Finite Group Databasebeta

← #15873477

Subgroups — #15873477

Order 3328.

902 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718380C211yesmaximal, characteristic
2C2×#11718637C211yesmaximal, characteristic
3#13117231C211yesmaximal, characteristic
4#13115596C212yesmaximal, complemented
5#13115593C212yesmaximal, complemented
6#13115028C211yesmaximal, characteristic
7#13115026C211yesmaximal, characteristic
8#13115024C211yesmaximal, characteristic
9#13115001C212yesmaximal, complemented
10#13114968C212yesmaximal, complemented
11C13×#1853C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C4⋊Dic13C2211yescharacteristic
14C22×#6101—21no—
15C22×#6101—21no—
16C22×C4×Dic13C2211yescharacteristic
17C2×C13×#106C2212yes—
18C2×C13×C22⋊C8C2211yescharacteristic
19C13×#380C2211yescharacteristic
20#11718873C2211yescharacteristic
21C2×C22⋊#1055C2211yescharacteristic
22C2×#88058C2212yes—
23C2×#88055C2212yes—
24C2×#88054C2212yes—
25#11718638C2211yescharacteristic
26#11718638C2211yescharacteristic
27#11718637—21no—
28#11718637—21no—
29#11718637C2212yes—
30#11718637C2212yes—
31C4⋊C4×Dic13C2211yescharacteristic
32C4⋊C4×Dic13C2211yescharacteristic
33C2×#88048C2212yes—
34C2×#88047C2212yes—
35#11718604—21no—
36C22⋊C4×Dic13—21no—
37#11718380C418yescomplemented
38#11718312—21no—
39#11718309—21no—
40C13×#340C2212yes—
41#11718143C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44C23×C4×C13—21no—
45C23×C4×C13C2311yescharacteristic
46C23×Dic13—21no—
47C23×Dic13D411yescharacteristic
48C23×Dic13D411yescharacteristic
49C22×C8×C13C2312yes—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—42no—
52C2×C13×C4⋊C4C2311yescharacteristic
53C2×C13×C4⋊C4C2311yescharacteristic
54C2×C13×C4⋊C4C2312yes—
55C2×C13×C22⋊C4—21no—
56C2×C22⋊Dic13—21no—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13—42no—
59C2×C4⋊Dic13C2312yes—
60C2×C4⋊Dic13C2311yescharacteristic
61C2×C4⋊Dic13C2311yescharacteristic
62C2×#6101—22no—
63C2×#6101—22no—
64C2×#6101—22no—
65C2×#6101—22no—
66C2×#6101—44no—
67C2×#6101—44no—
68C2×C4×Dic13—21no—
69C2×C4×Dic13—21no—
70C2×C4×Dic13C2×C414yes—
71C2×C4×Dic13D411yescharacteristic
72C2×C4×Dic13D411yescharacteristic
73C2×C4×Dic13Q814yes—
74C2×C4×Dic13C2311yescharacteristic
75C2×C4×Dic13C2311yescharacteristic
76C22×#1055C2312yes—
77C13×#106—42no—
78C13×C22⋊C8C2×C414yes—
79C13×#95—21no—
80#88071—21no—
81#88071—21no—
82#88071—21no—
83#88071—21no—
84#88071—21no—
85#88071—21no—
86#88071—21no—
87C22⋊#1055C2×C414yes—
88#88058—42no—
89#88055C2×C418yescomplemented
90#88054C2×C418yescomplemented
91#88048—42no—
92#88047—42no—
93#21987—131nomaximal, Sylow
94C24×C13C2×D411yescharacteristic
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—22no—
100C22×C4×C13—42no—
101C22×C4×C13—42no—
102C22×C4×C13—42no—
103C22×C4×C13C22×C412yes—
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×Q812yes—
106C22×C4×C13C2411yescharacteristic
107C22×Dic13—22no—
108C22×Dic13—22no—
109C22×Dic13—22no—
110C22×Dic13—22no—
111C22×Dic13—21no—
112C22×Dic13—21no—
113C22×Dic13—22no—
114C22×Dic13—42no—
115C22×Dic13—42no—
116C22×Dic13—42no—
117C22×Dic13C4⋊C414yes—
118C22×Dic13C4⋊C414yes—
119C22×Dic13C2×D411yescharacteristic
120C22×Dic13C2×D411yescharacteristic
121C22×Dic13C2×D411yescharacteristic
122C22×Dic13C2×D411yescharacteristic
123C2×C8×C13—22no—
124C2×C8×C13—22no—
125C2×C8×C13C22×C414yes—
126C13×C4⋊C4—22no—
127C13×C4⋊C4—22no—
128C13×C4⋊C4—22no—
129C13×C4⋊C4—22no—
130C13×C4⋊C4—42no—
131C13×C22⋊C4—42no—
132C22⋊Dic13—42no—
133C4⋊Dic13—22no—
