Finite Group Databasebeta

← #15865097

Subgroups — #15865097

Order 3328.

974 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718542C211yesmaximal, characteristic
2D13×#389C211yesmaximal, characteristic
3C4×#88146C211yesmaximal, characteristic
4#13115430C211yesmaximal, characteristic, complemented
5#13115426C211yesmaximal, characteristic, complemented
6#13115424C211yesmaximal, characteristic, complemented
7#13115420C211yesmaximal, characteristic, complemented
8#13115415C211yesmaximal, characteristic, complemented
9#13115411C211yesmaximal, characteristic, complemented
10#13115407C211yesmaximal, characteristic, complemented
11#13114554C211yesmaximal, characteristic
12#13114554C211yesmaximal, characteristic
13#13114554C211yesmaximal, characteristic
14#13114528C211yesmaximal, characteristic
15C13×#1918C211yesmaximal, characteristic, complemented
16C22×#6094C2211yescharacteristic
17C22×#6094C2211yescharacteristic
18C2×#88146C2211yescharacteristic
19C2×#88146C2211yescharacteristic
20C2×C4⋊C4×D13—21no—
21C2×C4⋊C4×D13C2211yescharacteristic
22C2×C4⋊C4×D13C2211yescharacteristic
23C2×C42×D13C2211yescharacteristic
24C2×C13×#107C2211yescharacteristic
25C13×#389C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic
27C2×#88057C2211yescharacteristic
28#11718646C2211yescharacteristic
29C4⋊C4×Dic13C2211yescharacteristic
30C4⋊C4×Dic13C2211yescharacteristic
31#11718634C2211yescharacteristic
32#11718633—21no—
33C2×#88048C2211yescharacteristic
34C2×#88047C2211yescharacteristic
35C4×#6103—21no—
36C4×C4⋊Dic13C2211yescharacteristic
37C42×Dic13—21no—
38#11718589C2211yescharacteristic
39#11718542C418yescomplemented
40#11718327—21no—
41D13×#95—21no—
42#11718309—21no—
43#11718308—21no—
44C13×#340C2211yescharacteristic
45C13×#340C2211yescharacteristic
46C13×#340C2211yescharacteristic
47C13×#336C2211yescharacteristic
48#11718143C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×C4×D13—21no—
61C22×C4×D13—21no—
62C22×C4×D13D411yescharacteristic
63C22×C4×D13D411yescharacteristic
64C22×C4×D13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C42×C13—21no—
73C2×C42×C13C2311yescharacteristic
74C2×#6103—21no—
75C2×#6103—21no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×#6101—21no—
82C2×#6101—21no—
83C2×#6101—21no—
84C2×#6101—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13D411yescharacteristic
91C2×C4×Dic13D411yescharacteristic
92C2×C4×Dic13C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C2×#6094—22no—
96C2×#6094—22no—
97C2×#6094—22no—
98C2×#6094—22no—
99C2×#6094—22no—
100C2×#6094C2×C414yes—
101#88146—22no—
102#88146—22no—
103#88146C2×C414yes—
104#88146Q814yes—
105C4⋊C4×D13—22no—
106C4⋊C4×D13—22no—
107C4⋊C4×D13—22no—
108C4⋊C4×D13—44no—
109C4⋊C4×D13C2×C414yes—
110C42×D13—22no—
111C42×D13—22no—
112C13×#107C2×C414yescomplemented
113C13×#95—21no—
114C13×#95—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121#88057C2×C414yescomplemented
122#88048C2×C414yescomplemented
123#88047C2×C414yescomplemented
124#21034—131nomaximal, Sylow
125C23×D13C2×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×C13C2411yescharacteristic
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13C2×D411yescharacteristic
138C22×Dic13C2×D411yescharacteristic
139C22×Dic13C2×D411yescharacteristic
140C2×C4×D13—24no—
141C2×C4×D13—22no—
142C2×C4×D13—22no—
143C2×C4×D13—22no—
144C2×C4×D13—22no—
145C2×C4×D13—41no—
146C2×C4×D13—41no—
147C2×C4×D13—42no—
148C2×C4×D13—42no—
149C2×C4×D13—42no—
150C2×C4×D13—42no—
151C2×C4×D13—42no—
152C2×C4×D13C22×C412yes—
153C2×C4×D13C2×Q812yes—
154C2×C4×D13#4112yes—
155C2×C4×D13#4112yes—
156C2×C4×D13#4112yes—
157C2×C4×D13#4112yes—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13C22×C412yes—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—42no—
170C13×C4⋊C4C22×C412yes—
171C13×C4⋊C4C22×C412yes—
172C13×C4⋊C4C2×Q812yes—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—42no—
176#6103—24no—
177#6103—24no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—42no—
184C4⋊Dic13C22×C412yes—
185C4⋊Dic13C22×C412yes—
186C4⋊Dic13C2×Q812yes—
187#6101—24no—
