Finite Group Databasebeta

← #15871169

Subgroups — #15871169

Order 3328.

712 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88152C211yesmaximal, characteristic
2#13115450C211yesmaximal, characteristic
3#13115448C211yesmaximal, characteristic
4#13115440C211yesmaximal, characteristic
5#13115399C211yesmaximal, characteristic, complemented
6#13115397C211yesmaximal, characteristic, complemented
7#13115395C211yesmaximal, characteristic, complemented
8#13114978C211yesmaximal, characteristic, complemented
9#13114710C211yesmaximal, characteristic, complemented
10#13114703C211yesmaximal, characteristic, complemented
11#13114619C211yesmaximal, characteristic
12#13114619C211yesmaximal, characteristic
13#13114619C211yesmaximal, characteristic
14C4×#88055C211yesmaximal, characteristic, complemented
15C8×C13×C4⋊C4C211yesmaximal, characteristic, complemented
16C22×#6094C2211yescharacteristic
17C2×#88152C411yescharacteristic
18C2×C13×C4⋊C8C2211yescharacteristic
19C2×C4×C8×C13C2211yescharacteristic
20C2×C4×C8×C13C2211yescharacteristic
21C2×C4×C8×C13C2211yescharacteristic
22C4×C13×C4⋊C4C2211yescharacteristic
23C2×#88060C2211yescharacteristic
24C2×#88060C2211yescharacteristic
25C2×#88060C2211yescharacteristic
26C2×#88055C2211yescharacteristic
27C2×#88055C2211yescharacteristic
28C2×#88055C2211yescharacteristic
29C2×#88055C2211yescharacteristic
30C2×#88055C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32#11718651C411yescharacteristic
33#11718642C411yescharacteristic
34#11718639C411yescharacteristic
35C4×#6103C2211yescharacteristic
36C4×#6103C2211yescharacteristic
37C4×#6103C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39C4×#6101C2211yescharacteristic
40C42×Dic13C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4×#1055C2211yescharacteristic
43#11718331C411yescharacteristic
44#11718330C411yescharacteristic
45#11718315C411yescharacteristic
46#11718312C411yescharacteristic
47C13×#336C2211yescharacteristic
48C13×#336C2211yescharacteristic
49#11718142C2211yescharacteristic
50#11718142C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×C4×D13C2311yescharacteristic
60C22×C8×C13C2311yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C2×C13×C4⋊C4C2×C411yescharacteristic
65C2×C13×C4⋊C4C2×C411yescharacteristic
66C2×C42×C13C2311yescharacteristic
67C2×C42×C13C2311yescharacteristic
68C2×C42×C13C2311yescharacteristic
69C2×#6103C2×C411yescharacteristic
70C2×#6103C2×C411yescharacteristic
71C2×#6103C2×C411yescharacteristic
72C2×#6103C2×C411yescharacteristic
73C2×#6103C2×C411yescharacteristic
74C2×#6103C2×C411yescharacteristic
75C2×C4⋊Dic13C2×C411yescharacteristic
76C2×C4⋊Dic13C2×C411yescharacteristic
77C2×#6101C2×C411yescharacteristic
78C2×#6101C2×C411yescharacteristic
79C2×C4×Dic13C2×C411yescharacteristic
80C2×C4×Dic13C2×C411yescharacteristic
81C2×C4×Dic13C2×C411yescharacteristic
82C2×C4×Dic13C2×C411yescharacteristic
83C2×C4×Dic13C2311yescharacteristic
84C2×C4×Dic13C2311yescharacteristic
85C2×C4×Dic13C2311yescharacteristic
86C22×#1055C2311yescharacteristic
87C22×#1055C2311yescharacteristic
88C22×#1055C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C2×#6094—22no—
91C2×#6094—22no—
92C2×#6094—22no—
93#88152—24no—
94C13×C4⋊C8—22no—
95C4×C8×C13—22no—
96C4×C8×C13—22no—
