Finite Group Databasebeta

← #15865183

Subgroups — #15865183

Order 3328.

790 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13×#427C211yesmaximal, characteristic
2#13123397C211yesmaximal, characteristic
3#13123252C211yesmaximal, characteristic
4#13115438C211yesmaximal, characteristic, complemented
5#13115437C211yesmaximal, characteristic, complemented
6#13115436C211yesmaximal, characteristic, complemented
7#13115435C211yesmaximal, characteristic, complemented
8#13115434C211yesmaximal, characteristic, complemented
9#13115433C211yesmaximal, characteristic, complemented
10#13115432C211yesmaximal, characteristic, complemented
11D13×#341C211yesmaximal, characteristic
12#13114544C211yesmaximal, characteristic
13#13114544C211yesmaximal, characteristic
14#13114531C211yesmaximal, characteristic
15C13×#1922C211yesmaximal, characteristic, complemented
16C2×M16×D13C2211yescharacteristic
17C2×M16×D13C2211yescharacteristic
18C22×#6094C2211yescharacteristic
19C22×C8×D13C2211yescharacteristic
20D13×#117C2211yescharacteristic
21D13×#117C2211yescharacteristic
22C2×#88126C2211yescharacteristic
23C13×#427C2211yescharacteristic
24C13×#424C2211yescharacteristic
25C13×#405C2211yescharacteristic
26#11718783C2211yescharacteristic
27#11718780C2211yescharacteristic
28#11718767C2211yescharacteristic
29#11718763C2211yescharacteristic
30#11718762C2211yescharacteristic
31#11718660C2211yescharacteristic
32#11718659C2211yescharacteristic
33#11718659C2211yescharacteristic
34#11718658C2211yescharacteristic
35#11718541C411yescharacteristic, complemented
36#11718541C411yescharacteristic, complemented
37D13×#107C411yescharacteristic, complemented
38D13×#107C411yescharacteristic, complemented
39#11718521C411yescharacteristic, complemented
40#11718521C411yescharacteristic, complemented
41D13×#106C411yescharacteristic, complemented
42D13×#106C411yescharacteristic, complemented
43#11718500—21no—
44#11718500—21no—
45#11718498—21no—
46#11718498—21no—
47#11718369—21no—
48#11718368—21no—
49#11718350—21no—
50C4×#6094—21no—
51C13×#341C2211yescharacteristic
52C13×#339C2211yescharacteristic
53C13×#339C2211yescharacteristic
54C13×#336C2211yescharacteristic
55#11718150C2211yescharacteristic
56#11718150C2211yescharacteristic
57#11718147C2211yescharacteristic
58#11718147C2211yescharacteristic
59#11718144C2211yescharacteristic
60#11718142C2211yescharacteristic
61#11718142C2211yescharacteristic
62#11718124C2211yescharacteristic
63#11718124C2211yescharacteristic
64#11718116C2211yescharacteristic
65#11718115C2211yescharacteristic
66#11718115C2211yescharacteristic
67C22×C4×D13C2311yescharacteristic
68C2×C13×M16C2311yescharacteristic
69C2×C13×M16C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C13×#117C2311yescharacteristic
73C13×#117C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×#6103—21no—
76#88180C2311yescharacteristic
77#88180C2311yescharacteristic
78C2×#6101—21no—
79C2×C4×Dic13C2311yescharacteristic
80C2×#6099C2311yescharacteristic
81C2×#6099C2311yescharacteristic
82C22×#1055C2311yescharacteristic
83C22×#1055C2311yescharacteristic
84M16×D13—22no—
85M16×D13—22no—
86M16×D13—22no—
87M16×D13Q814yes—
88C2×#6094—21no—
89C2×#6094—22no—