188#6101—42no—
189#6101—42no—
190#6101—42no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—24no—
194C4×Dic13—24no—
195C4×Dic13—22no—
196C4×Dic13—22no—
197C4×Dic13—42no—
198C4×Dic13—42no—
199C4×Dic13—42no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055C22×C412yes—
206#6094—28no—
207#6094—44no—
208C2×#428—131no—
209C2×#389—131no—
210C4×#117—131no—
211#1921—131no—
212#1921—131no—
213#1920—131no—
214#1920—131no—
215#1919—131no—
216#1919—131no—
217#1918—131no—
218#1918D1311yescharacteristic, complemented
219#1736—131no—
220#1736—131no—
221#1736—131no—
222#1728—131no—
223C23×C13C22×D411yescharacteristic
224C22×D13—21no—
225C22×D13—21no—
226C22×D13—21no—
227C22×D13—21no—
228C22×D13C4×D412yes—
229C22×D13C22⋊Q812yes—
230C22×D13#12312yes—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
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×C13AGL(1,ℤ/8)12yes—
249C2×C4×C13C23×C411yescharacteristic
250C2×C4×C13C22×Q811yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
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×Dic13C4×D412yes—
273C2×Dic13C22⋊Q812yes—
274C2×Dic13#12312yes—
275C2×Dic13#13712yes—
276C4×D13—44no—
277C4×D13—44no—
278C4×D13—48no—
279C4×D13—84no—
280C4×D13#11714yes—
281C4×D13C4×Q814yes—
282C4×D13#12514yes—
283C4×D13#12614yes—
284C8×C13—22no—
285C8×C13—41no—
286#1055—22no—
287#1055—41no—
288C22×M16—131no—
289C22×M16—131no—
290C2×#117—131no—
291C2×#117—131no—
292C22×C4⋊C4—131no—
293C22×C4⋊C4—131no—
294C22×C4⋊C4—261no—
295C22×C42—131no—
296#428—138no—
297C2×#107—131no—
298C2×#107C2×D1311yescharacteristic
299C2×#106—131no—
300C2×#106—131no—
301#389—131no—
302#389—131no—
303#389—131no—
304#389—261no—
305#389—261no—
306#389C2×D1311yescharacteristic
307C4×C4⋊C4—131no—
308C4×C4⋊C4—131no—
309C4×C4⋊C4—131no—
310C4×C4⋊C4C2×D1311yescharacteristic
311C4×C22⋊C4—261no—
312C4×C22⋊C4—261no—
313#376—261no—
314C2×#95—261no—
315C43—261no—
316#340—131no—
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#340C2×D1311yescharacteristic
326#340C2×D1311yescharacteristic
327#340C2×D1311yescharacteristic
328#336—131no—
329#336—131no—
330#336—131no—
331#336C2×D1311yescharacteristic
332C22×C13C2×C4×D411yescharacteristic
333C22×C13C2×C22⋊Q811yescharacteristic
334C22×C13C2×#12311yescharacteristic
335C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C13C2×#13711yescharacteristic
337C22×C13#57511yescharacteristic
338C22×C13#57511yescharacteristic
339C2×D13—22no—
340C2×D13—22no—
341C2×D13—22no—
342C2×D13—22no—
343C2×D13—22no—
344C2×D13—22no—
345C2×D13#38714yes—
346C4×C13—22no—
347C4×C13—42no—
348C4×C13—41no—
349C4×C13—42no—
350C4×C13—42no—
351C4×C13—81no—
352C4×C13C2×#11711yescharacteristic
353C4×C13C2×C4×Q811yescharacteristic
354C4×C13C2×#12511yescharacteristic
355C4×C13C2×#12611yescharacteristic
356Dic13—22no—
357Dic13—42no—
358Dic13—41no—
359Dic13—42no—
360Dic13—42no—
361Dic13—81no—
362Dic13#38714yes—
363C23×C4—131no—
364C23×C4—131no—
365C23×C4—131no—
366C23×C4—261no—
367C23×C4—261no—
368C2×M16—134no—
369C2×M16—262no—
370C2×M16—262no—
371C2×M16—262no—
372C2×M16—262no—
373C2×M16—262no—
374C22×C8—131no—
375C22×C8—131no—
376C22×C8C22×D1311yescharacteristic
377C22×C8C22×D1311yescharacteristic
378#117—134no—
379#117—134no—
380#117—262no—
381#117—262no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—131no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—134no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—262no—
389C2×C4⋊C4—262no—
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—524no—
397C2×C4⋊C4C22×D1311yescharacteristic
398C2×C4⋊C4C22×D1311yescharacteristic
399C2×C4⋊C4C22×D1311yescharacteristic
400C2×C4⋊C4C22×D1311yescharacteristic
401C2×C22⋊C4—261no—
402C2×C22⋊C4—261no—
403C2×C42—21no—
404C2×C42—131no—
405C2×C42—131no—
406C2×C42—131no—
407C2×C42—262no—
408C2×C42—262no—
409C2×C42—261no—
410C2×C42—261no—
411C2×C42—261no—
412C2×C42—261no—
413C2×C42—261no—
414C2×C42C22×D1311yescharacteristic
415#107—134no—
416#107C4×D1314yescomplemented
417#106—134no—
418#106—134no—
419#95—21no—
420#95—21no—
421#95—261no—
422#95—261no—
423#95—261no—
