Finite Group Databasebeta

← #15770743

Subgroups — #15770743

Order 3328.

886 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
1C22×#88065C211yesmaximal, characteristic
2C2×#11718774C211yesmaximal, characteristic
3C2×#11718790C211yesmaximal, characteristic
4C2×#11718147C211yesmaximal, characteristic, complemented
5#13114534C211yesmaximal, characteristic, complemented
6C2×#11718142C211yesmaximal, characteristic, complemented
7C2×C13×#341C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C23×C8×C13C2211yescharacteristic
12C2×#88180C2211yescharacteristic
13C22×C4×Dic13C2211yescharacteristic
14C23×#1055C2211yescharacteristic
15C2×#88065—22no—
16C2×#88065—22no—
17C2×#88065—22no—
18#11718790—22no—
19#11718790—22no—
20#11718774—22no—
21#11718774—22no—
22C2×#88061C412yescomplemented
23C2×#88060—22no—
24C2×#88056C412yescomplemented
25C13×#341—22no—
26#11718147—22no—
27#11718142—22no—
28#11718142—22no—
29C23×C4×C13C2311yescharacteristic
30C22×C22⋊D13—21no—
31C23×Dic13—21no—
32C2×#6127—21no—
33C2×#6127—21no—
34C2×#6127—21no—
35C2×#6127—21no—
36C2×#6127—21no—
37C2×#6127—21no—
38C2×#6127—21no—
39C2×#6127—21no—
40C2×#6127—21no—
41C2×#6127—21no—
42C2×#6127D412yes—
43C2×#6127D412yes—
44C22×D52C2×C411yescharacteristic
45C22×C4×D13—21no—
46C22×Dic26C2×C411yescharacteristic
47C2×C13×M16—21no—
48C2×C13×M16—21no—
49C2×C13×M16—21no—
50C2×C13×M16—21no—
51C2×C13×M16—21no—
52C2×C13×M16—21no—
53C2×C13×M16—21no—
54C2×C13×M16—21no—
55C2×C13×M16—21no—
56C2×C13×M16—21no—
57C2×C13×M16D412yes—
58C2×C13×M16D412yes—
59C22×C8×C13—21no—
60C22×C8×C13—21no—
61C22×C8×C13—21no—
62C22×C8×C13—21no—
63C22×C8×C13—21no—
64C22×C8×C13—21no—
65C22×C8×C13—21no—
66C22×C8×C13—21no—
67C22×C8×C13C2×C412yes—
68C2×C22⋊Dic13—21no—
69#88180—21no—
70#88180—21no—
71#88180—21no—
72#88180—21no—
73C2×C4⋊Dic13C2×C412yes—
74C2×C4×Dic13—21no—
75C2×C4×Dic13—21no—
76C2×C4×Dic13—21no—
77C2×C4×Dic13—21no—
78C2×C4×Dic13—21no—
79C2×C4×Dic13—21no—
80C2×C4×Dic13D412yes—
81C22×#1055—21no—
82C22×#1055—21no—
83C22×#1055—21no—
84C22×#1055—21no—
85C22×#1055—21no—
86C22×#1055—21no—
87C22×#1055D412yes—
88#88065—28no—
89#88061—24no—
90#88060—28no—
91#88056—24no—
92#11191—131nomaximal, Sylow
93C24×C13#4111yescharacteristic
94C23×D13—21no—
95C22×C4×C13C22×C411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13#4111yescharacteristic
103C22×C4×C13#4111yescharacteristic
104C22×C4×C13#4111yescharacteristic
105C22×C4×C13#4111yescharacteristic
106C22×C4×C13#4111yescharacteristic
107C22×C4×C13#4111yescharacteristic
108C22×C4×C13#4111yescharacteristic
109C2×C22⋊D13—22no—
110C2×C22⋊D13—22no—
111C2×C22⋊D13—41no—
112C2×C22⋊D13—41no—
113C2×C22⋊D13—41no—
114C2×C22⋊D13—41no—
115C22×Dic13—24no—
116C22×Dic13—21no—
117C22×Dic13—22no—
118C22×Dic13—22no—
119C22×Dic13—42no—
120C22×Dic13—41no—
121C22×Dic13—41no—
122#6127—22no—
123#6127—22no—
124#6127—22no—
125#6127—22no—
126#6127—22no—
127#6127—22no—
128#6127—22no—
129#6127—22no—
130#6127—41no—
131#6127—41no—
132#6127—41no—
133#6127—41no—
134#6127—41no—
135#6127—41no—
136#6127—41no—
137#6127—41no—
138C2×D52—21no—
139C2×D52—21no—
140C2×D52—21no—
141C2×D52—21no—
142C2×D52—21no—
143C2×D52C22⋊C412yes—
144C2×C4×D13—22no—
145C2×C4×D13—22no—
146C2×C4×D13—41no—
147C2×C4×D13—41no—
148C2×C4×D13—41no—
149C2×C4×D13—41no—
150C2×Dic26—21no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26C22⋊C412yes—
156C13×M16—22no—
