Finite Group Databasebeta

← #15930899

Subgroups — #15930899

Order 3328.

694 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118623C211yesmaximal, characteristic
2#13116337C211yesmaximal, characteristic, complemented
3#13116077C211yesmaximal, characteristic
4#13115984C211yesmaximal, characteristic, complemented
5#13115979C211yesmaximal, characteristic
6#13115768C211yesmaximal, characteristic
7#13115525C211yesmaximal, characteristic, complemented
8#13115470C211yesmaximal, characteristic, complemented
9#13115470C211yesmaximal, characteristic, complemented
10#13115463C211yesmaximal, characteristic
11#13115414C211yesmaximal, characteristic, complemented
12#13115402C211yesmaximal, characteristic, complemented
13#13115096C211yesmaximal, characteristic
14#13114664C211yesmaximal, characteristic
15C13×#2370C211yesmaximal, characteristic, complemented
16C2×C13×#125C2211yescharacteristic
17C2×#88129C2211yescharacteristic
18C2×C4×D52C2211yescharacteristic
19C13×#389—21no—
20C13×#389C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#387—21no—
23C13×#387—21no—
24C4×C13×C4⋊C4—21no—
25C4×C13×C4⋊C4C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29#11718654—21no—
30#11718650—21no—
31C2×#88050C2211yescharacteristic
32C2×#88050C2211yescharacteristic
33C2×#88050C2211yescharacteristic
34C2×#88050C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41#11718600C2211yescharacteristic
42#11718590C2211yescharacteristic
43#11718590C2211yescharacteristic
44#11718589C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×#88043C2211yescharacteristic
47#11718336—21no—
48#11718325—21no—
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D52C2311yescharacteristic
60C22×C4×D13—21no—
61C22×Dic26C2311yescharacteristic
62C13×#125—22no—
63C13×#125—22no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4D411yescharacteristic
69C2×C13×C4⋊C4D411yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C42×C13—21no—
75C2×C42×C13—21no—
76C2×C42×C13—21no—
77C2×C42×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×#6103—21no—
81C2×#6103—21no—
82C2×#6103—21no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×#6101—21no—
88C22×#1055C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92#88129—22no—
93#88129—41no—
94C4×D52—22no—
95C4×D52—41no—
96C13×#95—21no—
97C13×#95—21no—
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95D411yescharacteristic
102C13×#95D411yescharacteristic
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88050—22no—
109#88050—22no—
110#88050—22no—
111#88050—41no—
112#88049—22no—
113#88049—22no—
114#88049—22no—
115#88049—22no—
116#88048—22no—
117#88048—41no—
118C4⋊#1055—41no—
119#88043—41no—
120#26717—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×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2411yescharacteristic
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×D52#4112yes—
142C2×C4×D13—42no—
143C2×C4×D13—42no—
144C2×C4×D13—81no—
145C2×Dic26—21no—
146C2×Dic26—21no—
147C2×Dic26—21no—
148C2×Dic26—21no—
149C2×Dic26—21no—
150C2×Dic26—21no—
151C13×C4⋊C4—24no—
152C13×C4⋊C4—24no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—41no—
159C13×C4⋊C4—41no—
160C13×C4⋊C4—42no—
161C13×C4⋊C4—81no—
162C13×C4⋊C4#4112yes—
163C13×C4⋊C4#4112yes—
164C13×C4⋊C4#4112yes—
165C42×C13—21no—
166C42×C13—21no—
167C42×C13—21no—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—42no—
172C42×C13—81no—
173C42×C13—81no—
174#6103—42no—
175#6103—42no—
176#6103—42no—
177#6103—42no—
178#6103—81no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183#6101—81no—