424#95—261no—
425#95—261no—
426#95—261no—
427C2×C13C2×#38711yescharacteristic
428C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
429C2×C13C4×#13711yescharacteristic
430C2×C13#307911yescharacteristic
431C2×C13#308011yescharacteristic
432C2×C13#309411yescharacteristic
433C2×C13#309511yescharacteristic
434D13—24no—
435C24—131no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—131no—
441C22×C4—132no—
442C22×C4—132no—
443C22×C4—132no—
444C22×C4—132no—
445C22×C4—132no—
446C22×C4—132no—
447C22×C4—131no—
448C22×C4—131no—
449C22×C4—262no—
450C22×C4—262no—
451C22×C4—262no—
452C22×C4—264no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—262no—
457C22×C4—261no—
458C22×C4—521no—
459C22×C4—521no—
460C22×C4—522no—
461C22×C4—522no—
462C22×C4—522no—
463C22×C4—522no—
464C22×C4—522no—
465C22×C4D4×D1311yescharacteristic
466C22×C4D4×D1311yescharacteristic
467C22×C4C23×D1311yescharacteristic
468M16—268no—
469M16—524no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—132no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8C2×C4×D1312yes—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—42no—
488C4⋊C4—132no—
489C4⋊C4—132no—
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—
502C4⋊C4C2×C4×D1312yes—
503C4⋊C4Q8×D1312yes—
504C22⋊C4—264no—
505C22⋊C4—264no—
506C42—21no—
507C42—21no—
508C42—42no—
509C42—262no—
510C42—262no—
511C42—264no—
512C42—264no—
513C42—261no—
514C42—261no—
515C42—522no—
516C42—522no—
517C42—522no—
518C13#2103411yescharacteristic, complemented, Sylow
519C23—132no—
520C23—132no—
521C23—132no—
522C23—261no—
523C23—261no—
524C23—261no—
525C23—261no—
526C23C2×D4×D1311yescharacteristic
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—132no—
545C2×C4—132no—
546C2×C4—132no—
547C2×C4—134no—
548C2×C4—134no—
549C2×C4—134no—
550C2×C4—134no—
551C2×C4—132no—
552C2×C4—261no—
553C2×C4—261no—
554C2×C4—261no—
555C2×C4—261no—
556C2×C4—262no—
557C2×C4—262no—
558C2×C4—262no—
559C2×C4—261no—
560C2×C4—524no—
561C2×C4—524no—
562C2×C4—528no—
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#8816512yes—
574C2×C4C22×C4×D1311yescharacteristic
575C2×C4C2×Q8×D1311yescharacteristic
576C2×C4#41×D1311yescharacteristic
577C2×C4#41×D1311yescharacteristic
578C2×C4#41×D1311yescharacteristic
579C2×C4#41×D1311yescharacteristic
580C8—22no—
581C8—41no—
582C8—262no—
583C8—521no—
584C22—134no—
585C22—262no—
586C22—262no—
587C22—262no—
588C22—262no—
589C22—262no—
590C22—262no—
591C22C4×D4×D1311yescharacteristic
592C22D13×C22⋊Q811yescharacteristic
593C22D13×#12311yescharacteristic
594C22C2×#8816511yescharacteristic
595C22#1171947311yescharacteristic
596C22D13×#13711yescharacteristic
597C22#1171948211yescharacteristic
598C4—22no—
599C4—42no—
600C4—42no—
601C4—42no—
602C4—41no—
603C4—81no—
604C4—134no—
605C4—262no—
606C4—522no—
607C4—522no—
608C4—522no—
609C4—521no—
610C4—1041no—
611C4D13×#11711yescharacteristic
612C4C4×Q8×D1311yescharacteristic
613C4D13×#12511yescharacteristic
614C4D13×#12611yescharacteristic
615C2—264no—
616C2D13×#38711yescharacteristic
617C2C4×#8816511yescharacteristic
618C2#1312365211yescharacteristic
619C2#1312464411yescharacteristic
620C2#1312465511yescharacteristic
621C2#1312477111yescharacteristic
622C2#1312478311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1918C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1918D13
hypocenterC13#21034
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
4. #13115430C2semidirect
5. #13115426C2semidirect
6. #13115424C2semidirect
7. #13115420C2semidirect
8. #13115415C2semidirect
9. #13115411C2semidirect
10. #13115407C2semidirect
15. C13×#1918C2semidirect
39. #11718542C4semidirect
112. C13×#107C2×C4semidirect
121. #88057C2×C4semidirect
122. #88048C2×C4semidirect
123. #88047C2×C4semidirect
218. #1918D13semidirect
416. #107C4×D13semidirect
518. C13#21034semidirect

Maximal subgroups

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

subgroupindex
C2×#117185422
D13×#3892
C4×#881462
#131154302
#131154262
#131154242
#131154202
#131154152
#131154112
#131154072
#131145542
#131145282
C13×#19182
#2103413