Finite Group Databasebeta

← #15770514

Subgroups — #15770514

Order 3328.

826 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
1C2×#11718666C211yesmaximal, characteristic
2C2×#11718627C211yesmaximal, characteristic
3C2×#11718793C211yesmaximal, characteristic
4C2×#11718125C211yesmaximal, characteristic, complemented
5C2×#11718122C211yesmaximal, characteristic, complemented
6#13114562C211yesmaximal, characteristic, complemented
7C13×#1736C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C2×C13×#117C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×#6099C2211yescharacteristic
13C22×#6099C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15C2×#88064—21no—
16#11718793—22no—
17#11718793C414yescomplemented
18C2×#88063—21no—
19#11718666—22no—
20#11718666—22no—
21C2×#88050—21no—
22#11718627—22no—
23#11718627—22no—
24C2×#88049—21no—
25C2×#88045—22no—
26C13×#340—22no—
27#11718150—22no—
28#11718125—22no—
29#11718122—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×#117D412yes—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4D412yes—
66C2×C13×C22⋊C4—21no—
67C2×C42×C13—21no—
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×#6099C2×C412yes—
84C2×#6099D412yes—
85C2×#6099D412yes—
86C22×#1055—21no—
87C22×#1055—21no—
88C22×#1055—21no—
89#88064—24no—
90#88063—24no—
91#88050—24no—
92#88049—24no—
93#88045—28no—
94#11152—131nomaximal, Sylow
95C24×C13#4111yescharacteristic
96C23×D13—21no—
97C22×C4×C13—22no—
98C22×C4×C13—41no—
99C22×C4×C13—41no—
100C22×C4×C13—41no—
101C22×C4×C13—82no—
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×C4⋊C4—22no—
167C13×C4⋊C4—41no—
168C13×C4⋊C4—41no—
169C13×C4⋊C4—41no—
170C13×C22⋊C4—22no—
171C13×C22⋊C4—41no—
172C42×C13—22no—
173C42×C13—41no—
174#6099—22no—
175#6099—22no—
176#6099—22no—
177#6099—22no—
178#6099—22no—
179#6099—22no—
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—41no—
190C2×#1055—41no—
191C2×#1055—41no—
192C2×#1055—41no—
193C2×#1055—41no—
194C2×#1055—41no—
195C2×#421—131no—
196C2×#417—131no—
197C2×#413—131no—
198C2×#344—131no—
199C2×#343—131no—
200#1738—131no—
201#1736D1311yescharacteristic, complemented
202C23×C13—41no—
203C23×C13—41no—
204C23×C13#11711yescharacteristic
205C23×C13#12111yescharacteristic
206C23×C13#12311yescharacteristic
207C23×C13#12311yescharacteristic
208C23×C13#12311yescharacteristic
209C23×C13#12411yescharacteristic
210C23×C13#12611yescharacteristic
211C22×D13—22no—
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—81no—
215C22×D13—81no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—81no—
219C2×C4×C13—81no—
220C2×C4×C13—82no—
221C2×C4×C13—82no—
222C2×C4×C13—82no—
223C2×C4×C13C2×C22⋊C411yescharacteristic
224C2×C4×C13#11711yescharacteristic
225C2×C4×C13C4×D411yescharacteristic
226C2×C4×C13C4×D411yescharacteristic
227C2×C4×C13C4×D411yescharacteristic
228C2×C4×C13C4×D411yescharacteristic
229C2×C4×C13#12011yescharacteristic
230C2×C4×C13#12011yescharacteristic
231C2×C4×C13#12111yescharacteristic
232C2×C4×C13#12111yescharacteristic
233C2×C4×C13#12111yescharacteristic
234C2×C4×C13#12111yescharacteristic
235C2×C4×C13#12111yescharacteristic
236C2×C4×C13#12111yescharacteristic
237C2×C4×C13#12111yescharacteristic
238C2×C4×C13#12311yescharacteristic
239C2×C4×C13#12311yescharacteristic
240C2×C4×C13#12311yescharacteristic
241C2×C4×C13#12311yescharacteristic
242C2×C4×C13#12311yescharacteristic
243C2×C4×C13#12311yescharacteristic
244C2×C4×C13#12311yescharacteristic
245C2×C4×C13#12411yescharacteristic
