131no—
221#1588—131no—
222#1586—131no—
223#1582—131no—
224#1581—131no—
225SD16⋊C8—131no—
226C8×D8—131no—
227#1574—131no—
228#1495—131no—
229#1478D1311yescharacteristic, complemented
230#1453—131no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—42no—
234C23×C13—42no—
235C23×C13—81no—
236C23×C13C4×D411yescharacteristic
237C22×D13—21no—
238D4×C13—21no—
239D4×C13—21no—
240D4×C13—21no—
241D4×C13—42no—
242D4×C13#13112yes—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—41no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13C4×D411yescharacteristic
258C2×C4×C13C4×D411yescharacteristic
259C2×C4×C13C4×D411yescharacteristic
260C2×C4×C13C23×C411yescharacteristic
261C2×C4×C13C22×D411yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C22⋊D13—81no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267D52—21no—
268D52—21no—
269C4×D13—41no—
270C4×D13—41no—
271Dic26—21no—
272Dic26—21no—
273C8×C13—41no—
274C8×C13—41no—
275C8×C13—41no—
276C8×C13—41no—
277#1055—21no—
278#1055—21no—
279#1055—21no—
280#1055—21no—
281#1055—21no—
282#1055—21no—
283#1055—21no—
284#1055—41no—
285#1055—41no—
286#1055AGL(1,ℤ/8)12yes—
287C22×M16—261no—
288#529—131no—
289C2×C4×D4C2×D1311yescharacteristic
290#484—131no—
291#481—131no—
292#478—131no—
293#478—131no—
294#463—131no—
295#463—131no—
296#450—131no—
297#447—131no—
298#446—131no—
299C8×Q8—131no—
300C4×SD16—131no—
301C4×SD16—131no—
302C4×D8—131no—
303C4×D8—131no—
304#436—131no—
305#436—131no—
306#436—131no—
307#436—261no—
308#435—261no—
309#435—261no—
310#435—261no—
311C8×D4—131no—
312C8×D4—131no—
313C8×D4—131no—
314#433—261no—
315#431—131no—
316#431C2×D1311yescharacteristic
317#431C2×D1311yescharacteristic
318#423—131no—
319#407—261no—
320#405—261no—
321C4×M16—131no—
322#335—131no—
323#335—131no—
324#334—131no—
325#334—131no—
326Q8⋊C8—131no—
327Q8⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8C2×D1311yescharacteristic
331D4⋊C8C2×D1311yescharacteristic
332D4⋊C8C2×D1311yescharacteristic
333D4⋊C8C2×D1311yescharacteristic
334#322—131no—
335#322—131no—
336#322—131no—
337C82—131no—
338C22×C13—21no—
339C22×C13—22no—
340C22×C13—21no—
341C22×C13—21no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13—41no—
346C22×C13—41no—
347C22×C13—84no—
348C22×C13C2×C4×D411yescharacteristic
349C2×D13—41no—
350C2×D13—41no—
351C2×D13—41no—
352C4×C13—21no—
353C4×C13—21no—
354C4×C13—21no—
355C4×C13—21no—
356C4×C13—41no—
357C4×C13—41no—
358C4×C13C2×#13111yescharacteristic
359C4×C13#56811yescharacteristic
360C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
361C4×C13#57511yescharacteristic
362Dic13—41no—
363Dic13—41no—
364Dic13—41no—
365C22×D4C4×D1311yescharacteristic
366C23×C4—21no—
367C2×SD16—131no—
368C2×SD16—131no—
369C2×D8—131no—
370C2×D8—131no—
371C2×M16—131no—
372C2×M16—131no—
373C2×M16—261no—
374C2×M16—261no—
375C2×M16—261no—
376C2×M16—261no—
377C2×M16—524no—
378C22×C8—261no—
379C22×C8—261no—
380C22×C8—261no—
381#126—261no—
382#125—131no—
383#124—131no—
384#123—261no—
385C22⋊Q8—131no—
386#121—131no—
387C4×Q8—131no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—131no—
391C4×D4—261no—
392C4×D4C4×D1311yescharacteristic
393C4×D4C4×D1311yescharacteristic
394C4×D4C22×D1311yescharacteristic
395C4×D4C22×D1311yescharacteristic
396#117—261no—
397C2×C4⋊C4C4×D1311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C42C22×D1311yescharacteristic
400#107—131no—
401#107—131no—
402#106—131no—
403#106—131no—
404C4⋊C8—21no—
405C4⋊C8—131no—
406C4⋊C8—131no—
407C4⋊C8—131no—
408C4⋊C8—131no—
409C4⋊C8—261no—
410C4⋊C8—261no—
411C4⋊C8—261no—
412C4⋊C8C22×D1311yescharacteristic
413C4⋊C8C22×D1311yescharacteristic
414#103—131no—
415#103—131no—
416#102—131no—
417#102—131no—
418#102—131no—
419#102—131no—
420#102—131no—
421#102—131no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—131no—
425C22⋊C8—131no—
426C22⋊C8—261no—
427C22⋊C8—261no—
428C22⋊C8—261no—
429C22⋊C8—261no—
430C22⋊C8—261no—
431C22⋊C8—261no—
432#97—131no—
433#97—131no—
434#97—261no—
435C4×C8—21no—
436C4×C8—131no—
437C4×C8—131no—
438C4×C8—131no—
439C4×C8—131no—
440C4×C8—261no—
