Finite Group Databasebeta

← #15890534

Subgroups — #15890534

Order 3328.

1362 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123425C211yesmaximal, characteristic, complemented
2C2×#11718897C211yesmaximal, characteristic
3#13123355C211yesmaximal, characteristic
4C22×#88076C211yesmaximal, characteristic, complemented
5#13117422C211yesmaximal, characteristic, complemented
6#13116050C218yesmaximal, complemented
7#13114545C211yesmaximal, characteristic, complemented
8C2×C13×#536C211yesmaximal, characteristic
9C22×C13×#41C2211yescharacteristic
10C23×Q8×C13C2211yescharacteristic
11C13×#536—22no—
12C13×#536—22no—
13C13×#536—22no—
14C13×#536C2214yes—
15C2×C13×C4⋊Q8—21no—
16C2×C13×#124—21no—
17C2×C13×#123—22no—
18C2×C13×C22⋊Q8—22no—
19C2×C13×#117C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C2×#88180C2211yescharacteristic
22C22×#6099C2211yescharacteristic
23C22×#6099C2211yescharacteristic
24#11718897—24no—
25C2×#88077C2214yes—
26#11718894—22no—
27#11718893C2214yes—
28#11718891—22no—
29#11718891C2214yescomplemented
30C2×#88076—24no—
31C2×#88076C2214yescomplemented
32#11718886—21no—
33#11718876—21no—
34#11718872—22no—
35#11718659—22no—
36#11718656C2214yescomplemented
37#11718625—22no—
38#11718124C2214yescomplemented
39C2×C13×#41—21no—
40C2×C13×#41—21no—
41C2×C13×#41—22no—
42C2×C13×#41—22no—
43C2×C13×#41—22no—
44C2×C13×#41—22no—
45C2×C13×#41D412yes—
46C2×C13×#41C2312yes—
47C22×Q8×C13—21no—
48C22×Q8×C13—21no—
49C22×Q8×C13—21no—
50C22×Q8×C13—21no—
51C22×Q8×C13—22no—
52C22×Q8×C13—22no—
53C22×Q8×C13—22no—
54C22×Q8×C13—22no—
55C22×Q8×C13D411yescharacteristic
56C22×Q8×C13D412yes—
57C22×Q8×C13C2312yes—
58C22×D4×C13—21no—
59C22×D4×C13D411yescharacteristic
60C23×C4×C13—21no—
61C23×C4×C13D412yes—
62C23×C4×C13C2311yescharacteristic
63C13×C4⋊Q8—24no—
64C13×C4⋊Q8—24no—
65C13×#124—24no—
66C13×#124—24no—
67C13×#123—28no—
68C13×#123—28no—
69C13×C22⋊Q8—28no—
70C13×C22⋊Q8—28no—
71C13×#117—21no—
72C13×#117—21no—
73C13×#117D412yes—
74C13×#117C2312yes—
75C2×C13×C4⋊C4—24no—
76C2×C13×C4⋊C4D412yes—
77C2×C13×C22⋊C4—24no—
78C2×C13×C22⋊C4—21no—
79C2×C42×C13—21no—
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13—21no—
82#88180—22no—
83#88180—22no—
84#88180—21no—
85#88180—21no—
86#88180—21no—
87#88180—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13C2312yes—
90C2×C4×Dic13—21no—
91C2×C4×Dic13C2312yes—
92C2×#6099—21no—
93C2×#6099—22no—
94C2×#6099—21no—
95C2×#6099—22no—
96C2×#6099—22no—
97C2×#6099D414yes—
98C2×#6099C2312yes—
99C2×#6099C2312yes—
100C22×#1055—21no—
101C22×#1055—21no—
102#88077—28no—
103#88076—28no—
104#88075—24no—
105#88072—24no—
106#88071—28no—
107#88048—24no—
108#88047—24no—
109#23494—131nomaximal, Sylow
110C24×C13—21no—
111C24×C13C2×D411yescharacteristic
112C13×#41—24no—
113C13×#41—24no—
114C13×#41—22no—
115C13×#41—22no—
116C13×#41—22no—
117C13×#41—22no—
118C13×#41—42no—
119C13×#41—42no—
120C13×#41—42no—
121C13×#41—42no—
122C2×Q8×C13—22no—
123C2×Q8×C13—22no—
124C2×Q8×C13—21no—
125C2×Q8×C13—24no—
126C2×Q8×C13—24no—
127C2×Q8×C13—22no—