134C4⋊Dic13—22no—
135C4⋊Dic13—22no—
136C4⋊Dic13—22no—
137C4⋊Dic13—42no—
138#6101—44no—
139#6101—44no—
140#6101—44no—
141#6101—44no—
142C4×Dic13—42no—
143C4×Dic13—42no—
144C4×Dic13C4⋊C414yes—
145C4×Dic13C4⋊C414yes—
146C4×Dic13C22×C412yes—
147C4×Dic13C22×C412yes—
148C4×Dic13C2×Q812yes—
149C4×Dic13C2×Q812yes—
150C2×#1055—22no—
151C2×#1055—22no—
152C2×#1055C22×C414yes—
153C2×#432—131no—
154C2×#384—131no—
155#2283—131no—
156#1948—132no—
157#1947—132no—
158#1853—131no—
159#1853D1311yescharacteristic
160#1852—131no—
161#1852—131no—
162#1847—132no—
163#1836—132no—
164C23×C13—21no—
165C23×C13—21no—
166C23×C13—21no—
167C23×C13—21no—
168C23×C13C2×C4⋊C412yes—
169C23×C13AGL(1,ℤ/8)12yes—
170C23×C13#13712yes—
171C23×C13C22×D411yescharacteristic
172C2×C4×C13—21no—
173C2×C4×C13—21no—
174C2×C4×C13—24no—
175C2×C4×C13—24no—
176C2×C4×C13—42no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—42no—
181C2×C4×C13—42no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—84no—
186C2×C4×C13C2×C4⋊C412yes—
187C2×C4×C13C23×C411yescharacteristic
188C2×C4×C13C22×Q811yescharacteristic
189C2×C4×C13H(5,𝔽2)12yes—
190C2×C4×C132−1+412yes—
191C2×Dic13—21no—
192C2×Dic13—21no—
193C2×Dic13—21no—
194C2×Dic13—21no—
195C2×Dic13—21no—
196C2×Dic13—21no—
197C2×Dic13—28no—
198C2×Dic13—28no—
199C2×Dic13—42no—
200C2×Dic13—41no—
201C2×Dic13—41no—
202C2×Dic13—41no—
203C2×Dic13—42no—
204C2×Dic13—42no—
205C2×Dic13—41no—
206C2×Dic13—41no—
207C2×Dic13—41no—
208C2×Dic13—84no—
209C2×Dic13C2×C4⋊C412yes—
210C2×Dic13C2×C4⋊C412yes—
211C2×Dic13C2×C4⋊C412yes—
212C2×Dic13C2×C4⋊C412yes—
213C2×Dic13AGL(1,ℤ/8)12yes—
214C2×Dic13#13712yes—
215C8×C13—24no—
216#1055—24no—
217C22×C4⋊C4—131no—
218C22×C4⋊C4—261no—
219C22×C4⋊C4—261no—
220C22×C4⋊C4C2×D1311yescharacteristic
221C22×C42—131no—
222#432—138no—
223C2×#107—132no—
224C2×#107—132no—
225C2×#106—132no—
226C2×#106C2×D1312yes—
227C2×C4⋊C8—132no—
228C2×C22⋊C8—131no—
229C2×C22⋊C8C2×D1311yescharacteristic
230C2×#97—132no—
231#384—132no—
232#384—132no—
233#384—261no—
234#384—261no—
235#383—261no—
236#382—131no—
237#382—131no—
238#381—261no—
239#380—131no—
240#380C2×D1311yescharacteristic
241C4×C4⋊C4—131no—
242C4×C4⋊C4—131no—
243C4×C22⋊C4—261no—
244#376—261no—
245#340—132no—
246#340—132no—
247#340—132no—
248#340C2×D1312yes—
249C22×C13—22no—
250C22×C13—22no—
251C22×C13—22no—
252C22×C13—22no—
253C22×C13—22no—
254C22×C13—22no—
255C22×C13#42814yes—
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
263C4×C13—22no—
264C4×C13—82no—
265C4×C13—81no—
266C4×C13—81no—
267C4×C13#52012yes—
268C4×C13#54412yes—
269Dic13—22no—
270Dic13—22no—
271Dic13—22no—
272Dic13—81no—
273Dic13—82no—
274Dic13—81no—
275Dic13#42814yes—
276C23×C4—21no—
277C23×C4—131no—
278C23×C4—131no—
279C23×C4—261no—
280C23×C4C22×D1311yescharacteristic
281C22×C8—132no—
282C22×C8C22×D1312yes—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—132no—
286C2×C4⋊C4—131no—
287C2×C4⋊C4—131no—
288C2×C4⋊C4—262no—
289C2×C4⋊C4—262no—
290C2×C4⋊C4—262no—
291C2×C4⋊C4—262no—
292C2×C4⋊C4—261no—
293C2×C4⋊C4—522no—
294C2×C4⋊C4—524no—
295C2×C4⋊C4—524no—
296C2×C4⋊C4C22×D1312yes—
297C2×C4⋊C4C22×D1311yescharacteristic
298C2×C4⋊C4C22×D1311yescharacteristic
299C2×C22⋊C4—21no—
300C2×C22⋊C4—261no—
301C2×C42—134no—
302C2×C42—131no—
303C2×C42—131no—
304C2×C42—134no—
305C2×C42—131no—
306C2×C42—131no—
307C2×C42—261no—
308C2×C42—261no—
309#107—522no—
310#107—522no—
311#106—42no—
312#106—522no—
313C4⋊C8—138no—
314C22⋊C8—134no—
315C22⋊C8C4×D1314yes—
316#97—138no—
317#95—21no—
318#95—261no—
