Finite Group Databasebeta

← #15769352

Subgroups — #15769352

Order 3328.

966 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718666C211yesmaximal, characteristic
2C2×#11718794C211yesmaximal, characteristic
3C2×#11718667C211yesmaximal, characteristic
4#13117192C211yesmaximal, characteristic, complemented
5C2×#11718148C211yesmaximal, characteristic, complemented
6#13114557C211yesmaximal, characteristic, complemented
7C2×C13×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C2×C13×#117C2211yescharacteristic
11C2×C13×#117C2211yescharacteristic
12C2×#88180C2211yescharacteristic
13C22×C4⋊Dic13C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15#11718794—22no—
16#11718794—22no—
17C2×#88061C412yescomplemented
18C2×#88056C412yescomplemented
19#11718667—22no—
20#11718667C414yescomplemented
21#11718666—22no—
22#11718666C414yescomplemented
23C4⋊C4×Dic13—22no—
24C2×#88046—22no—
25C22⋊C4×Dic13—22no—
26C4×C4⋊Dic13—22no—
27C2×#88045—22no—
28C13×H(3,ℤ/4)—22no—
29#11718148—22no—
30#11718121—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×#6127C2×C412yes—
45C2×#6127C2×C412yes—
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—
55C22×C8×C13C2×C412yes—
56C13×#117—21no—
57C13×#117—21no—
58C13×#117—21no—
59C13×#117—21no—
60C13×#117—21no—
61C13×#117C2×C412yes—
62C13×#117C2×C412yes—
63C13×#117D412yes—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C22⋊C4—21no—
67C2×C13×C22⋊C4—21no—
68C2×C42×C13—21no—
69C2×C42×C13D412yes—
70C2×C22⋊Dic13D412yes—
71#88180—21no—
72#88180—21no—
73#88180C2×C412yes—
74#88180D412yes—
75C2×C4⋊Dic13—21no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13C2×C412yes—
80C2×C4⋊Dic13D412yes—
81C2×C4⋊Dic13D412yes—
82C2×C4×Dic13—21no—
83C2×C4×Dic13—24no—
84C2×#6099—21no—
85C2×#6099—21no—
86C2×#6099—21no—
87C2×#6099—21no—
88C2×#6099—21no—
89C2×#6099C2×C412yes—
90C22×#1055—21no—
91#88071—24no—
92#88061—24no—
93#88056—24no—
94#88046—28no—
95#88045—28no—
96#10954—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—22no—
124C22×Dic13—22no—
125C22×Dic13—22no—
126C22×Dic13—82no—
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×D52C4212yescomplemented
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×Dic26C4212yescomplemented
161C13×M16—41no—
162C13×M16—41no—
163C13×M16—41no—
164C13×M16—41no—
165C2×C8×C13—22no—
166C2×C8×C13—22no—
167C2×C8×C13—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—41no—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—22no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—41no—
176C42×C13—22no—
177C42×C13—22no—
178C42×C13—41no—
179C42×C13C22⋊C414yes—
180C22⋊Dic13—22no—
181C22⋊Dic13C22⋊C414yes—
182C4⋊Dic13—22no—
183C4⋊Dic13—22no—
184C4⋊Dic13—22no—
185C4⋊Dic13—22no—
186C4⋊Dic13—22no—
187C4⋊Dic13C22⋊C414yes—
188C4×Dic13—22no—
189C4×Dic13—22no—
190C4×Dic13—84no—
191#6099—22no—
192#6099—22no—
193#6099—41no—
194#6099—41no—
195C2×#1055—22no—
196C2×#1055—41no—
197C2×#1055—41no—
198C2×#421—131no—
199C2×#417—131no—
200C2×#410—131no—
201#2274—131no—
202C2×#344—131no—
203#1736—131no—
204C2×H(3,ℤ/4)D1311yescharacteristic, complemented
205C23×C13—41no—
206C23×C13—41no—
207C23×C13C2×C22⋊C411yescharacteristic
208C23×C13C4×D411yescharacteristic
209C23×C13C4×D411yescharacteristic
210C23×C13#12011yescharacteristic
