Finite Group Databasebeta

← #15931589

Subgroups — #15931589

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#13119363C211yesmaximal, characteristic, complemented
2#13116239C211yesmaximal, characteristic
3#13116224C211yesmaximal, characteristic
4#13116072C211yesmaximal, characteristic
5#13116072C211yesmaximal, characteristic
6#13115515C211yesmaximal, characteristic, complemented
7#13115474C211yesmaximal, characteristic, complemented
8#13115414C211yesmaximal, characteristic, complemented
9#13115407C211yesmaximal, characteristic, complemented
10#13115395C211yesmaximal, characteristic, complemented
11#13115104C211yesmaximal, characteristic, complemented
12#13115097C211yesmaximal, characteristic
13#13114841C211yesmaximal, characteristic, complemented
14C4×#88072C211yesmaximal, characteristic
15C13×#2367C211yesmaximal, characteristic
16C2×C13×#124C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C13×#391C2211yescharacteristic
20C13×#390C2211yescharacteristic
21C13×#388—21no—
22C13×#388—21no—
23C13×#385—21no—
24C4×C13×C4⋊C4C2211yescharacteristic
25C4×C13×C4⋊C4C2211yescharacteristic
26C4×C13×C22⋊C4—21no—
27C2×#88075C2211yescharacteristic
28C2×#88075C2211yescharacteristic
29C2×#88075C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35#11718645—21no—
36#11718642—21no—
37C2×#88048C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39#11718596C2211yescharacteristic
40C4×C4⋊Dic13C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43#11718589C2211yescharacteristic
44#11718589C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47#11718318—21no—
48#11718308—21no—
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C13×#124—22no—
63C13×#124—22no—
64C4×Q8×C13—22no—
65C4×Q8×C13—41no—
66C4×D4×C13—22no—
67C4×D4×C13—41no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4D411yescharacteristic
70C2×C13×C4⋊C4D411yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C42×C13—21no—
79C2×C42×C13—21no—
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×#6101—21no—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×C4×Dic13—21no—
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95D411yescharacteristic
102C13×#95D411yescharacteristic
103#88075—22no—
104#88075—22no—
105#88075—22no—
106#88075—41no—
107#88072—22no—
108#88072—22no—
109#88072—22no—
110#88072—41no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88048—22no—
117#88047—22no—
118C4⋊#1055—41no—
119C4×#1055—41no—
120#26763—131nomaximal, Sylow
121C24×C13—21no—
122C2×Q8×C13—21no—
123C2×Q8×C13—21no—
124C2×Q8×C13—21no—
125C2×Q8×C13—21no—
126C2×Q8×C13—21no—
127C2×Q8×C13#4112yes—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13#4112yes—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—42no—
138C22×C4×C13—42no—
139C22×C4×C13—81no—
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2411yescharacteristic
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—42no—
157C13×C4⋊C4#4112yes—
158C13×C22⋊C4—24no—
159C13×C22⋊C4—24no—
160C13×C22⋊C4—42no—
161C13×C22⋊C4—42no—
162C13×C22⋊C4—81no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—21no—
167C42×C13—21no—
168C42×C13—21no—
169C42×C13—42no—
170C42×C13—81no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—81no—
179C4⋊Dic13—81no—
180C4⋊Dic13#4112yes—
181#6101—42no—
182#6101—81no—
183#6101—81no—
184#6101—81no—
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#2507—131no—
199#2367D1311yescharacteristic
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×C13—22no—
214C23×C13—41no—
215C23×C13—41no—
216C23×C13—41no—
217C23×C13—41no—
218C23×C13—41no—
219C23×C13—41no—
220C23×C13C22×D411yescharacteristic
221Q8×C13—22no—
222Q8×C13—22no—
223Q8×C13—41no—
224Q8×C13—41no—
225D4×C13—22no—
226D4×C13—22no—
227D4×C13—41no—
228D4×C13—41no—
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—22no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—22no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—84no—
255C2×C4×C13#13512yes—
256C2×C4×C13#13712yes—
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13H(5,𝔽2)11yescharacteristic
262C2×C4×C132−1+411yescharacteristic
263C2×Dic13—22no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275#1055—41no—
276#1055—41no—
277#1055—41no—
278#1055—41no—
279C2×#124C2×D1311yescharacteristic
280C2×C4×Q8C2×D1311yescharacteristic
281C2×C4×D4C2×D1311yescharacteristic
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—261no—
295#398—261no—
296#391C2×D1311yescharacteristic
297#390C2×D1311yescharacteristic
298#389—131no—
299#389—131no—
300#389—131no—
301#389—131no—
302#389—261no—
303#388—21no—
304#388—21no—
305#387—261no—
306#385—21no—
307#384—131no—
308C4×C4⋊C4—131no—
309C4×C4⋊C4C2×D1311yescharacteristic
310C4×C4⋊C4C2×D1311yescharacteristic
