Finite Group Databasebeta

← #15926558

Subgroups — #15926558

Order 3328.

818 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118538C211yesmaximal, characteristic
2#13117839C211yesmaximal, characteristic
3#13116400C211yesmaximal, characteristic, complemented
4#13116329C211yesmaximal, characteristic, complemented
5#13116230C211yesmaximal, characteristic, complemented
6#13115978C211yesmaximal, characteristic, complemented
7#13115783C211yesmaximal, characteristic, complemented
8#13115429C211yesmaximal, characteristic, complemented
9#13115259C211yesmaximal, characteristic
10#13115141C211yesmaximal, characteristic
11#13115093C211yesmaximal, characteristic, complemented
12#13115026C211yesmaximal, characteristic
13#13114842C211yesmaximal, characteristic, complemented
14C2×#11718143C211yesmaximal, characteristic
15C13×#1850C211yesmaximal, characteristic
16C23×C8×C13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
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×#88058C2211yescharacteristic
30C2×#88056C2211yescharacteristic
31C2×#88056C2211yescharacteristic
32C2×#88056C2211yescharacteristic
33C2×#88056C2211yescharacteristic
34#11718611—21no—
35#11718607—21no—
36C22⋊C4×Dic13—21no—
37#11718596C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39#11718590C2211yescharacteristic
40#11718589C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43#11718322—21no—
44#11718317—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×Dic26—21no—
63C22×Dic26C2311yescharacteristic
64C22×C8×C13—22no—
65C22×C8×C13—41no—
66C22×C8×C13—41no—
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C2×C13×C22⋊C4D411yescharacteristic
72C2×C13×C22⋊C4D411yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×C22⋊Dic13—21no—
76C2×C22⋊Dic13—21no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—22no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—41no—
85C2×C4⋊Dic13—41no—
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93#88178—22no—
94#88178Q814yescomplemented
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—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#88058—41no—
121#88056—22no—
122#88056—41no—
123#88056—41no—
124#88056—41no—
125#26414—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—42no—
150C22×Dic13—42no—
151C22×Dic13—81no—
152C22×Dic13—81no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26—21no—
157C2×Dic26—21no—
158C2×Dic26—42no—
159C2×Dic26—42no—
160C2×Dic26—81no—
161C2×Dic26C2×Q812yes—
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—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—44no—
175C13×C22⋊C4—22no—
176C13×C22⋊C4Q1614yes—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—21no—
181C22⋊Dic13—24no—
182C22⋊Dic13—42no—
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—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—42no—
195C4⋊Dic13—42no—
196C4⋊Dic13—42no—
197C4⋊Dic13—42no—
198C4⋊Dic13—81no—
199C4⋊Dic13C2×Q812yes—
200C4⋊Dic13#4112yes—
201C4⋊Dic13#4112yes—
202#6101—24no—
203#6101—42no—
204#6101—42no—
205#6101—42no—
206#6101—81no—
207C4×Dic13—42no—
208C4×Dic13—81no—
209#2440—131no—
210#2360—131no—
211#2100—131no—
212#2087—131no—
213#2068—131no—
214#2024—131no—
215#1987—131no—
216#1921—131no—
217#1892—131no—
218#1872—131no—
219#1863—131no—
220#1852—131no—
221#1850D1311yescharacteristic
222#1803—131no—
223C2×#340—131no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13C22⋊Q812yes—
229C23×C13C2×Q1612yes—
230C23×C13AGL(1,ℤ/8)12yes—
231C23×C13C22×D411yescharacteristic
