Finite Group Databasebeta

← #15840358

Subgroups — #15840358

Order 3328.

1126 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125758C211yesmaximal, characteristic, complemented
2C2×#11718740C211yesmaximal, characteristic, complemented
3#13124651C211yesmaximal, characteristic, complemented
4#13114120C214yesmaximal, complemented
5#13114099C214yesmaximal, complemented
6#13113508C211yesmaximal, characteristic, complemented
7#13113287C211yesmaximal, characteristic, complemented
8#13113218C211yesmaximal, characteristic, complemented
9C13×#3499C211yesmaximal, characteristic
10C2×C13×2−1+4—21no—
11D4×Q8×C13—21no—
12D4×Q8×C13C2212yes—
13C13×#547—22no—
14C13×#547—21no—
15C13×#547—22no—
16C13×#547C2212yes—
17C13×#536—22no—
18C13×#536—21no—
19C13×#532—21no—
20C13×#532C2211yescharacteristic
21C2×C13×C4⋊Q8—21no—
22C2×C13×C4⋊Q8C2211yescharacteristic
23C4×C13×#41C2211yescharacteristic
24C2×#88123C2211yescharacteristic
25#11718893—21no—
26#11718754—21no—
27#11718740—22no—
28#11718740C2214yes—
29#11718737—21no—
30#11718701—22no—
31#11718682—21no—
32#11718681C2212yes—
33#11718680C2214yes—
34#11718669—21no—
35#11718668C2212yes—
36#11718656—21no—
37C2×#88048—22no—
38#11718586C2211yescharacteristic
39#11718585C2211yescharacteristic
40C2×C4×#1055C2211yescharacteristic
41#11718139C2214yes—
42Q8⋊#1055C2212yes—
43D4⋊#1055C2212yes—
44D4⋊#1055C2214yes—
45C13×2−1+4—44no—
46C13×2−1+4—44no—
47C2×C13×#41—22no—
48C2×C13×#41—24no—
49C2×C13×#41—22no—
50C2×C13×#41—21no—
51C2×C13×#41D411yescharacteristic
52C22×Q8×C13—22no—
53C22×Q8×C13—22no—
54C22×Q8×C13—21no—
55C22×Dic26—21no—
56C13×C4⋊Q8—22no—
57C13×C4⋊Q8—22no—
58C13×C4⋊Q8—22no—
59C13×C4⋊Q8—21no—
60C13×C4⋊Q8—21no—
61C13×C4⋊Q8D412yes—
62C13×C4⋊Q8D411yescharacteristic
63C13×C4⋊Q8C2312yes—
64C13×#127D411yescharacteristic
65C13×#124—22no—
66C13×#124—21no—
67C13×#123—24no—
68C13×#123—24no—
69C13×#123—24no—
70C13×C22⋊Q8—24no—
71C13×C22⋊Q8—22no—
72C13×C22⋊Q8—24no—
73C13×C22⋊Q8—22no—
74C13×#121—22no—
75C13×#121—22no—
76C13×#121—21no—
77C13×#121D412yes—
78C4×Q8×C13D411yescharacteristic
79C4×Q8×C13C2311yescharacteristic
80C4×D4×C13—22no—
81C4×D4×C13—22no—
82C4×D4×C13—21no—
83C4×D4×C13—21no—
84C4×D4×C13—21no—
85C4×D4×C13D411yescharacteristic
86C4×D4×C13C2311yescharacteristic
87C4×D4×C13C2312yes—
88C13×#117—21no—
89C13×#117D411yescharacteristic
90C2×C13×C4⋊C4—22no—
91C2×C13×C4⋊C4—21no—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4D412yes—
94C2×C42×C13—21no—
95C2×C42×C13C2311yescharacteristic
96C2×#6105—24no—
97C2×C4⋊Dic13—21no—
98C2×C4⋊Dic13—21no—
99C2×#6099—21no—
100C22×#1055—21no—
101#88123—21no—
102#88123—21no—
103#88123—21no—
104#88123C2312yes—
105#88075—22no—
106#88072—22no—
107C22⋊#1055—21no—
108#88050—24no—
109#88048—22no—
110#88048—28no—
111#88047—22no—
112C4⋊#1055—21no—
113C4⋊#1055C2312yes—
114C4⋊#1055C2312yes—
115C4×#1055—21no—
116C4×#1055—21no—
117C4×#1055C2312yes—
