Finite Group Databasebeta

← #15769286

Subgroups — #15769286

Order 3328.

930 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718800C211yesmaximal, characteristic
2C2×#11718774C211yesmaximal, characteristic
3C2×#11718667C211yesmaximal, characteristic
4#13114568C211yesmaximal, characteristic, complemented
5#13114553C211yesmaximal, characteristic, complemented
6#13114547C211yesmaximal, characteristic, complemented
7C2×C13×#405C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C23×C8×C13C2211yescharacteristic
11C2×C13×#117C2211yescharacteristic
12C2×#88180C2211yescharacteristic
13C2×#88180C2211yescharacteristic
14C2×#88180C2211yescharacteristic
15C13×#405—22no—
16C13×#405—22no—
17C2×C13×#97—21no—
18C2×C4×C8×C13—21no—
19#11718800—22no—
20#11718800C414yescomplemented
21C2×#88065—22no—
22#11718774—22no—
23#11718774—21no—
24#11718774—21no—
25C2×#88061C412yescomplemented
26C2×#88056C412yescomplemented
27#11718667—22no—
28#11718667C414yescomplemented
29C2×#88046—22no—
30#11718147—22no—
31#11718143—22no—
32#11718119—22no—
33C23×C4×C13C2311yescharacteristic
34C22×C22⋊D13—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×#6127—21no—
45C2×#6127C2×C412yes—
46C2×#6127C2×C412yes—
47C22×D52C2×C411yescharacteristic
48C22×C4×D13—21no—
49C22×Dic26C2×C411yescharacteristic
50C2×C13×M16—21no—
51C2×C13×M16—21no—
52C2×C13×M16—21no—
53C2×C13×M16C2×C412yes—
54C2×C13×M16D412yes—
55C2×C13×M16D412yes—
56C22×C8×C13—21no—
57C22×C8×C13—21no—
58C22×C8×C13—21no—
59C22×C8×C13—21no—
60C22×C8×C13—21no—
61C22×C8×C13C2×C412yes—
62C22×C8×C13D412yes—
63C22×C8×C13D411yescharacteristic
64C22×C8×C13D411yescharacteristic
65C13×#117—21no—
66C13×#117—21no—
67C13×#117C2×C412yes—
68C13×#117D412yes—
69C2×C13×C4⋊C4—21no—
70C2×C13×C22⋊C4D412yes—
71C2×C42×C13—21no—
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75#88180—21no—
76#88180—21no—
77#88180—21no—
78#88180—21no—
79#88180—21no—
80#88180—21no—
81#88180—21no—
82#88180—21no—
83#88180—21no—
84#88180—21no—
85#88180C2×C412yes—
86#88180C2×C412yes—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13C2×C412yes—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C13×#97—24no—
94C4×C8×C13—24no—
95#88065—28no—
96#88061—22no—
97#88061—22no—
98#88056—22no—
99#88056—22no—
100#88046—28no—
101#10944—131nomaximal, Sylow
102C24×C13C2×D411yescharacteristic
103C23×D13—21no—
104C22×C4×C13—22no—
105C22×C4×C13C22×C411yescharacteristic
106C22×C4×C13C22×C411yescharacteristic
107C22×C4×C13C22×C411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13#4111yescharacteristic
114C22×C4×C13#4111yescharacteristic
115C22×C4×C13#4111yescharacteristic
116C22×C4×C13#4111yescharacteristic
117C22×C4×C13#4111yescharacteristic
118C22×C4×C13#4111yescharacteristic
119C2×C22⋊D13—22no—
120C2×C22⋊D13—22no—
121C2×C22⋊D13—41no—
122C2×C22⋊D13—41no—
123C2×C22⋊D13—41no—
124C2×C22⋊D13—41no—
125C22×Dic13—21no—
126C22×Dic13—22no—
127C22×Dic13—41no—
128C22×Dic13—41no—
129#6127—22no—
130#6127—22no—
131#6127—22no—
132#6127—22no—
133#6127—22no—
134#6127—22no—
135#6127—22no—
136#6127—22no—
137#6127—41no—
138#6127—41no—
139#6127—41no—
140#6127—41no—
141#6127—41no—
142#6127—41no—
143#6127—41no—
144#6127—41no—
145C2×D52—21no—
146C2×D52—21no—
147C2×D52—21no—
148C2×D52—21no—
149C2×D52—21no—
150C2×D52C4212yes—
151C2×C4×D13—22no—
