Finite Group Databasebeta

← #15889498

Subgroups — #15889498

Order 3328.

706 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125304C211yesmaximal, characteristic
2#13115333C211yesmaximal, characteristic, complemented
3#13115327C211yesmaximal, characteristic, complemented
4#13115326C211yesmaximal, characteristic, complemented
5#13115320C211yesmaximal, characteristic, complemented
6#13115316C211yesmaximal, characteristic, complemented
7#13115314C211yesmaximal, characteristic, complemented
8#13115309C211yesmaximal, characteristic, complemented
9#13115307C211yesmaximal, characteristic, complemented
10#13115238C211yesmaximal, characteristic, complemented
11#13115223C211yesmaximal, characteristic, complemented
12#13115220C211yesmaximal, characteristic, complemented
13#13114982C211yesmaximal, characteristic, complemented
14#13114982C211yesmaximal, characteristic, complemented
15C13×#1884C211yesmaximal, characteristic, complemented
16C13×#568C2211yescharacteristic
17C13×#532C2211yescharacteristic
18C2×#88205C2211yescharacteristic
19C2×#88205C2211yescharacteristic
20C2×#88203C2211yescharacteristic
21C2×#88203C2211yescharacteristic
22#11719524C2211yescharacteristic
23#11719226C2211yescharacteristic
24#11719221C2211yescharacteristic
25C2×#88129C2211yescharacteristic
26C13×#421C2211yescharacteristic
27C13×#421C2211yescharacteristic
28C13×#410C2211yescharacteristic
29#11718901C2211yescharacteristic
30#11718897C2211yescharacteristic
31#11718897C2211yescharacteristic
32C2×#88064C2211yescharacteristic
33#11718792C2211yescharacteristic
34C2×#88063C2211yescharacteristic
35#11718781C2211yescharacteristic
36#11718747C412yescomplemented
37#11718735C412yescomplemented
38#11718720C412yescomplemented
39#11718720C412yescomplemented
40#11718665C2211yescharacteristic
41#11718662C2211yescharacteristic
42C4×#6099C2211yescharacteristic
43C13×#339C2211yescharacteristic
44C13×#339C2211yescharacteristic
45#11718152C2211yescharacteristic
46#11718152C2211yescharacteristic
47#11718151C2211yescharacteristic
48#11718151C2211yescharacteristic
49#11718125C2211yescharacteristic
50#11718125C2211yescharacteristic
51#11718123C2211yescharacteristic
52#11718123C2211yescharacteristic
53#11718115C2211yescharacteristic
54#11718115C2211yescharacteristic
55C2×C13×#41C2311yescharacteristic
56C2×C13×#41C2311yescharacteristic
57C22×D52C2311yescharacteristic
58C22×Dic26C2311yescharacteristic
59C13×#131—41no—
60C13×#131—41no—
61C2×C13×M16—41no—
62C2×C13×M16C2311yescharacteristic
63C2×C13×M16C2311yescharacteristic
64C13×C4⋊Q8C2×C411yescharacteristic, complemented
65C13×#127C2×C411yescharacteristic, complemented
66C13×#124C2×C411yescharacteristic, complemented
67C13×#124C2×C411yescharacteristic, complemented
68C13×#121—41no—
69C4×D4×C13—41no—
70C13×#117C2311yescharacteristic
71C13×#117C2311yescharacteristic
72C2×C42×C13C2311yescharacteristic
73#88205—41no—
74#88205—41no—
75#88205—41no—
76#88205—41no—
77#88203—41no—
78#88203—41no—
79#88203—41no—
80#88203—41no—
81#88202—41no—
82#88202—41no—
83C2×#6107C2×C412yescomplemented
84C2×#6107C2×C412yescomplemented
85C2×#6106C2×C412yes—
86C2×#6106C2×C412yes—
87C2×#6105C2×C412yescomplemented
88C2×#6105C2×C412yescomplemented
89C2×#6104C2×C412yes—
90C2×#6104C2×C412yes—
91C2×#6103—41no—
92#88180C2311yescharacteristic
93#88180C2311yescharacteristic
94C2×#6099—41no—
95C2×#6099C2311yescharacteristic
96C2×#6099C2311yescharacteristic
97C2×#6099C2311yescharacteristic
98C2×#6099C2311yescharacteristic
99#88147—41no—
100#88141—41no—
101C22⋊C4×D13—41no—
102#88131—41no—
103#88129—41no—
104#88129C2×C412yes—
105#88129C2×C412yes—
106C4×D52—41no—
107C4×Dic26—41no—
108C13×#104—41no—
109C13×#104—41no—
110C13×#99—41no—
111#88077—41no—
112#88077—41no—
113#88074—41no—
114#88064—41no—
115#88063—41no—
116#88061—41no—
117#88056—41no—
118#88050—41no—
119#88049—41no—
120#88043C2×C412yescomplemented
121C4×#1055C2×C412yescomplemented
122#23362—131nomaximal, Sylow
123C23×D13—21no—
124C13×#41—21no—
125C13×#41—21no—
126C13×#41—21no—
127C13×#41—21no—
128C13×#41—21no—
129C13×#41—21no—
130C13×#41—21no—
131C13×#41—21no—
132C2×Q8×C13C22×C411yescharacteristic
133C2×Q8×C13C22×C411yescharacteristic
