Finite Group Databasebeta

← #15926783

Subgroups — #15926783

Order 3328.

784 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118538C211yesmaximal, characteristic
2#13117861C211yesmaximal, characteristic
3#13116400C211yesmaximal, characteristic, complemented
4#13116334C211yesmaximal, characteristic, complemented
5#13116216C211yesmaximal, characteristic, complemented
6#13115978C211yesmaximal, characteristic, complemented
7#13115787C211yesmaximal, characteristic, complemented
8#13115408C211yesmaximal, characteristic, complemented
9#13115269C211yesmaximal, characteristic
10#13115141C211yesmaximal, characteristic
11#13115093C211yesmaximal, characteristic, complemented
12#13115037C211yesmaximal, characteristic
13#13114842C211yesmaximal, characteristic, complemented
14#13114556C211yesmaximal, characteristic
15C13×#1851C211yesmaximal, characteristic
16C22×C13×M16C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C2×#88178C2211yescharacteristic
20C2×#88132—21no—
21C2×#88123C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×C22⋊C8C2211yescharacteristic
26C4×C13×C22⋊C4C2211yescharacteristic
27#11718873C2211yescharacteristic
28C2×#88058C2211yescharacteristic
29C2×#88057C2211yescharacteristic
30C2×#88056C2211yescharacteristic
31C2×#88056C2211yescharacteristic
32C2×#88056C2211yescharacteristic
33C2×#88056C2211yescharacteristic
34#11718611—21no—
35#11718606—21no—
36#11718605—21no—
37#11718596C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39#11718590C2211yescharacteristic
40#11718589C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43#11718322—21no—
44#11718317—21no—
45#11718313—21no—
46#11718310—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—
61C22×Dic26—21no—
62C22×Dic26C2311yescharacteristic
63C2×C13×M16—22no—
64C2×C13×M16—41no—
65C2×C13×M16—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×C22⋊Dic13—21no—
77#88180—22no—
78#88180—41no—
79C2×C4⋊Dic13—22no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—41no—
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92#88178—22no—
93#88178Q814yescomplemented
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13—21no—
102#88132—44no—
103#88123—22no—
104#88123—41no—
105C4×Dic26—22no—
106C4×Dic26—41no—
107C13×C4⋊C8—41no—
108C13×C4⋊C8—41no—
109C13×C22⋊C8—22no—
110C13×#95D411yescharacteristic
111C13×#95D411yescharacteristic
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88058—22no—
120#88057—41no—
121#88056—22no—
122#88056—41no—
123#88056—41no—
124#88056—41no—
125#26429—131nomaximal, Sylow
126C24×C13C2×D411yescharacteristic
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×Q812yes—
137C22×C4×C13#4112yes—
138C22×C4×C13C2411yescharacteristic
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—42no—
148C22×Dic13—42no—
149C22×Dic13—81no—
150C2×Dic26—21no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26—42no—
156C2×Dic26—42no—
157C2×Dic26—81no—
158C2×Dic26C2×Q812yes—
159C13×M16—44no—
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—21no—
171C2×C8×C13—21no—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—22no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—21no—
178C22⋊Dic13—24no—
179C22⋊Dic13—42no—
180C22⋊Dic13—42no—
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—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—42no—
193C4⋊Dic13—42no—
194C4⋊Dic13—42no—
195C4⋊Dic13—81no—
196C4⋊Dic13C2×Q812yes—
197C4⋊Dic13#4112yes—
198C4⋊Dic13#4112yes—
199#6101—24no—
200#6101—42no—
201#6101—42no—
202#6101—42no—
203#6101—42no—
204C4×Dic13—42no—
205C4×Dic13—42no—
206C4×Dic13—42no—
207#2440—131no—
208#2362—131no—
209#2100—131no—
210#2088—131no—
211#2066—131no—
212#2024—131no—
