Finite Group Databasebeta

← #15769331

Subgroups — #15769331

Order 3328.

916 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718666C211yesmaximal, characteristic
2#13123356C211yesmaximal, characteristic
3C2×#11718667C211yesmaximal, characteristic
4#13123254C211yesmaximal, characteristic, complemented
5#13114569C211yesmaximal, characteristic, complemented
6#13114545C211yesmaximal, characteristic, complemented
7C2×C13×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C2×C13×#117C2211yescharacteristic
11C2×C13×#117C2211yescharacteristic
12C2×#88180C2211yescharacteristic
13C2×#88180C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15#11718794—22no—
16#11718792C412yescomplemented
17#11718783—22no—
18#11718781C412yescomplemented
19M16×Dic13—22no—
20#11718774—22no—
21#11718762—22no—
22#11718667—22no—
23#11718667C414yescomplemented
24#11718666—22no—
25#11718666—22no—
26C2×#88046—22no—
27C2×#88045C414yescomplemented
28C13×H(3,ℤ/4)—22no—
29#11718124—22no—
30#11718118—22no—
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×#6127C2×C412yes—
45C22×D52C2×C411yescharacteristic
46C22×C4×D13—21no—
47C22×Dic26C2×C411yescharacteristic
48C2×C13×M16—21no—
49C2×C13×M16—21no—
50C2×C13×M16—21no—
51C2×C13×M16—21no—
52C2×C13×M16C2×C412yes—
53C2×C13×M16D412yes—
54C22×C8×C13D412yes—
55C13×#117—21no—
56C13×#117—21no—
57C13×#117—21no—
58C13×#117—21no—
59C13×#117—21no—
60C13×#117—21no—
61C13×#117—21no—
62C13×#117C2×C412yes—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C22⋊C4—21no—
66C2×C13×C22⋊C4—21no—
67C2×C42×C13—21no—
68C2×C42×C13C2×C412yes—
69C2×C22⋊Dic13—21no—
70C2×C22⋊Dic13D412yes—
71#88180—21no—
72#88180—21no—
73#88180—21no—
74#88180—21no—
75#88180—21no—
76#88180C2×C412yes—
77#88180C2×C412yes—
78#88180D412yes—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4×Dic13—21no—
82C2×C4×Dic13—21no—
83C2×#6099—21no—
84C2×#6099—21no—
85C2×#6099—21no—
86C2×#6099C2×C412yes—
87C2×#6099D412yes—
88C2×#6099D412yes—
89C22×#1055—21no—
90#88061—24no—
91#88056—24no—
92#88055—24no—
93C8×Dic13—24no—
94#88046—28no—
95#88045—28no—
96#10951—131nomaximal, Sylow
97C24×C13C2×D411yescharacteristic
98C23×D13—21no—
99C22×C4×C13—22no—
100C22×C4×C13—41no—
101C22×C4×C13C22×C411yescharacteristic
102C22×C4×C13C22×C411yescharacteristic
103C22×C4×C13C22×C411yescharacteristic
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
115C2×C22⋊D13—22no—
116C2×C22⋊D13—22no—
117C2×C22⋊D13—41no—
118C2×C22⋊D13—41no—
119C2×C22⋊D13—41no—
120C2×C22⋊D13—41no—
121C22×Dic13—21no—
122C22×Dic13—22no—
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×D52C4212yes—
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×Dic26C4212yes—
158C13×M16—22no—
159C13×M16—22no—
160C13×M16—22no—
161C13×M16—22no—
162C2×C8×C13—22no—
163C2×C8×C13—22no—
164C2×C8×C13C22⋊C414yes—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—41no—
167C13×C4⋊C4—41no—
168C13×C4⋊C4—41no—
169C13×C22⋊C4—22no—
170C13×C22⋊C4—41no—
171C13×C22⋊C4—41no—
172C13×C22⋊C4—41no—
173C42×C13—22no—
174C42×C13—22no—
175C42×C13—22no—
176C42×C13—41no—
177C22⋊Dic13—22no—
178C22⋊Dic13—22no—
179C22⋊Dic13—41no—
180C22⋊Dic13C22⋊C414yes—
181C4⋊Dic13—22no—