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—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13C22⋊Q812yes—
249C2×C4×C13C2×Q1612yes—
250C2×C4×C13C2×Q1612yes—
251C2×C4×C13C22×Q811yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C2×C4×C13H(5,𝔽2)11yescharacteristic
256C2×C4×C13H(5,𝔽2)11yescharacteristic
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—22no—
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—41no—
280C2×Dic13—41no—
281C2×Dic13—84no—
282C2×Dic13—84no—
283Dic26—22no—
284Dic26—22no—
285Dic26—41no—
286Dic26—41no—
287Dic26—84no—
288C8×C13—41no—
289C8×C13—41no—
290C8×C13—41no—
291C8×C13—41no—
292C23×C8C2×D1311yescharacteristic
293C2×C4⋊Q8—131no—
294C2×C22⋊Q8—131no—
295C2×C22⋊Q8—261no—
296C2×C4×Q8—131no—
297C22×C4⋊C4—131no—
298C22×C4⋊C4—131no—
299C2×#107—131no—
300C2×#107—131no—
301C2×C4⋊C8C2×D1311yescharacteristic
302C2×C4⋊C8C2×D1311yescharacteristic
303C2×#103—131no—
304C2×#103—131no—
305C2×#103—131no—
306C2×#103—131no—
307C2×C22⋊C8C2×D1311yescharacteristic
308#398—261no—
309#395—261no—
310#391—131no—
311#389—131no—
312#389—131no—
313#389—131no—
314#389—261no—
315#387—261no—
316#385—261no—
317#385—261no—
318#384—131no—
319#380—131no—
320C4×C4⋊C4—131no—
321C4×C22⋊C4—261no—
322C4×C22⋊C4C2×D1311yescharacteristic
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#336C2×D1311yescharacteristic
334#336C2×D1311yescharacteristic
335C22×C13—22no—
336C22×C13—22no—
337C22×C13—22no—
338C22×C13—22no—
339C22×C13—22no—
340C22×C13—22no—
341C22×C13#47714yes—
342C22×C13C2×C22⋊Q811yescharacteristic
343C22×C13#54611yescharacteristic
344C22×C13#54611yescharacteristic
345C22×C13C22×Q1611yescharacteristic
346C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C13#57711yescharacteristic
348C22×C13#57711yescharacteristic
349C4×C13—22no—
350C4×C13—22no—
351C4×C13—22no—
352C4×C13—41no—
353C4×C13—41no—
354C4×C13#52911yescharacteristic
355C4×C13#53811yescharacteristic
356C4×C13#55411yescharacteristic
357C4×C13#55411yescharacteristic
358Dic13—42no—
359Dic13—42no—
360Dic13—42no—
361Dic13—42no—
362Dic13—81no—
363Dic13—81no—
364Dic13—81no—
365Dic13—81no—
366C22×Q8—131no—
367C22×Q8—261no—
368C23×C4—261no—
369C23×C4—261no—
370C23×C4C22×D1311yescharacteristic
371C22×C8—22no—
372C22×C8—41no—
373C22×C8—41no—
374C22×C8C22×D1311yescharacteristic
375C22×C8C22×D1311yescharacteristic
376C22×C8C22×D1311yescharacteristic
377C22×C8C22×D1311yescharacteristic
378C4⋊Q8—262no—
379C4⋊Q8—521no—
380C22⋊Q8—134no—
381C22⋊Q8—262no—
382C22⋊Q8—524no—
383C4×Q8—262no—
384C4×Q8—521no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—131no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—262no—
393C2×C4⋊C4—262no—
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—261no—
401C2×C4⋊C4—261no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4—521no—
405C2×C4⋊C4—521no—
406C2×C22⋊C4—261no—
407C2×C22⋊C4—261no—
408C2×C22⋊C4D5211yescharacteristic
409C2×C22⋊C4D5211yescharacteristic
410C2×C42—261no—
411C2×C42—261no—
412C2×C42C22×D1311yescharacteristic
413C2×C42C22×D1311yescharacteristic
414#107—262no—
415#107—521no—
416C4⋊C8—41no—
417C4⋊C8—41no—
418#103—262no—
419#103—521no—
420#103—521no—
421#103—521no—
422C22⋊C8—22no—
423#95—261no—
424#95—261no—
425#95—261no—
426#95—261no—
427#95—261no—
428#95—261no—
429#95—261no—
430#95D5211yescharacteristic
431#95D5211yescharacteristic
432C2×C13—24no—
433C2×C13#245011yescharacteristic
434C2×C13C2×#47711yescharacteristic
435C2×C13#308411yescharacteristic
436C2×C13#329911yescharacteristic
437C2×C13#329911yescharacteristic
438C2×C13#330611yescharacteristic
439C2×C13#331011yescharacteristic