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—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196#2447—131no—
197#2370D1311yescharacteristic, complemented
198#2088—131no—
199#2042—131no—
200#2026—131no—
201#2025—131no—
202#1983—131no—
203#1935—131no—
204#1927—131no—
205#1927—131no—
206#1926—131no—
207#1919—131no—
208#1917—131no—
209#1864—131no—
210#1762—131no—
211C23×C13C22×D411yescharacteristic
212C22×D13—22no—
213C22×D13—41no—
214C22×D13—41no—
215C22×D13—41no—
216C22×D13—41no—
217C22×D13—41no—
218C22×D13—41no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
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—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13H(5,𝔽2)11yescharacteristic
254C2×C4×C132−1+411yescharacteristic
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264D52—22no—
265D52—22no—
266D52—41no—
267D52—41no—
268C4×D13—84no—
269Dic26—41no—
270Dic26—41no—
271Dic26—41no—
272Dic26—41no—
273#1055—41no—
274#1055—41no—
275#1055—41no—
276#1055—41no—
277C2×#125C2×D1311yescharacteristic
278C2×#124—131no—
279C2×C4×D4—131no—
280C2×#106—131no—
281C2×#106—131no—
282C2×C4⋊C8—131no—
283C2×#103—131no—
284C2×#103—131no—
285C2×#103—131no—
286C2×#103—131no—
287C2×#102—131no—
288C2×#102—131no—
289C2×#102—131no—
290C2×#102—131no—
291C2×#97—131no—
292#397—261no—
293#397—261no—
294#391—131no—
295#391—131no—
296#390—131no—
297#389—21no—
298#389—131no—
299#389C2×D1311yescharacteristic
300#389C2×D1311yescharacteristic
301#387—21no—
302#387—21no—
303#385—261no—
304#381—261no—
305C4×C4⋊C4—21no—
306C4×C4⋊C4C2×D1311yescharacteristic
307C4×C4⋊C4C2×D1311yescharacteristic
308C4×C4⋊C4C2×D1311yescharacteristic
309C4×C4⋊C4C2×D1311yescharacteristic
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#336—131no—
317#336—131no—
318#336—131no—
319#336—131no—
320C22×C13#52511yescharacteristic
321C22×C13#54611yescharacteristic
322C22×C13#54811yescharacteristic
323C22×C13#57511yescharacteristic
324C22×C13#57511yescharacteristic
325C22×C13#57711yescharacteristic
326C22×C13#57711yescharacteristic
327C2×D13—42no—
328C2×D13—42no—
329C2×D13—42no—
330C2×D13—81no—
331C2×D13—81no—
332C2×D13—81no—
333C2×D13—81no—
334C4×C13—41no—
335C4×C13—42no—
336C4×C13—42no—
337C4×C13—41no—
338C4×C13—42no—
339C4×C13—41no—
340C4×C13—41no—
341C4×C13—41no—
342C4×C13—41no—
343C4×C13—81no—
344C4×C13#52911yescharacteristic
345C4×C13#54211yescharacteristic
346C4×C13#55211yescharacteristic
347C4×C13#55911yescharacteristic
348Dic13—81no—
349Dic13—81no—
350Dic13—81no—
351C22×Q8—131no—
352C22×D4—131no—
353C23×C4—261no—
354C22×C8—131no—
355C22×C8—131no—
356C22×C8—131no—
357C22×C8—131no—
358#125—22no—
359#125—22no—
360#124—262no—
361#124—521no—
362C4×D4—262no—
363C4×D4—521no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4C22⋊D1311yescharacteristic
372C2×C4⋊C4C22⋊D1311yescharacteristic
373C2×C4⋊C4C22×D1311yescharacteristic
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C4⋊C4C22×D1311yescharacteristic
376C2×C4⋊C4C22×D1311yescharacteristic
377C2×C22⋊C4—261no—
378C2×C22⋊C4—261no—
379C2×C22⋊C4—261no—
380C2×C22⋊C4—261no—
381C2×C22⋊C4—261no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42C22×D1311yescharacteristic
386C2×C42C22×D1311yescharacteristic
387C2×C42C22×D1311yescharacteristic
388#106—262no—
389#106—521no—
390C4⋊C8—521no—
391#103—262no—
392#103—262no—
393#103—262no—
394#103—521no—
395#102—262no—
396#102—262no—
397#102—262no—
398#102—262no—
399#97—521no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—261no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95—261no—
