Finite Group Databasebeta

← #15921086

Subgroups — #15921086

Order 3328.

706 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117807C211yesmaximal, characteristic
2#13116221C211yesmaximal, characteristic
3#13116207C211yesmaximal, characteristic
4#13115979C211yesmaximal, characteristic
5#13115969C211yesmaximal, characteristic
6#13115794C211yesmaximal, characteristic, complemented
7#13115789C211yesmaximal, characteristic, complemented
8#13115604C211yesmaximal, characteristic, complemented
9#13115555C211yesmaximal, characteristic, complemented
10#13115425C211yesmaximal, characteristic, complemented
11#13115418C211yesmaximal, characteristic, complemented
12#13114966C211yesmaximal, characteristic, complemented
13#13114843C211yesmaximal, characteristic
14C4×#88049C211yesmaximal, characteristic
15C13×#2550C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×#125C2211yescharacteristic
18C2×C4×D52C2211yescharacteristic
19C13×#398—21no—
20C13×#395—21no—
21C13×#391—21no—
22C13×#389—21no—
23C13×#389C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#382C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28#11718651—21no—
29#11718651—21no—
30C2×#88049C2211yescharacteristic
31C2×#88049C2211yescharacteristic
32C2×#88049C2211yescharacteristic
33C2×#88049C2211yescharacteristic
34C2×#88048C2211yescharacteristic
35C2×#88047C2211yescharacteristic
36#11718600C2211yescharacteristic
37#11718600C2211yescharacteristic
38#11718597C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40C4×C4⋊Dic13C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×C4×#1055C2211yescharacteristic
45#11718327—21no—
46#11718325—21no—
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13—21no—
60C22×D52C2311yescharacteristic
61C22×C4×D13—21no—
62C13×C4⋊Q8—22no—
63C13×C4⋊Q8—41no—
64C13×#125—22no—
65C13×#125—41no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4D411yescharacteristic
72C2×C13×C4⋊C4D411yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C42×C13—21no—
78C2×C42×C13C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×#6103—21no—
82C2×#6103—21no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×#6103—21no—
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4×Dic13—21no—
90C2×C4×Dic13—21no—
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C4×D52—22no—
96C4×D52Q814yescomplemented
97C13×#95—21no—
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95D411yescharacteristic
103C13×#95D411yescharacteristic
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88049—22no—
109#88049—22no—
110#88049—41no—
111#88049—41no—
112#88048—22no—
113#88047—22no—
114C4⋊#1055—22no—
115C4⋊#1055—41no—
116C4⋊#1055—41no—
117C4×#1055—22no—
118#26028—131nomaximal, Sylow
119C23×D13—21no—
120C2×Q8×C13—42no—
121C2×Q8×C13—42no—
122C2×Q8×C13—81no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2411yescharacteristic
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C2×D52—21no—
138C2×D52—21no—
139C2×D52—21no—
140C2×D52—21no—
141C2×D52—21no—
142C2×D52C2×Q812yes—
143C2×C4×D13—24no—
144C2×C4×D13—81no—
145C2×C4×D13—81no—
146C13×C4⋊C4—22no—
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—41no—
154C13×C4⋊C4—42no—
155C13×C4⋊C4—42no—
156C13×C4⋊C4—42no—
157C13×C4⋊C4—42no—
158C13×C4⋊C4—81no—
159C13×C4⋊C4#4112yes—
160C13×C4⋊C4#4112yes—
161C42×C13—21no—
162C42×C13—21no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13—81no—
166C42×C13C2×Q812yes—
167C42×C13#4112yes—
168#6103—24no—
169#6103—42no—
170#6103—42no—
171#6103—81no—
172#6103—81no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13C2×Q812yes—
179C4×Dic13—81no—
180C4×Dic13—81no—
181C2×#1055—21no—