182C4⋊Dic13—22no—
183C4⋊Dic13—22no—
184C4⋊Dic13—41no—
185C4×Dic13—22no—
186C4×Dic13—22no—
187C4×Dic13—22no—
188C4×Dic13—41no—
189#6099—22no—
190#6099—22no—
191#6099—22no—
192#6099C22⋊C414yes—
193C2×#1055—22no—
194C2×#1055—22no—
195C2×#1055—22no—
196C2×#421—131no—
197#2896—131no—
198C2×#410—131no—
199#2873—131no—
200#1740—131no—
201#1733—131no—
202C2×H(3,ℤ/4)D1311yescharacteristic, complemented
203C23×C13—81no—
204C23×C13C2×C22⋊C411yescharacteristic
205C23×C13C4×D411yescharacteristic
206C23×C13C4×D411yescharacteristic
207C23×C13#12111yescharacteristic
208C23×C13#12111yescharacteristic
209C23×C13#12411yescharacteristic
210C23×C13#12711yescharacteristic
211C22×D13—22no—
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—82no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—82no—
218C2×C4×C13—82no—
219C2×C4×C13C2×C4211yescharacteristic
220C2×C4×C13C2×C22⋊C411yescharacteristic
221C2×C4×C13C2×C22⋊C411yescharacteristic
222C2×C4×C13#11711yescharacteristic
223C2×C4×C13#11711yescharacteristic
224C2×C4×C13#11711yescharacteristic
225C2×C4×C13C4×D411yescharacteristic
226C2×C4×C13C4×D411yescharacteristic
227C2×C4×C13C4×D411yescharacteristic
228C2×C4×C13C4×D411yescharacteristic
229C2×C4×C13C4×D411yescharacteristic
230C2×C4×C13C4×D411yescharacteristic
231C2×C4×C13C4×D411yescharacteristic
232C2×C4×C13C4×D411yescharacteristic
233C2×C4×C13C4×D411yescharacteristic
234C2×C4×C13C4×D411yescharacteristic
235C2×C4×C13#12011yescharacteristic
236C2×C4×C13#12111yescharacteristic
237C2×C4×C13#12111yescharacteristic
238C2×C4×C13#12111yescharacteristic
239C2×C4×C13#12111yescharacteristic
240C2×C4×C13#12311yescharacteristic
241C2×C4×C13#12311yescharacteristic
242C2×C4×C13#12311yescharacteristic
243C2×C4×C13#12411yescharacteristic
244C2×C4×C13#12411yescharacteristic
245C2×C4×C13#12611yescharacteristic
246C2×C4×C13#12611yescharacteristic
247C22⋊D13—42no—
248C22⋊D13—42no—
249C22⋊D13—42no—
250C22⋊D13—42no—
251C2×Dic13—22no—
252C2×Dic13—24no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—42no—
256C2×Dic13—82no—
257C2×Dic13—82no—
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—24no—
271#1055—24no—
272C22×#41—131no—
273C22×M16—131no—
274C22×M16C2×D1311yescharacteristic
275C2×#117—131no—
276C2×#117—131no—
277C2×#117C2×D1311yescharacteristic
278C2×#117C2×D1311yescharacteristic
279#421—262no—
280#421—262no—
281C2×#104—134no—
282#419—132no—
283#418—132no—
284#417—262no—
285#416—262no—
286#410—134no—
287#410—262no—
288C2×#99—262no—
289#405—262no—
290#405—262no—
291C4×M16—262no—
292#342—262no—
293#339—262no—
294H(3,ℤ/4)—22no—
295C22×C13—41no—
296C22×C13—41no—
297C22×C13—41no—
298C22×C13—41no—
299C22×C13—41no—
300C22×C13—41no—
301C22×C13—41no—
302C22×C13C4×C22⋊C411yescharacteristic
303C22×C13#38611yescharacteristic
304C22×C13#38811yescharacteristic
305C22×C13#38811yescharacteristic
306C22×C13#39011yescharacteristic
307C22×C13#39011yescharacteristic
308C22×C13#39011yescharacteristic
309C2×D13—42no—
310C2×D13—82no—
311C2×D13—82no—
312C2×D13—82no—
313C4×C13—82no—
314C4×C13—82no—
315C4×C13C4×C22⋊C411yescharacteristic
316C4×C13C4×C22⋊C411yescharacteristic
317C4×C13#38611yescharacteristic