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—41no—
137C2×D4×C13C22×C411yescharacteristic
138C2×D4×C13C22×C411yescharacteristic
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13C2411yescharacteristic
143C22×Dic13—21no—
144C2×D52—21no—
145C2×D52—21no—
146C2×D52—21no—
147C2×D52—21no—
148C2×D52—21no—
149C2×D52C22×C412yes—
150C2×C4×D13—42no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26C22×C412yes—
157C13×M16—21no—
158C13×M16—21no—
159C13×M16—21no—
160C13×M16—21no—
161C13×M16—42no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—42no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—41no—
168C13×C22⋊C4—21no—
169C13×C22⋊C4—21no—
170C13×C22⋊C4—41no—
171C13×C22⋊C4—41no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13C22×C411yescharacteristic
176C42×C13C22×C411yescharacteristic
177C22⋊Dic13—21no—
178C22⋊Dic13—21no—
179#6107—42no—
180#6107—42no—
181#6106—42no—
182#6106—42no—
183#6105—42no—
184#6105—42no—
185#6104—42no—
186#6104—42no—
187#6103—42no—
188#6103—42no—
189#6103—42no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192#6101—42no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—42no—
196#6099—21no—
197#6099—21no—
198#6099—21no—
199#6099—21no—
200#6099—21no—
201#6099—21no—
202#6099—21no—
203#6099—21no—
204#6099—42no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—42no—
208C2×#1055C22×C412yes—
209C2×#1055C22×C412yes—
210#3153—131no—
211#1905—131no—
212#1905—131no—
213#1904—131no—
214#1904—131no—
215#1903—131no—
216#1903—131no—
217#1902—131no—
218#1902—131no—
219#1888—131no—
220#1885—131no—
221#1884—131no—
222#1884D1311yescharacteristic, complemented
223#1841—131no—
224#1841—131no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13H(5,𝔽2)11yescharacteristic
228C22×D13—22no—
229C22×D13—41no—
230C22×D13—41no—
231C22×D13—82no—
232Q8×C13—21no—
233Q8×C13—21no—
234Q8×C13—21no—
235Q8×C13—21no—
236D4×C13—21no—
237D4×C13—21no—
238D4×C13—21no—
239D4×C13—21no—
240D4×C13—41no—
241D4×C13—41no—
242D4×C13—41no—
243D4×C13—41no—
244D4×C13—82no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—81no—
256C2×C4×C13C23×C411yescharacteristic
257C2×C4×C13H(5,𝔽2)11yescharacteristic
258C2×C4×C13H(5,𝔽2)11yescharacteristic
259C2×C4×C13H(5,𝔽2)11yescharacteristic
260C2×C4×C13H(5,𝔽2)11yescharacteristic
261C2×C4×C13H(5,𝔽2)11yescharacteristic
262C2×Dic13—22no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267D52—22no—
268D52—22no—
269D52—41no—
270D52—41no—
271C4×D13—162no—
272Dic26—22no—
273Dic26—22no—
274Dic26—41no—
275Dic26—41no—
276C8×C13—41no—
277C8×C13—41no—
278#1055—22no—
279#1055—22no—
280#1055—41no—
281#1055—41no—
282C2×#137—131no—
283C2×#137—131no—
284C2×AGL(1,ℤ/8)—131no—
285C2×AGL(1,ℤ/8)—131no—
286#568—131no—
287#568C2×D1311yescharacteristic
288#532C2×D1311yescharacteristic
289C2×#124—131no—
290#519—131no—
291#518—131no—
292#497—132no—
293#496—132no—
294#495—132no—
295#495—132no—
296#421—131no—
297#421—131no—
298#421C2×D1311yescharacteristic
299#421C2×D1311yescharacteristic
300#419—131no—
301#419—131no—
302#418—131no—
303#418—131no—
304C2×#101—131no—
305C2×#100—131no—
306#410—131no—
307#410C2×D1311yescharacteristic
308C4×M16—131no—
309#344—131no—
310#344—131no—
311#344—131no—
312#344—131no—
313#339—131no—
314#339—131no—
315#339C2×D1311yescharacteristic
316#339C2×D1311yescharacteristic
317#338—131no—
318#338—131no—
319H(3,ℤ/4)—131no—
320H(3,ℤ/4)—131no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13—81no—
325C22×C13—81no—
326C22×C13#51811yescharacteristic
327C22×C13#56011yescharacteristic
328C22×C13#56011yescharacteristic
329C2×D13—42no—
330C2×D13—82no—
331C2×D13—82no—
332C2×D13—161no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13—81no—
338C4×C13—81no—
339C4×C13#51811yescharacteristic
340C4×C13#51811yescharacteristic
341C4×C13#56011yescharacteristic
342C4×C13#56011yescharacteristic
343Dic13—42no—
344Dic13—81no—
345Dic13—81no—
346C2×#41C22×D1311yescharacteristic
347C2×#41C22×D1311yescharacteristic
348C22×Q8—131no—
349C22×D4—131no—
350#137—521no—
351#137—521no—
352#137—521no—
353#137—521no—
354AGL(1,ℤ/8)—521no—
355AGL(1,ℤ/8)—521no—
356AGL(1,ℤ/8)—521no—
357AGL(1,ℤ/8)—521no—
358C2×Q16—132no—
359C2×Q16—132no—
360C2×SD16—132no—
361C2×SD16—132no—
362C2×SD16—132no—
