Finite Group Databasebeta

← #15770511

Subgroups — #15770511

Order 3328.

850 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88045C211yesmaximal, characteristic
2#13123353C211yesmaximal, characteristic
3C2×#11718793C211yesmaximal, characteristic
4#13114575C211yesmaximal, characteristic, complemented
5C2×#11718152C211yesmaximal, characteristic, complemented
6#13114530C211yesmaximal, characteristic, complemented
7C2×C13×#339C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C2×C13×#117C2211yescharacteristic
11C22×C42×C13C2211yescharacteristic
12C22×#6099C2211yescharacteristic
13C22×#6099C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15C2×#88064—21no—
16#11718793—22no—
17#11718793C414yescomplemented
18C2×#88063—21no—
19#11718665—21no—
20#11718663—22no—
21#11718662—21no—
22#11718627—22no—
23C2×#88045—22no—
24C2×#88045—22no—
25C2×#88045—22no—
26C13×#339—22no—
27#11718152—22no—
28#11718122—22no—
29#11718116—22no—
30C23×C4×C13—21no—
31C23×C4×C13C2311yescharacteristic
32C22×C22⋊D13—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×#6127—21no—
43C2×#6127C2×C412yes—
44C2×#6127D412yes—
45C22×D52D411yescharacteristic
46C22×C4×D13—21no—
47C22×Dic26D411yescharacteristic
48C2×C13×M16—21no—
49C2×C13×M16—21no—
50C2×C13×M16—21no—
51C2×C13×M16—21no—
52C2×C13×M16—21no—
53C2×C13×M16C2×C412yes—
54C22×C8×C13—21no—
55C13×#117—21no—
56C13×#117—21no—
57C13×#117—21no—
58C13×#117—21no—
59C2×C13×C4⋊C4D412yes—
60C2×C13×C22⋊C4—21no—
61C2×C42×C13—21no—
62C2×C42×C13—21no—
63C2×C42×C13—21no—
64C2×C42×C13—21no—
65C2×C42×C13—21no—
66C2×C42×C13—21no—
67C2×C42×C13D412yes—
68C2×#6099—21no—
69C2×#6099—21no—
70C2×#6099—21no—
71C2×#6099—21no—
72C2×#6099—21no—
73C2×#6099—21no—
74C2×#6099—21no—
75C2×#6099—21no—
76C2×#6099—21no—
77C2×#6099—21no—
78C2×#6099—21no—
79C2×#6099—21no—
80C2×#6099—21no—
81C2×#6099—21no—
82C2×#6099—21no—
83C2×#6099—21no—
84C2×#6099C2×C412yes—
85C2×#6099D412yes—
86C22×#1055—21no—
87C22×#1055—21no—
88C22×#1055D412yes—
89#88064—24no—
90#88063—24no—
91#88050—24no—
92#88049—24no—
93#88045—28no—
94#11151—131nomaximal, Sylow
95C24×C13#4111yescharacteristic
96C23×D13—21no—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—44no—
100C22×C4×C13—41no—
101C22×C4×C13—41no—
102C22×C4×C13C22×C411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13#4111yescharacteristic
110C22×C4×C13#4111yescharacteristic
111C22×C4×C13#4111yescharacteristic
112C22×C4×C13#4111yescharacteristic
113C22×C4×C13#4111yescharacteristic
114C22×C4×C13#4111yescharacteristic
115C22×C4×C13#4111yescharacteristic
116C2×C22⋊D13—22no—
117C2×C22⋊D13—22no—
118C2×C22⋊D13—41no—
119C2×C22⋊D13—41no—
120C2×C22⋊D13—41no—
121C2×C22⋊D13—41no—
122C22×Dic13—21no—
123#6127—22no—
124#6127—22no—
125#6127—22no—
126#6127—22no—
127#6127—22no—
128#6127—22no—
129#6127—22no—
130#6127—22no—
131#6127—41no—
132#6127—41no—
133#6127—41no—
134#6127—41no—
135#6127—41no—
136#6127—41no—
137#6127—41no—
138#6127—41no—
139C2×D52—21no—
140C2×D52—21no—
141C2×D52—21no—
142C2×D52—21no—
143C2×D52—21no—
144C2×D52C22⋊C412yes—
145C2×C4×D13—22no—
146C2×C4×D13—22no—
147C2×C4×D13—41no—
148C2×C4×D13—41no—
149C2×C4×D13—41no—
150C2×C4×D13—41no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26C22⋊C412yes—
157C13×M16—22no—
158C13×M16—22no—
159C13×M16—41no—
160C13×M16—41no—
