Finite Group Databasebeta

← #15864136

Subgroups — #15864136

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
2C22×#88180C211yesmaximal, characteristic, complemented
3C2×#11718774C212yesmaximal, complemented
4#13115156C212yesmaximal, complemented
5#13115151C212yesmaximal, complemented
6#13115146C212yesmaximal, complemented
7#13115141C212yesmaximal, complemented
8#13114553C212yesmaximal, complemented
9C22×C13×C22⋊C8C211yesmaximal, characteristic, complemented
10C24×C4×C13C2211yescharacteristic
11C22×#6127C2211yescharacteristic
12C23×C8×C13C2212yes—
13C2×#88207—21no—
14C22×C22⋊Dic13—21no—
15#11719496—24no—
16#11719496C418yescomplemented
17C2×#88184C2211yescharacteristic
18C2×#88184C2211yescharacteristic
19C2×#88183—21no—
20C2×C4×C22⋊D13—21no—
21C2×C4×C22⋊D13—21no—
22C2×#88180—21no—
23C2×#88180—21no—
24C2×#88180—28no—
25C2×#88180C2212yes—
26C2×#88180C2211yescharacteristic
27C2×#88180C2212yes—
28C22×C4⋊Dic13C2212yes—
29C2×#88178C2211yescharacteristic
30C2×#88178C2211yescharacteristic
31C22×C4×Dic13—21no—
32C2×C13×C22⋊C8—24no—
33C2×C13×C22⋊C8C2212yes—
34C2×C13×C22⋊C8C2212yes—
35#11718774—28no—
36C2×#88061C2214yescomplemented
37C2×#88056C2214yescomplemented
38#11718143C2214yescomplemented
39#11718143C2214yescomplemented
40C25×C13D411yescharacteristic
41C23×C4×C13—24no—
42C23×C4×C13—24no—
43C23×C4×C13C2×C414yes—
44C23×C4×C13D411yescharacteristic
45C23×C4×C13D411yescharacteristic
46C23×C4×C13D411yescharacteristic
47C23×C4×C13D414yes—
48C23×C4×C13C2311yescharacteristic
49C23×C4×C13C2311yescharacteristic
50C23×C4×C13C2311yescharacteristic
51C22×C22⋊D13—21no—
52C22×C22⋊D13—21no—
53C22×C22⋊D13—21no—
54C23×Dic13—22no—
55C2×#6127—22no—
56C2×#6127—24no—
57C2×#6127—24no—
58C2×#6127C2×C414yescomplemented
59C22×D52C2311yescharacteristic
60C22×C4×D13—21no—
61C22×Dic26C2311yescharacteristic
62C22×C8×C13—24no—
63C22×C8×C13—24no—
64C22×C8×C13—24no—
65C22×C8×C13C2314yes—
66#88207—28no—
67C2×C22⋊Dic13—28no—
68C2×C22⋊Dic13—21no—
69C2×C22⋊Dic13—21no—
70C2×C22⋊Dic13—22no—
71C2×C22⋊Dic13—22no—
72C2×C22⋊Dic13—21no—
73#88184—22no—
74#88184—22no—
75#88184C2×C414yes—
76#88184C2×C414yescomplemented
77#88183—28no—
78C4×C22⋊D13—28no—
79C4×C22⋊D13—28no—
80C2×#6103—21no—
81C2×#6103—21no—
82#88180—28no—
83#88180—28no—
84#88180—24no—
85#88180—22no—
86#88180—28no—
87#88180C2×C414yescomplemented
88#88180D418yescomplemented
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13—28no—
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2314yes—
94#88178—22no—
95#88178—22no—
96#88178C2×C414yes—
97#88178C2×C414yescomplemented
98C2×#6101—21no—
99C2×#6101—21no—
100C2×C4×Dic13—28no—
101C2×C4×Dic13—22no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—21no—
104C13×C22⋊C8—24no—
105C13×C22⋊C8—24no—
106#88061—28no—
107#88056—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×C13C22⋊C414yes—
131C22×C4×C13C22⋊C414yes—
132C22×C4×C13C22⋊C414yes—
133C22×C4×C13C22×C412yes—
134C22×C4×C13C22×C412yes—
135C22×C4×C13C22×C412yes—
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D414yes—
140C22×C4×C13C2×D412yes—
141C22×C4×C13C2×D412yes—
142C22×C4×C13C2×D412yes—
143C22×C4×C13#4114yes—
144C22×C4×C13C2411yescharacteristic
145C2×C22⋊D13—24no—
146C2×C22⋊D13—24no—
147C2×C22⋊D13—24no—
148C2×C22⋊D13—44no—
149C2×C22⋊D13—42no—
150C2×C22⋊D13—42no—
151C2×C22⋊D13—44no—
152C22×Dic13—28no—
153C22×Dic13—24no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—44no—
158C22×Dic13—44no—
