Finite Group Databasebeta

← #15863796

Subgroups — #15863796

Order 3328.

1422 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719532C211yesmaximal, characteristic
2#13123425C211yesmaximal, characteristic, complemented
3C2×#11718897C211yesmaximal, characteristic
4#13117456C211yesmaximal, characteristic, complemented
5#13115067C214yesmaximal, complemented
6#13115060C214yesmaximal, complemented
7C2×#11718146C211yesmaximal, characteristic, complemented
8#13114547C211yesmaximal, characteristic, complemented
9C13×#2896C211yesmaximal, characteristic
10C22×C13×#41C2211yescharacteristic
11C22×C13×M16C2211yescharacteristic
12C2×C13×#117C2211yescharacteristic
13#11719532—22no—
14#11719532—22no—
15#11719532—22no—
16#11719532C2214yes—
17C2×Q8×Dic13—21no—
18C2×D4×Dic13—21no—
19C2×D4×Dic13—22no—
20C2×#88180—21no—
21C2×#88180C2211yescharacteristic
22C2×#88180C2211yescharacteristic
23C22×C4⋊Dic13—21no—
24C22×C4⋊Dic13C2211yescharacteristic
25C22×#6099C2211yescharacteristic
26C13×#419—21no—
27C13×#418—21no—
28C13×#417C2212yes—
29C13×#417C2212yes—
30C13×#416—22no—
31#11718897C418yescomplemented
32C2×#88077C2214yes—
33#11718659—22no—
34#11718656—21no—
35#11718656—21no—
36#11718638C2212yescomplemented
37#11718637C2212yescomplemented
38#11718625C2212yescomplemented
39#11718625C2212yescomplemented
40#11718607—22no—
41#11718589—22no—
42#11718147C2214yescomplemented
43#11718146C2214yescomplemented
44C2×C13×#41—21no—
45C2×C13×#41—21no—
46C2×C13×#41—22no—
47C2×C13×#41—22no—
48C2×C13×#41C2×C414yes—
49C2×C13×#41D412yes—
50C2×C13×#41Q814yes—
51C2×C13×#41C2312yes—
52C22×Q8×C13D411yescharacteristic
53C22×D4×C13—21no—
54C22×D4×C13D411yescharacteristic
55C23×C4×C13—21no—
56C23×C4×C13C2311yescharacteristic
57C23×Dic13—22no—
58C23×Dic13D412yes—
59C2×C13×M16—21no—
60C2×C13×M16—22no—
61C2×C13×M16—22no—
62C2×C13×M16C2312yes—
63C22×C8×C13—21no—
64C13×#117—21no—
65C13×#117—21no—
66C13×#117—21no—
67C13×#117—21no—
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C22⋊C4—21no—
71C2×C42×C13—21no—
72C2×C22⋊Dic13—22no—
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75Q8×Dic13—24no—
76Q8×Dic13—24no—
77D4×Dic13—28no—
78D4×Dic13—24no—
79D4×Dic13—24no—
80D4×Dic13—28no—
81#88180—24no—
82#88180—21no—
83#88180—21no—
84#88180—22no—
85#88180—24no—
86#88180C2×C414yescomplemented
87#88180D412yes—
88#88180C2312yes—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13—24no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13—21no—
96C2×C4⋊Dic13—24no—
97C2×C4⋊Dic13D412yes—
98C2×C4⋊Dic13D411yescharacteristic
99C2×C4⋊Dic13D411yescharacteristic
100C2×C4⋊Dic13C2312yes—
101C2×#6101—24no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—21no—
104C2×C4×Dic13C2312yes—
105C2×#6099—21no—
106C2×#6099—22no—
107C2×#6099C2×C414yescomplemented
108C2×#6099C2312yes—
109C22×#1055—21no—
110C13×#103—22no—
111C13×#103—22no—
112C13×#102—22no—
113C13×#102—22no—
114#88077C2×C4116yescomplemented
115#88071—24no—
116#88048—22no—
117#88048—22no—
118#88047—22no—
119#88047—22no—
120#20864—131nomaximal, Sylow
121C24×C13—21no—
122C24×C13C2×D411yescharacteristic
123C13×#41—24no—
124C13×#41—24no—
125C13×#41—24no—
126C13×#41—24no—
127C13×#41—24no—
128C13×#41—22no—
129C13×#41—22no—
130C13×#41C4⋊C418yescomplemented
131C13×#41C22×C414yes—
132C13×#41C2×Q814yes—
133C2×Q8×C13—21no—
134C2×Q8×C13—22no—
135C2×Q8×C13C4⋊C414yescomplemented
136C2×Q8×C13C2×D412yes—
137C2×D4×C13—24no—
138C2×D4×C13—22no—