161C2×C8×C13—22no—
162C2×C8×C13—41no—
163C2×C8×C13—41no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C22⋊C4—41no—
167C13×C22⋊C4—41no—
168C42×C13—22no—
169C42×C13—22no—
170C42×C13—41no—
171C42×C13—41no—
172C42×C13—41no—
173C42×C13—41no—
174#6099—22no—
175#6099—22no—
176#6099—22no—
177#6099—22no—
178#6099—41no—
179#6099—41no—
180#6099—41no—
181#6099—41no—
182#6099—41no—
183#6099—41no—
184#6099—41no—
185#6099—41no—
186C2×#1055—22no—
187C2×#1055—22no—
188C2×#1055—22no—
189C2×#1055—22no—
190C2×#1055—22no—
191C2×#1055—41no—
192C2×#1055—41no—
193C2×#1055—41no—
194C2×#1055—41no—
195C22×#104—131no—
196#2896—131no—
197C2×#413—131no—
198#1742—131no—
199C2×#339D1311yescharacteristic, complemented
200C2×#338—131no—
201#1728—131no—
202C23×C13—42no—
203C23×C13#11711yescharacteristic
204C23×C13#12111yescharacteristic
205C23×C13#12311yescharacteristic
206C23×C13#12311yescharacteristic
207C23×C13#12311yescharacteristic
208C23×C13#12411yescharacteristic
209C23×C13#12611yescharacteristic
210C22×D13—22no—
211C22×D13—41no—
212C22×D13—41no—
213C22×D13—82no—
214C2×C4×C13—24no—
215C2×C4×C13—42no—
216C2×C4×C13—44no—
217C2×C4×C13—44no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—82no—
221C2×C4×C13C2×C22⋊C411yescharacteristic
222C2×C4×C13#11711yescharacteristic
223C2×C4×C13C4×D411yescharacteristic
224C2×C4×C13C4×D411yescharacteristic
225C2×C4×C13C4×D411yescharacteristic
226C2×C4×C13C4×D411yescharacteristic
227C2×C4×C13#12011yescharacteristic
228C2×C4×C13#12011yescharacteristic
229C2×C4×C13#12111yescharacteristic
230C2×C4×C13#12111yescharacteristic
231C2×C4×C13#12111yescharacteristic
232C2×C4×C13#12111yescharacteristic
233C2×C4×C13#12111yescharacteristic
234C2×C4×C13#12111yescharacteristic
235C2×C4×C13#12111yescharacteristic
236C2×C4×C13#12311yescharacteristic
237C2×C4×C13#12311yescharacteristic
238C2×C4×C13#12311yescharacteristic
239C2×C4×C13#12311yescharacteristic
240C2×C4×C13#12311yescharacteristic
241C2×C4×C13#12311yescharacteristic
242C2×C4×C13#12311yescharacteristic
243C2×C4×C13#12411yescharacteristic
244C2×C4×C13#12411yescharacteristic
245C2×C4×C13#12411yescharacteristic
246C2×C4×C13#12611yescharacteristic
247C2×C4×C13#12611yescharacteristic
248C2×C4×C13#12611yescharacteristic
249C22⋊D13—42no—
250C22⋊D13—42no—
251C22⋊D13—42no—
252C22⋊D13—42no—
253C2×Dic13—22no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256D52—22no—
257D52—22no—
258D52—41no—
259D52—41no—
260C4×D13—42no—
261C4×D13—42no—
262C4×D13—42no—
263C4×D13—42no—
264Dic26—22no—
265Dic26—22no—
266Dic26—41no—
267Dic26—41no—
268C8×C13—42no—
269#1055—42no—
270#1055—42no—
271#1055—42no—
272C22×#41—131no—
273C22×M16—131no—
274C22×M16—131no—
275C22×M16—131no—
276C22×M16C2×D1311yescharacteristic
277C2×#117C2×D1311yescharacteristic
278C22×C42C2×D1311yescharacteristic
279C2×#104—262no—
280C2×#104—262no—
281C2×#104—262no—
282#419—261no—
283#418—261no—
284#417—262no—
285#416—262no—
286#413—134no—
287#413—262no—
288C2×#101—261no—
289C2×#100—261no—
290#343—262no—
291#339—22no—
292#338—262no—
293#336—262no—
294C22×C13—22no—
295C22×C13—22no—
296C22×C13—22no—
297C22×C13—41no—
298C22×C13—41no—
299C22×C13—41no—
300C22×C13—41no—
301C22×C13#38111yescharacteristic
302C22×C13#38811yescharacteristic
303C22×C13#38811yescharacteristic
304C22×C13#39411yescharacteristic