152C2×C4×D13—22no—
153C2×C4×D13—41no—
154C2×C4×D13—41no—
155C2×C4×D13—41no—
156C2×C4×D13—41no—
157C2×Dic26—21no—
158C2×Dic26—21no—
159C2×Dic26—21no—
160C2×Dic26—21no—
161C2×Dic26—21no—
162C2×Dic26C4212yes—
163C13×M16—22no—
164C13×M16—22no—
165C13×M16—22no—
166C13×M16C22⋊C414yes—
167C2×C8×C13—22no—
168C2×C8×C13—22no—
169C2×C8×C13—22no—
170C2×C8×C13—21no—
171C2×C8×C13—22no—
172C2×C8×C13—21no—
173C2×C8×C13—22no—
174C2×C8×C13—22no—
175C2×C8×C13—22no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13C22⋊C412yes—
179C2×C8×C13C22⋊C412yes—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—22no—
182C13×C22⋊C4—22no—
183C13×C22⋊C4C22⋊C414yes—
184C42×C13—22no—
185C42×C13—22no—
186C22⋊Dic13—22no—
187C22⋊Dic13—22no—
188C22⋊Dic13—41no—
189C22⋊Dic13—41no—
190C22⋊Dic13—41no—
191C22⋊Dic13—41no—
192C4⋊Dic13—22no—
193C4⋊Dic13—22no—
194C4⋊Dic13—22no—
195C4⋊Dic13—22no—
196C4⋊Dic13—41no—
197C4⋊Dic13—41no—
198C4×Dic13—22no—
199C4×Dic13—22no—
200C4×Dic13—41no—
201C4×Dic13—41no—
202C4×Dic13—41no—
203C4×Dic13—41no—
204C2×#421—131no—
205C2×#416—131no—
206C2×#410—131no—
207C2×#405D1311yescharacteristic, complemented
208#1740—131no—
209#1735—131no—
210#1733—131no—
211C23×C13—42no—
212C23×C13C2×C22⋊C411yescharacteristic
213C23×C13C4×D411yescharacteristic
214C23×C13C4×D411yescharacteristic
215C23×C13#12111yescharacteristic
216C23×C13#12111yescharacteristic
217C23×C13#12411yescharacteristic
218C23×C13#12711yescharacteristic
219C22×D13—22no—
220C22×D13—41no—
221C22×D13—41no—
222C22×D13—82no—
223C2×C4×C13—24no—
224C2×C4×C13—44no—
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#12011yescharacteristic
242C2×C4×C13#12111yescharacteristic
243C2×C4×C13#12111yescharacteristic
244C2×C4×C13#12111yescharacteristic
245C2×C4×C13#12111yescharacteristic
246C2×C4×C13#12311yescharacteristic
247C2×C4×C13#12311yescharacteristic
248C2×C4×C13#12311yescharacteristic
249C2×C4×C13#12411yescharacteristic
250C2×C4×C13#12411yescharacteristic
251C2×C4×C13#12611yescharacteristic
252C2×C4×C13#12611yescharacteristic
253C22⋊D13—42no—
254C22⋊D13—42no—
255C22⋊D13—42no—
256C22⋊D13—42no—
257C2×Dic13—22no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—42no—
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13—82no—
264C2×Dic13—82no—
265C2×Dic13—82no—
266D52—22no—
267D52—22no—
268D52—41no—
269D52—41no—
270C4×D13—42no—
271C4×D13—42no—
272C4×D13—42no—
273C4×D13—42no—
274Dic26—22no—
275Dic26—22no—
276Dic26—41no—
277Dic26—41no—
278C8×C13—22no—
279C8×C13—22no—
280C8×C13—24no—
281C22×#41—131no—
282C22×M16C2×D1311yescharacteristic
283C23×C8C2×D1311yescharacteristic
284C2×#117—131no—
285C2×#117—131no—
286C2×#117—131no—
287C2×#117C2×D1311yescharacteristic
288#421—134no—
289#421—262no—
290C2×#104—262no—
291#416—262no—
292#416—261no—
293#416—261no—
294C2×#103—132no—
295C2×#102—132no—
296#410—134no—
297#410—262no—
298C2×#99—262no—
299#405—22no—
300#405—22no—
301C2×#97—21no—
302C2×C4×C8—21no—
303#342—262no—
304#340—262no—
305#339—262no—
306C22×C13—22no—
307C22×C13—22no—
308C22×C13—22no—
309C22×C13—41no—
310C22×C13—41no—
311C22×C13—41no—
312C22×C13—41no—
313C22×C13C4×C22⋊C411yescharacteristic
314C22×C13#38611yescharacteristic
315C22×C13#38811yescharacteristic
316C22×C13#38811yescharacteristic
317C22×C13#39011yescharacteristic
318C22×C13#39011yescharacteristic
