Finite Group Databasebeta

← #15866044

Subgroups — #15866044

Order 3328.

862 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#13117479C211yesmaximal, characteristic
2#13117201C211yesmaximal, characteristic, complemented
3#13115465C211yesmaximal, characteristic
4#13115458C211yesmaximal, characteristic
5#13115430C211yesmaximal, characteristic, complemented
6#13115409C211yesmaximal, characteristic, complemented
7#13115193C211yesmaximal, characteristic
8#13115193C211yesmaximal, characteristic
9#13115106C211yesmaximal, characteristic, complemented
10#13115092C211yesmaximal, characteristic, complemented
11#13114733C211yesmaximal, characteristic, complemented
12C4×#88075C211yesmaximal, characteristic, complemented
13C4×#88072C211yesmaximal, characteristic
14#13114589C211yesmaximal, characteristic, complemented
15C2×C13×#440C211yesmaximal, characteristic
16C22×C13×SD16C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C2×Q8×Dic13C2211yescharacteristic
20C2×Q8×Dic13C2211yescharacteristic
21C13×#440C418yescomplemented
22C2×C13×#107C2211yescharacteristic
23C2×C13×#103C2211yescharacteristic
24C2×C13×#102C2211yescharacteristic
25C2×C13×#97C2211yescharacteristic
26C2×#88075C2211yescharacteristic
27C2×#88075C2211yescharacteristic
28#11718882C2211yescharacteristic
29#11718882C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32#11718873—21no—
33#11718872—21no—
34C2×#88058C2211yescharacteristic
35C2×#88057C2211yescharacteristic
36#11718646C2211yescharacteristic
37#11718646C2211yescharacteristic
38C4⋊C4×Dic13—21no—
39C4⋊C4×Dic13—21no—
40C4⋊C4×Dic13C2211yescharacteristic
41C4⋊C4×Dic13C2211yescharacteristic
42#11718612—21no—
43#11718612—21no—
44C4×C4⋊Dic13—21no—
45C4×C4⋊Dic13C2211yescharacteristic
46C4×C4⋊Dic13C2211yescharacteristic
47#11718593—21no—
48#11718593C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×Q8×C13C2311yescharacteristic
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C2×C13×SD16—22no—
64C2×C13×SD16—22no—
65C2×C13×SD16C2×C414yes—
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C4×Q8×C13—22no—
69C4×Q8×C13C2×C414yes—
70C4×D4×C13—22no—
71C4×D4×C13C2×C414yes—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—21no—
76C2×C42×C13—21no—
77C2×C42×C13C2311yescharacteristic
78C2×C22⋊Dic13—21no—
79C2×C22⋊Dic13—21no—
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13—21no—
82Q8×Dic13—22no—
83Q8×Dic13—22no—
84Q8×Dic13—22no—
85Q8×Dic13—22no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4×Dic13—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13C2311yescharacteristic
101C2×C4×Dic13C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C13×#107C2×C414yes—
105C13×#103C2×C414yes—
106C13×#102C2×C414yes—
107C13×#97C2×C414yes—
108#88075—22no—
109#88075—22no—
110#88072—22no—
111#88072—22no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071D411yescharacteristic
119#88071D411yescharacteristic
120#88071D411yescharacteristic
121#88071D411yescharacteristic
122#88058—22no—
123#88057—22no—
124C4×#1055—22no—
125#21128—131nomaximal, Sylow
126C24×C13—21no—
127C2×Q8×C13—21no—
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13C22×C412yes—
131C2×Q8×C13#4112yes—
132C2×Q8×C13#4112yes—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13C22×C412yes—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—24no—
143C22×C4×C13—81no—
144C22×C4×C13—81no—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2411yescharacteristic
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155C22×Dic13C2×D411yescharacteristic
156C13×SD16—28no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13C22×C412yes—
162C2×C8×C13C22×C412yes—
163C13×C4⋊C4—24no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4C22×C412yes—
167C13×C4⋊C4C22×C412yes—
168C13×C22⋊C4—24no—
169C42×C13—24no—
170C42×C13C22×C412yes—
171C42×C13#4112yes—
172C22⋊Dic13—81no—
173C22⋊Dic13—81no—
174C22⋊Dic13—81no—
