Finite Group Databasebeta

← #15833175

Subgroups — #15833175

Order 3328.

726 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#13113750C211yesmaximal, characteristic, complemented
5#13113749C211yesmaximal, characteristic, complemented
6#13113747C211yesmaximal, characteristic, complemented
7#13113747C211yesmaximal, characteristic, complemented
8#13113702C211yesmaximal, characteristic, complemented
9#13113700C211yesmaximal, characteristic, complemented
10#13113698C211yesmaximal, characteristic, complemented
11#13113605C211yesmaximal, characteristic, complemented
12#13113259C211yesmaximal, characteristic, complemented
13#13113233C211yesmaximal, characteristic, complemented
14#13113127C211yesmaximal, characteristic, complemented
15C13×#1586C211yesmaximal, 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×#334C2211yescharacteristic, complemented
52C13×D4⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic, complemented
54C13×#322C2211yescharacteristic, complemented
55D4⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic, complemented
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic, complemented
59#11718072C2211yescharacteristic, complemented
60#11718072C2211yescharacteristic, complemented
61#11718051C2211yescharacteristic
62#11718051C2211yescharacteristic, complemented
63#11718049C2211yescharacteristic, complemented
64#11718047C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66#11718046C2211yescharacteristic, 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#17935—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—22no—
220C8×D13—42no—
221C8×D13—42no—
222#3100—131no—
223#2931—131no—
224C2×#436—131no—
225#1594—131no—
226#1594—131no—
227#1594—131no—
228#1594—131no—
229#1586—131no—
230#1586—131no—
231#1586—131no—
232#1586D1311yescharacteristic, complemented
233#1570—131no—
234#1486—131no—
235#1480—131no—
236#1452—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×D13AGL(1,ℤ/8)12yes—
283C4×D13AGL(1,ℤ/8)12yes—
284Dic26—42no—
285C8×C13—21no—
286C8×C13—21no—
287C8×C13—21no—
288C8×C13—21no—
289C8×C13—41no—
290C8×C13—41no—
291C8×C13—41no—
292#1055—21no—
293#1055—21no—
294#1055—21no—
295#1055—21no—
296#1055—41no—
297#1055—41no—
298#1055—41no—
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#334—131no—
335#334—131no—
336#334—131no—
337#334C2×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#322—131no—
348#322—131no—
349#322C2×D1311yescharacteristic, complemented
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×D13#44212yes—
367C4×C13—21no—
368C4×C13—41no—
369C4×C13—41no—
370C4×C13#56811yescharacteristic
371C4×C13#56811yescharacteristic
372C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
373C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
374Dic13—21no—
375Dic13—21no—
376Dic13—41no—
377Dic13—41no—
378Dic13#44212yes—
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×#44211yescharacteristic
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—131no—
510C2×C8—131no—
511C2×C8—131no—
512C2×C8—262no—
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#1793511yescharacteristic, 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—21no—
594C8—41no—
595C8—41no—
596C8—41no—
597C8—261no—
598C8—261no—
599C8—261no—
600C8—261no—
601C8—521no—
602C8—521no—
603C8—521no—
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
631C4D13×AGL(1,ℤ/8)11yescharacteristic
632C4D13×AGL(1,ℤ/8)11yescharacteristic
633C2—81no—
634C2—81no—
635C2—262no—
636C2—1041no—
637C2—1041no—
638C2#1312353411yescharacteristic
639C2D13×#44211yescharacteristic
640C2#1312373411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1586C2
socleC22×C13C2×C4×D4
prime radical#13124834C2
cosocleC42×C13C24
hypercenter#1586D13
hypocenterC13#17935
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
2. #13123543C2semidirect
3. D13×#436C2semidirect
4. #13113750C2semidirect
5. #13113749C2semidirect
6. #13113747C2semidirect
7. #13113747C2semidirect
8. #13113702C2semidirect
9. #13113700C2semidirect
10. #13113698C2semidirect
11. #13113605C2semidirect
12. #13113259C2semidirect
13. #13113233C2semidirect
14. #13113127C2semidirect
15. C13×#1586C2semidirect
22. C8×D4×C13C22semidirect
30. #11718673C22semidirect
34. #11718499C22semidirect
47. C8×D52C22semidirect
51. C13×#334C22semidirect
53. C13×D4⋊C8C22semidirect
54. C13×#322C22semidirect
56. D4⋊#1055C22semidirect
58. #11718075C22semidirect
59. #11718072C22semidirect
60. #11718072C22semidirect
62. #11718051C22semidirect
63. #11718049C22semidirect
64. #11718047C22semidirect
65. #11718046C22semidirect
66. #11718046C22semidirect
232. #1586D13semidirect
326. C8×D4C2×D13semidirect
337. #334C2×D13semidirect
345. D4⋊C8C2×D13semidirect
349. #322C2×D13semidirect
541. C13#17935semidirect

Maximal subgroups

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

subgroupindex
#131248342
#131235432
D13×#4362
#131137502
#131137492
#131137472
#131137022
#131137002
#131136982
#131136052
#131132592
#131132332
#131131272
C13×#15862
#1793513