Finite Group Databasebeta

← #15891875

Subgroups — #15891875

Order 3328.

888 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718785C211yesmaximal, characteristic, complemented
2#13123353C211yesmaximal, characteristic
3#13123353C211yesmaximal, characteristic
4C2×#11718793C211yesmaximal, characteristic
5#13116305C214yesmaximal, complemented
6#13116298C214yesmaximal, complemented
7C2×#11718125C211yesmaximal, characteristic, complemented
8C2×#11718125C211yesmaximal, characteristic, complemented
9C2×C13×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
10C22×#6127C2211yescharacteristic
11C22×C13×M16C2211yescharacteristic
12C2×C13×#117C2211yescharacteristic
13C2×C13×#117C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15C22×#6099C2211yescharacteristic
16C22×#6099C2211yescharacteristic
17C2×#88064C2212yes—
18#11718793—22no—
19#11718793—22no—
20C2×#88063C2212yes—
21#11718785—22no—
22#11718785C2214yes—
23C2×#88062—22no—
24#11718665C2212yes—
25#11718665C2212yes—
26#11718663—22no—
27#11718663—22no—
28#11718662C2212yes—
29#11718662C2212yes—
30#11718627—22no—
31#11718627—22no—
32C13×H(3,ℤ/4)C2214yes—
33#11718125C2214yes—
34#11718125C2214yes—
35C23×C4×C13C2311yescharacteristic
36C22×C22⋊D13—21no—
37C2×#6127—21no—
38C2×#6127—21no—
39C2×#6127—21no—
40C2×#6127—21no—
41C2×#6127—21no—
42C2×#6127—21no—
43C2×#6127—21no—
44C2×#6127—21no—
45C2×#6127—21no—
46C2×#6127—21no—
47C2×#6127D412yes—
48C2×#6127D412yes—
49C22×D52C2311yescharacteristic
50C22×C4×D13—21no—
51C22×Dic26C2311yescharacteristic
52C2×C13×M16—21no—
53C2×C13×M16—21no—
54C2×C13×M16—21no—
55C2×C13×M16—21no—
56C2×C13×M16—21no—
57C2×C13×M16C2312yes—
58C22×C8×C13—21no—
59C13×#117—21no—
60C13×#117—21no—
61C13×#117—21no—
62C13×#117—21no—
63C13×#117—21no—
64C13×#117—21no—
65C13×#117C2312yes—
66C13×#117C2312yes—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—21no—
71C2×C42×C13—21no—
72C2×C42×C13—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×#6099—21no—
85C2×#6099—21no—
86C2×#6099—21no—
87C2×#6099D412yes—
88C2×#6099C2312yes—
89C2×#6099C2312yes—
90C2×#6099C2312yes—
91C22×#1055—21no—
92C22×#1055—21no—
93C22×#1055D412yes—
94#88064—24no—
95#88063—24no—
96#88062—28no—
97#88050—24no—
98#88050—24no—
99#88049—24no—
100#88049—24no—
101#23652—131nomaximal, Sylow
102C24×C13#4111yescharacteristic
103C23×D13—21no—
104C22×C4×C13—41no—
105C22×C4×C13—41no—
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13#4111yescharacteristic
111C22×C4×C13#4111yescharacteristic
112C22×C4×C13#4111yescharacteristic
113C22×C4×C13#4111yescharacteristic
114C22×C4×C13#4111yescharacteristic
115C22×C4×C13#4111yescharacteristic
116C22×C4×C13#4111yescharacteristic
117C22×C4×C13#4111yescharacteristic
118C22×C4×C13#4111yescharacteristic
119C22×C4×C13C2411yescharacteristic
120C2×C22⋊D13—22no—
121C2×C22⋊D13—22no—
122C2×C22⋊D13—41no—
123C2×C22⋊D13—41no—
124C2×C22⋊D13—41no—
125C2×C22⋊D13—41no—
126C22×Dic13—21no—
127#6127—22no—
128#6127—22no—
129#6127—22no—
130#6127—22no—
131#6127—22no—
132#6127—22no—
133#6127—22no—
134#6127—22no—
135#6127—41no—
136#6127—41no—
137#6127—41no—
138#6127—41no—
139#6127—41no—
140#6127—41no—
141#6127—41no—
142#6127—41no—
143C2×D52—21no—
144C2×D52—21no—
145C2×D52—21no—
146C2×D52—21no—
147C2×D52—21no—
148C2×D52C2×D412yes—
