Finite Group Databasebeta

← #15833809

Subgroups — #15833809

Order 3328.

748 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124834C211yesmaximal, characteristic
2#13123581C211yesmaximal, characteristic, complemented
3#13123572C211yesmaximal, characteristic, complemented
4#13113718C211yesmaximal, characteristic, complemented
5#13113666C211yesmaximal, characteristic, complemented
6#13113664C211yesmaximal, characteristic, complemented
7#13113663C211yesmaximal, characteristic, complemented
8#13113663C211yesmaximal, characteristic, complemented
9C8×D104C211yesmaximal, characteristic, complemented
10#13113628C211yesmaximal, characteristic, complemented
11#13113609C211yesmaximal, characteristic, complemented
12#13113285C211yesmaximal, characteristic, complemented
13D13×D4⋊C8C211yesmaximal, characteristic, complemented
14C8×#6094C211yesmaximal, characteristic, complemented
15C13×#1589C211yesmaximal, characteristic, complemented
16C2×#88161—21no—
17C2×M16×D13—21no—
18#11719253C2211yescharacteristic
19C4×D4×D13C2211yescharacteristic
20C4×C13×D8C2211yescharacteristic
21C13×#436C2211yescharacteristic
22C13×#436C2211yescharacteristic, complemented
23#11718817C411yescharacteristic
24#11718811C411yescharacteristic
25#11718788—21no—
26#11718788—21no—
27C4×#6104C2211yescharacteristic
28C4×#6104C2211yescharacteristic
29#11718673C2211yescharacteristic
30D4×#1055C2211yescharacteristic, complemented
31#11718551C411yescharacteristic
32#11718543C411yescharacteristic
33#11718499C2211yescharacteristic, complemented
34#11718498C2211yescharacteristic
35#11718495C2211yescharacteristic
36D13×C4⋊C8C2211yescharacteristic
37#11718447C411yescharacteristic
38#11718435C411yescharacteristic
39#11718434C411yescharacteristic
40#11718420C411yescharacteristic
41#11718391—21no—
42#11718389—21no—
43#11718388—21no—
44#11718387—21no—
45C4×D104C2211yescharacteristic
46C4×#6094C2211yescharacteristic
47C8×D52C2211yescharacteristic
48C8×D52C2211yescharacteristic, complemented
49#11718346C2211yescharacteristic
50C4×C8×D13C2211yescharacteristic
51C13×#335C2211yescharacteristic, complemented
52C13×D4⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic, complemented
54C82×C13C2211yescharacteristic, complemented
55D4⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic, complemented
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic, complemented
59#11718071C2211yescharacteristic, complemented
60#11718071C2211yescharacteristic, complemented
61#11718051C2211yescharacteristic
62#11718051C2211yescharacteristic, complemented
63#11718050C2211yescharacteristic, complemented
64#11718047C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C2×D4×D13C2×C411yescharacteristic
68C2×#6127—21no—
69C22×C4×D13—21no—
70C2×C13×D8C2×C411yescharacteristic
71C2×C13×M16—21no—
72C2×C13×M16—21no—
73C4×D4×C13C2311yescharacteristic
74C4×D4×C13C2311yescharacteristic
75#88194C2×C411yescharacteristic
76#88192C2×C411yescharacteristic
77D4×Dic13C2×C411yescharacteristic
78C2×#6104C2×C411yescharacteristic
79C2×#6104C2×C411yescharacteristic
80C4×C22⋊D13—21no—
81C4×C22⋊D13—21no—
82C2×#6099—21no—
83C22×#1055—21no—
84#88161—44no—
85M16×D13—44no—
86C2×D104C2×C411yescharacteristic
87C2×#6094—21no—
88C2×#6094—21no—
89C2×#6094D411yescharacteristic
90C2×#6094D411yescharacteristic
91C2×C8×D13—21no—
92C2×C8×D13—21no—
93C2×C8×D13—21no—
94C2×C8×D13—21no—
95C2×C8×D13—21no—
96#88149C2×C411yescharacteristic
97#88147C2×C411yescharacteristic
98C4⋊C4×D13C2×C411yescharacteristic