90C2×#6094—22no—
91C2×#6094—21no—
92C2×#6094D411yescharacteristic
93C2×#6094D411yescharacteristic
94C2×#6094D411yescharacteristic
95C2×#6094D411yescharacteristic
96C2×C8×D13—21no—
97C2×C8×D13—22no—
98C2×C8×D13—22no—
99C2×C8×D13—21no—
100C2×C8×D13C2×C411yescharacteristic
101C2×C8×D13C2×C411yescharacteristic
102C2×C8×D13C2×C411yescharacteristic
103C2×C8×D13C2×C411yescharacteristic
104#88146C2×C411yescharacteristic
105#88146C2×C411yescharacteristic
106#88146C2×C411yescharacteristic
107#88146C2×C411yescharacteristic
108C4⋊C4×D13C2×C411yescharacteristic
109C4⋊C4×D13C2×C411yescharacteristic
110C4⋊C4×D13C2×C411yescharacteristic
111C4⋊C4×D13C2×C411yescharacteristic
112C22⋊C4×D13—21no—
113C22⋊C4×D13—21no—
114#88131—21no—
115#88131—21no—
116#88126—21no—
117#88126—21no—
118#88126—22no—
119#88126—22no—
120C42×D13—21no—
121C42×D13—21no—
122C13×#107C2×C411yescharacteristic
123C13×#107C2×C411yescharacteristic
124C13×#106C2×C411yescharacteristic
125C13×#106C2×C411yescharacteristic
126C13×C4⋊C8—21no—
127C13×C4⋊C8—21no—
128C13×#97—21no—
129C4×C8×C13—21no—
130#88058C2×C411yescharacteristic
131#88058C2×C411yescharacteristic
132#88057C2×C411yescharacteristic
133#88057C2×C411yescharacteristic
134#88055—21no—
135#88055—21no—
136#88054—21no—
137#88054—21no—
138#88054—21no—
139#88054—21no—
140C8×Dic13—21no—
141C8×Dic13—21no—
142#88048C2×C411yescharacteristic
143#88048C2×C411yescharacteristic
144#88048C2×C411yescharacteristic
145#88048C2×C411yescharacteristic
146#88047C2×C411yescharacteristic
147#88047C2×C411yescharacteristic
148#88047C2×C411yescharacteristic
149#88047C2×C411yescharacteristic
150C4⋊#1055—21no—
151C4⋊#1055—21no—
152#88043—21no—
153C4×#1055—21no—
154#21043—131nomaximal, Sylow
155C23×D13#4111yescharacteristic
156C22×C4×C13—21no—
157C22×C4×C13C2411yescharacteristic
158C22×Dic13—21no—
159C22×Dic13#4111yescharacteristic
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C2×C4×D13—21no—
164C2×C4×D13C22×C411yescharacteristic
165C2×C4×D13C22×C411yescharacteristic
166C2×C4×D13C2×D411yescharacteristic
167C2×C4×D13C2×D411yescharacteristic
168C2×C4×D13C2×Q812yes—
169C2×C4×D13#4112yes—
170C2×C4×D13#4112yes—
171C2×C4×D13#4112yes—
172C13×M16—21no—
173C13×M16—21no—
174C13×M16—21no—
175C13×M16C2×Q812yes—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13—21no—
180C2×C8×C13—21no—
181C2×C8×C13—21no—
182C2×C8×C13C22×C411yescharacteristic
183C2×C8×C13C22×C411yescharacteristic
184C2×C8×C13C2×D411yescharacteristic
185C2×C8×C13C2×D411yescharacteristic
186C13×C4⋊C4C22×C411yescharacteristic
187C13×C4⋊C4C22×C411yescharacteristic
188C13×C4⋊C4C22×C411yescharacteristic
189C13×C4⋊C4C22×C411yescharacteristic
190C13×C22⋊C4—21no—
191C13×C22⋊C4—21no—
192C42×C13—21no—
193C42×C13—21no—
194C42×C13—21no—
195C42×C13—21no—
196C22⋊Dic13—21no—
197C22⋊Dic13—21no—
198#6103—21no—
199#6103—21no—
200#6103—21no—
201#6103—21no—
202#6103—42no—
203C4⋊Dic13C22×C411yescharacteristic
204C4⋊Dic13C22×C411yescharacteristic
205C4⋊Dic13C22×C411yescharacteristic
206C4⋊Dic13C22×C411yescharacteristic
207#6101—21no—
208#6101—21no—
209#6101—21no—
210#6101—21no—
211#6101—42no—
212C4×Dic13—21no—
213C4×Dic13—21no—
214C4×Dic13—21no—
215C4×Dic13—21no—
