Finite Group Databasebeta

← #15770479

Subgroups — #15770479

Order 3328.

894 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718800C211yesmaximal, characteristic
2C22×#88065C211yesmaximal, characteristic
3C2×#11718793C211yesmaximal, characteristic
4C2×#11718148C211yesmaximal, characteristic, complemented
5C2×#11718147C211yesmaximal, characteristic, complemented
6#13114529C211yesmaximal, characteristic, complemented
7C2×C13×#430C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C22×C13×M16C2211yescharacteristic
12C2×#88180C2211yescharacteristic
13C22×C4×Dic13C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15C13×#430—22no—
16C13×#430—22no—
17C2×C13×#108—22no—
18#11718800—22no—
19#11718800—22no—
20C2×#88065—22no—
21C2×#88065—22no—
22C2×#88065—22no—
23C2×#88065—22no—
24C2×#88064C412yescomplemented
25#11718793—22no—
26#11718793—22no—
27C2×#88063C412yescomplemented
28#11718148—22no—
29#11718147—22no—
30#11718142—22no—
31C23×C4×C13C2311yescharacteristic
32C22×C22⋊D13—21no—
33C23×Dic13—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×#6127—21no—
43C2×#6127—21no—
44C2×#6127D412yes—
45C2×#6127Q812yes—
46C22×D52C2×C411yescharacteristic
47C22×C4×D13—21no—
48C22×Dic26C2×C411yescharacteristic
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×M16—21no—
58C2×C13×M16—21no—
59C2×C13×M16—21no—
60C2×C13×M16—21no—
61C2×C13×M16—21no—
62C2×C13×M16C2×C412yes—
63C2×C13×M16D412yes—
64C2×C13×M16D412yes—
65C2×C13×M16D412yes—
66C2×C13×M16D412yes—
67C22×C8×C13—21no—
68C22×C8×C13—21no—
69C22×C8×C13—21no—
70C2×C22⋊Dic13—21no—
71#88180—21no—
72#88180—21no—
73#88180—21no—
74#88180D412yes—
75C2×C4⋊Dic13—21no—
76C2×C4×Dic13—21no—
77C2×C4×Dic13—21no—
78C2×C4×Dic13—21no—
79C2×C4×Dic13—21no—
80C2×C4×Dic13—21no—
81C2×C4×Dic13—21no—
82C2×C4×Dic13D412yes—
83C2×#6099—21no—
84C2×#6099—21no—
85C2×#6099—21no—
86C2×#6099—21no—
87C2×#6099—21no—
88C2×#6099C2×C412yes—
89C22×#1055—21no—
90C13×#108—28no—
91#88065—28no—
92#88065—28no—
93#88064—24no—
94#88063—24no—
95#11146—131nomaximal, Sylow
96C24×C13#4111yescharacteristic
97C23×D13—21no—
98C22×C4×C13C22×C411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×Q811yescharacteristic
107C22×C4×C13#4111yescharacteristic
108C22×C4×C13#4111yescharacteristic
109C22×C4×C13#4111yescharacteristic
110C22×C4×C13#4111yescharacteristic
111C22×C4×C13#4111yescharacteristic
112C2×C22⋊D13—22no—
113C2×C22⋊D13—22no—
114C2×C22⋊D13—41no—
115C2×C22⋊D13—41no—
116C2×C22⋊D13—41no—
117C2×C22⋊D13—41no—
118C22×Dic13—21no—
119C22×Dic13—22no—
120C22×Dic13—44no—
121C22×Dic13—41no—
122C22×Dic13—41no—
123C22×Dic13—41no—
124#6127—22no—
125#6127—22no—
126#6127—22no—
127#6127—22no—
128#6127—22no—
129#6127—22no—
130#6127—22no—
131#6127—22no—
132#6127—41no—
133#6127—41no—
134#6127—41no—
135#6127—41no—
136#6127—41no—
137#6127—41no—
138#6127—41no—
139#6127—41no—
140C2×D52—21no—
141C2×D52—21no—
142C2×D52—21no—
143C2×D52—21no—
144C2×D52—21no—
145C2×D52C4⋊C412yes—
146C2×C4×D13—22no—
147C2×C4×D13—22no—
148C2×C4×D13—41no—
149C2×C4×D13—41no—
150C2×C4×D13—41no—
151C2×C4×D13—41no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26—21no—
157C2×Dic26C4⋊C412yes—
158C13×M16—22no—
159C13×M16—22no—
160C13×M16—22no—
161C13×M16—22no—
162C13×M16—22no—
163C13×M16—22no—
164C13×M16—22no—
