Finite Group Databasebeta

← #15832587

Subgroups — #15832587

Order 3328.

726 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123874C211yesmaximal, characteristic, complemented
2#13123857C211yesmaximal, characteristic, complemented
3C4×D8×D13C211yesmaximal, characteristic
4#13113702C211yesmaximal, characteristic, complemented
5#13113701C211yesmaximal, characteristic, complemented
6#13113699C211yesmaximal, characteristic, complemented
7#13113668C211yesmaximal, characteristic, complemented
8#13113665C211yesmaximal, characteristic, complemented
9#13113663C211yesmaximal, characteristic, complemented
10#13113662C211yesmaximal, characteristic, complemented
11#13113581C211yesmaximal, characteristic, complemented
12#13113225C211yesmaximal, characteristic, complemented
13#13113225C211yesmaximal, characteristic, complemented
14#13113127C211yesmaximal, characteristic, complemented
15C13×#1586C211yesmaximal, characteristic, complemented
16C2×D8×D13C411yescharacteristic
17C4×D4×D13C2211yescharacteristic
18C4×D4×D13C2211yescharacteristic
19C4×C13×D8C2211yescharacteristic
20C13×#436C2211yescharacteristic, complemented
21C8×D4×C13C2211yescharacteristic, complemented
22D8×Dic13C411yescharacteristic
23#11718789—21no—
24#11718787—21no—
25C8×C22⋊D13—21no—
26C2×#88060—21no—
27C4×#6104C2211yescharacteristic
28C4×#6104C2211yescharacteristic
29#11718673C2211yescharacteristic, complemented
30D4×#1055C2211yescharacteristic, complemented
31D13×#107C411yescharacteristic
32#11718533C411yescharacteristic
33#11718499C2211yescharacteristic, complemented
34#11718495C2211yescharacteristic, complemented
35#11718494C2211yescharacteristic
36#11718494C2211yescharacteristic
37D13×#102C411yescharacteristic
38D13×#102C411yescharacteristic
39#11718417C411yescharacteristic
40#11718417C411yescharacteristic
41#11718390—21no—
42#11718387—21no—
43#11718386—21no—
44D13×C22⋊C8—21no—
45C4×D104C2211yescharacteristic
46#11718349C2211yescharacteristic, complemented
47C8×D52C2211yescharacteristic, complemented
48#11718346C2211yescharacteristic
49#11718346C2211yescharacteristic
50C4×C8×D13C2211yescharacteristic
51C13×#334C2211yescharacteristic, complemented
52C13×D4⋊C8C2211yescharacteristic, complemented
53C13×D4⋊C8C2211yescharacteristic, complemented
54C13×#322C2211yescharacteristic, complemented
55D4⋊#1055C2211yescharacteristic, complemented
56D4⋊#1055C2211yescharacteristic, complemented
57#11718075C2211yescharacteristic, complemented
58#11718075C2211yescharacteristic, complemented
59#11718071C2211yescharacteristic, complemented
60#11718071C2211yescharacteristic, complemented
61#11718051C2211yescharacteristic, complemented
62#11718051C2211yescharacteristic, complemented
63#11718049C2211yescharacteristic, complemented
64#11718047C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66#11718046C2211yescharacteristic, complemented
67C2×D4×D13C2×C411yescharacteristic
68C2×D4×D13C2×C411yescharacteristic
69C22×C4×D13—21no—
70C22×C4×D13—21no—
71C2×C13×D8C2×C411yescharacteristic
72C2×C13×M16—21no—
73C22×C8×C13—21no—
74C4×D4×C13C2311yescharacteristic
75C4×D4×C13C2311yescharacteristic
76D4×Dic13C2×C411yescharacteristic
77D4×Dic13C2×C411yescharacteristic
78C2×#6104C2×C411yescharacteristic