319C22×C13#39011yescharacteristic
320C2×D13—42no—
321C2×D13—82no—
322C2×D13—82no—
323C2×D13—82no—
324C4×C13—44no—
325C4×C13C4×C22⋊C411yescharacteristic
326C4×C13C4×C22⋊C411yescharacteristic
327C4×C13#38611yescharacteristic
328C4×C13#38611yescharacteristic
329C4×C13#38811yescharacteristic
330C4×C13#38811yescharacteristic
331C4×C13#38811yescharacteristic
332C4×C13#38811yescharacteristic
333Dic13—42no—
334Dic13—82no—
335Dic13—82no—
336Dic13—82no—
337C2×#41—132no—
338C2×#41—132no—
339C2×#41—261no—
340C2×#41—261no—
341C2×#41—261no—
342C2×#41—261no—
343C2×#41—261no—
344C2×#41—261no—
345C2×#41—261no—
346C2×#41—261no—
347C2×#41—261no—
348C2×#41—261no—
349C22×Q8—131no—
350C22×D4—131no—
351C22×D4—261no—
352C23×C4—261no—
353C23×C4C22×D1311yescharacteristic
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16C4×D1312yes—
358C2×M16D5212yes—
359C2×M16C22⋊D1312yes—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8C4×D1312yes—
366C22×C8D5212yes—
367C22×C8C22⋊D1311yescharacteristic
368C22×C8C22⋊D1311yescharacteristic
369#117—21no—
370#117—21no—
371#117—132no—
372#117—132no—
373#117—261no—
374#117—261no—
375#117—261no—
376#117—261no—
377#117—261no—
378#117—261no—
379#117—261no—
380#117—261no—
381#117—261no—
382#117—261no—
383#117C4×D1312yes—
384#117C22⋊D1312yes—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—132no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C22⋊C4—261no—
390C2×C22⋊C4—261no—
391C2×C22⋊C4—261no—
392C2×C22⋊C4D5212yes—
393C2×C42—21no—
394C2×C42—261no—
395C2×C42—261no—
396C2×C42—261no—
397#104—268no—
398#103—262no—
399#103—262no—
400#102—262no—
401#102—262no—
402#99—268no—
403#97—24no—
404C4×C8—24no—
405C2×C13—21no—
406C2×C13—21no—
407C2×C13—21no—
408C2×C13—21no—
409C2×C13—21no—
410C2×C13—21no—
411C2×C13#143711yescharacteristic
412C2×C13#197612yes—
413D13—82no—
414C24—261no—
415C24C2×D5211yescharacteristic
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—261no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4—521no—
456C22×C4—521no—
457C22×C4—521no—
458C22×C4—521no—
459C22×C4—521no—
460C22×C4—521no—
461C22×C4C2×C4×D1311yescharacteristic
462C22×C4C2×C4×D1311yescharacteristic
463C22×C4C2×C4×D1311yescharacteristic
464C22×C4C2×D5211yescharacteristic
465C22×C4C2×D5211yescharacteristic
466C22×C4#612711yescharacteristic
467C22×C4#612711yescharacteristic
468C22×C4#612711yescharacteristic
469C22×C4#612711yescharacteristic
470C22×C4#612711yescharacteristic
471C22×C4#612711yescharacteristic
472C22×C4C2×C22⋊D1311yescharacteristic
473C22×C4C2×C22⋊D1311yescharacteristic
474C22×C4C2×C22⋊D1311yescharacteristic
475M16—22no—
476M16—22no—
477M16—22no—
478M16#610314yes—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—21no—
488C2×C8—22no—
489C2×C8—21no—
490C2×C8#610312yes—
491C2×C8#610312yes—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—262no—
495C4⋊C4—262no—
496C4⋊C4—262no—
497C4⋊C4—262no—
498C4⋊C4—521no—
499C4⋊C4—521no—
500C22⋊C4—22no—
501C22⋊C4—262no—
502C22⋊C4—262no—
503C22⋊C4—521no—
504C22⋊C4—521no—
505C22⋊C4—521no—
506C22⋊C4—521no—
507C22⋊C4#610314yes—
508C42—22no—
509C42—22no—
510C42—262no—
511C42—262no—
512C42—521no—
513C42—521no—
514C42—521no—
515C42—521no—
516C13#1094411yescharacteristic, complemented, Sylow
517C23—42no—
518C23—262no—
519C23—521no—
