Finite Group Databasebeta

← #15919914

Subgroups — #15919914

Order 3328.

1100 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718728C211yesmaximal, characteristic
2C2×#11718688C211yesmaximal, characteristic
3#13119835C211yesmaximal, characteristic
4#13115979C212yesmaximal, complemented
5#13115969C212yesmaximal, complemented
6#13115794C211yesmaximal, characteristic, complemented
7#13115777C211yesmaximal, characteristic, complemented
8#13115191C212yesmaximal, complemented
9#13115191C212yesmaximal, complemented
10#13114666C211yesmaximal, characteristic, complemented
11C2×C13×#557C211yesmaximal, characteristic, complemented
12C13×#557—24no—
13C13×#557—24no—
14C2×C13×C4⋊Q8—21no—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×#125—21no—
17C2×C13×#125—21no—
18C2×C13×#125C2211yescharacteristic
19C2×C13×#125C2211yescharacteristic
20C2×C4×Q8×C13—21no—
21C2×C4×Q8×C13C2211yescharacteristic
22C2×C4×Q8×C13C2211yescharacteristic
23C2×C4×Q8×C13C2211yescharacteristic
24C2×C4×Q8×C13C2211yescharacteristic
25C2×#88201—21no—
26C22×#6106C2212yes—
27C2×#88128C2211yescharacteristic
28C2×#88075C2212yes—
29#11718728—24no—
30#11718688—24no—
31#11718652—21no—
32#11718652—21no—
33#11718649—21no—
34C2×#88049C2212yes—
35C2×#88049C2212yes—
36C2×#88049C2212yes—
37#11718600C2212yes—
38#11718600C2212yes—
39C4×C4⋊Dic13C2211yescharacteristic
40C2×C4⋊#1055C2211yescharacteristic
41C2×#88043C2211yescharacteristic
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45#11718116C2212yes—
46#11718116C2212yes—
47C22×Q8×C13—21no—
48C22×Q8×C13D411yescharacteristic
49C22×Q8×C13C2311yescharacteristic
50C22×D52—21no—
51C22×D52—21no—
52C22×D52C2312yes—
53C13×C4⋊Q8—28no—
54C13×C4⋊Q8—22no—
55C13×C4⋊Q8—22no—
56C13×#125—28no—
57C13×#125—28no—
58C13×#125—22no—
59C13×#125—22no—
60C13×#125—22no—
61C13×#125D414yes—
62C4×Q8×C13—28no—
63C4×Q8×C13—22no—
64C4×Q8×C13—22no—
65C4×Q8×C13—22no—
66C4×Q8×C13—22no—
67C4×Q8×C13—22no—
68C4×Q8×C13—22no—
69C4×Q8×C13—22no—
70C4×Q8×C13D414yes—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4D411yescharacteristic
80C2×C13×C4⋊C4D411yescharacteristic
81C2×C13×C4⋊C4D411yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C42×C13—21no—
86C2×C42×C13—21no—
87C2×C42×C13—21no—
88C2×C42×C13C2311yescharacteristic
89C2×C42×C13C2311yescharacteristic
90C2×C42×C13C2311yescharacteristic
91#88201—44no—
92C2×#6106—24no—
93C2×#6106—24no—
94C2×#6106—24no—
95C2×#6103—22no—
96C2×#6103—22no—
97C2×#6103—22no—
98C2×#6103—22no—
99C2×C4⋊Dic13C2312yes—
100C2×C4×Dic13—21no—
101C22×#1055C2312yes—
102C22×#1055C2312yes—
103#88128—22no—
104#88128—22no—
105#88075—24no—
106#88071—21no—
107#88049—24no—
108#88049—24no—
109#88049—24no—
110C4⋊#1055—22no—
111#88043—22no—
112#25944—131nomaximal, Sylow
113C23×D13—22no—
114C2×Q8×C13—24no—
115C2×Q8×C13—22no—
116C2×Q8×C13—22no—
117C2×Q8×C13—21no—
118C2×Q8×C13—22no—
119C2×Q8×C13—41no—
120C2×Q8×C13—42no—
121C2×Q8×C13—42no—
122C2×Q8×C13C2×D412yes—
123C2×Q8×C13#4114yes—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2411yescharacteristic
135C22×Dic13—22no—
136C2×D52—22no—
137C2×D52—22no—
138C2×D52—22no—
139C2×D52—22no—
140C2×D52—22no—
141C2×D52—22no—
142C2×D52—42no—
143C2×D52—42no—
144C2×D52—42no—
145C2×D52—42no—
146C2×D52—82no—
147C13×C4⋊C4—24no—
148C13×C4⋊C4—24no—
149C13×C4⋊C4—24no—
150C13×C4⋊C4—24no—
151C13×C4⋊C4—24no—
152C13×C4⋊C4—24no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—24no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4C2×D412yes—
162C13×C4⋊C4C2×D412yes—
163C13×C4⋊C4C2×D412yes—
164C42×C13—24no—
165C42×C13—24no—
166C42×C13—24no—
