Finite Group Databasebeta

← #15867260

Subgroups — #15867260

Order 3328.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718687C211yesmaximal, characteristic
2#13117300C211yesmaximal, characteristic
3#13115720C211yesmaximal, characteristic
4#13115693C211yesmaximal, characteristic
5#13115571C211yesmaximal, characteristic, complemented
6#13115566C211yesmaximal, characteristic, complemented
7#13115532C211yesmaximal, characteristic
8#13115529C211yesmaximal, characteristic, complemented
9#13115518C211yesmaximal, characteristic
10#13115515C211yesmaximal, characteristic, complemented
11#13114734C211yesmaximal, characteristic, complemented
12#13114666C211yesmaximal, characteristic, complemented
13#13114664C211yesmaximal, characteristic
14C4×#88043C211yesmaximal, characteristic, complemented
15C13×#2295C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17C22×#6106C2211yescharacteristic
18C2×C4×D52C2211yescharacteristic
19C2×#88126—21no—
20C13×#391C2211yescharacteristic
21C13×#391C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#387—21no—
25C13×#387—21no—
26C4×C13×C4⋊C4—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C13×#376—21no—
29C43×C13C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33#11718687C418yescomplemented
34C2×#88049C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40#11718601—21no—
41#11718601—21no—
42#11718600C2211yescharacteristic
43#11718600C2211yescharacteristic
44C4×#6103—21no—
45C4×C4⋊Dic13C2211yescharacteristic
46#11718589C2211yescharacteristic
47#11718589C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49C2×#88043C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51C2×#88043C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
53C2×C4×#1055C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×Q8×C13C2311yescharacteristic
61C22×D52C2311yescharacteristic
62C22×C4×D13—21no—
63C4×Q8×C13—22no—
64C4×Q8×C13C2×C414yes—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C42×C13—21no—
72C2×C42×C13—21no—
73C2×C42×C13D411yescharacteristic
74C2×C42×C13D411yescharacteristic
75C2×C42×C13D411yescharacteristic
76C2×C42×C13D411yescharacteristic
77C2×C42×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×#6106—22no—
81C2×#6106—22no—
82C2×#6106C2×C414yes—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×#6103—21no—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×#6101—21no—
92C2×#6101—21no—
93C2×C4×Dic13—21no—
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C4×D52—22no—
99C4×D52C2×C414yes—
100#88126—44no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108#88075—22no—
109#88075—22no—
110#88075C2×C414yes—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88049—22no—
115#88049—22no—
116#88049C2×C414yes—
117#88048—22no—
118#88047—22no—
119#88047C2×C414yes—
120#88043—22no—
121#88043—22no—
122#88043—22no—
123#88043C2×C414yes—
124C4×#1055—22no—
125C4×#1055—22no—
126#21288—131nomaximal, Sylow
127C23×D13—21no—
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13—21no—
132C2×Q8×C13—21no—
133C2×Q8×C13C22×C412yes—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2411yescharacteristic
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C2×D52—21no—
149C2×D52—21no—
150C2×D52—21no—
151C2×D52—21no—
152C2×D52—21no—
153C2×D52C22×C412yes—
154C2×C4×D13—24no—
155C2×C4×D13—42no—
156C2×C4×D13—42no—
157C13×C4⋊C4—24no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—42no—
164C13×C4⋊C4—42no—
165C13×C4⋊C4C22×C412yes—
166C42×C13—24no—
167C42×C13—22no—
168C42×C13—22no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—41no—
174C42×C13—41no—
175C42×C13—42no—
176C42×C13C22×C412yes—
177C42×C13#4112yes—
178#6106—28no—
179#6103—24no—
180#6103—42no—
181#6103—42no—
182#6103—42no—
183#6103—42no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13C22×C412yes—
190#6101—42no—
191#6101—42no—
192C4×Dic13—42no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055C22×C412yes—
