Finite Group Databasebeta

← #15833106

Subgroups — #15833106

Order 3328.

734 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124834C211yesmaximal, characteristic
2#13123543C211yesmaximal, characteristic, complemented
3D13×#436C211yesmaximal, characteristic, complemented
4#13113721C211yesmaximal, characteristic, complemented
5#13113720C211yesmaximal, characteristic, complemented
6#13113718C211yesmaximal, characteristic, complemented
7#13113718C211yesmaximal, characteristic, complemented
8#13113667C211yesmaximal, characteristic, complemented
9#13113665C211yesmaximal, characteristic, complemented
10#13113663C211yesmaximal, characteristic, complemented
11#13113609C211yesmaximal, characteristic, complemented
12#13113259C211yesmaximal, characteristic, complemented
13#13113233C211yesmaximal, characteristic, complemented
14#13113121C211yesmaximal, characteristic, complemented
15C13×#1581C211yesmaximal, characteristic, complemented
16C2×M16×D13—21no—
17C2×#88155—21no—
18#11719253C2211yescharacteristic
19C4×D4×D13C2211yescharacteristic
20C4×C13×D8C2211yescharacteristic
21C13×#436C2211yescharacteristic
22C8×D4×C13C2211yescharacteristic, complemented
23#11718817C411yescharacteristic
24#11718811C411yescharacteristic
25#11718789—21no—
26C8×C22⋊D13—21no—
27C4×#6104C2211yescharacteristic
28C4×#6104C2211yescharacteristic
29#11718673C2211yescharacteristic
30#11718673C2211yescharacteristic, complemented
31#11718551C411yescharacteristic
32#11718543C411yescharacteristic
33#11718499C2211yescharacteristic
34#11718499C2211yescharacteristic, complemented
35#11718498C2211yescharacteristic
36D13×C4⋊C8C2211yescharacteristic
37#11718447C411yescharacteristic
38#11718435C411yescharacteristic
39#11718434C411yescharacteristic
40#11718420C411yescharacteristic
41#11718390—21no—
42#11718390—21no—
43#11718388—21no—
44D13×C22⋊C8—21no—
45C4×D104C2211yescharacteristic
46#11718349C2211yescharacteristic
47C8×D52C2211yescharacteristic, complemented
48#11718346C2211yescharacteristic
49#11718346C2211yescharacteristic
50C4×C8×D13C2211yescharacteristic
51C13×#335C2211yescharacteristic, complemented
52C13×D4⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic, complemented
54C13×#322C2211yescharacteristic, 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
65C8×#1055C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C2×D4×D13C2×C411yescharacteristic
68C2×#6127—21no—
69C22×C4×D13—21no—
70C2×C13×D8C2×C411yescharacteristic
71C2×C13×M16—21no—
72C22×C8×C13—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—
83C2×#6099—21no—
84M16×D13—44no—
85C2×D104C2×C411yescharacteristic
86#88155—44no—
87C2×#6094—21no—
88C2×#6094—21no—
89C2×#6094—21no—
90C2×#6094—21no—
91C2×C8×D13—21no—
92C2×C8×D13—21no—
93C2×C8×D13D411yescharacteristic
94C2×C8×D13D411yescharacteristic
95#88149C2×C411yescharacteristic
96#88147C2×C411yescharacteristic
97C4⋊C4×D13C2×C411yescharacteristic
98#88142C2×C411yescharacteristic
99#88139—21no—
100#88138—21no—
101#88135—21no—
102C22⋊C4×D13—21no—
103C4×D52C2311yescharacteristic
104C4×D52C2311yescharacteristic
105C42×D13C2311yescharacteristic
106C13×#107C2×C411yescharacteristic
107C13×C4⋊C8C2311yescharacteristic
108C13×C4⋊C8C2311yescharacteristic
109C13×#102C2×C411yescharacteristic
110C13×#102C2×C411yescharacteristic
111C13×C22⋊C8—21no—
112C13×C22⋊C8—21no—
113C4×C8×C13C2311yescharacteristic
114C4×C8×C13C2311yescharacteristic
115C4×C8×C13C2311yescharacteristic
