Finite Group Databasebeta

← #15873309

Subgroups — #15873309

Order 3328.

830 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718498C211yesmaximal, characteristic
2#13117241C211yesmaximal, characteristic
3#13117232C211yesmaximal, characteristic
4#13115607C212yesmaximal, complemented
5#13115605C212yesmaximal, complemented
6#13115599C211yesmaximal, characteristic, complemented
7#13115595C211yesmaximal, characteristic, complemented
8#13115592C211yesmaximal, characteristic, complemented
9#13114868C212yesmaximal
10#13114866C212yesmaximal
11C13×#1948C211yesmaximal, characteristic, complemented
12C22×#6094C2212yes—
13C2×#88146—21no—
14C2×C42×D13C2211yescharacteristic
15C2×C13×#106C2212yes—
16C2×C13×C4⋊C8C2211yescharacteristic
17C13×#384C2211yescharacteristic
18C4×C13×C4⋊C4C2211yescharacteristic
19C2×#88058C2212yes—
20C2×#88054C2212yes—
21#11718648—21no—
22#11718648C2211yescharacteristic
23#11718648C2211yescharacteristic
24#11718648C2212yes—
25#11718638—21no—
26#11718638C2211yescharacteristic
27#11718638C2211yescharacteristic
28C4⋊C4×Dic13—21no—
29C4⋊C4×Dic13C2212yes—
30C2×#88048C2212yes—
31C2×#88047C2212yes—
32C4×#6103—21no—
33#11718596C2211yescharacteristic
34C4×C4⋊Dic13C2211yescharacteristic
35#11718593—21no—
36C2×C4⋊#1055C2211yescharacteristic
37#11718498C418yescomplemented
38#11718325—21no—
39#11718312—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—22no—
56C2×#6103—21no—
57C2×#6103—21no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13C2311yescharacteristic
61C2×C4⋊Dic13C2312yes—
62C2×C4⋊Dic13C2311yescharacteristic
63C2×C4×Dic13—21no—
64C2×C4×Dic13—22no—
65C2×C4×Dic13D411yescharacteristic
66C2×C4×Dic13D411yescharacteristic
67C2×C4×Dic13C2311yescharacteristic
68C22×#1055C2312yes—
69C2×#6094—42no—
70C2×#6094—42no—
71C2×#6094C2×C418yes—
72#88146—44no—
73C42×D13C2×C414yes—
74C42×D13Q814yes—
75C13×#106—42no—
76C13×C4⋊C8C2×C414yes—
77C13×#95—21no—
78#88071—21no—
79#88071—21no—
80#88071—21no—
81#88071—21no—
82#88071—21no—
83#88071—21no—
84#88071—21no—
85#88071—22no—
86#88071—22no—
87#88058—42no—
88#88054C2×C418yes—
89#88048—42no—
90#88047—42no—
91C4⋊#1055C2×C414yes—
92#21963—131nomaximal, Sylow
93C23×D13C2×D411yescharacteristic
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—22no—
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—21no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4—22no—
127C13×C4⋊C4—42no—
128C13×C4⋊C4—42no—
129C42×C13—42no—
130C42×C13C22×C412yes—
131C42×C13C2×Q812yes—
132#6103—44no—
133#6103—42no—
134#6103—42no—
135C4⋊Dic13—21no—
136C4⋊Dic13—22no—
137C4⋊Dic13—21no—
138C4⋊Dic13—21no—
139C4⋊Dic13—22no—
140C4⋊Dic13—21no—
141C4⋊Dic13—42no—
142C4⋊Dic13—42no—
143C4×Dic13—44no—
144C4×Dic13—42no—
145C4×Dic13C4⋊C414yes—
146C4×Dic13C4⋊C414yes—
147C4×Dic13C22×C412yes—
148C4×Dic13C2×Q812yes—
149C2×#1055—22no—
150C2×#1055—22no—
151C2×#1055C22×C414yes—
152#6094—48no—
153C2×#423—131no—
154#2285—131no—
155#2283—131no—
156#1949—132no—
157#1949—132no—
158#1948—131no—
159#1948D1311yescharacteristic, complemented
160#1947—131no—
161#1947—131no—
162#1809—132no—
163#1809—132no—
164C23×C13C22×D411yescharacteristic
165C22×D13—21no—
166C22×D13—21no—
167C22×D13—21no—
168C22×D13—21no—
169C22×D13—21no—
170C22×D13—21no—
171C22×D13C2×C4⋊C412yes—
172C2×C4×C13—21no—
173C2×C4×C13—21no—
174C2×C4×C13—42no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
