Finite Group Databasebeta

← #15834805

Subgroups — #15834805

Order 3328.

656 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123841C211yesmaximal, characteristic, complemented
2#13123580C211yesmaximal, characteristic, complemented
3#13113739C211yesmaximal, characteristic, complemented
4#13113721C211yesmaximal, characteristic, complemented
5#13113701C211yesmaximal, characteristic, complemented
6#13113694C211yesmaximal, characteristic, complemented
7#13113680C211yesmaximal, characteristic, complemented
8#13113666C211yesmaximal, characteristic, complemented
9#13113660C211yesmaximal, characteristic, complemented
10SD16×#1055C211yesmaximal, characteristic, complemented
11#13113588C211yesmaximal, characteristic, complemented
12#13113253C211yesmaximal, characteristic, complemented
13#13113249C211yesmaximal, characteristic, complemented
14#13113139C211yesmaximal, characteristic, complemented
15C13×#3171C211yesmaximal, characteristic
16C13×#532C2211yescharacteristic
17C13×#529C2211yescharacteristic
18C2×#88202—21no—
19C13×#501C411yescharacteristic
20C13×#496C411yescharacteristic
21C13×#490C411yescharacteristic
22C13×#489C411yescharacteristic
23C13×#469C411yescharacteristic
24C13×#469C411yescharacteristic
25C13×#468C411yescharacteristic
26C13×#468C411yescharacteristic
27C4×C13×SD16C2211yescharacteristic
28C4×C13×SD16C2211yescharacteristic
29C4×C13×D8C2211yescharacteristic
30C4×C13×D8C2211yescharacteristic
31C4×C13×M16C2211yescharacteristic
32#11718895—21no—
33#11718685C2211yescharacteristic
34Q8×#1055C2211yescharacteristic
35#11718673—21no—
36#11718673C2211yescharacteristic
37#11718673C2211yescharacteristic
38#11718673C2211yescharacteristic
39#11718672—21no—
40#11718672—21no—
41#11718672—21no—
42D4×#1055C2211yescharacteristic
43D4×#1055C2211yescharacteristic
44D4×#1055C2211yescharacteristic
45#11718661—21no—
46#11718658—21no—
47#11718586C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C4×#6099C2211yescharacteristic
50C4×#6099C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55D4⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57D4⋊#1055C2211yescharacteristic
58D4⋊#1055C2211yescharacteristic
59#11718050C2211yescharacteristic
60#11718050C2211yescharacteristic
61#11718049C2211yescharacteristic
62#11718049C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41—21no—
68C2×C13×SD16C2×C411yescharacteristic
69C2×C13×SD16C2×C411yescharacteristic
70C2×C13×D8C2×C411yescharacteristic
71C2×C13×D8C2×C411yescharacteristic
72C2×C13×M16C2×C411yescharacteristic
73C2×C13×M16C2×C411yescharacteristic
74C13×C4⋊Q8C2×C411yescharacteristic
75C13×#127C2×C411yescharacteristic
76C13×#126—21no—
77C13×#125C2×C411yescharacteristic
78C13×#124—21no—
79C13×#124C2×C411yescharacteristic
80C13×#123—21no—
81C13×C22⋊Q8C2×C411yescharacteristic
82C13×#121—21no—
83C13×#121C2×C411yescharacteristic
84C13×#121C2×C411yescharacteristic
85C13×#121C2×C411yescharacteristic
86C4×Q8×C13C2311yescharacteristic
87C4×D4×C13—21no—
88C4×D4×C13—21no—
89C4×D4×C13C2311yescharacteristic
90C4×D4×C13C2311yescharacteristic
91C4×D4×C13C2311yescharacteristic
92C13×#117—21no—
93C2×C42×C13C2311yescharacteristic
94#88202—44no—
95C2×#6099—21no—
96C2×#6099—21no—
97C2×#6099—21no—
98C2×#6099—21no—
99C2×#6099D411yescharacteristic
100C2×#6099D411yescharacteristic
101C22×#1055—21no—
102C22×#1055—21no—
103C22×#1055—21no—
104C22×#1055—21no—
105C13×#107C2×C411yescharacteristic
106C13×#107C2×C411yescharacteristic
107C13×#106C2×C411yescharacteristic
108C13×#106C2×C411yescharacteristic
109C13×#103C2×C411yescharacteristic
