Finite Group Databasebeta

← #15926588

Subgroups — #15926588

Order 3328.

774 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118560C211yesmaximal, characteristic
2#13117839C211yesmaximal, characteristic
3#13116405C211yesmaximal, characteristic, complemented
4#13116334C211yesmaximal, characteristic, complemented
5#13116216C211yesmaximal, characteristic, complemented
6#13115988C211yesmaximal, characteristic, complemented
7#13115791C211yesmaximal, characteristic, complemented
8#13115422C211yesmaximal, characteristic, complemented
9#13115259C211yesmaximal, characteristic
10#13115141C211yesmaximal, characteristic
11#13115107C211yesmaximal, characteristic, complemented
12#13115031C211yesmaximal, characteristic
13#13114852C211yesmaximal, characteristic, complemented
14C2×#11718143C211yesmaximal, characteristic
15C13×#1850C211yesmaximal, characteristic
16C23×C8×C13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C2×#88178C2211yescharacteristic
20C2×#88124C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic
24C2×C13×C22⋊C8C2211yescharacteristic
25C4×C13×C22⋊C4C2211yescharacteristic
26#11718873C2211yescharacteristic
27C2×#88057C2211yescharacteristic
28C2×#88057C2211yescharacteristic
29C2×#88056C2211yescharacteristic
30C2×#88056C2211yescharacteristic
31C2×#88056C2211yescharacteristic
32C2×#88056C2211yescharacteristic
33#11718607—21no—
34#11718607—21no—
35#11718603—21no—
36C22⋊C4×Dic13—21no—
37#11718597C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39#11718590C2211yescharacteristic
40#11718589C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43#11718321—21no—
44#11718318—21no—
45#11718316—21no—
46#11718308—21no—
47C13×#336C2211yescharacteristic
48C13×#336C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×Dic13—21no—
61C23×Dic13—21no—
62C22×Dic26C2311yescharacteristic
63C22×C8×C13—22no—
64C22×C8×C13—41no—
65C22×C8×C13—41no—
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C2×C13×C22⋊C4D411yescharacteristic
71C2×C13×C22⋊C4D411yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76C2×C4⋊Dic13—22no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—41no—
81C2×C4⋊Dic13—41no—
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89#88178—22no—
90#88178Q814yes—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100#88124—22no—
101#88124—41no—
102C4×Dic26—22no—
103C4×Dic26—41no—
104C13×C4⋊C8—41no—
105C13×C4⋊C8—41no—
106C13×C22⋊C8—22no—
107C13×#95D411yescharacteristic
108C13×#95D411yescharacteristic
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88057—22no—
119#88057—41no—
120#88056—22no—
121#88056—41no—
122#88056—41no—
123#88056—41no—
124#26416—131nomaximal, Sylow
125C24×C13C2×D411yescharacteristic
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×Q812yes—
136C22×C4×C13#4112yes—
137C22×C4×C13C2411yescharacteristic
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—42no—
147C22×Dic13—42no—
148C22×Dic13—42no—
149C22×Dic13—42no—
150C22×Dic13—81no—
151C22×Dic13—81no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26—21no—
157C2×Dic26C2×Q812yes—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—44no—
171C13×C22⋊C4—22no—
172C13×C22⋊C4—22no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—21no—
177C22⋊Dic13—24no—
178C22⋊Dic13—42no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—42no—
191C4⋊Dic13—42no—
192C4⋊Dic13C2×Q812yes—
193C4⋊Dic13#4112yes—
194C4⋊Dic13#4112yes—
195#6101—24no—
196#6101—42no—
197#6101—42no—
198#6101—42no—
199#6101—81no—
200#6101—81no—
201#6101—81no—
202C4×Dic13—42no—
203C4×Dic13—81no—
204#2442—131no—
205#2360—131no—