118#18651—131nomaximal, Sylow
119C13×#41—22no—
120C13×#41—48no—
121C13×#41—416no—
122C13×#41—44no—
123C13×#41—44no—
124C13×#41—42no—
125C13×#41—42no—
126C13×#41SD1614yescomplemented
127C2×Q8×C13—24no—
128C2×Q8×C13—22no—
129C2×Q8×C13—21no—
130C2×Q8×C13—22no—
131C2×Q8×C13—48no—
132C2×Q8×C13—44no—
133C2×Q8×C13—44no—
134C2×Q8×C13—42no—
135C2×Q8×C13—42no—
136C2×Q8×C13C2×D411yescharacteristic
137C2×D4×C13—21no—
138C2×D4×C13—24no—
139C2×D4×C13—22no—
140C2×D4×C13—21no—
141C2×D4×C13—21no—
142C2×D4×C13C2×D412yes—
143C2×D4×C13C2×D411yescharacteristic
144C22×C4×C13—21no—
145C22×C4×C13—24no—
146C22×C4×C13—24no—
147C22×C4×C13—22no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—22no—
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×Dic13—41no—
155C2×Dic26—22no—
156C2×Dic26—41no—
157C2×Dic26—82no—
158C13×C4⋊C4—24no—
159C13×C4⋊C4—24no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4C2×D412yes—
167C13×C4⋊C4C2×D414yes—
168C13×C4⋊C4C2×D411yescharacteristic
169C13×C4⋊C4C2×D411yescharacteristic
170C13×C22⋊C4—24no—
171C13×C22⋊C4—24no—
172C13×C22⋊C4—21no—
173C13×C22⋊C4—21no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—21no—
176C13×C22⋊C4—22no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13C2×D411yescharacteristic
181C42×C13C2×D411yescharacteristic
182C42×C13C2×D411yescharacteristic
183C42×C13C2411yescharacteristic
184#6105—84no—
185C4⋊Dic13—22no—
186C4⋊Dic13—22no—
187C4⋊Dic13—41no—
188C4⋊Dic13—41no—
189#6099—42no—
190C2×#1055—24no—
191C2×#1055—22no—
192C2×#1055—22no—
193C2×#1055—22no—
194#3499D1311yescharacteristic
195#3206—131no—
196C2×#498—131no—
197#3079—131no—
198#1654—134no—
199#1651—134no—
200#1546—131no—
201#1492—131no—
202#1476—131no—
203C23×C13—21no—
204C23×C13—22no—
205C23×C13#12011yescharacteristic
206Q8×C13—21no—
207Q8×C13—48no—
208Q8×C13—42no—
209Q8×C13—42no—
210Q8×C13—42no—
211Q8×C13—44no—
212Q8×C13C2×SD1612yes—
213D4×C13—24no—
214D4×C13—21no—
215D4×C13—24no—
216D4×C13—48no—
217D4×C13—44no—
218D4×C13—42no—
219D4×C13—42no—
220D4×C13C2×SD1612yes—
221C2×C4×C13—21no—
222C2×C4×C13—22no—
223C2×C4×C13—24no—
224C2×C4×C13—22no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—24no—
228C2×C4×C13—22no—
229C2×C4×C13—48no—
230C2×C4×C13—48no—
231C2×C4×C13—44no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13#12011yescharacteristic
237C2×C4×C13#12011yescharacteristic
238C2×C4×C13#12011yescharacteristic
239C2×C4×C13C2×SD1612yes—
240C2×C4×C13AGL(1,ℤ/8)12yes—
241C2×C4×C13C22×D411yescharacteristic
242C2×C4×C13C22×D411yescharacteristic
243C2×C4×C13C22×D411yescharacteristic
244C2×Dic13—42no—
245C2×Dic13—82no—
246Dic26—44no—
247Dic26—82no—
248#1055—24no—
249#1055—42no—
250#1055—42no—
251C2×2−1+4—21no—
252D4×Q8—21no—
253D4×Q8C2×D1312yes—
254#547—22no—
255#547—21no—
256#547—22no—
257#547C2×D1312yes—
258#536—22no—
259#536—21no—
260#532—21no—
261#532C2×D1311yescharacteristic