363C2×SD16—132no—
364C2×D8—132no—
365C2×D8—132no—
366#131—41no—
367#131—41no—
368#131—521no—
369#131—521no—
370C2×M16—41no—
371C2×M16—131no—
372C2×M16—131no—
373C2×M16—131no—
374C2×M16—131no—
375C2×M16—521no—
376C2×M16C22×D1311yescharacteristic
377C2×M16C22×D1311yescharacteristic
378C4⋊Q8C4×D1311yescharacteristic, complemented
379#127C4×D1311yescharacteristic, complemented
380#124—132no—
381#124—132no—
382#124—521no—
383#124C4×D1311yescharacteristic, complemented
384#124C4×D1311yescharacteristic, complemented
385#121—41no—
386C4×Q8—521no—
387C4×Q8—521no—
388C4×D4—41no—
389C4×D4—521no—
390C4×D4—521no—
391#117—131no—
392#117—131no—
393#117—521no—
394#117C22×D1311yescharacteristic
395#117C22×D1311yescharacteristic
396C2×C22⋊C4—521no—
397C2×C22⋊C4—521no—
398C2×C42C22×D1311yescharacteristic
399#104—41no—
400#104—41no—
401#104—521no—
402#104—521no—
403#103—521no—
404#103—521no—
405#102—521no—
406#102—521no—
407#101—521no—
408#100—521no—
409#99—41no—
410#99—521no—
411#97—132no—
412C4×C8—132no—
413C2×C13—21no—
414C2×C13—21no—
415C2×C13—21no—
416C2×C13—81no—
417C2×C13—81no—
418C2×C13#238011yescharacteristic
419D13—82no—
420C24—261no—
421#41—21no—
422#41—21no—
423#41—21no—
424#41—21no—
425#41—21no—
426#41—21no—
427#41—21no—
428#41—21no—
429C2×Q8—132no—
430C2×Q8—261no—
431C2×Q8—261no—
432C2×Q8—261no—
433C2×Q8—261no—
434C2×Q8—261no—
435C2×Q8C2×C4×D1311yescharacteristic
436C2×Q8C2×C4×D1311yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—41no—
440C2×D4—132no—
441C2×D4—261no—
442C2×D4—261no—
443C2×D4—261no—
444C2×D4—261no—
445C2×D4—261no—
446C2×D4C2×C4×D1311yescharacteristic
447C2×D4C2×C4×D1311yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—261no—
452C22×C4—522no—
453C22×C4C23×D1311yescharacteristic
454Q16—522no—
455Q16—522no—
456SD16—522no—
457SD16—522no—
458SD16—522no—
459SD16—522no—
460D8—522no—
461D8—522no—
462M16—21no—
463M16—21no—
464M16—21no—
465M16—21no—
466M16—42no—
467M16—261no—
468M16—261no—
469M16—261no—
470M16—261no—
471M16—261no—
472M16—261no—
473M16—261no—
474M16—261no—
475M16—522no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—42no—
479C2×C8—132no—
480C2×C8—132no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—522no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—522no—
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—261no—
495C22⋊C4—261no—
496C22⋊C4—522no—
497C22⋊C4—522no—
498C22⋊C4—522no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—261no—
503C42—261no—
504C42—522no—
505C42C2×C4×D1311yescharacteristic
506C42C2×C4×D1311yescharacteristic
507C13#2336211yescharacteristic, complemented, Sylow
508C23—21no—
509C23—21no—
510C23—262no—
511C23—521no—
512C23—521no—
513C23—1042no—
514C23#8825111yescharacteristic
515Q8—21no—
516Q8—21no—
517Q8—21no—
518Q8—21no—
519Q8—262no—
520Q8—262no—
521Q8—521no—
522Q8—521no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—82no—
532D4—262no—
533D4—262no—
534D4—521no—
535D4—521no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—81no—
547C2×C4—262no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—2082no—
553C2×C4C22×C4×D1311yescharacteristic
554C2×C4#8825111yescharacteristic
555C2×C4#8825111yescharacteristic
556C2×C4#8825111yescharacteristic
557C2×C4#8825611yescharacteristic
558C2×C4#8825611yescharacteristic
559C8—41no—
560C8—41no—
561C8—262no—
562C8—262no—
563C8—521no—
564C8—521no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—81no—
569C22—81no—
570C22—522no—
571C22—1042no—
572C22—1042no—
573C22—2081no—
574C22#1171919111yescharacteristic
575C22#1171932511yescharacteristic
576C22#1171932511yescharacteristic
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—522no—
584C4—1041no—
585C4—1041no—
586C4#1171925011yescharacteristic
587C4#1171925011yescharacteristic
588C4#1171930011yescharacteristic
589C4#1171937111yescharacteristic
590C2—21no—
591C2—21no—
592C2—21no—
593C2—81no—
594C2—81no—
595C2—1042no—
596C2#1311801111yescharacteristic
subgroupG/H
centerC2#13118011
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1884C2
socleC2×C13#2380
prime radical#13125304C2
cosocleC22×C4×C13C24
hypercenter#1884D13
hypocenterC13#23362
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1884