79C2×#6104C2×C411yescharacteristic
80C4×C22⋊D13—21no—
81C4×C22⋊D13—21no—
82C2×#6099—21no—
83C22×#1055—21no—
84D8×D13—24no—
85C2×D104C2×C411yescharacteristic
86C2×#6094—21no—
87C2×#6094—21no—
88C2×C8×D13—21no—
89C2×C8×D13—21no—
90C2×C8×D13C2×C411yescharacteristic
91C2×C8×D13C2×C411yescharacteristic
92#88147C2×C411yescharacteristic
93#88147C2×C411yescharacteristic
94C4⋊C4×D13C2×C411yescharacteristic
95C4⋊C4×D13C2×C411yescharacteristic
96#88135—21no—
97#88135—21no—
98C22⋊C4×D13—21no—
99C22⋊C4×D13—21no—
100C4×D52C2311yescharacteristic
101C4×D52C2311yescharacteristic
102C42×D13C2311yescharacteristic
103C13×#107C2×C411yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C13×C4⋊C8C2311yescharacteristic
106C13×#102C2×C411yescharacteristic
107C13×#102C2×C411yescharacteristic
108C13×C22⋊C8—21no—
109C13×C22⋊C8—21no—
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113#88072C2×C411yescharacteristic
114#88072C2×C411yescharacteristic
115C22⋊#1055—21no—
116C22⋊#1055—21no—
117#88061C2×C411yescharacteristic
118#88061C2×C411yescharacteristic
119#88060—21no—
120#88060—21no—
121#88060—21no—
122#88060—21no—
123#88060—21no—
124#88060—21no—
125#88060—21no—
126#88060D411yescharacteristic
127#88060D411yescharacteristic
128#88058C2×C411yescharacteristic
129#88054—21no—
130#88054D411yescharacteristic
131#88054D411yescharacteristic
132C8×Dic13—21no—
133C8×Dic13—21no—
134C8×Dic13C2×C411yescharacteristic
135C8×Dic13C2×C411yescharacteristic
136#88049C2×C411yescharacteristic
137#88049C2×C411yescharacteristic
138#88047C2×C411yescharacteristic
139#88047C2×C411yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#17877—131nomaximal, Sylow
146C23×D13—21no—
147C23×D13—21no—
148C2×D4×C13C22×C411yescharacteristic
149C2×D4×C13C22×C411yescharacteristic
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C2×C22⋊D13—21no—
153C2×C22⋊D13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156D4×D13—22no—
157D4×D13—22no—
158D4×D13—22no—
159D4×D13M1614yescomplemented
160C2×D52C22×C411yescharacteristic
161C2×D52C22×C411yescharacteristic
162C2×C4×D13—21no—
163C2×C4×D13—21no—
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×C4×D13—21no—
167C2×C4×D13—21no—
168C2×C4×D13—81no—
169C2×C4×D13—81no—
170C2×C4×D13—81no—
171C2×C4×D13—81no—
172C2×C4×D13C22×C411yescharacteristic
173C2×C4×D13C2×D411yescharacteristic
174C2×C4×D13#4111yescharacteristic
175C13×D8—22no—
176C13×M16—81no—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13—21no—
180C2×C8×C13—81no—
181C2×C8×C13C22×C411yescharacteristic
182C2×C8×C13C22×C411yescharacteristic
183C2×C8×C13C2×D411yescharacteristic
184C2×C8×C13C2×D411yescharacteristic
185C13×C4⋊C4C22×C411yescharacteristic
186C13×C4⋊C4C22×C411yescharacteristic
187C13×C22⋊C4—21no—
188C13×C22⋊C4—21no—
189C42×C13C2411yescharacteristic
190C22⋊Dic13—21no—
191C22⋊Dic13—21no—
192#6104—22no—
193#6104—22no—
194#6103—21no—
195#6103—21no—
196#6103—21no—
197#6103—21no—
198C4⋊Dic13C22×C411yescharacteristic
199C4⋊Dic13C22×C411yescharacteristic
200#6101—21no—
201#6101—21no—
202C4×Dic13C22×C411yescharacteristic
203C4×Dic13C2×D411yescharacteristic
204C4×Dic13#4111yescharacteristic
205#6099—81no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—81no—