440C24C2×D5211yescharacteristic
441C2×Q8—132no—
442C2×Q8—261no—
443C2×Q8—261no—
444C2×Q8—261no—
445C2×Q8—261no—
446C2×Q8—261no—
447C2×Q8—522no—
448C2×Q8—522no—
449C2×Q8—1041no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—522no—
463C22×C4—522no—
464C22×C4—522no—
465C22×C4—522no—
466C22×C4—1041no—
467C22×C4—1041no—
468C22×C4C2×D5211yescharacteristic
469C22×C4C2×D5211yescharacteristic
470C22×C4C2×D5211yescharacteristic
471C22×C4C2×D5211yescharacteristic
472C22×C4C2×D5211yescharacteristic
473C22×C4#612912yes—
474C22×C4Q8×D1312yes—
475C22×C4C23×D1311yescharacteristic
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—44no—
489C4⋊C4—132no—
490C4⋊C4—132no—
491C4⋊C4—132no—
492C4⋊C4—264no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4—261no—
500C4⋊C4—261no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—522no—
505C4⋊C4—522no—
506C4⋊C4—522no—
507C4⋊C4—522no—
508C4⋊C4—522no—
509C4⋊C4—522no—
510C4⋊C4—522no—
511C4⋊C4—1041no—
512C4⋊C4—1041no—
513C22⋊C4—22no—
514C22⋊C4—264no—
515C22⋊C4—522no—
516C22⋊C4Dic5214yes—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—522no—
522C42—1041no—
523C13#2641411yescharacteristic, complemented, Sylow
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23#8815112yes—
529C23C2×Dic5212yes—
530C23#8816212yes—
531C23C22×D5211yescharacteristic
532Q8—262no—
533Q8—262no—
534Q8—521no—
535Q8—521no—
536Q8—1044no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—262no—
554C2×C4—262no—
555C2×C4—262no—
556C2×C4—262no—
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—521no—
573C2×C4—521no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—1044no—
578C2×C4—1044no—
579C2×C4#8815112yes—
580C2×C4C2×Dic5212yes—
581C2×C4C2×Dic5212yes—
582C2×C4C2×#612911yescharacteristic
583C2×C4#8825111yescharacteristic
584C2×C4#8825111yescharacteristic
585C2×C4C2×Q8×D1311yescharacteristic
586C2×C4#41×D1311yescharacteristic
587C2×C4#41×D1311yescharacteristic
588C8—41no—
589C8—41no—
590C8—41no—
591C8—41no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22#1171851114yes—
599C22C2×#8815111yescharacteristic
600C22#1171925911yescharacteristic
601C22#1171925911yescharacteristic
602C22C22×Dic5211yescharacteristic
603C22C2×#8816211yescharacteristic
604C22#1171945611yescharacteristic
605C22#1171945611yescharacteristic
606C4—22no—
607C4—22no—
608C4—22no—
609C4—41no—
610C4—41no—
611C4—522no—
612C4—522no—
613C4—522no—
614C4—522no—
615C4—1041no—
616C4—1041no—
617C4—1041no—
618C4—1041no—
619C4#1171929811yescharacteristic
620C4#1171934111yescharacteristic
621C4#1171934111yescharacteristic
622C4#1171935411yescharacteristic
623C2—24no—
624C2#1311865811yescharacteristic
625C2C2×#1171851111yescharacteristic
626C2#1312470011yescharacteristic
627C2#1312671311yescharacteristic
628C2#1312671311yescharacteristic
629C2#1312679911yescharacteristic
630C2#1312685911yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1850C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1850D13
hypocenterC13#26414
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. #13116400C2semidirect
4. #13116329C2semidirect
5. #13116230C2semidirect
6. #13115978C2semidirect
7. #13115783C2semidirect
8. #13115429C2semidirect
11. #13115093C2semidirect
13. #13114842C2semidirect
94. #88178Q8semidirect
523. C13#26414semidirect

Maximal subgroups

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

subgroupindex
#131185382
#131178392
#131164002
#131163292
#131162302
#131159782
#131157832
#131154292
#131152592
#131151412
#131150932
#131150262
#131148422
C2×#117181432
C13×#18502
#2641413