318C4×C13#38611yescharacteristic
319C4×C13#38811yescharacteristic
320C4×C13#38811yescharacteristic
321C4×C13#38811yescharacteristic
322C4×C13#38811yescharacteristic
323Dic13—44no—
324Dic13—42no—
325Dic13—82no—
326C2×#41—132no—
327C2×#41—132no—
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—
337C2×#41—261no—
338C22×Q8—131no—
339C22×D4—131no—
340C22×D4—261no—
341C23×C4—261no—
342C23×C4C22×D1311yescharacteristic
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—132no—
348C2×M16—132no—
349C2×M16—132no—
350C2×M16—261no—
351C2×M16—261no—
352C2×M16—261no—
353C2×M16C4×D1312yes—
354C2×M16C22⋊D1312yes—
355C22×C8—261no—
356C22×C8D5212yes—
357#117—21no—
358#117—21no—
359#117—21no—
360#117—21no—
361#117—21no—
362#117—21no—
363#117—21no—
364#117—132no—
365#117—132no—
366#117—132no—
367#117—261no—
368#117—261no—
369#117—261no—
370#117—261no—
371#117—261no—
372#117C4×D1312yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—132no—
380C2×C22⋊C4—261no—
381C2×C42—21no—
382C2×C42—261no—
383C2×C42—261no—
384C2×C42C4×D1312yes—
385#104—268no—
386#103—264no—
387#102—264no—
388#99—268no—
389#97—264no—
390C4×C8—264no—
391C2×C13—21no—
392C2×C13—21no—
393C2×C13—21no—
394C2×C13—21no—
395C2×C13—21no—
396C2×C13—21no—
397C2×C13—21no—
398C2×C13#143711yescharacteristic
399D13—82no—
400C24—261no—
401C24D4×D1311yescharacteristic
402#41—262no—
403#41—262no—
404#41—262no—
405#41—262no—
406#41—262no—
407#41—262no—
408#41—262no—
409#41—262no—
410#41—521no—
411#41—521no—
412#41—521no—
413#41—521no—
414#41—521no—
415#41—521no—
416#41—521no—
417#41—521no—
418C2×Q8—132no—
419C2×Q8—261no—
420C2×Q8—261no—
421C2×Q8—261no—
422C2×Q8—261no—
423C2×Q8—261no—
424C2×D4—132no—
425C2×D4—262no—
426C2×D4—262no—
427C2×D4—261no—
428C2×D4—261no—
429C2×D4—261no—
430C2×D4—261no—
431C2×D4—261no—
432C2×D4—521no—
433C2×D4—521no—
434C2×D4—521no—
435C2×D4—521no—
436C22×C4—22no—
437C22×C4—41no—
438C22×C4—261no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—521no—
443C22×C4—521no—
444C22×C4—521no—
445C22×C4—521no—
446C22×C4—521no—
447C22×C4C2×C4×D1311yescharacteristic
448C22×C4C2×C4×D1311yescharacteristic
449C22×C4C2×C4×D1311yescharacteristic
450C22×C4C2×D5211yescharacteristic
451C22×C4#612711yescharacteristic
452C22×C4#612711yescharacteristic
453C22×C4D4×D1311yescharacteristic
454C22×C4D4×D1311yescharacteristic
455C22×C4D4×D1311yescharacteristic
456C22×C4#612911yescharacteristic
457C22×C4#612911yescharacteristic
458C22×C4#613111yescharacteristic
459C22×C4#613111yescharacteristic
460C22×C4C2×C22⋊D1311yescharacteristic
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—134no—
466M16—262no—
467M16—262no—
468M16—262no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—262no—
472C2×C8—262no—
473C2×C8—262no—
474C2×C8#610314yes—
475C4⋊C4—22no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—262no—
480C4⋊C4—262no—
481C4⋊C4—262no—
482C4⋊C4—521no—
483C22⋊C4—22no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—134no—
488C22⋊C4—262no—
489C22⋊C4—262no—
490C22⋊C4—521no—
491C42—22no—
492C42—22no—
493C42—22no—
494C42—41no—
495C42—262no—
496C42—262no—
497C42—262no—
498C42—521no—
499C13#1095111yescharacteristic, complemented, Sylow