206#2101—131no—
207#2088—131no—
208#2066—131no—
209#2026—131no—
210#1989—131no—
211#1920—131no—
212#1892—131no—
213#1872—131no—
214#1865—131no—
215#1853—131no—
216#1850D1311yescharacteristic
217#1805—131no—
218C2×#340—131no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13C22⋊Q812yes—
224C23×C13#13512yes—
225C23×C13#13712yes—
226C23×C13C22×D411yescharacteristic
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
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—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13C22⋊Q812yes—
246C2×C4×C13C22×Q811yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13H(5,𝔽2)11yescharacteristic
251C2×C4×C13H(5,𝔽2)11yescharacteristic
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
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—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—84no—
277C2×Dic13—84no—
278Dic26—22no—
279Dic26—22no—
280Dic26—41no—
281Dic26—41no—
282C8×C13—41no—
283C8×C13—41no—
284C8×C13—41no—
285C8×C13—41no—
286C23×C8C2×D1311yescharacteristic
287C2×#125—131no—
288C2×C22⋊Q8—131no—
289C2×C4×Q8—131no—
290C22×C4⋊C4—131no—
291C22×C4⋊C4—131no—
292C2×#106—131no—
293C2×#106—131no—
294C2×C4⋊C8C2×D1311yescharacteristic
295C2×C4⋊C8C2×D1311yescharacteristic
296C2×#103—131no—
297C2×#103—131no—
298C2×#103—131no—
299C2×#103—131no—
300C2×C22⋊C8C2×D1311yescharacteristic
301#400—261no—
302#398—261no—
303#391—131no—
304#389—131no—
305#389—131no—
306#389—131no—
307#389—261no—
308#387—261no—
309#385—261no—
310#385—261no—
311#382—131no—
312#380—131no—
313#380—261no—
314C4×C4⋊C4—131no—
315C4×C22⋊C4—261no—
316C4×C22⋊C4C2×D1311yescharacteristic
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#336C2×D1311yescharacteristic
328#336C2×D1311yescharacteristic
329C22×C13—22no—
330C22×C13—22no—
331C22×C13—22no—
332C22×C13—22no—
333C22×C13—22no—
334C22×C13—22no—
335C22×C13#47914yes—
336C22×C13C2×C22⋊Q811yescharacteristic
337C22×C13#54611yescharacteristic
338C22×C13#54611yescharacteristic
339C22×C13C2×#13511yescharacteristic
340C22×C13C2×#13711yescharacteristic
341C22×C13#57711yescharacteristic
342C22×C13#57711yescharacteristic
343C4×C13—22no—
344C4×C13—41no—
345C4×C13—41no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13#52911yescharacteristic
349C4×C13#53811yescharacteristic
350C4×C13#55411yescharacteristic
351C4×C13#55411yescharacteristic
352Dic13—42no—
353Dic13—42no—
354Dic13—42no—
355Dic13—42no—
356Dic13—81no—
357Dic13—81no—
358Dic13—81no—
359Dic13—81no—
360C22×Q8—131no—
361C23×C4—261no—
362C23×C4—261no—
363C23×C4C22×D1311yescharacteristic
364C22×C8—22no—
365C22×C8—41no—
366C22×C8—41no—
367C22×C8C22×D1311yescharacteristic
368C22×C8C22×D1311yescharacteristic
369C22×C8C22×D1311yescharacteristic
370C22×C8C22×D1311yescharacteristic
371#125—262no—
372#125—521no—
373C22⋊Q8—134no—
374C22⋊Q8—262no—
375C4×Q8—262no—
376C4×Q8—521no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—262no—
385C2×C4⋊C4—262no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—261no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4—261no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4—521no—
396C2×C4⋊C4—521no—
397C2×C22⋊C4—261no—
398C2×C22⋊C4—261no—
399C2×C22⋊C4D5211yescharacteristic
400C2×C22⋊C4D5211yescharacteristic
401C2×C42—261no—
402C2×C42—261no—
403C2×C42C22×D1311yescharacteristic
404C2×C42C22×D1311yescharacteristic
405#106—262no—
406#106—521no—
407C4⋊C8—41no—
408C4⋊C8—41no—
409#103—262no—
410#103—521no—
411#103—521no—
412#103—521no—
413C22⋊C8—22no—
414#95—261no—
415#95—261no—
416#95—261no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95D5211yescharacteristic
