Finite Group Databasebeta

← #15931591

Subgroups — #15931591

Order 3328.

712 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117905C211yesmaximal, characteristic
2#13116240C211yesmaximal, characteristic
3#13116221C211yesmaximal, characteristic
4#13116077C211yesmaximal, characteristic
5#13116077C211yesmaximal, characteristic
6#13115511C211yesmaximal, characteristic, complemented
7#13115477C211yesmaximal, characteristic, complemented
8#13115411C211yesmaximal, characteristic, complemented
9#13115404C211yesmaximal, characteristic, complemented
10#13115395C211yesmaximal, characteristic, complemented
11#13115103C211yesmaximal, characteristic, complemented
12#13115096C211yesmaximal, characteristic
13#13114838C211yesmaximal, characteristic, complemented
14C4×#88049C211yesmaximal, characteristic
15C13×#2507C211yesmaximal, characteristic, complemented
16C2×#88129C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C2×C4×Dic26C2211yescharacteristic
19C13×#398—21no—
20C13×#398—21no—
21C13×#389—21no—
22C13×#389C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#389C2211yescharacteristic
26C13×#387—21no—
27C13×#384C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30#11718651—21no—
31#11718650—21no—
32C2×#88050C2211yescharacteristic
33C2×#88050C2211yescharacteristic
34C2×#88050C2211yescharacteristic
35C2×#88050C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88049C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42#11718600C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44#11718590C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47#11718330—21no—
48#11718327—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
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
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×C13C2311yescharacteristic
76C2×C42×C13C2311yescharacteristic
77C2×C42×C13C2311yescharacteristic
78C2×#6103—21no—
79C2×#6103—21no—
80C2×#6103—21no—
81C2×#6103—21no—
82C2×#6103—21no—
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×#6101—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C22×#1055C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92#88129—22no—
93#88129—22no—
94C4×D52—22no—
95C4×D52—41no—
96C4×Dic26—22no—
97C4×Dic26—41no—
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95D411yescharacteristic
104C13×#95D411yescharacteristic
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—41no—
116#88048—22no—
117#88047—22no—
118C4⋊#1055—41no—
119C4×#1055—41no—
120#26763—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#4112yes—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—42no—
161C13×C4⋊C4—81no—
162C13×C4⋊C4—81no—
163C13×C4⋊C4—81no—
164C13×C4⋊C4—81no—
165C13×C4⋊C4—81no—
166C13×C4⋊C4#4112yes—
167C42×C13—21no—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—81no—
174#6103—24no—
175#6103—24no—
176#6103—42no—
177#6103—42no—
178#6103—81no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13#4112yes—
183#6101—42no—
184C4×Dic13—42no—
185C4×Dic13—81no—
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—21no—
197C2×#1055—21no—
198#2507D1311yescharacteristic, complemented
199#2367—131no—
200#2071—131no—
201#2067—131no—
202#2042—131no—
203#2042—131no—
204#1933—131no—
205#1928—131no—
206#1919—131no—
207#1918—131no—
208#1916—131no—
209#1865—131no—
210#1864—131no—
211#1803—131no—
212C4×#102—131no—
213C23×C13C22×D411yescharacteristic
214C22×D13—22no—
215C22×D13—41no—
216C22×D13—41no—
217C22×D13—41no—
218C22×D13—41no—
219C22×D13—41no—
220C22×D13—41no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—22no—
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—41no—
239C2×C4×C13—41no—
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×C13#13512yes—
250C2×C4×C13#13712yes—
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C2×C4×C13H(5,𝔽2)11yescharacteristic
256C2×C4×C132−1+411yescharacteristic
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266D52—22no—
267D52—22no—
268D52—41no—
269D52—41no—
270C4×D13—84no—
271Dic26—22no—
272Dic26—22no—
273Dic26—41no—
274Dic26—41no—
275#1055—41no—
276#1055—41no—
277#1055—41no—
278#1055—41no—
279C2×#124—131no—
280C2×C4×Q8—131no—
281C2×C4×D4—131no—
282C2×#107—131no—
283C2×#106—131no—
284C2×C4⋊C8—131no—
285C2×#103—131no—
286C2×#103—131no—
287C2×#103—131no—
288C2×#103—131no—
289C2×#102—131no—
290C2×#102—131no—
291C2×#102—131no—
292C2×#102—131no—
293C2×C4×C8—131no—
294#398—21no—
295#398—21no—
296#391—131no—
297#390—131no—
298#389—21no—
299#389C2×D1311yescharacteristic
300#389C2×D1311yescharacteristic
301#389C2×D1311yescharacteristic
302#389C2×D1311yescharacteristic
303#388—261no—
304#388—261no—
305#387—21no—
306#385—261no—
307#384C2×D1311yescharacteristic
308C4×C4⋊C4—131no—
309C4×C4⋊C4C2×D1311yescharacteristic
310C4×C4⋊C4C2×D1311yescharacteristic
311C4×C22⋊C4—261no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#336—131no—
319#336—131no—
320#336—131no—
321#336—131no—
322C22×C13#52511yescharacteristic
323C22×C13#54611yescharacteristic
324C22×C13#54811yescharacteristic
325C22×C13C2×#13511yescharacteristic
326C22×C13C2×#13711yescharacteristic
327C22×C13#57611yescharacteristic
328C22×C13#57711yescharacteristic
329C2×D13—42no—
330C2×D13—42no—