319#95—261no—
320#95—261no—
321#95—261no—
322#95—261no—
323#95—261no—
324#95—261no—
325C2×C13—24no—
326C2×C13#231711yescharacteristic
327C2×C13C2×#42811yescharacteristic
328C2×C13C2×#42811yescharacteristic
329C2×C13#321711yescharacteristic
330C2×C13#321811yescharacteristic
331C2×C13#323811yescharacteristic
332C2×C13#323911yescharacteristic
333C24D4×D1311yescharacteristic
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—131no—
343C22×C4—134no—
344C22×C4—134no—
345C22×C4—131no—
346C22×C4—131no—
347C22×C4—131no—
348C22×C4—262no—
349C22×C4—262no—
350C22×C4—262no—
351C22×C4—262no—
352C22×C4—261no—
353C22×C4—261no—
354C22×C4—262no—
355C22×C4—522no—
356C22×C4—522no—
357C22×C4—522no—
358C22×C4C2×C4×D1312yes—
359C22×C4D4×D1311yescharacteristic
360C22×C4Q8×D1312yes—
361C22×C4C23×D1311yescharacteristic
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—134no—
365C2×C8—262no—
366C2×C8—262no—
367C2×C8C2×C4×D1314yes—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—42no—
373C4⋊C4—262no—
374C4⋊C4—262no—
375C4⋊C4—262no—
376C4⋊C4—262no—
377C4⋊C4—522no—
378C4⋊C4—524no—
379C4⋊C4—524no—
380C4⋊C4—524no—
381C4⋊C4—524no—
382C22⋊C4—42no—
383C22⋊C4—522no—
384C42—134no—
385C42—134no—
386C42—132no—
387C42—132no—
388C42—132no—
389C42—132no—
390C42—522no—
391C42—522no—
392C13#2198711yescharacteristic, complemented, Sylow
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23C4⋊C4×D1312yes—
398C23#8816812yes—
399C23#8816912yes—
400C23C2×D4×D1311yescharacteristic
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—84no—
415C2×C4—132no—
416C2×C4—132no—
417C2×C4—132no—
418C2×C4—132no—
419C2×C4—132no—
420C2×C4—132no—
421C2×C4—268no—
422C2×C4—261no—
423C2×C4—261no—
424C2×C4—261no—
425C2×C4—261no—
426C2×C4—261no—
427C2×C4—261no—
428C2×C4—268no—
429C2×C4—521no—
430C2×C4—521no—
431C2×C4—522no—
432C2×C4—521no—
433C2×C4—522no—
434C2×C4—521no—
435C2×C4—522no—
436C2×C4—521no—
437C2×C4—521no—
438C2×C4—1044no—
439C2×C4C4⋊C4×D1312yes—
440C2×C4C22×C4×D1311yescharacteristic
441C2×C4#8825112yes—
442C2×C4C2×Q8×D1311yescharacteristic
443C2×C4#8825712yes—
444C8—24no—
445C8—264no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22#1171852214yes—
453C22C2×C4⋊C4×D1311yescharacteristic
454C22#1171929711yescharacteristic
455C22#1171935311yescharacteristic
456C22C2×#8816811yescharacteristic
457C22C2×#8816911yescharacteristic
458C22D13×AGL(1,ℤ/8)11yescharacteristic
459C22D13×#13711yescharacteristic
460C4—22no—
461C4—81no—
462C4—82no—
463C4—81no—
464C4—134no—
465C4—262no—
466C4—262no—
467C4—262no—
468C4—1041no—
469C4—1041no—
470C4—1042no—
471C4#1171925112yes—
472C4#1171932812yes—
473C2—24no—
474C2#1311745511yescharacteristic
475C2D13×#42811yescharacteristic
476C2C2×#1171852211yescharacteristic
477C2#1312585711yescharacteristic
478C2#1312586111yescharacteristic
479C2#1312606011yescharacteristic
480C2#1312606411yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1853C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenter#1853D13
hypocenterC13#21987
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
4. #13115596C2semidirect
5. #13115593C2semidirect
9. #13115001C2semidirect
10. #13114968C2semidirect
37. #11718380C4semidirect
89. #88055C2×C4semidirect
90. #88054C2×C4semidirect
392. C13#21987semidirect

Maximal subgroups

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

subgroupindex
C2×#117183802
C2×#117186372
#131172312
#131155962
#131155932
#131150282
#131150262
#131150242
#131150012
#131149682
C13×#18532
#2198713