182C2×#1055—21no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193#2550D1311yescharacteristic, complemented
194#2357—131no—
195#2067—131no—
196#2065—131no—
197#2025—131no—
198#2023—131no—
199#1989—131no—
200#1988—131no—
201#1949—131no—
202#1939—131no—
203#1921—131no—
204#1920—131no—
205#1835—131no—
206#1804—131no—
207C4×#102—131no—
208C23×C13C22×D411yescharacteristic
209C22×D13—22no—
210C22×D13—41no—
211C22×D13—41no—
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—41no—
215C22×D13—41no—
216Q8×C13—84no—
217C2×C4×C13—21no—
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—22no—
227C2×C4×C13—22no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13C22⋊Q812yes—
245C2×C4×C13C22⋊Q812yes—
246C2×C4×C13#13512yes—
247C2×C4×C13C22×Q811yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13H(5,𝔽2)11yescharacteristic
252C2×C4×C132−1+411yescharacteristic
253C2×Dic13—22no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262D52—22no—
263D52—22no—
264D52—41no—
265D52—41no—
266C4×D13—84no—
267#1055—41no—
268#1055—41no—
269#1055—41no—
270#1055—41no—
271C2×C4⋊Q8C2×D1311yescharacteristic
272C2×#125C2×D1311yescharacteristic
273C2×C4×D4—131no—
274C2×#107—131no—
275C2×#106—131no—
276C2×C4⋊C8—131no—
277C2×C4⋊C8—131no—
278C2×C4⋊C8—131no—
279C2×#102—131no—
280C2×#102—131no—
281C2×#102—131no—
282C2×#102—131no—
283C2×C4×C8—131no—
284#398—21no—
285#395—21no—
286#391—21no—
287#390—131no—
288#390—131no—
289#389—21no—
290#389C2×D1311yescharacteristic
291#389C2×D1311yescharacteristic
292#388—261no—
293#388—261no—
294#382—131no—
295#382C2×D1311yescharacteristic
296#381—261no—
297C4×C4⋊C4—131no—
298C4×C4⋊C4—131no—
299C4×C4⋊C4C2×D1311yescharacteristic
300C4×C4⋊C4C2×D1311yescharacteristic
301C4×C22⋊C4—261no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#336—131no—
313#336—131no—
314C22×C13C2×C22⋊Q811yescharacteristic
315C22×C13#54611yescharacteristic
316C22×C13#54811yescharacteristic
317C22×C13C2×#13511yescharacteristic
318C22×C13#57511yescharacteristic
319C22×C13#57611yescharacteristic
320C22×C13#57711yescharacteristic
321C2×D13—42no—
322C2×D13—42no—
323C2×D13—42no—
324C2×D13—81no—
325C2×D13—81no—
326C2×D13—81no—
327C2×D13—81no—
328C4×C13—22no—
329C4×C13—22no—
330C4×C13—22no—
331C4×C13—42no—
332C4×C13—41no—
333C4×C13—42no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13—81no—
337C4×C13—81no—
338C4×C13#53311yescharacteristic
339C4×C13#54411yescharacteristic
340C4×C13#55511yescharacteristic
341C4×C13#55611yescharacteristic
342Dic13—42no—
343Dic13—81no—
344Dic13—81no—
345C22×Q8—21no—
346C22×D4—131no—
347C23×C4—261no—
348C22×C8—131no—
349C22×C8—131no—
350C22×C8—131no—
351C22×C8—131no—
352C4⋊Q8—22no—
353C4⋊Q8—41no—
354#125—22no—
355#125—41no—
356C4×D4—134no—
357C4×D4—262no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4C22⋊D1311yescharacteristic
367C2×C4⋊C4C22⋊D1311yescharacteristic
368C2×C4⋊C4C22×D1311yescharacteristic
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C4⋊C4C22×D1311yescharacteristic
371C2×C4⋊C4C22×D1311yescharacteristic
372C2×C22⋊C4—261no—
373C2×C22⋊C4—261no—
374C2×C22⋊C4—261no—
375C2×C22⋊C4—261no—
376C2×C22⋊C4—261no—
377C2×C42—21no—
378C2×C42—261no—
379C2×C42—261no—
380C2×C42C22×D1311yescharacteristic
381C2×C42C22×D1311yescharacteristic
382C2×C42C22×D1311yescharacteristic
383#107—262no—
384#106—262no—
385C4⋊C8—262no—
386C4⋊C8—521no—
387C4⋊C8—521no—
388#102—262no—
389#102—262no—
390#102—521no—
391#102—521no—
392C4×C8—262no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—261no—
399#95—261no—
400#95—261no—
401#95—261no—
402#95C22⋊D1311yescharacteristic
403#95C22⋊D1311yescharacteristic
404C2×C13#243911yescharacteristic
405C2×C13#307611yescharacteristic
406C2×C13#308111yescharacteristic
