Finite Group Databasebeta

← #15966043

Subgroups — #15966043

Order 3328.

724 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123203C211yesmaximal, characteristic
2#13116337C211yesmaximal, characteristic, complemented
3#13116231C211yesmaximal, characteristic, complemented
4#13116221C211yesmaximal, characteristic
5#13116151C211yesmaximal, characteristic
6#13115693C211yesmaximal, characteristic
7#13115566C211yesmaximal, characteristic, complemented
8#13115518C211yesmaximal, characteristic
9#13115515C211yesmaximal, characteristic, complemented
10#13115456C211yesmaximal, characteristic
11#13115421C211yesmaximal, characteristic, complemented
12#13115191C211yesmaximal, characteristic
13#13115090C211yesmaximal, characteristic, complemented
14C4×C4⋊#1055C211yesmaximal, characteristic, complemented
15C13×#2295C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17C22×#6106C2211yescharacteristic
18C2×#88130—21no—
19C13×#391C2211yescharacteristic
20C13×#391C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#387—21no—
24C13×#387—21no—
25C4×C13×C4⋊C4—21no—
26C4×C13×C4⋊C4C2211yescharacteristic
27C13×#376—21no—
28C43×C13C2211yescharacteristic
29C2×#88075C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88049C2211yescharacteristic
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C2×#88047C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38#11718601—21no—
39#11718601—21no—
40#11718601—21no—
41#11718600C2211yescharacteristic
42#11718600C2211yescharacteristic
43#11718600C2211yescharacteristic
44#11718589C2211yescharacteristic
45#11718589C2211yescharacteristic
46#11718589C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C22×D52C2311yescharacteristic
61C4×Q8×C13—22no—
62C4×Q8×C13—22no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C42×C13—21no—
70C2×C42×C13—21no—
71C2×C42×C13D411yescharacteristic
72C2×C42×C13D411yescharacteristic
73C2×C42×C13D411yescharacteristic
74C2×C42×C13D411yescharacteristic
75C2×C42×C13C2311yescharacteristic
76C2×C42×C13C2311yescharacteristic
77C2×C42×C13C2311yescharacteristic
78C2×#6106—22no—
79C2×#6106—22no—
80C2×#6106—41no—
81C2×#6103—21no—
82C2×#6103—21no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97#88130—44no—
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95—21no—
105#88075—22no—
106#88075—22no—
107#88075—41no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88049—22no—
112#88049—22no—
113#88049—41no—
114#88048—22no—
115#88047—22no—
116#88047—41no—
117C4⋊#1055—22no—
118C4⋊#1055—22no—
119C4×#1055—41no—
120C4×#1055—41no—
121#29435—131nomaximal, Sylow
122C23×D13—21no—
123C2×Q8×C13—21no—
124C2×Q8×C13—21no—
125C2×Q8×C13—21no—
126C2×Q8×C13—21no—
127C2×Q8×C13—21no—
128C2×Q8×C13#4112yes—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2411yescharacteristic
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C2×D52—21no—
144C2×D52—21no—
145C2×D52—21no—
146C2×D52—21no—
147C2×D52—21no—
148C2×D52—21no—
149C13×C4⋊C4—24no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—42no—
156C13×C4⋊C4—42no—
157C13×C4⋊C4#4112yes—
158C42×C13—24no—
159C42×C13—22no—
160C42×C13—22no—
161C42×C13—22no—
162C42×C13—22no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—21no—
167C42×C13—21no—
168C42×C13—21no—
169C42×C13—42no—
170#6106—44no—
171#6103—42no—
172#6103—42no—
173#6103—42no—
174#6103—42no—
175#6103—42no—
176#6103—42no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183#6101—42no—
184#6101—42no—
185#6101—42no—
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—
196C2×#1055#4112yes—
197C2×#1055#4112yes—
198#2860—131no—
199#2295D1311yescharacteristic, complemented
200#2088—131no—
