Finite Group Databasebeta

← #15925540

Subgroups — #15925540

Order 3328.

838 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
1C2×#11718518C211yesmaximal, characteristic, complemented
2#13118554C211yesmaximal, characteristic
3#13117841C211yesmaximal, characteristic
4#13116385C211yesmaximal, characteristic, complemented
5#13116335C211yesmaximal, characteristic, complemented
6#13116212C211yesmaximal, characteristic, complemented
7#13116176C211yesmaximal, characteristic, complemented
8#13115605C211yesmaximal, characteristic, complemented
9#13115423C211yesmaximal, characteristic, complemented
10#13115259C211yesmaximal, characteristic
11#13115143C211yesmaximal, characteristic
12#13115101C211yesmaximal, characteristic, complemented
13#13115024C211yesmaximal, characteristic
14#13115014C211yesmaximal, characteristic
15C22×C13×#106C211yesmaximal, characteristic
16C23×C8×C13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88178C2211yescharacteristic
20C2×#88144C2211yescharacteristic
21C2×#88141C2211yescharacteristic
22C2×C13×#106—24no—
23C2×C13×#106C2211yescharacteristic
24C2×C13×#106C2211yescharacteristic
25C2×C13×#106C2211yescharacteristic
26C2×C13×#106C2211yescharacteristic
27#11718873—21no—
28#11718873C2211yescharacteristic
29#11718871—21no—
30#11718871—21no—
31C4×C22⋊Dic13—21no—
32C4×C22⋊Dic13C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×#88056C2211yescharacteristic
35C2×#88056C2211yescharacteristic
36C2×#88054C2211yescharacteristic
37C2×#88054C2211yescharacteristic
38#11718647—21no—
39#11718646C2211yescharacteristic
40#11718645—21no—
41#11718639—21no—
42#11718638C2211yescharacteristic
43C4⋊C4×Dic13C2211yescharacteristic
44#11718635C2211yescharacteristic
45#11718634C2211yescharacteristic
46#11718634C2211yescharacteristic
47#11718633—21no—
48C2×#88050C2211yescharacteristic
49C2×#88050C2211yescharacteristic
50C2×#88047C2211yescharacteristic
51C2×#88047C2211yescharacteristic
52#11718518—24no—
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C23×C4×C13—21no—
62C23×C4×C13—21no—
63C23×C4×C13C2311yescharacteristic
64C22×Dic26C2311yescharacteristic
65C22×C8×C13—22no—
66C22×C8×C13—22no—
67C22×C8×C13—22no—
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—41no—
75C2×C13×C4⋊C4—41no—
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13—21no—
82C2×C22⋊Dic13D411yescharacteristic
83C2×C22⋊Dic13D411yescharacteristic
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13—21no—
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×C4×Dic13—21no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13C2311yescharacteristic
99C2×C4×Dic13C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102#88144—22no—
103#88144—41no—
104#88141—22no—
105#88141—41no—
106C13×#106—22no—
107C13×#106—22no—
108C13×#106—22no—
109C13×#106D414yes—
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#88071—21no—
119#88071D411yescharacteristic
120#88071D411yescharacteristic
121C22⋊#1055—22no—
122#88056—22no—
123#88056—22no—
124#88054—22no—
125#88054—22no—
126#88050—22no—
127#88050—41no—
128#88047—22no—
129#88047—41no—
130#26346—131nomaximal, Sylow
131C24×C13C2×D411yescharacteristic
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—42no—
141C22×C4×C13—42no—
142C22×C4×C13—42no—
143C22×C4×C13—42no—
144C22×C4×C13—81no—
145C22×C4×C13—81no—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×Q812yes—
148C22×C4×C13#4112yes—
149C22×C4×C13C2411yescharacteristic
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13C2×D411yescharacteristic
155C22×Dic13C2×D411yescharacteristic
156C22×Dic13C2×D411yescharacteristic
157C22×Dic13C2×D411yescharacteristic
158C2×Dic26—21no—
159C2×Dic26—21no—
160C2×Dic26—21no—
161C2×Dic26—21no—
162C2×Dic26—21no—
163C2×Dic26C2×Q812yes—
164C2×C8×C13—28no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13C2×D412yes—
170C2×C8×C13#4112yes—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—42no—
178C13×C4⋊C4—42no—
179C13×C4⋊C4C2×D412yes—
