Finite Group Databasebeta

← #15873465

Subgroups — #15873465

Order 3328.

806 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718494C211yesmaximal, characteristic
2#13117241C211yesmaximal, characteristic
3#13117232C211yesmaximal, characteristic
4#13115599C211yesmaximal, characteristic, complemented
5#13115597C211yesmaximal, characteristic, complemented
6#13115595C211yesmaximal, characteristic, complemented
7#13115038C212yesmaximal
8#13115032C212yesmaximal
9#13114999C212yesmaximal, complemented
10#13114965C212yesmaximal, complemented
11C13×#1947C211yesmaximal, characteristic, complemented
12C2×#88146C2212yes—
13C2×C42×D13C2211yescharacteristic
14C2×C13×#107C2212yes—
15C2×C13×C4⋊C8C2211yescharacteristic
16C13×#384C2211yescharacteristic
17C4×C13×C4⋊C4C2211yescharacteristic
18C2×#88060C2212yes—
19C2×#88058C2212yes—
20C2×C8×Dic13C2212yes—
21#11718648—21no—
22#11718648—21no—
23#11718648C2211yescharacteristic
24#11718648C2211yescharacteristic
25#11718638C2211yescharacteristic
26#11718638C2211yescharacteristic
27#11718638C2212yes—
28C4⋊C4×Dic13—21no—
29C4⋊C4×Dic13—21no—
30C2×#88048C2212yes—
31C2×#88048C2212yes—
32C4×#6103—21no—
33#11718596C2211yescharacteristic
34C4×C4⋊Dic13C2211yescharacteristic
35#11718593—21no—
36C2×C4⋊#1055C2211yescharacteristic
37#11718494C418yescomplemented
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⋊Dic13C2312yes—
61C2×C4⋊Dic13C2311yescharacteristic
62C2×C4⋊Dic13C2311yescharacteristic
63C2×C4×Dic13—21no—
64C2×C4×Dic13—22no—
65C2×C4×Dic13D411yescharacteristic
66C2×C4×Dic13D411yescharacteristic
67C2×C4×Dic13C2311yescharacteristic
68C22×#1055C2312yes—
69#88146—42no—
70#88146—42no—
71C42×D13C2×C414yes—
72C42×D13Q814yes—
73C13×#107—42no—
74C13×C4⋊C8C2×C414yes—
75C13×#95—21no—
76#88071—21no—
77#88071—21no—
78#88071—21no—
79#88071—21no—
80#88071—21no—
81#88071—21no—
82#88071—21no—
83#88071—22no—
84#88071—22no—
85#88060C2×C418yes—
86#88058—42no—
87C8×Dic13C2×C418yes—
88#88048—42no—
89#88048—42no—
90C4⋊#1055C2×C414yes—
91#21985—131nomaximal, Sylow
92C23×D13C2×D411yescharacteristic
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—22no—
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2411yescharacteristic
99C22×Dic13—21no—
100C22×Dic13—21no—
101C22×Dic13—22no—
102C22×Dic13C2×D411yescharacteristic
103C22×Dic13C2×D411yescharacteristic
104C22×Dic13C2×D411yescharacteristic
105C2×C4×D13—22no—
106C2×C4×D13—22no—
107C2×C4×D13—21no—
108C2×C4×D13—21no—
109C2×C4×D13—21no—
110C2×C4×D13—21no—
111C2×C4×D13—41no—
112C2×C4×D13—41no—
113C2×C4×D13C4⋊C414yes—
114C2×C4×D13C4⋊C414yes—
115C2×C4×D13C22×C412yes—
116C2×C4×D13C2×Q812yes—
117C2×C8×C13—22no—
118C2×C8×C13—22no—
119C2×C8×C13C22×C414yes—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4—42no—
127C13×C4⋊C4—42no—
128C42×C13—42no—
129C42×C13C22×C412yes—
130C42×C13C2×Q812yes—
131#6103—44no—
132#6103—42no—
133#6103—42no—
134C4⋊Dic13—22no—
135C4⋊Dic13—22no—
136C4⋊Dic13—21no—
137C4⋊Dic13—21no—
138C4⋊Dic13—21no—
139C4⋊Dic13—21no—
140C4⋊Dic13—42no—
141C4⋊Dic13—42no—
142C4×Dic13—44no—
143C4×Dic13—42no—
144C4×Dic13C4⋊C414yes—
145C4×Dic13C4⋊C414yes—
146C4×Dic13C22×C412yes—
147C4×Dic13C2×Q812yes—
148C2×#1055—22no—
149C2×#1055—22no—
150C2×#1055C22×C414yes—
151C2×#431—131no—
152#2285—131no—
153#2283—131no—
154#1948—131no—
155#1948—131no—
156#1947—131no—
157#1947D1311yescharacteristic, complemented
158#1854—132no—
159#1854—132no—
160#1846—132no—
161#1835—132no—
162C23×C13C22×D411yescharacteristic
