Finite Group Databasebeta

← #15962690

Subgroups — #15962690

Order 3328.

690 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120811C211yesmaximal, characteristic, complemented
2#13116398C211yesmaximal, characteristic, complemented
3#13116393C211yesmaximal, characteristic, complemented
4#13116072C211yesmaximal, characteristic
5#13116072C211yesmaximal, characteristic
6#13115536C211yesmaximal, characteristic
7#13115529C211yesmaximal, characteristic, complemented
8#13115522C211yesmaximal, characteristic
9#13115515C211yesmaximal, characteristic, complemented
10#13114851C211yesmaximal, characteristic, complemented
11#13114846C211yesmaximal, characteristic
12#13114841C211yesmaximal, characteristic, complemented
13#13114836C211yesmaximal, characteristic
14#13114693C211yesmaximal, characteristic, complemented
15C13×#2326C211yesmaximal, characteristic
16C2×C13×#124C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C13×#391C2211yescharacteristic
20C13×#390C2211yescharacteristic
21C13×#388—21no—
22C13×#388—21no—
23C13×#385—21no—
24C13×#385—21no—
25C13×#384C2211yescharacteristic
26C13×#376C2211yescharacteristic
27C2×#88075C2211yescharacteristic
28C2×#88075C2211yescharacteristic
29C2×#88075C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35#11718597C2211yescharacteristic
36#11718596C2211yescharacteristic
37#11718589C2211yescharacteristic
38#11718589C2211yescharacteristic
39#11718589C2211yescharacteristic
40#11718589C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43C2×#88043C2211yescharacteristic
44C2×C4×#1055C2211yescharacteristic
45#11718321—21no—
46#11718321—21no—
47#11718318—21no—
48#11718318—21no—
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C13×#124—22no—
63C13×#124—22no—
64C4×Q8×C13—22no—
65C4×Q8×C13—22no—
66C4×D4×C13—22no—
67C4×D4×C13—22no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C42×C13—21no—
79C2×C42×C13C2311yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C2×#6101—21no—
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C13×#95—21no—
97C13×#95—21no—
98C13×#95D411yescharacteristic
99C13×#95D411yescharacteristic
100C13×#95D411yescharacteristic
101C13×#95D411yescharacteristic
102#88075—22no—
103#88075—22no—
104#88075—41no—
105#88075—41no—
106#88072—22no—
107#88072—22no—
108#88072—41no—
109#88072—41no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116C4⋊#1055—22no—
117C4⋊#1055—22no—
118#88043—41no—
119C4×#1055—41no—
120#29134—131nomaximal, Sylow
121C24×C13—21no—
122C2×Q8×C13—21no—
123C2×Q8×C13—21no—
124C2×Q8×C13—21no—
125C2×Q8×C13—21no—
126C2×Q8×C13—21no—
127C2×Q8×C13#4112yes—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13#4112yes—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—42no—
138C22×C4×C13—81no—
139C22×C4×C13—81no—
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2411yescharacteristic
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—42no—
156C13×C4⋊C4—81no—
157C13×C4⋊C4—81no—
158C13×C22⋊C4—24no—
159C13×C22⋊C4—24no—
160C13×C22⋊C4—42no—
161C13×C22⋊C4—81no—
162C13×C22⋊C4—81no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—21no—
167C42×C13—42no—
168C42×C13#4112yes—
169C42×C13#4112yes—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—81no—
179C4⋊Dic13—81no—
180#6101—81no—
181#6101—81no—
182#6101—81no—
183#6101—81no—
184C2×#1055—21no—
185C2×#1055—21no—
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—
196#2647—131no—
197#2326D1311yescharacteristic
198#2100—131no—
199#2099—131no—
200#2042—131no—
201#2042—131no—
202#1936—131no—
203#1935—131no—
204#1934—131no—
205#1933—131no—
206#1805—131no—
207#1804—131no—
208#1803—131no—
209#1802—131no—
210#1768—131no—
211C23×C13—22no—
212C23×C13—41no—
213C23×C13—41no—
214C23×C13—41no—
215C23×C13—41no—
216C23×C13—41no—
217C23×C13—41no—
218C23×C13C22×D411yescharacteristic
219Q8×C13—22no—
220Q8×C13—22no—
221Q8×C13—41no—
222Q8×C13—41no—
223D4×C13—22no—
224D4×C13—22no—
225D4×C13—41no—
226D4×C13—41no—
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—22no—
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—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
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—84no—
253C2×C4×C13#12412yes—
254C2×C4×C13#12412yes—
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—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273#1055—41no—
274#1055—41no—
275#1055—41no—
276#1055—41no—
277C2×#124C2×D1311yescharacteristic
278C2×C4×Q8C2×D1311yescharacteristic
279C2×C4×D4C2×D1311yescharacteristic
280C2×C4⋊C8—131no—
281C2×C4⋊C8—131no—
282C2×#103—131no—
283C2×#103—131no—
284C2×#103—131no—
285C2×#103—131no—
286C2×#102—131no—
287C2×#102—131no—
288C2×#102—131no—
289C2×#102—131no—
290C2×#97—131no—
291C2×C4×C8—131no—
292#400—261no—
293#400—261no—
294#398—261no—
295#398—261no—
296#391C2×D1311yescharacteristic
297#390C2×D1311yescharacteristic
298#389—131no—
299#389—131no—
300#389—131no—
301#389—131no—
302#388—21no—
303#388—21no—
304#385—21no—
305#385—21no—
306#384—131no—
307#384C2×D1311yescharacteristic
308#382—131no—
309#376C2×D1311yescharacteristic
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#336—131no—
319#336—131no—
320C22×C13—42no—
321C22×C13—42no—
322C22×C13—42no—
