Finite Group Databasebeta

← #15966240

Subgroups — #15966240

Order 3328.

734 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117300C211yesmaximal, characteristic
2#13116327C211yesmaximal, characteristic, complemented
3#13116221C211yesmaximal, characteristic
4#13116217C211yesmaximal, characteristic, complemented
5#13116151C211yesmaximal, characteristic
6#13115720C211yesmaximal, characteristic
7#13115576C211yesmaximal, characteristic, complemented
8#13115532C211yesmaximal, characteristic
9#13115529C211yesmaximal, characteristic, complemented
10#13115474C211yesmaximal, characteristic, complemented
11#13115425C211yesmaximal, characteristic, complemented
12#13115173C211yesmaximal, characteristic
13#13115096C211yesmaximal, characteristic
14#13114689C211yesmaximal, characteristic, complemented
15C13×#2863C211yesmaximal, characteristic, complemented
16C22×#6106C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C2×#88126—21no—
19C13×#391C2211yescharacteristic
20C13×#391C2211yescharacteristic
21C13×#391C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#387—21no—
26C13×#387—21no—
27C13×#387—21no—
28C13×#383—21no—
29C43×C13C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39#11718601—21no—
40#11718601—21no—
41#11718600C2211yescharacteristic
42#11718600C2211yescharacteristic
43C4×#6103—21no—
44C4×C4⋊Dic13C2211yescharacteristic
45#11718589C2211yescharacteristic
46#11718589C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C2×#88043C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C22×D52C2311yescharacteristic
61C22×C4×D13—21no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C42×C13D411yescharacteristic
69C2×C42×C13D411yescharacteristic
70C2×C42×C13D411yescharacteristic
71C2×C42×C13D411yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×#6106—22no—
76C2×#6106—22no—
77C2×#6106—41no—
78C2×#6103—21no—
79C2×#6103—21no—
80C2×#6103—21no—
81C2×#6103—21no—
82C2×#6103—21no—
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×#6101—21no—
87C2×#6101—21no—
88C2×C4×Dic13—21no—
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C4×D52—22no—
94C4×D52—22no—
95#88126—44no—
96C13×#95—21no—
97C13×#95—21no—
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95—21no—
105#88075—22no—
106#88075—22no—
107#88075—41no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88049—22no—
112#88049—22no—
113#88049—41no—
114#88048—22no—
115#88047—22no—
116#88047—41no—
117C4⋊#1055—22no—
118C4⋊#1055—22no—
119#88043—41no—
120#88043—41no—
121#29448—131nomaximal, Sylow
122C23×D13—21no—
123C2×Q8×C13—21no—
124C2×Q8×C13—21no—
125C2×Q8×C13—21no—
126C2×Q8×C13—21no—
127C2×Q8×C13—21no—
128C2×Q8×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2411yescharacteristic
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C2×D52—21no—
144C2×D52—21no—
145C2×D52—21no—
146C2×D52—21no—
147C2×D52—21no—
148C2×D52#4112yes—
149C2×C4×D13—24no—
150C2×C4×D13—42no—
151C2×C4×D13—42no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—42no—
159C13×C4⋊C4—42no—
160C13×C4⋊C4—42no—
161C42×C13—22no—
162C42×C13—22no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—21no—
167C42×C13—21no—
168C42×C13—21no—
169C42×C13—41no—
170C42×C13—41no—
171#6106—44no—
172#6103—24no—
173#6103—42no—
174#6103—42no—
175#6103—42no—
176#6103—42no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13#4112yes—
183#6101—42no—
184#6101—42no—
185C4×Dic13—42no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055#4112yes—
197C2×#1055#4112yes—
198#2863D1311yescharacteristic, complemented
