Finite Group Databasebeta

← #15834227

Subgroups — #15834227

Order 3328.

656 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124837C211yesmaximal, characteristic
2#13123902C211yesmaximal, characteristic, complemented
3#13123870C211yesmaximal, characteristic, complemented
4#13113751C211yesmaximal, characteristic, complemented
5#13113722C211yesmaximal, characteristic, complemented
6#13113702C211yesmaximal, characteristic, complemented
7#13113702C211yesmaximal, characteristic, complemented
8#13113667C211yesmaximal, characteristic, complemented
9#13113667C211yesmaximal, characteristic, complemented
10#13113661C211yesmaximal, characteristic, complemented
11C8×D104C211yesmaximal, characteristic, complemented
12#13113616C211yesmaximal, characteristic, complemented
13#13113306C211yesmaximal, characteristic, complemented
14#13113228C211yesmaximal, characteristic, complemented
15C13×#1454C211yesmaximal, characteristic, complemented
16#11719182C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C13×#431C2211yescharacteristic
21#11718587C2211yescharacteristic
22#11718586C2211yescharacteristic
23#11718507C411yescharacteristic
24#11718507C411yescharacteristic
25#11718504C411yescharacteristic
26#11718504C411yescharacteristic
27#11718499—21no—
28#11718497—21no—
29#11718497—21no—
30#11718495—21no—
31#11718397C411yescharacteristic
32#11718397C411yescharacteristic
33#11718393C411yescharacteristic
34#11718393C411yescharacteristic
35#11718388—21no—
36#11718388—21no—
37#11718387—21no—
38D13×C22⋊C8—21no—
39C4×D104C2211yescharacteristic
40C4×D104C2211yescharacteristic
41C4×D104C2211yescharacteristic
42C4×D104C2211yescharacteristic
43#11718349C2211yescharacteristic
44#11718349C2211yescharacteristic
45#11718349C2211yescharacteristic, complemented
46#11718349C2211yescharacteristic, complemented
47C8×D52C2211yescharacteristic
48C8×D52C2211yescharacteristic
49C8×D52C2211yescharacteristic, complemented
50C8×D52C2211yescharacteristic, complemented
51C13×#322C2211yescharacteristic, complemented
52C13×#322C2211yescharacteristic, complemented
53C13×#322C2211yescharacteristic, complemented
54C82×C13C2211yescharacteristic, complemented
55#11718051C2211yescharacteristic
56#11718051C2211yescharacteristic
57#11718051C2211yescharacteristic
58#11718051C2211yescharacteristic
59#11718051C2211yescharacteristic, complemented
60#11718051C2211yescharacteristic, complemented
61#11718051C2211yescharacteristic, complemented
62#11718051C2211yescharacteristic, complemented
63#11718050C2211yescharacteristic, complemented
64#11718050C2211yescharacteristic, complemented
65#11718049C2211yescharacteristic, complemented
66#11718049C2211yescharacteristic, complemented
67C2×#6127—21no—
68C22×D52C2×C411yescharacteristic
69C22×C4×D13—21no—
70C2×C42×C13C2311yescharacteristic
71#88184—21no—
72#88184C2×C411yescharacteristic
73#88184C2×C411yescharacteristic
74C2×#6103—21no—
75C2×C4⋊Dic13C2×C411yescharacteristic
76C2×D104C2×C411yescharacteristic
77C2×D104C2×C411yescharacteristic
78C2×D104C2×C411yescharacteristic
