Finite Group Databasebeta

← #15919627

Subgroups — #15919627

Order 3328.

1110 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718728C211yesmaximal, characteristic, complemented
2C2×#11718749C211yesmaximal, characteristic, complemented
3#13120586C211yesmaximal, characteristic
4#13115979C212yesmaximal, complemented
5#13115969C212yesmaximal, complemented
6#13115810C211yesmaximal, characteristic, complemented
7#13115802C211yesmaximal, characteristic, complemented
8#13115158C212yesmaximal, complemented
9#13115153C212yesmaximal, complemented
10#13114602C211yesmaximal, characteristic, complemented
11C2×C13×#544C211yesmaximal, characteristic, complemented
12C13×#544—24no—
13C13×#544—24no—
14C2×C13×C4⋊Q8—21no—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×#125—21no—
18C2×C13×#125C2211yescharacteristic
19C2×C13×#125C2211yescharacteristic
20C2×C13×C22⋊Q8—21no—
21C2×C13×C22⋊Q8—21no—
22C2×C13×#117C2211yescharacteristic
23C2×C13×#117C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C2×#88184C2212yes—
26C2×#88128C2211yescharacteristic
27C2×C22⋊#1055C2212yes—
28#11718749—24no—
29#11718728—24no—
30#11718652—21no—
31#11718652—21no—
32C2×#88049C2212yes—
33C2×#88049C2212yes—
34C2×#88049C2212yes—
35C2×#88049C2212yes—
36#11718621—21no—
37#11718621—21no—
38#11718600C2212yes—
39#11718597C2211yescharacteristic
40C2×#88043C2211yescharacteristic
41C2×C4×#1055C2211yescharacteristic
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45#11718121C2212yes—
46#11718116C2212yes—
47C22×Q8×C13—21no—
48C22×Q8×C13—21no—
49C23×C4×C13—21no—
50C23×C4×C13C2311yescharacteristic
51C22×C22⋊D13—22no—
52C22×D52—21no—
53C22×D52—21no—
54C22×D52C2312yes—
55C13×C4⋊Q8—28no—
56C13×C4⋊Q8—22no—
57C13×C4⋊Q8—22no—
58C13×C4⋊Q8—22no—
59C13×C4⋊Q8D414yescomplemented
60C13×#125—28no—
61C13×#125—22no—
62C13×#125—22no—
63C13×#125—22no—
64C13×#125D414yescomplemented
65C13×C22⋊Q8—28no—
66C13×C22⋊Q8—28no—
67C13×#117—22no—
68C13×#117—22no—
69C13×#117—22no—
70C13×#117—22no—
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—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4D411yescharacteristic
81C2×C13×C4⋊C4D411yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C4⋊C4C2311yescharacteristic
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4D411yescharacteristic
88C2×C13×C22⋊C4D411yescharacteristic
89C2×C42×C13—21no—
90C2×C42×C13C2311yescharacteristic
91C2×C42×C13C2311yescharacteristic
92#88184—28no—
93C2×#6103—22no—
94C2×#6103—22no—
95C2×#6103—22no—
96C2×C4⋊Dic13C2312yes—
97C22×#1055C2312yes—
98C22×#1055C2312yes—
99#88128—22no—
100#88128—22no—
101#88071—21no—
102#88071—21no—
103C22⋊#1055—24no—
104#88049—24no—
105#88049—24no—
106#88049—24no—
107#88049—24no—
108#88043—22no—
109C4×#1055—22no—
110#25915—131nomaximal, Sylow
111C24×C13C2×D411yescharacteristic
112C23×D13—22no—
113C2×Q8×C13—24no—
114C2×Q8×C13—24no—
115C2×Q8×C13—82no—
116C2×Q8×C13—82no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—22no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—24no—
125C22×C4×C13—82no—
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13#4114yes—
132C22×C4×C13C2411yescharacteristic
133C2×C22⋊D13—44no—
134C2×C22⋊D13—82no—
135C2×C22⋊D13—82no—
136C22×Dic13—22no—
137C2×D52—22no—
138C2×D52—22no—
139C2×D52—24no—
140C2×D52—24no—
141C2×D52—42no—
142C2×D52—42no—
143C2×D52—82no—
144C2×D52—82no—
145C13×C4⋊C4—24no—
146C13×C4⋊C4—24no—
147C13×C4⋊C4—24no—
148C13×C4⋊C4—24no—
149C13×C4⋊C4—24no—
150C13×C4⋊C4—24no—
151C13×C4⋊C4—24no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4C2×D412yes—
159C13×C4⋊C4C2×D412yes—
160C13×C4⋊C4C2×D412yes—
161C13×C4⋊C4C2×D412yes—
162C13×C22⋊C4—24no—
163C13×C22⋊C4—22no—
164C13×C22⋊C4—22no—