128C2×Q8×C13—22no—
129C2×Q8×C13—22no—
130C2×Q8×C13—22no—
131C2×Q8×C13—22no—
132C2×Q8×C13—22no—
133C2×Q8×C13—22no—
134C2×Q8×C13—22no—
135C2×Q8×C13—42no—
136C2×Q8×C13—42no—
137C2×Q8×C13—42no—
138C2×Q8×C13—42no—
139C2×Q8×C13—42no—
140C2×Q8×C13—42no—
141C2×Q8×C13—42no—
142C2×Q8×C13—42no—
143C2×Q8×C13C2×D412yes—
144C2×D4×C13—22no—
145C2×D4×C13—22no—
146C2×D4×C13—21no—
147C2×D4×C13—22no—
148C2×D4×C13—22no—
149C2×D4×C13—42no—
150C2×D4×C13—42no—
151C2×D4×C13C2×D412yes—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—21no—
155C22×C4×C13—22no—
156C22×C4×C13—24no—
157C22×C4×C13—24no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—42no—
161C22×C4×C13—42no—
162C22×C4×C13C2×D412yes—
163C22×C4×C13C2×D414yes—
164C22×C4×C13C2×D411yescharacteristic
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13#4112yes—
170C22×C4×C13#4112yes—
171C22×C4×C13#4112yes—
172C22×C4×C13C2411yescharacteristic
173C22×Dic13—22no—
174C22×Dic13—22no—
175C13×C4⋊C4—216no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4C2×D414yes—
178C13×C22⋊C4—216no—
179C13×C22⋊C4—22no—
180C13×C22⋊C4—22no—
181C42×C13—22no—
182C42×C13—22no—
183C22⋊Dic13—41no—
184C22⋊Dic13—41no—
185C22⋊Dic13—42no—
186C4⋊Dic13—22no—
187C4⋊Dic13—22no—
188C4⋊Dic13—42no—
189C4×Dic13—22no—
190C4×Dic13—22no—
191C4×Dic13—41no—
192C4×Dic13—41no—
193#6099—24no—
194#6099—22no—
195#6099—22no—
196#6099—22no—
197#6099—42no—
198#6099C2×D414yes—
199C2×#1055—24no—
200C2×#1055—22no—
201C2×#1055—22no—
202C2×#1055—42no—
203C2×#536D1311yescharacteristic
204#2911—131no—
205C2×#421—131no—
206#2896—131no—
207C22×#101—131no—
208#2310—131no—
209#2038—138no—
210#1733—131no—
211C23×C13—22no—
212C23×C13—42no—
213C23×C13—44no—
214C23×C13—42no—
215C23×C13#12011yescharacteristic
216C23×C13#12011yescharacteristic
217C23×C13#12112yes—
218C23×C13#12312yes—
219C23×C13C22×D411yescharacteristic
220Q8×C13—22no—
221Q8×C13—22no—
222Q8×C13—42no—
223Q8×C13—42no—
224Q8×C13—42no—
225Q8×C13—42no—
226Q8×C13—44no—
227Q8×C13—44no—
228Q8×C13—42no—
229D4×C13—22no—
230D4×C13—22no—
231D4×C13—42no—
232D4×C13—42no—
233D4×C13—44no—
234D4×C13—42no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—22no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—44no—
241C2×C4×C13—44no—
242C2×C4×C13—44no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—44no—
247C2×C4×C13#12011yescharacteristic
248C2×C4×C13#12011yescharacteristic
249C2×C4×C13#12112yes—
250C2×C4×C13#12112yes—
251C2×C4×C13#12112yes—
252C2×C4×C13#12112yes—
253C2×C4×C13#12112yes—
254C2×C4×C13#12312yes—
255C2×C4×C13#12312yes—
256C2×C4×C13#12312yes—
257C2×C4×C13#12412yes—
258C2×C4×C13#12412yes—
259C2×C4×C13C22×D411yescharacteristic
260C2×C4×C13C22×D411yescharacteristic
261C2×C4×C13C22×D411yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×Dic13—44no—
266C2×Dic13—44no—
267C2×Dic13—42no—
268C2×Dic13—42no—
269#1055—24no—
270#1055—42no—
271C22×#41C2×D1311yescharacteristic
272C23×Q8C2×D1311yescharacteristic
273C22×M16—131no—
274C22×M16—131no—
275#536—22no—
276#536—22no—
277#536—22no—