424#95D5211yescharacteristic
425C2×C13—24no—
426C2×C13#245011yescharacteristic
427C2×C13C2×#47911yescharacteristic
428C2×C13#308411yescharacteristic
429C2×C13#329611yescharacteristic
430C2×C13#329611yescharacteristic
431C2×C13#331611yescharacteristic
432C2×C13#332011yescharacteristic
433C24C2×D5211yescharacteristic
434C2×Q8—132no—
435C2×Q8—261no—
436C2×Q8—261no—
437C2×Q8—261no—
438C2×Q8—261no—
439C2×Q8—261no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4—261no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—522no—
453C22×C4—522no—
454C22×C4—522no—
455C22×C4—522no—
456C22×C4—1041no—
457C22×C4—1041no—
458C22×C4C2×D5211yescharacteristic
459C22×C4C2×D5211yescharacteristic
460C22×C4C2×D5211yescharacteristic
461C22×C4C2×D5211yescharacteristic
462C22×C4C2×D5211yescharacteristic
463C22×C4#612912yes—
464C22×C4Q8×D1312yes—
465C22×C4C23×D1311yescharacteristic
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—44no—
479C4⋊C4—132no—
480C4⋊C4—132no—
481C4⋊C4—132no—
482C4⋊C4—264no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—522no—
495C4⋊C4—522no—
496C4⋊C4—522no—
497C4⋊C4—522no—
498C4⋊C4—522no—
499C4⋊C4—1041no—
500C4⋊C4—1041no—
501C4⋊C4—1041no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—264no—
505C22⋊C4—522no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—522no—
511C42—1041no—
512C13#2641611yescharacteristic, complemented, Sylow
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23#8815112yes—
518C23#8815812yes—
519C23#8816312yes—
520C23C22×D5211yescharacteristic
521Q8—262no—
522Q8—262no—
523Q8—521no—
524Q8—521no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—262no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—1044no—
568C2×C4—1044no—
569C2×C4#8815112yes—
570C2×C4C2×#612911yescharacteristic
571C2×C4#8825111yescharacteristic
572C2×C4#8825111yescharacteristic
573C2×C4C2×Q8×D1311yescharacteristic
574C2×C4#41×D1311yescharacteristic
575C2×C4#41×D1311yescharacteristic
576C8—41no—
577C8—41no—
578C8—41no—
579C8—41no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22#1171849014yes—
587C22C2×#8815111yescharacteristic
588C22#1171925911yescharacteristic
589C22#1171925911yescharacteristic
590C22C2×#8815811yescharacteristic
591C22C2×#8816311yescharacteristic
592C22#1171945611yescharacteristic
593C22#1171945611yescharacteristic
594C4—22no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—522no—
600C4—522no—
601C4—522no—
602C4—522no—
603C4—1041no—
604C4—1041no—
605C4—1041no—
606C4—1041no—
607C4#1171929811yescharacteristic
608C4#1171934111yescharacteristic
609C4#1171934111yescharacteristic
610C4#1171935411yescharacteristic
611C2—24no—
612C2#1311865811yescharacteristic
613C2C2×#1171849011yescharacteristic
614C2#1312470011yescharacteristic
615C2#1312667311yescharacteristic
616C2#1312667311yescharacteristic
617C2#1312694911yescharacteristic
618C2#1312700911yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1850C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1850D13
hypocenterC13#26416
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
3. #13116405C2semidirect
4. #13116334C2semidirect
5. #13116216C2semidirect
6. #13115988C2semidirect
7. #13115791C2semidirect
8. #13115422C2semidirect
11. #13115107C2semidirect
13. #13114852C2semidirect
512. C13#26416semidirect

Maximal subgroups

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

subgroupindex
#131185602
#131178392
#131164052
#131163342
#131162162
#131159882
#131157912
#131154222
#131152592
#131151412
#131151072
#131150312
#131148522
C2×#117181432
C13×#18502
#2641613