Finite Group Databasebeta

← #15935645

Subgroups — #15935645

Order 3328.

700 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119247C211yesmaximal, characteristic
2#13116254C211yesmaximal, characteristic, complemented
3#13116231C211yesmaximal, characteristic, complemented
4#13116036C211yesmaximal, characteristic
5#13116029C211yesmaximal, characteristic
6#13115604C211yesmaximal, characteristic, complemented
7#13115566C211yesmaximal, characteristic, complemented
8#13115444C211yesmaximal, characteristic
9#13115418C211yesmaximal, characteristic, complemented
10#13115407C211yesmaximal, characteristic, complemented
11#13115090C211yesmaximal, characteristic, complemented
12#13115024C211yesmaximal, characteristic
13#13114922C211yesmaximal, characteristic
14C4×#88075C211yesmaximal, characteristic, complemented
15C13×#2360C211yesmaximal, characteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C13×#391C2211yescharacteristic
20C13×#389—21no—
21C13×#389C2211yescharacteristic
22C13×#387—21no—
23C13×#385—21no—
24C4×C13×C4⋊C4C2211yescharacteristic
25C4×C13×C22⋊C4—21no—
26C4×C13×C22⋊C4C2211yescharacteristic
27C2×#88075C2211yescharacteristic
28C2×#88075C2211yescharacteristic
29C2×#88075C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31#11718873C2211yescharacteristic
32#11718873C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C2×#88047C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39#11718613—21no—
40#11718605—21no—
41#11718597C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43#11718589C2211yescharacteristic
44#11718589C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47#11718319—21no—
48#11718312—21no—
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C13×C22⋊Q8—22no—
63C13×C22⋊Q8—22no—
64C4×Q8×C13—22no—
65C4×Q8×C13—41no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—41no—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4D411yescharacteristic
77C2×C13×C22⋊C4D411yescharacteristic
78C2×C42×C13—21no—
79C2×C42×C13—21no—
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×C22⋊Dic13—21no—
83C2×C22⋊Dic13—21no—
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×#6101—21no—
89C2×#6101—21no—
90C2×C4×Dic13—21no—
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C13×#95—21no—
96C13×#95—21no—
97C13×#95—21no—
98C13×#95—21no—
99C13×#95D411yescharacteristic
100C13×#95D411yescharacteristic
101#88075—22no—
102#88075—22no—
103#88075—22no—
104#88075—41no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112C22⋊#1055—22no—
113C22⋊#1055—41no—
114#88048—22no—
115#88047—22no—
116#88047—22no—
117#88047—41no—
118C4⋊#1055—22no—
119C4×#1055—41no—
120#27035—131nomaximal, Sylow
121C24×C13C2×D411yescharacteristic
122C2×Q8×C13—21no—
123C2×Q8×C13—21no—
124C2×Q8×C13—21no—
125C2×Q8×C13—21no—
126C2×Q8×C13—21no—
127C2×Q8×C13#4112yes—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—42no—
139C22×C4×C13—42no—
140C22×C4×C13—81no—
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—24no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—42no—
157C13×C4⋊C4—42no—
158C13×C4⋊C4—81no—
159C13×C4⋊C4#4112yes—
160C13×C4⋊C4#4112yes—
161C13×C22⋊C4—24no—
162C13×C22⋊C4—22no—
163C13×C22⋊C4—22no—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—21no—
167C42×C13—21no—
168C42×C13—42no—
169C42×C13—81no—
170C22⋊Dic13—42no—
171C22⋊Dic13—81no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180#6101—81no—
181#6101—81no—
182C4×Dic13—42no—
183C2×#1055—21no—
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#4112yes—
195#2495—131no—
196#2360D1311yescharacteristic
197#2074—131no—
198#2068—131no—
199#2036—131no—
200#2035—131no—
201#1949—131no—
202#1942—131no—
203#1923—131no—
204#1920—131no—
205#1918—131no—
206#1863—131no—
207#1852—131no—
208#1823—131no—
209C4×#103—131no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13#13512yes—
217C23×C13C22×D411yescharacteristic
218Q8×C13—22no—
219Q8×C13—22no—
220Q8×C13—41no—
221Q8×C13—41no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—22no—
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—41no—
240C2×C4×C13—41no—
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—84no—
253C2×C4×C13#13712yes—
254C2×C4×C13C2×#4111yescharacteristic
255C2×C4×C13C2×#4111yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C13H(5,𝔽2)11yescharacteristic
259C2×C4×C132−1+411yescharacteristic
260C2×Dic13—41no—
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—
272#1055—22no—
273#1055—41no—
274#1055—41no—
275#1055—41no—
276C2×C22⋊Q8C2×D1311yescharacteristic
277C2×C4×Q8C2×D1311yescharacteristic
278C22×C4⋊C4C2×D1311yescharacteristic
279C2×#107—131no—
280C2×#107—131no—
281C2×#107—131no—
282C2×#106—131no—
283C2×C4⋊C8—131no—
284C2×#103—131no—
285C2×#103—131no—
286C2×#103—131no—
287C2×#103—131no—
288C2×C22⋊C8—131no—
289C2×C22⋊C8—131no—
290C2×C4×C8—131no—
291#400—261no—
292#397—261no—
293#391C2×D1311yescharacteristic
294#389—21no—
295#389—131no—
296#389—131no—
297#389C2×D1311yescharacteristic
298#388—261no—
299#387—21no—
300#385—21no—
301#383—261no—
302#382—131no—
303#380—131no—
304#380—131no—
305C4×C4⋊C4—131no—