97C4×C8×C13—22no—
98C13×#95C2×C411yescharacteristic
99C13×#95C2×C411yescharacteristic
100#88071C2×C411yescharacteristic
101#88071C2×C411yescharacteristic
102#88071C2×C411yescharacteristic
103#88071C2×C411yescharacteristic
104#88071C2×C411yescharacteristic
105#88071C2×C411yescharacteristic
106#88071C2×C411yescharacteristic
107#88071C2×C411yescharacteristic
108#88071C2×C411yescharacteristic
109#88071C2×C411yescharacteristic
110#88060—22no—
111#88060—22no—
112#88060—22no—
113#88055—22no—
114#88055—22no—
115#88055—22no—
116#88055—22no—
117#88055—22no—
118#88054—22no—
119C4⋊#1055—22no—
120C4×#1055—22no—
121#21667—131nomaximal, Sylow
122C23×D13C22×C411yescharacteristic
123C22×C4×C13C22×C411yescharacteristic
124C22×C4×C13C22×C411yescharacteristic
125C22×C4×C13C22×C411yescharacteristic
126C22×C4×C13C22×C411yescharacteristic
127C22×C4×C13C22×C411yescharacteristic
128C22×C4×C13C22×C411yescharacteristic
129C22×C4×C13C2411yescharacteristic
130C22×Dic13C22×C411yescharacteristic
131C22×Dic13C22×C411yescharacteristic
132C22×Dic13C22×C411yescharacteristic
133C22×Dic13C22×C411yescharacteristic
134C22×Dic13C22×C411yescharacteristic
135C22×Dic13C22×C411yescharacteristic
136C22×Dic13C22×C411yescharacteristic
137C2×C4×D13—21no—
138C2×C4×D13—21no—
139C2×C4×D13—21no—
140C2×C4×D13—21no—
141C2×C4×D13—21no—
142C2×C4×D13—21no—
143C2×C8×C13—21no—
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13#4112yes—
152C2×C8×C13#4112yes—
153C2×C8×C13#4112yes—
154C2×C8×C13#4112yes—
155C13×C4⋊C4—22no—
156C13×C4⋊C4M1614yescomplemented
157C42×C13—21no—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13—21no—
161C42×C13—21no—
162C42×C13—21no—
163#6103—22no—
164#6103—22no—
165#6103—22no—
166#6103—22no—
167#6103—41no—
168#6103—41no—
169C4⋊Dic13—22no—
170C4⋊Dic13—41no—
171#6101—22no—
172#6101—41no—
173C4×Dic13—22no—
174C4×Dic13—22no—
175C4×Dic13—21no—
176C4×Dic13—21no—
177C4×Dic13—21no—
178C4×Dic13—21no—
179C4×Dic13—21no—
180C4×Dic13—21no—
181C4×Dic13—41no—
182C4×Dic13—41no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055#4112yes—
194C2×#1055#4112yes—
195#6094—44no—
196C4×#126—131no—
197#1924—131no—
198#1924—131no—
199#1923—131no—
200#1917—131no—
201#1917—131no—
202#1916—131no—
203#1839—131no—
204#1771—131no—
205#1770—131no—
206C8×C4⋊C4D1311yescharacteristic, complemented
207#1753—131no—
208#1753—131no—
209#1753—131no—
210C4×#97—131no—
211C23×C13C23×C411yescharacteristic
212C22×D13—21no—
213C22×D13—21no—
214C22×D13—21no—
215C22×D13—21no—
216C22×D13—21no—
217C22×D13—21no—
218C22×D13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13C2×M1612yes—
234C2×C4×C13C2×M1612yes—
235C2×C4×C13C2×M1612yes—
236C2×C4×C13#13112yes—
237C2×C4×C13C2×#4111yescharacteristic
238C2×C4×C13C2×#4111yescharacteristic
239C2×C4×C13C2×#4111yescharacteristic
240C2×C4×C13C2×#4111yescharacteristic
241C2×C4×C13C2×#4111yescharacteristic
242C2×C4×C13C2×#4111yescharacteristic
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C4×D13—41no—
265C4×D13—41no—
266C4×D13—41no—
267C4×D13—41no—
268C8×C13—22no—
269C8×C13—41no—
270C8×C13—41no—
271C8×C13#12614yescomplemented
272#1055—22no—
273#1055—22no—
274#1055—41no—
275#1055—41no—
276C22×M16—131no—
277C2×#126—131no—
278C2×C4⋊C8—131no—
279C2×C4⋊C8—131no—
280C2×C4⋊C8C2×D1311yescharacteristic
