Finite Group Databasebeta

← #15870554

Subgroups — #15870554

Order 3328.

988 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718551C211yesmaximal, characteristic
2#13117407C211yesmaximal, characteristic, complemented
3C4×#88147C211yesmaximal, characteristic
4#13115786C211yesmaximal, characteristic, complemented
5#13115598C211yesmaximal, characteristic, complemented
6#13115428C211yesmaximal, characteristic, complemented
7#13115100C211yesmaximal, characteristic
8#13115096C211yesmaximal, characteristic
9#13114835C211yesmaximal, characteristic
10#13114735C211yesmaximal, characteristic, complemented
11#13114732C211yesmaximal, characteristic, complemented
12#13114688C211yesmaximal, characteristic, complemented
13#13114660C211yesmaximal, characteristic
14#13114660C211yesmaximal, characteristic
15C13×#1921C211yesmaximal, characteristic, complemented
16C2×#88147C2211yescharacteristic
17C2×#88147C2211yescharacteristic
18C2×#88142C2211yescharacteristic
19C2×#88141—21no—
20C2×C4×D52C2211yescharacteristic
21C2×C42×D13—21no—
22C2×C13×#107C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C4×C13×C4⋊C4C2211yescharacteristic
25C2×#88061C2211yescharacteristic
26C2×#88061C2211yescharacteristic
27C2×#88057C2211yescharacteristic
28C2×#88055C2211yescharacteristic
29C2×#88055C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32#11718637C2211yescharacteristic
33C4⋊C4×Dic13C2211yescharacteristic
34C4⋊C4×Dic13C2211yescharacteristic
35C4⋊C4×Dic13C2211yescharacteristic
36C4⋊C4×Dic13C2211yescharacteristic
37#11718633—21no—
38C2×#88049C2211yescharacteristic
39C2×#88049C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C4×#6103—21no—
43C42×Dic13C2211yescharacteristic
44#11718589C2211yescharacteristic
45#11718551C418yescomplemented
46#11718327—21no—
47#11718327—21no—
48#11718310—21no—
49#11718307—21no—
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52C13×#340C2211yescharacteristic
53C13×#336C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×D52C2311yescharacteristic
61C22×C4×D13—21no—
62C22×C4×D13—21no—
63C22×C4×D13—21no—
64C22×Dic26—21no—
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C42×C13—21no—
73C2×C42×C13C2311yescharacteristic
74C2×#6103—21no—
75C2×#6103—21no—
76C2×#6103—21no—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×#6101—21no—
81C2×#6101—21no—
82C2×#6101—21no—
83C2×#6101—21no—
84C2×C4×Dic13—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13D411yescharacteristic
89C2×C4×Dic13D411yescharacteristic
90C2×C4×Dic13D411yescharacteristic
91C2×C4×Dic13D411yescharacteristic
92C2×C4×Dic13C2311yescharacteristic
93C2×C4×Dic13C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96#88147—22no—
97#88147—22no—
98#88147C2×C414yes—
99#88147Q814yescomplemented
100#88142—22no—
101#88142C2×C414yescomplemented
102#88141—44no—
103C4×D52—22no—
104C4×D52—22no—
105C42×D13—44no—
106C13×#107C2×C414yescomplemented
107C13×#95—21no—
108C13×#95—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88061—22no—
115#88061C2×C414yes—
116#88057—22no—
117#88055—22no—
118#88055—22no—
119#88054—22no—
120#88054C2×C414yescomplemented
121#88049—22no—
122#88049C2×C414yes—