199#2293—131no—
200#2086—131no—
201#2067—131no—
202#2066—131no—
203#2055—131no—
204#1973—131no—
205#1944—131no—
206#1936—131no—
207#1935—131no—
208#1928—131no—
209#1921—131no—
210#1877—131no—
211#1864—131no—
212#1767—131no—
213C23×C13C22×D411yescharacteristic
214C22×D13—22no—
215C22×D13—41no—
216C22×D13—41no—
217C22×D13—41no—
218C22×D13—41no—
219C22×D13—41no—
220C22×D13—41no—
221Q8×C13—41no—
222Q8×C13—41no—
223Q8×C13—41no—
224Q8×C13—41no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13AGL(1,ℤ/8)12yes—
254C2×C4×C13#13712yes—
255C2×C4×C13C2×#4111yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×C4×C13H(5,𝔽2)11yescharacteristic
260C2×C4×C132−1+411yescharacteristic
261C2×Dic13—22no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270D52—22no—
271D52—22no—
272D52—41no—
273D52—41no—
274C4×D13—48no—
275#1055—22no—
276#1055—22no—
277#1055—41no—
278#1055—41no—
279C22×SD16—131no—
280C2×C4×D4—131no—
281C2×#117—261no—
282C2×#107—131no—
283C2×#107—131no—
284C2×#106—131no—
285C2×C4⋊C8—131no—
286C2×C4⋊C8—131no—
287C2×#103—131no—
288C2×#103—131no—
289C2×#103—131no—
290C2×#102—131no—
291C2×#102—131no—
292C2×#102—131no—
293C2×#97—131no—
294C2×#97—131no—
295#391C2×D1311yescharacteristic
296#391C2×D1311yescharacteristic
297#391C2×D1311yescharacteristic
298#390—131no—
299#390—131no—
300#389—131no—
301#389—131no—
302#389C2×D1311yescharacteristic
303#389C2×D1311yescharacteristic
304#389C2×D1311yescharacteristic
305#388—261no—
306#388—261no—
307#387—21no—
308#387—21no—
309#387—21no—
310#383—21no—
311C4×C4⋊C4—131no—
312C4×C22⋊C4—261no—
313C43C2×D1311yescharacteristic
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#336—131no—
321#336—131no—
322C22×C13#52511yescharacteristic
323C22×C13#53211yescharacteristic
324C22×C13#53711yescharacteristic
325C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C13C2×#13711yescharacteristic
327C22×C13#57511yescharacteristic
328C22×C13#57511yescharacteristic
329C2×D13—42no—
330C2×D13—42no—
331C2×D13—42no—
332C2×D13—81no—
333C2×D13—81no—
334C2×D13—81no—
335C2×D13—81no—
336C4×C13—22no—
337C4×C13—22no—
338C4×C13—41no—
339C4×C13—41no—
340C4×C13—41no—
341C4×C13—41no—
342C4×C13—81no—
343C4×C13—81no—
344C4×C13—81no—
345C4×C13—81no—
346C4×C13#55111yescharacteristic
347C4×C13#55211yescharacteristic
348C4×C13#55311yescharacteristic
349C4×C13#55611yescharacteristic
350Dic13—42no—
351Dic13—81no—
352Dic13—81no—
353C22×Q8C22×D1311yescharacteristic
354C22×D4—131no—
355C23×C4—261no—
356C2×SD16—262no—
357C2×SD16—262no—
358C2×SD16—521no—
359C22×C8—131no—
360C22×C8—131no—
361C22×C8—131no—
362C22×C8—131no—
363C4×D4—262no—
364C4×D4—262no—
365#117—524no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C4⋊C4C22×D1311yescharacteristic
376C2×C4⋊C4C22×D1311yescharacteristic
377C2×C22⋊C4—261no—
378C2×C22⋊C4—261no—
379C2×C22⋊C4—261no—
380C2×C22⋊C4—261no—
381C2×C22⋊C4—261no—
382C2×C42—261no—
383C2×C42C22⋊D1311yescharacteristic
384C2×C42C22⋊D1311yescharacteristic
385C2×C42C22⋊D1311yescharacteristic
386C2×C42C22⋊D1311yescharacteristic
387C2×C42C22×D1311yescharacteristic
388C2×C42C22×D1311yescharacteristic
389C2×C42C22×D1311yescharacteristic
390#107—262no—
391#107—521no—
392#106—262no—
393C4⋊C8—262no—
394C4⋊C8—262no—
395#103—262no—
396#103—262no—
397#103—521no—
398#102—262no—
399#102—262no—
400#102—521no—
401#97—521no—
402#97—521no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—261no—
413#95—261no—
414#95—261no—
415C2×C13#260111yescharacteristic
416C2×C13#311011yescharacteristic