281C2×C22⋊C8—131no—
282C2×C22⋊C8—131no—
283C2×C22⋊C8—131no—
284C2×#97—131no—
285C2×#97—131no—
286C2×#97—131no—
287C2×#97—131no—
288C2×#97—131no—
289C2×C4×C8—131no—
290C2×C4×C8C2×D1311yescharacteristic
291C2×C4×C8C2×D1311yescharacteristic
292C2×C4×C8C2×D1311yescharacteristic
293#388—131no—
294#388—131no—
295#388—131no—
296#387—131no—
297#387—131no—
298#387—131no—
299#383—131no—
300C4×C4⋊C4—131no—
301C4×C4⋊C4—131no—
302C4×C4⋊C4C2×D1311yescharacteristic
303C4×C22⋊C4—131no—
304C4×C22⋊C4—131no—
305C4×C22⋊C4—131no—
306C43—131no—
307#336—131no—
308#336—131no—
309#336—131no—
310#336—131no—
311#336—131no—
312#336—131no—
313#336—131no—
314#336—131no—
315#336—131no—
316#336—131no—
317#336C2×D1311yescharacteristic
318#336C2×D1311yescharacteristic
319C22×C13C4×#4111yescharacteristic
320C22×C13C4×#4111yescharacteristic
321C22×C13C4×#4111yescharacteristic
322C22×C13C22×M1611yescharacteristic
323C22×C13C2×#13111yescharacteristic
324C22×C13#56811yescharacteristic
325C22×C13#56811yescharacteristic
326C2×D13—41no—
327C2×D13—41no—
328C2×D13—41no—
329C2×D13—41no—
330C2×D13—41no—
331C2×D13—41no—
332C2×D13—41no—
333C4×C13—22no—
334C4×C13—22no—
335C4×C13—22no—
336C4×C13—22no—
337C4×C13—41no—
338C4×C13—41no—
339C4×C13C2×#12611yescharacteristic
340C4×C13#52911yescharacteristic
341C4×C13#52911yescharacteristic
342C4×C13#52911yescharacteristic
343Dic13—41no—
344Dic13—41no—
345Dic13—41no—
346Dic13—41no—
347Dic13—41no—
348Dic13—41no—
349Dic13—41no—
350C23×C4—131no—
351C2×M16—262no—
352C2×M16—262no—
353C2×M16—262no—
354C22×C8—131no—
355C22×C8—131no—
356C22×C8—131no—
357C22×C8—131no—
358C22×C8C22×D1311yescharacteristic
359C22×C8C22×D1311yescharacteristic
360C22×C8C22×D1311yescharacteristic
361C22×C8C22×D1311yescharacteristic
362#126—264no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4C4×D1311yescharacteristic
368C2×C4⋊C4C4×D1311yescharacteristic
369C2×C22⋊C4—131no—
370C2×C22⋊C4—131no—
371C2×C22⋊C4—131no—
372C2×C22⋊C4—131no—
373C2×C22⋊C4—131no—
374C2×C22⋊C4—131no—
375C2×C42—131no—
376C2×C42—131no—
377C2×C42—131no—
378C2×C42—131no—
379C2×C42—131no—
380C2×C42—131no—
381C2×C42—131no—
382C2×C42C22×D1311yescharacteristic
383C2×C42C22×D1311yescharacteristic
384C2×C42C22×D1311yescharacteristic
385C4⋊C8—22no—
386C4⋊C8—262no—
387C4⋊C8—262no—
388C22⋊C8—262no—
389C22⋊C8—262no—
390C22⋊C8—262no—
391#97—262no—
392#97—262no—
393#97—262no—
394#97—262no—
395#97—262no—
396C4×C8—22no—
397C4×C8—22no—
398C4×C8—22no—
399C4×C8—262no—
400#95—131no—
401#95—131no—
402#95—131no—
403#95—131no—
404#95—131no—
405#95—131no—
406#95—131no—
407#95—131no—
408#95—131no—
409#95—131no—
410#95C4×D1311yescharacteristic
411#95C4×D1311yescharacteristic
412C2×C13C4×#12611yescharacteristic
413C2×C13#296511yescharacteristic
414C2×C13#296711yescharacteristic
415C2×C13#296811yescharacteristic
416C2×C13#296911yescharacteristic
417C2×C13#297011yescharacteristic
418C2×C13#297111yescharacteristic
419D13—81no—
420C24—131no—
421C22×C4—131no—
422C22×C4—131no—
423C22×C4—131no—
424C22×C4—131no—
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—131no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—261no—
431C22×C4—261no—
432C22×C4—261no—
433C22×C4—261no—
434C22×C4C2×C4×D1311yescharacteristic
435C22×C4C2×C4×D1311yescharacteristic