305C22×C13#39411yescharacteristic
306C22×C13#39711yescharacteristic
307C22×C13#39711yescharacteristic
308C2×D13—42no—
309C2×D13—82no—
310C2×D13—82no—
311C2×D13—82no—
312C4×C13—44no—
313C4×C13—82no—
314C4×C13#38611yescharacteristic
315C4×C13#38611yescharacteristic
316C4×C13#38811yescharacteristic
317C4×C13#38811yescharacteristic
318C4×C13#39411yescharacteristic
319C4×C13#39411yescharacteristic
320C4×C13#39711yescharacteristic
321C4×C13#39711yescharacteristic
322Dic13—42no—
323C2×#41—132no—
324C2×#41—132no—
325C2×#41—261no—
326C2×#41—261no—
327C2×#41—261no—
328C2×#41—261no—
329C2×#41—261no—
330C2×#41—261no—
331C2×#41—261no—
332C2×#41—261no—
333C2×#41—261no—
334C2×#41—261no—
335C22×Q8—131no—
336C22×D4—131no—
337C22×D4—261no—
338C23×C4—21no—
339C23×C4—261no—
340C23×C4C22×D1311yescharacteristic
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—132no—
347C2×M16—132no—
348C2×M16—261no—
349C2×M16—261no—
350C2×M16—261no—
351C2×M16—261no—
352C2×M16—261no—
353C2×M16—261no—
354C2×M16—261no—
355C2×M16—261no—
356C2×M16—261no—
357C2×M16—261no—
358C2×M16—261no—
359C2×M16—261no—
360C2×M16—261no—
361C2×M16—261no—
362C2×M16—261no—
363C2×M16—261no—
364C2×M16C4×D1312yes—
365C22×C8—21no—
366C22×C8—132no—
367C22×C8—261no—
368C22×C8—261no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373C2×C4⋊C4D5212yes—
374C2×C22⋊C4—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42C22⋊D1312yes—
382#104—268no—
383#103—264no—
384#102—264no—
385#101—264no—
386#100—264no—
387C2×C13—21no—
388C2×C13—21no—
389C2×C13—21no—
390C2×C13—21no—
391C2×C13—21no—
392C2×C13—21no—
393C2×C13#144011yescharacteristic
394C2×C13#205012yes—
395D13—82no—
396C24—261no—
397C24#612911yescharacteristic
398#41—262no—
399#41—262no—
400#41—262no—
401#41—262no—
402#41—262no—
403#41—262no—
404#41—262no—
405#41—262no—
406#41—521no—
407#41—521no—
408#41—521no—
409#41—521no—
410#41—521no—
411#41—521no—
412#41—521no—
413#41—521no—
414C2×Q8—132no—
415C2×Q8—261no—
416C2×Q8—261no—
417C2×Q8—261no—
418C2×Q8—261no—
419C2×Q8—261no—
420C2×D4—132no—
421C2×D4—262no—
422C2×D4—262no—
423C2×D4—261no—
424C2×D4—261no—
425C2×D4—261no—
426C2×D4—261no—
427C2×D4—261no—
428C2×D4—521no—
429C2×D4—521no—
430C2×D4—521no—
431C2×D4—521no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—44no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—261no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—521no—
441C22×C4—521no—
442C22×C4—521no—
443C22×C4—521no—
444C22×C4C2×C4×D1311yescharacteristic
445C22×C4C2×D5211yescharacteristic
446C22×C4#612711yescharacteristic
447C22×C4#612711yescharacteristic
448C22×C4#612711yescharacteristic
449C22×C4#612711yescharacteristic
450C22×C4D4×D1311yescharacteristic
451C22×C4D4×D1311yescharacteristic
452C22×C4D4×D1311yescharacteristic
453C22×C4D4×D1311yescharacteristic
454C22×C4#612911yescharacteristic
455C22×C4#613111yescharacteristic
456C22×C4#613111yescharacteristic
457C22×C4C2×C22⋊D1311yescharacteristic
458M16—22no—
459M16—22no—
460M16—41no—
461M16—41no—
462M16—262no—
463M16—262no—
464M16—262no—
465M16—262no—
466M16—521no—
467M16—521no—
468M16—521no—
469M16—521no—
470M16—521no—
471M16—521no—
472M16—521no—
473M16—521no—
474C2×C8—22no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—262no—
478C2×C8—262no—
479C2×C8—262no—
