Finite Group Databasebeta

← #15873485

Subgroups — #15873485

Order 3328.

902 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718496C211yesmaximal, characteristic
2D13×#384C211yesmaximal, characteristic
3#13117232C211yesmaximal, characteristic
4#13115600C211yesmaximal, characteristic, complemented
5#13115597C211yesmaximal, characteristic, complemented
6#13115594C211yesmaximal, characteristic, complemented
7#13115030C212yesmaximal
8#13115022C212yesmaximal
9#13115003C212yesmaximal, complemented
10#13114968C212yesmaximal, complemented
11C13×#1947C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×D13—21no—
13C2×C4⋊C4×D13—21no—
14C2×C4⋊C4×D13C2212yes—
15C2×C42×D13C2211yescharacteristic
16C2×C13×#107C2212yes—
17C2×C13×C4⋊C8C2211yescharacteristic
18C13×#384C2211yescharacteristic
19C4×C13×C4⋊C4C2211yescharacteristic
20C2×#88060C2212yes—
21C2×#88057C2212yes—
22C2×#88055C2212yes—
23#11718648C2211yescharacteristic
24#11718648C2211yescharacteristic
25#11718638C2211yescharacteristic
26#11718638C2211yescharacteristic
27#11718637—21no—
28#11718637—21no—
29#11718637C2212yes—
30C2×#88048C2212yes—
31C2×#88047C2212yes—
32C4×#6103—21no—
33#11718596C2211yescharacteristic
34C4×C4⋊Dic13C2211yescharacteristic
35#11718593—21no—
36C2×C4⋊#1055C2211yescharacteristic
37#11718496C418yescomplemented
38#11718325—21no—
39#11718312—21no—
40C13×#340C2212yes—
41#11718143C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44C22×C4×D13—22no—
45C22×C4×D13D411yescharacteristic
46C22×C4×D13D411yescharacteristic
47C22×C4×D13C2311yescharacteristic
48C22×C8×C13C2312yes—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4C2311yescharacteristic
52C2×C13×C4⋊C4C2311yescharacteristic
53C2×C13×C4⋊C4C2312yes—
54C2×C42×C13—21no—
55C2×C42×C13C2311yescharacteristic
56C2×#6103—21no—
57C2×#6103—21no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13C2312yes—
61C2×C4⋊Dic13C2311yescharacteristic
62C2×C4⋊Dic13C2311yescharacteristic
63C2×#6101—22no—
64C2×#6101—22no—
65C2×#6101—22no—
66C2×C4×Dic13—21no—
67C2×C4×Dic13D411yescharacteristic
68C2×C4×Dic13D411yescharacteristic
69C2×C4×Dic13C2311yescharacteristic
70C22×#1055C2312yes—
71C4⋊C4×D13—42no—
72C4⋊C4×D13—42no—
73C4⋊C4×D13—44no—
74C4⋊C4×D13—44no—
75C42×D13C2×C414yes—
76C42×D13Q814yes—
77C13×#107—42no—
78C13×C4⋊C8C2×C414yescomplemented
79C13×#95—21no—
80#88071—21no—
81#88071—21no—
82#88071—21no—
83#88071—21no—
84#88071—21no—
85#88071—21no—
86#88071—21no—
87#88060C2×C418yes—
88#88057—42no—
89#88055C2×C418yescomplemented
90#88048—42no—
91#88047—42no—
92C4⋊#1055C2×C414yescomplemented
93#21987—131nomaximal, Sylow
94C23×D13C2×D411yescharacteristic
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—22no—
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2411yescharacteristic
101C22×Dic13—21no—
102C22×Dic13—21no—
103C22×Dic13—22no—
104C22×Dic13C2×D411yescharacteristic