157C13×M16—22no—
158C13×M16—22no—
159C13×M16—22no—
160C13×M16—41no—
161C13×M16—41no—
162C13×M16—41no—
163C13×M16—41no—
164C2×C8×C13—22no—
165C2×C8×C13—22no—
166C2×C8×C13—22no—
167C2×C8×C13—22no—
168C2×C8×C13—22no—
169C2×C8×C13—41no—
170C2×C8×C13—41no—
171C2×C8×C13—41no—
172C2×C8×C13—41no—
173C2×C8×C13—41no—
174C2×C8×C13—41no—
175C2×C8×C13—41no—
176C2×C8×C13—41no—
177C22⋊Dic13—41no—
178C22⋊Dic13—41no—
179C4⋊Dic13—22no—
180C4⋊Dic13—22no—
181C4×Dic13—22no—
182C4×Dic13—22no—
183C4×Dic13—41no—
184C4×Dic13—41no—
185C4×Dic13—41no—
186C4×Dic13—41no—
187C2×#1055—22no—
188C2×#1055—22no—
189C2×#1055—22no—
190C2×#1055—41no—
191C2×#1055—41no—
192C2×#1055—41no—
193C2×#1055—41no—
194C22×#104—131no—
195C2×#416—131no—
196C2×#408—131no—
197C2×#341D1311yescharacteristic, complemented
198C2×#339—131no—
199#1729—131no—
200C2×#336—131no—
201C23×C13—22no—
202C23×C13—22no—
203C23×C13C4×D411yescharacteristic
204C23×C13#12111yescharacteristic
205C23×C13#12311yescharacteristic
206C23×C13#12311yescharacteristic
207C23×C13#12411yescharacteristic
208C23×C13#12611yescharacteristic
209C23×C13#12611yescharacteristic
210C22×D13—22no—
211C22×D13—41no—
212C22×D13—41no—
213C22×D13—42no—
214C22×D13—42no—
215C2×C4×C13C2×C22⋊C411yescharacteristic
216C2×C4×C13#11711yescharacteristic
217C2×C4×C13#11711yescharacteristic
218C2×C4×C13C4×D411yescharacteristic
219C2×C4×C13C4×D411yescharacteristic
220C2×C4×C13C4×D411yescharacteristic
221C2×C4×C13#12011yescharacteristic
222C2×C4×C13#12011yescharacteristic
223C2×C4×C13#12111yescharacteristic
224C2×C4×C13#12111yescharacteristic
225C2×C4×C13#12111yescharacteristic
226C2×C4×C13#12111yescharacteristic
227C2×C4×C13#12111yescharacteristic
228C2×C4×C13#12111yescharacteristic
229C2×C4×C13#12111yescharacteristic
230C2×C4×C13#12311yescharacteristic
231C2×C4×C13#12311yescharacteristic
232C2×C4×C13#12311yescharacteristic
233C2×C4×C13#12311yescharacteristic
234C2×C4×C13#12311yescharacteristic
235C2×C4×C13#12311yescharacteristic
236C2×C4×C13#12311yescharacteristic
237C2×C4×C13#12311yescharacteristic
238C2×C4×C13#12411yescharacteristic
239C2×C4×C13#12411yescharacteristic
240C2×C4×C13#12411yescharacteristic
241C2×C4×C13#12611yescharacteristic
242C2×C4×C13#12611yescharacteristic
243C22⋊D13—42no—
244C22⋊D13—42no—
245C22⋊D13—42no—
246C22⋊D13—42no—
247C2×Dic13—24no—
248C2×Dic13—22no—
249C2×Dic13—44no—
250C2×Dic13—44no—
251C2×Dic13—42no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258D52—22no—
259D52—22no—
260D52—41no—
261D52—41no—
262C4×D13—42no—
263C4×D13—42no—
264C4×D13—42no—
265C4×D13—42no—
266Dic26—22no—
267Dic26—22no—
268Dic26—41no—
269Dic26—41no—
270C8×C13—42no—
271C8×C13—42no—
272C8×C13—42no—
273#1055—42no—
274C22×#41—131no—
275C22×M16C2×D1311yescharacteristic
276C22×M16C2×D1311yescharacteristic
277C23×C8—131no—
278C23×C8C2×D1311yescharacteristic
279C2×#117—131no—
280C22×C42—131no—
281C2×#104—262no—
282C2×#104—262no—
283C2×#104—262no—
284#416—262no—
285#416—262no—
286C2×#103—132no—
287C2×#102—132no—
288#408—262no—
289#408—262no—
290C2×C22⋊C8—262no—
291#341—22no—
292#339—262no—
293#336—262no—
294#336—262no—
295C22×C13—22no—
296C22×C13—22no—
297C22×C13—22no—
298C22×C13—22no—
299C22×C13—21no—
300C22×C13—21no—
301C22×C13—21no—
302C22×C13—21no—
303C22×C13#38611yescharacteristic
304C22×C13#38811yescharacteristic
305C22×C13#38811yescharacteristic
306C22×C13#39411yescharacteristic