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—
172C2×C8×C13—24no—
173C2×C8×C13—24no—
174C2×C8×C13—24no—
175C2×C8×C13—48no—
176C22⋊Dic13—28no—
177C22⋊Dic13—24no—
178C22⋊Dic13—24no—
179C22⋊Dic13—24no—
180C22⋊Dic13—28no—
181#6103—24no—
182#6103—24no—
183C4⋊Dic13—28no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—24no—
187C4⋊Dic13C22×C412yes—
188C4⋊Dic13C22×C412yes—
189C4⋊Dic13C2×D418yes—
190#6101—24no—
191#6101—24no—
192C4×Dic13—28no—
193C4×Dic13—24no—
194C4×Dic13—28no—
195C2×#525—131no—
196C22×#117—131no—
197C2×#416—132no—
198C22×C22⋊C8D1311yescharacteristic, complemented
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×C13C2×C22⋊C412yes—
242C2×C4×C13C2×C22⋊C412yes—
243C2×C4×C13C2×C22⋊C412yes—
244C2×C4×C13C4×D418yes—
245C2×C4×C13#12012yes—
246C2×C4×C13#12118yes—
247C2×C4×C13#12312yes—
248C2×C4×C13C23×C411yescharacteristic
249C2×C4×C13C22×D412yes—
250C2×C4×C13C22×D411yescharacteristic
251C2×C4×C13C2×#4112yes—
252C22⋊D13—48no—
253C22⋊D13—48no—
254C22⋊D13—48no—
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—28no—
259C2×Dic13—416no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—44no—
263C2×Dic13—42no—
264C2×Dic13—44no—
265C2×Dic13—42no—
266D52—24no—
267D52—42no—
268C4×D13—48no—
269Dic26—24no—
270Dic26—42no—
271C8×C13—44no—
272C22×#41—131no—
273C24×C4C2×D1311yescharacteristic
274C23×C8C2×D1312yes—
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—132no—
286C2×#117—131no—
287C2×#117—132no—
288C2×#117—268no—
289C2×#117—261no—
290C2×#117—261no—
291C22×C4⋊C4—132no—
292C22×C22⋊C4—261no—
293C22×C42—261no—
294#416—268no—
295C2×#103—134no—
296C2×#102—134no—
297C2×C22⋊C8—24no—
298C2×C22⋊C8C2×D1312yes—
299C2×C22⋊C8C2×D1312yes—
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#38614yes—
331C4×C13C2×C4×D412yes—
332C4×C13C2×#12112yes—
333Dic13—42no—
334Dic13—42no—
335Dic13—48no—
336Dic13—42no—
337C25D5211yescharacteristic
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—262no—
350C23×C4—261no—
351C23×C4C4×D1314yes—
352C23×C4D5211yescharacteristic
353C23×C4D5211yescharacteristic
354C23×C4D5211yescharacteristic
355C23×C4C22⋊D1314yes—
356C23×C4C22×D1311yescharacteristic
357C23×C4C22×D1311yescharacteristic
358C23×C4C22×D1311yescharacteristic
359C22×C8—24no—
360C22×C8—24no—
361C22×C8—24no—
362C22×C8C22×D1314yes—
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—134no—
376#117—138no—
377#117—268no—
378#117—268no—
379#117—268no—
380#117—264no—
381#117—262no—
382C2×C4⋊C4—134no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—131no—
385C2×C4⋊C4—268no—
386C2×C4⋊C4—262no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C22⋊C4—268no—
390C2×C22⋊C4—262no—
391C2×C22⋊C4—262no—
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C22⋊C4—261no—
395C2×C22⋊C4—261no—
396C2×C22⋊C4—261no—
397C2×C42—268no—
398C2×C42—262no—
399C2×C42—262no—
400C2×C42—261no—
401#103—268no—
402#102—268no—
403C22⋊C8—24no—
404C22⋊C8—24no—
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—22no—
416C24—24no—
417C24—42no—
418C24—261no—
419C24#610314yes—
420C24C2×D5211yescharacteristic
421C24C2×D5211yescharacteristic
422C24C2×D5211yescharacteristic
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—262no—
434C2×D4—262no—
435C2×D4—261no—
436C2×D4—524no—
437C2×D4—522no—
438C2×D4—522no—
439C2×D4—524no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—216no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—216no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—268no—
