Finite Group Databasebeta

← #15834658

Subgroups — #15834658

Order 3328.

718 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123869C211yesmaximal, characteristic, complemented
2#13123868C211yesmaximal, characteristic, complemented
3C4×D8×D13C211yesmaximal, characteristic
4#13113748C211yesmaximal, characteristic, complemented
5#13113747C211yesmaximal, characteristic, complemented
6#13113667C211yesmaximal, characteristic, complemented
7#13113666C211yesmaximal, characteristic, complemented
8#13113664C211yesmaximal, characteristic, complemented
9#13113658C211yesmaximal, characteristic, complemented
10#13113657C211yesmaximal, characteristic, complemented
11#13113598C211yesmaximal, characteristic, complemented
12#13113277C211yesmaximal, characteristic, complemented
13#13113277C211yesmaximal, characteristic, complemented
14#13113124C211yesmaximal, characteristic, complemented
15C13×#1581C211yesmaximal, characteristic, complemented
16C2×D8×D13C411yescharacteristic
17C4×D4×D13C2211yescharacteristic
18C4×D4×D13C2211yescharacteristic
19C4×C13×D8C2211yescharacteristic
20C13×#436C2211yescharacteristic, complemented
21C8×D4×C13C2211yescharacteristic, complemented
22D8×Dic13C411yescharacteristic
23#11718788—21no—
24#11718787—21no—
25#11718772—21no—
26C2×#88060—21no—
27C4×#6104C2211yescharacteristic
28C4×#6104C2211yescharacteristic
29#11718673C2211yescharacteristic, complemented
30D4×#1055C2211yescharacteristic, complemented
31D13×#107C411yescharacteristic
32#11718533C411yescharacteristic
33#11718499C2211yescharacteristic, complemented
34#11718496C2211yescharacteristic
35#11718496C2211yescharacteristic
36#11718495C2211yescharacteristic, complemented
37D13×#102C411yescharacteristic
38D13×#102C411yescharacteristic
39#11718417C411yescharacteristic
40#11718417C411yescharacteristic
41#11718391—21no—
42#11718389—21no—
43#11718387—21no—
44D13×C22⋊C8—21no—
45C4×D104C2211yescharacteristic
46#11718349C2211yescharacteristic, complemented
47C4×#6094C2211yescharacteristic
48C8×D52C2211yescharacteristic, complemented
49#11718346C2211yescharacteristic
50C4×C8×D13C2211yescharacteristic
51C13×#335C2211yescharacteristic, 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#11718072C2211yescharacteristic, complemented
60#11718072C2211yescharacteristic, complemented
61#11718051C2211yescharacteristic, complemented
62#11718051C2211yescharacteristic, complemented
63#11718050C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, 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×#6094—21no—
89C2×C8×D13—21no—
90C2×C8×D13—21no—
91C2×C8×D13C2×C411yescharacteristic
92C2×C8×D13C2×C411yescharacteristic
93#88147C2×C411yescharacteristic
94#88147C2×C411yescharacteristic
95C4⋊C4×D13C2×C411yescharacteristic
96C4⋊C4×D13C2×C411yescharacteristic
97#88135—21no—
98#88135—21no—
99C22⋊C4×D13—21no—
100C22⋊C4×D13—21no—
101C4×D52C2311yescharacteristic
102C4×D52C2311yescharacteristic
103C42×D13C2311yescharacteristic
104C13×#107C2×C411yescharacteristic
105C13×C4⋊C8C2311yescharacteristic
106C13×C4⋊C8C2311yescharacteristic
107C13×#102C2×C411yescharacteristic
108C13×#102C2×C411yescharacteristic
109C13×C22⋊C8—21no—
110C13×C22⋊C8—21no—
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114#88072C2×C411yescharacteristic
115#88072C2×C411yescharacteristic
