Finite Group Databasebeta

← #15926864

Subgroups — #15926864

Order 3328.

748 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118543C211yesmaximal, characteristic
2#13117845C211yesmaximal, characteristic
3#13116402C211yesmaximal, characteristic, complemented
4#13116336C211yesmaximal, characteristic, complemented
5#13116215C211yesmaximal, characteristic, complemented
6#13115985C211yesmaximal, characteristic, complemented
7#13115790C211yesmaximal, characteristic, complemented
8#13115420C211yesmaximal, characteristic, complemented
9#13115270C211yesmaximal, characteristic
10#13115106C211yesmaximal, characteristic, complemented
11#13115031C211yesmaximal, characteristic
12#13115018C211yesmaximal, characteristic
13#13114839C211yesmaximal, characteristic, complemented
14#13114557C211yesmaximal, characteristic
15C13×#1873C211yesmaximal, characteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C2×Q8×Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×#6099C2211yescharacteristic
21C2×#88144C2211yescharacteristic
22C2×C13×#103C2211yescharacteristic
23C2×C13×#103C2211yescharacteristic
24C2×C13×C22⋊C8C2211yescharacteristic
25#11718891C2211yescharacteristic
26C2×#88075C2211yescharacteristic
27C2×#88075C2211yescharacteristic
28#11718873C2211yescharacteristic
29C4×C22⋊Dic13C2211yescharacteristic
30C2×#88057C2211yescharacteristic
31C2×#88057C2211yescharacteristic
32C2×#88054C2211yescharacteristic
33C2×#88054C2211yescharacteristic
34#11718646—21no—
35#11718646C2211yescharacteristic
36#11718646C2211yescharacteristic
37#11718642—21no—
38#11718637C2211yescharacteristic
39C4⋊C4×Dic13C2211yescharacteristic
40#11718634C2211yescharacteristic
41#11718611—21no—
42#11718610—21no—
43#11718609—21no—
44C22⋊C4×Dic13—21no—
45#11718594—21no—
46#11718589—21no—
47C13×#340C2211yescharacteristic
48C13×#340C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—21no—
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8Q814yes—
66C13×#117—22no—
67C13×#117—41no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C22⋊C4—21no—
73C2×C13×C22⋊C4—21no—
74C2×C42×C13—21no—
75C2×C22⋊Dic13—21no—
76C2×C22⋊Dic13D411yescharacteristic
77C2×C22⋊Dic13D411yescharacteristic
78Q8×Dic13—22no—
79Q8×Dic13—41no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—41no—
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C2×C4×Dic13C2311yescharacteristic
98C2×C4×Dic13C2311yescharacteristic
99C2×#6099—22no—
100C2×#6099—41no—
101C2×#6099—41no—
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104#88144—22no—
105#88144—41no—
106C13×#103—22no—
107C13×#103—41no—
108C13×C22⋊C8—22no—
109#88075—41no—
110#88075—41no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071D411yescharacteristic
119#88071D411yescharacteristic
120#88057—22no—
121#88057—41no—
122#88054—41no—
123#88054—41no—
124#26434—131nomaximal, Sylow
125C24×C13C2×D411yescharacteristic
126C2×Q8×C13—21no—
127C2×Q8×C13—21no—
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13C2×Q812yes—
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—21no—
139C22×C4×C13—21no—
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×Q812yes—
142C22×C4×C13#4112yes—
143C22×C4×C13C2411yescharacteristic
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—42no—
149C22×Dic13—42no—
150C22×Dic13—81no—
151C22×Dic13C2×D411yescharacteristic
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C13×C4⋊C4—24no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4C2×Q812yes—
167C13×C4⋊C4#4112yes—
168C13×C22⋊C4—24no—
169C13×C22⋊C4—42no—
170C42×C13—42no—
171C22⋊Dic13—22no—
172C22⋊Dic13—41no—
173C22⋊Dic13—81no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—42no—
182C4⋊Dic13—42no—
