Finite Group Databasebeta

← #15875004

Subgroups — #15875004

Order 3328.

796 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718508C211yesmaximal, characteristic
2C4×#88124C211yesmaximal, characteristic, complemented
3#13117300C211yesmaximal, characteristic
4#13115791C211yesmaximal, characteristic, complemented
5#13115606C211yesmaximal, characteristic, complemented
6#13115569C211yesmaximal, characteristic, complemented
7#13115564C211yesmaximal, characteristic, complemented
8#13115519C211yesmaximal, characteristic
9#13115519C211yesmaximal, characteristic
10#13115464C211yesmaximal, characteristic
11#13115457C211yesmaximal, characteristic
12#13115429C211yesmaximal, characteristic, complemented
13#13115422C211yesmaximal, characteristic, complemented
14#13114847C211yesmaximal, characteristic
15C4×C13×C4⋊C8C211yesmaximal, characteristic, complemented
16C2×C4×D52C2211yescharacteristic
17C2×#88126—21no—
18C2×#88124C2211yescharacteristic
19C2×C13×C4⋊C8C2211yescharacteristic
20C2×C13×C4⋊C8C2211yescharacteristic
21C2×C4×C8×C13C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C43×C13C2211yescharacteristic
24C2×#88061C2211yescharacteristic
25C2×#88061C2211yescharacteristic
26C2×#88061C2211yescharacteristic
27C2×#88061C2211yescharacteristic
28C2×#88058C2211yescharacteristic
29C2×#88058C2211yescharacteristic
30C2×#88057C2211yescharacteristic
31C2×#88057C2211yescharacteristic
32#11718601—21no—
33#11718601—21no—
34#11718600C2211yescharacteristic
35#11718600C2211yescharacteristic
36C4×#6103—21no—
37#11718597C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40C4×C4⋊Dic13C2211yescharacteristic
41#11718594—21no—
42#11718594—21no—
43C4×#6101—21no—
44C4×#6101—21no—
45#11718589C2211yescharacteristic
46#11718589C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49#11718508C418yescomplemented
50C13×#336C2211yescharacteristic
51C13×#336C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60C22×D52C2311yescharacteristic
61C22×C4×D13—21no—
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C2×C42×C13D411yescharacteristic
67C2×C42×C13D411yescharacteristic
68C2×C42×C13D411yescharacteristic
69C2×C42×C13D411yescharacteristic
70C2×C42×C13C2311yescharacteristic
71C2×C42×C13C2311yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×#6103—21no—
74C2×#6103—21no—
75C2×#6103—21no—
76C2×#6103—21no—
77C2×#6103—21no—
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×#6101—21no—
86C2×#6101—21no—
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13—21no—
94C4×D52—22no—
95C4×D52C2×C414yes—
96#88126—44no—
97#88124—22no—
98#88124C2×C414yes—
99C13×C4⋊C8—22no—
100C13×C4⋊C8C2×C414yes—
101C4×C8×C13—41no—
102C4×C8×C13—41no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88061—41no—
113#88061—41no—
114#88061C2×C414yes—
115#88061C2×C414yes—
116#88058—41no—
117#88058C2×C414yes—
118#88057—41no—
119#88057C2×C414yes—
120#22114—131nomaximal, Sylow
121C23×D13—21no—
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2×D411yescharacteristic
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2411yescharacteristic
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C2×D52—21no—
137C2×D52—21no—
138C2×D52—21no—
139C2×D52—21no—
140C2×D52—21no—
141C2×D52C22×C412yes—
142C2×C4×D13—24no—
143C2×C4×D13—42no—
144C2×C4×D13—42no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13C22×C412yes—
156C2×C8×C13C22×C412yes—
157C42×C13—22no—
158C42×C13—22no—
159C42×C13—22no—
160C42×C13—21no—
161C42×C13—21no—
162C42×C13—21no—
163C42×C13—21no—
164C42×C13—41no—
165C42×C13C22×C412yes—
166C42×C13#4112yes—
167#6103—24no—
168#6103—42no—
169#6103—42no—
170#6103—42no—
171#6103—42no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13C22×C412yes—
184C4⋊Dic13C22×C412yes—
185C4⋊Dic13C22×C412yes—
186#6101—24no—
187#6101—24no—
188#6101—42no—
189#6101—42no—
190#6101—42no—
191#6101—42no—
192C4×Dic13—42no—