149C2×C4×D13—22no—
150C2×C4×D13—22no—
151C2×C4×D13—41no—
152C2×C4×D13—41no—
153C2×C4×D13—41no—
154C2×C4×D13—41no—
155C2×Dic26—21no—
156C2×Dic26—21no—
157C2×Dic26—21no—
158C2×Dic26—21no—
159C2×Dic26—21no—
160C2×Dic26C2×D412yes—
161C13×M16—22no—
162C13×M16—22no—
163C13×M16—41no—
164C13×M16—41no—
165C2×C8×C13—22no—
166C2×C8×C13—41no—
167C2×C8×C13—41no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—41no—
171C13×C4⋊C4—41no—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—22no—
174C13×C22⋊C4—41no—
175C13×C22⋊C4—41no—
176C42×C13—22no—
177C42×C13—22no—
178C42×C13—41no—
179C42×C13—41no—
180#6099—22no—
181#6099—22no—
182#6099—22no—
183#6099—22no—
184#6099—22no—
185#6099—22no—
186#6099—22no—
187#6099—22no—
188#6099—41no—
189#6099—41no—
190#6099—41no—
191#6099—41no—
192C2×#1055—22no—
193C2×#1055—22no—
194C2×#1055—22no—
195C2×#1055—22no—
196C2×#1055—41no—
197C2×#1055—41no—
198C2×#1055—41no—
199C2×#1055—41no—
200C2×#1055C2×D414yes—
201C2×#430—131no—
202#2896—131no—
203#2896—131no—
204C2×#413—131no—
205#2082—134no—
206#2081—134no—
207C2×#344—131no—
208C2×#344—131no—
209C2×H(3,ℤ/4)D1311yescharacteristic, complemented
210C23×C13—81no—
211C23×C13#12311yescharacteristic
212C23×C13#12311yescharacteristic
213C23×C13#12411yescharacteristic
214C23×C13#12411yescharacteristic
215C23×C13#12611yescharacteristic
216C23×C13#12611yescharacteristic
217C23×C13C2×#4111yescharacteristic
218C22×D13—22no—
219C22×D13—41no—
220C22×D13—41no—
221C22×D13—82no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—82no—
225C2×C4×C13—82no—
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#12311yescharacteristic
239C2×C4×C13#12311yescharacteristic
240C2×C4×C13#12411yescharacteristic
241C2×C4×C13#12411yescharacteristic
242C2×C4×C13#12611yescharacteristic
243C2×C4×C13#12611yescharacteristic
244C2×C4×C13#12611yescharacteristic
245C2×C4×C13#12611yescharacteristic
246C2×C4×C13#12611yescharacteristic
247C2×C4×C13#12611yescharacteristic
248C2×C4×C13C22×D411yescharacteristic
249C2×C4×C13C22×D411yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C22⋊D13—42no—
255C22⋊D13—42no—
256C22⋊D13—42no—
257C22⋊D13—42no—
258C2×Dic13—22no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261D52—22no—
262D52—22no—
263D52—41no—
264D52—41no—
265C4×D13—42no—
266C4×D13—42no—
267C4×D13—42no—
268C4×D13—42no—
269Dic26—22no—
270Dic26—22no—
271Dic26—41no—
272Dic26—41no—
273C8×C13—42no—
274#1055—24no—
275#1055—42no—
276#1055—42no—
277C22×#41—131no—
278C22×M16—131no—
279C22×M16—131no—
280C22×M16—131no—
281C22×M16C2×D1311yescharacteristic
282C2×#117C2×D1311yescharacteristic
283C2×#117C2×D1311yescharacteristic
284#430—134no—
285#430—262no—
286C2×#108—262no—
287#419—132no—
288#419—132no—
289#418—132no—
290#418—132no—
291#417—262no—
292#417—262no—
293#416—262no—
294#416—262no—
295#413—262no—
296#413—262no—
297C2×#101—132no—
298C2×#100—132no—
299#344—134no—
300#344—134no—
301H(3,ℤ/4)C2×D1314yes—
302C22×C13—41no—
303C22×C13—41no—
304C22×C13—41no—
305C22×C13—41no—
306C22×C13—41no—
307C22×C13—41no—
308C22×C13—41no—
309C22×C13#39711yescharacteristic
310C22×C13#39711yescharacteristic
311C22×C13#39711yescharacteristic
312C22×C13#39711yescharacteristic
313C22×C13C2×#12311yescharacteristic
314C22×C13C2×#12411yescharacteristic
315C22×C13C2×#12611yescharacteristic