139C2×D4×C13—24no—
140C2×D4×C13—22no—
141C2×D4×C13—21no—
142C2×D4×C13—22no—
143C2×D4×C13C4⋊C414yescomplemented
144C2×D4×C13C2×D412yes—
145C22×C4×C13—21no—
146C22×C4×C13—24no—
147C22×C4×C13—22no—
148C22×C4×C13—24no—
149C22×C4×C13—22no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13C22×C412yes—
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×Q812yes—
159C22×C4×C13#4112yes—
160C22×C4×C13#4112yes—
161C22×C4×C13C2411yescharacteristic
162C22×Dic13—21no—
163C22×Dic13—22no—
164C22×Dic13—21no—
165C22×Dic13—22no—
166C22×Dic13—28no—
167C22×Dic13—22no—
168C22×Dic13—82no—
169C22×Dic13—84no—
170C22×Dic13C2×D414yes—
171C13×M16—22no—
172C13×M16—22no—
173C13×M16—42no—
174C2×C8×C13—22no—
175C2×C8×C13—42no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C22⋊C4—41no—
181C13×C22⋊C4—41no—
182C42×C13—41no—
183C42×C13—41no—
184C22⋊Dic13—28no—
185C22⋊Dic13—24no—
186C22⋊Dic13—22no—
187C22⋊Dic13—22no—
188C4⋊Dic13—28no—
189C4⋊Dic13—24no—
190C4⋊Dic13—22no—
191C4⋊Dic13—21no—
192C4⋊Dic13—22no—
193C4⋊Dic13—21no—
194C4⋊Dic13—22no—
195C4⋊Dic13—22no—
196C4⋊Dic13C2×D412yes—
197C4⋊Dic13C2×D412yes—
198#6101—84no—
199C4×Dic13—28no—
200C4×Dic13—22no—
201C4×Dic13—22no—
202C4×Dic13—22no—
203C4×Dic13C22×C414yescomplemented
204#6099—24no—
205#6099—22no—
206#6099C22×C414yescomplemented
207C2×#1055—24no—
208C2×#1055—22no—
209C2×#520—131no—
210#2911—131no—
211C2×#421—131no—
212#2896D1311yescharacteristic
213#2317—131no—
214#1860—134no—
215#1859—134no—
216C2×#343—131no—
217#1733—131no—
218C23×C13—22no—
219C23×C13—24no—
220C23×C13—41no—
221C23×C13—41no—
222C23×C13—42no—
223C23×C13—42no—
224C23×C13C4×D412yes—
225C23×C13#12011yescharacteristic
226C23×C13#12011yescharacteristic
227C23×C13C22⋊Q812yes—
228C23×C13C22×D411yescharacteristic
229Q8×C13—22no—
230Q8×C13—24no—
231Q8×C13C2×C4⋊C414yes—
232D4×C13—24no—
233D4×C13—24no—
234D4×C13—28no—
235D4×C13—22no—
236D4×C13—24no—
237D4×C13C2×C4⋊C414yes—
238C2×C4×C13—22no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—28no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13C2×C4⋊C412yes—
248C2×C4×C13C2×C4⋊C412yes—
249C2×C4×C13C4×D412yes—
250C2×C4×C13C4×D412yes—
251C2×C4×C13C4×D412yes—
252C2×C4×C13#12011yescharacteristic
253C2×C4×C13#12011yescharacteristic
254C2×C4×C13C22⋊Q812yes—
255C2×C4×C13C22⋊Q812yes—
256C2×C4×C13C22⋊Q812yes—
257C2×C4×C13#12312yes—
258C2×C4×C13#12312yes—
259C2×C4×C13C23×C411yescharacteristic
260C2×C4×C13C22×D411yescharacteristic
261C2×C4×C13C22×D411yescharacteristic
262C2×C4×C13C22×Q811yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×Dic13—24no—
266C2×Dic13—22no—
267C2×Dic13—24no—
268C2×Dic13—22no—
269C2×Dic13—42no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13—44no—
273C2×Dic13—42no—
274C2×Dic13—44no—
275C2×Dic13—82no—
276C2×Dic13—88no—
277C8×C13—42no—
278#1055—24no—
279C22×#41C2×D1311yescharacteristic
280C22×M16—131no—
281C22×M16C2×D1311yescharacteristic
282#520—134no—
283#520—262no—
284#520—262no—
285#520—262no—
286C2×C4×Q8—261no—
287C2×C4×D4—262no—
288C2×C4×D4—261no—
289C2×#117—131no—
290C2×#117—131no—
291C2×#117—261no—
292C2×#117C2×D1311yescharacteristic
293C22×C4⋊C4—131no—
294C22×C4⋊C4—261no—
295#428—132no—
296#428—132no—
297#428—261no—
298#428—261no—
299#427—262no—
300#421—138no—
301C2×#104—134no—
302#419—21no—
303#418—21no—
304#417C2×D1312yes—
305#417C2×D1312yes—
306#416—22no—
307#389—262no—
308#385—262no—
309#384—132no—
310#382—132no—
311#343—134no—
312#339—134no—