210C2×#1055C22×C411yescharacteristic
211C2×#1055C22×C411yescharacteristic
212C2×#1055C2×D411yescharacteristic
213C2×#1055C2×D411yescharacteristic
214D104—22no—
215#6094—81no—
216#6094—81no—
217C8×D13—22no—
218C8×D13—22no—
219C8×D13—81no—
220C8×D13—81no—
221#2975—131no—
222#2972—131no—
223C2×C4×D8—131no—
224#1586—131no—
225#1586—131no—
226#1586—131no—
227#1586D1311yescharacteristic, complemented
228#1581—131no—
229#1581—131no—
230#1581—131no—
231#1581—131no—
232#1564—131no—
233#1478—131no—
234#1478—131no—
235#1452—131no—
236C23×C13—21no—
237C23×C13—21no—
238C22×D13—21no—
239C22×D13—24no—
240C22×D13—21no—
241C22×D13—42no—
242C22×D13—81no—
243C22×D13—81no—
244C22×D13—81no—
245C22×D13—81no—
246C22×D13C4×D411yescharacteristic
247D4×C13—21no—
248D4×C13—21no—
249D4×C13—21no—
250D4×C13C2×M1612yes—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13C23×C411yescharacteristic
258C2×C4×C13C22×D411yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C22⋊D13—24no—
261C22⋊D13—42no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—81no—
265C2×Dic13—81no—
266C2×Dic13C4×D411yescharacteristic
267C2×Dic13C4×D411yescharacteristic
268C2×Dic13C4×D411yescharacteristic
269D52—21no—
270D52—21no—
271D52—21no—
272D52C2×M1612yes—
273C4×D13—21no—
274C4×D13—21no—
275C4×D13—41no—
276C4×D13—41no—
277C4×D13—41no—
278C4×D13—41no—
279C4×D13—41no—
280C4×D13—81no—
281C4×D13—81no—
282C4×D13—81no—
283C4×D13—81no—
284C4×D13C2×M1612yes—
285C4×D13#13112yes—
286C8×C13—21no—
287C8×C13—21no—
288C8×C13—21no—
289C8×C13—21no—
290C8×C13—41no—
291C8×C13—41no—
292C8×C13—41no—
293#1055—21no—
294#1055—21no—
295#1055—21no—
296#1055—21no—
297#1055—41no—
298#1055—41no—
299#1055—41no—
300C22×D8—131no—
301C2×C4×D4—131no—
302C2×C4×D4—131no—
303C4×D8—131no—
304C4×D8—131no—
305C4×D8—131no—
306C4×D8—131no—
307C4×D8—131no—
308C4×D8—131no—
309C4×D8—131no—
310C4×D8C2×D1311yescharacteristic
311#436—131no—
312#436—131no—
313#436—131no—
314#436—261no—
315#436—261no—
316#436C2×D1311yescharacteristic, complemented
317C8×D4—131no—
318C8×D4—131no—
319C8×D4—131no—
320C8×D4—261no—
321C8×D4—261no—
322C8×D4C2×D1311yescharacteristic, complemented
323#431—131no—
324#431—131no—
325#431—131no—
326#431—131no—
327C2×#107—131no—
328C2×#102—131no—
329C2×#102—131no—
330#407—261no—
331#407—261no—
332C2×C22⋊C8—261no—
333C2×C22⋊C8—261no—
334C2×C4×C8—131no—
335#335—131no—
336#335—131no—
337#334—131no—
338#334C2×D1311yescharacteristic, complemented
339D4⋊C8—131no—
340D4⋊C8—131no—
341D4⋊C8—131no—
342D4⋊C8—131no—
343D4⋊C8—131no—
344D4⋊C8—131no—
345D4⋊C8C2×D1311yescharacteristic, complemented
346D4⋊C8C2×D1311yescharacteristic, complemented
347#322—131no—
348#322—131no—
349#322—131no—
350#322C2×D1311yescharacteristic, complemented
351C22×C13—22no—
352C22×C13—41no—
353C22×C13—41no—
354C22×C13—41no—
355C22×C13—41no—
356C22×C13—41no—
357C22×C13C2×C4×D411yescharacteristic
358C2×D13—21no—
359C2×D13—21no—
360C2×D13—22no—
361C2×D13—41no—
362C2×D13—41no—
363C2×D13—41no—
364C2×D13—41no—
365C2×D13—41no—
366C2×D13—84no—
367C2×D13—84no—
368C2×D13#43512yes—
369C4×C13—21no—
370C4×C13—41no—
371C4×C13—41no—
372C4×C13C22×M1611yescharacteristic
373C4×C13C2×#13111yescharacteristic
374C4×C13#57611yescharacteristic