175C22⋊Dic13—81no—
176C4⋊Dic13—24no—
177C4⋊Dic13—24no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—81no—
185C4⋊Dic13—81no—
186C4⋊Dic13#4112yes—
187C4⋊Dic13#4112yes—
188C4×Dic13—24no—
189C4×Dic13—24no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—81no—
195C4×Dic13—81no—
196C4×Dic13—81no—
197C4×Dic13—81no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#440D1311yescharacteristic
205#2319—131no—
206#2276—131no—
207#1926—131no—
208#1925—131no—
209#1921—131no—
210#1918—131no—
211#1880—131no—
212#1880—131no—
213#1865—131no—
214#1863—131no—
215#1776—131no—
216C4×#103—131no—
217C4×#102—131no—
218#1746—131no—
219C23×C13—22no—
220C23×C13—41no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13—41no—
226C23×C13C22×D411yescharacteristic
227Q8×C13—22no—
228Q8×C13—22no—
229Q8×C13—22no—
230Q8×C13#11714yes—
231D4×C13—22no—
232D4×C13—22no—
233D4×C13—41no—
234D4×C13—41no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—84no—
249C2×C4×C13C4×D412yes—
250C2×C4×C13C4×D412yes—
251C2×C4×C13C23×C411yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C2×C4×C13C2×#4111yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
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—41no—
280C2×Dic13—41no—
281C8×C13—22no—
282C8×C13—22no—
283#1055—41no—
284#1055—41no—
285C22×SD16C2×D1311yescharacteristic
286C2×C4×Q8—131no—
287C2×C4×Q8—131no—
288C2×C4×Q8C2×D1311yescharacteristic
289C2×C4×D4C2×D1311yescharacteristic
290#440Dic1318yescomplemented
291C2×#107—131no—
292C2×#107C2×D1311yescharacteristic
293C2×#106—131no—
294C2×#103—131no—
295C2×#103—131no—
296C2×#103C2×D1311yescharacteristic
297C2×#102—131no—
298C2×#102—131no—
299C2×#102C2×D1311yescharacteristic
300C2×#97C2×D1311yescharacteristic
301C2×C4×C8—131no—
302#390—131no—
303#390—131no—
304#389—131no—
305#389—131no—
306#388—261no—
307#388—261no—
308#381—261no—
309#380—261no—
310C4×C4⋊C4—131no—
311C4×C4⋊C4—131no—
312C4×C4⋊C4—131no—
313C4×C4⋊C4—131no—
314C4×C4⋊C4—261no—
315C4×C4⋊C4—261no—
316C4×C4⋊C4—261no—
317#376—131no—
318#376—261no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#336—131no—
326#336—131no—
327#336—131no—
328#336—131no—
329C22×C13—42no—
330C22×C13—42no—
331C22×C13—42no—
332C22×C13—81no—
333C22×C13—81no—
334C22×C13—81no—
335C22×C13—81no—
336C22×C13C2×C4×D411yescharacteristic
337C22×C13#52511yescharacteristic
338C22×C13#52511yescharacteristic
339C22×C13#57611yescharacteristic
340C22×C13#57711yescharacteristic
341C22×C13#57711yescharacteristic
342C22×C13#57811yescharacteristic
343C4×C13—22no—
344C4×C13—22no—
345C4×C13—24no—
346C4×C13—42no—
347C4×C13—42no—
348C4×C13C2×#11711yescharacteristic
349C4×C13C4×#4111yescharacteristic
350C4×C13#52911yescharacteristic
351C4×C13#52911yescharacteristic
352Dic13—41no—
353Dic13—42no—
354Dic13—41no—
355Dic13—41no—
356Dic13—42no—
357Dic13—41no—
358Dic13—81no—
359Dic13—81no—
360C22×Q8C22×D1311yescharacteristic
361C22×D4C22×D1311yescharacteristic
362C23×C4—21no—
363C2×SD16—22no—
364C2×SD16—22no—
365C2×SD16C2×Dic1314yes—
366C22×C8—131no—
367C22×C8—131no—
368C22×C8C22×D1311yescharacteristic
369C22×C8C22×D1311yescharacteristic
370C4×Q8—22no—
371C4×Q8—262no—
372C4×Q8—262no—
373C4×Q8—262no—
374C4×Q8—262no—
375C4×Q8C2×Dic1314yes—
376C4×D4—22no—
377C4×D4C2×Dic1314yes—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4C22×D1311yescharacteristic
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—261no—
391C2×C22⋊C4—261no—
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C42—21no—
395C2×C42—131no—
396C2×C42—131no—
397C2×C42—261no—
398C2×C42—261no—
399C2×C42—261no—
400C2×C42—261no—
401C2×C42—261no—
402C2×C42—261no—
403C2×C42C22×D1311yescharacteristic
404#107—262no—
405#107C2×Dic1314yes—
406#106—262no—
407#103—262no—
408#103—262no—
409#103C2×Dic1314yes—
410#102—262no—
411#102—262no—
412#102C2×Dic1314yes—
413#97C2×Dic1314yes—
414C4×C8—262no—
415#95—131no—
416#95—131no—
417#95—131no—