167C42×C13—21no—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13C2×D412yes—
172C42×C13C2×D412yes—
173#6106—48no—
174#6103—44no—
175#6103—44no—
176#6103—82no—
177#6103—82no—
178C4⋊Dic13—22no—
179C4⋊Dic13—22no—
180C4×Dic13—42no—
181C2×#1055—22no—
182C2×#1055—22no—
183C2×#1055—22no—
184C2×#1055—22no—
185C2×#1055—22no—
186C2×#1055—22no—
187C2×#557D1311yescharacteristic, complemented
188C2×#490—131no—
189C2×#460—131no—
190#2548—131no—
191#2025—132no—
192#2023—132no—
193#1989—131no—
194#1985—131no—
195#1880—132no—
196#1880—132no—
197#1763—131no—
198C23×C13C22×D411yescharacteristic
199C22×D13—42no—
200C22×D13—42no—
201C22×D13—42no—
202C22×D13—42no—
203C22×D13—42no—
204C22×D13—42no—
205C22×D13—42no—
206Q8×C13—22no—
207Q8×C13—24no—
208Q8×C13—44no—
209Q8×C13—48no—
210Q8×C13#12414yescomplemented
211C2×C4×C13—22no—
212C2×C4×C13—21no—
213C2×C4×C13—24no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—22no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—22no—
221C2×C4×C13—21no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—42no—
233C2×C4×C13#12012yes—
234C2×C4×C13#12012yes—
235C2×C4×C13AGL(1,ℤ/8)12yes—
236C2×C4×C13C22×D411yescharacteristic
237C2×C4×C13C22×D411yescharacteristic
238C2×C4×C13C2×#4112yes—
239C2×C4×C132−1+412yes—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13—42no—
243D52—42no—
244D52—42no—
245D52—42no—
246D52—42no—
247D52—84no—
248D52—84no—
249#1055—42no—
250#1055—42no—
251C22×SD16—132no—
252#557—24no—
253#557—24no—
254C2×C4⋊Q8—21no—
255C2×C4⋊Q8C2×D1311yescharacteristic
256C2×#127—131no—
257C2×#125—21no—
258C2×#125—21no—
259C2×#125C2×D1311yescharacteristic
260C2×#125C2×D1311yescharacteristic
261C2×#124—261no—
262C2×C4×Q8—21no—
263C2×C4×Q8C2×D1311yescharacteristic
264C2×C4×Q8C2×D1311yescharacteristic
265C2×C4×Q8C2×D1311yescharacteristic
266C2×C4×Q8C2×D1311yescharacteristic
267#490—264no—
268#460—264no—
269C2×C4⋊C8—131no—
270C2×#103—132no—
271C2×#102—132no—
272C2×#102—132no—
273C2×#102—132no—
274C2×#97—131no—
275#394—261no—
276#394—261no—
277#390—132no—
278#390—132no—
279#390—261no—
280C4×C4⋊C4—131no—
281#340—132no—
282#340—132no—
283#340—132no—
284#336—132no—
285#336—132no—
286C22×C13C2×#12011yescharacteristic
287C22×C13#54812yes—
288C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C13#57511yescharacteristic
290C22×C13#57712yes—
291C2×D13—82no—
292C2×D13—82no—
293C2×D13—82no—
294C2×D13—82no—
295C2×D13—82no—
296C2×D13—82no—
297C2×D13—82no—
298C4×C13—24no—
299C4×C13—22no—
300C4×C13—22no—
301C4×C13—22no—
302C4×C13—41no—
303C4×C13—42no—
304C4×C13—42no—
305C4×C13—41no—
306C4×C13—41no—
307C4×C13—42no—
308C4×C13C2×#12411yescharacteristic
309C4×C13#53611yescharacteristic
310C4×C13#54812yes—
311Dic13—82no—
312C22×Q8—21no—
313C22×Q8C22⋊D1311yescharacteristic
314C22×Q8C22×D1311yescharacteristic
315C22×D4—132no—
316C22×D4—261no—
317C22×D4—261no—
318C2×SD16—264no—
319C2×SD16—264no—
320C2×SD16—264no—
321C22×C8—132no—
322C22×C8—132no—
323C4⋊Q8—28no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326#127—262no—
327#127—262no—
328#125—28no—
329#125—28no—
330#125—22no—
331#125—22no—
332#125—22no—
333#125C22⋊D1314yes—
334#124—524no—
335C4×Q8—28no—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×Q8C22⋊D1314yes—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—132no—
353C2×C4⋊C4C22⋊D1311yescharacteristic
354C2×C4⋊C4C22⋊D1311yescharacteristic
355C2×C4⋊C4C22⋊D1311yescharacteristic
356C2×C4⋊C4C22×D1311yescharacteristic
357C2×C4⋊C4C22×D1311yescharacteristic
358C2×C4⋊C4C22×D1311yescharacteristic
359C2×C22⋊C4—262no—
360C2×C22⋊C4—262no—
361C2×C22⋊C4—262no—
362C2×C22⋊C4—262no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—261no—