520C23—521no—
521C23—1042no—
522C23C4×D5211yescharacteristic
523C23C4×D5211yescharacteristic
524C23#8812811yescharacteristic
525C23#8812911yescharacteristic
526C23C2×#610311yescharacteristic
527C23#8818411yescharacteristic
528C23#8818411yescharacteristic
529Q8—262no—
530Q8—262no—
531Q8—521no—
532Q8—521no—
533D4—262no—
534D4—262no—
535D4—522no—
536D4—522no—
537D4—522no—
538D4—522no—
539D4—521no—
540D4—521no—
541C2×C4—24no—
542C2×C4—44no—
543C2×C4—262no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—522no—
547C2×C4—522no—
548C2×C4—522no—
549C2×C4—522no—
550C2×C4—522no—
551C2×C4—522no—
552C2×C4—522no—
553C2×C4—1042no—
554C2×C4—1042no—
555C2×C4—1042no—
556C2×C4C42×D1311yescharacteristic
557C2×C4#8812611yescharacteristic
558C2×C4#8812611yescharacteristic
559C2×C4#8812611yescharacteristic
560C2×C4C4×D5211yescharacteristic
561C2×C4C4×D5211yescharacteristic
562C2×C4C4×D5211yescharacteristic
563C2×C4C4×D5211yescharacteristic
564C2×C4#8812911yescharacteristic
565C2×C4#8812911yescharacteristic
566C2×C4#8813011yescharacteristic
567C2×C4#8813011yescharacteristic
568C2×C4C2×#610311yescharacteristic
569C2×C4C2×#610311yescharacteristic
570C2×C4C4×C22⋊D1311yescharacteristic
571C2×C4C4×C22⋊D1311yescharacteristic
572C2×C4C4×C22⋊D1311yescharacteristic
573C2×C4C4×C22⋊D1311yescharacteristic
574C2×C4C4×C22⋊D1311yescharacteristic
575C2×C4C4×C22⋊D1311yescharacteristic
576C2×C4#8818311yescharacteristic
577C2×C4#8818311yescharacteristic
578C2×C4#8818311yescharacteristic
579C2×C4#8818411yescharacteristic
580C2×C4#8818411yescharacteristic
581C2×C4#8818411yescharacteristic
582C2×C4#8818411yescharacteristic
583C2×C4#8820711yescharacteristic
584C8—22no—
585C8—22no—
586C8—24no—
587C22—22no—
588C22—22no—
589C22—22no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—522no—
595C22—1042no—
596C22—1042no—
597C22—1042no—
598C22C4×#610311yescharacteristic
599C22#1171860011yescharacteristic
600C22#1171860011yescharacteristic
601C22#1171860011yescharacteristic
602C22#1171860111yescharacteristic
603C22#1171860111yescharacteristic
604C22#1171887411yescharacteristic
605C4—44no—
606C4—522no—
607C4—1042no—
608C4—1042no—
609C4—1042no—
610C4C4×#610311yescharacteristic
611C4C4×#610311yescharacteristic
612C4#1171860111yescharacteristic
613C4#1171860111yescharacteristic
614C4#1171860111yescharacteristic
615C4#1171860111yescharacteristic
616C4#1171887411yescharacteristic
617C4#1171887411yescharacteristic
618C2—21no—
619C2—21no—
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—1042no—
625C2#1311307411yescharacteristic
626C2#1311573412yes—
subgroupG/H
centerC2×C4#88184
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC2×C13×#405C2
socleC22×C13#390
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenterC2×#405D13
hypocenterC13#10944
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
4. #13114568C2semidirect
5. #13114553C2semidirect
6. #13114547C2semidirect
7. C2×C13×#405C2semidirect
20. #11718800C4semidirect
25. C2×#88061C4semidirect
26. C2×#88056C4semidirect
28. #11718667C4semidirect
207. C2×#405D13semidirect
516. C13#10944semidirect

Maximal subgroups

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

subgroupindex
C2×#117188002
C2×#117187742
C2×#117186672
#131145682
#131145532
#131145472
C2×C13×#4052
#1094413