116#88072C2×C411yescharacteristic
117#88072C2×C411yescharacteristic
118C22⋊#1055—21no—
119C22⋊#1055—21no—
120#88061C2×C411yescharacteristic
121#88061C2×C411yescharacteristic
122#88060—21no—
123#88060—21no—
124#88060—21no—
125#88060—21no—
126#88060—21no—
127#88060C2×C411yescharacteristic
128#88060C2×C411yescharacteristic
129#88058C2×C411yescharacteristic
130#88054—21no—
131#88054—21no—
132#88054—21no—
133#88054C2×C411yescharacteristic
134#88054C2×C411yescharacteristic
135C8×Dic13D411yescharacteristic
136C8×Dic13D411yescharacteristic
137#88049C2×C411yescharacteristic
138#88049C2×C411yescharacteristic
139#88047C2×C411yescharacteristic
140#88047C2×C411yescharacteristic
141C4⋊#1055C2311yescharacteristic
142C4⋊#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145C4×#1055C2311yescharacteristic
146#17928—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—41no—
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—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13—42no—
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—41no—
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—
205#6099—42no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055C22×C411yescharacteristic
210C2×#1055C22×C411yescharacteristic
211C2×#1055C2×D411yescharacteristic
212C2×#1055C2×D411yescharacteristic
213D104—41no—
214#6094—42no—
215#6094—42no—
216#6094—42no—
217#6094—42no—
218C8×D13—22no—
219C8×D13—42no—
220C8×D13—42no—
221C8×D13D814yescomplemented
222#3100—131no—
223#2931—131no—
224C2×#436—131no—
225#1589—131no—
226#1589—131no—
227#1589—131no—
228#1589—131no—
229#1581—131no—
230#1581—131no—
231#1581—131no—
232#1581D1311yescharacteristic, complemented
233#1571—131no—
234#1486—131no—
235#1480—131no—
236#1450—131no—
237C23×C13—21no—
238C23×C13—21no—
239C22×D13—21no—
240C22×D13—21no—
241C22×D13—42no—
242C22×D13—42no—
243C22×D13—42no—
244C22×D13C4×D411yescharacteristic
245D4×C13—21no—
246D4×C13—21no—
247D4×C13—21no—
248D4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13C23×C411yescharacteristic
256C2×C4×C13C22×D411yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C22⋊D13—42no—
259C22⋊D13—42no—
260C22⋊D13—42no—
261C22⋊D13—42no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—42no—
265C2×Dic13C4×D411yescharacteristic
266C2×Dic13C4×D411yescharacteristic
267C2×Dic13C4×D411yescharacteristic
268D52—21no—
269D52—21no—
270D52—21no—
271D52—21no—
272D52—42no—
273C4×D13—21no—
274C4×D13—21no—
275C4×D13—41no—
276C4×D13—42no—
277C4×D13—41no—
278C4×D13—41no—
279C4×D13—41no—
280C4×D13—41no—
281C4×D13—42no—
282C4×D13C2×D812yes—
283C4×D13#13512yes—
284Dic26—42no—
285C8×C13—21no—
286C8×C13—21no—
287C8×C13—21no—
288C8×C13—41no—
289C8×C13—41no—
290C8×C13—41no—
291C8×C13C2×D812yes—
292#1055—21no—
293#1055—21no—
294#1055—21no—
295#1055—41no—
296#1055—41no—
297#1055—41no—
298#1055C2×D812yes—
299C2×#131—261no—
300C22×M16—261no—
301#532—131no—
302C2×C4×D4—131no—
303#480—131no—
304#480—131no—
305#474—131no—
306#474—131no—
307#459—131no—
308#459—131no—
309#447—131no—
310#447—131no—
311C4×D8—131no—
312C4×D8—131no—
313C4×D8—131no—
314C4×D8C2×D1311yescharacteristic
315#436—131no—
316#436—131no—
317#436—131no—
318#436—131no—
319#436—131no—
320#436—261no—
321#436—261no—
322#436—261no—
323#436C2×D1311yescharacteristic
324C8×D4—131no—
325C8×D4—261no—
326C8×D4C2×D1311yescharacteristic, complemented
327#431—131no—
328#431—131no—
329#423—131no—
330C2×C4⋊C8—131no—