313C22×C13—21no—
314C22×C13—21no—
315C22×C13—21no—
316C22×C13—21no—
317C22×C13—21no—
318C22×C13—21no—
319C22×C13—24no—
320C22×C13—42no—
321C22×C13—42no—
322C22×C13—48no—
323C22×C13—42no—
324C22×C13—42no—
325C22×C13#38512yes—
326C22×C13#38512yes—
327C22×C13C2×C4×D411yescharacteristic
328C22×C13C2×#12011yescharacteristic
329C22×C13C2×C22⋊Q811yescharacteristic
330C4×C13—24no—
331C4×C13—81no—
332C4×C13—81no—
333C4×C13#38512yes—
334C4×C13#38512yes—
335C4×C13C22×C4⋊C411yescharacteristic
336C4×C13C2×C4×D411yescharacteristic
337C4×C13C2×C22⋊Q811yescharacteristic
338C4×C13C2×#12311yescharacteristic
339Dic13—44no—
340Dic13—44no—
341Dic13—42no—
342Dic13—42no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41Dic2614yes—
348C2×#41C4×D1314yes—
349C2×#41C22⋊D1312yes—
350C2×#41C22×D1312yes—
351C22×Q8C22⋊D1311yescharacteristic
352C22×D4—21no—
353C22×D4C22⋊D1311yescharacteristic
354C23×C4—21no—
355C23×C4—132no—
356C23×C4—262no—
357C23×C4C22×D1311yescharacteristic
358C2×M16—21no—
359C2×M16—22no—
360C2×M16—22no—
361C2×M16—134no—
362C2×M16—132no—
363C2×M16—261no—
364C2×M16—262no—
365C2×M16C22×D1312yes—
366C22×C8—21no—
367C22×C8—261no—
368C4×Q8—264no—
369C4×Q8—264no—
370C4×D4—268no—
371C4×D4—268no—
372C4×D4—264no—
373C4×D4—264no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—134no—
379#117—132no—
380#117—132no—
381#117—264no—
382#117—264no—
383#117—261no—
384#117—262no—
385#117—261no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—132no—
389C2×C4⋊C4—132no—
390C2×C4⋊C4—264no—
391C2×C4⋊C4—262no—
392C2×C4⋊C4—264no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4—261no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—264no—
399C2×C4⋊C4C22×D1311yescharacteristic
400C2×C4⋊C4C22×D1311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—262no—
403C2×C22⋊C4—261no—
404C2×C22⋊C4—261no—
405C2×C42—21no—
406C2×C42—132no—
407C2×C42—262no—
408C2×C42—261no—
409#107—262no—
410#107—262no—
411#106—262no—
412#106—262no—
413#104—1316no—
414#103—22no—
415#103—22no—
416#102—22no—
417#102—22no—
418#95—264no—
419C2×C13—21no—
420C2×C13—22no—
421C2×C13—21no—
422C2×C13—22no—
423C2×C13—44no—
424C2×C13C2×#38511yescharacteristic
425C2×C13#301911yescharacteristic
426C2×C13#302011yescharacteristic
427C24—21no—
428C24D4×D1311yescharacteristic
429#41—24no—
430#41—24no—
431#41—24no—
432#41—24no—
433#41—24no—
434#41—22no—
435#41—22no—
436#41#610118yescomplemented
437#41C2×Dic2614yes—
438#41C2×C4×D1314yes—
439C2×Q8—22no—
440C2×Q8—21no—
441C2×Q8#610114yescomplemented
442C2×Q8C2×C22⋊D1312yes—
443C2×D4—24no—
444C2×D4—24no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4#610114yescomplemented
450C2×D4C2×C22⋊D1312yes—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—134no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—262no—
462C22×C4—262no—
463C22×C4—268no—
464C22×C4—262no—
465C22×C4—1042no—
466C22×C4—1044no—
467C22×C4C2×Dic2612yes—
468C22×C4C2×C4×D1312yes—
469C22×C4D4×D1311yescharacteristic
470C22×C4D4×D1311yescharacteristic
471C22×C4D4×D1311yescharacteristic
472C22×C4#612912yes—
473C22×C4#612912yes—
474C22×C4C2×C22⋊D1311yescharacteristic
475C22×C4C2×C22⋊D1311yescharacteristic
476C22×C4C23×D1311yescharacteristic
477M16—22no—
478M16—22no—
479M16—42no—
480M16—134no—
481M16—264no—
482M16—262no—
483C2×C8—22no—
484C2×C8—42no—
485C2×C8—264no—
486C2×C8—262no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—132no—
492C4⋊C4—132no—
493C4⋊C4—268no—
