Finite Group Databasebeta

← #15880552

Subgroups — #15880552

Order 3328.

778 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718521C211yesmaximal, characteristic
2#13117728C211yesmaximal, characteristic
3#13117720C211yesmaximal, characteristic
4#13115565C211yesmaximal, characteristic, complemented
5#13115431C211yesmaximal, characteristic, complemented
6#13115425C211yesmaximal, characteristic, complemented
7#13115410C211yesmaximal, characteristic, complemented
8#13115404C211yesmaximal, characteristic, complemented
9#13114930C211yesmaximal, characteristic
10#13114929C211yesmaximal, characteristic
11#13114858C211yesmaximal, characteristic
12#106×Dic13C211yesmaximal, characteristic, complemented
13C4×#88057C211yesmaximal, characteristic, complemented
14C8×#6103C211yesmaximal, characteristic
15C13×#1941C211yesmaximal, characteristic, complemented
16C22×C8×D13C2211yescharacteristic
17C2×#88146C2211yescharacteristic
18C2×#88146C2211yescharacteristic
19C2×C13×#106C2211yescharacteristic
20C2×C13×#106C2211yescharacteristic
21C2×C4×C8×C13C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C2×#88060C2211yescharacteristic
25C2×#88057C2211yescharacteristic
26C2×#88057C2211yescharacteristic
27C2×C8×Dic13C2211yescharacteristic
28#11718651—21no—
29#11718651—21no—
30#11718648C2211yescharacteristic
31#11718648C2211yescharacteristic
32#11718646C2211yescharacteristic
33#11718646C2211yescharacteristic
34#11718638—21no—
35C4⋊C4×Dic13—21no—
36C4⋊C4×Dic13C2211yescharacteristic
37C4⋊C4×Dic13C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C4×#6103C2211yescharacteristic
41C4×C4⋊Dic13C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43#11718521C418yescomplemented
44#11718331—21no—
45#11718331—21no—
46#11718312—21no—
47#11718309—21no—
48C13×#340C2211yescharacteristic
49C13×#340C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×C4×D13C2311yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C42×C13C2311yescharacteristic
70C2×#6103—21no—
71C2×#6103—21no—
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103D411yescharacteristic
75C2×#6103D411yescharacteristic
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4×Dic13—21no—
83C2×C4×Dic13—21no—
84C2×C4×Dic13—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C2×C8×D13—22no—
92C2×C8×D13—22no—
93C2×C8×D13C2×C414yes—
94#88146—22no—
95#88146—22no—
96#88146C2×C414yes—
97#88146C2×C414yes—
98C13×#106—22no—
99C13×#106C2×C414yes—
100C4×C8×C13—22no—
101C13×#95—21no—
102C13×#95—21no—
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#88071D411yescharacteristic
112#88071D411yescharacteristic
113#88060—22no—
114#88057—22no—
115#88057C2×C414yes—
116C8×Dic13—22no—
117#88047C2×C414yes—
118#88047C2×C414yes—
119#22610—131nomaximal, Sylow
120C23×D13C2×D411yescharacteristic
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2411yescharacteristic
128C22×Dic13—21no—
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13C2×D411yescharacteristic
133C22×Dic13C2×D411yescharacteristic
134C22×Dic13C2×D411yescharacteristic
135C2×C4×D13—21no—
136C2×C4×D13—21no—
137C2×C4×D13—21no—
138C2×C4×D13—21no—
139C2×C4×D13C22×C412yes—
140C2×C4×D13#4112yes—
141C2×C8×C13—21no—
142C2×C8×C13—21no—
143C2×C8×C13—21no—
144C2×C8×C13C22×C412yes—
145C2×C8×C13#4112yes—
146C2×C8×C13#4112yes—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—42no—
154C13×C4⋊C4—81no—
155C13×C4⋊C4C22×C412yes—
156C13×C4⋊C4C22×C412yes—
157C42×C13—21no—
158C42×C13—21no—
159#6103—24no—
160#6103—24no—
161#6103—22no—
162#6103—22no—
163#6103—81no—
164#6103—81no—
165C4⋊Dic13—21no—
166C4⋊Dic13—21no—
167C4⋊Dic13—21no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—42no—
172C4⋊Dic13—81no—
173C4⋊Dic13C22×C412yes—
174C4⋊Dic13C22×C412yes—
175C4×Dic13—21no—
176C4×Dic13—21no—
177C4×Dic13—24no—
178C4×Dic13—24no—
179C4×Dic13—42no—
180C4×Dic13—42no—
181C4×Dic13—81no—
182C4×Dic13—81no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055C22×C412yes—