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×C13C2×C4⋊C412yes—
184C2×C4×C13C2×C4⋊C412yes—
185C2×C4×C13AGL(1,ℤ/8)12yes—
186C2×C4×C13#13712yes—
187C2×C4×C13C23×C411yescharacteristic
188C2×C4×C13C22×Q811yescharacteristic
189C2×C4×C13H(5,𝔽2)11yescharacteristic
190C2×C4×C13H(5,𝔽2)11yescharacteristic
191C2×C4×C132−1+411yescharacteristic
192C2×C4×C132−1+411yescharacteristic
193C2×Dic13—21no—
194C2×Dic13—21no—
195C2×Dic13—21no—
196C2×Dic13—21no—
197C2×Dic13—21no—
198C2×Dic13—21no—
199C2×Dic13—41no—
200C2×Dic13—42no—
201C2×Dic13—41no—
202C2×Dic13—42no—
203C2×Dic13—41no—
204C2×Dic13—41no—
205C2×Dic13—42no—
206C2×Dic13—41no—
207C2×Dic13—41no—
208C2×Dic13C2×C4⋊C412yes—
209C2×Dic13C2×C4⋊C412yes—
210C2×Dic13C2×C4⋊C412yes—
211C4×D13—22no—
212C4×D13—22no—
213C4×D13—22no—
214C4×D13—22no—
215C4×D13—28no—
216C4×D13—44no—
217C8×C13—24no—
218#1055—24no—
219C22×M16—132no—
220C2×#117—261no—
221C22×C42—131no—
222C2×#107—132no—
223C2×#107—132no—
224C2×#106—132no—
225C2×#106C2×D1312yes—
226#423—138no—
227C2×C4⋊C8—132no—
228C2×C4⋊C8—131no—
229C2×C4⋊C8C2×D1311yescharacteristic
230#384—131no—
231#384C2×D1311yescharacteristic
232#383—261no—
233#382—131no—
234#382—131no—
235#382—261no—
236#381—261no—
237#380—131no—
238#380—131no—
239#380—132no—
240#380—261no—
241C4×C4⋊C4—132no—
242C4×C4⋊C4—131no—
243C4×C4⋊C4—261no—
244C4×C4⋊C4C2×D1311yescharacteristic
245C4×C22⋊C4—261no—
246#376—261no—
247#340—132no—
248#340—132no—
249#340—132no—
250#340C2×D1312yes—
251C22×C13C22×C4⋊C411yescharacteristic
252C22×C13#53711yescharacteristic
253C22×C13#53711yescharacteristic
254C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
255C22×C13C2×#13711yescharacteristic
256C22×C13#57511yescharacteristic
257C22×C13#57511yescharacteristic
258C2×D13—22no—
259C2×D13—22no—
260C2×D13—22no—
261C2×D13—41no—
262C2×D13—41no—
263C2×D13—41no—
264C2×D13—41no—
265C4×C13—22no—
266C4×C13—82no—
267C4×C13—81no—
268C4×C13—81no—
269C4×C13#42814yes—
270C4×C13#51811yescharacteristic
271C4×C13#51911yescharacteristic
272C4×C13#54411yescharacteristic
273C4×C13#54411yescharacteristic
274Dic13—22no—
275Dic13—22no—
276Dic13—22no—
277Dic13—81no—
278Dic13—82no—
279Dic13—81no—
280C23×C4—131no—
281C23×C4—131no—
282C23×C4—131no—
283C2×M16—138no—
284C2×M16—522no—
285C2×M16—522no—
286C22×C8—132no—
287C22×C8C22×D1312yes—
288#117—524no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—131no—
292C2×C4⋊C4—131no—
293C2×C4⋊C4—132no—
294C2×C4⋊C4—261no—
295C2×C4⋊C4—261no—
296C2×C4⋊C4C22×D1311yescharacteristic
297C2×C4⋊C4C22×D1312yes—
298C2×C4⋊C4C22×D1311yescharacteristic
299C2×C22⋊C4—262no—
300C2×C22⋊C4—261no—
301C2×C22⋊C4—261no—
302C2×C42—21no—
303C2×C42—131no—
304C2×C42—131no—
305C2×C42—131no—
306C2×C42—134no—
307C2×C42—134no—
308C2×C42—262no—
309C2×C42—261no—
310C2×C42C22×D1311yescharacteristic
311#107—522no—
312#107—522no—
313#106—42no—
314#106—522no—
315C4⋊C8—138no—
316C4⋊C8—134no—
317C4⋊C8C4×D1314yes—
318#95—21no—
319#95—261no—
320#95—261no—
321#95—261no—
322#95—261no—
323#95—261no—
324#95—261no—
325#95—262no—
326#95—262no—
327#95—261no—
328C2×C13#231611yescharacteristic
329C2×C13C2×#42811yescharacteristic
330C2×C13#291111yescharacteristic
331C2×C13#325111yescharacteristic
332C2×C13#325111yescharacteristic
333C2×C13#325211yescharacteristic
334C2×C13#325211yescharacteristic
335D13—42no—