367C2×C42C22×D1311yescharacteristic
368C2×C42C22×D1311yescharacteristic
369C2×C42C22×D1311yescharacteristic
370C4⋊C8—262no—
371#103—264no—
372#102—264no—
373#102—264no—
374#102—264no—
375#97—262no—
376#95—261no—
377C2×C13#243611yescharacteristic
378C2×C13#300611yescharacteristic
379C2×C13#301011yescharacteristic
380C2×C13#336812yes—
381C2×C13#337112yes—
382D13—162no—
383C24—262no—
384C2×Q8—24no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—21no—
389C2×Q8—41no—
390C2×Q8—42no—
391C2×Q8—42no—
392C2×Q8#613114yes—
393C2×Q8C2×C22⋊D1312yes—
394C2×D4—262no—
395C2×D4—262no—
396C2×D4—262no—
397C2×D4—262no—
398C2×D4—262no—
399C2×D4—262no—
400C2×D4—522no—
401C2×D4—522no—
402C2×D4—522no—
403C2×D4—522no—
404C2×D4—1042no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—262no—
410C22×C4C2×C22⋊D1311yescharacteristic
411C22×C4C2×C22⋊D1311yescharacteristic
412C22×C4C2×C22⋊D1311yescharacteristic
413C22×C4C2×C22⋊D1311yescharacteristic
414C22×C4C2×C22⋊D1311yescharacteristic
415C22×C4C2×C22⋊D1311yescharacteristic
416C22×C4C23×D1311yescharacteristic
417SD16—528no—
418C2×C8—262no—
419C2×C8—262no—
420C2×C8—262no—
421C2×C8—262no—
422C2×C8—262no—
423C2×C8—262no—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—262no—
439C4⋊C4—262no—
440C4⋊C4C2×C22⋊D1312yes—
441C4⋊C4C2×C22⋊D1312yes—
442C4⋊C4C2×C22⋊D1312yes—
443C22⋊C4—524no—
444C22⋊C4—524no—
445C22⋊C4—1042no—
446C22⋊C4—1042no—
447C42—24no—
448C42—24no—
449C42—24no—
450C42—21no—
451C42—21no—
452C42—21no—
453C42—21no—
454C42—522no—
455C42C2×C22⋊D1312yes—
456C42C2×C22⋊D1312yes—
457C13#2594411yescharacteristic, complemented, Sylow
458C23—522no—
459C23—522no—
460C23—522no—
461C23—522no—
462C23—522no—
463C23—522no—
464C23—522no—
465C23C22×C22⋊D1311yescharacteristic
466Q8—22no—
467Q8—24no—
468Q8—44no—
469Q8—48no—
470Q8#8820114yescomplemented
471D4—522no—
472D4—522no—
473D4—522no—
474D4—522no—
475D4—1044no—
476D4—1044no—
477C2×C4—24no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—522no—
500C2×C4—522no—
501C2×C4—522no—
502C2×C4#8820312yes—
503C2×C4#8820712yes—
504C2×C4#8820712yes—
505C2×C4C2×#613112yes—
506C2×C4#8825412yes—
507C2×C4C22×C22⋊D1311yescharacteristic
508C2×C4C22×C22⋊D1311yescharacteristic
509C8—522no—
510C8—522no—
511C22—1042no—
512C22—1042no—
513C22—1042no—
514C22—1042no—
515C22—1042no—
516C22—1042no—
517C22—1042no—
518C22#1171952212yes—
519C22C2×#8820311yescharacteristic
520C22#1171952711yescharacteristic
521C22#1171954212yes—
522C22C2×#8820711yescharacteristic
523C4—24no—
524C4—22no—
525C4—22no—
526C4—22no—
527C4—41no—
528C4—41no—
529C4—42no—
530C4—41no—
531C4—42no—
532C4—42no—
533C4—1042no—
534C4C2×#8820111yescharacteristic
535C4#1171952111yescharacteristic
536C4#1171952212yes—
537C2—2082no—
538C2#1311849011yescharacteristic
539C2#1312408811yescharacteristic
540C2#1312412211yescharacteristic
541C2#1312756512yes—
542C2#1312760412yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#557C2
socleC23×C13C22×D4
prime radicalC2×#88128C22
hypercenterC2×#557D13
hypocenterC13#25944
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
4. #13115979C2semidirect
5. #13115969C2semidirect
6. #13115794C2semidirect
7. #13115777C2semidirect
8. #13115191C2semidirect
9. #13115191C2semidirect
10. #13114666C2semidirect
11. C2×C13×#557C2semidirect
187. C2×#557D13semidirect
210. Q8×C13#124semidirect
457. C13#25944semidirect
470. Q8#88201semidirect

Maximal subgroups

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

subgroupindex
C2×#117187282
C2×#117186882
#131198352
#131159792
#131159692
#131157942
#131157772
#131151912
#131146662
C2×C13×#5572
#2594413