99#88142C2×C411yescharacteristic
100#88139—21no—
101#88138—21no—
102#88135—21no—
103C22⋊C4×D13—21no—
104C4×D52C2311yescharacteristic
105C4×D52C2311yescharacteristic
106C42×D13C2311yescharacteristic
107C13×#107C2×C411yescharacteristic
108C13×C4⋊C8C2311yescharacteristic
109C13×C4⋊C8C2311yescharacteristic
110C13×#102C2×C411yescharacteristic
111C13×#102C2×C411yescharacteristic
112C13×C22⋊C8—21no—
113C13×C22⋊C8—21no—
114C4×C8×C13C2311yescharacteristic
115C4×C8×C13C2311yescharacteristic
116C4×C8×C13C2311yescharacteristic
117#88072C2×C411yescharacteristic
118#88072C2×C411yescharacteristic
119C22⋊#1055—21no—
120C22⋊#1055—21no—
121#88061C2×C411yescharacteristic
122#88061C2×C411yescharacteristic
123#88060—21no—
124#88060—21no—
125#88060—21no—
126#88060—21no—
127#88060C2×C411yescharacteristic
128#88060C2×C411yescharacteristic
129#88058C2×C411yescharacteristic
130#88055D411yescharacteristic
131#88055D411yescharacteristic
132#88054—21no—
133#88054—21no—
134#88054C2×C411yescharacteristic
135#88054C2×C411yescharacteristic
136C8×Dic13—21no—
137#88049C2×C411yescharacteristic
138#88049C2×C411yescharacteristic
139#88047C2×C411yescharacteristic
140#88047C2×C411yescharacteristic
141C4⋊#1055C2311yescharacteristic
142C4⋊#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145C4×#1055C2311yescharacteristic
146#17994—131nomaximal, Sylow
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—
154C2×C22⋊D13—21no—
155C2×C22⋊D13—21no—
156C22×Dic13—21no—
157D4×D13—22no—
158D4×D13—41no—
159#6127—42no—
160#6127—42no—
161C2×D52—21no—
162C2×D52C22×C411yescharacteristic
163C2×D52C22×C411yescharacteristic
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×C4×D13—21no—
167C2×C4×D13—21no—
168C2×C4×D13—42no—
169C2×C4×D13—42no—
170C2×C4×D13C22×C411yescharacteristic
171C2×C4×D13C2×D411yescharacteristic
172C2×C4×D13#4111yescharacteristic
173C2×Dic26—21no—
174C13×D8—41no—
175C13×M16—42no—
176C13×M16—42no—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13—21no—
180C2×C8×C13C22×C411yescharacteristic
181C2×C8×C13C22×C411yescharacteristic
182C2×C8×C13C2×D411yescharacteristic
183C2×C8×C13C2×D411yescharacteristic
184C13×C4⋊C4C22×C411yescharacteristic
185C13×C4⋊C4C22×C411yescharacteristic
186C13×C22⋊C4—21no—
187C13×C22⋊C4—21no—
188C42×C13C2411yescharacteristic
189C22⋊Dic13—21no—
190C22⋊Dic13—21no—
191#6104—22no—
192#6104—41no—
193#6103—21no—
194#6103—21no—
195#6103—21no—
196#6103—21no—
197C4⋊Dic13C22×C411yescharacteristic
198C4⋊Dic13C22×C411yescharacteristic
199#6101—21no—
200#6101—21no—
201C4×Dic13C22×C411yescharacteristic
202C4×Dic13C2×D411yescharacteristic
203C4×Dic13#4111yescharacteristic
204#6099—42no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—42no—
209C2×#1055C22×C411yescharacteristic
210C2×#1055C22×C411yescharacteristic
211C2×#1055C2×D411yescharacteristic
212C2×#1055C2×D411yescharacteristic
213D104—22no—
214#6094—22no—
215#6094—42no—
216#6094—42no—
217#6094D814yescomplemented
218C8×D13—42no—
219C8×D13—42no—
220C8×D13—42no—
221C8×D13—42no—
222C8×D13—42no—
223#3100—131no—
224#2935—131no—
225D4×M16—131no—
226#1589—131no—
227#1589D1311yescharacteristic, complemented
228#1581—131no—
229#1581—131no—
230#1581—131no—
231#1581—131no—
232C8×D8—131no—
233C8×D8—131no—
234#1571—131no—
235#1492—131no—
236C2×D4⋊C8—131no—
237C8×M16—131no—
238C23×C13—21no—
239C23×C13—21no—
240C22×D13—21no—
241C22×D13—21no—
242C22×D13—42no—
243C22×D13—42no—
244C22×D13—81no—
245C22×D13C4×D411yescharacteristic
246D4×C13—21no—
247D4×C13—21no—
248D4×C13—21no—