494C4⋊C4—264no—
495C4⋊C4—261no—
496C4⋊C4—262no—
497C4⋊C4—262no—
498C4⋊C4—261no—
499C4⋊C4—262no—
500C4⋊C4—262no—
501C4⋊C4—1044no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—268no—
505C22⋊C4—264no—
506C22⋊C4—262no—
507C22⋊C4—262no—
508C42—41no—
509C42—41no—
510C42—134no—
511C42—268no—
512C42—262no—
513C42—262no—
514C42—262no—
515C13#2086411yescharacteristic, complemented, Sylow
516C23—22no—
517C23—24no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—42no—
522C23#8813212yes—
523C23#8813512yes—
524C23#8819111yescharacteristic
525C23#8819111yescharacteristic
526C23C2×D4×D1311yescharacteristic
527Q8—22no—
528Q8—24no—
529Q8C2×#610114yes—
530D4—24no—
531D4—24no—
532D4—28no—
533D4—22no—
534D4—24no—
535D4C2×#610114yes—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—28no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—264no—
546C2×C4—262no—
547C2×C4—262no—
548C2×C4—264no—
549C2×C4—522no—
550C2×C4—522no—
551C2×C4—522no—
552C2×C4—524no—
553C2×C4—522no—
554C2×C4—524no—
555C2×C4—1042no—
556C2×C4—1048no—
557C2×C4#8813212yes—
558C2×C4#8813212yes—
559C2×C4#8813212yes—
560C2×C4#8813512yes—
561C2×C4#8813512yes—
562C2×C4#8813512yes—
563C2×C4C2×#610112yes—
564C2×C4C2×#610112yes—
565C2×C4#8818912yes—
566C2×C4#8818912yes—
567C2×C4#8819111yescharacteristic
568C2×C4#8819111yescharacteristic
569C2×C4C22×Dic2611yescharacteristic
570C2×C4C22×C4×D1311yescharacteristic
571C2×C4C2×D4×D1311yescharacteristic
572C2×C4C2×#612911yescharacteristic
573C2×C4C2×#612911yescharacteristic
574C2×C4C22×C22⋊D1311yescharacteristic
575C8—42no—
576C8—264no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—24no—
584C22—42no—
585C22—42no—
586C22—48no—
587C22—42no—
588C22—42no—
589C22#1171860712yes—
590C22#1171860712yes—
591C22C2×#8813211yescharacteristic
592C22C2×#8813511yescharacteristic
593C22C2×#8819111yescharacteristic
594C4—24no—
595C4—81no—
596C4—81no—
597C4—524no—
598C4—524no—
599C4—522no—
600C4—522no—
601C4#1171860712yes—
602C4#1171860712yes—
603C4C2×#8813211yescharacteristic
604C4C2×#8813511yescharacteristic
605C4C22×#610111yescharacteristic
606C4C2×#8818911yescharacteristic
607C2—21no—
608C2—22no—
609C2—21no—
610C2—22no—
611C2—44no—
612C2C2×#1171860711yescharacteristic
613C2#1312419111yescharacteristic
614C2#1312419811yescharacteristic
subgroupG/H
centerC22C2×#88191
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2896C2
socleC22×C13C2×#120
prime radicalC22×C13×#41C22
cosocleC22×C4×C13C24
hypercenter#2896D13
hypocenterC13#20864
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
2. #13123425C2semidirect
4. #13117456C2semidirect
5. #13115067C2semidirect
6. #13115060C2semidirect
7. C2×#11718146C2semidirect
8. #13114547C2semidirect
31. #11718897C4semidirect
36. #11718638C22semidirect
37. #11718637C22semidirect
38. #11718625C22semidirect
39. #11718625C22semidirect
42. #11718147C22semidirect
43. #11718146C22semidirect
86. #88180C2×C4semidirect
107. C2×#6099C2×C4semidirect
114. #88077C2×C4semidirect
130. C13×#41C4⋊C4semidirect
135. C2×Q8×C13C4⋊C4semidirect
143. C2×D4×C13C4⋊C4semidirect
203. C4×Dic13C22×C4semidirect
206. #6099C22×C4semidirect
436. #41#6101semidirect
441. C2×Q8#6101semidirect
449. C2×D4#6101semidirect
515. C13#20864semidirect

Maximal subgroups

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

subgroupindex
C2×#117195322
#131234252
C2×#117188972
#131174562
#131150672
#131150602
C2×#117181462
#131145472
C13×#28962
#2086413