116C22⋊#1055—21no—
117C22⋊#1055—21no—
118#88061C2×C411yescharacteristic
119#88061C2×C411yescharacteristic
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#88055—21no—
130#88055—21no—
131#88055—21no—
132#88054D411yescharacteristic
133#88054D411yescharacteristic
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#18064—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—41no—
159D4×D13—41no—
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#6104M1614yescomplemented
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—42no—
216#6094—81no—
217#6094—81no—
218C8×D13—22no—
219C8×D13—41no—
220C8×D13—81no—
221C8×D13—81no—
222#2974—131no—
223#2974—131no—
224C2×C4×D8—131no—
225#1594—131no—
226#1594—131no—
227#1581—131no—
228#1581—131no—
229#1581—131no—
230#1581D1311yescharacteristic, complemented
231#1580—131no—
232#1580—131no—
233#1568—131no—
234#1490—131no—
235#1490—131no—
236#1451—131no—
237C23×C13—21no—
238C23×C13—21no—
239C22×D13—21no—
240C22×D13—21no—
241C22×D13—42no—
242C22×D13—42no—
243C22×D13—42no—
244C22×D13—42no—
245C22×D13—81no—
246C22×D13—81no—
247C22×D13C4×D411yescharacteristic
248D4×C13—21no—
249D4×C13—21no—
250D4×C13—21no—
251D4×C13C2×M1612yes—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13C23×C411yescharacteristic
259C2×C4×C13C22×D411yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C22⋊D13—42no—
262C22⋊D13—42no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—81no—
266C2×Dic13—81no—
267C2×Dic13C4×D411yescharacteristic
268C2×Dic13C4×D411yescharacteristic
269C2×Dic13C4×D411yescharacteristic
270D52—21no—
271D52—21no—
272D52—21no—
273D52C2×M1612yes—
274C4×D13—22no—
275C4×D13—21no—
276C4×D13—21no—
277C4×D13—21no—
278C4×D13—21no—
279C4×D13—41no—
280C4×D13—41no—
281C4×D13—41no—
282C4×D13—41no—
283C4×D13—81no—
284C4×D13—81no—
285C4×D13—81no—
286C4×D13—81no—
287C8×C13—21no—
288C8×C13—21no—
289C8×C13—21no—
290C8×C13—21no—
291C8×C13—41no—
292C8×C13—41no—
293C8×C13—41no—
294#1055—21no—
295#1055—21no—
296#1055—21no—
297#1055—41no—
298#1055—41no—
299#1055—41no—
300#1055C2×M1612yes—
301C22×D8—131no—
302C2×C4×D4—131no—
303C2×C4×D4—131no—
304C4×D8—131no—
305C4×D8—131no—
306C4×D8—131no—
307C4×D8—131no—
308C4×D8—131no—
309C4×D8—131no—
310C4×D8—131no—
311C4×D8C2×D1311yescharacteristic
312#436—131no—
313#436—131no—
314#436—131no—
315#436C2×D1311yescharacteristic, complemented
316#435—261no—
317#435—261no—
318#435—261no—
319#435—261no—
320C8×D4—131no—
321C8×D4—131no—
322C8×D4—131no—
323C8×D4C2×D1311yescharacteristic, complemented
324#432—131no—
325#432—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—
334C4×M16—131no—
335C2×C4×C8—131no—
336#335—131no—
337#335C2×D1311yescharacteristic, complemented
338#334—131no—
339#334—131no—
340D4⋊C8—131no—
341D4⋊C8—131no—
342D4⋊C8—131no—
343D4⋊C8—131no—
344D4⋊C8—131no—
345D4⋊C8—131no—
346D4⋊C8C2×D1311yescharacteristic, complemented
347D4⋊C8C2×D1311yescharacteristic, complemented
348#322—131no—
349#322—131no—
350#322—131no—
351#322C2×D1311yescharacteristic, complemented
352C22×C13—22no—
353C22×C13—41no—
354C22×C13—41no—
355C22×C13—41no—
356C22×C13—41no—
357C22×C13—41no—
358C22×C13C2×C4×D411yescharacteristic
359C2×D13—21no—
360C2×D13—21no—
361C2×D13—22no—
362C2×D13—41no—
363C2×D13—41no—
364C2×D13—41no—
365C2×D13—41no—
366C2×D13—41no—
367C2×D13—84no—