307C22×C13#39711yescharacteristic
308C22×C13#39711yescharacteristic
309C22×C13#39711yescharacteristic
310C22×C13#44312yes—
311C22×C13#44412yes—
312C2×D13—44no—
313C2×D13—42no—
314C2×D13—82no—
315C2×D13—81no—
316C2×D13—81no—
317C4×C13#38111yescharacteristic
318C4×C13#38611yescharacteristic
319C4×C13#38811yescharacteristic
320C4×C13#38811yescharacteristic
321C4×C13#39411yescharacteristic
322C4×C13#39411yescharacteristic
323C4×C13#39411yescharacteristic
324C4×C13#39711yescharacteristic
325Dic13—44no—
326Dic13—42no—
327Dic13—82no—
328C2×#41—132no—
329C2×#41—132no—
330C2×#41—261no—
331C2×#41—261no—
332C2×#41—261no—
333C2×#41—261no—
334C2×#41—261no—
335C2×#41—261no—
336C2×#41—261no—
337C2×#41—261no—
338C2×#41—261no—
339C2×#41—261no—
340C22×Q8—131no—
341C22×D4—131no—
342C22×D4—261no—
343C23×C4—261no—
344C23×C4—261no—
345C23×C4C22×D1311yescharacteristic
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16D5212yes—
357C2×M16C22⋊D1312yes—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—132no—
367C22×C8—261no—
368C22×C8—261no—
369C22×C8—261no—
370C22×C8—261no—
371C22×C8—261no—
372C22×C8—261no—
373C22×C8C4×D1312yes—
374#117—261no—
375#117—261no—
376#117—261no—
377#117—261no—
378C2×C4⋊C4—132no—
379C2×C22⋊C4—261no—
380C2×C42—132no—
381C2×C42—261no—
382C2×C42—261no—
383C2×C42—261no—
384C2×C42—261no—
385C2×C42—261no—
386C2×C42—261no—
387#104—268no—
388#103—264no—
389#102—264no—
390C22⋊C8—268no—
391C2×C13—21no—
392C2×C13—21no—
393C2×C13—21no—
394C2×C13—21no—
395C2×C13#144011yescharacteristic
396C2×C13#187612yes—
397C2×C13#192912yes—
398C2×C13#193711yescharacteristic
399C2×C13#193811yescharacteristic
400D13—82no—
401C24—261no—
402C24#613111yescharacteristic
403#41—262no—
404#41—262no—
405#41—262no—
406#41—262no—
407#41—262no—
408#41—262no—
409#41—262no—
410#41—262no—
411#41—521no—
412#41—521no—
413#41—521no—
414#41—521no—
415#41—521no—
416#41—521no—
417#41—521no—
418#41—521no—
419C2×Q8—132no—
420C2×Q8—261no—
421C2×Q8—261no—
422C2×Q8—261no—
423C2×Q8—261no—
424C2×Q8—261no—
425C2×D4—132no—
426C2×D4—262no—
427C2×D4—262no—
428C2×D4—261no—
429C2×D4—261no—
430C2×D4—261no—
431C2×D4—261no—
432C2×D4—261no—
433C2×D4—521no—
434C2×D4—521no—
435C2×D4—521no—
436C2×D4—521no—
437C22×C4—264no—
438C22×C4—261no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—262no—
443C22×C4—522no—
444C22×C4—521no—
445C22×C4—521no—
446C22×C4—521no—
447C22×C4—521no—
448C22×C4—521no—
449C22×C4—521no—
450C22×C4C2×C4×D1311yescharacteristic
451C22×C4C2×D5211yescharacteristic
452C22×C4#612711yescharacteristic
453C22×C4#612711yescharacteristic
454C22×C4#612711yescharacteristic
455C22×C4#612711yescharacteristic
456C22×C4D4×D1311yescharacteristic
457C22×C4D4×D1311yescharacteristic
458C22×C4D4×D1311yescharacteristic
459C22×C4D4×D1311yescharacteristic
460C22×C4#612911yescharacteristic
461C22×C4#612911yescharacteristic
462C22×C4#613111yescharacteristic
463C22×C4C2×C22⋊D1311yescharacteristic
464M16—22no—
465M16—22no—
466M16—22no—
467M16—22no—
468M16—41no—
469M16—41no—
470M16—41no—
471M16—41no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—262no—
486C2×C8—262no—
487C2×C8—262no—
488C2×C8—521no—
489C2×C8—521no—
490C2×C8—521no—
491C2×C8—521no—
492C4⋊C4—262no—
493C4⋊C4—262no—
494C22⋊C4—521no—
495C22⋊C4—521no—
496C42—262no—
497C42—262no—
498C42—521no—
499C42—521no—
500C42—521no—
501C42—521no—
502C13#1119111yescharacteristic, complemented, Sylow