110C13×#103C2×C411yescharacteristic
111C13×#102C2×C411yescharacteristic
112C13×#102C2×C411yescharacteristic
113C13×#102C2×C411yescharacteristic
114C13×#102C2×C411yescharacteristic
115C13×#102C2×C411yescharacteristic
116C13×#102C2×C411yescharacteristic
117C13×#97C2×C411yescharacteristic
118C13×#97C2×C411yescharacteristic
119C4×C8×C13C2311yescharacteristic
120C4×C8×C13C2311yescharacteristic
121C22⋊#1055—21no—
122C22⋊#1055—21no—
123C22⋊#1055—21no—
124C22⋊#1055—21no—
125C22⋊#1055—21no—
126C22⋊#1055—21no—
127C22⋊#1055—21no—
128C4⋊#1055—21no—
129C4⋊#1055—21no—
130C4⋊#1055—21no—
131C4⋊#1055C2311yescharacteristic
132C4⋊#1055C2311yescharacteristic
133C4⋊#1055C2311yescharacteristic
134C4⋊#1055C2311yescharacteristic
135#88043—21no—
136#88043—21no—
137#88043D411yescharacteristic
138#88043D411yescharacteristic
139C4×#1055—21no—
140C4×#1055—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#18078—131nomaximal, Sylow
146C13×#41—42no—
147C13×#41—42no—
148C2×Q8×C13—21no—
149C2×Q8×C13C22×C411yescharacteristic
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—21no—
154C2×D4×C13—21no—
155C2×D4×C13C22×C411yescharacteristic
156C2×D4×C13C22×C411yescharacteristic
157C2×D4×C13C22×C411yescharacteristic
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13C22×C411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13#4111yescharacteristic
164C13×SD16—22no—
165C13×SD16—41no—
166C13×D8—22no—
167C13×D8—41no—
168C13×M16—22no—
169C13×M16—41no—
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C22×C411yescharacteristic
172C2×C8×C13C22×C411yescharacteristic
173C2×C8×C13C22×C411yescharacteristic
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4C22×C411yescharacteristic
180C13×C4⋊C4C22×C411yescharacteristic
181C13×C4⋊C4C22×C411yescharacteristic
182C13×C4⋊C4C22×C411yescharacteristic
183C13×C22⋊C4—21no—
184C13×C22⋊C4—21no—
185C13×C22⋊C4—21no—
186C13×C22⋊C4—21no—
187C13×C22⋊C4—21no—
188C13×C22⋊C4—21no—
189C13×C22⋊C4—21no—
190C13×C22⋊C4—21no—
191C13×C22⋊C4—21no—
192C42×C13—21no—
193C42×C13C22×C411yescharacteristic
194C42×C13C2×D411yescharacteristic
195C42×C13#4111yescharacteristic
196C42×C13C2411yescharacteristic
197#6099—22no—
198#6099—41no—
199#6099—42no—
200#6099—42no—
201#6099—42no—
202#6099—42no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—42no—
210C2×#1055—42no—
211C2×#1055—42no—
212C2×#1055—42no—
213C2×#1055C2×D411yescharacteristic
214C2×#1055C2×D411yescharacteristic
215C2×#1055C2×D411yescharacteristic
216C2×#1055C2×D411yescharacteristic
217#3171D1311yescharacteristic
218#2969—131no—
219#2935—131no—
220#1592—131no—
221#1589—131no—
222#1586—131no—
223#1585—131no—
224#1583—131no—
225#1581—131no—
226#1580—131no—
227C8×SD16—131no—
228#1565—131no—
229#1484—131no—
230#1483—131no—
231#1455—131no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13C4×D411yescharacteristic
236Q8×C13—21no—
237Q8×C13—21no—
238Q8×C13—42no—
239D4×C13—21no—
240D4×C13—21no—
241D4×C13—21no—
242D4×C13—21no—
243D4×C13—21no—
244D4×C13—21no—
245D4×C13—42no—
246D4×C13—42no—
247D4×C13—42no—
248D4×C13—81no—
249D4×C13—81no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13C4×D411yescharacteristic
267C2×C4×C13C4×D411yescharacteristic
268C2×C4×C13C4×D411yescharacteristic
269C2×C4×C13C23×C411yescharacteristic
270C2×C4×C13C22×D411yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C8×C13—21no—
273C8×C13—21no—
274C8×C13—21no—
275C8×C13#13112yescomplemented
276#1055—22no—
277#1055—21no—
278#1055—21no—
279#1055—21no—
280#1055—41no—
281#1055—41no—
282#1055—41no—
283#1055—41no—
284#1055—41no—