189C8×D13—28no—
190C2×#427—131no—
191#2347—131no—
192#2346—131no—
193#1941—131no—
194#1941D1311yescharacteristic, complemented
195#1921—131no—
196#1921—131no—
197#1918—131no—
198#1918—131no—
199#1825—131no—
200#1825—131no—
201#1807—131no—
202C4×#106—131no—
203C4×#106—131no—
204C8×C22⋊C4—131no—
205C23×C13C22×D411yescharacteristic
206C22×D13—21no—
207C22×D13—21no—
208C22×D13—21no—
209C22×D13—21no—
210C22×D13—21no—
211C22×D13—21no—
212C22×D13C4×D412yes—
213C2×C4×C13—21no—
214C2×C4×C13—21no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13#13512yes—
231C2×C4×C13C23×C411yescharacteristic
232C2×C4×C13C2×#4111yescharacteristic
233C2×C4×C13C2×#4111yescharacteristic
234C2×C4×C13C2×#4111yescharacteristic
235C2×C4×C132−1+411yescharacteristic
236C2×C4×C132−1+411yescharacteristic
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—22no—
242C2×Dic13—22no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
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×Dic13C4×D412yes—
257C2×Dic13#13512yes—
258C4×D13—22no—
259C4×D13—22no—
260C4×D13—22no—
261C4×D13—22no—
262C8×C13—41no—
263C8×C13#11714yes—
264#1055—22no—
265#1055—41no—
266C23×C8—131no—
267C2×#117—131no—
268C2×#117—131no—
269#427—138no—
270C2×#107—131no—
271C2×#107—131no—
272C2×#106—131no—
273C2×#106—131no—
274C2×#106C2×D1311yescharacteristic
275C2×#106C2×D1311yescharacteristic
276C2×C22⋊C8—131no—
277C2×C4×C8—131no—
278C2×C4×C8C2×D1311yescharacteristic
279#389—131no—
280#389—131no—
281#389C2×D1311yescharacteristic
282#389C2×D1311yescharacteristic
283#388—261no—
284#388—261no—
285#388—261no—
286#388—261no—
287#383—261no—
288#382—261no—
289#380—131no—
290#380—131no—
291C4×C4⋊C4—131no—
292C4×C4⋊C4—131no—
293C4×C4⋊C4—131no—
294C4×C4⋊C4—131no—
295C4×C4⋊C4—261no—
296C4×C22⋊C4—131no—
297#376—261no—
298#340—131no—
299#340—131no—
300#340—131no—
301#340—131no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340C2×D1311yescharacteristic
307#340C2×D1311yescharacteristic
308#336—131no—
309#336—131no—
310C22×C13C2×C4×D411yescharacteristic
311C22×C13#54711yescharacteristic
312C22×C13#54711yescharacteristic
313C22×C13C2×#13511yescharacteristic
314C22×C13C2×#13511yescharacteristic
315C22×C13#57711yescharacteristic
316C22×C13#57711yescharacteristic
317C2×D13—22no—
318C2×D13—22no—
319C2×D13—22no—
320C2×D13—41no—
321C2×D13—41no—
322C2×D13—41no—
323C2×D13—41no—
324C4×C13—22no—
325C4×C13—41no—
326C4×C13—42no—
327C4×C13—42no—
328C4×C13—81no—
329C4×C13—81no—
330C4×C13C2×#11711yescharacteristic
331C4×C13#51911yescharacteristic
332C4×C13#55211yescharacteristic
333C4×C13#55211yescharacteristic
334Dic13—22no—
335Dic13—22no—
336Dic13—41no—
337Dic13—42no—
338Dic13—42no—
339Dic13—81no—
340Dic13—81no—
341C23×C4—131no—
342C22×C8—131no—
343C22×C8—134no—
344C22×C8—131no—
345C22×C8—262no—
346C22×C8—262no—
347C22×C8C22×D1311yescharacteristic
348C22×C8C22×D1311yescharacteristic
349#117—134no—
350#117—134no—
351#117—262no—
352#117—262no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—131no—
356C2×C4⋊C4—131no—
357C2×C4⋊C4—131no—
358C2×C4⋊C4—131no—
359C2×C4⋊C4—261no—
360C2×C4⋊C4—261no—
361C2×C4⋊C4C22×D1311yescharacteristic
362C2×C4⋊C4C22×D1311yescharacteristic
363C2×C4⋊C4C22×D1311yescharacteristic
364C2×C4⋊C4C22×D1311yescharacteristic
365C2×C22⋊C4—131no—
366C2×C22⋊C4—131no—
367C2×C22⋊C4—261no—
368C2×C22⋊C4—261no—
369C2×C22⋊C4—261no—
370C2×C22⋊C4—261no—
371C2×C42—131no—
372C2×C42—261no—
373C2×C42—261no—
374C2×C42—261no—
375C2×C42—261no—
376C2×C42—261no—
377C2×C42—261no—
378C2×C42C22×D1311yescharacteristic
379#107—134no—
380#107—134no—
381#106—22no—
382#106—134no—
383#106—262no—
384#106C4×D1314yes—
385C22⋊C8—262no—
386C4×C8—22no—
387C4×C8—262no—
388#95—21no—
389#95—21no—
390#95—131no—
391#95—131no—
392#95—261no—
393#95—261no—
394#95—261no—
395#95—261no—
396#95—261no—
397#95—261no—
398#95—261no—
399#95—261no—
400C2×C13#234411yescharacteristic