336C24—131no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—131no—
341C22×C4—131no—
342C22×C4—131no—
343C22×C4—134no—
344C22×C4—132no—
345C22×C4—132no—
346C22×C4—134no—
347C22×C4—262no—
348C22×C4—262no—
349C22×C4—261no—
350C22×C4—261no—
351C22×C4—261no—
352C22×C4—261no—
353C22×C4—261no—
354C22×C4—261no—
355C22×C4—262no—
356C22×C4—521no—
357C22×C4—521no—
358C22×C4D4×D1311yescharacteristic
359C22×C4D4×D1311yescharacteristic
360C22×C4C23×D1311yescharacteristic
361M16—528no—
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—134no—
365C2×C8—262no—
366C2×C8—262no—
367C2×C8C2×C4×D1314yes—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—261no—
377C4⋊C4—261no—
378C4⋊C4—262no—
379C4⋊C4—262no—
380C4⋊C4—261no—
381C4⋊C4—261no—
382C4⋊C4—522no—
383C4⋊C4—522no—
384C22⋊C4—524no—
385C22⋊C4—522no—
386C22⋊C4—522no—
387C42—42no—
388C42—134no—
389C42—134no—
390C42—132no—
391C42—132no—
392C42—524no—
393C42—522no—
394C42C2×C4×D1312yes—
395C42Q8×D1312yes—
396C13#2196311yescharacteristic, complemented, Sylow
397C23—132no—
398C23—261no—
399C23—261no—
400C23—261no—
401C23—261no—
402C23—261no—
403C23—261no—
404C23C2×D4×D1311yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—132no—
417C2×C4—132no—
418C2×C4—132no—
419C2×C4—261no—
420C2×C4—261no—
421C2×C4—261no—
422C2×C4—261no—
423C2×C4—261no—
424C2×C4—261no—
425C2×C4—262no—
426C2×C4—262no—
427C2×C4—262no—
428C2×C4—268no—
429C2×C4—262no—
430C2×C4—524no—
431C2×C4—522no—
432C2×C4—521no—
433C2×C4—521no—
434C2×C4—521no—
435C2×C4—521no—
436C2×C4—522no—
437C2×C4—521no—
438C2×C4—522no—
439C2×C4—521no—
440C2×C4C4⋊C4×D1312yes—
441C2×C4C4⋊C4×D1312yes—
442C2×C4#8816812yes—
443C2×C4#8816912yes—
444C2×C4C22×C4×D1311yescharacteristic
445C2×C4#8825111yescharacteristic
446C2×C4C2×Q8×D1311yescharacteristic
447C2×C4#8825411yescharacteristic
448C2×C4#8825611yescharacteristic
449C2×C4#8825711yescharacteristic
450C8—24no—
451C8—264no—
452C22—262no—
453C22—262no—
454C22—262no—
455C22—521no—
456C22—521no—
457C22—521no—
458C22—521no—
459C22C2×C4⋊C4×D1311yescharacteristic
460C22#1171931311yescharacteristic
461C22#1171933411yescharacteristic
462C22C2×#8816811yescharacteristic
463C22C2×#8816911yescharacteristic
464C22#1171947811yescharacteristic
465C22#1171948211yescharacteristic
466C4—22no—
467C4—82no—
468C4—81no—
469C4—81no—
470C4—262no—
471C4—262no—
472C4—262no—
473C4—1041no—
474C4—1042no—
475C4—1041no—
476C4#1171852214yes—
477C4#1171925011yescharacteristic
478C4#1171927711yescharacteristic
479C4#1171939411yescharacteristic
480C4#1171943411yescharacteristic
481C2—522no—
482C2#1311745111yescharacteristic
483C2C2×#1171852211yescharacteristic
484C2#1312342311yescharacteristic
485C2#1312619611yescharacteristic
486C2#1312620111yescharacteristic
487C2#1312620511yescharacteristic
488C2#1312621111yescharacteristic
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#21963
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. #13115607C2semidirect
5. #13115605C2semidirect
6. #13115599C2semidirect
7. #13115595C2semidirect
8. #13115592C2semidirect
11. C13×#1948C2semidirect
37. #11718498C4semidirect
159. #1948D13semidirect
396. C13#21963semidirect

Maximal subgroups

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

subgroupindex
C2×#117184982
#131172412
#131172322
#131156072
#131156052
#131155992
#131155952
#131155922
#131148682
#131148662
C13×#19482
#2196313