331#408—261no—
332C2×C22⋊C8—261no—
333C2×C4×C8—131no—
334#335—131no—
335#335—131no—
336#335—131no—
337#335C2×D1311yescharacteristic, complemented
338D4⋊C8—131no—
339D4⋊C8—131no—
340D4⋊C8—131no—
341D4⋊C8—131no—
342D4⋊C8—131no—
343D4⋊C8—131no—
344D4⋊C8C2×D1311yescharacteristic
345D4⋊C8C2×D1311yescharacteristic, complemented
346#322—131no—
347#322C2×D1311yescharacteristic, complemented
348C82—131no—
349C82—131no—
350C22×C13—41no—
351C22×C13—41no—
352C22×C13—41no—
353C22×C13—41no—
354C22×C13—41no—
355C22×C13—41no—
356C22×C13C2×C4×D411yescharacteristic
357C2×D13—21no—
358C2×D13—21no—
359C2×D13—41no—
360C2×D13—41no—
361C2×D13—41no—
362C2×D13—41no—
363C2×D13—41no—
364C2×D13—41no—
365C2×D13—84no—
366C2×D13C4×D812yes—
367C4×C13—21no—
368C4×C13—41no—
369C4×C13—41no—
370C4×C13#56811yescharacteristic
371C4×C13#56811yescharacteristic
372C4×C13C22×D811yescharacteristic
373C4×C13C2×#13511yescharacteristic
374Dic13—21no—
375Dic13—21no—
376Dic13—41no—
377Dic13—41no—
378Dic13C4×D812yes—
379C2×#41—261no—
380C22×D4—131no—
381C23×C4—261no—
382C2×D8—131no—
383C2×D8—131no—
384C2×D8—131no—
385C2×D8C4×D1311yescharacteristic
386#131—524no—
387C2×M16—21no—
388C2×M16—261no—
389C2×M16—261no—
390C2×M16—261no—
391C2×M16—261no—
392C2×M16—261no—
393C2×M16—261no—
394C2×M16—524no—
395C22×C8—21no—
396C22×C8—131no—
397C22×C8—131no—
398C22×C8—261no—
399C22×C8—261no—
400C4⋊Q8—131no—
401#127—131no—
402#124—261no—
403#121—131no—
404#121—131no—
405#121—261no—
406C4×D4—131no—
407C4×D4—131no—
408C4×D4—131no—
409C4×D4—131no—
410C4×D4—261no—
411C4×D4—261no—
412C4×D4—261no—
413C4×D4C22×D1311yescharacteristic
414C4×D4C22×D1311yescharacteristic
415C2×C4⋊C4—131no—
416C2×C22⋊C4—261no—
417C2×C42—131no—
418#107—131no—
419#107—131no—
420#107—131no—
421#107C4×D1311yescharacteristic
422C4⋊C8—131no—
423C4⋊C8—131no—
424C4⋊C8—131no—
425C4⋊C8—131no—
426C4⋊C8—261no—
427C4⋊C8—261no—
428C4⋊C8—261no—
429C4⋊C8C22×D1311yescharacteristic
430C4⋊C8C22×D1311yescharacteristic
431#102—131no—
432#102—131no—
433#102—131no—
434#102—131no—
435#102—131no—
436#102—131no—
437#102C4×D1311yescharacteristic
438#102C4×D1311yescharacteristic
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8—131no—
442C22⋊C8—131no—
443C22⋊C8—261no—
444C22⋊C8—261no—
445C22⋊C8—261no—
446C22⋊C8—261no—
447C22⋊C8—261no—
448C22⋊C8—261no—
449C22⋊C8—261no—
450C4×C8—131no—
451C4×C8—131no—
452C4×C8—131no—
453C4×C8—131no—
454C4×C8—131no—
455C4×C8C22×D1311yescharacteristic
456C4×C8C22×D1311yescharacteristic
457C4×C8C22×D1311yescharacteristic
458C2×C13—81no—
459C2×C13—81no—
460C2×C13#293011yescharacteristic
461C2×C13C2×C4×D811yescharacteristic
462C2×C13#295511yescharacteristic
463D13—22no—
464D13—81no—
465D13—81no—
466C24—261no—
467#41—522no—
468#41—522no—
469C2×Q8—261no—
470C2×D4—131no—
471C2×D4—131no—
472C2×D4—261no—
473C2×D4—261no—
474C2×D4—261no—
475C2×D4—261no—
476C2×D4—261no—
477C2×D4—521no—
478C2×D4—521no—
479C2×D4C2×C4×D1311yescharacteristic
480C2×D4C2×C4×D1311yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—131no—
484C22×C4—131no—
485C22×C4—131no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—522no—
492C22×C4—522no—
493D8—41no—
494D8—521no—
495D8—521no—
496D8—521no—
497M16—42no—
498M16—522no—
499M16—522no—
500M16—522no—
501M16—522no—
502M16—522no—
503M16—522no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—42no—
508C2×C8—131no—
509C2×C8—134no—
510C2×C8—131no—
511C2×C8—131no—
512C2×C8—131no—