163C22×D13—21no—
164C22×D13—21no—
165C22×D13—21no—
166C22×D13—21no—
167C22×D13—21no—
168C22×D13—21no—
169C22×D13C2×C4⋊C412yes—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—42no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—42no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—42no—
181C2×C4×C13C2×C4⋊C412yes—
182C2×C4×C13C2×C4⋊C412yes—
183C2×C4×C13#13512yes—
184C2×C4×C13#13512yes—
185C2×C4×C13C23×C411yescharacteristic
186C2×C4×C13C22×Q811yescharacteristic
187C2×C4×C13H(5,𝔽2)11yescharacteristic
188C2×C4×C13H(5,𝔽2)11yescharacteristic
189C2×C4×C132−1+411yescharacteristic
190C2×C4×C132−1+411yescharacteristic
191C2×Dic13—21no—
192C2×Dic13—21no—
193C2×Dic13—21no—
194C2×Dic13—21no—
195C2×Dic13—21no—
196C2×Dic13—21no—
197C2×Dic13—42no—
198C2×Dic13—41no—
199C2×Dic13—41no—
200C2×Dic13—41no—
201C2×Dic13—41no—
202C2×Dic13—42no—
203C2×Dic13—42no—
204C2×Dic13—41no—
205C2×Dic13—41no—
206C2×Dic13C2×C4⋊C412yes—
207C2×Dic13C2×C4⋊C412yes—
208C2×Dic13C2×C4⋊C412yes—
209C4×D13—22no—
210C4×D13—22no—
211C4×D13—22no—
212C4×D13—22no—
213C4×D13—28no—
214C4×D13—44no—
215C8×C13—24no—
216#1055—24no—
217C2×#117—132no—
218C22×C42—131no—
219#431—138no—
220C2×#107—132no—
221C2×#107C2×D1312yes—
222C2×#106—132no—
223C2×#106—132no—
224C2×C4⋊C8—131no—
225C2×C4⋊C8C2×D1311yescharacteristic
226C2×C22⋊C8—132no—
227C2×C4×C8—132no—
228#384—131no—
229#384C2×D1311yescharacteristic
230#383—261no—
231#382—131no—
232#382—132no—
233#382—131no—
234#381—261no—
235#380—131no—
236#380—131no—
237#380—261no—
238#380—261no—
239C4×C4⋊C4—131no—
240C4×C4⋊C4—261no—
241C4×C4⋊C4—261no—
242C4×C4⋊C4C2×D1311yescharacteristic
243C4×C22⋊C4—261no—
244#376—261no—
245#340—132no—
246#340—132no—
247#340—132no—
248#340C2×D1312yes—
249C22×C13C22×C4⋊C411yescharacteristic
250C22×C13#53511yescharacteristic
251C22×C13#53611yescharacteristic
252C22×C13C2×#13511yescharacteristic
253C22×C13C2×#13511yescharacteristic
254C22×C13#57511yescharacteristic
255C22×C13#57511yescharacteristic
256C2×D13—22no—
257C2×D13—22no—
258C2×D13—22no—
259C2×D13—41no—
260C2×D13—41no—
261C2×D13—41no—
262C2×D13—41no—
263C4×C13—22no—
264C4×C13—82no—
265C4×C13—81no—
266C4×C13—81no—
267C4×C13#42714yes—
268C4×C13#52011yescharacteristic
269C4×C13#52011yescharacteristic
270C4×C13#54411yescharacteristic
271C4×C13#54411yescharacteristic
272Dic13—22no—
273Dic13—22no—
274Dic13—22no—
275Dic13—82no—
276Dic13—81no—
277Dic13—81no—
278C23×C4—131no—
279C23×C4—131no—
280C23×C4—131no—
281C22×C8—132no—
282C22×C8C22×D1312yes—
283#117—522no—
284#117—522no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—132no—
288C2×C4⋊C4—131no—
289C2×C4⋊C4—131no—
290C2×C4⋊C4—261no—
291C2×C4⋊C4—261no—
292C2×C4⋊C4C22×D1312yes—
293C2×C4⋊C4C22×D1311yescharacteristic
294C2×C4⋊C4C22×D1311yescharacteristic
295C2×C22⋊C4—262no—
296C2×C22⋊C4—261no—
297C2×C22⋊C4—261no—
298C2×C42—21no—
299C2×C42—131no—
300C2×C42—131no—
301C2×C42—131no—
302C2×C42—134no—
303C2×C42—134no—
304C2×C42—262no—
305C2×C42—261no—
306C2×C42C22×D1311yescharacteristic
307#107—42no—
308#107—522no—
309#106—522no—
310#106—522no—
311C4⋊C8—134no—
312C4⋊C8C4×D1314yes—
313C22⋊C8—138no—
314C4×C8—138no—
315#95—21no—
316#95—261no—
317#95—261no—
318#95—261no—
319#95—261no—
320#95—261no—
321#95—261no—
322#95—262no—
323#95—262no—
324#95—261no—
325C2×C13#231711yescharacteristic
326C2×C13C2×#42711yescharacteristic
327C2×C13#291111yescharacteristic
328C2×C13#321211yescharacteristic
329C2×C13#321211yescharacteristic
330C2×C13#323311yescharacteristic