105C22×Dic13C2×D411yescharacteristic
106C22×Dic13C2×D411yescharacteristic
107C2×C4×D13—22no—
108C2×C4×D13—22no—
109C2×C4×D13—22no—
110C2×C4×D13—22no—
111C2×C4×D13—21no—
112C2×C4×D13—21no—
113C2×C4×D13—21no—
114C2×C4×D13—21no—
115C2×C4×D13—44no—
116C2×C4×D13—44no—
117C2×C4×D13—44no—
118C2×C4×D13C4⋊C414yes—
119C2×C4×D13C4⋊C414yes—
120C2×C4×D13C22×C412yes—
121C2×C4×D13C2×Q812yes—
122C2×C8×C13—22no—
123C2×C8×C13—22no—
124C2×C8×C13C22×C414yes—
125C13×C4⋊C4—21no—
126C13×C4⋊C4—22no—
127C13×C4⋊C4—22no—
128C13×C4⋊C4—21no—
129C13×C4⋊C4—21no—
130C13×C4⋊C4—21no—
131C13×C4⋊C4—42no—
132C13×C4⋊C4—42no—
133C42×C13—42no—
134C42×C13C22×C412yes—
135C42×C13C2×Q812yes—
136#6103—42no—
137#6103—42no—
138C4⋊Dic13—22no—
139C4⋊Dic13—22no—
140C4⋊Dic13—21no—
141C4⋊Dic13—21no—
142C4⋊Dic13—21no—
143C4⋊Dic13—21no—
144C4⋊Dic13—42no—
145C4⋊Dic13—42no—
146#6101—44no—
147#6101—44no—
148#6101—44no—
149C4×Dic13—42no—
150C4×Dic13C4⋊C414yes—
151C4×Dic13C4⋊C414yes—
152C4×Dic13C22×C412yes—
153C4×Dic13C2×Q812yes—
154C2×#1055—22no—
155C2×#1055—22no—
156C2×#1055C22×C414yes—
157C2×#432—131no—
158C2×#384—131no—
159#2283—131no—
160#1948—131no—
161#1948—131no—
162#1947—131no—
163#1947D1311yescharacteristic, complemented
164#1853—132no—
165#1852—132no—
166#1847—132no—
167#1836—132no—
168C23×C13C22×D411yescharacteristic
169C22×D13—21no—
170C22×D13—21no—
171C22×D13—21no—
172C22×D13—21no—
173C22×D13C2×C4⋊C412yes—
174C22×D13AGL(1,ℤ/8)12yes—
175C22×D13#13712yes—
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—42no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—42no—
182C2×C4×C13—42no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13C2×C4⋊C412yes—
188C2×C4×C13C2×C4⋊C412yes—
189C2×C4×C13AGL(1,ℤ/8)12yes—
190C2×C4×C13#13712yes—
191C2×C4×C13C23×C411yescharacteristic
192C2×C4×C13C22×Q811yescharacteristic
193C2×C4×C13H(5,𝔽2)11yescharacteristic
194C2×C4×C13H(5,𝔽2)11yescharacteristic
195C2×C4×C132−1+411yescharacteristic
196C2×C4×C132−1+411yescharacteristic
197C2×Dic13—21no—
198C2×Dic13—21no—
199C2×Dic13—21no—
200C2×Dic13—21no—
201C2×Dic13—21no—
202C2×Dic13—21no—
203C2×Dic13—42no—
204C2×Dic13—41no—
205C2×Dic13—41no—
206C2×Dic13—42no—
207C2×Dic13—42no—
208C2×Dic13—41no—
209C2×Dic13—41no—
210C2×Dic13—41no—
211C2×Dic13—41no—
212C2×Dic13C2×C4⋊C412yes—
213C2×Dic13C2×C4⋊C412yes—
214C2×Dic13C2×C4⋊C412yes—
215C4×D13—28no—
216C4×D13—22no—
217C4×D13—22no—
218C4×D13—22no—
219C4×D13—22no—
220C4×D13—28no—
221C4×D13—88no—
222C8×C13—24no—
223#1055—24no—
224C22×C4⋊C4—132no—
225C22×C4⋊C4—261no—
226C22×C4⋊C4—261no—
227C22×C42—131no—
228#432—138no—
229C2×#107—132no—
230C2×#107C2×D1312yes—
231C2×#106—132no—
232C2×#106—132no—
233C2×C4⋊C8—131no—
234C2×C4⋊C8C2×D1311yescharacteristic
235C2×C22⋊C8—132no—
236C2×#97—132no—
237#384—132no—
238#384—131no—
239#384—261no—
240#384—261no—
241#384C2×D1311yescharacteristic
242#383—261no—
243#382—131no—
244#382—131no—