193C4×Dic13—42no—
194C4×Dic13—42no—
195C2×#478—131no—
196C4×#125—131no—
197#2293—131no—
198#1989—131no—
199#1949—131no—
200#1942—131no—
201#1941—131no—
202#1934—131no—
203#1934—131no—
204#1926—131no—
205#1925—131no—
206#1921—131no—
207#1920—131no—
208#1804—131no—
209C4×C4⋊C8D1311yescharacteristic, complemented
210C23×C13C22×D411yescharacteristic
211C22×D13—22no—
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—41no—
215C22×D13—41no—
216C22×D13—41no—
217C22×D13—41no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13C4×D412yes—
232C2×C4×C13C4×D412yes—
233C2×C4×C13#13512yes—
234C2×C4×C13#13512yes—
235C2×C4×C13AGL(1,ℤ/8)12yes—
236C2×C4×C13C23×C411yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C2×C4×C13H(5,𝔽2)11yescharacteristic
239C2×C4×C132−1+411yescharacteristic
240C2×C4×C132−1+411yescharacteristic
241C2×C4×C132−1+411yescharacteristic
242C2×Dic13—22no—
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—41no—
246C2×Dic13—41no—
247C2×Dic13—41no—
248C2×Dic13—41no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263D52—22no—
264D52—22no—
265D52—41no—
266D52—41no—
267C4×D13—48no—
268C8×C13—22no—
269C8×C13—22no—
270C8×C13—41no—
271C8×C13—41no—
272C2×#125—131no—
273C2×C4×D4—131no—
274C2×#117—261no—
275#478—138no—
276C2×#107—131no—
277C2×#107—131no—
278C2×#106—131no—
279C2×#106—131no—
280C2×C4⋊C8C2×D1311yescharacteristic
281C2×C4⋊C8C2×D1311yescharacteristic
282C2×#102—131no—
283C2×#102—131no—
284C2×#102—131no—
285C2×#102—131no—
286C2×C4×C8C2×D1311yescharacteristic
287C2×C4×C8C2×D1311yescharacteristic
288#390—131no—
289#390—131no—
290#389—131no—
291#389—131no—
292#389—131no—
293#389—131no—
294#388—261no—
295#388—261no—
296#387—261no—
297#387—261no—
298#382—131no—
299C4×C4⋊C4—131no—
300C4×C4⋊C4—131no—
301C4×C4⋊C4—131no—
302C4×C4⋊C4—261no—
303C4×C4⋊C4—261no—
304C4×C22⋊C4—261no—
305C43C2×D1311yescharacteristic
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#336C2×D1311yescharacteristic
315#336C2×D1311yescharacteristic
316C22×C13C2×C4×D411yescharacteristic
317C22×C13#53611yescharacteristic
318C22×C13#53711yescharacteristic
319C22×C13C2×#13511yescharacteristic
320C22×C13C2×#13511yescharacteristic
321C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
322C22×C13#57511yescharacteristic
323C2×D13—42no—
324C2×D13—42no—
325C2×D13—42no—
326C2×D13—81no—
327C2×D13—81no—
328C2×D13—81no—
329C2×D13—81no—
330C4×C13—22no—
331C4×C13—22no—
332C4×C13—22no—
333C4×C13—22no—
334C4×C13—22no—
335C4×C13—41no—
336C4×C13#51911yescharacteristic
337C4×C13#52011yescharacteristic
338C4×C13#54111yescharacteristic
339C4×C13#54211yescharacteristic
340Dic13—42no—
341Dic13—42no—
342Dic13—42no—
343Dic13—81no—
344Dic13—81no—
345Dic13—81no—
346Dic13—81no—
347C22×D4—131no—
348C23×C4—261no—
349C22×C8C22×D1311yescharacteristic
350C22×C8C22×D1311yescharacteristic
351C22×C8C22×D1311yescharacteristic
352C22×C8C22×D1311yescharacteristic
353#125—134no—
354#125—262no—
355C4×D4—134no—
356C4×D4—262no—
357#117—524no—
358C2×C4⋊C4—131no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4—261no—
371C2×C22⋊C4—261no—
372C2×C22⋊C4—261no—
373C2×C22⋊C4—261no—
374C2×C22⋊C4—261no—
375C2×C22⋊C4—261no—
376C2×C42—261no—
377C2×C42—261no—
378C2×C42—261no—
379C2×C42D5211yescharacteristic
380C2×C42D5211yescharacteristic
381C2×C42D5211yescharacteristic
382C2×C42D5211yescharacteristic
383C2×C42C22×D1311yescharacteristic
384C2×C42C22×D1311yescharacteristic
385C2×C42C22×D1311yescharacteristic
386#107—134no—
387#107—521no—
388#106—134no—
389#106—521no—
390C4⋊C8—22no—
391C4⋊C8C4×D1314yes—
392#102—134no—
393#102—134no—
394#102—521no—
395#102—521no—
396C4×C8—41no—
397C4×C8—41no—
398#95—261no—
399#95—261no—
400#95—261no—
401#95—261no—
402#95—261no—
403#95—261no—
404#95—261no—
405#95—261no—
406#95—261no—
407C2×C13#232311yescharacteristic
408C2×C13C4×#13511yescharacteristic