180C13×C4⋊C4C2×D412yes—
181C22⋊Dic13—24no—
182C22⋊Dic13—22no—
183C22⋊Dic13—22no—
184C22⋊Dic13—42no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—42no—
191C4⋊Dic13—81no—
192C4⋊Dic13C2×Q812yes—
193#6101—24no—
194#6101—42no—
195#6101—42no—
196#6101—81no—
197#6101—81no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C4×Dic13—42no—
203C4×Dic13—81no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#479—131no—
211C22×#106D1311yescharacteristic
212#2442—131no—
213#2360—131no—
214#2097—131no—
215#2088—131no—
216#2066—131no—
217#2059—131no—
218#1949—131no—
219#1920—131no—
220#1892—131no—
221#1872—131no—
222#1865—131no—
223#1852—131no—
224#1850—131no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13C22⋊Q812yes—
230C23×C13#13512yes—
231C23×C13#13712yes—
232C23×C13C22×D411yescharacteristic
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
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—41no—
250C2×C4×C13—41no—
251C2×C4×C13—84no—
252C2×C4×C13—84no—
253C2×C4×C13C22⋊Q812yes—
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13C22×Q811yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C13H(5,𝔽2)11yescharacteristic
259C2×C4×C132−1+411yescharacteristic
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284Dic26—22no—
285Dic26—22no—
286Dic26—41no—
287Dic26—41no—
288C8×C13—22no—
289C8×C13—22no—
290#1055—41no—
291#1055—41no—
292C23×C8C2×D1311yescharacteristic
293C2×#125—131no—
294C2×C22⋊Q8—131no—
295C2×C4×Q8—131no—
296C22×C4⋊C4C2×D1311yescharacteristic
297C22×C4⋊C4C2×D1311yescharacteristic
298#479—264no—
299C2×#107—131no—
300C2×#107—131no—
301C2×#106—24no—
302C2×#106C2×D1311yescharacteristic
303C2×#106C2×D1311yescharacteristic
304C2×#106C2×D1311yescharacteristic
305C2×#106C2×D1311yescharacteristic
306C2×C4⋊C8—131no—
307C2×C4⋊C8—131no—
308C2×#103—131no—
309C2×#103—131no—
310C2×#103—131no—
311C2×#103—131no—
312C2×C22⋊C8—131no—
313#400—261no—
314#398—261no—
315#391—131no—
316#389—131no—
317#389—131no—
318#389—131no—
319#389—261no—
320#387—261no—
321#385—261no—
322#385—261no—
323#382—131no—
324#380—131no—
325#380—261no—
326C4×C4⋊C4—131no—
327C4×C22⋊C4—131no—
328C4×C22⋊C4—261no—
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#340—131no—
334#340—131no—
335#336—131no—
336#336—131no—
337C22×C13—22no—
338C22×C13—22no—
339C22×C13—22no—
340C22×C13—22no—
341C22×C13—22no—
342C22×C13—22no—
343C22×C13#47914yescomplemented
344C22×C13C2×C22⋊Q811yescharacteristic
345C22×C13D4211yescharacteristic
346C22×C13#54711yescharacteristic
347C22×C13C2×#13511yescharacteristic
348C22×C13C2×#13711yescharacteristic
349C22×C13#57711yescharacteristic
350C22×C13#57711yescharacteristic
351C4×C13—22no—
352C4×C13—42no—
353C4×C13—42no—
354C4×C13—81no—
355C4×C13—81no—
356C4×C13#52511yescharacteristic
357C4×C13#53911yescharacteristic
358C4×C13D4×Q811yescharacteristic
359C4×C13#55411yescharacteristic
360Dic13—41no—
361Dic13—42no—
362Dic13—41no—
363Dic13—42no—
364Dic13—41no—
365Dic13—41no—
366Dic13—81no—
367Dic13—81no—
368C22×Q8—131no—
369C23×C4—21no—
370C23×C4—21no—
371C23×C4C22×D1311yescharacteristic
372C22×C8—22no—
373C22×C8—22no—
374C22×C8—22no—
375C22×C8—131no—
376C22×C8—131no—
377C22×C8C22×D1311yescharacteristic
378C22×C8C22×D1311yescharacteristic
379#125—262no—
380#125—521no—
381C22⋊Q8—134no—
382C22⋊Q8—262no—
383C4×Q8—262no—
384C4×Q8—521no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—41no—
390C2×C4⋊C4—41no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—131no—
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⋊C4C22×D1311yescharacteristic
402C2×C4⋊C4C22×D1311yescharacteristic
403C2×C4⋊C4C22×D1311yescharacteristic
404C2×C4⋊C4C22×D1311yescharacteristic
405C2×C22⋊C4—131no—
406C2×C22⋊C4—131no—
407C2×C22⋊C4—261no—
408C2×C22⋊C4—261no—
409C2×C42—131no—
410C2×C42—131no—
411C2×C42—261no—
412C2×C42—261no—
413#107—262no—
414#107—521no—
415#106—22no—
416#106—22no—
417#106—22no—
418#106C22⋊D1314yes—
419C4⋊C8—262no—
420C4⋊C8—262no—
421#103—262no—
422#103—262no—