316C2×D13—42no—
317C2×D13—82no—
318C2×D13—82no—
319C2×D13—82no—
320C4×C13—82no—
321C4×C13—82no—
322C4×C13#39711yescharacteristic
323C4×C13#39711yescharacteristic
324C4×C13#39711yescharacteristic
325C4×C13#39711yescharacteristic
326C4×C13C2×#12111yescharacteristic
327C4×C13C2×#12311yescharacteristic
328C4×C13C2×#12311yescharacteristic
329C4×C13C2×#12611yescharacteristic
330Dic13—42no—
331C2×#41—132no—
332C2×#41—132no—
333C2×#41—261no—
334C2×#41—261no—
335C2×#41—261no—
336C2×#41—261no—
337C2×#41—261no—
338C2×#41—261no—
339C2×#41—261no—
340C2×#41—261no—
341C2×#41—261no—
342C2×#41—261no—
343C22×Q8—131no—
344C22×D4—131no—
345C22×D4—261no—
346C23×C4—261no—
347C23×C4C22×D1311yescharacteristic
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—132no—
354C2×M16—132no—
355C2×M16—132no—
356C2×M16—132no—
357C2×M16—261no—
358C2×M16—261no—
359C2×M16—261no—
360C2×M16—261no—
361C2×M16—261no—
362C2×M16—261no—
363C2×M16—261no—
364C2×M16—261no—
365C2×M16—261no—
366C2×M16—261no—
367C2×M16—261no—
368C2×M16—261no—
369C2×M16—261no—
370C2×M16—261no—
371C2×M16C22×D1312yes—
372C22×C8—21no—
373C22×C8—132no—
374C22×C8—261no—
375C22×C8—261no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117C22×D1312yes—
383#117C22×D1312yes—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C42—21no—
389C2×C42—21no—
390#108—268no—
391#103—264no—
392#103—264no—
393#102—264no—
394#102—264no—
395#101—264no—
396#100—264no—
397C2×C13—21no—
398C2×C13—21no—
399C2×C13—21no—
400C2×C13—21no—
401C2×C13—21no—
402C2×C13—21no—
403C2×C13—21no—
404C2×C13C2×#39711yescharacteristic
405D13—82no—
406C24—261no—
407C24#612911yescharacteristic
408#41—262no—
409#41—262no—
410#41—262no—
411#41—262no—
412#41—262no—
413#41—262no—
414#41—262no—
415#41—262no—
416#41—521no—
417#41—521no—
418#41—521no—
419#41—521no—
420#41—521no—
421#41—521no—
422#41—521no—
423#41—521no—
424C2×Q8—132no—
425C2×Q8—261no—
426C2×Q8—261no—
427C2×Q8—261no—
428C2×Q8—261no—
429C2×Q8—261no—
430C2×D4—132no—
431C2×D4—262no—
432C2×D4—262no—
433C2×D4—261no—
434C2×D4—261no—
435C2×D4—261no—
436C2×D4—261no—
437C2×D4—261no—
438C2×D4—521no—
439C2×D4—521no—
440C2×D4—521no—
441C2×D4—521no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—261no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—521no—
448C22×C4—521no—
449C22×C4—521no—
450C22×C4—521no—
451C22×C4#612711yescharacteristic
452C22×C4#612711yescharacteristic
453C22×C4#612711yescharacteristic
454C22×C4#612711yescharacteristic
455C22×C4#612711yescharacteristic
456C22×C4#612711yescharacteristic
457C22×C4D4×D1311yescharacteristic
458C22×C4D4×D1311yescharacteristic
459C22×C4D4×D1311yescharacteristic
460C22×C4D4×D1311yescharacteristic
461C22×C4#612911yescharacteristic
462C22×C4#613111yescharacteristic
463C22×C4#613111yescharacteristic
464C22×C4C23×D1311yescharacteristic
465M16—22no—
466M16—22no—
467M16—41no—
468M16—41no—
469M16—262no—
470M16—262no—
471M16—262no—
472M16—262no—
473M16—262no—
474M16—262no—
475M16—262no—
476M16—262no—
477M16—521no—
478M16—521no—
479M16—521no—
480M16—521no—
481C2×C8—22no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—134no—
485C2×C8—262no—
486C2×C8—262no—
487C2×C8—262no—
488C2×C8—262no—
489C2×C8—521no—
490C2×C8—521no—
491C2×C8—521no—
