Finite Group Databasebeta

← #15864140

Subgroups — #15864140

Order 3328.

1986 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719496C211yesmaximal, characteristic
2C2×#11718663C212yesmaximal, complemented
3C22×C22⋊#1055C211yesmaximal, characteristic, complemented
4#13115158C212yesmaximal, complemented
5#13115153C212yesmaximal, complemented
6#13115148C212yesmaximal, complemented
7#13115143C212yesmaximal, complemented
8#13114552C212yesmaximal, complemented
9C22×C13×#117C211yesmaximal, characteristic, complemented
10C24×C4×C13C2211yescharacteristic
11C22×#6127C2211yescharacteristic
12C2×C13×#117—21no—
13C2×C13×#117—21no—
14C2×C13×#117—28no—
15C2×C13×#117C2212yes—
16C2×C13×#117C2212yes—
17C22×C13×C4⋊C4C2212yes—
18C22×C13×C22⋊C4—21no—
19C22×C42×C13—21no—
20C2×#88207—21no—
21#11719496—24no—
22#11719496C418yescomplemented
23C2×#88184C2211yescharacteristic
24C2×#88184C2211yescharacteristic
25C2×#88183—21no—
26C2×C4×C22⋊D13—21no—
27C2×C4×C22⋊D13—21no—
28C2×#88180C2211yescharacteristic
29C2×#88178C2211yescharacteristic
30C2×#88178C2211yescharacteristic
31C23×#1055C2212yes—
32C2×C22⋊#1055—24no—
33C2×C22⋊#1055C2212yes—
34C2×C22⋊#1055C2212yes—
35#11718663—28no—
36C2×#88050C2214yescomplemented
37C2×#88049C2214yescomplemented
38#11718121C2214yescomplemented
39#11718121C2214yescomplemented
40C25×C13D411yescharacteristic
41C23×C4×C13—24no—
42C23×C4×C13—24no—
43C23×C4×C13—22no—
44C23×C4×C13C2×C414yes—
45C23×C4×C13D414yes—
46C23×C4×C13D411yescharacteristic
47C23×C4×C13D411yescharacteristic
48C23×C4×C13D411yescharacteristic
49C23×C4×C13C2311yescharacteristic
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C22×C22⋊D13—21no—
53C22×C22⋊D13—21no—
54C22×C22⋊D13—21no—
55C2×#6127—22no—
56C2×#6127—24no—
57C2×#6127—24no—
58C2×#6127C2×C414yescomplemented
59C22×D52C2311yescharacteristic
60C22×C4×D13—21no—
61C22×Dic26C2311yescharacteristic
62C13×#117—28no—
63C13×#117—28no—
64C13×#117—24no—
65C13×#117—28no—
66C13×#117D418yescomplemented
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—28no—
69C2×C13×C4⋊C4C2314yes—
70C2×C13×C22⋊C4—28no—
71C2×C13×C22⋊C4—22no—
72C2×C13×C22⋊C4—22no—
73C2×C42×C13—28no—
74C2×C42×C13—22no—
75C2×C42×C13—22no—
76#88207—28no—
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13—21no—
79C2×C22⋊Dic13—21no—
80#88184—22no—
81#88184—22no—
82#88184C2×C414yes—
83#88184C2×C414yescomplemented
84#88183—28no—
85C4×C22⋊D13—28no—
86C4×C22⋊D13—28no—
87C2×#6103—21no—
88C2×#6103—21no—
89#88180—22no—
90#88180C2×C414yescomplemented
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93#88178—22no—
94#88178—22no—
95#88178C2×C414yes—
96#88178C2×C414yescomplemented
97C2×#6101—21no—
98C2×#6101—21no—
99C2×C4×Dic13—21no—
100C22×#1055—24no—
101C22×#1055—24no—
102C22×#1055—24no—
103C22×#1055C2314yes—
104C22⋊#1055—24no—
105C22⋊#1055—24no—
106#88050—28no—
107#88049—28no—
108#20908—131nomaximal, Sylow
109C24×C13—22no—
110C24×C13—22no—
111C24×C13—24no—
112C24×C13—42no—
113C24×C13C22⋊C414yes—
114C24×C13C2×D411yescharacteristic
115C24×C13C2×D411yescharacteristic
116C24×C13C2×D411yescharacteristic
117C23×D13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—216no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—216no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—28no—
131C22×C4×C13—24no—
132C22×C4×C13—44no—
133C22×C4×C13—44no—
134C22×C4×C13C22⋊C414yes—
