Finite Group Databasebeta

← #15873489

Subgroups — #15873489

Order 3328.

830 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718496C211yesmaximal, characteristic
2#13117241C211yesmaximal, characteristic
3#13117240C211yesmaximal, characteristic
4#13115597C211yesmaximal, characteristic, complemented
5#13115595C211yesmaximal, characteristic, complemented
6#13115594C211yesmaximal, characteristic, complemented
7#13115038C212yesmaximal
8#13115034C212yesmaximal
9#13115001C212yesmaximal, complemented
10#13114968C212yesmaximal, complemented
11C13×#1948C211yesmaximal, characteristic, complemented
12C2×#88146C2212yes—
13C2×#88126—21no—
14C2×C42×D13C2211yescharacteristic
15C2×C13×#106C2212yes—
16C2×C13×C4⋊C8C2211yescharacteristic
17C13×#384C2211yescharacteristic
18C4×C13×C4⋊C4C2211yescharacteristic
19C2×#88060C2212yes—
20C2×#88058C2212yes—
21C2×#88055C2212yes—
22#11718648—21no—
23#11718648—21no—
24#11718648C2211yescharacteristic
25#11718648C2211yescharacteristic
26#11718638C2212yes—
27#11718637C2211yescharacteristic
28#11718637C2211yescharacteristic
29C4⋊C4×Dic13—21no—
30C4⋊C4×Dic13—21no—
31C2×#88048C2212yes—
32C2×#88047C2212yes—
33#11718596C2211yescharacteristic
34C4×C4⋊Dic13C2211yescharacteristic
35C4×#6101—21no—
36C2×C4⋊#1055C2211yescharacteristic
37#11718496C418yescomplemented
38#11718328—21no—
39#11718311—21no—
40C13×#340C2212yes—
41#11718143C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44C22×C4×D13D411yescharacteristic
45C22×C4×D13D411yescharacteristic
46C22×C4×D13C2311yescharacteristic
47C22×C8×C13C2312yes—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4C2311yescharacteristic
51C2×C13×C4⋊C4C2311yescharacteristic
52C2×C13×C4⋊C4C2312yes—
53C2×C42×C13—21no—
54C2×C42×C13C2311yescharacteristic
55C2×#6103—21no—
56C2×#6103—21no—
57C2×#6103—22no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13C2312yes—
61C2×C4⋊Dic13C2311yescharacteristic
62C2×C4⋊Dic13C2311yescharacteristic
63C2×#6101—21no—
64C2×#6101—21no—
65C2×#6101—21no—
66C2×#6101—21no—
67C2×C4×Dic13—21no—
68C2×C4×Dic13—22no—
69C2×C4×Dic13D411yescharacteristic
70C2×C4×Dic13D411yescharacteristic
71C2×C4×Dic13C2311yescharacteristic
72C22×#1055C2312yes—
73#88146—42no—
74#88146—42no—
75#88126—44no—
76C42×D13C2×C414yes—
77C42×D13Q814yes—
78C13×#106—42no—
79C13×C4⋊C8C2×C414yes—
80C13×#95—21no—
81#88071—21no—
82#88071—21no—
83#88071—21no—
84#88071—22no—
85#88071—22no—
86#88060C2×C418yes—
87#88058—42no—
88#88055C2×C418yes—
89#88048—42no—
90#88047—42no—
91C4⋊#1055C2×C414yes—
92#21988—131nomaximal, Sylow
93C23×D13C2×D411yescharacteristic
94C22×C4×C13—22no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2411yescharacteristic
100C22×Dic13—21no—
101C22×Dic13—21no—
102C22×Dic13—22no—
103C22×Dic13C2×D411yescharacteristic
104C22×Dic13C2×D411yescharacteristic