249D4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13C23×C411yescharacteristic
257C2×C4×C13C22×D411yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C22⋊D13—42no—
260C22⋊D13—42no—
261C22⋊D13—42no—
262C22⋊D13—81no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—42no—
266C2×Dic13C4×D411yescharacteristic
267C2×Dic13C4×D411yescharacteristic
268C2×Dic13C4×D411yescharacteristic
269D52—21no—
270D52—21no—
271D52—21no—
272D52—42no—
273D52#13112yescomplemented
274C4×D13—21no—
275C4×D13—21no—
276C4×D13—41no—
277C4×D13—42no—
278C4×D13—41no—
279C4×D13—41no—
280C4×D13—41no—
281C4×D13—41no—
282C4×D13—42no—
283C4×D13C2×D812yes—
284C4×D13#13512yes—
285Dic26—42no—
286C8×C13—22no—
287C8×C13—21no—
288C8×C13—21no—
289C8×C13—21no—
290C8×C13—41no—
291C8×C13—41no—
292C8×C13C2×D812yes—
293#1055—21no—
294#1055—21no—
295#1055—21no—
296#1055—41no—
297#1055—41no—
298#1055—41no—
299#1055C2×D812yes—
300C2×#131—261no—
301C22×M16—261no—
302#532—131no—
303C2×C4×D4—131no—
304#480—131no—
305#480—131no—
306#474—131no—
307#474—131no—
308#459—131no—
309#459—131no—
310#447—131no—
311#447—131no—
312C4×D8—131no—
313C4×D8—131no—
314C4×D8—131no—
315C4×D8C2×D1311yescharacteristic
316#436—131no—
317#436—131no—
318#436C2×D1311yescharacteristic
319#436C2×D1311yescharacteristic, complemented
320#435—261no—
321#435—261no—
322#435—261no—
323#435—261no—
324C8×D4—131no—
325C8×D4—131no—
326C8×D4—131no—
327C8×D4—131no—
328#431—131no—
329#423—131no—
330C2×C4⋊C8—131no—
331#408—261no—
332#407—261no—
333C4×M16—131no—
334C2×C4×C8—131no—
335#335—131no—
336#335—131no—
337#335—131no—
338#335C2×D1311yescharacteristic, complemented
339D4⋊C8—131no—
340D4⋊C8—131no—
341D4⋊C8—131no—
342D4⋊C8—131no—
343D4⋊C8—131no—
344D4⋊C8—131no—
345D4⋊C8C2×D1311yescharacteristic
346D4⋊C8C2×D1311yescharacteristic, complemented
347#322—131no—
348#322—131no—
349C82—131no—
350C82C2×D1311yescharacteristic, complemented
351C22×C13—41no—
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×D13C4×D812yes—
368C4×C13—21no—
369C4×C13—41no—
370C4×C13—41no—
371C4×C13C2×#13111yescharacteristic
372C4×C13#56811yescharacteristic
373C4×C13C22×D811yescharacteristic
374C4×C13C2×#13511yescharacteristic
375Dic13—21no—
376Dic13—21no—
377Dic13—41no—
378Dic13—41no—
379Dic13C4×D812yes—
380C2×#41—261no—
381C22×D4—131no—
382C23×C4—261no—
383C2×D8—131no—
384C2×D8—131no—
385C2×D8—131no—
386C2×D8C4×D1311yescharacteristic
387#131—524no—
388C2×M16—21no—
389C2×M16—21no—
390C2×M16—131no—
391C2×M16—131no—
392C2×M16—261no—
393C2×M16—261no—
394C2×M16—261no—
395C2×M16—524no—
396C22×C8—261no—
397C22×C8—261no—
398C22×C8—261no—
399C22×C8—261no—
400C22×C8—261no—
401C22×C8—261no—
402C4⋊Q8—131no—
403#127—131no—
404#124—261no—
405#121—131no—
406#121—131no—
407#121—261no—
408C4×D4—131no—
409C4×D4—131no—
410C4×D4—131no—
411C4×D4—131no—
412C4×D4—261no—
413C4×D4—261no—
414C4×D4—261no—
415C4×D4C22×D1311yescharacteristic
416C4×D4C22×D1311yescharacteristic
417C2×C4⋊C4—131no—
418C2×C22⋊C4—261no—
419C2×C42—131no—
420#107—131no—
421#107—131no—
422#107—131no—
423#107C4×D1311yescharacteristic
424C4⋊C8—131no—
425C4⋊C8—131no—
426C4⋊C8—131no—
427C4⋊C8—131no—
428C4⋊C8—261no—
429C4⋊C8—261no—
430C4⋊C8C22×D1311yescharacteristic
431C4⋊C8C22×D1311yescharacteristic
432#102—131no—
433#102—131no—
434#102—131no—
435#102—131no—
436#102—131no—
437#102—131no—
438#102C4×D1311yescharacteristic
439#102C4×D1311yescharacteristic
440C22⋊C8—21no—
441C22⋊C8—21no—
442C22⋊C8—131no—
443C22⋊C8—131no—
444C22⋊C8—261no—
445C22⋊C8—261no—
446C22⋊C8—261no—
447C22⋊C8—261no—