331C2×D13—42no—
332C2×D13—81no—
333C2×D13—81no—
334C2×D13—81no—
335C2×D13—81no—
336C4×C13—22no—
337C4×C13—22no—
338C4×C13—42no—
339C4×C13—41no—
340C4×C13—41no—
341C4×C13—41no—
342C4×C13—41no—
343C4×C13—81no—
344C4×C13—81no—
345C4×C13—81no—
346C4×C13#52911yescharacteristic
347C4×C13#53911yescharacteristic
348C4×C13#55211yescharacteristic
349C4×C13#55311yescharacteristic
350Dic13—42no—
351Dic13—42no—
352Dic13—81no—
353C22×Q8—131no—
354C22×D4—131no—
355C23×C4—261no—
356C22×C8—131no—
357C22×C8—131no—
358C22×C8—131no—
359C22×C8—131no—
360#124—262no—
361#124—262no—
362C4×Q8—262no—
363C4×Q8—521no—
364C4×D4—262no—
365C4×D4—521no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4C22⋊D1311yescharacteristic
376C2×C4⋊C4C22⋊D1311yescharacteristic
377C2×C4⋊C4C22×D1311yescharacteristic
378C2×C4⋊C4C22×D1311yescharacteristic
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C22⋊C4—261no—
382C2×C22⋊C4—261no—
383C2×C22⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C22⋊C4—261no—
386C2×C42—21no—
387C2×C42—261no—
388C2×C42—261no—
389C2×C42C22×D1311yescharacteristic
390C2×C42C22×D1311yescharacteristic
391C2×C42C22×D1311yescharacteristic
392#107—262no—
393#106—262no—
394C4⋊C8—521no—
395#103—262no—
396#103—262no—
397#103—262no—
398#103—521no—
399#102—262no—
400#102—262no—
401#102—262no—
402#102—521no—
403C4×C8—521no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—261no—
410#95—261no—
411#95—261no—
412#95C22⋊D1311yescharacteristic
413#95C22⋊D1311yescharacteristic
414C2×C13#246011yescharacteristic
415C2×C13#310711yescharacteristic
416C2×C13#311911yescharacteristic
417C2×C13#330111yescharacteristic
418C2×C13#331411yescharacteristic
419C2×C13#336111yescharacteristic
420C2×C13#336911yescharacteristic
421D13—82no—
422C24—261no—
423C2×Q8—132no—
424C2×Q8—261no—
425C2×Q8—261no—
426C2×Q8—261no—
427C2×Q8—261no—
428C2×Q8—261no—
429C2×D4—132no—
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×C4—522no—
443C22×C4—522no—
444C22×C4—1041no—
445C22×C4C2×C22⋊D1311yescharacteristic
446C22×C4C2×C22⋊D1311yescharacteristic
447C22×C4C2×C22⋊D1311yescharacteristic
448C22×C4C2×C22⋊D1311yescharacteristic
449C22×C4C2×C22⋊D1311yescharacteristic
450C22×C4C2×C22⋊D1311yescharacteristic
451C22×C4C23×D1311yescharacteristic
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—
462C2×C8—261no—
463C2×C8—261no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—42no—
474C4⋊C4—81no—
475C4⋊C4—81no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4—132no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—522no—
484C4⋊C4#613112yes—
485C22⋊C4—264no—
486C22⋊C4—264no—
487C22⋊C4—522no—
488C22⋊C4—522no—
489C22⋊C4—1041no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—81no—
497C42—522no—
498C42—1041no—
499C13#2676311yescharacteristic, complemented, Sylow
500C23—262no—
501C23—521no—
502C23—521no—
503C23—521no—
504C23—521no—
505C23—521no—
506C23—521no—
507C23C22×C22⋊D1311yescharacteristic
508Q8—262no—
509Q8—262no—
510Q8—521no—
511Q8—521no—
512D4—262no—
513D4—262no—
514D4—521no—
515D4—521no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
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—41no—
543C2×C4—41no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—1044no—
554C2×C4#8819612yes—
555C2×C4#8820412yes—
556C2×C4C2×#613111yescharacteristic
557C2×C4#8825411yescharacteristic
558C2×C4#41×D1311yescharacteristic
559C2×C4#41×D1311yescharacteristic
560C2×C4#41×D1311yescharacteristic
561C2×C4#8825611yescharacteristic
562C8—521no—
563C8—521no—
564C8—521no—
565C8—521no—
566C22—522no—
567C22—522no—
568C22—522no—
569C22—1041no—
570C22—1041no—
571C22—1041no—
572C22—1041no—
573C22C2×#8819611yescharacteristic
574C22#1171952211yescharacteristic
575C22C2×#8820411yescharacteristic
576C22#1171953311yescharacteristic
577C22#1171953411yescharacteristic
578C22#1171954011yescharacteristic
579C22#1171954111yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—42no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—522no—
591C4—522no—
592C4—1041no—
593C4#1171939611yescharacteristic
594C4#1171939711yescharacteristic
595C4#1171939811yescharacteristic
596C4#1171940011yescharacteristic
597C2—1042no—
598C2#1311878411yescharacteristic
599C2#1312490111yescharacteristic
600C2#1312502911yescharacteristic
601C2#1312673211yescharacteristic
602C2#1312691111yescharacteristic
603C2#1312749611yescharacteristic
604C2#1312757611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2507C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2507D13
hypocenterC13#26763
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2507

Complements

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

NH ≅ G/Ntype
6. #13115511C2semidirect
7. #13115477C2semidirect
8. #13115411C2semidirect
9. #13115404C2semidirect
10. #13115395C2semidirect
11. #13115103C2semidirect
13. #13114838C2semidirect
15. C13×#2507C2semidirect
198. #2507D13semidirect
499. C13#26763semidirect

Maximal subgroups

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

subgroupindex
#131179052
#131162402
#131162212
#131160772
#131155112
#131154772
#131154112
#131154042
#131153952
#131151032
#131150962
#131148382
C4×#880492
C13×#25072
#2676313