211C23×C13#12111yescharacteristic
212C23×C13#12111yescharacteristic
213C23×C13#12311yescharacteristic
214C22×D13—22no—
215C22×D13—41no—
216C22×D13—41no—
217C22×D13—81no—
218C22×D13—81no—
219C2×C4×C13—24no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—81no—
224C2×C4×C13—81no—
225C2×C4×C13C2×C4211yescharacteristic
226C2×C4×C13C2×C22⋊C411yescharacteristic
227C2×C4×C13C2×C22⋊C411yescharacteristic
228C2×C4×C13#11711yescharacteristic
229C2×C4×C13#11711yescharacteristic
230C2×C4×C13#11711yescharacteristic
231C2×C4×C13C4×D411yescharacteristic
232C2×C4×C13C4×D411yescharacteristic
233C2×C4×C13C4×D411yescharacteristic
234C2×C4×C13C4×D411yescharacteristic
235C2×C4×C13C4×D411yescharacteristic
236C2×C4×C13C4×D411yescharacteristic
237C2×C4×C13C4×D411yescharacteristic
238C2×C4×C13C4×D411yescharacteristic
239C2×C4×C13C4×D411yescharacteristic
240C2×C4×C13C4×D411yescharacteristic
241C2×C4×C13#12111yescharacteristic
242C2×C4×C13#12111yescharacteristic
243C2×C4×C13#12111yescharacteristic
244C2×C4×C13#12111yescharacteristic
245C2×C4×C13#12311yescharacteristic
246C2×C4×C13#12311yescharacteristic
247C2×C4×C13#12411yescharacteristic
248C2×C4×C13#12411yescharacteristic
249C2×C4×C13#12411yescharacteristic
250C2×C4×C13#12611yescharacteristic
251C2×C4×C13#12611yescharacteristic
252C2×C4×C13#12711yescharacteristic
253C22⋊D13—42no—
254C22⋊D13—42no—
255C22⋊D13—42no—
256C22⋊D13—42no—
257C2×Dic13—22no—
258C2×Dic13—24no—
259C2×Dic13—24no—
260C2×Dic13—42no—
261C2×Dic13—44no—
262C2×Dic13—42no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—82no—
266C2×Dic13—82no—
267D52—22no—
268D52—22no—
269D52—41no—
270D52—41no—
271C4×D13—42no—
272C4×D13—42no—
273C4×D13—42no—
274C4×D13—42no—
275Dic26—22no—
276Dic26—22no—
277Dic26—41no—
278Dic26—41no—
279C8×C13—42no—
280#1055—42no—
281C22×#41—131no—
282C22×M16—131no—
283C22×M16C2×D1311yescharacteristic
284C2×#117—131no—
285C2×#117C2×D1311yescharacteristic
286C2×#117C2×D1311yescharacteristic
287C22×C4⋊C4—131no—
288#421—134no—
289#421—262no—
290C2×#104—262no—
291#417—262no—
292#417—262no—
293C2×#103—132no—
294C2×#102—132no—
295#410—134no—
296#410—262no—
297C2×#99—262no—
298C4×C4⋊C4—262no—
299C4×C4⋊C4—262no—
300C4×C22⋊C4—262no—
301#344—262no—
302#340—262no—
303H(3,ℤ/4)—22no—
304C22×C13—21no—
305C22×C13—21no—
306C22×C13—21no—
307C22×C13—21no—
308C22×C13—21no—
309C22×C13—21no—
310C22×C13—41no—
311C22×C13—41no—
312C22×C13—41no—
313C22×C13—41no—
314C22×C13C4×C22⋊C411yescharacteristic
315C22×C13#38611yescharacteristic
316C22×C13#38611yescharacteristic
317C22×C13#38611yescharacteristic
318C22×C13#38811yescharacteristic
319C22×C13#38811yescharacteristic
320C22×C13#39011yescharacteristic
321C2×D13—42no—
322C2×D13—82no—
323C2×D13—81no—
324C2×D13—81no—
325C2×D13—82no—
326C4×C13—44no—
327C4×C13—82no—
328C4×C13C4×C22⋊C411yescharacteristic
329C4×C13C4×C22⋊C411yescharacteristic
330C4×C13#38811yescharacteristic
331C4×C13#38811yescharacteristic
332C4×C13#38811yescharacteristic
333C4×C13#38811yescharacteristic
334C4×C13#39011yescharacteristic
335C4×C13#39011yescharacteristic
336Dic13—44no—
337Dic13—44no—
338Dic13—42no—
339C2×#41—132no—
340C2×#41—132no—
341C2×#41—261no—
342C2×#41—261no—
343C2×#41—261no—
344C2×#41—261no—
345C2×#41—261no—
346C2×#41—261no—
347C2×#41—261no—
