Finite Group Databasebeta

← #15875009

Subgroups — #15875009

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×#11718532C211yesmaximal, characteristic
2C4×#88144C211yesmaximal, characteristic, complemented
3#13117294C211yesmaximal, characteristic
4#13115792C211yesmaximal, characteristic, complemented
5#13115603C211yesmaximal, characteristic, complemented
6#13115568C211yesmaximal, characteristic, complemented
7#13115565C211yesmaximal, characteristic, complemented
8#13115520C211yesmaximal, characteristic
9#13115517C211yesmaximal, characteristic
10#13115464C211yesmaximal, characteristic
11#13115456C211yesmaximal, characteristic
12#13115425C211yesmaximal, characteristic, complemented
13#13114845C211yesmaximal, characteristic
14#13114684C211yesmaximal, characteristic, complemented
15C13×#1920C211yesmaximal, characteristic, complemented
16C2×#88147C2211yescharacteristic
17C2×#88146—21no—
18C2×#88144C2211yescharacteristic
19C2×C13×#106C2211yescharacteristic
20C13×#389C2211yescharacteristic
21C4×C13×C4⋊C4C2211yescharacteristic
22C2×#88061C2211yescharacteristic
23C2×#88061C2211yescharacteristic
24C2×#88057C2211yescharacteristic
25C2×#88054C2211yescharacteristic
26C2×#88054C2211yescharacteristic
27C2×C8×Dic13C2211yescharacteristic
28C2×C8×Dic13C2211yescharacteristic
29#11718651—21no—
30#11718649C2211yescharacteristic
31#11718646C2211yescharacteristic
32#11718646C2211yescharacteristic
33#11718638C2211yescharacteristic
34C4⋊C4×Dic13C2211yescharacteristic
35#11718634C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40#11718600C2211yescharacteristic
41C4×C4⋊Dic13—21no—
42C4×C4⋊Dic13C2211yescharacteristic
43C4×#6101—21no—
44C42×Dic13C2211yescharacteristic
45#11718532C418yescomplemented
46#11718331—21no—
47#11718327—21no—
48#11718316—21no—
49#11718315—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×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C42×C13—21no—
70C2×C42×C13C2311yescharacteristic
71C2×#6103—21no—
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103—21no—
75C2×#6103—21no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×#6101—21no—
83C2×#6101—21no—
84C2×C4×Dic13—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13D411yescharacteristic
87C2×C4×Dic13D411yescharacteristic
88C2×C4×Dic13D411yescharacteristic
89C2×C4×Dic13D411yescharacteristic
90C2×C4×Dic13C2311yescharacteristic
91C2×C4×Dic13C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94#88147—22no—
95#88147C2×C414yes—
96#88146—44no—
97#88144—22no—
98#88144C2×C414yes—
99C13×#106C2×C414yes—
100C13×#95—21no—
101C13×#95—21no—
102#88071—21no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88061—41no—
110#88061C2×C414yes—
111#88057—41no—
112#88054—22no—
113#88054C2×C414yes—
114C8×Dic13—41no—
115C8×Dic13—41no—
116#88049—41no—
117#88049C2×C414yes—
118#88047—41no—
119#88047C2×C414yes—
120#22114—131nomaximal, Sylow
121C23×D13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2411yescharacteristic
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13C2×D411yescharacteristic
133C22×Dic13C2×D411yescharacteristic
134C22×Dic13C2×D411yescharacteristic
135C22×Dic13C2×D411yescharacteristic
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×C13C22×C412yes—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—42no—
158C13×C4⋊C4C22×C412yes—
159C13×C4⋊C4C22×C412yes—
160C42×C13—21no—
161C42×C13—21no—