213#1988—131no—
214#1918—131no—
215#1894—131no—
216#1872—131no—
217#1863—131no—
218#1854—131no—
219#1851D1311yescharacteristic
220#1803—131no—
221#1736—131no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13C22⋊Q812yes—
229C23×C13C22×D411yescharacteristic
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—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
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×C13C22⋊Q812yes—
247C2×C4×C13AGL(1,ℤ/8)12yes—
248C2×C4×C13#13712yes—
249C2×C4×C13C22×Q811yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13H(5,𝔽2)11yescharacteristic
254C2×C4×C13H(5,𝔽2)11yescharacteristic
255C2×Dic13—22no—
256C2×Dic13—22no—
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—
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—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—84no—
280Dic26—22no—
281Dic26—22no—
282Dic26—41no—
283Dic26—41no—
284Dic26—84no—
285C8×C13—41no—
286C8×C13—41no—
287C8×C13—41no—
288C8×C13—41no—
289C22×M16C2×D1311yescharacteristic
290C2×C4⋊Q8—131no—
291C2×C22⋊Q8—131no—
292C2×C22⋊Q8—261no—
293C2×C4×Q8—131no—
294C2×#117—131no—
295C22×C4⋊C4—131no—
296C2×#107—131no—
297C2×#106—131no—
298C2×C4⋊C8C2×D1311yescharacteristic
299C2×C4⋊C8C2×D1311yescharacteristic
300C2×#103—131no—
301C2×#103—131no—
302C2×#103—131no—
303C2×#103—131no—
304C2×C22⋊C8C2×D1311yescharacteristic
305#398—261no—
306#395—261no—
307#391—131no—
308#389—131no—
309#389—131no—
310#389—131no—
311#388—261no—
312#388—261no—
313#387—261no—
314#385—261no—
315#384—131no—
316#380—131no—
317C4×C4⋊C4—131no—
318C4×C4⋊C4—261no—
319C4×C22⋊C4C2×D1311yescharacteristic
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#336C2×D1311yescharacteristic
331#336C2×D1311yescharacteristic
332C22×C13—22no—
333C22×C13—22no—
334C22×C13—22no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13C2×C22⋊Q811yescharacteristic
340C22×C13#54611yescharacteristic
341C22×C13#54611yescharacteristic
342C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C13C2×#13711yescharacteristic
344C22×C13#57711yescharacteristic
345C22×C13#57811yescharacteristic
346C4×C13—22no—
347C4×C13—22no—
348C4×C13—22no—
349C4×C13—41no—
350C4×C13—41no—
351C4×C13#52911yescharacteristic
352C4×C13#53811yescharacteristic
353C4×C13#55411yescharacteristic
354C4×C13#55411yescharacteristic
355Dic13—42no—
356Dic13—42no—
357Dic13—42no—
358Dic13—42no—
359Dic13—81no—
360Dic13—81no—
361Dic13—81no—
362Dic13—81no—
363C22×Q8—131no—
364C22×Q8—261no—
365C23×C4—261no—
366C23×C4C22×D1311yescharacteristic
367C2×M16—22no—
368C2×M16—41no—
369C2×M16—41no—
370C22×C8C22×D1311yescharacteristic
371C22×C8C22×D1311yescharacteristic
372C22×C8C22×D1311yescharacteristic
373C22×C8C22×D1311yescharacteristic
374C4⋊Q8—262no—
375C4⋊Q8—521no—
376C22⋊Q8—134no—
377C22⋊Q8—262no—
378C22⋊Q8—524no—
379C4×Q8—262no—
380C4×Q8—521no—
381#117—262no—
382#117—521no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—131no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—262no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4—261no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4—261no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4—521no—
401C2×C22⋊C4—261no—
402C2×C22⋊C4—261no—
403C2×C22⋊C4—261no—
404C2×C22⋊C4D5211yescharacteristic
405C2×C22⋊C4D5211yescharacteristic
406C2×C42—261no—
407C2×C42—261no—
408C2×C42—261no—
409C2×C42C22×D1311yescharacteristic
410C2×C42C22×D1311yescharacteristic
411#107—262no—
412#106—521no—
413C4⋊C8—41no—
414C4⋊C8—41no—
415#103—262no—
416#103—521no—
417#103—521no—
418#103—521no—
419C22⋊C8—22no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95—261no—
424#95—261no—
425#95—261no—
426#95—261no—