216C4×Dic13—21no—
217C4×Dic13—21no—
218C4×Dic13—21no—
219C4×Dic13—21no—
220#6099—21no—
221#6099—21no—
222#6099—21no—
223#6099C2×Q812yes—
224C2×#1055—21no—
225C2×#1055—21no—
226C2×#1055—21no—
227C2×#1055—21no—
228C2×#1055—21no—
229C2×#1055—21no—
230C2×#1055C22×C411yescharacteristic
231C2×#1055C22×C411yescharacteristic
232C2×#1055C2×D411yescharacteristic
233C2×#1055C2×D411yescharacteristic
234#6094—24no—
235#6094—22no—
236#6094—22no—
237#6094—22no—
238#6094—22no—
239#6094—42no—
240C8×D13—22no—
241C8×D13—22no—
242C8×D13—22no—
243C8×D13—22no—
244C8×D13—24no—
245C8×D13—42no—
246C2×#427—131no—
247#2905—131no—
248#2873—131no—
249#1922—131no—
250#1922—131no—
251#1922—131no—
252#1922—131no—
253#1922—131no—
254#1922—131no—
255#1922—131no—
256#1922D1311yescharacteristic, complemented
257C2×#341—131no—
258#1733—131no—
259#1733—131no—
260#1729—131no—
261C23×C13C2×#4111yescharacteristic
262C22×D13—41no—
263C22×D13—41no—
264C22×D13C4×D411yescharacteristic
265C22×D13C4×D411yescharacteristic
266C22×D13#12512yes—
267C22×D13#12612yes—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13C23×C411yescharacteristic
276C2×C4×C13C22×D411yescharacteristic
277C2×C4×C13C22×Q811yescharacteristic
278C2×C4×C13C2×#4111yescharacteristic
279C2×C4×C13C2×#4111yescharacteristic
280C2×C4×C13C2×#4111yescharacteristic
281C2×Dic13—21no—
282C2×Dic13—21no—
283C2×Dic13—21no—
284C2×Dic13—21no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13C4×D411yescharacteristic
289C2×Dic13C4×D411yescharacteristic
290C2×Dic13#12512yes—
291C2×Dic13#12612yes—
292C4×D13—81no—
293C4×D13—81no—
294C4×D13—81no—
295C4×D13—81no—
296C4×D13#11712yes—
297C4×D13#11712yes—
298C4×D13C4×Q812yes—
299C4×D13C4×Q812yes—
300C4×D13C22⋊Q812yes—
301C4×D13C22⋊Q812yes—
302C4×D13#12312yes—
303C4×D13#12312yes—
304C8×C13—21no—
305C8×C13—21no—
306C8×C13—22no—
307C8×C13—21no—
308C8×C13—21no—
309C8×C13—41no—
310#1055—21no—
311#1055—21no—
312#1055—22no—
313#1055—21no—
314#1055—21no—
315#1055—41no—
316C22×M16—131no—
317C22×M16—131no—
318C22×M16—131no—
319C23×C8—131no—
320C2×#117—131no—
321C2×#117—131no—
322C2×#117—131no—
323#427—131no—
324#427—131no—
325#427—131no—
326#427—131no—
327#427—131no—
328#427—131no—
329#427—131no—
330#427C2×D1311yescharacteristic
331C2×#107—131no—
332C2×#107—131no—
333C2×#106—131no—
334C2×#106—131no—
335#424—131no—
336#424—131no—
337#424—131no—
338#424—261no—
339#424—261no—
340#424C2×D1311yescharacteristic
341#423—261no—
342#423—261no—
343#405—131no—
344#405—131no—
345#405—131no—
346#405—261no—
347#405—261no—
348#405C2×D1311yescharacteristic
349C4×M16—261no—
350C4×M16—261no—
351#341—131no—
352#341—131no—
353#341—131no—
354#341C2×D1311yescharacteristic
355#339—131no—
356#339—131no—
357#339—131no—
358#339—131no—
359#339—131no—
360#339—131no—
361#339C2×D1311yescharacteristic
362#339C2×D1311yescharacteristic
363#336—131no—
364#336—131no—
365#336—131no—
366#336C2×D1311yescharacteristic
367C22×C13—21no—
368C22×C13—21no—
369C22×C13C2×C4×D411yescharacteristic
370C22×C13C2×#12511yescharacteristic
371C22×C13C2×#12611yescharacteristic
372C2×D13—21no—
373C2×D13—21no—
374C2×D13—21no—
375C2×D13—21no—
376C2×D13—42no—
377C2×D13—42no—
378C2×D13#38712yes—
379C2×D13#38712yes—