410#95C22⋊D1311yescharacteristic
411#95C22⋊D1311yescharacteristic
412C2×C13#245811yescharacteristic
413C2×C13#311111yescharacteristic
414C2×C13#312511yescharacteristic
415C2×C13#330711yescharacteristic
416C2×C13#332311yescharacteristic
417C2×C13#337111yescharacteristic
418C2×C13#337611yescharacteristic
419D13—82no—
420C24—261no—
421C2×Q8—261no—
422C2×Q8—261no—
423C2×Q8—261no—
424C2×Q8—261no—
425C2×Q8—261no—
426C2×Q8—261no—
427C2×D4—132no—
428C2×D4—261no—
429C2×D4—261no—
430C2×D4—261no—
431C2×D4—261no—
432C2×D4—261no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—261no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—522no—
441C22×C4—522no—
442C22×C4—1041no—
443C22×C4C2×C22⋊D1311yescharacteristic
444C22×C4C2×C22⋊D1311yescharacteristic
445C22×C4C2×C22⋊D1311yescharacteristic
446C22×C4C2×C22⋊D1311yescharacteristic
447C22×C4C2×C22⋊D1311yescharacteristic
448C22×C4C2×C22⋊D1311yescharacteristic
449C22×C4C23×D1311yescharacteristic
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—42no—
472C4⋊C4—81no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—1041no—
478C4⋊C4#612712yes—
479C4⋊C4#612712yes—
480C4⋊C4#613112yes—
481C22⋊C4—522no—
482C22⋊C4—522no—
483C22⋊C4—522no—
484C22⋊C4—522no—
485C22⋊C4—1041no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—42no—
493C42—81no—
494C42—81no—
495C13#2671711yescharacteristic, complemented, Sylow
496C23—262no—
497C23—521no—
498C23—521no—
499C23—521no—
500C23—521no—
501C23—521no—
502C23—521no—
503C23C22×C22⋊D1311yescharacteristic
504Q8—521no—
505Q8—521no—
506Q8—521no—
507Q8—521no—
508D4—262no—
509D4—262no—
510D4—521no—
511D4—521no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—1044no—
552C2×C4C2×#612711yescharacteristic
553C2×C4C2×#612711yescharacteristic
554C2×C4C2×#613111yescharacteristic
555C2×C4#8825411yescharacteristic
556C2×C4#41×D1311yescharacteristic
557C2×C4#8825611yescharacteristic
558C8—521no—
559C8—521no—
560C8—521no—
561C8—521no—
562C22—522no—
563C22—522no—
564C22—522no—
565C22—1041no—
566C22—1041no—
567C22—1041no—
568C22—1041no—
569C22#1171949611yescharacteristic
570C22#1171952211yescharacteristic
571C22#1171952711yescharacteristic
572C22#1171952711yescharacteristic
573C22#1171953411yescharacteristic
574C22#1171954111yescharacteristic
575C22#1171954211yescharacteristic
576C4—41no—
577C4—42no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—41no—
584C4—42no—
585C4—81no—
586C4—1041no—
587C4—1041no—
588C4—1041no—
589C4#1171928511yescharacteristic
590C4#1171928611yescharacteristic
591C4#1171928711yescharacteristic
592C4#1171929011yescharacteristic
593C2—1042no—
594C2#1311875211yescharacteristic
595C2#1312494511yescharacteristic
596C2#1312511311yescharacteristic
597C2#1312680611yescharacteristic
598C2#1312704611yescharacteristic
599C2#1312760411yescharacteristic
600C2#1312766311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2370C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2370D13
hypocenterC13#26717
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
2. #13116337C2semidirect
4. #13115984C2semidirect
7. #13115525C2semidirect
8. #13115470C2semidirect
9. #13115470C2semidirect
11. #13115414C2semidirect
12. #13115402C2semidirect
15. C13×#2370C2semidirect
197. #2370D13semidirect
495. C13#26717semidirect

Maximal subgroups

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

subgroupindex
#131186232
#131163372
#131160772
#131159842
#131159792
#131157682
#131155252
#131154702
#131154632
#131154142
#131154022
#131150962
#131146642
C13×#23702
#2671713