200C2×#1055C22×C412yes—
201C2×#1055#4112yes—
202C2×#1055#4112yes—
203C2×#1055#4112yes—
204C2×#1055#4112yes—
205C2×#440—131no—
206#2295D1311yescharacteristic, complemented
207#2293—131no—
208#1973—131no—
209#1968—131no—
210#1943—131no—
211#1942—131no—
212#1936—131no—
213#1935—131no—
214#1934—131no—
215#1933—131no—
216#1776—131no—
217#1763—131no—
218#1762—131no—
219C4×#97—131no—
220C23×C13C22×D411yescharacteristic
221C22×D13—22no—
222C22×D13—41no—
223C22×D13—41no—
224C22×D13—41no—
225C22×D13—41no—
226C22×D13—41no—
227C22×D13—41no—
228Q8×C13—22no—
229Q8×C13—22no—
230Q8×C13—41no—
231Q8×C13—41no—
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—21no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13C4×D412yes—
259C2×C4×C13C4×D412yes—
260C2×C4×C13AGL(1,ℤ/8)12yes—
261C2×C4×C13#13712yes—
262C2×C4×C13C23×C411yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13C2×#4111yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×Dic13—22no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277D52—22no—
278D52—22no—
279D52—41no—
280D52—41no—
281C4×D13—48no—
282#1055—22no—
283#1055—22no—
284#1055—22no—
285#1055#11714yescomplemented
286C22×SD16—131no—
287C2×C4×Q8C2×D1311yescharacteristic
288C2×C4×D4—131no—
289C2×#117—261no—
290#440—138no—
291C2×#107—131no—
292C2×#107—131no—
293C2×#106—131no—
294C2×#103—131no—
295C2×#103—131no—
296C2×#103—131no—
297C2×#102—131no—
298C2×#102—131no—
299C2×#102—131no—
300C2×#97—131no—
301C2×#97—131no—
302C2×#97—131no—
303C2×#97—131no—
304C2×C4×C8—131no—
305C2×C4×C8—131no—
306#391C2×D1311yescharacteristic
307#391C2×D1311yescharacteristic
308#390—131no—
309#390—131no—
310#389—131no—
311#389—131no—
312#389C2×D1311yescharacteristic
313#389C2×D1311yescharacteristic
314#388—261no—
315#388—261no—
316#387—21no—
317#387—21no—
318C4×C4⋊C4—21no—
319C4×C4⋊C4—131no—
320C4×C4⋊C4C2×D1311yescharacteristic
321C4×C22⋊C4—261no—
322#376—21no—
323C43C2×D1311yescharacteristic
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330C22×C13C2×C4×D411yescharacteristic
331C22×C13#53211yescharacteristic
332C22×C13#53211yescharacteristic
333C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C13C2×#13711yescharacteristic
335C22×C13#57511yescharacteristic
336C22×C13#57511yescharacteristic
337C2×D13—42no—
338C2×D13—42no—
339C2×D13—42no—
340C2×D13—81no—
341C2×D13—81no—
342C2×D13—81no—
343C2×D13—81no—
344C4×C13—22no—
345C4×C13—22no—
346C4×C13—22no—
347C4×C13—22no—
348C4×C13—41no—
349C4×C13—41no—
350C4×C13—42no—
351C4×C13—42no—
352C4×C13—81no—
353C4×C13—81no—
354C4×C13C2×#11711yescharacteristic
355C4×C13C4×#4111yescharacteristic
356C4×C13#52911yescharacteristic
357C4×C13#52911yescharacteristic
358Dic13—42no—
359Dic13—81no—
360Dic13—81no—
361C22×Q8C22×D1311yescharacteristic
362C22×D4—131no—
363C23×C4—261no—
364C2×SD16—134no—
365C2×SD16—262no—
366C2×SD16—262no—
367C22×C8—131no—
368C22×C8—131no—
369C22×C8—131no—
370C22×C8—131no—
371C4×Q8—22no—
372C4×Q8C4×D1314yes—
373C4×D4—134no—
374C4×D4—262no—
375#117—524no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4C22×D1311yescharacteristic
385C2×C4⋊C4C22×D1311yescharacteristic
386C2×C4⋊C4C22×D1311yescharacteristic
387C2×C22⋊C4—261no—
388C2×C22⋊C4—261no—
389C2×C22⋊C4—261no—
390C2×C22⋊C4—261no—
391C2×C22⋊C4—261no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—261no—
395C2×C42C22⋊D1311yescharacteristic
396C2×C42C22⋊D1311yescharacteristic
397C2×C42C22⋊D1311yescharacteristic
398C2×C42C22⋊D1311yescharacteristic
399C2×C42C22×D1311yescharacteristic
400C2×C42C22×D1311yescharacteristic
401C2×C42C22×D1311yescharacteristic
402#107—134no—
403#107—262no—
404#106—262no—
405#103—134no—
406#103—262no—
407#103—262no—
408#102—134no—
409#102—262no—
410#102—262no—
411#97—134no—
412#97—262no—
413#97—262no—
414#97—262no—
415C4×C8—262no—
416C4×C8—262no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—261no—
425#95—261no—
426#95—261no—
427C2×C13#229311yescharacteristic
428C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