165C42×C13—24no—
166C42×C13—21no—
167C42×C13—21no—
168C42×C13C2×D412yes—
169C42×C13C2×D412yes—
170#6103—44no—
171#6103—82no—
172#6103—82no—
173C4⋊Dic13—24no—
174C2×#1055—22no—
175C2×#1055—22no—
176C2×#1055—22no—
177C2×#1055—22no—
178C2×#1055—22no—
179C2×#1055—22no—
180C2×#544D1311yescharacteristic, complemented
181C2×#490—131no—
182C2×#486—131no—
183#2619—131no—
184#2025—132no—
185#2023—132no—
186#1993—131no—
187#1991—131no—
188#1875—132no—
189#1874—132no—
190#1750—131no—
191C23×C13—21no—
192C23×C13—21no—
193C23×C13—22no—
194C23×C13—22no—
195C23×C13#12412yes—
196C23×C13C22×D411yescharacteristic
197C22×D13—42no—
198C22×D13—42no—
199C22×D13—42no—
200C22×D13—42no—
201C22×D13—42no—
202C22×D13—42no—
203C22×D13—42no—
204Q8×C13—84no—
205Q8×C13—84no—
206C2×C4×C13—21no—
207C2×C4×C13—21no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—24no—
211C2×C4×C13—24no—
212C2×C4×C13—21no—
213C2×C4×C13—22no—
214C2×C4×C13—21no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—84no—
225C2×C4×C13#12012yes—
226C2×C4×C13#12012yes—
227C2×C4×C13#12412yes—
228C2×C4×C13C22×D411yescharacteristic
229C2×C4×C13C22×D411yescharacteristic
230C2×C4×C13C2×#4112yes—
231C2×C4×C132−1+412yes—
232C22⋊D13—88no—
233C2×Dic13—42no—
234C2×Dic13—42no—
235C2×Dic13—42no—
236D52—44no—
237D52—44no—
238D52—84no—
239D52—84no—
240#1055—42no—
241#1055—42no—
242#544—24no—
243#544—24no—
244C2×C4⋊Q8—21no—
245C2×C4⋊Q8C2×D1311yescharacteristic
246C2×C4⋊Q8C2×D1311yescharacteristic
247C2×#127—131no—
248C2×#125—21no—
249C2×#125C2×D1311yescharacteristic
250C2×#125C2×D1311yescharacteristic
251C2×C22⋊Q8—21no—
252C2×C22⋊Q8—21no—
253C2×#121—132no—
254C2×#117C2×D1311yescharacteristic
255C2×#117C2×D1311yescharacteristic
256C22×C4⋊C4C2×D1311yescharacteristic
257#490—264no—
258#486—264no—
259C2×#102—132no—
260C2×#102—132no—
261C2×#102—132no—
262C2×#102—132no—
263C2×C22⋊C8—132no—
264C2×#97—131no—
265C2×C4×C8—131no—
266#394—261no—
267#394—261no—
268#392—261no—
269#392—261no—
270#390—132no—
271#382—131no—
272#340—132no—
273#340—132no—
274#340—132no—
275#340—132no—
276#336—132no—
277C22×C13—24no—
278C22×C13—22no—
279C22×C13—42no—
280C22×C13—41no—
281C22×C13—41no—
282C22×C13C2×#12011yescharacteristic
283C22×C13C2×#12411yescharacteristic
284C22×C13#53611yescharacteristic
285C22×C13#57612yes—
286C22×C13#57712yes—
287C2×D13—82no—
288C2×D13—82no—
289C2×D13—82no—
290C2×D13—82no—
291C2×D13—82no—
292C2×D13—82no—
293C2×D13—82no—
294C4×C13—22no—
295C4×C13—22no—
296C4×C13—22no—
297C4×C13—41no—
298C4×C13—42no—
299C4×C13—42no—
300C4×C13—42no—
301C4×C13—41no—
302C4×C13—42no—
303C4×C13#54812yes—
304C4×C13#54812yes—
305Dic13—82no—
306C22×Q8—21no—
307C22×Q8—21no—
308C22×D4—132no—
309C22×D4—262no—
310C22×D4—261no—
311C22×D4—261no—
312C23×C4—21no—
313C23×C4C22×D1311yescharacteristic
314C22×C8—132no—
315C22×C8—132no—
316C4⋊Q8—28no—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—22no—
320C4⋊Q8C22⋊D1314yescomplemented
321#127—262no—
322#127—262no—
323#125—28no—
324#125—22no—
325#125—22no—
326#125—22no—
327#125C22⋊D1314yescomplemented
328C22⋊Q8—28no—
329C22⋊Q8—28no—
330#121—268no—
331#117—22no—
332#117—22no—
333#117—22no—
334#117—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—132no—
345C2×C4⋊C4C22⋊D1311yescharacteristic
346C2×C4⋊C4C22⋊D1311yescharacteristic
347C2×C4⋊C4C22×D1311yescharacteristic
348C2×C4⋊C4C22×D1311yescharacteristic
349C2×C4⋊C4C22×D1311yescharacteristic
350C2×C4⋊C4C22×D1311yescharacteristic
351C2×C22⋊C4—21no—
352C2×C22⋊C4—262no—
353C2×C22⋊C4—262no—
354C2×C22⋊C4—262no—
355C2×C22⋊C4C22⋊D1311yescharacteristic
356C2×C22⋊C4C22⋊D1311yescharacteristic
357C2×C42—21no—
358C2×C42C22×D1311yescharacteristic
359C2×C42C22×D1311yescharacteristic