441C4×C8C22×D1311yescharacteristic
442C4×C8C22×D1311yescharacteristic
443C2×C13—41no—
444C2×C13—42no—
445C2×C13—81no—
446C2×C13#293311yescharacteristic
447C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
448C2×C13#295711yescharacteristic
449D13—81no—
450C24—21no—
451C2×Q8—131no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—131no—
456C2×D4—261no—
457C2×D4C2×C4×D1311yescharacteristic
458C2×D4C2×C4×D1311yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—261no—
467C22×C4C2×C4×D1311yescharacteristic
468C22×C4D4×D1311yescharacteristic
469C22×C4#612911yescharacteristic
470SD16—262no—
471SD16—521no—
472D8—262no—
473D8—521no—
474M16—262no—
475M16—522no—
476M16—522no—
477M16—521no—
478M16—522no—
479M16—522no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—131no—
485C2×C8—131no—
486C2×C8—131no—
487C2×C8—131no—
488C2×C8—131no—
489C2×C8—131no—
490C2×C8—131no—
491C2×C8—131no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—522no—
495C2×C8—522no—
496C2×C8—522no—
497C4⋊C4—21no—
498C4⋊C4—131no—
499C4⋊C4—131no—
500C4⋊C4—261no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4C2×C4×D1311yescharacteristic
505C4⋊C4C2×C4×D1311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—261no—
511C22⋊C4—261no—
512C22⋊C4—261no—
513C22⋊C4—261no—
514C22⋊C4—261no—
515C42—261no—
516C42C2×C4×D1311yescharacteristic
517C42D4×D1311yescharacteristic
518C42#612911yescharacteristic
519C42C23×D1311yescharacteristic
520C13#1800611yescharacteristic, complemented, Sylow
521C23—21no—
522C23—21no—
523C23—42no—
524C23—42no—
525C23—81no—
526C23—261no—
527C23#8813511yescharacteristic
528Q8—261no—
529Q8—261no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—261no—
535D4—261no—
536D4—1041no—
537D4#8815512yes—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—261no—
553C2×C4—261no—
554C2×C4—261no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4#8813511yescharacteristic
558C2×C4#8813511yescharacteristic
559C2×C4#8813511yescharacteristic
560C2×C4C22×C4×D1311yescharacteristic
561C2×C4C2×D4×D1311yescharacteristic
562C2×C4C2×#612911yescharacteristic
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—132no—
568C8—261no—
569C8—261no—
570C8—261no—
571C8—261no—
572C8—261no—
573C8—261no—
574C8—261no—
575C8—521no—
576C8—521no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—84no—
587C22—521no—
588C22—521no—
589C22—521no—
590C22C2×#8813511yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—41no—
596C4—41no—
597C4—521no—
598C4—521no—
599C4—521no—
600C4C2×#8815511yescharacteristic
601C4#1171945011yescharacteristic
602C4D13×AGL(1,ℤ/8)11yescharacteristic
603C4#1171947811yescharacteristic
604C2—41no—
605C2—42no—
606C2—81no—
607C2—1041no—
608C2#1312355711yescharacteristic
609C2#1312364011yescharacteristic
610C2#1312374911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1478C2
socleC22×C13C2×C4×D4
prime radical#11718878C4
cosocleC42×C13C24
hypercenter#1478D13
hypocenterC13#18006
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #13123834C2semidirect
3. D4×#6099C2semidirect
4. #13113747C2semidirect
5. #13113729C2semidirect
6. #13113717C2semidirect
7. #13113697C2semidirect
8. #13113669C2semidirect
9. #13113668C2semidirect
10. #13113645C2semidirect
11. #13113628C2semidirect
12. #13113624C2semidirect
13. #13113302C2semidirect
14. #13113131C2semidirect
15. C13×#1478C2semidirect
43. #11718499C22semidirect
44. #11718495C22semidirect
45. #11718492C22semidirect
46. #11718491C22semidirect
55. #11718072C22semidirect
56. #11718072C22semidirect
57. #11718071C22semidirect
58. #11718071C22semidirect
59. #11718051C22semidirect
60. #11718051C22semidirect
61. #11718048C22semidirect
62. #11718048C22semidirect
63. #11718047C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. C8×#1055C22semidirect
229. #1478D13semidirect
520. C13#18006semidirect

Maximal subgroups

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

subgroupindex
#131248832
#131238342
D4×#60992
#131137472
#131137292
#131137172
#131136972
#131136692
#131136682
#131136452
#131136282
#131136242
#131133022
#131131312
C13×#14782
#1800613