Finite Group Databasebeta

← #15870984

Subgroups — #15870984

Order 3328.

886 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718426C211yesmaximal, characteristic
2#13117407C211yesmaximal, characteristic, complemented
3#13117383C211yesmaximal, characteristic
4#13115807C211yesmaximal, characteristic, complemented
5#13115651C211yesmaximal, characteristic
6#13115536C211yesmaximal, characteristic
7#13115526C211yesmaximal, characteristic, complemented
8#13115525C211yesmaximal, characteristic, complemented
9#13114968C211yesmaximal, characteristic, complemented
10#13114655C211yesmaximal, characteristic, complemented
11#13114655C211yesmaximal, characteristic, complemented
12#102×Dic13C211yesmaximal, characteristic
13#102×Dic13C211yesmaximal, characteristic
14#97×Dic13C211yesmaximal, characteristic, complemented
15C13×#1936C211yesmaximal, characteristic
16C2×#88190C2211yescharacteristic
17C2×D4×Dic13C2211yescharacteristic
18C2×#88142C2211yescharacteristic
19C2×#88141—21no—
20C2×#88141C2211yescharacteristic
21C2×C13×#102C2211yescharacteristic
22C2×C13×#102C2211yescharacteristic
23C2×C13×#97C2211yescharacteristic
24C13×#390C2211yescharacteristic
25C13×#389C2211yescharacteristic
26C2×#88072C2211yescharacteristic
27C2×#88072C2211yescharacteristic
28C2×#88056C2211yescharacteristic
29C2×#88056C2211yescharacteristic
30C2×#88055C2211yescharacteristic
31C2×#88055C2211yescharacteristic
32C2×C8×Dic13C2211yescharacteristic
33C2×C8×Dic13C2211yescharacteristic
34#11718638C2211yescharacteristic
35#11718637C2211yescharacteristic
36C4⋊C4×Dic13C2211yescharacteristic
37C4⋊C4×Dic13C2211yescharacteristic
38#11718633—21no—
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41#11718605—21no—
42#11718605—21no—
43C22⋊C4×Dic13—21no—
44C22⋊C4×Dic13—21no—
45C42×Dic13C2211yescharacteristic
46#11718590C2211yescharacteristic
47#11718589C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49#11718426C418yescomplemented
50#11718310—21no—
51#11718307—21no—
52C13×#340C2211yescharacteristic
53C13×#340C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×Dic13—21no—
62C22×Dic26—21no—
63C22×Dic26C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C22⋊C4—21no—
71C2×C13×C22⋊C4—21no—
72C2×C42×C13C2311yescharacteristic
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76#88190—22no—
77#88190C2×C414yes—
78D4×Dic13—22no—
79D4×Dic13—22no—
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×#6101—21no—
84C2×#6101—21no—
85C2×#6101—21no—
86C2×#6101—21no—
87C2×#6101—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13D411yescharacteristic
92C2×C4×Dic13D411yescharacteristic
93C2×C4×Dic13D411yescharacteristic
94C2×C4×Dic13D411yescharacteristic
95C2×C4×Dic13C2311yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99#88142—22no—
100#88142C2×C414yescomplemented
101#88141—22no—
102#88141—22no—
103#88141—44no—
104C13×#102—22no—
105C13×#102C2×C414yes—
106C13×#97—22no—
107C13×#95—21no—
108#88072—22no—
109#88072C2×C414yes—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88056—22no—
118#88056C2×C414yescomplemented
119#88055—22no—
120#88055C2×C414yescomplemented
121C8×Dic13—22no—
122C8×Dic13—22no—
123#88050—22no—
124#88050C2×C414yescomplemented
125#88043—22no—
126C4×#489—131nomaximal, Sylow
127C24×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13C22×C412yes—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2411yescharacteristic
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—42no—
145C22×Dic13—42no—
146C22×Dic13—42no—
147C22×Dic13C2×D411yescharacteristic
148C22×Dic13C2×D411yescharacteristic
149C22×Dic13C2×D411yescharacteristic
150C22×Dic13C2×D411yescharacteristic
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26—24no—
157C2×Dic26—42no—
158C2×Dic26—42no—
159C2×Dic26C22×C412yes—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13C22×C412yes—
165C2×C8×C13#4112yes—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—42no—
172C13×C4⋊C4C22×C412yes—
173C13×C22⋊C4—42no—
174C13×C22⋊C4—42no—
175C42×C13—21no—
176C42×C13—21no—
177C22⋊Dic13—24no—
178C22⋊Dic13—24no—
179C22⋊Dic13—42no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13C22×C412yes—
186#6101—24no—
187#6101—42no—
188#6101—42no—