285#1055AGL(1,ℤ/8)12yes—
286C2×#131—261no—
287#532C2×D1311yescharacteristic
288#529C2×D1311yescharacteristic
289#501Dic1311yescharacteristic
290#496Dic1311yescharacteristic
291#490Dic1311yescharacteristic
292#489Dic1311yescharacteristic
293#469Dic1311yescharacteristic
294#469Dic1311yescharacteristic
295#468Dic1311yescharacteristic
296#468Dic1311yescharacteristic
297#446—131no—
298C8×Q8—131no—
299C4×SD16C2×D1311yescharacteristic
300C4×SD16C2×D1311yescharacteristic
301C4×D8C2×D1311yescharacteristic
302C4×D8C2×D1311yescharacteristic
303#436—131no—
304#436—131no—
305#436—131no—
306#436—261no—
307#435—261no—
308#435—261no—
309#435—261no—
310C8×D4—131no—
311C8×D4—131no—
312C8×D4—131no—
313#433—261no—
314#431—131no—
315C2×C4⋊C8—131no—
316#408—261no—
317#405—261no—
318C4×M16—131no—
319C4×M16—131no—
320C4×M16C2×D1311yescharacteristic
321#335—131no—
322#335—131no—
323#334—131no—
324#334—131no—
325Q8⋊C8—131no—
326Q8⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331D4⋊C8—131no—
332D4⋊C8—131no—
333#322—131no—
334#322—131no—
335#322—131no—
336C82—131no—
337C22×C13—21no—
338C22×C13—21no—
339C22×C13—21no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13—41no—
346C22×C13—41no—
347C22×C13—41no—
348C22×C13—41no—
349C22×C13C2×C4×D411yescharacteristic
350C4×C13—21no—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—21no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13—41no—
357C4×C13—41no—
358C4×C13—41no—
359C4×C13C2×#13111yescharacteristic
360C4×C13#56811yescharacteristic
361C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
362C4×C13#57511yescharacteristic
363C2×#41—21no—
364C2×SD16C2×Dic1311yescharacteristic
365C2×SD16C2×Dic1311yescharacteristic
366C2×D8C2×Dic1311yescharacteristic
367C2×D8C2×Dic1311yescharacteristic
368#131—524no—
369C2×M16—131no—
370C2×M16—131no—
371C2×M16—261no—
372C2×M16—261no—
373C2×M16—261no—
374C2×M16—261no—
375C2×M16C2×Dic1311yescharacteristic
376C2×M16C2×Dic1311yescharacteristic
377C22×C8—261no—
378C22×C8—261no—
379C22×C8—261no—
380C22×C8—261no—
381C4⋊Q8C2×Dic1311yescharacteristic
382#127C2×Dic1311yescharacteristic
383#126—21no—
384#125C2×Dic1311yescharacteristic
385#124—21no—
386#124C2×Dic1311yescharacteristic
387#123—21no—
388C22⋊Q8C2×Dic1311yescharacteristic
389#121—21no—
390#121C2×Dic1311yescharacteristic
391#121C2×Dic1311yescharacteristic
392#121C2×Dic1311yescharacteristic
393C4×Q8C22×D1311yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C22×D1311yescharacteristic
397C4×D4C22×D1311yescharacteristic
398C4×D4C22×D1311yescharacteristic
399#117—21no—
400C2×C42C22×D1311yescharacteristic
401#107C2×Dic1311yescharacteristic
402#107C2×Dic1311yescharacteristic
403#106C2×Dic1311yescharacteristic
404#106C2×Dic1311yescharacteristic
405C4⋊C8—131no—
406C4⋊C8—131no—
407C4⋊C8—131no—
408C4⋊C8—131no—
409C4⋊C8—261no—
410C4⋊C8—261no—
411C4⋊C8—261no—
412#103C2×Dic1311yescharacteristic
413#103C2×Dic1311yescharacteristic
414#102C2×Dic1311yescharacteristic
415#102C2×Dic1311yescharacteristic
416#102C2×Dic1311yescharacteristic
417#102C2×Dic1311yescharacteristic
418#102C2×Dic1311yescharacteristic
419#102C2×Dic1311yescharacteristic
420C22⋊C8—261no—
421C22⋊C8—261no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427#97—131no—
428#97—131no—
429#97—261no—
430#97—261no—
431#97C2×Dic1311yescharacteristic
432#97C2×Dic1311yescharacteristic
433C4×C8—131no—
434C4×C8—131no—
435C4×C8—131no—
436C4×C8—131no—
437C4×C8—261no—
438C4×C8—261no—
439C4×C8C22×D1311yescharacteristic
440C4×C8C22×D1311yescharacteristic
441C2×C13—41no—
442C2×C13—81no—
443C2×C13—81no—