423#103—262no—
424#103—521no—
425C22⋊C8—262no—
426#95—131no—
427#95—131no—
428#95—261no—
429#95—261no—
430#95—261no—
431#95—261no—
432#95—261no—
433#95—261no—
434#95—261no—
435#95—261no—
436#95—261no—
437C2×C13—24no—
438C2×C13#244911yescharacteristic
439C2×C13C2×#47911yescharacteristic
440C2×C13#308411yescharacteristic
441C2×C13#326611yescharacteristic
442C2×C13#328211yescharacteristic
443C2×C13#333711yescharacteristic
444C2×C13#334411yescharacteristic
445C24D4×D1311yescharacteristic
446C2×Q8—132no—
447C2×Q8—261no—
448C2×Q8—261no—
449C2×Q8—261no—
450C2×Q8—261no—
451C2×Q8—261no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—81no—
465C22×C4—81no—
466C22×C4—131no—
467C22×C4—131no—
468C22×C4—131no—
469C22×C4—131no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4#612712yes—
475C22×C4D4×D1311yescharacteristic
476C22×C4Q8×D1312yes—
477C22×C4C23×D1311yescharacteristic
478C2×C8—28no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8#612712yes—
490C2×C8C2×C22⋊D1312yes—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—132no—
500C4⋊C4—264no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—522no—
507C4⋊C4—522no—
508C4⋊C4—522no—
509C4⋊C4—1041no—
510C4⋊C4—1041no—
511C4⋊C4—1041no—
512C4⋊C4C2×C22⋊D1312yes—
513C4⋊C4C2×C22⋊D1312yes—
514C22⋊C4—264no—
515C22⋊C4—262no—
516C22⋊C4—262no—
517C22⋊C4—522no—
518C42—261no—
519C42—261no—
520C42—261no—
521C42—261no—
522C42—522no—
523C42—1041no—
524C13#2634611yescharacteristic, complemented, Sylow
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23#8815012yes—
530C23#8816912yes—
531C23#8817012yes—
532C23C2×D4×D1311yescharacteristic
533Q8—262no—
534Q8—262no—
535Q8—521no—
536Q8—521no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—84no—
556C2×C4—84no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—261no—
560C2×C4—261no—
561C2×C4—261no—
562C2×C4—261no—
563C2×C4—261no—
564C2×C4—261no—
565C2×C4—261no—
566C2×C4—261no—
567C2×C4—262no—
568C2×C4—262no—
569C2×C4—261no—
570C2×C4—261no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4#8815012yes—
582C2×C4C2×#612711yescharacteristic
583C2×C4C2×#612711yescharacteristic
584C2×C4#8825111yescharacteristic
585C2×C4C2×Q8×D1311yescharacteristic
586C2×C4#8825411yescharacteristic
587C2×C4C22×C22⋊D1311yescharacteristic
588C8—22no—
589C8—22no—
590C8—521no—
591C8—521no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22#1171851814yescomplemented
599C22#1171921211yescharacteristic
600C22C2×#8815011yescharacteristic
601C22C2×#8816911yescharacteristic
602C22C2×#8817011yescharacteristic
603C22#1171946711yescharacteristic
604C22#1171946711yescharacteristic
605C22D4×C22⋊D1311yescharacteristic
606C4—22no—
607C4—42no—
608C4—42no—
609C4—81no—
610C4—81no—
611C4—521no—
612C4—522no—
613C4—521no—
614C4—521no—
615C4—522no—
616C4—521no—
617C4—1041no—
618C4—1041no—
619C4#1171921611yescharacteristic
620C4#1171922011yescharacteristic
621C4#1171949611yescharacteristic
622C4Q8×C22⋊D1311yescharacteristic
623C2—24no—
624C2#1311864511yescharacteristic
625C2C2×#1171851811yescharacteristic
626C2#1312470311yescharacteristic
627C2#1312634611yescharacteristic
628C2#1312654311yescharacteristic
629C2#1312721111yescharacteristic
630C2#1312728711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×#106C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC22×#106D13
hypocenterC13#26346
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
1. C2×#11718518C2semidirect
4. #13116385C2semidirect
5. #13116335C2semidirect
6. #13116212C2semidirect
7. #13116176C2semidirect
8. #13115605C2semidirect
9. #13115423C2semidirect
12. #13115101C2semidirect
343. C22×C13#479semidirect
524. C13#26346semidirect
598. C22#11718518semidirect

Maximal subgroups

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

subgroupindex
C2×#117185182
#131185542
#131178412
#131163852
#131163352
#131162122
#131161762
#131156052
#131154232
#131152592
#131151432
#131151012
#131150242
#131150142
C22×C13×#1062
#2634613