189#6101—42no—
190#6101—42no—
191C4×Dic13—22no—
192C4×Dic13—22no—
193C4×Dic13—41no—
194C4×Dic13—41no—
195C4×Dic13—42no—
196C4×Dic13—42no—
197C4×Dic13—42no—
198C4×Dic13C22×C412yes—
199C4×Dic13#4112yes—
200C4×Dic13#4112yes—
201C4×Dic13#4112yes—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055C22×C412yes—
207C2×#1055#4112yes—
208C2×#489—131no—
209C4×C4⋊Q8—131no—
210C4×#124—131no—
211#1993—131no—
212#1959—131no—
213#1936—131no—
214#1936D1311yescharacteristic
215#1935—131no—
216#1935—131no—
217#1836—131no—
218C4×#103—131no—
219C4×#103—131no—
220C4×#102—131no—
221C4×#102—131no—
222C4×#97—131no—
223C23×C13—22no—
224C23×C13—41no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13—41no—
228C23×C13—41no—
229C23×C13—41no—
230C23×C13C22×D411yescharacteristic
231D4×C13—22no—
232D4×C13—22no—
233D4×C13—41no—
234D4×C13—41no—
235C2×C4×C13—22no—
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—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×C13C23×C411yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C2×C4×C13C2×#4111yescharacteristic
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—22no—
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—84no—
275C2×Dic13C4×D412yes—
276C2×Dic13C4×D412yes—
277C2×Dic13#12412yes—
278C2×Dic13#12412yes—
279C2×Dic13AGL(1,ℤ/8)12yes—
280C2×Dic13#13712yes—
281Dic26—22no—
282Dic26—22no—
283Dic26—48no—
284Dic26—41no—
285Dic26—41no—
286C8×C13—22no—
287C8×C13—22no—
288#1055—22no—
289#1055—22no—
290C2×C4⋊Q8—131no—
291C2×#124—131no—
292C2×C4×Q8—131no—
293C2×C4×Q8—261no—
294C2×C4×D4—131no—
295#489—138no—
296C2×#103—131no—
297C2×#103—131no—
298C2×#103—131no—
299C2×#103—131no—
300C2×#102—131no—
301C2×#102—131no—
302C2×#102C2×D1311yescharacteristic
303C2×#102C2×D1311yescharacteristic
304C2×#97—131no—
305C2×#97—131no—
306C2×#97—131no—
307C2×#97C2×D1311yescharacteristic
308C2×C4×C8—131no—
309C2×C4×C8—131no—
310#391—131no—
311#391—261no—
312#390C2×D1311yescharacteristic
313#389—131no—
314#389—261no—
315#389C2×D1311yescharacteristic
316#388—261no—
317#388—261no—
318#384—131no—
319#382—131no—
320C4×C4⋊C4—131no—
321C4×C4⋊C4—131no—
322C4×C4⋊C4—261no—
323C4×C22⋊C4—261no—
324C4×C22⋊C4—261no—
325C43—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332#340C2×D1311yescharacteristic
333#340C2×D1311yescharacteristic
334C22×C13—42no—
335C22×C13—42no—
336C22×C13—42no—
337C22×C13—81no—
338C22×C13—81no—
339C22×C13—81no—
340C22×C13—81no—
341C22×C13C2×C4×D411yescharacteristic
342C22×C13C2×#12411yescharacteristic
343C22×C13#53211yescharacteristic
344C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
345C22×C13C2×#13711yescharacteristic
346C22×C13#57511yescharacteristic
347C22×C13#57511yescharacteristic
348C4×C13—41no—
349C4×C13—41no—
350C4×C13—42no—
351C4×C13—81no—
352C4×C13—81no—
353C4×C13C4×#4111yescharacteristic
354C4×C13C4×#4111yescharacteristic
355C4×C13#52911yescharacteristic
356C4×C13#52911yescharacteristic
357Dic13—22no—
358Dic13—22no—
359Dic13—22no—
360Dic13—42no—
361Dic13—42no—
362Dic13—81no—
363Dic13—81no—
364Dic13#48914yescomplemented
365C22×Q8—131no—
366C22×Q8—261no—
367C22×D4C22×D1311yescharacteristic
368C23×C4—261no—
369C22×C8—131no—
370C22×C8—131no—
371C22×C8C22×D1311yescharacteristic
372C22×C8C22×D1311yescharacteristic
373C4⋊Q8—134no—
374C4⋊Q8—262no—
375#124—134no—
376#124—262no—
377C4×Q8—262no—
378C4×Q8—262no—
379C4×Q8—524no—
380C4×D4—262no—
381C4×D4—262no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—131no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—261no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4C22×D1311yescharacteristic
392C2×C4⋊C4C22×D1311yescharacteristic
393C2×C4⋊C4C22×D1311yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—261no—
397C2×C22⋊C4—261no—
398C2×C22⋊C4—261no—
399C2×C42—131no—
400C2×C42—131no—
401C2×C42—131no—
402C2×C42—131no—
403C2×C42—131no—
404C2×C42—131no—
405C2×C42—261no—
406C2×C42—261no—
407C2×C42—261no—
408C2×C42C22×D1311yescharacteristic
409#103—134no—
410#103—134no—
411#103—262no—
412#103—262no—
413#102—22no—
414#102—134no—
415#102—262no—
416#102C4×D1314yes—
417#97—22no—
418#97—134no—
419#97—262no—
420#97—262no—
421C4×C8—262no—
422C4×C8—262no—
423#95—21no—