448C22⋊C8—261no—
449C22⋊C8—261no—
450#97—131no—
451#97—131no—
452C4×C8—131no—
453C4×C8—131no—
454C4×C8—131no—
455C4×C8—261no—
456C4×C8C22×D1311yescharacteristic
457C4×C8C22×D1311yescharacteristic
458C4×C8C22×D1311yescharacteristic
459C2×C13—81no—
460C2×C13—81no—
461C2×C13#293311yescharacteristic
462C2×C13C2×C4×D811yescharacteristic
463C2×C13#295611yescharacteristic
464D13—22no—
465D13—42no—
466D13—81no—
467C24—261no—
468#41—522no—
469#41—522no—
470C2×Q8—261no—
471C2×D4—131no—
472C2×D4—131no—
473C2×D4—261no—
474C2×D4—261no—
475C2×D4—261no—
476C2×D4—261no—
477C2×D4—262no—
478C2×D4—261no—
479C2×D4—521no—
480C2×D4C2×C4×D1311yescharacteristic
481C2×D4C2×C4×D1311yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—131no—
485C22×C4—131no—
486C22×C4—131no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—522no—
493C22×C4—522no—
494D8—41no—
495D8—262no—
496D8—262no—
497D8—521no—
498M16—42no—
499M16—42no—
500M16—134no—
501M16—262no—
502M16—522no—
503M16—522no—
504M16—522no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—131no—
509C2×C8—131no—
510C2×C8—131no—
511C2×C8—131no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—522no—
516C2×C8—522no—
517C2×C8—522no—
518C2×C8—522no—
519C2×C8—522no—
520C2×C8—522no—
521C2×C8C2×C4×D1311yescharacteristic
522C2×C8C2×C4×D1311yescharacteristic
523C2×C8D4×D1311yescharacteristic
524C2×C8D4×D1311yescharacteristic
525C4⋊C4—131no—
526C4⋊C4—131no—
527C4⋊C4—261no—
528C4⋊C4—261no—
529C4⋊C4C2×C4×D1311yescharacteristic
530C4⋊C4C2×C4×D1311yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—261no—
534C22⋊C4—261no—
535C22⋊C4—261no—
536C22⋊C4—261no—
537C22⋊C4—261no—
538C22⋊C4—261no—
539C42—131no—
540C42—131no—
541C42—131no—
542C42C23×D1311yescharacteristic
543C13#1799411yescharacteristic, complemented, Sylow
544C23—21no—
545C23—21no—
546C23—131no—
547C23—261no—
548C23—261no—
549C23—522no—
550C23—522no—
551C23—1041no—
552Q8—522no—
553D4—21no—
554D4—21no—
555D4—21no—
556D4—21no—
557D4—132no—
558D4—261no—
559D4—261no—
560D4—261no—
561D4—522no—
562D4—522no—
563D4—522no—
564D4—522no—
565D4—1041no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—131no—
573C2×C4—132no—
574C2×C4—132no—
575C2×C4—131no—
576C2×C4—131no—
577C2×C4—261no—
578C2×C4—261no—
579C2×C4—261no—
580C2×C4—261no—
581C2×C4—521no—
582C2×C4—522no—
583C2×C4—522no—
584C2×C4—522no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4C22×C4×D1311yescharacteristic
590C2×C4C2×D4×D1311yescharacteristic
591C2×C4#41×D1311yescharacteristic
592C8—22no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—132no—
599C8—261no—
600C8—261no—
601C8—261no—
602C8—521no—
603C8—521no—
604C8—521no—
605C8D8×D1312yes—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—132no—
613C22—261no—
614C22—261no—
615C22—262no—
616C22—521no—
617C22—521no—
618C22—521no—
619C22—521no—
620C22—521no—
621C22—1044no—
622C22C4×D4×D1311yescharacteristic
623C4—21no—
624C4—41no—
625C4—41no—
626C4—132no—
627C4—261no—
628C4—261no—
629C4—521no—
630C4—521no—
631C4#1171945011yescharacteristic
632C4D13×#13111yescharacteristic
633C4C2×D8×D1311yescharacteristic
634C4D13×#13511yescharacteristic
635C2—81no—
636C2—81no—
637C2—262no—
638C2—522no—
639C2—1041no—
640C2#1312356511yescharacteristic
641C2C4×D8×D1311yescharacteristic
642C2#1312374111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1589C2
socleC22×C13C2×C4×D4
prime radical#13124834C2
cosocleC42×C13C24
hypercenter#1589D13
hypocenterC13#17994
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1589