135C22×C4×C13C22⋊C414yes—
136C22×C4×C13C22⋊C414yes—
137C22×C4×C13C22×C412yes—
138C22×C4×C13C22×C412yes—
139C22×C4×C13C22×C412yes—
140C22×C4×C13C2×D412yes—
141C22×C4×C13C2×D412yes—
142C22×C4×C13C2×D412yes—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D414yes—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13#4114yes—
148C22×C4×C13C2411yescharacteristic
149C2×C22⋊D13—24no—
150C2×C22⋊D13—24no—
151C2×C22⋊D13—24no—
152C2×C22⋊D13—44no—
153C2×C22⋊D13—42no—
154C2×C22⋊D13—42no—
155C2×C22⋊D13—44no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159#6127—216no—
160#6127—48no—
161C2×D52—22no—
162C2×D52—22no—
163C2×D52—21no—
164C2×D52C22×C412yes—
165C2×C4×D13—24no—
166C2×C4×D13—42no—
167C2×C4×D13—42no—
168C2×Dic26—22no—
169C2×Dic26—22no—
170C2×Dic26—21no—
171C2×Dic26C22×C412yes—
172C13×C4⋊C4—28no—
173C13×C4⋊C4—24no—
174C13×C4⋊C4C2×D418yes—
175C13×C22⋊C4—28no—
176C13×C22⋊C4—28no—
177C42×C13—28no—
178C42×C13—28no—
179C22⋊Dic13—24no—
180C22⋊Dic13—24no—
181C22⋊Dic13—24no—
182#6103—24no—
183#6103—24no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13C22×C412yes—
187C4⋊Dic13C22×C412yes—
188#6101—24no—
189#6101—24no—
190C4×Dic13—24no—
191C2×#1055—24no—
192C2×#1055—24no—
193C2×#1055—24no—
194C2×#1055—48no—
195C2×#525—131no—
196C22×#117D1311yescharacteristic, complemented
197C2×#416—132no—
198C22×C22⋊C8—131no—
199#1875—132no—
200#1874—132no—
201#1873—132no—
202#1872—132no—
203#1735—132no—
204C23×C13—21no—
205C23×C13—21no—
206C23×C13—22no—
207C23×C13—22no—
208C23×C13—22no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—22no—
212C23×C13—22no—
213C23×C13—28no—
214C23×C13—28no—
215C23×C13—44no—
216C23×C13—48no—
217C23×C13—48no—
218C23×C13C2×C22⋊C412yes—
219C23×C13C2×C22⋊C412yes—
220C23×C13C2×C22⋊C412yes—
221C23×C13#12012yes—
222C23×C13#12312yes—
223C23×C13#13514yes—
224C23×C13C22×D411yescharacteristic
225C22×D13—22no—
226C22×D13—41no—
227C22×D13—41no—
228C22×D13—42no—
229C22×D13—42no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—28no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—24no—
238C2×C4×C13—24no—
239C2×C4×C13—28no—
240C2×C4×C13—28no—
241C2×C4×C13—28no—
242C2×C4×C13—416no—
243C2×C4×C13—44no—
244C2×C4×C13—44no—
245C2×C4×C13C2×C22⋊C412yes—
246C2×C4×C13C2×C22⋊C412yes—
247C2×C4×C13C2×C22⋊C412yes—
248C2×C4×C13C4×D418yes—
249C2×C4×C13#12012yes—
250C2×C4×C13#12118yes—
251C2×C4×C13#12312yes—
252C2×C4×C13C23×C411yescharacteristic
253C2×C4×C13C22×D412yes—
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13C2×#4112yes—
256C22⋊D13—48no—
257C22⋊D13—48no—
258C22⋊D13—48no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266D52—24no—
267D52—42no—
268C4×D13—48no—
269Dic26—24no—
270Dic26—42no—
271#1055—44no—
272C22×#41—131no—
273C24×C4C2×D1311yescharacteristic
274C23×C8—132no—
275#525—138no—
276#525—264no—
277C2×#123—261no—
278C2×C22⋊Q8—131no—
279C2×C22⋊Q8—131no—
280C2×#121—131no—
281C2×#121—131no—
282C2×#120—261no—
283C2×C4×D4—261no—
284C2×C4×D4—261no—
285C2×#117—21no—
286C2×#117—21no—
287C2×#117—28no—
288C2×#117—131no—
289C2×#117C2×D1312yes—
290C2×#117C2×D1312yes—
291C22×C4⋊C4C2×D1312yes—
292C22×C22⋊C4—21no—
293C22×C42—21no—
294#416—268no—
295C2×#103—134no—
296C2×#102—134no—
297C2×C22⋊C8—132no—
298C2×C22⋊C8—132no—
299C2×C22⋊C8—264no—
300#340—134no—
301#340—134no—
302C22×C13—24no—
303C22×C13—24no—
304C22×C13—22no—
305C22×C13—22no—
306C22×C13—22no—
307C22×C13—24no—