380C4×C13—41no—
381C4×C13—41no—
382C4×C13—41no—
383C4×C13—41no—
384C4×C13—81no—
385C4×C13C2×#11711yescharacteristic
386C4×C13C2×C4×Q811yescharacteristic
387C4×C13C2×C22⋊Q811yescharacteristic
388C4×C13C2×#12311yescharacteristic
389Dic13—41no—
390Dic13—41no—
391Dic13—41no—
392Dic13—41no—
393Dic13—81no—
394Dic13#38712yes—
395Dic13#38712yes—
396C23×C4—131no—
397C2×M16—131no—
398C2×M16—131no—
399C2×M16—131no—
400C2×M16—131no—
401C2×M16—131no—
402C2×M16—134no—
403C2×M16—131no—
404C2×M16—262no—
405C2×M16—262no—
406C2×M16—261no—
407C2×M16—261no—
408C2×M16—262no—
409C2×M16—262no—
410C2×M16—262no—
411C2×M16C22×D1311yescharacteristic
412C2×M16C22×D1311yescharacteristic
413C22×C8—131no—
414C22×C8—131no—
415C22×C8—131no—
416C22×C8—131no—
417C22×C8—131no—
418C22×C8—131no—
419C22×C8—262no—
420C22×C8—262no—
421C22×C8—261no—
422C22×C8—261no—
423C22×C8C22×D1311yescharacteristic
424C22×C8C22×D1311yescharacteristic
425#117—131no—
426#117—131no—
427#117—131no—
428#117—131no—
429#117—131no—
430#117—131no—
431#117—261no—
432#117—261no—
433#117—262no—
434#117—262no—
435#117—261no—
436#117—261no—
437#117C22×D1311yescharacteristic
438#117C22×D1311yescharacteristic
439C2×C4⋊C4—131no—
440C2×C4⋊C4—131no—
441C2×C4⋊C4—131no—
442C2×C4⋊C4—131no—
443C2×C4⋊C4—261no—
444C2×C22⋊C4—261no—
445C2×C22⋊C4—261no—
446C2×C22⋊C4—261no—
447C2×C42—131no—
448C2×C42—261no—
449C2×C42—261no—
450C2×C42C22×D1311yescharacteristic
451#107—131no—
452#107—131no—
453#107—131no—
454#107—131no—
455#107—131no—
456#107—131no—
457#107C4×D1311yescharacteristic
458#107C4×D1311yescharacteristic
459#106—131no—
460#106—131no—
461#106—131no—
462#106—131no—
463#106—131no—
464#106—131no—
465#106C4×D1311yescharacteristic
466#106C4×D1311yescharacteristic
467C4⋊C8—21no—
468C4⋊C8—21no—
469C4⋊C8—261no—
470C4⋊C8—261no—
471C4⋊C8—261no—
472C4⋊C8—261no—
473C4⋊C8—261no—
474C4⋊C8—261no—
475#97—21no—
476#97—261no—
477#97—261no—
478#97—261no—
479C4×C8—21no—
480C4×C8—261no—
481C4×C8—261no—
482C4×C8—261no—
483C2×C13—21no—
484C2×C13—21no—
485C2×C13C2×#38711yescharacteristic
486C2×C13#295711yescharacteristic
487C2×C13#295711yescharacteristic
488D13—22no—
489D13—22no—
490C24—131no—
491C22×C4—21no—
492C22×C4—131no—
493C22×C4—131no—
494C22×C4—131no—
495C22×C4—131no—
496C22×C4—131no—
497C22×C4—132no—
498C22×C4—132no—
499C22×C4—132no—
500C22×C4—132no—
501C22×C4—261no—
502C22×C4—261no—
503C22×C4—261no—
504C22×C4—261no—
505C22×C4—261no—
506C22×C4C23×D1311yescharacteristic
507M16—21no—
508M16—21no—
509M16—21no—
510M16—132no—
511M16—264no—
512M16—262no—
513M16—262no—
514M16—262no—
515M16—262no—
516M16—261no—
517M16—261no—
518M16—261no—
519M16—522no—
520M16Q8×D1312yes—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—131no—
528C2×C8—131no—
529C2×C8—131no—
530C2×C8—131no—
531C2×C8—262no—
532C2×C8—262no—
533C2×C8—262no—
534C2×C8—262no—
535C2×C8—264no—
536C2×C8—261no—
537C2×C8—261no—
538C2×C8—261no—
539C2×C8—261no—
540C2×C8—261no—
541C2×C8—261no—
542C2×C8—522no—
543C2×C8C2×C4×D1311yescharacteristic
544C2×C8C2×C4×D1311yescharacteristic
545C2×C8D4×D1311yescharacteristic
546C2×C8D4×D1311yescharacteristic
547C4⋊C4—131no—
548C4⋊C4—131no—
549C4⋊C4—131no—
550C4⋊C4—131no—
551C4⋊C4—261no—