201#2068—131no—
202#2067—131no—
203#2055—131no—
204#1968—131no—
205#1942—131no—
206#1934—131no—
207#1933—131no—
208#1925—131no—
209#1920—131no—
210#1880—131no—
211#1863—131no—
212C4×C4⋊C8—131no—
213C23×C13C22×D411yescharacteristic
214C22×D13—41no—
215C22×D13—41no—
216C22×D13—41no—
217C22×D13—41no—
218C22×D13—41no—
219C22×D13—41no—
220C22×D13—41no—
221Q8×C13—22no—
222Q8×C13—22no—
223Q8×C13—41no—
224Q8×C13—41no—
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×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
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×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13#13512yes—
252C2×C4×C13#13512yes—
253C2×C4×C13AGL(1,ℤ/8)12yes—
254C2×C4×C13#13712yes—
255C2×C4×C13C2×#4111yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×C4×C13H(5,𝔽2)11yescharacteristic
260C2×C4×C132−1+411yescharacteristic
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270D52—41no—
271D52—41no—
272D52—41no—
273D52—41no—
274#1055—22no—
275#1055—22no—
276#1055—41no—
277#1055—41no—
278C22×SD16—131no—
279C2×#126—261no—
280C2×C4×Q8C2×D1311yescharacteristic
281C2×#107—131no—
282C2×#107—131no—
283C2×#106—131no—
284C2×C4⋊C8—131no—
285C2×C4⋊C8—131no—
286C2×#103—131no—
287C2×#103—131no—
288C2×#103—131no—
289C2×#102—131no—
290C2×#102—131no—
291C2×#102—131no—
292C2×C4×C8—131no—
293C2×C4×C8—131no—
294#391C2×D1311yescharacteristic
295#391C2×D1311yescharacteristic
296#390—131no—
297#390—131no—
298#390—131no—
299#389—131no—
300#389—131no—
301#389—131no—
302#389C2×D1311yescharacteristic
303#389C2×D1311yescharacteristic
304#388—261no—
305#388—261no—
306#388—261no—
307#387—21no—
308#387—21no—
309C4×C4⋊C4—21no—
310C4×C4⋊C4C2×D1311yescharacteristic
311#376—21no—
312C43C2×D1311yescharacteristic
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#336—131no—
320#336—131no—
321C22×C13#52511yescharacteristic
322C22×C13#53211yescharacteristic
323C22×C13#53711yescharacteristic
324C22×C13C2×#13511yescharacteristic
325C22×C13C2×#13511yescharacteristic
326C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C13C2×#13711yescharacteristic
328C2×D13—81no—
329C2×D13—81no—
330C2×D13—81no—
331C2×D13—81no—
332C2×D13—81no—
333C2×D13—81no—
334C2×D13—81no—
335C4×C13—22no—
336C4×C13—22no—
337C4×C13—22no—
338C4×C13—22no—
339C4×C13—41no—
340C4×C13—42no—
341C4×C13—42no—
342C4×C13—41no—
343C4×C13—81no—
344C4×C13—81no—
345C4×C13#55111yescharacteristic
346C4×C13#55211yescharacteristic
347C4×C13#55311yescharacteristic
348C4×C13#55611yescharacteristic
349Dic13—81no—
350Dic13—81no—
351Dic13—81no—
352C22×Q8C22×D1311yescharacteristic
353C22×D4—131no—
354C2×SD16—262no—
355C2×SD16—262no—
356C2×SD16—521no—
357C22×C8—131no—
358C22×C8—131no—
359C22×C8—131no—
360C22×C8—131no—
361#126—524no—
362C4×Q8—22no—
363C4×Q8—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4C22×D1311yescharacteristic
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C4⋊C4C22×D1311yescharacteristic
376C2×C22⋊C4—261no—
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×C42C22⋊D1311yescharacteristic
385C2×C42C22⋊D1311yescharacteristic
386C2×C42C22⋊D1311yescharacteristic
387C2×C42C22⋊D1311yescharacteristic
388C2×C42C22×D1311yescharacteristic
389C2×C42C22×D1311yescharacteristic
390C2×C42C22×D1311yescharacteristic
391#107—262no—
392#107—521no—
393#106—262no—
394C4⋊C8—262no—
395C4⋊C8—262no—
396#103—262no—
397#103—262no—
398#103—521no—
399#102—262no—
400#102—262no—
401#102—521no—
402C4×C8—521no—
403C4×C8—521no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—261no—
412#95—261no—
413#95—261no—
414C2×C13#260111yescharacteristic
415C2×C13#310611yescharacteristic