418#95—131no—
419#95—261no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95—261no—
424#95—261no—
425C2×C13—82no—
426C2×C13#229011yescharacteristic
427C2×C13#294611yescharacteristic
428C2×C13#294711yescharacteristic
429C2×C13#311911yescharacteristic
430C2×C13#312111yescharacteristic
431C2×C13#312411yescharacteristic
432C2×C13#312611yescharacteristic
433C24—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8#612712yes—
438C2×Q8#612712yes—
439C2×Q8C22×Dic1312yes—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4C22×Dic1312yes—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—24no—
450C22×C4—81no—
451C22×C4—81no—
452C22×C4—131no—
453C22×C4—131no—
454C22×C4—131no—
455C22×C4—131no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4D4×D1311yescharacteristic
461C22×C4D4×D1311yescharacteristic
462C22×C4C23×D1311yescharacteristic
463SD16—28no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8C22×Dic1312yes—
475C2×C8C22×Dic1312yes—
476C4⋊C4—24no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—132no—
480C4⋊C4—132no—
481C4⋊C4—264no—
482C4⋊C4—264no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—1041no—
490C4⋊C4—1041no—
491C4⋊C4C22×Dic1312yes—
492C4⋊C4C22×Dic1312yes—
493C22⋊C4—24no—
494C22⋊C4—1041no—
495C22⋊C4—1041no—
496C22⋊C4—1041no—
497C22⋊C4—1041no—
498C42—24no—
499C42—264no—
500C42—264no—
501C42—261no—
502C42—261no—
503C42—261no—
504C42—261no—
505C42—1041no—
506C42—1041no—
507C42—1041no—
508C42—1041no—
509C42#612912yes—
510C42C22×Dic1312yes—
511C13#2112811yescharacteristic, complemented, Sylow
512C23—22no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23C2×D4×D1311yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—22no—
523Q8#8818014yes—
524D4—22no—
525D4—22no—
526D4—41no—
527D4—41no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—84no—
542C2×C4—261no—
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—262no—
553C2×C4—262no—
554C2×C4—261no—
555C2×C4—261no—
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×C4D4×Dic1312yes—
567C2×C4D4×Dic1312yes—
568C2×C4C2×#612711yescharacteristic
569C2×C4C2×#612711yescharacteristic
570C2×C4C2×#612911yescharacteristic
571C2×C4#41×D1311yescharacteristic
572C2×C4#41×D1311yescharacteristic
573C2×C4C23×Dic1311yescharacteristic
574C8—22no—
575C8—22no—
576C8—521no—
577C8—521no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22#1171925211yescharacteristic
586C22#1171925211yescharacteristic
587C22#1171947911yescharacteristic
588C22#1171948011yescharacteristic
589C22#1171948311yescharacteristic
590C22#1171948411yescharacteristic
591C22C2×D4×Dic1311yescharacteristic
592C4—22no—
593C4—22no—
594C4—24no—
595C4—42no—
596C4—42no—
597C4—521no—
598C4—521no—
599C4—522no—
600C4—521no—
601C4—521no—
602C4—522no—
603C4—1041no—
604C4—1041no—
605C4#1171924311yescharacteristic
606C4#1171924311yescharacteristic
607C4C2×#8818011yescharacteristic
608C4#41×Dic1311yescharacteristic
609C2—82no—
610C2#1311728111yescharacteristic
611C2#1312366911yescharacteristic
612C2#1312368011yescharacteristic
613C2#1312503311yescharacteristic
614C2#1312506311yescharacteristic
615C2#1312509611yescharacteristic
616C2#1312512611yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#440C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenterC2×#440D13
hypocenterC13#21128
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. #13117201C2semidirect
5. #13115430C2semidirect
6. #13115409C2semidirect
9. #13115106C2semidirect
10. #13115092C2semidirect
11. #13114733C2semidirect
12. C4×#88075C2semidirect
14. #13114589C2semidirect
21. C13×#440C4semidirect
290. #440Dic13semidirect
511. C13#21128semidirect

Maximal subgroups

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

subgroupindex
#131174792
#131172012
#131154652
#131154582
#131154302
#131154092
#131151932
#131151062
#131150922
#131147332
C4×#880752
C4×#880722
#131145892
C2×C13×#4402
#2112813