79C2×D104C2×C411yescharacteristic
80C2×#6094—21no—
81C2×#6094—21no—
82C2×#6094—21no—
83C2×#6094—21no—
84C2×C8×D13—21no—
85C2×C8×D13—21no—
86C2×C8×D13—21no—
87C2×C8×D13—21no—
88#88129—21no—
89#88128C2×C411yescharacteristic
90C4×D52—21no—
91C4×D52—21no—
92C4×D52—21no—
93C4×D52C2×C411yescharacteristic
94C4×D52C2×C411yescharacteristic
95C4×D52C2311yescharacteristic
96C4×D52C2311yescharacteristic
97C4×D52C2311yescharacteristic
98C4×D52C2311yescharacteristic
99#88123C2×C411yescharacteristic
100C13×C4⋊C8—21no—
101C13×C4⋊C8C2×C411yescharacteristic
102C13×C4⋊C8C2×C411yescharacteristic
103C13×C4⋊C8D411yescharacteristic
104C13×C4⋊C8D411yescharacteristic
105C13×C22⋊C8—21no—
106C13×C22⋊C8C2×C411yescharacteristic
107C13×C22⋊C8C2×C411yescharacteristic
108C13×C22⋊C8D411yescharacteristic
109C13×C22⋊C8D411yescharacteristic
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114C4×C8×C13C2311yescharacteristic
115C4×C8×C13C2311yescharacteristic
116C22⋊#1055—21no—
117C22⋊#1055—21no—
118#88061C2×C411yescharacteristic
119#88061C2×C411yescharacteristic
120#88061C2×C411yescharacteristic
121#88061C2×C411yescharacteristic
122#88061C2×C411yescharacteristic
123#88061C2×C411yescharacteristic
124#88061C2×C411yescharacteristic
125#88061C2×C411yescharacteristic
126#88060—21no—
127#88060—21no—
128#88060—21no—
129#88060—21no—
130#88060—21no—
131#88060—21no—
132#88060—21no—
133#88060—21no—
134#88058C2×C411yescharacteristic
135#88058C2×C411yescharacteristic
136#88058C2×C411yescharacteristic
137#88058C2×C411yescharacteristic
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142#88043—21no—
143C4×#1055—21no—
144#18026—131nomaximal, Sylow
145C23×D13—21no—
146C22×C4×C13C22×C411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13#4111yescharacteristic
149C2×C22⋊D13—21no—
150C2×C22⋊D13—21no—
151C22×Dic13—21no—
152#6127—81no—
153#6127—81no—
154C2×D52—22no—
155C2×D52—21no—
156C2×D52—21no—
157C2×D52—21no—
158C2×D52—41no—
159C2×D52C22×C411yescharacteristic
160C2×D52C22×C411yescharacteristic
161C2×D52C22×C411yescharacteristic
162C2×D52C22×C411yescharacteristic
163C2×C4×D13—21no—
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×C4×D13—21no—
167C2×C4×D13—21no—
168C2×C4×D13—21no—
169C2×C4×D13—81no—
170C2×C4×D13—81no—
171C2×Dic26—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13C22×C411yescharacteristic
175C2×C8×C13C22×C411yescharacteristic
176C2×C8×C13C22×C411yescharacteristic
177C2×C8×C13C22×C411yescharacteristic
178C2×C8×C13C2×D411yescharacteristic
179C2×C8×C13C2×D411yescharacteristic
180C2×C8×C13C2×D411yescharacteristic
181C2×C8×C13C2×D411yescharacteristic
182C42×C13C22×C411yescharacteristic
183C42×C13C2×D411yescharacteristic
184C42×C13#4111yescharacteristic
185C42×C13C2411yescharacteristic
186#6103—21no—
187#6103—21no—
188#6103—21no—
189#6103—21no—
190#6103—21no—
191#6103—21no—
192#6103—21no—
193#6103—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13C22×C411yescharacteristic
197C4⋊Dic13C22×C411yescharacteristic
198C4⋊Dic13C22×C411yescharacteristic