500C23—81no—
501C23—262no—
502C23—521no—
503C23—521no—
504C23—1042no—
505C23C22⋊C4×D1311yescharacteristic
506C23#8813511yescharacteristic
507C23#8813811yescharacteristic
508C23#8813911yescharacteristic
509C23#8814711yescharacteristic
510C23#8814911yescharacteristic
511C23#8819411yescharacteristic
512Q8—262no—
513Q8—262no—
514Q8—521no—
515Q8—521no—
516D4—262no—
517D4—262no—
518D4—522no—
519D4—522no—
520D4—522no—
521D4—522no—
522D4—521no—
523D4—521no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—264no—
529C2×C4—262no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4—522no—
537C2×C4—1042no—
538C2×C4—1042no—
539C2×C4C42×D1311yescharacteristic
540C2×C4#8812611yescharacteristic
541C2×C4C4×D5211yescharacteristic
542C2×C4C4×D5211yescharacteristic
543C2×C4C22⋊C4×D1311yescharacteristic
544C2×C4#8813511yescharacteristic
545C2×C4#8813511yescharacteristic
546C2×C4#8813511yescharacteristic
547C2×C4#8813611yescharacteristic
548C2×C4#8813811yescharacteristic
549C2×C4#8813911yescharacteristic
550C2×C4#8814011yescharacteristic
551C2×C4#8814611yescharacteristic
552C2×C4#8814611yescharacteristic
553C2×C4#8814711yescharacteristic
554C2×C4#8814711yescharacteristic
555C2×C4#8814711yescharacteristic
556C2×C4#8814811yescharacteristic
557C2×C4#8814811yescharacteristic
558C2×C4#8814911yescharacteristic
559C2×C4#8815211yescharacteristic
560C2×C4#8815211yescharacteristic
561C2×C4C2×#610311yescharacteristic
562C2×C4C4×C22⋊D1311yescharacteristic
563C2×C4C4×C22⋊D1311yescharacteristic
564C2×C4#8819311yescharacteristic
565C2×C4#8819311yescharacteristic
566C2×C4#8820111yescharacteristic
567C8—24no—
568C8—264no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—522no—
577C22—1042no—
578C22—1042no—
579C22—1042no—
580C22#1171832611yescharacteristic
581C22#1171832711yescharacteristic
582C22#1171833011yescharacteristic
583C22#1171833111yescharacteristic
584C22#1171861811yescharacteristic
585C22#1171861811yescharacteristic
586C22#1171864911yescharacteristic
587C4—82no—
588C4—82no—
589C4—524no—
590C4—522no—
591C4—1042no—
592C4#1171832611yescharacteristic
593C4#1171832711yescharacteristic
594C4#1171833011yescharacteristic
595C4#1171833111yescharacteristic
596C4C4×#610311yescharacteristic
597C4#1171861911yescharacteristic
598C4#1171865111yescharacteristic
599C4#1171865111yescharacteristic
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—1042no—
608C2#1311307211yescharacteristic
subgroupG/H
centerC4#11718326
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC2×C13×H(3,ℤ/4)C2
socleC2×C13#1437
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenterC2×H(3,ℤ/4)D13
hypocenterC13#10951
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #13123254C2semidirect
5. #13114569C2semidirect
6. #13114545C2semidirect
7. C2×C13×H(3,ℤ/4)C2semidirect
16. #11718792C4semidirect
18. #11718781C4semidirect
23. #11718667C4semidirect
27. C2×#88045C4semidirect
202. C2×H(3,ℤ/4)D13semidirect
499. C13#10951semidirect

Maximal subgroups

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

subgroupindex
C2×#117186662
#131233562
C2×#117186672
#131232542
#131145692
#131145452
C2×C13×H(3,ℤ/4)2
#1095113