246C2×C4×C13#12411yescharacteristic
247C2×C4×C13#12411yescharacteristic
248C2×C4×C13#12611yescharacteristic
249C2×C4×C13#12611yescharacteristic
250C2×C4×C13#12611yescharacteristic
251C22⋊D13—42no—
252C22⋊D13—42no—
253C22⋊D13—42no—
254C22⋊D13—42no—
255C2×Dic13—22no—
256C2×Dic13—41no—
257C2×Dic13—41no—
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—
271#1055—42no—
272#1055—42no—
273#1055—42no—
274C22×#41—131no—
275C22×M16—131no—
276C22×M16—131no—
277C22×M16—131no—
278C22×M16C2×D1311yescharacteristic
279C2×#117C2×D1311yescharacteristic
280C22×C4⋊C4C2×D1311yescharacteristic
281#421—262no—
282#421—262no—
283C2×#104—262no—
284#417—262no—
285#417—262no—
286C2×#103—261no—
287C2×#102—261no—
288#413—134no—
289#413—262no—
290C2×#101—261no—
291C2×#100—261no—
292#344—262no—
293#343—262no—
294#341—262no—
295#340—22no—
296C22×C13—21no—
297C22×C13—21no—
298C22×C13—21no—
299C22×C13—21no—
300C22×C13—21no—
301C22×C13—21no—
302C22×C13—41no—
303C22×C13—41no—
304C22×C13—41no—
305C22×C13—41no—
306C22×C13#38111yescharacteristic
307C22×C13#38811yescharacteristic
308C22×C13#38811yescharacteristic
309C22×C13#39411yescharacteristic
310C22×C13#39411yescharacteristic
311C22×C13#39711yescharacteristic
312C22×C13#39711yescharacteristic
313C2×D13—42no—
314C2×D13—82no—
315C2×D13—81no—
316C2×D13—81no—
317C2×D13—82no—
318C4×C13—82no—
319C4×C13—82no—
320C4×C13#38611yescharacteristic
321C4×C13#38611yescharacteristic
322C4×C13#38811yescharacteristic
323C4×C13#38811yescharacteristic
324C4×C13#39411yescharacteristic
325C4×C13#39411yescharacteristic
326C4×C13#39711yescharacteristic
327C4×C13#39711yescharacteristic
328Dic13—42no—
329C2×#41—132no—
330C2×#41—132no—
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—
340C2×#41—261no—
341C22×Q8—131no—
342C22×D4—131no—
343C22×D4—261no—
344C23×C4—21no—
345C23×C4—261no—
346C23×C4C22×D1311yescharacteristic
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—132no—
353C2×M16—132no—
354C2×M16—132no—
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×M16—261no—
365C2×M16—261no—
366C2×M16—261no—
367C2×M16—261no—
368C2×M16—261no—
369C2×M16—261no—
370C2×M16C4×D1312yes—
371C22×C8—21no—
372C22×C8—261no—
373C22×C8—261no—
374C22×C8—261no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117D5212yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4C22⋊D1312yes—
386C2×C22⋊C4—21no—
387C2×C42—21no—
388#104—268no—
389#103—264no—
390#102—264no—
391#101—264no—
392#100—264no—
393C2×C13—21no—
394C2×C13—21no—
395C2×C13—21no—
396C2×C13—21no—
397C2×C13—21no—
398C2×C13—21no—
399C2×C13#144011yescharacteristic
400C2×C13#204811yescharacteristic
401C2×C13#204911yescharacteristic
402D13—82no—
403C24—261no—
404C24#612911yescharacteristic
405#41—262no—
406#41—262no—
407#41—262no—
408#41—262no—
409#41—262no—
410#41—262no—
411#41—262no—
412#41—262no—
413#41—521no—
414#41—521no—
415#41—521no—
416#41—521no—
417#41—521no—
418#41—521no—
419#41—521no—
420#41—521no—
421C2×Q8—132no—
422C2×Q8—261no—
423C2×Q8—261no—
424C2×Q8—261no—
425C2×Q8—261no—
426C2×Q8—261no—
427C2×D4—132no—
428C2×D4—262no—
429C2×D4—262no—
430C2×D4—261no—
431C2×D4—261no—
432C2×D4—261no—
433C2×D4—261no—
434C2×D4—261no—
435C2×D4—521no—
436C2×D4—521no—
437C2×D4—521no—
438C2×D4—521no—
439C22×C4—22no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—82no—
444C22×C4—261no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—521no—
448C22×C4—521no—
449C22×C4—521no—
450C22×C4—521no—
451C22×C4C2×C4×D1311yescharacteristic