444C2×C13—81no—
445C2×C13#293511yescharacteristic
446C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
447C2×C13#295611yescharacteristic
448#41—42no—
449#41—42no—
450C2×Q8—21no—
451C2×Q8C22×Dic1311yescharacteristic
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4C22×Dic1311yescharacteristic
458C2×D4C22×Dic1311yescharacteristic
459C2×D4C22×Dic1311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4D4×D1311yescharacteristic
464C22×C4#612911yescharacteristic
465C22×C4C22×Dic1311yescharacteristic
466SD16—22no—
467SD16—41no—
468D8—22no—
469D8—41no—
470M16—22no—
471M16—41no—
472M16—262no—
473M16—522no—
474M16—522no—
475M16—521no—
476M16—522no—
477M16—522no—
478C2×C8—131no—
479C2×C8—131no—
480C2×C8—131no—
481C2×C8—131no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—522no—
489C2×C8—522no—
490C2×C8—522no—
491C2×C8—522no—
492C2×C8C22×Dic1311yescharacteristic
493C2×C8C22×Dic1311yescharacteristic
494C2×C8C22×Dic1311yescharacteristic
495C2×C8C22×Dic1311yescharacteristic
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4C22×Dic1311yescharacteristic
502C4⋊C4C22×Dic1311yescharacteristic
503C4⋊C4C22×Dic1311yescharacteristic
504C4⋊C4C22×Dic1311yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C42—21no—
515C42D4×D1311yescharacteristic
516C42#612911yescharacteristic
517C42C22×Dic1311yescharacteristic
518C42C23×D1311yescharacteristic
519C13#1807811yescharacteristic, complemented, Sylow
520C23—21no—
521C23—21no—
522C23—21no—
523C23D4×Dic1311yescharacteristic
524Q8—21no—
525Q8—21no—
526Q8—42no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—42no—
535D4—42no—
536D4—81no—
537D4—81no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4D4×Dic1311yescharacteristic
555C2×C4D4×Dic1311yescharacteristic
556C2×C4D4×Dic1311yescharacteristic
557C2×C4C2×D4×D1311yescharacteristic
558C2×C4C2×#612911yescharacteristic
559C2×C4C23×Dic1311yescharacteristic
560C8—21no—
561C8—21no—
562C8—21no—
563C8—132no—
564C8—262no—
565C8—261no—
566C8—261no—
567C8—261no—
568C8—521no—
569C8—521no—
570C8—521no—
571C8—521no—
572C8—521no—
573C8#8820212yescomplemented
574C22—21no—
575C22—21no—
576C22—21no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22C2×D4×Dic1311yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4D13×AGL(1,ℤ/8)11yescharacteristic
597C4#1171947811yescharacteristic
598C4C2×#8820211yescharacteristic
599C4#1171952411yescharacteristic
600C2—41no—
601C2—81no—
602C2—81no—
603C2—81no—
604C2#1312358011yescharacteristic
605C2AGL(1,ℤ/8)×Dic1311yescharacteristic
606C2#1312374611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
Fitting, prime radicalC13×#3171C2
socleC22×C13C2×C4×D4
cosocleC42×C13C24
hypercenter#3171D13
hypocenterC13#18078
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3171

Complements

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

NH ≅ G/Ntype
1. #13123841C2semidirect
2. #13123580C2semidirect
3. #13113739C2semidirect
4. #13113721C2semidirect
5. #13113701C2semidirect
6. #13113694C2semidirect
7. #13113680C2semidirect
8. #13113666C2semidirect
9. #13113660C2semidirect
10. SD16×#1055C2semidirect
11. #13113588C2semidirect
12. #13113253C2semidirect
13. #13113249C2semidirect
14. #13113139C2semidirect
275. C8×C13#131semidirect
519. C13#18078semidirect
573. C8#88202semidirect

Maximal subgroups

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

subgroupindex
#131238412
#131235802
#131137392
#131137212
#131137012
#131136942
#131136802
#131136662
#131136602
SD16×#10552
#131135882
#131132532
#131132492
#131131392
C13×#31712
#1807813