245#381—261no—
246#380—131no—
247#380—131no—
248C4×C4⋊C4—131no—
249C4×C4⋊C4C2×D1311yescharacteristic
250C4×C22⋊C4—261no—
251#376—261no—
252#340—132no—
253#340—132no—
254#340—132no—
255#340C2×D1312yes—
256C22×C13C22×C4⋊C411yescharacteristic
257C22×C13#53511yescharacteristic
258C22×C13#53611yescharacteristic
259C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C13C2×#13711yescharacteristic
262C22×C13C2×#13711yescharacteristic
263C2×D13—22no—
264C2×D13—22no—
265C2×D13—22no—
266C2×D13—22no—
267C2×D13—22no—
268C2×D13—22no—
269C2×D13#42814yes—
270C4×C13—22no—
271C4×C13—82no—
272C4×C13—81no—
273C4×C13—81no—
274C4×C13#42814yes—
275C4×C13#52011yescharacteristic
276C4×C13#52011yescharacteristic
277C4×C13#54411yescharacteristic
278C4×C13#54411yescharacteristic
279Dic13—22no—
280Dic13—22no—
281Dic13—22no—
282Dic13—82no—
283Dic13—81no—
284Dic13—81no—
285C23×C4—131no—
286C23×C4—131no—
287C23×C4—131no—
288C23×C4—262no—
289C22×C8—132no—
290C22×C8C22×D1312yes—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—132no—
294C2×C4⋊C4—131no—
295C2×C4⋊C4—131no—
296C2×C4⋊C4—262no—
297C2×C4⋊C4—262no—
298C2×C4⋊C4—262no—
299C2×C4⋊C4—261no—
300C2×C4⋊C4—261no—
301C2×C4⋊C4—522no—
302C2×C4⋊C4—522no—
303C2×C4⋊C4—524no—
304C2×C4⋊C4—524no—
305C2×C4⋊C4C22×D1312yes—
306C2×C4⋊C4C22×D1311yescharacteristic
307C2×C4⋊C4C22×D1311yescharacteristic
308C2×C22⋊C4—261no—
309C2×C22⋊C4—261no—
310C2×C42—21no—
311C2×C42—131no—
312C2×C42—131no—
313C2×C42—131no—
314C2×C42—134no—
315C2×C42—134no—
316C2×C42—261no—
317C2×C42C22×D1311yescharacteristic
318#107—42no—
319#107—522no—
320#106—522no—
321#106—522no—
322C4⋊C8—134no—
323C4⋊C8C4×D1314yescomplemented
324C22⋊C8—138no—
325#97—138no—
326#95—21no—
327#95—261no—
328#95—261no—
329#95—261no—
330#95—261no—
331#95—261no—
332#95—261no—
333#95—261no—
334C2×C13#231711yescharacteristic
335C2×C13C2×#42811yescharacteristic
336C2×C13C2×#42811yescharacteristic
337C2×C13#321711yescharacteristic
338C2×C13#321811yescharacteristic
339C2×C13#323811yescharacteristic
340C2×C13#323911yescharacteristic
341D13—24no—
342C24—131no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—131no—
347C22×C4—131no—
348C22×C4—131no—
349C22×C4—134no—
350C22×C4—134no—
351C22×C4—132no—
352C22×C4—132no—
353C22×C4—262no—
354C22×C4—262no—
355C22×C4—262no—
356C22×C4—262no—
357C22×C4—261no—
358C22×C4—261no—
359C22×C4—261no—
360C22×C4—261no—
361C22×C4—261no—
362C22×C4—261no—
363C22×C4—262no—
364C22×C4—524no—
365C22×C4—524no—
366C22×C4—524no—
367C22×C4D4×D1311yescharacteristic
368C22×C4D4×D1311yescharacteristic
369C22×C4C23×D1311yescharacteristic
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—134no—
373C2×C8—262no—
374C2×C8—262no—
375C2×C8C2×C4×D1314yes—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—42no—
383C4⋊C4—42no—
384C4⋊C4—261no—
385C4⋊C4—262no—
386C4⋊C4—261no—
387C4⋊C4—261no—
388C4⋊C4—262no—