503C23—22no—
504C23—22no—
505C23—262no—
506C23—522no—
507C23—522no—
508C23—521no—
509C23—521no—
510C23#8814711yescharacteristic
511C23#8814811yescharacteristic
512C23#8814811yescharacteristic
513C23#8814911yescharacteristic
514C23#8815211yescharacteristic
515C23#8815211yescharacteristic
516C23#8820111yescharacteristic
517Q8—262no—
518Q8—262no—
519Q8—521no—
520Q8—521no—
521D4—262no—
522D4—262no—
523D4—522no—
524D4—522no—
525D4—522no—
526D4—522no—
527D4—521no—
528D4—521no—
529C2×C4—264no—
530C2×C4—262no—
531C2×C4—524no—
532C2×C4—524no—
533C2×C4—522no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—522no—
537C2×C4—522no—
538C2×C4—522no—
539C2×C4—522no—
540C2×C4—522no—
541C2×C4—522no—
542C2×C4—522no—
543C2×C4—522no—
544C2×C4#8812611yescharacteristic
545C2×C4C4×D5211yescharacteristic
546C2×C4#8812911yescharacteristic
547C2×C4#8813011yescharacteristic
548C2×C4C22⋊C4×D1311yescharacteristic
549C2×C4#8813511yescharacteristic
550C2×C4#8813611yescharacteristic
551C2×C4#8813711yescharacteristic
552C2×C4#8813711yescharacteristic
553C2×C4#8813711yescharacteristic
554C2×C4#8813811yescharacteristic
555C2×C4#8813811yescharacteristic
556C2×C4#8813811yescharacteristic
557C2×C4#8813911yescharacteristic
558C2×C4#8813911yescharacteristic
559C2×C4#8814011yescharacteristic
560C2×C4#8814611yescharacteristic
561C2×C4#8814811yescharacteristic
562C2×C4#8814811yescharacteristic
563C2×C4#8814811yescharacteristic
564C2×C4#8814911yescharacteristic
565C2×C4#8815211yescharacteristic
566C2×C4C4×C22⋊D1311yescharacteristic
567C2×C4#8818311yescharacteristic
568C2×C4#8818411yescharacteristic
569C2×C4#8819111yescharacteristic
570C2×C4#8819211yescharacteristic
571C2×C4#8819311yescharacteristic
572C8—42no—
573C8—42no—
574C8—42no—
575C8—522no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—22no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—524no—
585C22—522no—
586C22—1042no—
587C22—1041no—
588C22—1041no—
589C22#1171832611yescharacteristic
590C22#1171833011yescharacteristic
591C22#1171833511yescharacteristic
592C22#1171833611yescharacteristic
593C22#1171855512yes—
594C22#1171855612yes—
595C22#1171865111yescharacteristic
596C22#1171865211yescharacteristic
597C22#1171865411yescharacteristic
598C4—524no—
599C4—522no—
600C4—1042no—
601C4#1171832511yescharacteristic
602C4#1171833111yescharacteristic
603C4#1171833311yescharacteristic
604C4#1171833611yescharacteristic
605C4#1171860111yescharacteristic
606C4#1171861711yescharacteristic
607C4#1171862011yescharacteristic
608C4#1171862211yescharacteristic
609C2—21no—
610C2—21no—
611C2—21no—
612C2—21no—
613C2—1042no—
614C2#1311308411yescharacteristic
615C2#1311516412yes—
616C2#1311548312yes—
617C2#1311553811yescharacteristic
618C2#1311554511yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#341C2
socleC23×C13C4×D4
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenterC2×#341D13
hypocenterC13#11191
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
4. C2×#11718147C2semidirect
5. #13114534C2semidirect
6. C2×#11718142C2semidirect
7. C2×C13×#341C2semidirect
22. C2×#88061C4semidirect
24. C2×#88056C4semidirect
197. C2×#341D13semidirect
502. C13#11191semidirect

Maximal subgroups

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

subgroupindex
C22×#880652
C2×#117187742
C2×#117187902
C2×#117181472
#131145342
C2×#117181422
C2×C13×#3412
#1119113