278#536C2×D1314yes—
279C2×C4⋊Q8—21no—
280C2×#124—21no—
281C2×#123—22no—
282C2×C22⋊Q8—22no—
283C2×#117—131no—
284C2×#117—131no—
285C2×#117C2×D1311yescharacteristic
286#428—134no—
287#428—262no—
288#427—262no—
289#421—264no—
290C2×#104—134no—
291#419—261no—
292#418—261no—
293#417—134no—
294#416—262no—
295C2×#101—134no—
296C2×#101—264no—
297#391—134no—
298#391—262no—
299#381—262no—
300#339—134no—
301C22×C13—22no—
302C22×C13—22no—
303C22×C13—22no—
304C22×C13—42no—
305C22×C13—42no—
306C22×C13—42no—
307C22×C13—44no—
308C22×C13—84no—
309C22×C13#39412yes—
310C22×C13#39412yes—
311C22×C13C2×#12011yescharacteristic
312C22×C13C2×#12111yescharacteristic
313C22×C13C2×#12311yescharacteristic
314C4×C13—44no—
315C4×C13—42no—
316C4×C13—44no—
317C4×C13#39412yes—
318C4×C13#39412yes—
319C4×C13C2×#12111yescharacteristic
320C4×C13C2×#12111yescharacteristic
321C4×C13C2×#12311yescharacteristic
322C4×C13C2×#12411yescharacteristic
323Dic13—82no—
324Dic13—82no—
325C2×#41—21no—
326C2×#41—21no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41C22⋊D1312yes—
332C2×#41C22×D1312yes—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—21no—
338C22×Q8—21no—
339C22×Q8—21no—
340C22×Q8—21no—
341C22×Q8C22⋊D1311yescharacteristic
342C22×Q8C22⋊D1312yes—
343C22×Q8C22×D1312yes—
344C22×D4—21no—
345C22×D4C22⋊D1311yescharacteristic
346C23×C4—21no—
347C23×C4C22⋊D1312yes—
348C23×C4C22×D1311yescharacteristic
349C2×M16—134no—
350C2×M16—132no—
351C2×M16—132no—
352C2×M16—262no—
353C2×M16—261no—
354C2×M16—261no—
355C2×M16—262no—
356C2×M16—262no—
357C22×C8—261no—
358C22×C8—261no—
359C4⋊Q8—24no—
360C4⋊Q8—24no—
361#124—24no—
362#124—24no—
363#123—28no—
364#123—28no—
365C22⋊Q8—28no—
366C22⋊Q8—28no—
367#117—21no—
368#117—21no—
369#117—262no—
370#117—262no—
371#117—261no—
372#117—261no—
373#117—261no—
374#117—261no—
375#117C22⋊D1312yes—
376#117C22×D1312yes—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—132no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4C22⋊D1312yes—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C42—21no—
386C2×C42—132no—
387C2×C42—261no—
388#107—264no—
389#106—264no—
390#104—268no—
391#103—264no—
392#102—264no—
393#101—268no—
394#95—268no—
395C2×C13—21no—
396C2×C13—22no—
397C2×C13—21no—
398C2×C13—22no—
399C2×C13—82no—
400C2×C13C2×#39411yescharacteristic
401C2×C13#302012yes—
402C24—21no—
403C24C2×C22⋊D1311yescharacteristic
404#41—24no—
405#41—24no—
406#41—22no—
407#41—22no—
408#41—22no—
409#41—22no—
410#41—42no—
411#41—42no—
412#41—42no—
413#41—42no—
414C2×Q8—24no—
415C2×Q8—24no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—21no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—42no—
428C2×Q8—42no—
429C2×Q8—42no—
430C2×Q8—42no—
431C2×Q8—42no—
432C2×Q8—42no—
433C2×Q8—42no—
434C2×Q8—42no—
435C2×Q8C2×C22⋊D1312yes—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4C2×C22⋊D1312yes—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—262no—
455C22×C4—262no—
456C22×C4D4×D1312yes—
457C22×C4#612912yes—
458C22×C4#612912yes—
459C22×C4#612912yes—
460C22×C4C2×C22⋊D1314yes—