183C4⋊Dic13—42no—
184C4⋊Dic13—42no—
185C4⋊Dic13—81no—
186C4⋊Dic13#4112yes—
187#6101—42no—
188#6101—42no—
189#6101—81no—
190#6101—81no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—42no—
196C4×Dic13—81no—
197#6099—44no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204#2441—131no—
205#2360—131no—
206#2100—131no—
207#2088—131no—
208#2066—131no—
209#2026—131no—
210#1989—131no—
211#1920—131no—
212#1894—131no—
213#1873D1311yescharacteristic
214#1865—131no—
215#1853—131no—
216#1851—131no—
217#1803—131no—
218#1736—131no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13C22⋊Q812yes—
226C23×C13C22×D411yescharacteristic
227Q8×C13—22no—
228Q8×C13—22no—
229Q8×C13—41no—
230Q8×C13—41no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
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×C13C22⋊Q812yes—
250C2×C4×C13C22×Q811yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×C4×C13H(5,𝔽2)11yescharacteristic
255C2×C4×C13H(5,𝔽2)11yescharacteristic
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—22no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—84no—
280C2×Dic13#13712yes—
281C8×C13—41no—
282C8×C13—41no—
283#1055—41no—
284#1055—41no—
285C22×M16—131no—
286C2×#125—131no—
287C2×C22⋊Q8C2×D1311yescharacteristic
288C2×C4×Q8—131no—
289C2×#117C2×D1311yescharacteristic
290C22×C4⋊C4—131no—
291C2×#106—131no—
292C2×#106—131no—
293C2×C4⋊C8—131no—
294C2×C4⋊C8—131no—
295C2×#103—131no—
296C2×#103—131no—
297C2×#103C2×D1311yescharacteristic
298C2×#103C2×D1311yescharacteristic
299C2×C22⋊C8C2×D1311yescharacteristic
300#399—261no—
301#396—261no—
302#391—131no—
303#389—131no—
304#389—131no—
305#389—131no—
306#389—261no—
307#389—261no—
308#387—261no—
309#387—261no—
310#385—261no—
311#384—131no—
312#380—131no—
313C4×C4⋊C4—131no—
314C4×C22⋊C4—131no—
315C4×C22⋊C4—261no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340C2×D1311yescharacteristic
325#340C2×D1311yescharacteristic
326#336—131no—
327#336—131no—
328C22×C13—22no—
329C22×C13—22no—
330C22×C13—22no—
331C22×C13—41no—
332C22×C13—41no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13C2×C22⋊Q811yescharacteristic
336C22×C13#54611yescharacteristic
337C22×C13#54611yescharacteristic
338C22×C13C2×#13711yescharacteristic
339C22×C13#57511yescharacteristic
340C22×C13#57711yescharacteristic
341C22×C13#57711yescharacteristic
342C4×C13—22no—
343C4×C13—42no—
344C4×C13—42no—
345C4×C13—42no—
346C4×C13—81no—
347C4×C13#52911yescharacteristic
348C4×C13#53811yescharacteristic
349C4×C13#55411yescharacteristic
350C4×C13#55411yescharacteristic
351Dic13—22no—
352Dic13—41no—
353Dic13—41no—
354Dic13—41no—
355Dic13—42no—
356Dic13—81no—
357Dic13—81no—
358Dic13—81no—
359C22×Q8C22×D1311yescharacteristic
360C23×C4—261no—
361C23×C4C22×D1311yescharacteristic
362C2×M16—262no—
363C2×M16—521no—
364C2×M16—521no—
365C22×C8—131no—
366C22×C8—131no—
367C22×C8C22×D1311yescharacteristic
368C22×C8C22×D1311yescharacteristic
369#125—262no—
370#125—521no—
371C22⋊Q8—22no—
372C22⋊Q8Dic2614yes—
373C4×Q8—262no—
374C4×Q8—521no—
375#117—22no—
376#117—41no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—262no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—261no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4—521no—
393C2×C4⋊C4C22×D1311yescharacteristic
394C2×C4⋊C4C22×D1311yescharacteristic
395C2×C4⋊C4C22×D1311yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—131no—
399C2×C22⋊C4—131no—
400C2×C22⋊C4—261no—
401C2×C42—21no—
402C2×C42—131no—
403C2×C42—131no—
404C2×C42—261no—
405C2×C42—261no—
406#106—262no—
407#106—521no—
408C4⋊C8—521no—
409C4⋊C8—521no—
410#103—22no—
411#103—41no—
412#103—521no—
413#103—521no—
414C22⋊C8—22no—
415#95—131no—