262C2×C4⋊Q8—21no—
263C2×C4⋊Q8—131no—
264C2×C4⋊Q8C2×D1311yescharacteristic
265C4×#41C2×D1311yescharacteristic
266#498—134no—
267#498—262no—
268#492—261no—
269#487—261no—
270#477—261no—
271#476—261no—
272#475—132no—
273#474—132no—
274#461—134no—
275#448—262no—
276#431—131no—
277#428—261no—
278C2×#106—262no—
279#423—131no—
280#417—261no—
281C2×C4×C8—131no—
282#332—134no—
283Q8⋊C8—132no—
284D4⋊C8—134no—
285D4⋊C8—132no—
286C22×C13—21no—
287C22×C13—21no—
288C22×C13—22no—
289C22×C13—41no—
290C22×C13—41no—
291C22×C13—42no—
292C22×C13—42no—
293C22×C13—42no—
294C22×C13#45012yes—
295C22×C13C2×#12011yescharacteristic
296C4×C13—22no—
297C4×C13—21no—
298C4×C13—21no—
299C4×C13—44no—
300C4×C13—42no—
301C4×C13—41no—
302C4×C13—41no—
303C4×C13#45012yes—
304C4×C13#45612yes—
305C4×C13C22×SD1611yescharacteristic
306C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
307C4×C13#57712yes—
308Dic13—82no—
3092−1+4—44no—
3102−1+4—44no—
311C2×#41—22no—
312C2×#41—24no—
313C2×#41—22no—
314C2×#41—21no—
315C2×#41C22⋊D1311yescharacteristic
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—21no—
319C22×Q8—261no—
320C2×SD16—264no—
321C2×M16—261no—
322C22×C8—261no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—21no—
327C4⋊Q8—21no—
328C4⋊Q8—132no—
329C4⋊Q8—261no—
330C4⋊Q8—261no—
331C4⋊Q8—261no—
332C4⋊Q8C22⋊D1311yescharacteristic
333C4⋊Q8C22⋊D1312yes—
334C4⋊Q8C22×D1312yes—
335#127C22⋊D1311yescharacteristic
336#124—22no—
337#124—21no—
338#123—24no—
339#123—24no—
340#123—24no—
341C22⋊Q8—24no—
342C22⋊Q8—22no—
343C22⋊Q8—24no—
344C22⋊Q8—22no—
345#121—22no—
346#121—22no—
347#121—21no—
348#121C22⋊D1312yes—
349C4×Q8C22⋊D1311yescharacteristic
350C4×Q8C22×D1311yescharacteristic
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4C22⋊D1311yescharacteristic
357C4×D4C22×D1311yescharacteristic
358C4×D4C22×D1312yes—
359#117—21no—
360#117C22⋊D1311yescharacteristic
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4C22⋊D1312yes—
367C2×C42—21no—
368C2×C42C22×D1311yescharacteristic
369#107—262no—
370#106—268no—
371#106—262no—
372C4⋊C8—132no—
373C4⋊C8—132no—
374C4⋊C8—261no—
375#103—262no—
376#103—264no—
377#102—262no—
378C22⋊C8—261no—
379C4×C8—132no—
380C4×C8—261no—
381C4×C8—261no—
382C2×C13—22no—
383C2×C13—42no—
384C2×C13—82no—
385C2×C13C2×#45011yescharacteristic
386C2×C13#301011yescharacteristic
387C2×C13C2×#45611yescharacteristic
388#41—22no—
389#41—48no—
390#41—416no—
391#41—44no—
392#41—44no—
393#41—42no—
394#41—42no—
395#41#610514yescomplemented
396C2×Q8—24no—
397C2×Q8—22no—
398C2×Q8—21no—
399C2×Q8—22no—
400C2×Q8—48no—
401C2×Q8—44no—
402C2×Q8—44no—
403C2×Q8—42no—
404C2×Q8—42no—
405C2×Q8—262no—
406C2×Q8—521no—
407C2×Q8—1042no—
408C2×Q8C2×C22⋊D1311yescharacteristic
409C2×D4—21no—
410C2×D4—24no—
411C2×D4—22no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4C2×C22⋊D1312yes—
415C2×D4C2×C22⋊D1311yescharacteristic