436C22×C4C2×C4×D1311yescharacteristic
437C22×C4C2×C4×D1311yescharacteristic
438C22×C4C2×C4×D1311yescharacteristic
439C22×C4C2×C4×D1311yescharacteristic
440C22×C4C23×D1311yescharacteristic
441M16—524no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—132no—
451C2×C8—132no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8#612712yes—
463C2×C8#612712yes—
464C2×C8#612912yes—
465C2×C8#613112yes—
466C4⋊C4—22no—
467C4⋊C4—262no—
468C4⋊C4—262no—
469C4⋊C4—521no—
470C4⋊C4—521no—
471C4⋊C4#609414yescomplemented
472C22⋊C4—262no—
473C22⋊C4—262no—
474C22⋊C4—262no—
475C22⋊C4—262no—
476C22⋊C4—521no—
477C22⋊C4—521no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—262no—
485C42—262no—
486C42—261no—
487C42—261no—
488C42—261no—
489C42—261no—
490C42—261no—
491C42—261no—
492C42—521no—
493C42—521no—
494C13#2166711yescharacteristic, complemented, Sylow
495C23—261no—
496C23—261no—
497C23—261no—
498C23—261no—
499C23—261no—
500C23—261no—
501C23—261no—
502C23C22×C4×D1311yescharacteristic
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—261no—
518C2×C4—261no—
519C2×C4—261no—
520C2×C4—261no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4C2×#609412yes—
543C2×C4C2×#609412yes—
544C2×C4C2×#609412yes—
545C2×C4#8815512yes—
546C2×C4C2×#612711yescharacteristic
547C2×C4C2×#612711yescharacteristic
548C2×C4C2×#612911yescharacteristic
549C2×C4C2×#613111yescharacteristic
550C2×C4#41×D1311yescharacteristic
551C2×C4#41×D1311yescharacteristic
552C8—22no—
553C8—41no—
554C8—41no—
555C8—262no—
556C8—262no—
557C8—521no—
558C8—521no—
559C8#8815214yescomplemented
560C22—521no—
561C22—521no—
562C22—521no—
563C22—521no—
564C22—521no—
565C22—521no—
566C22—521no—
567C22C4×#612711yescharacteristic
568C22C4×#612911yescharacteristic
569C22C4×#613111yescharacteristic
570C22C22×#609411yescharacteristic
571C22C2×#8815511yescharacteristic
572C22#1171945511yescharacteristic
573C22#1171945511yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—22no—
578C4—41no—
579C4—41no—
580C4—521no—
581C4—521no—
582C4—521no—
583C4—521no—
584C4—521no—
585C4—521no—
586C4—521no—
587C4C2×#8815211yescharacteristic
588C4#1171923311yescharacteristic
589C4#1171924311yescharacteristic
590C4#1171928511yescharacteristic
591C2—1041no—
592C2C4×#8815211yescharacteristic
593C2#1312380211yescharacteristic
594C2#1312381711yescharacteristic
595C2#1312382411yescharacteristic
596C2#1312383911yescharacteristic
597C2#1312384411yescharacteristic
598C2#1312385511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC8×C13×C4⋊C4C2
prime radicalC23×D13C22×C4
cosocleC22×C4×C13C24
hypercenterC8×C4⋊C4D13
hypocenterC13#21667
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. #13115399C2semidirect
6. #13115397C2semidirect
7. #13115395C2semidirect
8. #13114978C2semidirect
9. #13114710C2semidirect
10. #13114703C2semidirect
14. C4×#88055C2semidirect
15. C8×C13×C4⋊C4C2semidirect
156. C13×C4⋊C4M16semidirect
206. C8×C4⋊C4D13semidirect
271. C8×C13#126semidirect
471. C4⋊C4#6094semidirect
494. C13#21667semidirect
559. C8#88152semidirect

Maximal subgroups

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

subgroupindex
C4×#881522
#131154502
#131154482
#131154402
#131153992
#131153972
#131153952
#131149782
#131147102
#131147032
#131146192
C4×#880552
C8×C13×C4⋊C42
#2166713