424#95—261no—
425#95—261no—
426#95—261no—
427#95—261no—
428#95—261no—
429#95—261no—
430#95—261no—
431C2×C13—82no—
432C2×C13C4×#12411yescharacteristic
433C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
434C2×C13C4×#13711yescharacteristic
435C2×C13C2×#48911yescharacteristic
436C2×C13#313511yescharacteristic
437C2×C13#317111yescharacteristic
438C2×C13#317211yescharacteristic
439C24—21no—
440C2×Q8—132no—
441C2×Q8—264no—
442C2×Q8—261no—
443C2×Q8—261no—
444C2×Q8—261no—
445C2×Q8—261no—
446C2×Q8—261no—
447C2×Q8—522no—
448C2×Q8—522no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4C2×C4×D1312yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—131no—
459C22×C4—131no—
460C22×C4—131no—
461C22×C4—131no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—522no—
467C22×C4—522no—
468C22×C4—522no—
469C22×C4D4×D1311yescharacteristic
470C22×C4D4×D1311yescharacteristic
471C22×C4C23×D1311yescharacteristic
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—132no—
477C2×C8—132no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8C2×C4×D1312yes—
483C2×C8#612912yes—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—42no—
490C4⋊C4—132no—
491C4⋊C4—264no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—522no—
498C4⋊C4—522no—
499C4⋊C4—522no—
500C4⋊C4—522no—
501C4⋊C4C2×C4×D1312yes—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C22⋊C4—264no—
505C22⋊C4—264no—
506C22⋊C4—522no—
507C42—21no—
508C42—21no—
509C42—132no—
510C42—132no—
511C42—132no—
512C42—132no—
513C42—262no—
514C42—262no—
515C42—521no—
516C42—521no—
517C42—522no—
518C42—522no—
519C42—522no—
520C13C4×#48911yescharacteristic, complemented, Sylow
521C23—22no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23C2×D4×D1311yescharacteristic
529Q8—262no—
530Q8—262no—
531Q8—528no—
532Q8—521no—
533Q8—521no—
534D4—22no—
535D4—22no—
536D4—41no—
537D4—41no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
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—132no—
554C2×C4—132no—
555C2×C4—132no—
556C2×C4—132no—
557C2×C4—132no—
558C2×C4—132no—
559C2×C4—261no—
560C2×C4—261no—
561C2×C4—261no—
562C2×C4—261no—
563C2×C4—261no—
564C2×C4—261no—
565C2×C4—262no—
566C2×C4—262no—
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×C4C22×C4×D1311yescharacteristic
579C2×C4C2×#612911yescharacteristic
580C2×C4#41×D1311yescharacteristic
581C2×C4#41×D1311yescharacteristic
582C2×C4#41×D1311yescharacteristic
583C2×C4#41×D1311yescharacteristic
584C8—22no—
585C8—22no—
586C8—262no—
587C8—262no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22C4×D4×D1311yescharacteristic
596C22#1171930111yescharacteristic
597C22D13×#12411yescharacteristic
598C22D13×AGL(1,ℤ/8)11yescharacteristic
599C22#1171947811yescharacteristic
600C22#1171947811yescharacteristic
601C22D13×#13711yescharacteristic
602C4—41no—
603C4—41no—
604C4—42no—
605C4—81no—
606C4—81no—
607C4—134no—
608C4—262no—
609C4—262no—
610C4—262no—
611C4—522no—
612C4—522no—
613C4—1041no—
614C4—1041no—
615C4#1171922711yescharacteristic
616C4C4×#612911yescharacteristic
617C4#1171935411yescharacteristic
618C4#1171941111yescharacteristic
619C2—82no—
620C2#1311737711yescharacteristic
621C2#1312364711yescharacteristic
622C2#1312365811yescharacteristic
623C2D13×#48911yescharacteristic
624C2#1312518011yescharacteristic
625C2#1312542611yescharacteristic
626C2#1312543511yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1936C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenter#1936D13
hypocenterC13C4×#489
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
2. #13117407C2semidirect
4. #13115807C2semidirect
7. #13115526C2semidirect
8. #13115525C2semidirect
9. #13114968C2semidirect
10. #13114655C2semidirect
11. #13114655C2semidirect
14. #97×Dic13C2semidirect
49. #11718426C4semidirect
100. #88142C2×C4semidirect
118. #88056C2×C4semidirect
120. #88055C2×C4semidirect
124. #88050C2×C4semidirect
364. Dic13#489semidirect
520. C13C4×#489semidirect

Maximal subgroups

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

subgroupindex
C2×#117184262
#131174072
#131173832
#131158072
#131156512
#131155362
#131155262
#131155252
#131149682
#131146552
#102×Dic132
#97×Dic132
C13×#19362
C4×#48913