162C42×C13—42no—
163#6103—24no—
164#6103—42no—
165#6103—42no—
166#6103—42no—
167#6103—42no—
168C4⋊Dic13—21no—
169C4⋊Dic13—24no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—42no—
175C4⋊Dic13—42no—
176C4⋊Dic13C22×C412yes—
177#6101—24no—
178#6101—42no—
179C4×Dic13—22no—
180C4×Dic13—21no—
181C4×Dic13—21no—
182C4×Dic13—22no—
183C4×Dic13—22no—
184C4×Dic13—41no—
185C4×Dic13—42no—
186C4×Dic13—42no—
187C4×Dic13C22×C412yes—
188C4×Dic13#4112yes—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055C22×C412yes—
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#1920D1311yescharacteristic, complemented
208#1804—131no—
209C4×C4⋊C8—131no—
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—22no—
221C2×C4×C13—22no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13#13512yes—
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—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—22no—
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×Dic13C4×D412yes—
260C2×Dic13C4×D412yes—
261C2×Dic13#13512yes—
262C2×Dic13AGL(1,ℤ/8)12yes—
263D52—22no—
264D52—22no—
265D52—41no—
266D52—41no—
267C4×D13—48no—
268C8×C13—22no—
269C8×C13—41no—
270#1055—22no—
271#1055—41no—
272C2×#125—131no—
273C2×C4×D4—131no—
274C2×#117—261no—
275#478—138no—
276C2×#107—131no—
277C2×#107—131no—
278C2×#106—131no—
279C2×#106C2×D1311yescharacteristic
280C2×C4⋊C8—131no—
281C2×C4⋊C8—131no—
282C2×#102—131no—
283C2×#102—131no—
284C2×#102—131no—
285C2×#102—131no—
286C2×C4×C8—131no—
287C2×C4×C8—131no—
288#390—131no—
289#390—131no—
290#389—131no—
291#389—131no—
292#389—131no—
293#389C2×D1311yescharacteristic
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—261no—
302C4×C4⋊C4—261no—
303C4×C4⋊C4C2×D1311yescharacteristic
304C4×C22⋊C4—261no—
305C43—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340C2×D1311yescharacteristic
312#340C2×D1311yescharacteristic
313#340C2×D1311yescharacteristic
314#336—131no—
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—42no—
332C4×C13—42no—
333C4×C13—41no—
334C4×C13—81no—
335C4×C13—81no—
336C4×C13#51911yescharacteristic
337C4×C13#52011yescharacteristic
338C4×C13#54111yescharacteristic
339C4×C13#54211yescharacteristic
340Dic13—22no—
341Dic13—22no—
342Dic13—22no—
343Dic13—22no—
344Dic13—42no—
345Dic13—81no—
346Dic13—81no—
347C22×D4—131no—
348C23×C4—261no—
349C22×C8—131no—
350C22×C8—131no—
351C22×C8C22×D1311yescharacteristic
352C22×C8C22×D1311yescharacteristic
353#125—134no—
354#125—262no—
355C4×D4—134no—
356C4×D4—262no—
357#117—524no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—261no—
363C2×C4⋊C4—261no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4C22×D1311yescharacteristic
368C2×C4⋊C4C22×D1311yescharacteristic
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C4⋊C4C22×D1311yescharacteristic
371C2×C22⋊C4—261no—
372C2×C22⋊C4—261no—
373C2×C22⋊C4—261no—
374C2×C22⋊C4—261no—
375C2×C22⋊C4—261no—
376C2×C42—21no—
377C2×C42—131no—
378C2×C42—131no—
379C2×C42—131no—
380C2×C42—131no—
381C2×C42—131no—
382C2×C42—131no—
383C2×C42—261no—
384C2×C42—261no—
385C2×C42C22×D1311yescharacteristic
386#107—134no—
387#107—521no—
388#106—521no—
389#106C4×D1314yes—
390C4⋊C8—134no—
391C4⋊C8—262no—
392#102—134no—
393#102—134no—
394#102—521no—
395#102—521no—
396C4×C8—521no—
397C4×C8—521no—
398#95—21no—
399#95—21no—
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—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—131no—