123#88048—22no—
124#88047C2×C414yescomplemented
125#21613—131nomaximal, Sylow
126C23×D13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2411yescharacteristic
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13C2×D411yescharacteristic
138C22×Dic13C2×D411yescharacteristic
139C22×Dic13C2×D411yescharacteristic
140C22×Dic13C2×D411yescharacteristic
141C2×D52—21no—
142C2×D52—21no—
143C2×D52—21no—
144C2×D52C22×C412yes—
145C2×D52C2×Q812yes—
146C2×D52#4112yes—
147C2×C4×D13—24no—
148C2×C4×D13—24no—
149C2×C4×D13—24no—
150C2×C4×D13—42no—
151C2×C4×D13—42no—
152C2×C4×D13—42no—
153C2×C4×D13—42no—
154C2×C4×D13—42no—
155C2×C4×D13—42no—
156C2×Dic26—24no—
157C2×Dic26—42no—
158C2×Dic26—42no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13C22×C412yes—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—42no—
171C13×C4⋊C4C22×C412yes—
172C13×C4⋊C4C22×C412yes—
173C13×C4⋊C4C2×Q812yes—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—42no—
177#6103—24no—
178#6103—24no—
179#6103—24no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13C22×C412yes—
185C4⋊Dic13#4112yes—
186#6101—24no—
187#6101—42no—
188#6101—42no—
189#6101—42no—
190C4×Dic13—22no—
191C4×Dic13—22no—
192C4×Dic13—22no—
193C4×Dic13—41no—
194C4×Dic13—42no—
195C4×Dic13—42no—
196C4×Dic13—42no—
197C4×Dic13—42no—
198C4×Dic13C22×C412yes—
199C4×Dic13C2×Q812yes—
200C4×Dic13#4112yes—
201C4×Dic13#4112yes—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055C22×C412yes—
208C2×#474—131no—
209C4×C4⋊Q8—131no—
210C42×D4—131no—
211#1988—131no—
212#1948—131no—
213#1921—131no—
214#1921D1311yescharacteristic, complemented
215#1864—131no—
216#1864—131no—
217#1802—131no—
218#1776—131no—
219#1776—131no—
220#1767—131no—
221#1762—131no—
222#1762—131no—
223C23×C13C22×D411yescharacteristic
224C22×D13—22no—
225C22×D13—22no—
226C22×D13—22no—
227C22×D13—41no—
228C22×D13—41no—
229C22×D13—41no—
230C22×D13—41no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
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#13712yes—
249C2×C4×C13C23×C411yescharacteristic
250C2×C4×C13C22×Q811yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13C4×D412yes—
271C2×Dic13C4×D412yes—
272C2×Dic13C22⋊Q812yes—
273C2×Dic13C22⋊Q812yes—
274C2×Dic13AGL(1,ℤ/8)12yes—
275C2×Dic13AGL(1,ℤ/8)12yes—
276D52—22no—
277D52—22no—
278D52—22no—
279D52C4×Q814yescomplemented
280C4×D13—48no—
281C4×D13—48no—
282C4×D13—48no—
283Dic26—48no—
284C8×C13—22no—
285C8×C13—41no—
286#1055—22no—
287#1055—41no—
288C2×C4⋊Q8—131no—
289C2×C4×Q8—261no—
290C2×C4×D4—131no—
291C2×C4×D4—131no—
292C2×C4×D4—131no—
293C22×C42—261no—
294#474—138no—
295C2×#107—131no—
296C2×#107C2×D1311yescharacteristic
297C2×#106—131no—
298C2×#106—131no—
299C2×C4⋊C8—131no—
300C2×C4⋊C8—131no—
301C2×#102—131no—
302C2×#102—131no—
303C2×#102—131no—
304C2×#102—131no—
305C2×#97—131no—
306C2×#97—131no—
307#391—261no—
308#389—131no—
309#389—261no—
310#389C2×D1311yescharacteristic
311#384—131no—
312C4×C4⋊C4—131no—
313C4×C4⋊C4—131no—
314C4×C4⋊C4—131no—
315C4×C4⋊C4—131no—
316C4×C4⋊C4—261no—
317C4×C4⋊C4C2×D1311yescharacteristic
318C4×C22⋊C4—261no—
319C4×C22⋊C4—261no—
320C4×C22⋊C4—261no—