Complements

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

NH ≅ G/Ntype
2. #13123581C2semidirect
3. #13123572C2semidirect
4. #13113718C2semidirect
5. #13113666C2semidirect
6. #13113664C2semidirect
7. #13113663C2semidirect
8. #13113663C2semidirect
9. C8×D104C2semidirect
10. #13113628C2semidirect
11. #13113609C2semidirect
12. #13113285C2semidirect
13. D13×D4⋊C8C2semidirect
14. C8×#6094C2semidirect
15. C13×#1589C2semidirect
22. C13×#436C22semidirect
30. D4×#1055C22semidirect
33. #11718499C22semidirect
48. C8×D52C22semidirect
51. C13×#335C22semidirect
53. C13×D4⋊C8C22semidirect
54. C82×C13C22semidirect
56. D4⋊#1055C22semidirect
58. #11718075C22semidirect
59. #11718071C22semidirect
60. #11718071C22semidirect
62. #11718051C22semidirect
63. #11718050C22semidirect
64. #11718047C22semidirect
65. #11718046C22semidirect
66. C8×#1055C22semidirect
217. #6094D8semidirect
227. #1589D13semidirect
273. D52#131semidirect
319. #436C2×D13semidirect
338. #335C2×D13semidirect
346. D4⋊C8C2×D13semidirect
350. C82C2×D13semidirect
543. C13#17994semidirect

Maximal subgroups

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

subgroupindex
#131248342
#131235812
#131235722
#131137182
#131136662
#131136642
#131136632
C8×D1042
#131136282
#131136092
#131132852
D13×D4⋊C82
C8×#60942
C13×#15892
#1799413