417C2×C13#311111yescharacteristic
418C2×C13#317211yescharacteristic
419C2×C13#318011yescharacteristic
420C2×C13#325111yescharacteristic
421C2×C13#325211yescharacteristic
422D13—82no—
423C24—261no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×D4—132no—
431C2×D4—261no—
432C2×D4—261no—
433C2×D4—261no—
434C2×D4—261no—
435C2×D4—261no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—264no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—522no—
445C22×C4—522no—
446C22×C4C2×C22⋊D1311yescharacteristic
447C22×C4C2×C22⋊D1311yescharacteristic
448C22×C4C2×C22⋊D1311yescharacteristic
449C22×C4C2×C22⋊D1311yescharacteristic
450C22×C4C2×C22⋊D1311yescharacteristic
451C22×C4C2×C22⋊D1311yescharacteristic
452C22×C4C23×D1311yescharacteristic
453SD16—524no—
454C2×C8—132no—
455C2×C8—132no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—261no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—132no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—522no—
482C4⋊C4—522no—
483C22⋊C4—264no—
484C22⋊C4—522no—
485C22⋊C4—522no—
486C22⋊C4—522no—
487C22⋊C4—522no—
488C42—22no—
489C42—22no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—41no—
497C42—41no—
498C42—522no—
499C13#2944811yescharacteristic, complemented, Sylow
500C23—262no—
501C23—521no—
502C23—521no—
503C23—521no—
504C23—521no—
505C23—521no—
506C23—521no—
507C23C22×C22⋊D1311yescharacteristic
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512D4—262no—
513D4—262no—
514D4—521no—
515D4—521no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—262no—
545C2×C4—528no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4#8819612yes—
555C2×C4#8820312yes—
556C2×C4#41×D1311yescharacteristic
557C2×C4#41×D1311yescharacteristic
558C2×C4#41×D1311yescharacteristic
559C2×C4#41×D1311yescharacteristic
560C2×C4#8825611yescharacteristic
561C2×C4#8825711yescharacteristic
562C8—262no—
563C8—262no—
564C8—521no—
565C8—521no—
566C22—522no—
567C22—522no—
568C22—522no—
569C22—1041no—
570C22—1041no—
571C22—1041no—
572C22—1041no—
573C22C2×#8819611yescharacteristic
574C22C2×#8820311yescharacteristic
575C22#1171952711yescharacteristic
576C22#1171952711yescharacteristic
577C22#1171953311yescharacteristic
578C22#1171953711yescharacteristic
579C22#1171953811yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—522no—
591C4—1041no—
592C4—1041no—
593C4#1171940711yescharacteristic
594C4#1171941011yescharacteristic
595C4#1171941311yescharacteristic
596C4#1171941411yescharacteristic
597C2—1042no—
598C2#1312043511yescharacteristic
599C2#1312493111yescharacteristic
600C2#1312493911yescharacteristic
601C2#1312543611yescharacteristic
602C2#1312553511yescharacteristic
603C2#1312619811yescharacteristic
604C2#1312620311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2863C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2863D13
hypocenterC13#29448
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #2863

Complements

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

NH ≅ G/Ntype
2. #13116327C2semidirect
4. #13116217C2semidirect
7. #13115576C2semidirect
9. #13115529C2semidirect
10. #13115474C2semidirect
11. #13115425C2semidirect
14. #13114689C2semidirect
15. C13×#2863C2semidirect
198. #2863D13semidirect
499. C13#29448semidirect

Maximal subgroups

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

subgroupindex
#131173002
#131163272
#131162212
#131162172
#131161512
#131157202
#131155762
#131155322
#131155292
#131154742
#131154252
#131151732
#131150962
#131146892
C13×#28632
#2944813