321C43—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#340C2×D1311yescharacteristic
328#340C2×D1311yescharacteristic
329#340C2×D1311yescharacteristic
330#336—131no—
331#336C2×D1311yescharacteristic
332C22×C13C2×C4×D411yescharacteristic
333C22×C13C2×C22⋊Q811yescharacteristic
334C22×C13#52511yescharacteristic
335C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
337C22×C13C2×#13711yescharacteristic
338C22×C13#57511yescharacteristic
339C2×D13—24no—
340C2×D13—42no—
341C2×D13—42no—
342C2×D13—42no—
343C2×D13—42no—
344C2×D13—42no—
345C2×D13—42no—
346C4×C13—22no—
347C4×C13—42no—
348C4×C13—41no—
349C4×C13—42no—
350C4×C13—42no—
351C4×C13—81no—
352C4×C13C2×C4×Q811yescharacteristic
353C4×C13C4×#4111yescharacteristic
354C4×C13#52911yescharacteristic
355C4×C13#53311yescharacteristic
356Dic13—22no—
357Dic13—22no—
358Dic13—22no—
359Dic13—42no—
360Dic13—42no—
361Dic13—81no—
362Dic13#44214yes—
363C22×Q8—261no—
364C22×D4—131no—
365C23×C4—261no—
366C23×C4—261no—
367C23×C4—261no—
368C22×C8—131no—
369C22×C8—131no—
370C22×C8C22×D1311yescharacteristic
371C22×C8C22×D1311yescharacteristic
372C4⋊Q8—134no—
373C4⋊Q8—262no—
374C4×Q8—524no—
375C4×D4—134no—
376C4×D4—134no—
377C4×D4—262no—
378C4×D4—262no—
379C4×D4—262no—
380C4×D4—262no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—131no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4C22×D1311yescharacteristic
390C2×C4⋊C4C22×D1311yescharacteristic
391C2×C4⋊C4C22×D1311yescharacteristic
392C2×C4⋊C4C22×D1311yescharacteristic
393C2×C22⋊C4—261no—
394C2×C22⋊C4—261no—
395C2×C22⋊C4—261no—
396C2×C42—21no—
397C2×C42—131no—
398C2×C42—131no—
399C2×C42—131no—
400C2×C42—131no—
401C2×C42—131no—
402C2×C42—131no—
403C2×C42—261no—
404C2×C42—261no—
405C2×C42—261no—
406C2×C42—261no—
407C2×C42—524no—
408C2×C42C22×D1311yescharacteristic
409#107—134no—
410#107C4×D1314yescomplemented
411#106—262no—
412#106—262no—
413C4⋊C8—134no—
414C4⋊C8—262no—
415#102—134no—
416#102—134no—
417#102—262no—
418#102—262no—
419#97—262no—
420#97—262no—
421#95—21no—
422#95—21no—
423#95—261no—
424#95—261no—
425#95—261no—
426#95—261no—
427#95—261no—
428C2×C13C4×C22⋊Q811yescharacteristic
429C2×C13C2×#44211yescharacteristic
430C2×C13C4×#13711yescharacteristic
431C2×C13#307711yescharacteristic
432C2×C13#307911yescharacteristic
433C2×C13#311011yescharacteristic
434C2×C13#311511yescharacteristic
435D13—44no—
436C24—261no—
437C2×Q8—264no—
438C2×Q8—522no—
439C2×Q8—522no—
440C2×D4—132no—
441C2×D4—132no—
442C2×D4—132no—
443C2×D4—261no—
444C2×D4—261no—
445C2×D4—261no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—131no—
453C22×C4—131no—
454C22×C4—264no—
455C22×C4—264no—
456C22×C4—264no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—522no—
461C22×C4—522no—
462C22×C4—522no—
463C22×C4—522no—
464C22×C4—522no—
465C22×C4—522no—
466C22×C4D4×D1311yescharacteristic
467C22×C4D4×D1311yescharacteristic
468C22×C4C23×D1311yescharacteristic
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—132no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8C2×C4×D1312yes—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—42no—
487C4⋊C4—132no—
488C4⋊C4—132no—