427#95D5211yescharacteristic
428#95D5211yescharacteristic
429C2×C13—42no—
430C2×C13#245011yescharacteristic
431C2×C13#307911yescharacteristic
432C2×C13#308211yescharacteristic
433C2×C13#331011yescharacteristic
434C2×C13#331611yescharacteristic
435C2×C13#332811yescharacteristic
436C2×C13#333011yescharacteristic
437C24C2×D5211yescharacteristic
438C2×Q8—132no—
439C2×Q8—261no—
440C2×Q8—261no—
441C2×Q8—261no—
442C2×Q8—261no—
443C2×Q8—261no—
444C2×Q8—522no—
445C2×Q8—522no—
446C2×Q8—1041no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—522no—
460C22×C4—522no—
461C22×C4—1041no—
462C22×C4C2×D5211yescharacteristic
463C22×C4C2×D5211yescharacteristic
464C22×C4C2×D5211yescharacteristic
465C22×C4C2×D5211yescharacteristic
466C22×C4C2×D5211yescharacteristic
467C22×C4#612912yes—
468C22×C4Q8×D1312yes—
469C22×C4C23×D1311yescharacteristic
470M16—44no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C4⋊C4—132no—
484C4⋊C4—132no—
485C4⋊C4—132no—
486C4⋊C4—264no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—522no—
499C4⋊C4—522no—
500C4⋊C4—522no—
501C4⋊C4—522no—
502C4⋊C4—522no—
503C4⋊C4—522no—
504C4⋊C4—522no—
505C4⋊C4—1041no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—264no—
509C22⋊C4—522no—
510C22⋊C4—522no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—522no—
516C42—522no—
517C42—522no—
518C13#2642911yescharacteristic, complemented, Sylow
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23#8815112yes—
526C23C22×D5211yescharacteristic
527Q8—262no—
528Q8—262no—
529Q8—521no—
530Q8—521no—
531Q8—1044no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—262no—
549C2×C4—262no—
550C2×C4—262no—
551C2×C4—262no—
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—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—1044no—
573C2×C4#8815112yes—
574C2×C4#8816212yes—
575C2×C4#8816312yes—
576C2×C4C2×#612911yescharacteristic
577C2×C4#8825111yescharacteristic
578C2×C4#8825111yescharacteristic
579C2×C4C2×Q8×D1311yescharacteristic
580C2×C4#41×D1311yescharacteristic
581C2×C4#41×D1311yescharacteristic
582C8—41no—
583C8—41no—
584C8—41no—
585C8—41no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C2×#8815111yescharacteristic
594C22#1171925911yescharacteristic
595C22#1171925911yescharacteristic
596C22C2×#8816211yescharacteristic
597C22C2×#8816311yescharacteristic
598C22#1171945611yescharacteristic
599C22#1171945811yescharacteristic
600C4—22no—
601C4—22no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—522no—
606C4—522no—
607C4—522no—
608C4—522no—
609C4—1041no—
610C4—1041no—
611C4—1041no—
612C4—1041no—
613C4#1171929811yescharacteristic
614C4#1171934111yescharacteristic
615C4#1171934111yescharacteristic
616C4#1171935411yescharacteristic
617C2—42no—
618C2#1311865811yescharacteristic
619C2#1312465211yescharacteristic
620C2#1312467911yescharacteristic
621C2#1312685911yescharacteristic
622C2#1312694911yescharacteristic
623C2#1312712011yescharacteristic
624C2#1312714211yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1851C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1851D13
hypocenterC13#26429
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
3. #13116400C2semidirect
4. #13116334C2semidirect
5. #13116216C2semidirect
6. #13115978C2semidirect
7. #13115787C2semidirect
8. #13115408C2semidirect
11. #13115093C2semidirect
13. #13114842C2semidirect
93. #88178Q8semidirect
518. C13#26429semidirect

Maximal subgroups

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

subgroupindex
#131185382
#131178612
#131164002
#131163342
#131162162
#131159782
#131157872
#131154082
#131152692
#131151412
#131150932
#131150372
#131148422
#131145562
C13×#18512
#2642913