368C2×D13—84no—
369C2×D13#44412yes—
370C4×C13—21no—
371C4×C13—41no—
372C4×C13—41no—
373C4×C13C22×M1611yescharacteristic
374C4×C13#56811yescharacteristic
375C4×C13#57611yescharacteristic
376C4×C13#57611yescharacteristic
377Dic13—21no—
378Dic13—21no—
379Dic13—21no—
380Dic13—41no—
381Dic13—41no—
382C22×D4—131no—
383C22×D4—131no—
384C23×C4—261no—
385C23×C4—261no—
386C2×D8—131no—
387C2×D8—131no—
388C2×D8—131no—
389C2×D8—264no—
390C2×D8C4×D1311yescharacteristic
391C2×M16—21no—
392C2×M16—261no—
393C2×M16—261no—
394C2×M16—261no—
395C2×M16—261no—
396C22×C8—21no—
397C22×C8—131no—
398C22×C8—131no—
399C22×C8—261no—
400C22×C8—261no—
401C22×C8—261no—
402C4×D4—131no—
403C4×D4—131no—
404C4×D4—131no—
405C4×D4—131no—
406C4×D4—131no—
407C4×D4—131no—
408C4×D4—261no—
409C4×D4—261no—
410C4×D4—261no—
411C4×D4—261no—
412C4×D4C22×D1311yescharacteristic
413C4×D4C22×D1311yescharacteristic
414C2×C4⋊C4—131no—
415C2×C4⋊C4—131no—
416C2×C22⋊C4—261no—
417C2×C22⋊C4—261no—
418C2×C42—131no—
419#107—131no—
420#107—131no—
421#107—131no—
422#107C4×D1311yescharacteristic
423C4⋊C8—131no—
424C4⋊C8—131no—
425C4⋊C8—131no—
426C4⋊C8—131no—
427C4⋊C8C22×D1311yescharacteristic
428C4⋊C8C22×D1311yescharacteristic
429#102—131no—
430#102—131no—
431#102—131no—
432#102—131no—
433#102—131no—
434#102—131no—
435#102C4×D1311yescharacteristic
436#102C4×D1311yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—131no—
440C22⋊C8—131no—
441C22⋊C8—261no—
442C22⋊C8—261no—
443C22⋊C8—261no—
444C22⋊C8—261no—
445C22⋊C8—261no—
446C22⋊C8—261no—
447C22⋊C8—261no—
448C22⋊C8—261no—
449#97—261no—
450#97—261no—
451#97—261no—
452C4×C8—131no—
453C4×C8—131no—
454C4×C8—131no—
455C4×C8—131no—
456C4×C8—131no—
457C4×C8C22×D1311yescharacteristic
458C4×C8C22×D1311yescharacteristic
459C4×C8C22×D1311yescharacteristic
460C2×C13—42no—
461C2×C13—81no—
462C2×C13D4×M1611yescharacteristic
463C2×C13#294811yescharacteristic
464C2×C13C2×#44411yescharacteristic
465D13—22no—
466D13—42no—
467D13—81no—
468C24—261no—
469C24—261no—
470C2×D4—131no—
471C2×D4—131no—
472C2×D4—261no—
473C2×D4—261no—
474C2×D4—262no—
475C2×D4—262no—
476C2×D4—521no—
477C2×D4—521no—
478C2×D4C2×C4×D1311yescharacteristic
479C2×D4C2×C4×D1311yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—131no—
483C22×C4—131no—
484C22×C4—131no—
485C22×C4—261no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4—1041no—
494C22×C4—1041no—
495C22×C4—1041no—
496C22×C4—1041no—
497D8—22no—
498D8—134no—
499D8—262no—
500D8—262no—
501M16—81no—
502M16—522no—
503M16—1041no—
504M16—1041no—
505M16—1041no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—81no—
510C2×C8—131no—
511C2×C8—131no—
512C2×C8—131no—
513C2×C8—131no—
514C2×C8—262no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—521no—
519C2×C8—1041no—
520C2×C8—1041no—
521C2×C8—1041no—
522C2×C8C2×C4×D1311yescharacteristic
523C2×C8C2×C4×D1311yescharacteristic
524C2×C8D4×D1311yescharacteristic
525C2×C8D4×D1311yescharacteristic
526C4⋊C4—131no—
527C4⋊C4—131no—
528C4⋊C4—261no—
529C4⋊C4—261no—
530C4⋊C4C2×C4×D1311yescharacteristic
531C4⋊C4C2×C4×D1311yescharacteristic
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—261no—
535C22⋊C4—261no—
536C22⋊C4—261no—
537C22⋊C4—261no—
538C22⋊C4—261no—
539C22⋊C4—261no—
540C42—131no—
541C42—131no—
542C42—131no—
543C42C23×D1311yescharacteristic