165C13×M16—41no—
166C13×M16—41no—
167C13×M16—41no—
168C13×M16—41no—
169C13×M16C22⋊C414yes—
170C2×C8×C13—22no—
171C2×C8×C13—22no—
172C2×C8×C13—22no—
173C2×C8×C13—22no—
174C2×C8×C13—22no—
175C2×C8×C13—41no—
176C2×C8×C13—41no—
177C2×C8×C13—41no—
178C2×C8×C13—41no—
179C22⋊Dic13—22no—
180C22⋊Dic13—41no—
181C4⋊Dic13—22no—
182C4⋊Dic13—41no—
183C4×Dic13—22no—
184C4×Dic13—22no—
185C4×Dic13—22no—
186C4×Dic13—41no—
187C4×Dic13—41no—
188C4×Dic13—41no—
189#6099—22no—
190#6099—22no—
191#6099—41no—
192#6099—41no—
193C2×#1055—22no—
194C2×#1055—41no—
195C2×#1055—41no—
196C2×#430D1311yescharacteristic, complemented
197C2×#421—131no—
198C22×#104—131no—
199C2×#413—131no—
200C2×#344—131no—
201C2×#339—131no—
202#1728—131no—
203C23×C13—42no—
204C23×C13#11711yescharacteristic
205C23×C13#12111yescharacteristic
206C23×C13C22⋊Q811yescharacteristic
207C23×C13#12311yescharacteristic
208C23×C13#12311yescharacteristic
209C23×C13#12411yescharacteristic
210C23×C13#12411yescharacteristic
211C22×D13—22no—
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—82no—
215C2×C4×C13C2×C22⋊C411yescharacteristic
216C2×C4×C13C2×C4⋊C411yescharacteristic
217C2×C4×C13C4×D411yescharacteristic
218C2×C4×C13C4×D411yescharacteristic
219C2×C4×C13C4×D411yescharacteristic
220C2×C4×C13C4×D411yescharacteristic
221C2×C4×C13#12011yescharacteristic
222C2×C4×C13#12011yescharacteristic
223C2×C4×C13#12011yescharacteristic
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#12111yescharacteristic
231C2×C4×C13C22⋊Q811yescharacteristic
232C2×C4×C13C22⋊Q811yescharacteristic
233C2×C4×C13C22⋊Q811yescharacteristic
234C2×C4×C13C22⋊Q811yescharacteristic
235C2×C4×C13C22⋊Q811yescharacteristic
236C2×C4×C13#12311yescharacteristic
237C2×C4×C13#12311yescharacteristic
238C2×C4×C13#12311yescharacteristic
239C2×C4×C13#12411yescharacteristic
240C2×C4×C13#12611yescharacteristic
241C2×C4×C13#12611yescharacteristic
242C2×C4×C13#12711yescharacteristic
243C22⋊D13—42no—
244C22⋊D13—42no—
245C22⋊D13—42no—
246C22⋊D13—42no—
247C2×Dic13—24no—
248C2×Dic13—22no—
249C2×Dic13—42no—
250C2×Dic13—44no—
251C2×Dic13—44no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—82no—
257D52—22no—
258D52—22no—
259D52—41no—
260D52—41no—
261C4×D13—42no—
262C4×D13—42no—
263C4×D13—42no—
264C4×D13—42no—
265Dic26—22no—
266Dic26—22no—
267Dic26—41no—
268Dic26—41no—
269C8×C13—24no—
270C8×C13—42no—
271C8×C13—42no—
272#1055—42no—
273C22×#41—131no—
274C22×M16—131no—
275C22×M16C2×D1311yescharacteristic
276C22×M16C2×D1311yescharacteristic
277C22×M16C2×D1311yescharacteristic
278C2×#117—131no—
279C22×C42—131no—
280#430—22no—
281#430—22no—
282C2×#108—22no—
283#421—262no—
284#421—262no—
285C2×#104—262no—
286C2×#104—262no—
287C2×#104—262no—
288C2×#104—262no—
289#413—262no—
290#413—262no—
291C2×#101—132no—
292C2×#100—132no—
293#344—262no—
294#339—262no—
295#336—262no—
296C22×C13—22no—
297C22×C13—22no—
298C22×C13—22no—
299C22×C13—41no—
300C22×C13—41no—
301C22×C13—41no—
302C22×C13—41no—
303C22×C13#38011yescharacteristic
304C22×C13#38811yescharacteristic
305C22×C13#38811yescharacteristic
306C22×C13#39311yescharacteristic
307C22×C13#39411yescharacteristic
308C22×C13#39411yescharacteristic
309C22×C13#39911yescharacteristic
310C2×D13—42no—
311C2×D13—82no—
312C2×D13—82no—