348C2×#41—261no—
349C2×#41—261no—
350C2×#41—261no—
351C22×Q8—131no—
352C22×D4—131no—
353C22×D4—261no—
354C23×C4—261no—
355C23×C4—261no—
356C23×C4C22×D1311yescharacteristic
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—132no—
364C2×M16—261no—
365C2×M16—261no—
366C2×M16—261no—
367C2×M16—261no—
368C2×M16—261no—
369C22×C8—261no—
370C22×C8C4×D1312yes—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—132no—
377#117—132no—
378#117—261no—
379#117—261no—
380#117C4×D1312yes—
381#117C4×D1312yes—
382#117C22⋊D1312yes—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—132no—
386C2×C4⋊C4—132no—
387C2×C4⋊C4—132no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—261no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4—261no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—132no—
395C2×C42—21no—
396C2×C42—261no—
397C2×C42—264no—
398C2×C42D5212yes—
399#104—268no—
400#103—264no—
401#102—264no—
402#99—268no—
403#95—264no—
404C2×C13—21no—
405C2×C13—21no—
406C2×C13—21no—
407C2×C13—21no—
408C2×C13—21no—
409C2×C13—21no—
410C2×C13#143711yescharacteristic
411C2×C13#190411yescharacteristic
412C2×C13#190511yescharacteristic
413D13—82no—
414C24—261no—
415C24D4×D1311yescharacteristic
416#41—262no—
417#41—262no—
418#41—262no—
419#41—262no—
420#41—262no—
421#41—262no—
422#41—262no—
423#41—262no—
424#41—521no—
425#41—521no—
426#41—521no—
427#41—521no—
428#41—521no—
429#41—521no—
430#41—521no—
431#41—521no—
432C2×Q8—132no—
433C2×Q8—261no—
434C2×Q8—261no—
435C2×Q8—261no—
436C2×Q8—261no—
437C2×Q8—261no—
438C2×D4—132no—
439C2×D4—262no—
440C2×D4—262no—
441C2×D4—261no—
442C2×D4—261no—
443C2×D4—261no—
444C2×D4—261no—
445C2×D4—261no—
446C2×D4—521no—
447C2×D4—521no—
448C2×D4—521no—
449C2×D4—521no—
450C22×C4—22no—
451C22×C4—41no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—261no—
455C22×C4—262no—
456C22×C4—262no—
457C22×C4—262no—
458C22×C4—262no—
459C22×C4—521no—
460C22×C4—521no—
461C22×C4—521no—
462C22×C4—521no—
463C22×C4—1042no—
464C22×C4C2×C4×D1311yescharacteristic
465C22×C4C2×C4×D1311yescharacteristic
466C22×C4C2×C4×D1311yescharacteristic
467C22×C4C2×D5211yescharacteristic
468C22×C4#612711yescharacteristic
469C22×C4#612711yescharacteristic
470C22×C4D4×D1311yescharacteristic
471C22×C4D4×D1311yescharacteristic
472C22×C4D4×D1311yescharacteristic
473C22×C4#612911yescharacteristic
474C22×C4#612911yescharacteristic
475C22×C4#613111yescharacteristic
476C22×C4#613111yescharacteristic
477C22×C4C2×C22⋊D1311yescharacteristic
478M16—41no—
479M16—41no—
480M16—41no—
481M16—41no—
482M16—262no—
483M16—262no—
484M16—521no—
485M16—521no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—262no—
490C2×C8—521no—
491C2×C8—521no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—134no—
497C4⋊C4—262no—
498C4⋊C4—262no—
499C4⋊C4—262no—
500C4⋊C4—262no—
501C4⋊C4—262no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—41no—
506C22⋊C4—134no—
507C22⋊C4—262no—
508C42—22no—
509C42—22no—
510C42—41no—
511C42—262no—
512C42—262no—
513C42—1044no—
514C42#610314yes—
515C13#1095411yescharacteristic, complemented, Sylow
516C23—41no—
517C23—41no—
518C23—262no—
519C23—521no—
520C23—521no—
521C23—1041no—
522C23—1041no—
523C23C22⋊C4×D1311yescharacteristic
524C23#8813511yescharacteristic
525C23#8813611yescharacteristic