427C22×C4—131no—
428C22×C4—131no—
429C22×C4—131no—
430C22×C4—264no—
431C22×C4—261no—
432C22×C4—261no—
433C22×C4—261no—
434C22×C4—522no—
435C22×C4—522no—
436C22×C4D4×D1311yescharacteristic
437C22×C4D4×D1311yescharacteristic
438C22×C4C23×D1311yescharacteristic
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—132no—
445C2×C8—261no—
446C2×C8—261no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8C2×C4×D1312yes—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—42no—
458C4⋊C4—132no—
459C4⋊C4—264no—
460C4⋊C4—264no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—522no—
467C4⋊C4—522no—
468C4⋊C4—522no—
469C4⋊C4C2×C4×D1312yes—
470C4⋊C4C2×C4×D1312yes—
471C22⋊C4—264no—
472C22⋊C4—522no—
473C22⋊C4—522no—
474C22⋊C4—522no—
475C22⋊C4—522no—
476C42—21no—
477C42—21no—
478C42—42no—
479C42—132no—
480C42—132no—
481C42—262no—
482C42—262no—
483C42—262no—
484C42—261no—
485C42—261no—
486C42—521no—
487C42—522no—
488C42—522no—
489C13#2211411yescharacteristic, complemented, Sylow
490C23—262no—
491C23—521no—
492C23—521no—
493C23—521no—
494C23—521no—
495C23—521no—
496C23—521no—
497C23C2×D4×D1311yescharacteristic
498D4—262no—
499D4—262no—
500D4—521no—
501D4—521no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—132no—
520C2×C4—132no—
521C2×C4—132no—
522C2×C4—132no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—262no—
532C2×C4—528no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4#8817012yes—
542C2×C4C22×C4×D1311yescharacteristic
543C2×C4#8825411yescharacteristic
544C2×C4#41×D1311yescharacteristic
545C2×C4#8825611yescharacteristic
546C2×C4#8825711yescharacteristic
547C2×C4#8825711yescharacteristic
548C8—22no—
549C8—41no—
550C8—262no—
551C8—521no—
552C22—522no—
553C22—522no—
554C22—522no—
555C22—1041no—
556C22—1041no—
557C22—1041no—
558C22—1041no—
559C22C4×D4×D1311yescharacteristic
560C22#1171933411yescharacteristic
561C22#1171935311yescharacteristic
562C22C2×#8817011yescharacteristic
563C22D13×#13511yescharacteristic
564C22D13×AGL(1,ℤ/8)11yescharacteristic
565C22#1171948211yescharacteristic
566C4—22no—
567C4—42no—
568C4—42no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—262no—
573C4—262no—
574C4—262no—
575C4—262no—
576C4—522no—
577C4—1041no—
578C4—1041no—
579C4#1171922811yescharacteristic
580C4#1171927711yescharacteristic
581C4#1171940111yescharacteristic
582C4#1171941511yescharacteristic
583C2—1042no—
584C2#1311751711yescharacteristic
585C2C4×#8817011yescharacteristic
586C2#1312364111yescharacteristic
587C2#1312597011yescharacteristic
588C2#1312600711yescharacteristic
589C2#1312616411yescharacteristic
590C2#1312619011yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1920C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1920D13
hypocenterC13#22114
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
2. C4×#88144C2semidirect
4. #13115792C2semidirect
5. #13115603C2semidirect
6. #13115568C2semidirect
7. #13115565C2semidirect
12. #13115425C2semidirect
14. #13114684C2semidirect
15. C13×#1920C2semidirect
45. #11718532C4semidirect
207. #1920D13semidirect
489. C13#22114semidirect

Maximal subgroups

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

subgroupindex
C2×#117185322
C4×#881442
#131172942
#131157922
#131156032
#131155682
#131155652
#131155202
#131155172
#131154642
#131154562
#131154252
#131148452
#131146842
C13×#19202
#2211413