331C2×C13#323311yescharacteristic
332D13—42no—
333C24—131no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—131no—
338C22×C4—131no—
339C22×C4—131no—
340C22×C4—134no—
341C22×C4—132no—
342C22×C4—132no—
343C22×C4—134no—
344C22×C4—262no—
345C22×C4—262no—
346C22×C4—261no—
347C22×C4—261no—
348C22×C4—261no—
349C22×C4—261no—
350C22×C4—261no—
351C22×C4—261no—
352C22×C4—262no—
353C22×C4—521no—
354C22×C4—521no—
355C22×C4D4×D1311yescharacteristic
356C22×C4D4×D1311yescharacteristic
357C22×C4C23×D1311yescharacteristic
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—134no—
361C2×C8—262no—
362C2×C8—262no—
363C2×C8C2×C4×D1314yes—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—42no—
371C4⋊C4—42no—
372C4⋊C4—261no—
373C4⋊C4—262no—
374C4⋊C4—261no—
375C4⋊C4—261no—
376C4⋊C4—262no—
377C4⋊C4—261no—
378C4⋊C4—522no—
379C4⋊C4—522no—
380C22⋊C4—524no—
381C22⋊C4—522no—
382C22⋊C4—522no—
383C42—42no—
384C42—134no—
385C42—134no—
386C42—132no—
387C42—132no—
388C42—524no—
389C42—522no—
390C42C2×C4×D1312yes—
391C42Q8×D1312yes—
392C13#2198511yescharacteristic, complemented, Sylow
393C23—132no—
394C23—261no—
395C23—261no—
396C23—261no—
397C23—261no—
398C23—261no—
399C23—261no—
400C23C2×D4×D1311yescharacteristic
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—132no—
413C2×C4—132no—
414C2×C4—132no—
415C2×C4—261no—
416C2×C4—261no—
417C2×C4—261no—
418C2×C4—261no—
419C2×C4—261no—
420C2×C4—261no—
421C2×C4—262no—
422C2×C4—262no—
423C2×C4—262no—
424C2×C4—268no—
425C2×C4—262no—
426C2×C4—524no—
427C2×C4—521no—
428C2×C4—521no—
429C2×C4—522no—
430C2×C4—521no—
431C2×C4—521no—
432C2×C4—522no—
433C2×C4—522no—
434C2×C4—521no—
435C2×C4—521no—
436C2×C4C4⋊C4×D1312yes—
437C2×C4C4⋊C4×D1312yes—
438C2×C4#8816612yes—
439C2×C4#8817312yes—
440C2×C4C22×C4×D1311yescharacteristic
441C2×C4#8825111yescharacteristic
442C2×C4C2×Q8×D1311yescharacteristic
443C2×C4#8825411yescharacteristic
444C2×C4#8825611yescharacteristic
445C2×C4#8825711yescharacteristic
446C8—24no—
447C8—264no—
448C22—262no—
449C22—262no—
450C22—262no—
451C22—521no—
452C22—521no—
453C22—521no—
454C22—521no—
455C22C2×C4⋊C4×D1311yescharacteristic
456C22#1171931211yescharacteristic
457C22#1171933311yescharacteristic
458C22C2×#8816611yescharacteristic
459C22C2×#8817311yescharacteristic
460C22#1171947811yescharacteristic
461C22#1171948211yescharacteristic
462C4—22no—
463C4—81no—
464C4—81no—
465C4—82no—
466C4—262no—
467C4—262no—
468C4—262no—
469C4—1041no—
470C4—1041no—
471C4—1042no—
472C4#1171854114yes—
473C4#1171925111yescharacteristic
474C4#1171927911yescharacteristic
475C4#1171939411yescharacteristic
476C4#1171943411yescharacteristic
477C2—522no—
478C2#1311745811yescharacteristic
479C2C2×#1171854111yescharacteristic
480C2#1312342311yescharacteristic
481C2#1312581011yescharacteristic
482C2#1312581711yescharacteristic
483C2#1312601311yescharacteristic
484C2#1312602011yescharacteristic
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#21985
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. #13115599C2semidirect
5. #13115597C2semidirect
6. #13115595C2semidirect
9. #13114999C2semidirect
10. #13114965C2semidirect
11. C13×#1947C2semidirect
37. #11718494C4semidirect
157. #1947D13semidirect
392. C13#21985semidirect

Maximal subgroups

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

subgroupindex
C2×#117184942
#131172412
#131172322
#131155992
#131155972
#131155952
#131150382
#131150322
#131149992
#131149652
C13×#19472
#2198513