313C2×D13—82no—
314C4×C13#38511yescharacteristic
315C4×C13#38511yescharacteristic
316C4×C13#38611yescharacteristic
317C4×C13#39011yescharacteristic
318C4×C13#39211yescharacteristic
319C4×C13#39611yescharacteristic
320C4×C13#39611yescharacteristic
321C4×C13#39711yescharacteristic
322Dic13—44no—
323Dic13—42no—
324Dic13—82no—
325C2×#41—132no—
326C2×#41—132no—
327C2×#41—261no—
328C2×#41—261no—
329C2×#41—261no—
330C2×#41—261no—
331C2×#41—261no—
332C2×#41—261no—
333C2×#41—261no—
334C2×#41—261no—
335C2×#41—261no—
336C2×#41—261no—
337C22×Q8—131no—
338C22×D4—131no—
339C22×D4—261no—
340C23×C4—261no—
341C23×C4—261no—
342C23×C4C22×D1311yescharacteristic
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
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×M16—132no—
357C2×M16—261no—
358C2×M16—261no—
359C2×M16—261no—
360C2×M16—261no—
361C2×M16—261no—
362C2×M16C4×D1312yes—
363C2×M16D5212yes—
364C2×M16C22⋊D1312yes—
365C2×M16C22⋊D1312yes—
366C2×M16C22⋊D1312yes—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—261no—
371#117—132no—
372#117—261no—
373#117—261no—
374#117—261no—
375C2×C4⋊C4—261no—
376C2×C22⋊C4—261no—
377C2×C42—132no—
378C2×C42—261no—
379C2×C42—261no—
380C2×C42—261no—
381C2×C42—261no—
382C2×C42—261no—
383C2×C42—261no—
384#108—28no—
385#104—268no—
386#104—268no—
387#101—264no—
388#100—264no—
389C2×C13—21no—
390C2×C13—21no—
391C2×C13—21no—
392C2×C13—21no—
393C2×C13—21no—
394C2×C13—21no—
395C2×C13#143911yescharacteristic
396C2×C13#193212yes—
397D13—82no—
398C24—261no—
399C24#613111yescharacteristic
400#41—262no—
401#41—262no—
402#41—262no—
403#41—262no—
404#41—262no—
405#41—262no—
406#41—262no—
407#41—262no—
408#41—521no—
409#41—521no—
410#41—521no—
411#41—521no—
412#41—521no—
413#41—521no—
414#41—521no—
415#41—521no—
416C2×Q8—132no—
417C2×Q8—261no—
418C2×Q8—261no—
419C2×Q8—261no—
420C2×Q8—261no—
421C2×Q8—261no—
422C2×D4—132no—
423C2×D4—262no—
424C2×D4—262no—
425C2×D4—261no—
426C2×D4—261no—
427C2×D4—261no—
428C2×D4—261no—
429C2×D4—261no—
430C2×D4—521no—
431C2×D4—521no—
432C2×D4—521no—
433C2×D4—521no—
434C22×C4—261no—
435C22×C4—262no—
436C22×C4—262no—
437C22×C4—262no—
438C22×C4—524no—
439C22×C4—521no—
440C22×C4—521no—
441C22×C4—521no—
442C22×C4—521no—
443C22×C4—521no—
444C22×C4—521no—
445C22×C4—521no—
446C22×C4C2×C4×D1311yescharacteristic
447C22×C4C2×D5211yescharacteristic
448C22×C4#612711yescharacteristic
449C22×C4#612711yescharacteristic
450C22×C4D4×D1311yescharacteristic
451C22×C4D4×D1311yescharacteristic
452C22×C4D4×D1311yescharacteristic
453C22×C4#612911yescharacteristic
454C22×C4Q8×D1311yescharacteristic
455C22×C4#613111yescharacteristic
456C22×C4#613111yescharacteristic
457C22×C4C2×C22⋊D1311yescharacteristic
458C22×C4C2×C22⋊D1311yescharacteristic
459C22×C4C2×C22⋊D1311yescharacteristic
460M16—22no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—22no—
466M16—22no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16—41no—
471M16—262no—
472M16—262no—
473M16—521no—
474M16—521no—
475M16#610314yes—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—262no—
486C2×C8—521no—
487C2×C8—521no—
488C4⋊C4—262no—
489C4⋊C4—521no—
490C22⋊C4—262no—
491C22⋊C4—521no—
492C42—262no—
493C42—262no—
494C42—262no—
495C42—521no—
496C42—521no—
497C42—521no—