Complements

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

NH ≅ G/Ntype
2. #13115333C2semidirect
3. #13115327C2semidirect
4. #13115326C2semidirect
5. #13115320C2semidirect
6. #13115316C2semidirect
7. #13115314C2semidirect
8. #13115309C2semidirect
9. #13115307C2semidirect
10. #13115238C2semidirect
11. #13115223C2semidirect
12. #13115220C2semidirect
13. #13114982C2semidirect
14. #13114982C2semidirect
15. C13×#1884C2semidirect
36. #11718747C4semidirect
37. #11718735C4semidirect
38. #11718720C4semidirect
39. #11718720C4semidirect
64. C13×C4⋊Q8C2×C4semidirect
65. C13×#127C2×C4semidirect
66. C13×#124C2×C4semidirect
67. C13×#124C2×C4semidirect
83. C2×#6107C2×C4semidirect
84. C2×#6107C2×C4semidirect
87. C2×#6105C2×C4semidirect
88. C2×#6105C2×C4semidirect
120. #88043C2×C4semidirect
121. C4×#1055C2×C4semidirect
222. #1884D13semidirect
378. C4⋊Q8C4×D13semidirect
379. #127C4×D13semidirect
383. #124C4×D13semidirect
384. #124C4×D13semidirect
507. C13#23362semidirect

Maximal subgroups

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

subgroupindex
#131253042
#131153332
#131153272
#131153262
#131153202
#131153162
#131153142
#131153092
#131153072
#131152382
#131152232
#131152202
#131149822
C13×#18842
#2336213