323C22×C13—81no—
324C22×C13—81no—
325C22×C13—81no—
326C22×C13—81no—
327C22×C13#52511yescharacteristic
328C22×C13C2×#12411yescharacteristic
329C22×C13#53711yescharacteristic
330C22×C13#57611yescharacteristic
331C22×C13#57711yescharacteristic
332C22×C13#57711yescharacteristic
333C22×C13#57811yescharacteristic
334C4×C13—22no—
335C4×C13—22no—
336C4×C13—42no—
337C4×C13—41no—
338C4×C13—41no—
339C4×C13—41no—
340C4×C13—41no—
341C4×C13—81no—
342C4×C13—81no—
343C4×C13#55211yescharacteristic
344C4×C13#55211yescharacteristic
345C4×C13#55311yescharacteristic
346C4×C13#55311yescharacteristic
347Dic13—81no—
348Dic13—81no—
349Dic13—81no—
350Dic13—81no—
351C22×Q8C22×D1311yescharacteristic
352C22×D4C22×D1311yescharacteristic
353C23×C4—21no—
354C22×C8—131no—
355C22×C8—131no—
356C22×C8—131no—
357C22×C8—131no—
358#124—22no—
359#124—22no—
360C4×Q8—22no—
361C4×Q8—22no—
362C4×D4—22no—
363C4×D4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4C22×D1311yescharacteristic
378C2×C4⋊C4C22×D1311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C42—21no—
385C2×C42C22×D1311yescharacteristic
386C2×C42C22×D1311yescharacteristic
387C2×C42C22×D1311yescharacteristic
388C4⋊C8—262no—
389C4⋊C8—262no—
390#103—262no—
391#103—262no—
392#103—521no—
393#103—521no—
394#102—262no—
395#102—262no—
396#102—521no—
397#102—521no—
398#97—521no—
399C4×C8—521no—
400#95—21no—
401#95—21no—
402#95—261no—
403#95—261no—
404#95—261no—
405#95—261no—
406#95—261no—
407#95—261no—
408#95C22⋊D1311yescharacteristic
409#95C22⋊D1311yescharacteristic
410#95C22⋊D1311yescharacteristic
411#95C22⋊D1311yescharacteristic
412C2×C13—82no—
413C2×C13#256211yescharacteristic
414C2×C13#311911yescharacteristic
415C2×C13#312011yescharacteristic
416C2×C13#313611yescharacteristic
417C2×C13#313711yescharacteristic
418C2×C13#326211yescharacteristic
419C2×C13#326311yescharacteristic
420C24—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8#612712yes—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4#612712yes—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—42no—
437C22×C4—81no—
438C22×C4—81no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4C2×C22⋊D1311yescharacteristic
444C22×C4C2×C22⋊D1311yescharacteristic
445C22×C4C2×C22⋊D1311yescharacteristic
446C22×C4C2×C22⋊D1311yescharacteristic
447C22×C4C2×C22⋊D1311yescharacteristic
448C22×C4C2×C22⋊D1311yescharacteristic
449C22×C4C23×D1311yescharacteristic
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—42no—
467C4⋊C4—81no—
468C4⋊C4—81no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—1041no—
478C4⋊C4—1041no—
479C4⋊C4—1041no—
480C4⋊C4—1041no—
481C4⋊C4—1041no—
482C4⋊C4—1041no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—42no—
486C22⋊C4—81no—
487C22⋊C4—81no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—42no—
493C42#612912yes—
494C42#612912yes—
495C13#2913411yescharacteristic, complemented, Sylow
496C23—22no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23C22×C22⋊D1311yescharacteristic
504Q8—22no—
505Q8—22no—
506Q8—41no—
507Q8—41no—
508D4—22no—
509D4—22no—
510D4—41no—
511D4—41no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
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—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—84no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4#8819012yes—
551C2×C4#8819012yes—
552C2×C4C2×#612711yescharacteristic
553C2×C4C2×#612711yescharacteristic
554C2×C4C2×#612911yescharacteristic
555C2×C4C2×#612911yescharacteristic
556C2×C4#8825611yescharacteristic
557C2×C4#8825711yescharacteristic
558C8—521no—
559C8—521no—
560C8—521no—
561C8—521no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22#1171949611yescharacteristic
570C22C2×#8819011yescharacteristic
571C22#1171953811yescharacteristic
572C22#1171954011yescharacteristic
573C22#1171954111yescharacteristic
574C22#1171954211yescharacteristic
575C22#1171954311yescharacteristic
576C4—22no—
577C4—22no—
578C4—42no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—1041no—
586C4—1041no—
587C4—1041no—
588C4—1041no—
589C4#1171924611yescharacteristic
590C4#1171924611yescharacteristic
591C4#1171927011yescharacteristic
592C4#1171927011yescharacteristic
593C2—82no—
594C2#1312000211yescharacteristic
595C2#1312503511yescharacteristic
596C2#1312505011yescharacteristic
597C2#1312519011yescharacteristic
598C2#1312520111yescharacteristic
599C2#1312629211yescharacteristic
600C2#1312630111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2326C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenter#2326D13
hypocenterC13#29134
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ #376 ◁ #2326

Complements

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

NH ≅ G/Ntype
1. #13120811C2semidirect
2. #13116398C2semidirect
3. #13116393C2semidirect
7. #13115529C2semidirect
9. #13115515C2semidirect
10. #13114851C2semidirect
12. #13114841C2semidirect
14. #13114693C2semidirect
495. C13#29134semidirect

Maximal subgroups

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

subgroupindex
#131208112
#131163982
#131163932
#131160722
#131155362
#131155292
#131155222
#131155152
#131148512
#131148462
#131148412
#131148362
#131146932
C13×#23262
#2913413