513C2×C8—262no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—522no—
518C2×C8—522no—
519C2×C8C2×C4×D1311yescharacteristic
520C2×C8C2×C4×D1311yescharacteristic
521C2×C8D4×D1311yescharacteristic
522C2×C8D4×D1311yescharacteristic
523C4⋊C4—131no—
524C4⋊C4—131no—
525C4⋊C4—261no—
526C4⋊C4—261no—
527C4⋊C4C2×C4×D1311yescharacteristic
528C4⋊C4C2×C4×D1311yescharacteristic
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—261no—
532C22⋊C4—261no—
533C22⋊C4—261no—
534C22⋊C4—261no—
535C22⋊C4—261no—
536C22⋊C4—261no—
537C42—131no—
538C42—131no—
539C42—131no—
540C42C23×D1311yescharacteristic
541C13#1792811yescharacteristic, complemented, Sylow
542C23—21no—
543C23—21no—
544C23—131no—
545C23—261no—
546C23—261no—
547C23—522no—
548C23—522no—
549C23—522no—
550Q8—522no—
551D4—21no—
552D4—21no—
553D4—21no—
554D4—21no—
555D4—261no—
556D4—261no—
557D4—261no—
558D4—261no—
559D4—522no—
560D4—522no—
561D4—522no—
562D4—522no—
563D4—522no—
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—522no—
581C2×C4—522no—
582C2×C4—522no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4C22×C4×D1311yescharacteristic
588C2×C4C2×D4×D1311yescharacteristic
589C2×C4#41×D1311yescharacteristic
590C8—21no—
591C8—21no—
592C8—21no—
593C8—41no—
594C8—41no—
595C8—41no—
596C8—132no—
597C8—261no—
598C8—261no—
599C8—261no—
600C8—521no—
601C8—521no—
602C8—521no—
603C8D8×D1312yes—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—132no—
611C22—261no—
612C22—261no—
613C22—521no—
614C22—521no—
615C22—521no—
616C22—521no—
617C22—521no—
618C22—521no—
619C22—1044no—
620C22C4×D4×D1311yescharacteristic
621C4—21no—
622C4—41no—
623C4—41no—
624C4—132no—
625C4—261no—
626C4—261no—
627C4—521no—
628C4—521no—
629C4#1171945011yescharacteristic
630C4#1171945511yescharacteristic
631C4C2×D8×D1311yescharacteristic
632C4D13×#13511yescharacteristic
633C2—81no—
634C2—81no—
635C2—262no—
636C2—1041no—
637C2—1041no—
638C2#1312353411yescharacteristic
639C2C4×D8×D1311yescharacteristic
640C2#1312373611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1581C2
socleC22×C13C2×C4×D4
prime radical#13124834C2
cosocleC42×C13C24
hypercenter#1581D13
hypocenterC13#17928
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
2. #13123543C2semidirect
3. D13×#436C2semidirect
4. #13113721C2semidirect
5. #13113720C2semidirect
6. #13113718C2semidirect
7. #13113718C2semidirect
8. #13113667C2semidirect
9. #13113665C2semidirect
10. #13113663C2semidirect
11. #13113609C2semidirect
12. #13113259C2semidirect
13. #13113233C2semidirect
14. #13113121C2semidirect
15. C13×#1581C2semidirect
22. C8×D4×C13C22semidirect
30. #11718673C22semidirect
34. #11718499C22semidirect
47. C8×D52C22semidirect
51. C13×#335C22semidirect
53. C13×D4⋊C8C22semidirect
54. C13×#322C22semidirect
56. D4⋊#1055C22semidirect
58. #11718075C22semidirect
59. #11718071C22semidirect
60. #11718071C22semidirect
62. #11718051C22semidirect
63. #11718050C22semidirect
64. #11718047C22semidirect
65. C8×#1055C22semidirect
66. C8×#1055C22semidirect
221. C8×D13D8semidirect
232. #1581D13semidirect
326. C8×D4C2×D13semidirect
337. #335C2×D13semidirect
345. D4⋊C8C2×D13semidirect
347. #322C2×D13semidirect
541. C13#17928semidirect

Maximal subgroups

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

subgroupindex
#131248342
#131235432
D13×#4362
#131137212
#131137202
#131137182
#131136672
#131136652
#131136632
#131136092
#131132592
#131132332
#131131212
C13×#15812
#1792813