416C2×C13#310811yescharacteristic
417C2×C13#316811yescharacteristic
418C2×C13#318211yescharacteristic
419C2×C13#324711yescharacteristic
420C2×C13#324811yescharacteristic
421D13—161no—
422C24—261no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8#612712yes—
429C2×D4—261no—
430C2×D4—261no—
431C2×D4—261no—
432C2×D4—261no—
433C2×D4—261no—
434C2×D4—261no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4C2×C22⋊D1311yescharacteristic
443C22×C4C2×C22⋊D1311yescharacteristic
444C22×C4C2×C22⋊D1311yescharacteristic
445C22×C4C2×C22⋊D1311yescharacteristic
446C22×C4C2×C22⋊D1311yescharacteristic
447C22×C4C2×C22⋊D1311yescharacteristic
448C22×C4C23×D1311yescharacteristic
449SD16—524no—
450C2×C8—132no—
451C2×C8—132no—
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—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—522no—
477C4⋊C4—522no—
478C4⋊C4—522no—
479C4⋊C4#612712yes—
480C22⋊C4—522no—
481C22⋊C4—522no—
482C22⋊C4—522no—
483C22⋊C4—522no—
484C22⋊C4—522no—
485C22⋊C4—522no—
486C42—24no—
487C42—22no—
488C42—22no—
489C42—22no—
490C42—22no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—42no—
498C13#2943511yescharacteristic, complemented, Sylow
499C23—521no—
500C23—521no—
501C23—521no—
502C23—521no—
503C23—521no—
504C23—521no—
505C23—521no—
506C23C22×C22⋊D1311yescharacteristic
507Q8—22no—
508Q8—22no—
509Q8—41no—
510Q8—41no—
511D4—521no—
512D4—521no—
513D4—521no—
514D4—521no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
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—521no—
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#8819612yes—
551C2×C4#8820312yes—
552C2×C4#8820412yes—
553C2×C4#8820412yes—
554C2×C4C2×#612711yescharacteristic
555C2×C4C2×#612711yescharacteristic
556C2×C4#41×D1311yescharacteristic
557C2×C4#41×D1311yescharacteristic
558C2×C4#8825611yescharacteristic
559C2×C4#8825711yescharacteristic
560C8—262no—
561C8—262no—
562C8—521no—
563C8—521no—
564C22—1041no—
565C22—1041no—
566C22—1041no—
567C22—1041no—
568C22—1041no—
569C22—1041no—
570C22—1041no—
571C22#1171949611yescharacteristic
572C22C2×#8819611yescharacteristic
573C22C2×#8820311yescharacteristic
574C22C2×#8820411yescharacteristic
575C22C2×#8820411yescharacteristic
576C22#1171953711yescharacteristic
577C22#1171953811yescharacteristic
578C4—22no—
579C4—22no—
580C4—22no—
581C4—22no—
582C4—41no—
583C4—42no—
584C4—42no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4—1041no—
589C4—1041no—
590C4—1041no—
591C4#1171923211yescharacteristic
592C4#1171923511yescharacteristic
593C4#1171923611yescharacteristic
594C4#1171923811yescharacteristic
595C2—2081no—
596C2#1312043311yescharacteristic
597C2#1312489611yescharacteristic
598C2#1312491611yescharacteristic
599C2#1312540011yescharacteristic
600C2#1312555511yescharacteristic
601C2#1312616211yescharacteristic
602C2#1312616711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2295C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2295D13
hypocenterC13#29435
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #2295

Complements

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

NH ≅ G/Ntype
2. #13116337C2semidirect
3. #13116231C2semidirect
7. #13115566C2semidirect
9. #13115515C2semidirect
11. #13115421C2semidirect
13. #13115090C2semidirect
14. C4×C4⋊#1055C2semidirect
15. C13×#2295C2semidirect
199. #2295D13semidirect
498. C13#29435semidirect

Maximal subgroups

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

subgroupindex
#131232032
#131163372
#131162312
#131162212
#131161512
#131156932
#131155662
#131155182
#131155152
#131154562
#131154212
#131151912
#131150902
C4×C4⋊#10552
C13×#22952
#2943513