452C22×C4C2×D5211yescharacteristic
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×C4C2×C22⋊D1311yescharacteristic
465M16—22no—
466M16—22no—
467M16—41no—
468M16—41no—
469M16—262no—
470M16—262no—
471M16—262no—
472M16—262no—
473M16—262no—
474M16—262no—
475M16—521no—
476M16—521no—
477M16—521no—
478M16—521no—
479M16—521no—
480M16—521no—
481C2×C8—22no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—262no—
485C2×C8—262no—
486C2×C8—262no—
487C2×C8—521no—
488C2×C8—521no—
489C2×C8—521no—
490C2×C8—521no—
491C2×C8—521no—
492C2×C8—521no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C22⋊C4—22no—
500C22⋊C4—41no—
501C42—22no—
502C42—41no—
503C13#1115211yescharacteristic, complemented, Sylow
504C23—41no—
505C23—41no—
506C23—262no—
507C23—521no—
508C23—521no—
509C23—1041no—
510C23—1041no—
511C23#8813711yescharacteristic
512C23#8813711yescharacteristic
513C23#8813911yescharacteristic
514C23#8814011yescharacteristic
515C23#8814611yescharacteristic
516C23#8815211yescharacteristic
517C23#8819311yescharacteristic
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—81no—
535C2×C4—81no—
536C2×C4—82no—
537C2×C4—262no—
538C2×C4—521no—
539C2×C4—521no—
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#8813811yescharacteristic
553C2×C4#8813811yescharacteristic
554C2×C4#8813811yescharacteristic
555C2×C4#8813911yescharacteristic
556C2×C4#8814711yescharacteristic
557C2×C4#8814811yescharacteristic
558C2×C4#8814811yescharacteristic
559C2×C4#8814811yescharacteristic
560C2×C4#8814811yescharacteristic
561C2×C4#8814811yescharacteristic
562C2×C4#8814911yescharacteristic
563C2×C4#8814911yescharacteristic
564C2×C4#8815211yescharacteristic
565C2×C4#8815211yescharacteristic
566C2×C4C4×C22⋊D1311yescharacteristic
567C2×C4#8818311yescharacteristic
568C2×C4#8818411yescharacteristic
569C2×C4#8819111yescharacteristic
570C2×C4#8819211yescharacteristic
571C2×C4#8820111yescharacteristic
572C8—42no—
573C8—522no—
574C8—522no—
575C8—522no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—522no—
587C22—1042no—
588C22—1042no—
589C22—1041no—
590C22—1041no—
591C22#1171832511yescharacteristic
592C22#1171833111yescharacteristic
593C22#1171833511yescharacteristic
594C22#1171833611yescharacteristic
595C22#1171862011yescharacteristic
596C22#1171862211yescharacteristic
597C22#1171865111yescharacteristic
598C4—82no—
599C4—82no—
600C4—522no—
601C4#1171832611yescharacteristic
602C4#1171833011yescharacteristic
603C4#1171833311yescharacteristic
604C4#1171833611yescharacteristic
605C4#1171860111yescharacteristic
606C4#1171861711yescharacteristic
607C4#1171865211yescharacteristic
608C4#1171865411yescharacteristic
609C2—21no—
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—1042no—
616C2#1311308411yescharacteristic
617C2#1311610711yescharacteristic
618C2#1311611411yescharacteristic
subgroupG/H
centerC22#11718620
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1736C2
socleC22×C13#394
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenter#1736D13
hypocenterC13#11152
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. C2×#11718125C2semidirect
5. C2×#11718122C2semidirect
6. #13114562C2semidirect
7. C13×#1736C2semidirect
17. #11718793C4semidirect
201. #1736D13semidirect
503. C13#11152semidirect

Maximal subgroups

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

subgroupindex
C2×#117186662
C2×#117186272
C2×#117187932
C2×#117181252
C2×#117181222
#131145622
C13×#17362
#1115213