105C22×Dic13C2×D411yescharacteristic
106C2×C4×D13—22no—
107C2×C4×D13—22no—
108C2×C4×D13—21no—
109C2×C4×D13—21no—
110C2×C4×D13—21no—
111C2×C4×D13—21no—
112C2×C4×D13—41no—
113C2×C4×D13—41no—
114C2×C4×D13C4⋊C414yes—
115C2×C4×D13C4⋊C414yes—
116C2×C4×D13C22×C412yes—
117C2×C4×D13C2×Q812yes—
118C2×C8×C13—22no—
119C2×C8×C13—22no—
120C2×C8×C13C22×C414yes—
121C13×C4⋊C4—21no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—22no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4—21no—
127C13×C4⋊C4—42no—
128C13×C4⋊C4—42no—
129C42×C13—42no—
130C42×C13C22×C412yes—
131C42×C13C2×Q812yes—
132#6103—42no—
133#6103—42no—
134#6103—44no—
135C4⋊Dic13—22no—
136C4⋊Dic13—22no—
137C4⋊Dic13—21no—
138C4⋊Dic13—21no—
139C4⋊Dic13—21no—
140C4⋊Dic13—21no—
141C4⋊Dic13—42no—
142C4⋊Dic13—42no—
143#6101—42no—
144#6101—42no—
145#6101—42no—
146#6101—42no—
147C4×Dic13—44no—
148C4×Dic13—42no—
149C4×Dic13C4⋊C414yes—
150C4×Dic13C4⋊C414yes—
151C4×Dic13C22×C412yes—
152C4×Dic13C2×Q812yes—
153C2×#1055—22no—
154C2×#1055—22no—
155C2×#1055C22×C414yes—
156C2×#432—131no—
157#2285—131no—
158#2285—131no—
159#1948—131no—
160#1948D1311yescharacteristic, complemented
161#1947—131no—
162#1947—131no—
163#1854—132no—
164#1854—132no—
165#1847—132no—
166#1836—132no—
167C23×C13C22×D411yescharacteristic
168C22×D13—21no—
169C22×D13—21no—
170C22×D13—21no—
171C22×D13—21no—
172C22×D13—21no—
173C22×D13—21no—
174C22×D13C2×C4⋊C412yes—
175C2×C4×C13—21no—
176C2×C4×C13—21no—
177C2×C4×C13—42no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—42no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—42no—
186C2×C4×C13C2×C4⋊C412yes—
187C2×C4×C13C2×C4⋊C412yes—
188C2×C4×C13AGL(1,ℤ/8)12yes—
189C2×C4×C13#13712yes—
190C2×C4×C13C23×C411yescharacteristic
191C2×C4×C13C22×Q811yescharacteristic
192C2×C4×C13H(5,𝔽2)11yescharacteristic
193C2×C4×C13H(5,𝔽2)11yescharacteristic
194C2×C4×C132−1+411yescharacteristic
195C2×C4×C132−1+411yescharacteristic
196C2×Dic13—21no—
197C2×Dic13—21no—
198C2×Dic13—21no—
199C2×Dic13—21no—
200C2×Dic13—21no—
201C2×Dic13—21no—
202C2×Dic13—42no—
203C2×Dic13—41no—
204C2×Dic13—41no—
205C2×Dic13—41no—
206C2×Dic13—41no—
207C2×Dic13—42no—
208C2×Dic13—41no—
209C2×Dic13—41no—
210C2×Dic13—42no—
211C2×Dic13C2×C4⋊C412yes—
212C2×Dic13C2×C4⋊C412yes—
213C2×Dic13C2×C4⋊C412yes—
214C4×D13—22no—
215C4×D13—22no—
216C4×D13—22no—
217C4×D13—22no—
218C4×D13—28no—
219C4×D13—44no—
220C8×C13—24no—
221#1055—24no—
222C2×#117—132no—
223C2×#117—261no—
224C22×C42—131no—
225#432—138no—
226C2×#107—132no—
227C2×#107—132no—
228C2×#106—132no—
229C2×#106C2×D1312yes—
230C2×C4⋊C8—131no—
231C2×C4⋊C8C2×D1311yescharacteristic
232C2×C22⋊C8—132no—
233C2×#97—132no—
234#384—131no—
235#384—131no—
236#384—131no—
237#384C2×D1311yescharacteristic
238#382—132no—
239#382—261no—
240#380—131no—
241#380—131no—
242#380—261no—