360#102—264no—
361#102—264no—
362#102—264no—
363#102—264no—
364C22⋊C8—264no—
365#97—262no—
366C4×C8—262no—
367#95—261no—
368#95—261no—
369C2×C13—42no—
370C2×C13#243611yescharacteristic
371C2×C13#300811yescharacteristic
372C2×C13#301011yescharacteristic
373C2×C13#313612yes—
374C2×C13#324112yes—
375D13—162no—
376C24—262no—
377C24C2×C22⋊D1311yescharacteristic
378C2×Q8—24no—
379C2×Q8—24no—
380C2×Q8—82no—
381C2×Q8—82no—
382C2×D4—264no—
383C2×D4—264no—
384C2×D4—262no—
385C2×D4—262no—
386C2×D4—524no—
387C2×D4—522no—
388C2×D4—522no—
389C2×D4—1042no—
390C2×D4—1042no—
391C2×D4—1042no—
392C2×D4—1042no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—24no—
401C22×C4—82no—
402C22×C4—262no—
403C22×C4#613114yes—
404C22×C4C2×C22⋊D1311yescharacteristic
405C22×C4C2×C22⋊D1311yescharacteristic
406C22×C4C2×C22⋊D1311yescharacteristic
407C22×C4C2×C22⋊D1311yescharacteristic
408C22×C4C2×C22⋊D1311yescharacteristic
409C22×C4C23×D1311yescharacteristic
410C2×C8—262no—
411C2×C8—262no—
412C2×C8—262no—
413C2×C8—262no—
414C2×C8—262no—
415C2×C8—262no—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—24no—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—264no—
430C4⋊C4C2×C22⋊D1312yes—
431C4⋊C4C2×C22⋊D1312yes—
432C4⋊C4C2×C22⋊D1312yes—
433C4⋊C4C2×C22⋊D1312yes—
434C22⋊C4—24no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—524no—
438C22⋊C4—1042no—
439C22⋊C4—1042no—
440C42—24no—
441C42—21no—
442C42—21no—
443C42C2×C22⋊D1312yes—
444C42C2×C22⋊D1312yes—
445C13#2591511yescharacteristic, complemented, Sylow
446C23—21no—
447C23—22no—
448C23—22no—
449C23—21no—
450C23—522no—
451C23—522no—
452C23—522no—
453C23—522no—
454C23—522no—
455C23—522no—
456C23—522no—
457C23#8820112yes—
458C23C22×C22⋊D1311yescharacteristic
459Q8—84no—
460Q8—84no—
461D4—524no—
462D4—524no—
463D4—1044no—
464D4—1044no—
465D4—1048no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—84no—
485C2×C4—522no—
486C2×C4—522no—
487C2×C4—522no—
488C2×C4#8820112yes—
489C2×C4#8820712yes—
490C2×C4#8820712yes—
491C2×C4C2×#613112yes—
492C2×C4#8825412yes—
493C2×C4C22×C22⋊D1311yescharacteristic
494C2×C4C22×C22⋊D1311yescharacteristic
495C8—522no—
496C8—522no—
497C22—22no—
498C22—24no—
499C22—41no—
500C22—41no—
501C22—42no—
502C22—1042no—
503C22—1042no—
504C22—1042no—
505C22—1042no—
506C22—1042no—
507C22—1042no—
508C22—1042no—
509C22C2×#8820111yescharacteristic
510C22#1171952111yescharacteristic
511C22#1171954012yes—
512C22#1171954212yes—
513C22C2×#8820711yescharacteristic
514C4—22no—
515C4—22no—
516C4—22no—
517C4—41no—
518C4—42no—
519C4—42no—
520C4—42no—
521C4—41no—
522C4—42no—
523C4—1042no—
524C4#1171952212yes—
525C4#1171952212yes—
526C2—42no—
527C2—2082no—
528C2#1311849011yescharacteristic
529C2#1312410411yescharacteristic
530C2#1312412211yescharacteristic
531C2#1312519512yes—
532C2#1312608912yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#544C2
socleC23×C13C22×D4
prime radical#13120586C2
hypercenterC2×#544D13
hypocenterC13#25915
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. C2×#11718728C2semidirect
2. C2×#11718749C2semidirect
4. #13115979C2semidirect
5. #13115969C2semidirect
6. #13115810C2semidirect
7. #13115802C2semidirect
8. #13115158C2semidirect
9. #13115153C2semidirect
10. #13114602C2semidirect
11. C2×C13×#544C2semidirect
59. C13×C4⋊Q8D4semidirect
64. C13×#125D4semidirect
180. C2×#544D13semidirect
320. C4⋊Q8C22⋊D13semidirect
327. #125C22⋊D13semidirect
445. C13#25915semidirect

Maximal subgroups

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

subgroupindex
C2×#117187282
C2×#117187492
#131205862
#131159792
#131159692
#131158102
#131158022
#131151582
#131151532
#131146022
C2×C13×#5442
#2591513