416#95—131no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95—261no—
424C2×C13—42no—
425C2×C13#245011yescharacteristic
426C2×C13#307811yescharacteristic
427C2×C13#308411yescharacteristic
428C2×C13#331711yescharacteristic
429C2×C13#332011yescharacteristic
430C2×C13#332311yescharacteristic
431C2×C13#333111yescharacteristic
432C24D4×D1311yescharacteristic
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C2×Dic2612yes—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—131no—
448C22×C4—131no—
449C22×C4—131no—
450C22×C4—131no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—522no—
456C22×C4—522no—
457C22×C4—1041no—
458C22×C4C2×Dic2612yes—
459C22×C4D4×D1311yescharacteristic
460C22×C4#612912yes—
461C22×C4C23×D1311yescharacteristic
462M16—524no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C4⋊C4—24no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—132no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—522no—
489C4⋊C4—522no—
490C4⋊C4—522no—
491C4⋊C4—522no—
492C4⋊C4—522no—
493C4⋊C4—522no—
494C4⋊C4—1041no—
495C4⋊C4—1041no—
496C4⋊C4—1041no—
497C4⋊C4C2×Dic2612yes—
498C4⋊C4#612912yes—
499C22⋊C4—24no—
500C22⋊C4—42no—
501C22⋊C4—262no—
502C22⋊C4—521no—
503C22⋊C4—1041no—
504C42—42no—
505C42—261no—
506C42—261no—
507C42—261no—
508C42—261no—
509C42—522no—
510C42—1041no—
511C13#2643411yescharacteristic, complemented, Sylow
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23#8813212yes—
519C23C2×D4×D1311yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—41no—
523Q8—41no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
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—132no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—261no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—261no—
553C2×C4—261no—
554C2×C4—262no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—1044no—
567C2×C4#8813212yes—
568C2×C4C22×Dic2611yescharacteristic
569C2×C4C2×#612911yescharacteristic
570C2×C4C2×#612911yescharacteristic
571C2×C4#8825111yescharacteristic
572C2×C4#41×D1311yescharacteristic
573C2×C4#8825611yescharacteristic
574C8—41no—
575C8—41no—
576C8—521no—
577C8—521no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22C2×#8813211yescharacteristic
586C22#1171929611yescharacteristic
587C22#1171935911yescharacteristic
588C22#1171947511yescharacteristic
589C22#1171947511yescharacteristic
590C22D13×#13711yescharacteristic
591C22#1171948211yescharacteristic
592C4—22no—
593C4—42no—
594C4—42no—
595C4—42no—
596C4—81no—
597C4—262no—
598C4—521no—
599C4—521no—
600C4—522no—
601C4—521no—
602C4—1041no—
603C4—1041no—
604C4—1041no—
605C4#1171924411yescharacteristic
606C4#1171924811yescharacteristic
607C4#1171930511yescharacteristic
608C4#1171932211yescharacteristic
609C2—42no—
610C2#1311866411yescharacteristic
611C2#1312463811yescharacteristic
612C2#1312469611yescharacteristic
613C2#1312695511yescharacteristic
614C2#1312701011yescharacteristic
615C2#1312705011yescharacteristic
616C2#1312714511yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1873C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1873D13
hypocenterC13#26434
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
3. #13116402C2semidirect
4. #13116336C2semidirect
5. #13116215C2semidirect
6. #13115985C2semidirect
7. #13115790C2semidirect
8. #13115420C2semidirect
10. #13115106C2semidirect
13. #13114839C2semidirect
511. C13#26434semidirect

Maximal subgroups

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

subgroupindex
#131185432
#131178452
#131164022
#131163362
#131162152
#131159852
#131157902
#131154202
#131152702
#131151062
#131150312
#131150182
#131148392
#131145572
C13×#18732
#2643413