461C22×C4C2×C22⋊D1311yescharacteristic
462C22×C4C2×C22⋊D1311yescharacteristic
463C22×C4C2×C22⋊D1311yescharacteristic
464C22×C4C2×C22⋊D1311yescharacteristic
465C22×C4C2×C22⋊D1311yescharacteristic
466C22×C4C23×D1311yescharacteristic
467M16—134no—
468M16—264no—
469M16—262no—
470M16—262no—
471M16—262no—
472M16—522no—
473C2×C8—264no—
474C2×C8—262no—
475C2×C8—262no—
476C2×C8—522no—
477C4⋊C4—216no—
478C4⋊C4—22no—
479C4⋊C4—262no—
480C4⋊C4—262no—
481C4⋊C4—522no—
482C4⋊C4C2×C22⋊D1314yes—
483C22⋊C4—216no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—522no—
487C22⋊C4—521no—
488C22⋊C4—521no—
489C42—22no—
490C42—22no—
491C42—262no—
492C42—262no—
493C42—521no—
494C42—521no—
495C13#2349411yescharacteristic, complemented, Sylow
496C23—22no—
497C23—42no—
498C23—44no—
499C23—42no—
500C23#8818912yes—
501C23#8819312yes—
502C23#8820711yescharacteristic
503C23#8820711yescharacteristic
504C23C22×C22⋊D1311yescharacteristic
505Q8—22no—
506Q8—22no—
507Q8—42no—
508Q8—42no—
509Q8—42no—
510Q8—42no—
511Q8—44no—
512Q8—44no—
513Q8—42no—
514D4—22no—
515D4—22no—
516D4—42no—
517D4—42no—
518D4—44no—
519D4—42no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—524no—
533C2×C4—524no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4#8818912yes—
537C2×C4#8818912yes—
538C2×C4#8818912yes—
539C2×C4#8819012yes—
540C2×C4#8819012yes—
541C2×C4#8819212yes—
542C2×C4#8819212yes—
543C2×C4#8819312yes—
544C2×C4#8819312yes—
545C2×C4#8819312yes—
546C2×C4#8820711yescharacteristic
547C2×C4#8820711yescharacteristic
548C2×C4C2×D4×D1311yescharacteristic
549C2×C4C2×#612911yescharacteristic
550C2×C4C2×#612911yescharacteristic
551C2×C4C2×#612911yescharacteristic
552C2×C4C22×C22⋊D1311yescharacteristic
553C2×C4C22×C22⋊D1311yescharacteristic
554C8—264no—
555C8—522no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—44no—
563C22—84no—
564C22#1171888312yes—
565C22#1171888312yes—
566C22C2×#8818911yescharacteristic
567C22C2×#8819311yescharacteristic
568C22C2×#8820711yescharacteristic
569C4—44no—
570C4—42no—
571C4—44no—
572C4—1042no—
573C4—1042no—
574C4#1171888312yes—
575C4#1171888312yes—
576C4C2×#8818911yescharacteristic
577C4C2×#8819011yescharacteristic
578C4C2×#8819211yescharacteristic
579C4C2×#8819311yescharacteristic
580C2—21no—
581C2—22no—
582C2—21no—
583C2—22no—
584C2—82no—
585C2C2×#1171888311yescharacteristic
586C2#1312420012yes—
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#536C2
socleC22×C13C2×#120
prime radicalC22×C13×#41C22
hypercenterC2×#536D13
hypocenterC13#23494
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. #13123425C2semidirect
4. C22×#88076C2semidirect
5. #13117422C2semidirect
6. #13116050C2semidirect
7. #13114545C2semidirect
29. #11718891C22semidirect
31. C2×#88076C22semidirect
36. #11718656C22semidirect
38. #11718124C22semidirect
495. C13#23494semidirect

Maximal subgroups

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

subgroupindex
#131234252
C2×#117188972
#131233552
C22×#880762
#131174222
#131160502
#131145452
C2×C13×#5362
#2349413