409C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
410C2×C13#322811yescharacteristic
411C2×C13#323211yescharacteristic
412C2×C13#324711yescharacteristic
413C2×C13#325011yescharacteristic
414D13—82no—
415C24—261no—
416C2×D4—132no—
417C2×D4—261no—
418C2×D4—261no—
419C2×D4—261no—
420C2×D4—261no—
421C2×D4—261no—
422C22×C4—261no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4—264no—
426C22×C4—261no—
427C22×C4—261no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—522no—
431C22×C4—522no—
432C22×C4C2×D5211yescharacteristic
433C22×C4C2×D5211yescharacteristic
434C22×C4C2×D5211yescharacteristic
435C22×C4C2×D5211yescharacteristic
436C22×C4C2×D5211yescharacteristic
437C22×C4C2×D5211yescharacteristic
438C22×C4C23×D1311yescharacteristic
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8C2×C4×D1312yes—
450C2×C8C2×C4×D1312yes—
451C4⋊C4—132no—
452C4⋊C4—132no—
453C4⋊C4—132no—
454C4⋊C4—264no—
455C4⋊C4—264no—
456C4⋊C4—261no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—522no—
468C4⋊C4—522no—
469C4⋊C4—522no—
470C4⋊C4—522no—
471C22⋊C4—264no—
472C22⋊C4—522no—
473C22⋊C4—522no—
474C22⋊C4—522no—
475C22⋊C4—522no—
476C42—22no—
477C42—22no—
478C42—22no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—41no—
484C42—522no—
485C42—522no—
486C42—522no—
487C42C2×C4×D1312yes—
488C42#612712yes—
489C13#2211411yescharacteristic, complemented, Sylow
490C23—262no—
491C23—521no—
492C23—521no—
493C23—521no—
494C23—521no—
495C23—521no—
496C23—521no—
497C23C22×D5211yescharacteristic
498D4—262no—
499D4—262no—
500D4—521no—
501D4—521no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—262no—
516C2×C4—262no—
517C2×C4—262no—
518C2×C4—528no—
519C2×C4—521no—
520C2×C4—521no—
521C2×C4—521no—
522C2×C4—521no—
523C2×C4—521no—
524C2×C4—521no—
525C2×C4—521no—
526C2×C4—521no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4C4×D5212yes—
538C2×C4C4×D5212yes—
539C2×C4#8815812yes—
540C2×C4#8815812yes—
541C2×C4#8816212yes—
542C2×C4C22×C4×D1311yescharacteristic
543C2×C4C2×#612711yescharacteristic
544C2×C4#8825111yescharacteristic
545C2×C4#8825411yescharacteristic
546C2×C4#8825711yescharacteristic
547C2×C4#8825711yescharacteristic
548C8—22no—
549C8—22no—
550C8—41no—
551C8—41no—
552C22—522no—
553C22—522no—
554C22—522no—
555C22—1041no—
556C22—1041no—
557C22—1041no—
558C22—1041no—
559C22C2×C4×D5211yescharacteristic
560C22#1171921511yescharacteristic
561C22#1171923111yescharacteristic
562C22C2×#8815811yescharacteristic
563C22C2×#8815811yescharacteristic
564C22C2×#8816211yescharacteristic
565C22#1171945311yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—22no—
570C4—22no—
571C4—41no—
572C4—522no—
573C4—522no—
574C4—522no—
575C4—1041no—
576C4—1041no—
577C4—1041no—
578C4—1041no—
579C4#1171925111yescharacteristic
580C4#1171926611yescharacteristic
581C4#1171927711yescharacteristic
582C4#1171928811yescharacteristic
583C2—1042no—
584C2#1311751911yescharacteristic
585C2C4×#8815811yescharacteristic
586C2C4×#8816211yescharacteristic
587C2#1312597411yescharacteristic
588C2#1312600611yescharacteristic
589C2#1312616311yescharacteristic
590C2#1312618811yescharacteristic
subgroupG/H
centerC23C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×C4⋊C8C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenterC4×C4⋊C8D13
hypocenterC13#22114
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#88124C2semidirect
4. #13115791C2semidirect
5. #13115606C2semidirect
6. #13115569C2semidirect
7. #13115564C2semidirect
12. #13115429C2semidirect
13. #13115422C2semidirect
15. C4×C13×C4⋊C8C2semidirect
49. #11718508C4semidirect
209. C4×C4⋊C8D13semidirect
489. C13#22114semidirect

Maximal subgroups

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

subgroupindex
C2×#117185082
C4×#881242
#131173002
#131157912
#131156062
#131155692
#131155642
#131155192
#131154642
#131154572
#131154292
#131154222
#131148472
C4×C13×C4⋊C82
#2211413