429C2×C13C4×#13711yescharacteristic
430C2×C13#318011yescharacteristic
431C2×C13#318111yescharacteristic
432C2×C13#318211yescharacteristic
433C2×C13#318311yescharacteristic
434D13—82no—
435C24—261no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8C2×C4×D1312yes—
442C2×D4—132no—
443C2×D4—261no—
444C2×D4—261no—
445C2×D4—261no—
446C2×D4—261no—
447C2×D4—261no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—261no—
453C22×C4—264no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—522no—
457C22×C4—522no—
458C22×C4C2×C22⋊D1311yescharacteristic
459C22×C4C2×C22⋊D1311yescharacteristic
460C22×C4C2×C22⋊D1311yescharacteristic
461C22×C4C2×C22⋊D1311yescharacteristic
462C22×C4C2×C22⋊D1311yescharacteristic
463C22×C4C2×C22⋊D1311yescharacteristic
464C22×C4C23×D1311yescharacteristic
465SD16—268no—
466C2×C8—132no—
467C2×C8—132no—
468C2×C8—132no—
469C2×C8—132no—
470C2×C8—132no—
471C2×C8—132no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C4⋊C4—24no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4—132no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—522no—
493C4⋊C4—522no—
494C4⋊C4C2×C4×D1312yes—
495C22⋊C4—264no—
496C22⋊C4—522no—
497C22⋊C4—522no—
498C22⋊C4—522no—
499C22⋊C4—522no—
500C42—24no—
501C42—22no—
502C42—22no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—41no—
508C42—41no—
509C42—42no—
510C42—522no—
511C42C2×C4×D1312yes—
512C42#612712yes—
513C13#2128811yescharacteristic, complemented, Sylow
514C23—262no—
515C23—521no—
516C23—521no—
517C23—521no—
518C23—521no—
519C23—521no—
520C23—521no—
521C23C22×C22⋊D1311yescharacteristic
522Q8—22no—
523Q8—22no—
524Q8—41no—
525Q8—41no—
526D4—262no—
527D4—262no—
528D4—521no—
529D4—521no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—262no—
557C2×C4—528no—
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×C4C4×C22⋊D1312yes—
567C2×C4C4×C22⋊D1312yes—
568C2×C4#8819612yes—
569C2×C4#8820312yes—
570C2×C4C22×C4×D1311yescharacteristic
571C2×C4C2×#612711yescharacteristic
572C2×C4#41×D1311yescharacteristic
573C2×C4#41×D1311yescharacteristic
574C2×C4#41×D1311yescharacteristic
575C2×C4#41×D1311yescharacteristic
576C8—134no—
577C8—262no—
578C8—262no—
579C8—262no—
580C22—522no—
581C22—522no—
582C22—522no—
583C22—1041no—
584C22—1041no—
585C22—1041no—
586C22—1041no—
587C22C2×C4×C22⋊D1311yescharacteristic
588C22C2×#8819611yescharacteristic
589C22C2×#8820311yescharacteristic
590C22#1171952711yescharacteristic
591C22#1171952711yescharacteristic
592C22#1171953711yescharacteristic
593C22#1171953711yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—42no—
599C4—42no—
600C4—41no—
601C4—41no—
602C4—81no—
603C4—81no—
604C4—522no—
605C4—1041no—
606C4—1041no—
607C4D13×#11711yescharacteristic
608C4#1171922711yescharacteristic
609C4#1171923311yescharacteristic
610C4#1171923311yescharacteristic
611C2—1042no—
612C2#1311729511yescharacteristic
613C2C4×#8820311yescharacteristic
614C2C4×#8819611yescharacteristic
615C2#1312553511yescharacteristic
616C2#1312553911yescharacteristic
617C2#1312555511yescharacteristic
618C2#1312555911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2295C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#2295D13
hypocenterC13#21288
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #2295

Complements

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

NH ≅ G/Ntype
5. #13115571C2semidirect
6. #13115566C2semidirect
8. #13115529C2semidirect
10. #13115515C2semidirect
11. #13114734C2semidirect
12. #13114666C2semidirect
14. C4×#88043C2semidirect
15. C13×#2295C2semidirect
33. #11718687C4semidirect
206. #2295D13semidirect
285. #1055#117semidirect
513. C13#21288semidirect

Maximal subgroups

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

subgroupindex
C2×#117186872
#131173002
#131157202
#131156932
#131155712
#131155662
#131155322
#131155292
#131155182
#131155152
#131147342
#131146662
#131146642
C4×#880432
C13×#22952
#2128813