306C4×C4⋊C4C2×D1311yescharacteristic
307C4×C22⋊C4—21no—
308C4×C22⋊C4C2×D1311yescharacteristic
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#336—131no—
318#336—131no—
319C22×C13—22no—
320C22×C13—22no—
321C22×C13—22no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13—41no—
325C22×C13—41no—
326C22×C13#52511yescharacteristic
327C22×C13#54611yescharacteristic
328C22×C13#54711yescharacteristic
329C22×C13C2×#13511yescharacteristic
330C22×C13C2×#13711yescharacteristic
331C22×C13#57611yescharacteristic
332C22×C13#57811yescharacteristic
333C4×C13—22no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13—42no—
337C4×C13—41no—
338C4×C13—42no—
339C4×C13—41no—
340C4×C13—42no—
341C4×C13—81no—
342C4×C13#52911yescharacteristic
343C4×C13#53911yescharacteristic
344C4×C13#55311yescharacteristic
345C4×C13#55611yescharacteristic
346Dic13—81no—
347Dic13—81no—
348Dic13—81no—
349Dic13—81no—
350C22×Q8C22×D1311yescharacteristic
351C23×C4—21no—
352C23×C4C22×D1311yescharacteristic
353C22×C8—131no—
354C22×C8—131no—
355C22×C8—131no—
356C22×C8—131no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C4×Q8—22no—
360C4×Q8—41no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—41no—
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⋊C4C22×D1311yescharacteristic
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C4⋊C4C22×D1311yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—261no—
378C2×C22⋊C4—261no—
379C2×C22⋊C4C22⋊D1311yescharacteristic
380C2×C22⋊C4C22⋊D1311yescharacteristic
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—261no—
384C2×C42C22×D1311yescharacteristic
385C2×C42C22×D1311yescharacteristic
386#107—262no—
387#107—262no—
388#107—521no—
389#106—262no—
390C4⋊C8—262no—
391#103—262no—
392#103—262no—
393#103—262no—
394#103—521no—
395C22⋊C8—262no—
396C22⋊C8—521no—
397C4×C8—521no—
398#95—21no—
399#95—21no—
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#95—261no—
409#95C22⋊D1311yescharacteristic
410#95C22⋊D1311yescharacteristic
411C2×C13—42no—
412C2×C13#246611yescharacteristic
413C2×C13#310811yescharacteristic
414C2×C13#312411yescharacteristic
415C2×C13#329711yescharacteristic
416C2×C13#331211yescharacteristic
417C2×C13#333611yescharacteristic
418C2×C13#335711yescharacteristic
419C24C2×C22⋊D1311yescharacteristic
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8#612712yes—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—42no—
437C22×C4—42no—
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×C4C23×D1311yescharacteristic
449C2×C8—132no—
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—
461C4⋊C4—24no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—42no—
467C4⋊C4—42no—
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#612712yes—
480C4⋊C4#612912yes—
481C22⋊C4—24no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—522no—
485C22⋊C4—1041no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—42no—
491C42—81no—
492C42—522no—
493C13#2703511yescharacteristic, complemented, Sylow
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23#8820412yes—
501C23C22×C22⋊D1311yescharacteristic
502Q8—22no—
503Q8—22no—
504Q8—41no—
505Q8—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—84no—
537C2×C4—521no—
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#8819612yes—
550C2×C4C2×#612711yescharacteristic
551C2×C4C2×#612711yescharacteristic
552C2×C4C2×#612911yescharacteristic
553C2×C4#8825111yescharacteristic
554C2×C4#41×D1311yescharacteristic
555C2×C4#8825711yescharacteristic
556C8—262no—
557C8—521no—
558C8—521no—
559C8—521no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22#1171949611yescharacteristic
568C22#1171951111yescharacteristic
569C22C2×#8819611yescharacteristic
570C22C2×#8820411yescharacteristic
571C22#1171952911yescharacteristic
572C22#1171954011yescharacteristic
573C22#1171954311yescharacteristic
574C4—22no—
575C4—41no—
576C4—42no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—42no—
581C4—42no—
582C4—81no—
583C4—1041no—
584C4—1041no—
585C4—1041no—
586C4—1041no—
587C4#1171924311yescharacteristic
588C4#1171924711yescharacteristic
589C4#1171926311yescharacteristic
590C4#1171926911yescharacteristic
591C2—42no—
592C2#1311886611yescharacteristic
593C2#1312491611yescharacteristic
594C2#1312509811yescharacteristic
595C2#1312668611yescharacteristic
596C2#1312688711yescharacteristic
597C2#1312719811yescharacteristic
598C2#1312746211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2360C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2360D13
hypocenterC13#27035
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. #13116254C2semidirect
3. #13116231C2semidirect
6. #13115604C2semidirect
7. #13115566C2semidirect
9. #13115418C2semidirect
10. #13115407C2semidirect
11. #13115090C2semidirect
14. C4×#88075C2semidirect
493. C13#27035semidirect

Maximal subgroups

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

subgroupindex
#131192472
#131162542
#131162312
#131160362
#131160292
#131156042
#131155662
#131154442
#131154182
#131154072
#131150902
#131150242
#131149222
C4×#880752
C13×#23602
#2703513