375C4×C13#57611yescharacteristic
376Dic13—21no—
377Dic13—21no—
378Dic13—41no—
379Dic13—41no—
380Dic13#43512yes—
381C22×D4—131no—
382C22×D4—131no—
383C23×C4—261no—
384C23×C4—261no—
385C2×D8—131no—
386C2×D8—131no—
387C2×D8—131no—
388C2×D8—264no—
389C2×D8C4×D1311yescharacteristic
390C2×M16—21no—
391C2×M16—261no—
392C2×M16—261no—
393C2×M16—261no—
394C22×C8—21no—
395C22×C8—131no—
396C22×C8—131no—
397C22×C8—261no—
398C22×C8—261no—
399C22×C8—261no—
400C4×D4—131no—
401C4×D4—131no—
402C4×D4—131no—
403C4×D4—131no—
404C4×D4—131no—
405C4×D4—131no—
406C4×D4—261no—
407C4×D4—261no—
408C4×D4—261no—
409C4×D4—261no—
410C4×D4C22×D1311yescharacteristic
411C4×D4C22×D1311yescharacteristic
412C2×C4⋊C4—131no—
413C2×C4⋊C4—131no—
414C2×C22⋊C4—261no—
415C2×C22⋊C4—261no—
416C2×C42—131no—
417#107—131no—
418#107—131no—
419#107—131no—
420#107C4×D1311yescharacteristic
421C4⋊C8—131no—
422C4⋊C8—131no—
423C4⋊C8—131no—
424C4⋊C8—131no—
425C4⋊C8—261no—
426C4⋊C8C22×D1311yescharacteristic
427C4⋊C8C22×D1311yescharacteristic
428#102—131no—
429#102—131no—
430#102—131no—
431#102—131no—
432#102—131no—
433#102—131no—
434#102C4×D1311yescharacteristic
435#102C4×D1311yescharacteristic
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—131no—
439C22⋊C8—131no—
440C22⋊C8—261no—
441C22⋊C8—261no—
442C22⋊C8—261no—
443C22⋊C8—261no—
444C22⋊C8—261no—
445C22⋊C8—261no—
446C22⋊C8—261no—
447C22⋊C8—261no—
448C22⋊C8—261no—
449C4×C8—131no—
450C4×C8—131no—
451C4×C8—131no—
452C4×C8—131no—
453C4×C8—131no—
454C4×C8—261no—
455C4×C8—261no—
456C4×C8C22×D1311yescharacteristic
457C4×C8C22×D1311yescharacteristic
458C4×C8C22×D1311yescharacteristic
459C2×C13—42no—
460C2×C13—81no—
461C2×C13C2×#43511yescharacteristic
462C2×C13#294811yescharacteristic
463C2×C13#295711yescharacteristic
464D13—22no—
465D13—42no—
466D13—81no—
467C24—261no—
468C24—261no—
469C2×D4—134no—
470C2×D4—131no—
471C2×D4—131no—
472C2×D4—262no—
473C2×D4—262no—
474C2×D4—262no—
475C2×D4—261no—
476C2×D4—261no—
477C2×D4C2×C4×D1311yescharacteristic
478C2×D4C2×C4×D1311yescharacteristic
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—131no—
482C22×C4—131no—
483C22×C4—131no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—1041no—
493C22×C4—1041no—
494C22×C4—1041no—
495C22×C4—1041no—
496D8—22no—
497D8—262no—
498D8—262no—
499D8—262no—
500M16—81no—
501M16—1041no—
502M16—1041no—
503M16—1041no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—81no—
508C2×C8—131no—
509C2×C8—131no—
510C2×C8—131no—
511C2×C8—131no—
512C2×C8—262no—
513C2×C8—262no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—1041no—
518C2×C8—1041no—
519C2×C8—1041no—
520C2×C8C2×C4×D1311yescharacteristic
521C2×C8C2×C4×D1311yescharacteristic
522C2×C8D4×D1311yescharacteristic
523C2×C8D4×D1311yescharacteristic
524C4⋊C4—131no—
525C4⋊C4—131no—
526C4⋊C4—261no—
527C4⋊C4—261no—
528C4⋊C4C2×C4×D1311yescharacteristic
529C4⋊C4C2×C4×D1311yescharacteristic
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—261no—
533C22⋊C4—261no—
534C22⋊C4—261no—
535C22⋊C4—261no—
536C22⋊C4—261no—
537C22⋊C4—261no—
538C42—131no—
539C42—131no—
540C42—131no—
541C42C23×D1311yescharacteristic
542C13#1787711yescharacteristic, complemented, Sylow
543C23—21no—
544C23—21no—
545C23—131no—
546C23—264no—