544C13#1806411yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—131no—
548C23—261no—
549C23—261no—
550C23—522no—
551C23—522no—
552C23—522no—
553C23—522no—
554C23—1041no—
555C23—1041no—
556D4—21no—
557D4—21no—
558D4—21no—
559D4—132no—
560D4—261no—
561D4—261no—
562D4—261no—
563D4—522no—
564D4—522no—
565D4M16×D1312yes—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—131no—
573C2×C4—131no—
574C2×C4—131no—
575C2×C4—262no—
576C2×C4—261no—
577C2×C4—261no—
578C2×C4—261no—
579C2×C4—261no—
580C2×C4—261no—
581C2×C4—261no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—1041no—
587C2×C4—1041no—
588C2×C4—1041no—
589C2×C4—1041no—
590C2×C4—1041no—
591C2×C4—1041no—
592C2×C4C22×C4×D1311yescharacteristic
593C2×C4C2×D4×D1311yescharacteristic
594C2×C4#41×D1311yescharacteristic
595C8—21no—
596C8—21no—
597C8—21no—
598C8—21no—
599C8—41no—
600C8—41no—
601C8—41no—
602C8—132no—
603C8—261no—
604C8—261no—
605C8—261no—
606C8—521no—
607C8—521no—
608C8—521no—
609C22—22no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—132no—
616C22—261no—
617C22—261no—
618C22—262no—
619C22—521no—
620C22—521no—
621C22—521no—
622C22—521no—
623C22—521no—
624C22—1044no—
625C22—1044no—
626C22C4×D4×D1311yescharacteristic
627C4—21no—
628C4—41no—
629C4—41no—
630C4—261no—
631C4—261no—
632C4—261no—
633C4—521no—
634C4—521no—
635C4C2×M16×D1311yescharacteristic
636C4#1171945511yescharacteristic
637C4#1171946211yescharacteristic
638C4#1171947411yescharacteristic
639C2—42no—
640C2—81no—
641C2—262no—
642C2—522no—
643C2—1041no—
644C2#1312356911yescharacteristic
645C2#1312368311yescharacteristic
646C2D13×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1581C2
socleC22×C13C2×C4×D4
prime radicalC2×D8×D13C4
cosocleC42×C13C24
hypercenter#1581D13
hypocenterC13#18064
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
1. #13123869C2semidirect
2. #13123868C2semidirect
4. #13113748C2semidirect
5. #13113747C2semidirect
6. #13113667C2semidirect
7. #13113666C2semidirect
8. #13113664C2semidirect
9. #13113658C2semidirect
10. #13113657C2semidirect
11. #13113598C2semidirect
12. #13113277C2semidirect
13. #13113277C2semidirect
14. #13113124C2semidirect
15. C13×#1581C2semidirect
20. C13×#436C22semidirect
21. C8×D4×C13C22semidirect
29. #11718673C22semidirect
30. D4×#1055C22semidirect
33. #11718499C22semidirect
36. #11718495C22semidirect
46. #11718349C22semidirect
48. C8×D52C22semidirect
51. C13×#335C22semidirect
52. C13×D4⋊C8C22semidirect
53. C13×D4⋊C8C22semidirect
54. C13×#322C22semidirect
55. D4⋊#1055C22semidirect
56. D4⋊#1055C22semidirect
57. #11718075C22semidirect
58. #11718075C22semidirect
59. #11718072C22semidirect
60. #11718072C22semidirect
61. #11718051C22semidirect
62. #11718051C22semidirect
63. #11718050C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. #11718046C22semidirect
193. #6104M16semidirect
230. #1581D13semidirect
315. #436C2×D13semidirect
323. C8×D4C2×D13semidirect
337. #335C2×D13semidirect
346. D4⋊C8C2×D13semidirect
347. D4⋊C8C2×D13semidirect
351. #322C2×D13semidirect
544. C13#18064semidirect

Maximal subgroups

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

subgroupindex
#131238692
#131238682
C4×D8×D132
#131137482
#131137472
#131136672
#131136662
#131136642
#131136582
#131136572
#131135982
#131132772
#131131242
C13×#15812
#1806413