401C2×C13C4×#13511yescharacteristic
402C2×C13#295211yescharacteristic
403C2×C13#333711yescharacteristic
404C2×C13#333711yescharacteristic
405C2×C13#334011yescharacteristic
406C2×C13#334011yescharacteristic
407D13—42no—
408C24—131no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—131no—
414C22×C4—131no—
415C22×C4—132no—
416C22×C4—132no—
417C22×C4—131no—
418C22×C4—261no—
419C22×C4—261no—
420C22×C4—261no—
421C22×C4—261no—
422C22×C4—261no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4—261no—
426C22×C4D4×D1311yescharacteristic
427C22×C4D4×D1311yescharacteristic
428C22×C4C23×D1311yescharacteristic
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—132no—
433C2×C8—261no—
434C2×C8—261no—
435C2×C8—268no—
436C2×C8—261no—
437C2×C8—261no—
438C2×C8—261no—
439C2×C8C2×C4×D1312yes—
440C2×C8#612912yes—
441C2×C8#613112yes—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—42no—
449C4⋊C4—81no—
450C4⋊C4—132no—
451C4⋊C4—132no—
452C4⋊C4—261no—
453C4⋊C4—261no—
454C4⋊C4—261no—
455C4⋊C4—261no—
456C4⋊C4—261no—
457C4⋊C4—261no—
458C4⋊C4—522no—
459C4⋊C4—1041no—
460C4⋊C4C2×C4×D1312yes—
461C4⋊C4C2×C4×D1312yes—
462C22⋊C4—262no—
463C22⋊C4—264no—
464C22⋊C4—264no—
465C22⋊C4—262no—
466C22⋊C4—1041no—
467C22⋊C4—1041no—
468C42—21no—
469C42—21no—
470C42—264no—
471C42—264no—
472C42—261no—
473C42—261no—
474C42—522no—
475C42—522no—
476C42—1041no—
477C42—1041no—
478C13#2261011yescharacteristic, complemented, Sylow
479C23—132no—
480C23—261no—
481C23—261no—
482C23—261no—
483C23—261no—
484C23—261no—
485C23—261no—
486C23C2×D4×D1311yescharacteristic
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—132no—
505C2×C4—132no—
506C2×C4—261no—
507C2×C4—261no—
508C2×C4—261no—
509C2×C4—261no—
510C2×C4—262no—
511C2×C4—262no—
512C2×C4—262no—
513C2×C4—262no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—262no—
518C2×C4—262no—
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#8817012yes—
530C2×C4C22×C4×D1311yescharacteristic
531C2×C4C2×#612911yescharacteristic
532C2×C4C2×#613111yescharacteristic
533C2×C4#8825411yescharacteristic
534C2×C4#41×D1311yescharacteristic
535C2×C4#8825711yescharacteristic
536C8—41no—
537C8—262no—
538C8—521no—
539C8#8814614yes—
540C22—262no—
541C22—262no—
542C22—262no—
543C22—521no—
544C22—521no—
545C22—521no—
546C22—521no—
547C22C4×D4×D1311yescharacteristic
548C22#1171931611yescharacteristic
549C22#1171943111yescharacteristic
550C22C2×#8817011yescharacteristic
551C22#1171946711yescharacteristic
552C22D13×#13511yescharacteristic
553C22#1171947511yescharacteristic
554C4—22no—
555C4—42no—
556C4—41no—
557C4—42no—
558C4—81no—
559C4—81no—
560C4—262no—
561C4—262no—
562C4—522no—
563C4—521no—
564C4—522no—
565C4—1041no—
566C4—1041no—
567C4C2×#8814611yescharacteristic
568C4#1171927711yescharacteristic
569C4#1171934411yescharacteristic
570C4#1171939911yescharacteristic
571C2—522no—
572C2#1311770411yescharacteristic
573C2C4×#8817011yescharacteristic
574C2#1312371411yescharacteristic
575C2#1312721411yescharacteristic
576C2#1312722111yescharacteristic
577C2#1312724411yescharacteristic
578C2#1312724811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1941C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1941D13
hypocenterC13#22610
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1941

Complements

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

NH ≅ G/Ntype
4. #13115565C2semidirect
5. #13115431C2semidirect
6. #13115425C2semidirect
7. #13115410C2semidirect
8. #13115404C2semidirect
12. #106×Dic13C2semidirect
13. C4×#88057C2semidirect
15. C13×#1941C2semidirect
43. #11718521C4semidirect
194. #1941D13semidirect
478. C13#22610semidirect

Maximal subgroups

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

subgroupindex
C2×#117185212
#131177282
#131177202
#131155652
#131154312
#131154252
#131154102
#131154042
#131149302
#131149292
#131148582
#106×Dic132
C4×#880572
C8×#61032
C13×#19412
#2261013