199C4⋊Dic13C22×C411yescharacteristic
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204D104—22no—
205D104—22no—
206D104—41no—
207D104—41no—
208#6094—81no—
209#6094—81no—
210#6094—81no—
211#6094—81no—
212C8×D13—81no—
213C8×D13—81no—
214C8×D13—81no—
215C8×D13—81no—
216#3100—131no—
217#2979—131no—
218#2974—131no—
219#1594—131no—
220#1589—131no—
221#1586—131no—
222#1586—131no—
223#1581—131no—
224#1581—131no—
225#1580—131no—
226C8×D8—131no—
227#1572—131no—
228#1496—131no—
229#1478—131no—
230#1454D1311yescharacteristic, complemented
231C23×C13C4×D411yescharacteristic
232C22×D13—21no—
233C22×D13—21no—
234C22×D13—21no—
235C22×D13—21no—
236C22×D13—42no—
237C22×D13—42no—
238C22×D13—81no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—41no—
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13C4×D411yescharacteristic
246C2×C4×C13C4×D411yescharacteristic
247C2×C4×C13C23×C411yescharacteristic
248C2×C4×C13C22×D411yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C22⋊D13—81no—
251C22⋊D13—81no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—81no—
257D52—21no—
258D52—21no—
259D52—21no—
260D52—21no—
261D52—21no—
262D52—21no—
263D52—21no—
264D52—42no—
265D52—42no—
266D52—81no—
267D52#13112yes—
268C4×D13—41no—
269C4×D13—41no—
270C4×D13—41no—
271C4×D13—41no—
272C4×D13—41no—
273C4×D13—41no—
274C4×D13—41no—
275C4×D13—41no—
276C4×D13—81no—
277C4×D13—81no—
278Dic26—81no—
279C8×C13—21no—
280C8×C13—21no—
281C8×C13—21no—
282C8×C13—21no—
283C8×C13—21no—
284C8×C13—21no—
285C8×C13—21no—
286C8×C13—21no—
287C8×C13—41no—
288C8×C13—41no—
289#1055—41no—
290#1055—41no—
291#1055—41no—
292#1055—41no—
293#532—131no—
294C2×C4×D4—131no—
295#480—131no—
296#480—131no—
297#474—131no—
298#474—131no—
299#459—131no—
300#459—131no—
301#447—131no—
302#447—131no—
303C4×D8—131no—
304C4×D8—131no—
305C4×D8—131no—
306C4×D8—131no—
307#436—131no—
308#436—131no—
309#436—131no—
310#436—131no—
311#436—261no—
312#435—261no—
313#435—261no—
314C8×D4—131no—
315C8×D4—131no—
316C8×D4—131no—
317C8×D4—131no—
318C8×D4—261no—
319#432—131no—
320#431—131no—
321#431C2×D1311yescharacteristic
322#431C2×D1311yescharacteristic
323#431C2×D1311yescharacteristic
324#408—261no—
325#408—261no—
326#407—261no—
327C2×C22⋊C8—261no—
328#335—131no—
329#335—131no—
330#334—131no—
331#334—131no—
332D4⋊C8—131no—
333D4⋊C8—131no—
334D4⋊C8—131no—
335D4⋊C8—131no—
336D4⋊C8—131no—
337D4⋊C8—131no—
338D4⋊C8—131no—
339D4⋊C8—131no—
340#322C2×D1311yescharacteristic, complemented
341#322C2×D1311yescharacteristic, complemented
342#322C2×D1311yescharacteristic, complemented
343C82C2×D1311yescharacteristic, complemented
344C22×C13—21no—
345C22×C13—21no—
346C22×C13—21no—
347C22×C13C2×C4×D411yescharacteristic
348C2×D13—22no—
349C2×D13—41no—
350C2×D13—41no—
351C2×D13—41no—
352C2×D13—41no—
353C2×D13—41no—
354C2×D13—41no—
355C2×D13—41no—
356C2×D13—41no—
357C2×D13—41no—
358C2×D13—41no—
359C2×D13—41no—
360C2×D13—84no—
361C4×C13—21no—
362C4×C13—21no—
363C4×C13—21no—
364C4×C13—21no—
365C4×C13C2×#13111yescharacteristic
366C4×C13#56811yescharacteristic