547C23—261no—
548C23—261no—
549C23—522no—
550C23—1041no—
551C23—1041no—
552C23—1041no—
553C23—1041no—
554D4—21no—
555D4—21no—
556D4—21no—
557D4—132no—
558D4—264no—
559D4—261no—
560D4—261no—
561D4—261no—
562D4—522no—
563D4M16×D1312yes—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—131no—
571C2×C4—132no—
572C2×C4—132no—
573C2×C4—131no—
574C2×C4—131no—
575C2×C4—261no—
576C2×C4—261no—
577C2×C4—261no—
578C2×C4—261no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—1041no—
585C2×C4—1041no—
586C2×C4—1041no—
587C2×C4—1041no—
588C2×C4—1041no—
589C2×C4—1041no—
590C2×C4C22×C4×D1311yescharacteristic
591C2×C4C2×D4×D1311yescharacteristic
592C2×C4#41×D1311yescharacteristic
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—41no—
598C8—41no—
599C8—41no—
600C8—261no—
601C8—261no—
602C8—261no—
603C8—261no—
604C8—521no—
605C8—521no—
606C8—521no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—132no—
614C22—261no—
615C22—261no—
616C22—262no—
617C22—521no—
618C22—521no—
619C22—521no—
620C22—521no—
621C22—521no—
622C22—1044no—
623C22—1044no—
624C22C4×D4×D1311yescharacteristic
625C4—21no—
626C4—41no—
627C4—41no—
628C4—132no—
629C4—261no—
630C4—261no—
631C4—521no—
632C4—521no—
633C4C2×M16×D1311yescharacteristic
634C4D13×#13111yescharacteristic
635C4#1171947911yescharacteristic
636C4#1171947911yescharacteristic
637C2—42no—
638C2—81no—
639C2—262no—
640C2—522no—
641C2—1041no—
642C2D13×#43511yescharacteristic
643C2#1312368511yescharacteristic
644C2#1312374811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1586C2
socleC22×C13C2×C4×D4
prime radicalC2×D8×D13C4
cosocleC42×C13C24
hypercenter#1586D13
hypocenterC13#17877
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
1. #13123874C2semidirect
2. #13123857C2semidirect
4. #13113702C2semidirect
5. #13113701C2semidirect
6. #13113699C2semidirect
7. #13113668C2semidirect
8. #13113665C2semidirect
9. #13113663C2semidirect
10. #13113662C2semidirect
11. #13113581C2semidirect
12. #13113225C2semidirect
13. #13113225C2semidirect
14. #13113127C2semidirect
15. C13×#1586C2semidirect
20. C13×#436C22semidirect
21. C8×D4×C13C22semidirect
29. #11718673C22semidirect
30. D4×#1055C22semidirect
33. #11718499C22semidirect
34. #11718495C22semidirect
46. #11718349C22semidirect
47. C8×D52C22semidirect
51. C13×#334C22semidirect
52. C13×D4⋊C8C22semidirect
53. C13×D4⋊C8C22semidirect
54. C13×#322C22semidirect
55. D4⋊#1055C22semidirect
56. D4⋊#1055C22semidirect
57. #11718075C22semidirect
58. #11718075C22semidirect
59. #11718071C22semidirect
60. #11718071C22semidirect
61. #11718051C22semidirect
62. #11718051C22semidirect
63. #11718049C22semidirect
64. #11718047C22semidirect
65. #11718046C22semidirect
66. #11718046C22semidirect
159. D4×D13M16semidirect
227. #1586D13semidirect
316. #436C2×D13semidirect
322. C8×D4C2×D13semidirect
338. #334C2×D13semidirect
345. D4⋊C8C2×D13semidirect
346. D4⋊C8C2×D13semidirect
350. #322C2×D13semidirect
542. C13#17877semidirect

Maximal subgroups

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

subgroupindex
#131238742
#131238572
C4×D8×D132
#131137022
#131137012
#131136992
#131136682
#131136652
#131136632
#131136622
#131135812
#131132252
#131131272
C13×#15862
#1787713