498C13#1114611yescharacteristic, complemented, Sylow
499C23—42no—
500C23—262no—
501C23—521no—
502C23—521no—
503C23—1042no—
504C23#8814611yescharacteristic
505C23#8814811yescharacteristic
506C23#8814811yescharacteristic
507C23#8814911yescharacteristic
508C23#8820011yescharacteristic
509C23#8820111yescharacteristic
510C23#8820111yescharacteristic
511Q8—262no—
512Q8—262no—
513Q8—521no—
514Q8—521no—
515D4—262no—
516D4—262no—
517D4—522no—
518D4—522no—
519D4—522no—
520D4—522no—
521D4—521no—
522D4—521no—
523C2×C4—264no—
524C2×C4—262no—
525C2×C4—522no—
526C2×C4—524no—
527C2×C4—524no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—522no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4—1042no—
537C2×C4C4⋊C4×D1311yescharacteristic
538C2×C4#8814711yescharacteristic
539C2×C4#8814711yescharacteristic
540C2×C4#8814811yescharacteristic
541C2×C4#8814811yescharacteristic
542C2×C4#8814911yescharacteristic
543C2×C4#8814911yescharacteristic
544C2×C4#8815011yescharacteristic
545C2×C4#8815011yescharacteristic
546C2×C4#8815111yescharacteristic
547C2×C4#8815211yescharacteristic
548C2×C4#8815211yescharacteristic
549C2×C4C2×#610311yescharacteristic
550C2×C4C4×C22⋊D1311yescharacteristic
551C2×C4C4×C22⋊D1311yescharacteristic
552C2×C4#8818311yescharacteristic
553C2×C4#8818411yescharacteristic
554C2×C4#8818411yescharacteristic
555C2×C4#8819111yescharacteristic
556C2×C4#8819111yescharacteristic
557C2×C4#8819211yescharacteristic
558C2×C4#8819311yescharacteristic
559C2×C4#8819311yescharacteristic
560C2×C4#8819411yescharacteristic
561C2×C4#8820011yescharacteristic
562C2×C4#8820011yescharacteristic
563C2×C4#8820111yescharacteristic
564C2×C4#8820711yescharacteristic
565C8—24no—
566C8—42no—
567C8—42no—
568C8—522no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—522no—
577C22—1042no—
578C22—1042no—
579C22—1042no—
580C22#1171864811yescharacteristic
581C22#1171865111yescharacteristic
582C22#1171865111yescharacteristic
583C22#1171865211yescharacteristic
584C22#1171865211yescharacteristic
585C22#1171865311yescharacteristic
586C22#1171889211yescharacteristic
587C4—524no—
588C4—522no—
589C4—1042no—
590C4#1171864911yescharacteristic
591C4#1171865011yescharacteristic
592C4#1171865011yescharacteristic
593C4#1171865411yescharacteristic
594C4#1171865511yescharacteristic
595C4#1171865511yescharacteristic
596C4#1171887411yescharacteristic
597C4#1171888411yescharacteristic
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—1042no—
605C2#1311307811yescharacteristic
606C2#1311550412yes—
subgroupG/H
centerC2×C4#88193
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#430C2
socleC22×C13#388
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenterC2×#430D13
hypocenterC13#11146
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#430

Complements

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

NH ≅ G/Ntype
4. C2×#11718148C2semidirect
5. C2×#11718147C2semidirect
6. #13114529C2semidirect
7. C2×C13×#430C2semidirect
24. C2×#88064C4semidirect
27. C2×#88063C4semidirect
196. C2×#430D13semidirect
498. C13#11146semidirect

Maximal subgroups

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

subgroupindex
C2×#117188002
C22×#880652
C2×#117187932
C2×#117181482
C2×#117181472
#131145292
C2×C13×#4302
#1114613