243#380—261no—
244#380—261no—
245C4×C4⋊C4—131no—
246C4×C4⋊C4—261no—
247C4×C4⋊C4—261no—
248C4×C4⋊C4—261no—
249C4×C4⋊C4C2×D1311yescharacteristic
250#340—132no—
251#340—132no—
252#340—132no—
253#340C2×D1312yes—
254C22×C13C22×C4⋊C411yescharacteristic
255C22×C13#53511yescharacteristic
256C22×C13#53611yescharacteristic
257C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
258C22×C13C2×#13711yescharacteristic
259C22×C13#57511yescharacteristic
260C22×C13#57511yescharacteristic
261C2×D13—22no—
262C2×D13—22no—
263C2×D13—22no—
264C2×D13—41no—
265C2×D13—41no—
266C2×D13—41no—
267C2×D13—41no—
268C4×C13—22no—
269C4×C13—81no—
270C4×C13—82no—
271C4×C13—81no—
272C4×C13#42814yes—
273C4×C13#52011yescharacteristic
274C4×C13#52011yescharacteristic
275C4×C13#54411yescharacteristic
276C4×C13#54411yescharacteristic
277Dic13—22no—
278Dic13—22no—
279Dic13—22no—
280Dic13—82no—
281Dic13—81no—
282Dic13—81no—
283C23×C4—131no—
284C23×C4—131no—
285C23×C4—131no—
286C22×C8—132no—
287C22×C8C22×D1312yes—
288#117—524no—
289#117—522no—
290#117—522no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—132no—
294C2×C4⋊C4—131no—
295C2×C4⋊C4—131no—
296C2×C4⋊C4—261no—
297C2×C4⋊C4—261no—
298C2×C4⋊C4—261no—
299C2×C4⋊C4—261no—
300C2×C4⋊C4—261no—
301C2×C4⋊C4—261no—
302C2×C4⋊C4C22×D1312yes—
303C2×C4⋊C4C22×D1311yescharacteristic
304C2×C4⋊C4C22×D1311yescharacteristic
305C2×C22⋊C4—262no—
306C2×C22⋊C4—261no—
307C2×C22⋊C4—261no—
308C2×C42—21no—
309C2×C42—131no—
310C2×C42—131no—
311C2×C42—131no—
312C2×C42—134no—
313C2×C42—134no—
314C2×C42—262no—
315C2×C42—261no—
316C2×C42C22×D1311yescharacteristic
317#107—522no—
318#107—522no—
319#106—42no—
320#106—522no—
321C4⋊C8—134no—
322C4⋊C8C4×D1314yes—
323C22⋊C8—138no—
324#97—138no—
325#95—21no—
326#95—261no—
327#95—261no—
328#95—262no—
329#95—262no—
330#95—261no—
331C2×C13#231711yescharacteristic
332C2×C13C2×#42811yescharacteristic
333C2×C13#291111yescharacteristic
334C2×C13#321411yescharacteristic
335C2×C13#321611yescharacteristic
336C2×C13#323511yescharacteristic
337C2×C13#323711yescharacteristic
338D13—42no—
339C24—131no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—131no—
344C22×C4—131no—
345C22×C4—131no—
346C22×C4—134no—
347C22×C4—132no—
348C22×C4—132no—
349C22×C4—134no—
350C22×C4—262no—
351C22×C4—262no—
352C22×C4—261no—
353C22×C4—261no—
354C22×C4—261no—
355C22×C4—261no—
356C22×C4—261no—
357C22×C4—261no—
358C22×C4—262no—
359C22×C4—521no—
360C22×C4—521no—
361C22×C4D4×D1311yescharacteristic
362C22×C4D4×D1311yescharacteristic
363C22×C4C23×D1311yescharacteristic
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—134no—
367C2×C8—262no—
368C2×C8—262no—
369C2×C8C2×C4×D1314yes—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—42no—
377C4⋊C4—42no—
378C4⋊C4—261no—
379C4⋊C4—262no—
380C4⋊C4—261no—
381C4⋊C4—261no—