480C2×C8—262no—
481C2×C8—262no—
482C2×C8—521no—
483C2×C8—521no—
484C2×C8—521no—
485C2×C8—521no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C42—22no—
491C42—22no—
492C42—41no—
493C42—41no—
494C42—41no—
495C42—41no—
496C13#1115111yescharacteristic, complemented, Sylow
497C23—42no—
498C23—262no—
499C23—521no—
500C23—521no—
501C23—1042no—
502C23#8813711yescharacteristic
503C23#8813711yescharacteristic
504C23#8813911yescharacteristic
505C23#8814011yescharacteristic
506C23#8814611yescharacteristic
507C23#8815211yescharacteristic
508C23#8819311yescharacteristic
509Q8—262no—
510Q8—262no—
511Q8—521no—
512Q8—521no—
513D4—262no—
514D4—262no—
515D4—522no—
516D4—522no—
517D4—522no—
518D4—522no—
519D4—521no—
520D4—521no—
521C2×C4—24no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—82no—
528C2×C4—262no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—522no—
535C2×C4#8812611yescharacteristic
536C2×C4C4×D5211yescharacteristic
537C2×C4#8812911yescharacteristic
538C2×C4#8813011yescharacteristic
539C2×C4C22⋊C4×D1311yescharacteristic
540C2×C4#8813511yescharacteristic
541C2×C4#8813611yescharacteristic
542C2×C4#8813711yescharacteristic
543C2×C4#8813811yescharacteristic
544C2×C4#8813811yescharacteristic
545C2×C4#8813811yescharacteristic
546C2×C4#8813911yescharacteristic
547C2×C4#8814711yescharacteristic
548C2×C4#8814811yescharacteristic
549C2×C4#8814811yescharacteristic
550C2×C4#8814811yescharacteristic
551C2×C4#8814811yescharacteristic
552C2×C4#8814811yescharacteristic
553C2×C4#8814911yescharacteristic
554C2×C4#8814911yescharacteristic
555C2×C4#8815211yescharacteristic
556C2×C4#8815211yescharacteristic
557C2×C4C4×C22⋊D1311yescharacteristic
558C2×C4#8818311yescharacteristic
559C2×C4#8818411yescharacteristic
560C2×C4#8819111yescharacteristic
561C2×C4#8819211yescharacteristic
562C2×C4#8820111yescharacteristic
563C8—42no—
564C8—522no—
565C8—522no—
566C8—522no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—522no—
575C22—1042no—
576C22—1042no—
577C22—1042no—
578C22#1171832511yescharacteristic
579C22#1171833111yescharacteristic
580C22#1171833511yescharacteristic
581C22#1171833611yescharacteristic
582C22#1171862011yescharacteristic
583C22#1171862211yescharacteristic
584C22#1171865111yescharacteristic
585C4—44no—
586C4—82no—
587C4—522no—
588C4#1171832611yescharacteristic
589C4#1171833011yescharacteristic
590C4#1171833311yescharacteristic
591C4#1171833611yescharacteristic
592C4#1171860111yescharacteristic
593C4#1171861711yescharacteristic
594C4#1171865211yescharacteristic
595C4#1171865411yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—1042no—
603C2#1311308411yescharacteristic
604C2#1311612212yes—
subgroupG/H
centerC2×C4#88139
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#339C2
socleC22×C13#394
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenterC2×#339D13
hypocenterC13#11151
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. #13114575C2semidirect
5. C2×#11718152C2semidirect
6. #13114530C2semidirect
7. C2×C13×#339C2semidirect
17. #11718793C4semidirect
199. C2×#339D13semidirect
496. C13#11151semidirect

Maximal subgroups

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

subgroupindex
C22×#880452
#131233532
C2×#117187932
#131145752
C2×#117181522
#131145302
C2×C13×#3392
#1115113