453C22×C4—264no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—264no—
458C22×C4—524no—
459C22×C4—524no—
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×D5211yescharacteristic
469C22×C4C2×D5211yescharacteristic
470C22×C4C2×D5211yescharacteristic
471C22×C4D4×D1314yes—
472C22×C4#612914yes—
473C22×C4C2×C22⋊D1312yes—
474C22×C4C2×C22⋊D1312yes—
475C22×C4C2×C22⋊D1312yes—
476C22×C4C23×D1311yescharacteristic
477C2×C8—24no—
478C2×C8—24no—
479C2×C8—24no—
480C2×C8—48no—
481C4⋊C4—132no—
482C4⋊C4—132no—
483C4⋊C4—138no—
484C4⋊C4—268no—
485C4⋊C4—264no—
486C4⋊C4—264no—
487C4⋊C4—264no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C22⋊C4—268no—
491C22⋊C4—268no—
492C22⋊C4—264no—
493C22⋊C4—264no—
494C22⋊C4—264no—
495C22⋊C4—264no—
496C22⋊C4—264no—
497C42—268no—
498C42—268no—
499C42—264no—
500C13#2090811yescharacteristic, complemented, Sylow
501C23—22no—
502C23—21no—
503C23—21no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—21no—
508C23—21no—
509C23—22no—
510C23—28no—
511C23—28no—
512C23—44no—
513C23—48no—
514C23—48no—
515C23—262no—
516C23—522no—
517C23—521no—
518C23—521no—
519C23—522no—
520C23#8813612yes—
521C23#8814012yes—
522C23#8815814yes—
523C23C2×#610312yes—
524C23C2×#610312yes—
525C23C2×#610312yes—
526C23C22×D5211yescharacteristic
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—268no—
546C2×C4—262no—
547C2×C4—262no—
548C2×C4—262no—
549C2×C4—5216no—
550C2×C4—524no—
551C2×C4—522no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—524no—
555C2×C4—522no—
556C2×C4—528no—
557C2×C4#8813518yes—
558C2×C4#8813612yes—
559C2×C4#8814012yes—
560C2×C4C2×#610312yes—
561C2×C4C2×#610312yes—
562C2×C4C2×#610312yes—
563C2×C4#8819318yes—
564C2×C4C22×C4×D1311yescharacteristic
565C2×C4C2×D4×D1312yes—
566C2×C4C2×#612912yes—
567C2×C4C22×C22⋊D1311yescharacteristic
568C8—44no—
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#1171861914yes—
589C22#1171877414yescomplemented
590C22C2×#8813611yescharacteristic
591C22C2×#8814011yescharacteristic
592C22C2×#8815812yes—
593C22#1171945312yes—
594C22C22×#610311yescharacteristic
595C4—22no—
596C4—22no—
597C4—522no—
598C4—522no—
599C4—522no—
600C4—528no—
601C4#1171861914yes—
602C4C2×#8813512yes—
603C4C2×#8819312yes—
604C2—24no—
605C2—24no—
606C2—42no—
607C2—1042no—
608C2C2×#1171861911yescharacteristic
609C2C2×#1171877411yescharacteristic
610C2#1312335611yescharacteristic
611C2#1312405812yes—
612C2#1312475112yes—
subgroupG/H
centerC22×C4C2×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×C22⋊C8C2
socleC23×C13C22×D4
prime radicalC2×#11719496C2
cosocleC22×C4×C13C24
hypercenterC22×C22⋊C8D13
hypocenterC13#20908
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×#88180C2semidirect
3. C2×#11718774C2semidirect
4. #13115156C2semidirect
5. #13115151C2semidirect
6. #13115146C2semidirect
7. #13115141C2semidirect
8. #13114553C2semidirect
9. C22×C13×C22⋊C8C2semidirect
16. #11719496C4semidirect
36. C2×#88061C22semidirect
37. C2×#88056C22semidirect
38. #11718143C22semidirect
39. #11718143C22semidirect
58. C2×#6127C2×C4semidirect
76. #88184C2×C4semidirect
87. #88180C2×C4semidirect
88. #88180D4semidirect
97. #88178C2×C4semidirect
198. C22×C22⋊C8D13semidirect
317. C22×C13#416semidirect
500. C13#20908semidirect
589. C22#11718774semidirect

Maximal subgroups

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

subgroupindex
C2×#117194962
C22×#881802
C2×#117187742
#131151562
#131151512
#131151462
#131151412
#131145532
C22×C13×C22⋊C82
#2090813