308C22×C13—24no—
309C22×C13—22no—
310C22×C13—22no—
311C22×C13—22no—
312C22×C13—22no—
313C22×C13—416no—
314C22×C13—42no—
315C22×C13—42no—
316C22×C13#38614yes—
317C22×C13#41614yescomplemented
318C22×C13C22×C22⋊C411yescharacteristic
319C22×C13C2×#12011yescharacteristic
320C22×C13C2×#12311yescharacteristic
321C22×C13C2×#13512yes—
322C22×C13#57512yes—
323C2×D13—42no—
324C2×D13—42no—
325C2×D13—42no—
326C2×D13—82no—
327C2×D13—82no—
328C4×C13—22no—
329C4×C13—22no—
330C4×C13—48no—
331C4×C13#38614yes—
332C4×C13C2×C4×D412yes—
333C4×C13C2×#12112yes—
334Dic13—42no—
335Dic13—42no—
336Dic13—42no—
337C25C22⋊D1311yescharacteristic
338C2×#41—134no—
339C2×#41—262no—
340C2×#41—264no—
341C2×#41—264no—
342C22×Q8—131no—
343C22×D4—131no—
344C22×D4—261no—
345C22×D4—261no—
346C22×D4—261no—
347C23×C4—24no—
348C23×C4—24no—
349C23×C4—22no—
350C23×C4—261no—
351C23×C4C4×D1314yes—
352C23×C4D5214yes—
353C23×C4C22⋊D1311yescharacteristic
354C23×C4C22⋊D1311yescharacteristic
355C23×C4C22⋊D1311yescharacteristic
356C23×C4C22×D1311yescharacteristic
357C23×C4C22×D1311yescharacteristic
358C23×C4C22×D1311yescharacteristic
359C22×C8—134no—
360C22×C8—264no—
361C22×C8—264no—
362C22×C8—264no—
363#123—268no—
364C22⋊Q8—134no—
365C22⋊Q8—134no—
366C22⋊Q8—262no—
367C22⋊Q8—262no—
368#121—134no—
369#121—134no—
370#121—262no—
371#121—262no—
372#120—268no—
373C4×D4—268no—
374C4×D4—268no—
375#117—28no—
376#117—28no—
377#117—24no—
378#117—28no—
379#117—134no—
380#117—262no—
381#117C22⋊D1318yescomplemented
382C2×C4⋊C4—22no—
383C2×C4⋊C4—28no—
384C2×C4⋊C4—131no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4C22×D1314yes—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C22⋊C4—261no—
395C2×C22⋊C4—261no—
396C2×C22⋊C4—261no—
397C2×C42—28no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—261no—
401#103—268no—
402#102—268no—
403C22⋊C8—264no—
404C22⋊C8—264no—
405C2×C13—24no—
406C2×C13—24no—
407C2×C13—42no—
408C2×C13C2×#38611yescharacteristic
409C2×C13C2×#41611yescharacteristic
410C2×C13#289611yescharacteristic
411C2×C13#300212yes—
412C2×C13#309112yes—
413D13—82no—
414C24—22no—
415C24—24no—
416C24—22no—
417C24—42no—
418C24—261no—
419C24#610314yes—
420C24C2×C22⋊D1311yescharacteristic
421C24C2×C22⋊D1311yescharacteristic
422C24C2×C22⋊D1311yescharacteristic
423#41—2616no—
424#41—528no—
425C2×Q8—132no—
426C2×Q8—261no—
427C2×Q8—262no—
428C2×Q8—262no—
429C2×D4—132no—
430C2×D4—264no—
431C2×D4—264no—
432C2×D4—264no—
433C2×D4—261no—
434C2×D4—262no—
435C2×D4—262no—
436C2×D4—524no—
437C2×D4—522no—
438C2×D4—524no—
439C2×D4—522no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—216no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—216no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—24no—
454C22×C4—44no—
455C22×C4—44no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—264no—
460C22×C4—522no—
461C22×C4—522no—
462C22×C4#610314yes—
463C22×C4#610314yes—
464C22×C4#610314yes—
465C22×C4C2×C4×D1312yes—
466C22×C4C2×C4×D1312yes—
467C22×C4C2×C4×D1312yes—
468C22×C4C2×D5212yes—
469C22×C4C2×D5212yes—
470C22×C4C2×D5212yes—
471C22×C4#612714yes—
472C22×C4C2×C22⋊D1311yescharacteristic
473C22×C4C2×C22⋊D1311yescharacteristic
474C22×C4C2×C22⋊D1314yes—
475C22×C4C2×C22⋊D1311yescharacteristic
476C22×C4C23×D1311yescharacteristic
477C2×C8—264no—
478C2×C8—264no—
479C2×C8—264no—
480C2×C8—528no—
481C4⋊C4—28no—
482C4⋊C4—24no—