489C4⋊C4—264no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—522no—
495C4⋊C4—522no—
496C4⋊C4—522no—
497C4⋊C4C2×C4×D1312yes—
498C4⋊C4C2×C4×D1312yes—
499C4⋊C4Q8×D1312yes—
500C22⋊C4—264no—
501C22⋊C4—264no—
502C22⋊C4—264no—
503C42—21no—
504C42—21no—
505C42—42no—
506C42—132no—
507C42—132no—
508C42—132no—
509C42—132no—
510C42—262no—
511C42—262no—
512C42—262no—
513C42—521no—
514C42—522no—
515C42—522no—
516C42—522no—
517C42—522no—
518C13#2161311yescharacteristic, complemented, Sylow
519C23—262no—
520C23—262no—
521C23—262no—
522C23—521no—
523C23—521no—
524C23—521no—
525C23—521no—
526C23C2×D4×D1311yescharacteristic
527Q8—528no—
528D4—134no—
529D4—262no—
530D4—262no—
531D4—262no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—132no—
550C2×C4—132no—
551C2×C4—132no—
552C2×C4—132no—
553C2×C4—132no—
554C2×C4—132no—
555C2×C4—261no—
556C2×C4—261no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—261no—
560C2×C4—261no—
561C2×C4—262no—
562C2×C4—262no—
563C2×C4—528no—
564C2×C4—528no—
565C2×C4—528no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4#8817212yes—
574C2×C4C22×C4×D1311yescharacteristic
575C2×C4C2×Q8×D1311yescharacteristic
576C2×C4#41×D1311yescharacteristic
577C2×C4#41×D1311yescharacteristic
578C2×C4#41×D1311yescharacteristic
579C2×C4#41×D1311yescharacteristic
580C8—22no—
581C8—41no—
582C8—262no—
583C8—521no—
584C22—264no—
585C22—522no—
586C22—522no—
587C22—522no—
588C22—522no—
589C22—522no—
590C22—522no—
591C22C4×D4×D1311yescharacteristic
592C22D13×C22⋊Q811yescharacteristic
593C22#1171936111yescharacteristic
594C22C2×#8817211yescharacteristic
595C22#1171947311yescharacteristic
596C22D13×AGL(1,ℤ/8)11yescharacteristic
597C22D13×AGL(1,ℤ/8)11yescharacteristic
598C4—22no—
599C4—42no—
600C4—42no—
601C4—42no—
602C4—41no—
603C4—81no—
604C4—134no—
605C4—262no—
606C4—262no—
607C4—262no—
608C4—522no—
609C4—522no—
610C4—1041no—
611C4#1171922711yescharacteristic
612C4C4×Q8×D1311yescharacteristic
613C4#1171939311yescharacteristic
614C4#1171941111yescharacteristic
615C2—524no—
616C2#1311737011yescharacteristic
617C2D13×#44211yescharacteristic
618C2C4×#8817211yescharacteristic
619C2#1312463111yescharacteristic
620C2#1312465011yescharacteristic
621C2#1312493211yescharacteristic
622C2#1312498211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1921C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1921D13
hypocenterC13#21613
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
2. #13117407C2semidirect
4. #13115786C2semidirect
5. #13115598C2semidirect
6. #13115428C2semidirect
10. #13114735C2semidirect
11. #13114732C2semidirect
12. #13114688C2semidirect
15. C13×#1921C2semidirect
45. #11718551C4semidirect
99. #88147Q8semidirect
101. #88142C2×C4semidirect
106. C13×#107C2×C4semidirect
120. #88054C2×C4semidirect
124. #88047C2×C4semidirect
214. #1921D13semidirect
279. D52C4×Q8semidirect
410. #107C4×D13semidirect
518. C13#21613semidirect

Maximal subgroups

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

subgroupindex
C2×#117185512
#131174072
C4×#881472
#131157862
#131155982
#131154282
#131151002
#131150962
#131148352
#131147352
#131147322
#131146882
#131146602
C13×#19212
#2161313