389C4⋊C4—261no—
390C4⋊C4—522no—
391C4⋊C4—524no—
392C4⋊C4—524no—
393C4⋊C4—524no—
394C4⋊C4—522no—
395C22⋊C4—522no—
396C22⋊C4—522no—
397C42—42no—
398C42—134no—
399C42—134no—
400C42—132no—
401C42—132no—
402C42—522no—
403C42C2×C4×D1312yes—
404C42Q8×D1312yes—
405C13#2198711yescharacteristic, complemented, Sylow
406C23—132no—
407C23—132no—
408C23—132no—
409C23—261no—
410C23—261no—
411C23—261no—
412C23—261no—
413C23C2×D4×D1311yescharacteristic
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—132no—
426C2×C4—132no—
427C2×C4—132no—
428C2×C4—268no—
429C2×C4—261no—
430C2×C4—261no—
431C2×C4—261no—
432C2×C4—261no—
433C2×C4—261no—
434C2×C4—261no—
435C2×C4—262no—
436C2×C4—262no—
437C2×C4—262no—
438C2×C4—268no—
439C2×C4—262no—
440C2×C4—522no—
441C2×C4—521no—
442C2×C4—521no—
443C2×C4—521no—
444C2×C4—522no—
445C2×C4—521no—
446C2×C4—522no—
447C2×C4—521no—
448C2×C4—521no—
449C2×C4—1048no—
450C2×C4C4⋊C4×D1312yes—
451C2×C4C4⋊C4×D1312yes—
452C2×C4#8816512yes—
453C2×C4#8817212yes—
454C2×C4C22×C4×D1311yescharacteristic
455C2×C4#8825111yescharacteristic
456C2×C4C2×Q8×D1311yescharacteristic
457C2×C4#8825411yescharacteristic
458C2×C4#8825611yescharacteristic
459C2×C4#8825711yescharacteristic
460C8—24no—
461C8—264no—
462C22—134no—
463C22—262no—
464C22—262no—
465C22—262no—
466C22—262no—
467C22—262no—
468C22—262no—
469C22C2×C4⋊C4×D1311yescharacteristic
470C22#1171931211yescharacteristic
471C22#1171933311yescharacteristic
472C22C2×#8816511yescharacteristic
473C22C2×#8817211yescharacteristic
474C22D13×AGL(1,ℤ/8)11yescharacteristic
475C22D13×#13711yescharacteristic
476C4—22no—
477C4—81no—
478C4—81no—
479C4—82no—
480C4—262no—
481C4—262no—
482C4—262no—
483C4—1041no—
484C4—1042no—
485C4—1041no—
486C4#1171854214yes—
487C4#1171925111yescharacteristic
488C4#1171927911yescharacteristic
489C4#1171939411yescharacteristic
490C4#1171943411yescharacteristic
491C2—264no—
492C2#1311745811yescharacteristic
493C2D13×#42811yescharacteristic
494C2C2×#1171854211yescharacteristic
495C2#1312585311yescharacteristic
496C2#1312586711yescharacteristic
497C2#1312606111yescharacteristic
498C2#1312606511yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1947C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1947D13
hypocenterC13#21987
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
4. #13115600C2semidirect
5. #13115597C2semidirect
6. #13115594C2semidirect
9. #13115003C2semidirect
10. #13114968C2semidirect
11. C13×#1947C2semidirect
37. #11718496C4semidirect
78. C13×C4⋊C8C2×C4semidirect
89. #88055C2×C4semidirect
92. C4⋊#1055C2×C4semidirect
163. #1947D13semidirect
323. C4⋊C8C4×D13semidirect
405. C13#21987semidirect

Maximal subgroups

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

subgroupindex
C2×#117184962
D13×#3842
#131172322
#131156002
#131155972
#131155942
#131150302
#131150222
#131150032
#131149682
C13×#19472
#2198713