367C4×C13#57611yescharacteristic
368C4×C13#57611yescharacteristic
369Dic13—41no—
370Dic13—41no—
371Dic13—41no—
372Dic13—41no—
373C2×#41—261no—
374C22×D4—131no—
375C23×C4—261no—
376C2×D8—131no—
377C2×D8—131no—
378C2×D8—131no—
379C2×D8—131no—
380C2×M16—261no—
381C2×M16—261no—
382C2×M16—261no—
383C2×M16—261no—
384C22×C8—261no—
385C22×C8—261no—
386C22×C8—261no—
387C22×C8—261no—
388C4⋊Q8—131no—
389#127—131no—
390#124—261no—
391#121—131no—
392#121—131no—
393#121—261no—
394C4×D4—131no—
395C4×D4—131no—
396C4×D4—131no—
397C4×D4—131no—
398C4×D4—131no—
399C4×D4—131no—
400C4×D4—261no—
401C4×D4—261no—
402C4×D4—261no—
403C2×C4⋊C4—131no—
404C2×C22⋊C4—261no—
405C2×C42C22×D1311yescharacteristic
406#107—131no—
407#107—131no—
408#107—131no—
409#107—131no—
410C4⋊C8—21no—
411C4⋊C8—131no—
412C4⋊C8—131no—
413C4⋊C8—131no—
414C4⋊C8—131no—
415C4⋊C8C4×D1311yescharacteristic
416C4⋊C8C4×D1311yescharacteristic
417C4⋊C8D5211yescharacteristic
418C4⋊C8D5211yescharacteristic
419#102—131no—
420#102—131no—
421#102—131no—
422#102—131no—
423#102—131no—
424#102—131no—
425#102—131no—
426#102—131no—
427C22⋊C8—21no—
428C22⋊C8—261no—
429C22⋊C8—261no—
430C22⋊C8—261no—
431C22⋊C8—261no—
432C22⋊C8—261no—
433C22⋊C8—261no—
434C22⋊C8—261no—
435C22⋊C8—261no—
436C22⋊C8—261no—
437C22⋊C8—261no—
438C22⋊C8C4×D1311yescharacteristic
439C22⋊C8C4×D1311yescharacteristic
440C22⋊C8D5211yescharacteristic
441C22⋊C8D5211yescharacteristic
442#97—261no—
443C4×C8—261no—
444C4×C8C22×D1311yescharacteristic
445C4×C8C22×D1311yescharacteristic
446C4×C8C22×D1311yescharacteristic
447C4×C8C22×D1311yescharacteristic
448C4×C8C22×D1311yescharacteristic
449C4×C8C22×D1311yescharacteristic
450C2×C13—41no—
451C2×C13#293311yescharacteristic
452C2×C13#294811yescharacteristic
453C2×C13#295511yescharacteristic
454D13—42no—
455D13—81no—
456D13—81no—
457D13—81no—
458C24—261no—
459#41—1041no—
460#41—1041no—
461C2×Q8—261no—
462C2×D4—131no—
463C2×D4—131no—
464C2×D4—131no—
465C2×D4—131no—
466C2×D4—262no—
467C2×D4—261no—
468C2×D4—261no—
469C2×D4—261no—
470C2×D4—261no—
471C2×D4—261no—
472C2×D4—521no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—1041no—
481C22×C4—1041no—
482C22×C4C2×C4×D1311yescharacteristic
483C22×C4C2×D5211yescharacteristic
484C22×C4#612711yescharacteristic
485D8—262no—
486D8—262no—
487D8—521no—
488D8—521no—
489M16—1041no—
490M16—1041no—
491M16—1041no—
492M16—1041no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—1041no—
500C2×C8—1041no—
501C2×C8—1041no—
502C2×C8—1041no—
503C2×C8C2×C4×D1311yescharacteristic
504C2×C8C2×C4×D1311yescharacteristic
505C2×C8C2×C4×D1311yescharacteristic
506C2×C8C2×C4×D1311yescharacteristic
507C2×C8C2×D5211yescharacteristic
508C2×C8C2×D5211yescharacteristic
509C2×C8C2×D5211yescharacteristic
510C2×C8C2×D5211yescharacteristic
511C4⋊C4—131no—
512C4⋊C4—131no—
513C4⋊C4—131no—
514C4⋊C4—131no—
515C4⋊C4—261no—
516C4⋊C4—261no—
517C22⋊C4—261no—
518C22⋊C4—261no—
519C22⋊C4—261no—
520C22⋊C4—261no—
521C22⋊C4—261no—
522C22⋊C4—261no—
523C22⋊C4—261no—
524C22⋊C4—261no—
525C42C2×C4×D1311yescharacteristic