407C2×C13#329711yescharacteristic
408C2×C13#332611yescharacteristic
409C2×C13#336511yescharacteristic
410C2×C13#337011yescharacteristic
411D13—82no—
412C24—261no—
413C2×Q8—42no—
414C2×Q8—42no—
415C2×Q8—81no—
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—261no—
427C22×C4—264no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—1041no—
431C22×C4—1041no—
432C22×C4C2×C22⋊D1311yescharacteristic
433C22×C4C2×C22⋊D1311yescharacteristic
434C22×C4C2×C22⋊D1311yescharacteristic
435C22×C4C2×C22⋊D1311yescharacteristic
436C22×C4C2×C22⋊D1311yescharacteristic
437C22×C4C2×C22⋊D1311yescharacteristic
438C22×C4C23×D1311yescharacteristic
439C2×C8—261no—
440C2×C8—261no—
441C2×C8—261no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8—261no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—261no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—41no—
459C4⋊C4—42no—
460C4⋊C4—42no—
461C4⋊C4—42no—
462C4⋊C4—42no—
463C4⋊C4—81no—
464C4⋊C4—132no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4#612912yes—
471C4⋊C4#613112yes—
472C22⋊C4—264no—
473C22⋊C4—522no—
474C22⋊C4—522no—
475C22⋊C4—1041no—
476C22⋊C4—1041no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—81no—
482C42—1041no—
483C42—1041no—
484C42Q8×D1312yes—
485C42#613112yes—
486C13#2602811yescharacteristic, complemented, Sylow
487C23—262no—
488C23—521no—
489C23—521no—
490C23—521no—
491C23—521no—
492C23—521no—
493C23—521no—
494C23C22×C22⋊D1311yescharacteristic
495Q8—84no—
496D4—262no—
497D4—262no—
498D4—521no—
499D4—521no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—262no—
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—1044no—
537C2×C4#8820012yes—
538C2×C4#8820012yes—
539C2×C4#8820412yes—
540C2×C4C2×#612911yescharacteristic
541C2×C4#8825111yescharacteristic
542C2×C4C2×Q8×D1311yescharacteristic
543C2×C4C2×#613111yescharacteristic
544C2×C4C2×#613111yescharacteristic
545C2×C4#8825411yescharacteristic
546C8—521no—
547C8—521no—
548C8—521no—
549C8—521no—
550C22—522no—
551C22—522no—
552C22—522no—
553C22—1041no—
554C22—1041no—
555C22—1041no—
556C22—1041no—
557C22#1171951111yescharacteristic
558C22C2×#8820011yescharacteristic
559C22#1171952211yescharacteristic
560C22C2×#8820411yescharacteristic
561C22#1171952711yescharacteristic
562C22#1171954011yescharacteristic
563C22#1171954211yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—41no—
568C4—42no—
569C4—42no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—522no—
575C4—1041no—
576C4—1041no—
577C4#1171943311yescharacteristic
578C4#1171943411yescharacteristic
579C4#1171943711yescharacteristic
580C4#1171943911yescharacteristic
581C2—1042no—
582C2#1311852311yescharacteristic
583C2#1312461811yescharacteristic
584C2#1312466111yescharacteristic
585C2#1312668611yescharacteristic
586C2#1312708911yescharacteristic
587C2#1312753211yescharacteristic
588C2#1312758911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2550C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2550D13
hypocenterC13#26028
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2550

Complements

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

NH ≅ G/Ntype
6. #13115794C2semidirect
7. #13115789C2semidirect
8. #13115604C2semidirect
9. #13115555C2semidirect
10. #13115425C2semidirect
11. #13115418C2semidirect
12. #13114966C2semidirect
15. C13×#2550C2semidirect
96. C4×D52Q8semidirect
193. #2550D13semidirect
486. C13#26028semidirect

Maximal subgroups

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

subgroupindex
#131178072
#131162212
#131162072
#131159792
#131159692
#131157942
#131157892
#131156042
#131155552
#131154252
#131154182
#131149662
#131148432
C4×#880492
C13×#25502
#2602813