416C22×C4—21no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—521no—
424C22×C4C2×C22⋊D1311yescharacteristic
425C22×C4C2×C22⋊D1311yescharacteristic
426C22×C4C2×C22⋊D1311yescharacteristic
427SD16—1044no—
428M16—522no—
429C2×C8—264no—
430C2×C8—262no—
431C2×C8—262no—
432C2×C8—262no—
433C4⋊C4—24no—
434C4⋊C4—24no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—262no—
442C4⋊C4—262no—
443C4⋊C4—521no—
444C4⋊C4—521no—
445C4⋊C4C2×C22⋊D1312yes—
446C4⋊C4C2×C22⋊D1314yes—
447C4⋊C4C2×C22⋊D1311yescharacteristic
448C4⋊C4C2×C22⋊D1311yescharacteristic
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—21no—
452C22⋊C4—21no—
453C22⋊C4—22no—
454C22⋊C4—21no—
455C22⋊C4—22no—
456C42—21no—
457C42—21no—
458C42—21no—
459C42C2×C22⋊D1311yescharacteristic
460C42C2×C22⋊D1311yescharacteristic
461C42C2×C22⋊D1311yescharacteristic
462C42C23×D1311yescharacteristic
463C13#1865111yescharacteristic, complemented, Sylow
464C23—21no—
465C23—22no—
466C23#8820711yescharacteristic
467Q8—21no—
468Q8—48no—
469Q8—42no—
470Q8—42no—
471Q8—42no—
472Q8—44no—
473Q8—524no—
474Q8—1042no—
475Q8C2×#610512yes—
476D4—24no—
477D4—21no—
478D4—24no—
479D4—48no—
480D4—44no—
481D4—42no—
482D4—42no—
483D4C2×#610512yes—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—48no—
493C2×C4—48no—
494C2×C4—44no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—522no—
500C2×C4—1042no—
501C2×C4#8818612yes—
502C2×C4C2×#610512yes—
503C2×C4#8820711yescharacteristic
504C2×C4#8820711yescharacteristic
505C2×C4#8820711yescharacteristic
506C2×C4C22×C22⋊D1311yescharacteristic
507C2×C4C22×C22⋊D1311yescharacteristic
508C2×C4C22×C22⋊D1311yescharacteristic
509C8—264no—
510C8—522no—
511C8—522no—
512C22—21no—
513C22—21no—
514C22—22no—
515C22—41no—
516C22—41no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22#1171887912yes—
521C22C2×#8820711yescharacteristic
522C4—21no—
523C4—21no—
524C4—22no—
525C4—41no—
526C4—41no—
527C4—44no—
528C4—42no—
529C4—1042no—
530C4#1171887912yes—
531C4#1171890712yes—
532C4C2×#8818611yescharacteristic
533C4C22×#610511yescharacteristic
534C4#1171954212yes—
535C2—22no—
536C2—42no—
537C2—82no—
538C2C2×#1171887911yescharacteristic
539C2#1312412211yescharacteristic
540C2C2×#1171890711yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
Fitting, prime radicalC13×#3499C2
socleC22×C13C2×#120
hypercenter#3499D13
hypocenterC13#18651
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. #13125758C2semidirect
2. C2×#11718740C2semidirect
3. #13124651C2semidirect
4. #13114120C2semidirect
5. #13114099C2semidirect
6. #13113508C2semidirect
7. #13113287C2semidirect
8. #13113218C2semidirect
126. C13×#41SD16semidirect
395. #41#6105semidirect
463. C13#18651semidirect

Maximal subgroups

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

subgroupindex
#131257582
C2×#117187402
#131246512
#131141202
#131140992
#131135082
#131132872
#131132182
C13×#34992
#1865113