552C4⋊C4—261no—
553C4⋊C4—261no—
554C4⋊C4—261no—
555C4⋊C4—522no—
556C4⋊C4C2×C4×D1311yescharacteristic
557C4⋊C4C2×C4×D1311yescharacteristic
558C4⋊C4C2×C4×D1311yescharacteristic
559C4⋊C4C2×C4×D1311yescharacteristic
560C22⋊C4—21no—
561C22⋊C4—21no—
562C22⋊C4—261no—
563C22⋊C4—261no—
564C22⋊C4—261no—
565C22⋊C4—261no—
566C22⋊C4—261no—
567C22⋊C4—261no—
568C22⋊C4—522no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—261no—
574C42—261no—
575C42—261no—
576C42—261no—
577C42—261no—
578C42—261no—
579C42—261no—
580C42—261no—
581C13#2104311yescharacteristic, complemented, Sylow
582C23—131no—
583C23—131no—
584C23—132no—
585C23—132no—
586C23—521no—
587C23—521no—
588C23#41×D1311yescharacteristic
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—131no—
597C2×C4—131no—
598C2×C4—132no—
599C2×C4—132no—
600C2×C4—132no—
601C2×C4—132no—
602C2×C4—132no—
603C2×C4—132no—
604C2×C4—132no—
605C2×C4—132no—
606C2×C4—132no—
607C2×C4—132no—
608C2×C4—261no—
609C2×C4—261no—
610C2×C4—261no—
611C2×C4—261no—
612C2×C4—521no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4—1041no—
616C2×C4—1041no—
617C2×C4—1041no—
618C2×C4—1041no—
619C2×C4C22×C4×D1311yescharacteristic
620C2×C4C2×D4×D1311yescharacteristic
621C2×C4C2×Q8×D1311yescharacteristic
622C2×C4#41×D1311yescharacteristic
623C2×C4#41×D1311yescharacteristic
624C2×C4#41×D1311yescharacteristic
625C8—21no—
626C8—21no—
627C8—22no—
628C8—21no—
629C8—21no—
630C8—41no—
631C8—261no—
632C8—261no—
633C8—262no—
634C8—261no—
635C8—261no—
636C8—521no—
637C22—21no—
638C22—21no—
639C22—132no—
640C22—132no—
641C22—261no—
642C22—261no—
643C22—261no—
644C22—261no—
645C22—522no—
646C22—522no—
647C22C4×D4×D1311yescharacteristic
648C22D13×#12511yescharacteristic
649C22D13×#12611yescharacteristic
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—81no—
655C4—132no—
656C4—132no—
657C4—521no—
658C4—521no—
659C4—521no—
660C4—521no—
661C4—1041no—
662C4D13×#11711yescharacteristic
663C4C4×Q8×D1311yescharacteristic
664C4D13×C22⋊Q811yescharacteristic
665C4D13×#12311yescharacteristic
666C2—21no—
667C2—21no—
668C2—262no—
669C2—262no—
670C2D13×#38711yescharacteristic
671C2#1312374811yescharacteristic
672C2#1312375011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1922C2
socleC22×C13C2×C4×D4
prime radicalC23×D13#41
cosocleC22×C4×C13C24
hypercenter#1922D13
hypocenterC13#21043
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1922

Complements

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

NH ≅ G/Ntype
4. #13115438C2semidirect
5. #13115437C2semidirect
6. #13115436C2semidirect
7. #13115435C2semidirect
8. #13115434C2semidirect
9. #13115433C2semidirect
10. #13115432C2semidirect
15. C13×#1922C2semidirect
35. #11718541C4semidirect
36. #11718541C4semidirect
37. D13×#107C4semidirect
38. D13×#107C4semidirect
39. #11718521C4semidirect
40. #11718521C4semidirect
41. D13×#106C4semidirect
42. D13×#106C4semidirect
256. #1922D13semidirect
581. C13#21043semidirect

Maximal subgroups

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

subgroupindex
D13×#4272
#131233972
#131232522
#131154382
#131154372
#131154362
#131154352
#131154342
#131154332
#131154322
D13×#3412
#131145442
#131145312
C13×#19222
#2104313