382C4⋊C4—262no—
383C4⋊C4—261no—
384C4⋊C4—522no—
385C4⋊C4—522no—
386C4⋊C4—522no—
387C4⋊C4—522no—
388C4⋊C4—522no—
389C4⋊C4—522no—
390C22⋊C4—522no—
391C22⋊C4—522no—
392C22⋊C4—524no—
393C42—42no—
394C42—134no—
395C42—134no—
396C42—132no—
397C42—132no—
398C42—524no—
399C42—522no—
400C42C2×C4×D1312yes—
401C42Q8×D1312yes—
402C13#2198811yescharacteristic, complemented, Sylow
403C23—132no—
404C23—261no—
405C23—261no—
406C23—261no—
407C23—261no—
408C23—261no—
409C23—261no—
410C23C2×D4×D1311yescharacteristic
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—132no—
423C2×C4—132no—
424C2×C4—132no—
425C2×C4—261no—
426C2×C4—261no—
427C2×C4—261no—
428C2×C4—261no—
429C2×C4—261no—
430C2×C4—261no—
431C2×C4—262no—
432C2×C4—262no—
433C2×C4—262no—
434C2×C4—268no—
435C2×C4—262no—
436C2×C4—524no—
437C2×C4—521no—
438C2×C4—521no—
439C2×C4—522no—
440C2×C4—521no—
441C2×C4—522no—
442C2×C4—521no—
443C2×C4—522no—
444C2×C4—521no—
445C2×C4—521no—
446C2×C4C4⋊C4×D1312yes—
447C2×C4C4⋊C4×D1312yes—
448C2×C4#8816812yes—
449C2×C4#8816912yes—
450C2×C4C22×C4×D1311yescharacteristic
451C2×C4#8825111yescharacteristic
452C2×C4C2×Q8×D1311yescharacteristic
453C2×C4#8825411yescharacteristic
454C2×C4#8825611yescharacteristic
455C2×C4#8825711yescharacteristic
456C8—24no—
457C8—264no—
458C22—262no—
459C22—262no—
460C22—262no—
461C22—521no—
462C22—521no—
463C22—521no—
464C22—521no—
465C22C2×C4⋊C4×D1311yescharacteristic
466C22#1171931211yescharacteristic
467C22#1171933311yescharacteristic
468C22C2×#8816811yescharacteristic
469C22C2×#8816911yescharacteristic
470C22#1171947811yescharacteristic
471C22#1171948211yescharacteristic
472C4—22no—
473C4—81no—
474C4—81no—
475C4—82no—
476C4—262no—
477C4—262no—
478C4—262no—
479C4—1041no—
480C4—1041no—
481C4—1042no—
482C4#1171852214yes—
483C4#1171925111yescharacteristic
484C4#1171927911yescharacteristic
485C4#1171939411yescharacteristic
486C4#1171943411yescharacteristic
487C2—522no—
488C2#1311745811yescharacteristic
489C2C2×#1171852211yescharacteristic
490C2#1312342311yescharacteristic
491C2#1312583011yescharacteristic
492C2#1312584511yescharacteristic
493C2#1312603211yescharacteristic
494C2#1312604911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1948C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1948D13
hypocenterC13#21988
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
4. #13115597C2semidirect
5. #13115595C2semidirect
6. #13115594C2semidirect
9. #13115001C2semidirect
10. #13114968C2semidirect
11. C13×#1948C2semidirect
37. #11718496C4semidirect
160. #1948D13semidirect
402. C13#21988semidirect

Maximal subgroups

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

subgroupindex
C2×#117184962
#131172412
#131172402
#131155972
#131155952
#131155942
#131150382
#131150342
#131150012
#131149682
C13×#19482
#2198813