311C4×C22⋊C4—21no—
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—42no—
323C22×C13—42no—
324C22×C13—42no—
325C22×C13—81no—
326C22×C13—81no—
327C22×C13—81no—
328C22×C13—81no—
329C22×C13#52511yescharacteristic
330C22×C13#54611yescharacteristic
331C22×C13#54811yescharacteristic
332C22×C13C2×#13511yescharacteristic
333C22×C13C2×#13711yescharacteristic
334C22×C13#57611yescharacteristic
335C22×C13#57711yescharacteristic
336C4×C13—22no—
337C4×C13—22no—
338C4×C13—41no—
339C4×C13—41no—
340C4×C13—42no—
341C4×C13—41no—
342C4×C13—41no—
343C4×C13—42no—
344C4×C13—81no—
345C4×C13#52911yescharacteristic
346C4×C13#53911yescharacteristic
347C4×C13#55211yescharacteristic
348C4×C13#55311yescharacteristic
349Dic13—42no—
350Dic13—81no—
351Dic13—81no—
352Dic13—81no—
353C22×Q8C22×D1311yescharacteristic
354C22×D4C22×D1311yescharacteristic
355C23×C4—21no—
356C22×C8—131no—
357C22×C8—131no—
358C22×C8—131no—
359C22×C8—131no—
360#124—22no—
361#124—22no—
362C4×Q8—22no—
363C4×Q8—41no—
364C4×D4—22no—
365C4×D4—41no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4C22⋊D1311yescharacteristic
378C2×C4⋊C4C22⋊D1311yescharacteristic
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C42—21no—
387C2×C42—21no—
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—261no—
408#95—261no—
409#95—261no—
410#95—261no—
411#95—261no—
412#95C22⋊D1311yescharacteristic
413#95C22⋊D1311yescharacteristic
414C2×C13—82no—
415C2×C13#246011yescharacteristic
416C2×C13#310711yescharacteristic
417C2×C13#311911yescharacteristic
418C2×C13#330111yescharacteristic
419C2×C13#331411yescharacteristic
420C2×C13#336111yescharacteristic
421C2×C13#336911yescharacteristic
422C24—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8#612712yes—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4#612712yes—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—81no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
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—42no—
470C4⋊C4—132no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4—522no—
479C4⋊C4—1041no—
480C4⋊C4—1041no—
481C4⋊C4—1041no—
482C4⋊C4—1041no—
483C4⋊C4—1041no—
484C4⋊C4#612912yes—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—42no—
488C22⋊C4—42no—
489C22⋊C4—81no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—42no—
497C42—81no—
498C42—1041no—
499C13#2676311yescharacteristic, complemented, Sylow
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23C22×C22⋊D1311yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—41no—
511Q8—41no—
512D4—22no—
513D4—22no—
514D4—41no—
515D4—41no—
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—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—84no—
542C2×C4—262no—
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—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4#8820412yes—
555C2×C4#8820512yes—
556C2×C4C2×#612711yescharacteristic
557C2×C4C2×#612711yescharacteristic
558C2×C4C2×#612911yescharacteristic
559C2×C4#8825111yescharacteristic
560C2×C4#41×D1311yescharacteristic
561C2×C4#8825711yescharacteristic
562C8—521no—
563C8—521no—
564C8—521no—
565C8—521no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22#1171949611yescharacteristic
574C22#1171951111yescharacteristic
575C22C2×#8820411yescharacteristic
576C22C2×#8820511yescharacteristic
577C22#1171953611yescharacteristic
578C22#1171954011yescharacteristic
579C22#1171954211yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—42no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—41no—
588C4—81no—
589C4—522no—
590C4—1041no—
591C4—1041no—
592C4—1041no—
593C4#1171924311yescharacteristic
594C4#1171924511yescharacteristic
595C4#1171924611yescharacteristic
596C4#1171926911yescharacteristic
597C2—82no—
598C2#1311878211yescharacteristic
599C2#1312490711yescharacteristic
600C2#1312503511yescharacteristic
601C2#1312673811yescharacteristic
602C2#1312691711yescharacteristic
603C2#1312749211yescharacteristic
604C2#1312757211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2367C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenter#2367D13
hypocenterC13#26763
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2367

Complements

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

NH ≅ G/Ntype
1. #13119363C2semidirect
6. #13115515C2semidirect
7. #13115474C2semidirect
8. #13115414C2semidirect
9. #13115407C2semidirect
10. #13115395C2semidirect
11. #13115104C2semidirect
13. #13114841C2semidirect
499. C13#26763semidirect

Maximal subgroups

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

subgroupindex
#131193632
#131162392
#131162242
#131160722
#131155152
#131154742
#131154142
#131154072
#131153952
#131151042
#131150972
#131148412
C4×#880722
C13×#23672
#2676313