526C42C2×D5211yescharacteristic
527C42#612711yescharacteristic
528C42C23×D1311yescharacteristic
529C13#1802611yescharacteristic, complemented, Sylow
530C23—261no—
531C23—261no—
532C23—261no—
533C23—261no—
534C23—522no—
535C23—522no—
536C23—1041no—
537C23C4×D5211yescharacteristic
538Q8—1041no—
539D4—132no—
540D4—261no—
541D4—261no—
542D4—261no—
543D4—261no—
544D4—261no—
545D4—261no—
546D4—261no—
547D4—522no—
548D4—522no—
549D4—1041no—
550D4—1041no—
551D4—1041no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—261no—
560C2×C4—261no—
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—1041no—
570C2×C4—1041no—
571C2×C4—1041no—
572C2×C4C4×D5211yescharacteristic
573C2×C4C4×D5211yescharacteristic
574C2×C4C4×D5211yescharacteristic
575C2×C4C22×C4×D1311yescharacteristic
576C2×C4C22×D5211yescharacteristic
577C2×C4C2×#612711yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—21no—
586C8—41no—
587C8—41no—
588C8—521no—
589C8—521no—
590C8—521no—
591C8—521no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—262no—
596C22—521no—
597C22—521no—
598C22—521no—
599C22—521no—
600C22—521no—
601C22—521no—
602C22—521no—
603C22—521no—
604C22—521no—
605C22—521no—
606C22—521no—
607C22—1044no—
608C22C2×C4×D5211yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—521no—
614C4—521no—
615C4—521no—
616C4—521no—
617C4D13×#13111yescharacteristic
618C4#1171945511yescharacteristic
619C4#1171945711yescharacteristic
620C4#1171945711yescharacteristic
621C2—41no—
622C2—522no—
623C2—1041no—
624C2—1041no—
625C2—1041no—
626C2#1312356411yescharacteristic
627C2#1312368911yescharacteristic
628C2#1312374011yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1454C2
socleC22×C13C2×C4×D4
prime radical#13124837C2
cosocleC42×C13C24
hypercenter#1454D13
hypocenterC13#18026
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
2. #13123902C2semidirect
3. #13123870C2semidirect
4. #13113751C2semidirect
5. #13113722C2semidirect
6. #13113702C2semidirect
7. #13113702C2semidirect
8. #13113667C2semidirect
9. #13113667C2semidirect
10. #13113661C2semidirect
11. C8×D104C2semidirect
12. #13113616C2semidirect
13. #13113306C2semidirect
14. #13113228C2semidirect
15. C13×#1454C2semidirect
45. #11718349C22semidirect
46. #11718349C22semidirect
49. C8×D52C22semidirect
50. C8×D52C22semidirect
51. C13×#322C22semidirect
52. C13×#322C22semidirect
53. C13×#322C22semidirect
54. C82×C13C22semidirect
59. #11718051C22semidirect
60. #11718051C22semidirect
61. #11718051C22semidirect
62. #11718051C22semidirect
63. #11718050C22semidirect
64. #11718050C22semidirect
65. #11718049C22semidirect
66. #11718049C22semidirect
230. #1454D13semidirect
340. #322C2×D13semidirect
341. #322C2×D13semidirect
342. #322C2×D13semidirect
343. C82C2×D13semidirect
529. C13#18026semidirect

Maximal subgroups

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

subgroupindex
#131248372
#131239022
#131238702
#131137512
#131137222
#131137022
#131136672
#131136612
C8×D1042
#131136162
#131133062
#131132282
C13×#14542
#1802613