483C4⋊C4—132no—
484C4⋊C4—132no—
485C4⋊C4—264no—
486C4⋊C4—264no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4C2×C22⋊D1318yes—
490C22⋊C4—28no—
491C22⋊C4—28no—
492C22⋊C4—264no—
493C22⋊C4—264no—
494C22⋊C4—264no—
495C22⋊C4—264no—
496C22⋊C4—264no—
497C42—28no—
498C42—28no—
499C42—264no—
500C13#2090811yescharacteristic, complemented, Sylow
501C23—21no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—21no—
506C23—28no—
507C23—21no—
508C23—22no—
509C23—22no—
510C23—21no—
511C23—28no—
512C23—44no—
513C23—48no—
514C23—48no—
515C23—262no—
516C23—521no—
517C23—522no—
518C23—522no—
519C23—521no—
520C23C2×#610312yes—
521C23C2×#610312yes—
522C23C2×#610312yes—
523C23#8818312yes—
524C23#8820414yes—
525C23#8820712yes—
526C23C22×C22⋊D1311yescharacteristic
527Q8—264no—
528Q8—522no—
529D4—264no—
530D4—528no—
531D4—528no—
532D4—528no—
533D4—522no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—28no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—28no—
544C2×C4—28no—
545C2×C4—28no—
546C2×C4—416no—
547C2×C4—44no—
548C2×C4—44no—
549C2×C4—262no—
550C2×C4—262no—
551C2×C4—262no—
552C2×C4—521no—
553C2×C4—522no—
554C2×C4—522no—
555C2×C4—521no—
556C2×C4—528no—
557C2×C4C2×#610312yes—
558C2×C4C2×#610312yes—
559C2×C4C2×#610312yes—
560C2×C4C4×C22⋊D1318yes—
561C2×C4#8818312yes—
562C2×C4#8818418yes—
563C2×C4#8820712yes—
564C2×C4C22×C4×D1311yescharacteristic
565C2×C4C22×D5211yescharacteristic
566C2×C4C2×#612712yes—
567C2×C4C22×C22⋊D1312yes—
568C8—524no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—24no—
574C22—24no—
575C22—24no—
576C22—24no—
577C22—22no—
578C22—22no—
579C22—22no—
580C22—416no—
581C22—42no—
582C22—42no—
583C22—522no—
584C22—522no—
585C22—522no—
586C22—1042no—
587C22—1042no—
588C22#1171866314yescomplemented
589C22#1171887414yes—
590C22C22×#610311yescharacteristic
591C22C2×#8818311yescharacteristic
592C22C2×#8820412yes—
593C22#1171952712yes—
594C22C2×#8820711yescharacteristic
595C4—22no—
596C4—22no—
597C4—48no—
598C4—522no—
599C4—522no—
600C4—522no—
601C4#1171887414yes—
602C4C2×C4×C22⋊D1312yes—
603C4C2×#8818412yes—
604C2—24no—
605C2—24no—
606C2—42no—
607C2—1042no—
608C2C2×#1171887411yescharacteristic
609C2C2×#1171866311yescharacteristic
610C2#1312335311yescharacteristic
611C2#1312405412yes—
612C2#1312474912yes—
subgroupG/H
centerC22×C4C2×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×#117C2
socleC23×C13C22×D4
prime radicalC2×#11719496C2
cosocleC22×C4×C13C24
hypercenterC22×#117D13
hypocenterC13#20908
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. C2×#11718663C2semidirect
3. C22×C22⋊#1055C2semidirect
4. #13115158C2semidirect
5. #13115153C2semidirect
6. #13115148C2semidirect
7. #13115143C2semidirect
8. #13114552C2semidirect
9. C22×C13×#117C2semidirect
22. #11719496C4semidirect
36. C2×#88050C22semidirect
37. C2×#88049C22semidirect
38. #11718121C22semidirect
39. #11718121C22semidirect
58. C2×#6127C2×C4semidirect
66. C13×#117D4semidirect
83. #88184C2×C4semidirect
90. #88180C2×C4semidirect
96. #88178C2×C4semidirect
196. C22×#117D13semidirect
317. C22×C13#416semidirect
381. #117C22⋊D13semidirect
500. C13#20908semidirect
588. C22#11718663semidirect

Maximal subgroups

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

subgroupindex
C2×#117194962
C2×#117186632
C22×C22⋊#10552
#131151582
#131151532
#131151482
#131151432
#131145522
C22×C13×#1172
#2090813