492C2×C8—521no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C42—22no—
502C42—22no—
503C42—41no—
504C42—41no—
505C13#2365211yescharacteristic, complemented, Sylow
506C23—81no—
507C23—262no—
508C23—521no—
509C23—521no—
510C23—1042no—
511C23#8813711yescharacteristic
512C23#8813711yescharacteristic
513C23#8813911yescharacteristic
514C23#8813911yescharacteristic
515C23#8815211yescharacteristic
516C23#8815211yescharacteristic
517C23C2×#612911yescharacteristic
518Q8—262no—
519Q8—262no—
520Q8—521no—
521Q8—521no—
522D4—262no—
523D4—262no—
524D4—522no—
525D4—522no—
526D4—522no—
527D4—522no—
528D4—521no—
529D4—521no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—82no—
533C2×C4—82no—
534C2×C4—262no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—522no—
538C2×C4—522no—
539C2×C4—522no—
540C2×C4—522no—
541C2×C4#8813011yescharacteristic
542C2×C4#8813011yescharacteristic
543C2×C4#8813011yescharacteristic
544C2×C4#8813011yescharacteristic
545C2×C4#8813711yescharacteristic
546C2×C4#8813711yescharacteristic
547C2×C4#8813811yescharacteristic
548C2×C4#8813811yescharacteristic
549C2×C4#8813811yescharacteristic
550C2×C4#8813811yescharacteristic
551C2×C4#8813911yescharacteristic
552C2×C4#8813911yescharacteristic
553C2×C4#8814811yescharacteristic
554C2×C4#8814811yescharacteristic
555C2×C4#8814811yescharacteristic
556C2×C4#8814811yescharacteristic
557C2×C4#8814811yescharacteristic
558C2×C4#8814811yescharacteristic
559C2×C4#8814811yescharacteristic
560C2×C4#8814811yescharacteristic
561C2×C4#8815211yescharacteristic
562C2×C4#8815211yescharacteristic
563C2×C4C2×#612711yescharacteristic
564C2×C4C2×#612711yescharacteristic
565C2×C4C2×#612711yescharacteristic
566C2×C4C2×D4×D1311yescharacteristic
567C2×C4C2×D4×D1311yescharacteristic
568C2×C4C2×#613111yescharacteristic
569C8—42no—
570C8—264no—
571C8—522no—
572C8—522no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—522no—
581C22—1042no—
582C22—1042no—
583C22—1042no—
584C22#1171833611yescharacteristic
585C22#1171833611yescharacteristic
586C22#1171833611yescharacteristic
587C22#1171833611yescharacteristic
588C22C2×#8813711yescharacteristic
589C22C2×#8813911yescharacteristic
590C22C2×#8815211yescharacteristic
591C4—82no—
592C4—82no—
593C4—522no—
594C4#1171833611yescharacteristic
595C4#1171833611yescharacteristic
596C4#1171833611yescharacteristic
597C4#1171833611yescharacteristic
598C4C2×#8813011yescharacteristic
599C4C2×#8813811yescharacteristic
600C4C2×#8814811yescharacteristic
601C4C2×#8814811yescharacteristic
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2—21no—
609C2—1042no—
610C2C2×#1171833611yescharacteristic
subgroupG/H
centerC4#11718336
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×H(3,ℤ/4)C2
socleC2×C13C2×#397
prime radicalC22×#6127C22
hypercenterC2×H(3,ℤ/4)D13
hypocenterC13#23652
LCSG ▷ C22×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
1. C2×#11718785C2semidirect
5. #13116305C2semidirect
6. #13116298C2semidirect
7. C2×#11718125C2semidirect
8. C2×#11718125C2semidirect
9. C2×C13×H(3,ℤ/4)C2semidirect
209. C2×H(3,ℤ/4)D13semidirect
505. C13#23652semidirect

Maximal subgroups

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

subgroupindex
C2×#117187852
#131233532
C2×#117187932
#131163052
#131162982
C2×#117181252
C2×C13×H(3,ℤ/4)2
#2365213