526C23#8813811yescharacteristic
527C23#8814711yescharacteristic
528C23#8814811yescharacteristic
529C23#8819311yescharacteristic
530Q8—262no—
531Q8—262no—
532Q8—521no—
533Q8—521no—
534D4—262no—
535D4—262no—
536D4—522no—
537D4—522no—
538D4—522no—
539D4—522no—
540D4—521no—
541D4—521no—
542C2×C4—24no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4—264no—
549C2×C4—264no—
550C2×C4—262no—
551C2×C4—522no—
552C2×C4—524no—
553C2×C4—522no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—522no—
557C2×C4—522no—
558C2×C4—522no—
559C2×C4—522no—
560C2×C4—1042no—
561C2×C4—1042no—
562C2×C4C42×D1311yescharacteristic
563C2×C4#8812611yescharacteristic
564C2×C4C4×D5211yescharacteristic
565C2×C4C4×D5211yescharacteristic
566C2×C4C22⋊C4×D1311yescharacteristic
567C2×C4#8813511yescharacteristic
568C2×C4#8813511yescharacteristic
569C2×C4#8813511yescharacteristic
570C2×C4#8813811yescharacteristic
571C2×C4#8813911yescharacteristic
572C2×C4#8813911yescharacteristic
573C2×C4#8814011yescharacteristic
574C2×C4#8814611yescharacteristic
575C2×C4#8814611yescharacteristic
576C2×C4#8814711yescharacteristic
577C2×C4#8814711yescharacteristic
578C2×C4#8814711yescharacteristic
579C2×C4#8814811yescharacteristic
580C2×C4#8814911yescharacteristic
581C2×C4#8814911yescharacteristic
582C2×C4#8815211yescharacteristic
583C2×C4#8815211yescharacteristic
584C2×C4C2×#610311yescharacteristic
585C2×C4C4×C22⋊D1311yescharacteristic
586C2×C4C4×C22⋊D1311yescharacteristic
587C2×C4#8819311yescharacteristic
588C2×C4#8819411yescharacteristic
589C2×C4#8820111yescharacteristic
590C8—42no—
591C8—522no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—522no—
603C22—1042no—
604C22—1042no—
605C22—1041no—
606C22—1041no—
607C22#1171832611yescharacteristic
608C22#1171832611yescharacteristic
609C22#1171832711yescharacteristic
610C22#1171833011yescharacteristic
611C22#1171861811yescharacteristic
612C22#1171861911yescharacteristic
613C22#1171865111yescharacteristic
614C4—44no—
615C4—82no—
616C4—524no—
617C4—524no—
618C4—522no—
619C4#1171832711yescharacteristic
620C4#1171833011yescharacteristic
621C4#1171833111yescharacteristic
622C4#1171833111yescharacteristic
623C4C4×#610311yescharacteristic
624C4#1171861811yescharacteristic
625C4#1171864911yescharacteristic
626C4#1171865111yescharacteristic
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—1042no—
634C2#1311307211yescharacteristic
635C2#1311532411yescharacteristic
636C2#1311533111yescharacteristic
subgroupG/H
centerC22#11718326
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC2×C13×H(3,ℤ/4)C2
socleC22×C13#386
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenterC2×H(3,ℤ/4)D13
hypocenterC13#10954
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #13117192C2semidirect
5. C2×#11718148C2semidirect
6. #13114557C2semidirect
7. C2×C13×H(3,ℤ/4)C2semidirect
17. C2×#88061C4semidirect
18. C2×#88056C4semidirect
20. #11718667C4semidirect
22. #11718666C4semidirect
148. C2×D52C42semidirect
160. C2×Dic26C42semidirect
204. C2×H(3,ℤ/4)D13semidirect
515. C13#10954semidirect

Maximal subgroups

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

subgroupindex
C2×#117186662
C2×#117187942
C2×#117186672
#131171922
C2×#117181482
#131145572
C2×C13×H(3,ℤ/4)2
#1095413