Finite Group Databasebeta

← #15879520

Subgroups — #15879520

Order 3328.

1086 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×#11719435C211yesmaximal, characteristic
2C2×C8×Dic26C211yesmaximal, characteristic, complemented
3#13117795C211yesmaximal, characteristic, complemented
4#13115799C212yesmaximal, complemented
5#13115790C212yesmaximal, complemented
6#13115785C211yesmaximal, characteristic, complemented
7#13114845C212yesmaximal
8#13114833C211yesmaximal, characteristic
9C4×#88061C211yesmaximal, characteristic
10#13114650C212yesmaximal
11C13×#1990C211yesmaximal, characteristic, complemented
12C2×C13×C4⋊Q8C2211yescharacteristic
13C2×#88200—22no—
14#11719435—24no—
15#11719435C418yescomplemented
16C2×#88151—21no—
17C2×#88147C2212yes—
18C2×C4⋊C4×D13—21no—
19C2×#88144C2212yes—
20C2×C4×D52C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C13×#384C2211yescharacteristic
24C2×#88061C2211yescharacteristic
25C2×#88061C2211yescharacteristic
26C2×#88054C2212yes—
27C2×C8×Dic13C2212yes—
28#11718639—22no—
29#11718638C2212yes—
30C4⋊C4×Dic13—21no—
31C4⋊C4×Dic13C2212yes—
32#11718635—21no—
33C2×#88049C2212yes—
34C4×C4⋊Dic13C2211yescharacteristic
35C2×C4⋊#1055C2211yescharacteristic
36C8×Dic26—24no—
37C13×#340C2212yes—
38C13×#340C2212yes—
39#11718143C2211yescharacteristic
40#11718143C2211yescharacteristic
41#11718121C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44C22×Q8×C13—21no—
45C22×D52C2311yescharacteristic
46C22×C4×D13—21no—
47C22×C4×D13—22no—
48C22×Dic26D411yescharacteristic
49C22×C8×C13C2311yescharacteristic
50C22×C8×C13C2311yescharacteristic
51C13×C4⋊Q8—22no—
52C13×C4⋊Q8C2×C414yes—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4C2312yes—
57C2×C13×C4⋊C4C2312yes—
58C2×C42×C13C2311yescharacteristic
59#88200—216no—
60C2×#6103—21no—
61C2×#6103—22no—
62C2×C4⋊Dic13—22no—
63C2×C4⋊Dic13D411yescharacteristic
64C2×C4⋊Dic13C2311yescharacteristic
65C2×C4⋊Dic13C2311yescharacteristic
66C2×C4⋊Dic13C2311yescharacteristic
67C2×#6101—22no—
68C2×#6101D412yes—
69C2×C4×Dic13—21no—
70C2×C4×Dic13—22no—
71C2×C4×Dic13C2312yes—
72C22×#1055C2312yes—
73#88151—28no—
74#88147—24no—
75#88147C2×C418yes—
76C4⋊C4×D13—28no—
77#88144—24no—
78#88144C2×C418yes—
79C4×D52—22no—
80C4×D52C2×C414yes—
81C4×Dic26C2×C414yes—
82C4×Dic26D414yes—
83C4×C8×C13—22no—
84#88071—21no—
85#88071—22no—
86#88071—22no—
87#88071—22no—
88#88061—22no—
89#88061Q814yescomplemented
90#88054—24no—
91C8×Dic13—24no—
92#88049—24no—
93C4⋊#1055—22no—
94#22519—131nomaximal, Sylow
95C23×D13—21no—
96C2×Q8×C13—24no—
97C2×Q8×C13—81no—
98C2×Q8×C13—81no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2411yescharacteristic
104C22×Dic13—21no—
105C22×Dic13—21no—
106C22×Dic13—21no—
107C22×Dic13C2×D412yes—
108C22×Dic13C2×D412yes—
109C2×D52—21no—
110C2×D52—21no—
111C2×D52—21no—
112C2×D52C22×C412yes—
113C2×D52C2×Q812yes—
114C2×D52#4112yes—
115C2×C4×D13—24no—
116C2×C4×D13—28no—
117C2×C4×D13—42no—
118C2×C4×D13—42no—
119C2×C4×D13—82no—
120C2×C4×D13—82no—
121C2×Dic26—22no—
122C2×Dic26—22no—
123C2×Dic26C22⋊C414yes—
124C2×C8×C13—21no—
125C2×C8×C13—21no—
126C2×C8×C13—21no—
127C2×C8×C13—21no—
128C2×C8×C13—21no—
129C2×C8×C13C2×Q812yes—
130C13×C4⋊C4—24no—
131C13×C4⋊C4—22no—
132C13×C4⋊C4—22no—
133C13×C4⋊C4—22no—
134C13×C4⋊C4—42no—
135C13×C4⋊C4—81no—
136C13×C4⋊C4C22×C414yes—
137C42×C13C22×C412yes—
138C42×C13C2×D412yes—
139#6103—24no—
140#6103—28no—
141C4⋊Dic13—21no—
142C4⋊Dic13—21no—
143C4⋊Dic13—28no—
144C4⋊Dic13—21no—
145C4⋊Dic13—21no—
146C4⋊Dic13C22⋊C414yes—
147C4⋊Dic13C22×C412yes—
148C4⋊Dic13C2×Q812yes—
149#6101—28no—
150#6101C22⋊C418yes—
151C4×Dic13—42no—
152C4×Dic13—82no—
153C4×Dic13C22×C414yes—
154C4×Dic13C2×D414yes—
155C2×#1055—22no—
156C2×#1055—22no—
157C2×#1055—22no—
158C2×#554—131no—
159C2×C8×Q8—131no—
160#2355—131no—
161#1991—132no—
162#1990D1311yescharacteristic, complemented
163#1989—132no—
164#1987—131no—
165#1804—132no—
166#1802—131no—
167C4×#102—131no—
168C4×#102—132no—
169C23×C13C22×D411yescharacteristic
170C22×D13—22no—
171C22×D13—22no—
172C22×D13—22no—
173C22×D13—41no—
174C22×D13—41no—
175C22×D13—41no—
176C22×D13—41no—
177Q8×C13—84no—
178C2×C4×C13—21no—
179C2×C4×C13—21no—
180C2×C4×C13—24no—
181C2×C4×C13—42no—
182C2×C4×C13—42no—
183C2×C4×C13—42no—
184C2×C4×C13—42no—
185C2×C4×C13—42no—
186C2×C4×C13C2×C22⋊C412yes—
187C2×C4×C13C2×C22⋊C412yes—
188C2×C4×C13#13512yes—
189C2×C4×C13#13512yes—
190C2×C4×C13C23×C411yescharacteristic
191C2×C4×C13C22×D411yescharacteristic
192C2×C4×C13C22×Q811yescharacteristic
193C2×C4×C13C2×#4111yescharacteristic
194C2×C4×C132−1+411yescharacteristic
195C2×C4×C132−1+411yescharacteristic
196C2×Dic13—22no—
197C2×Dic13—22no—
198C2×Dic13—22no—
199C2×Dic13—22no—
200C2×Dic13—22no—
201C2×Dic13—22no—
202C2×Dic13—41no—
203C2×Dic13—41no—
204C2×Dic13—41no—
205C2×Dic13—41no—
206C2×Dic13—41no—
207C2×Dic13—41no—
208C2×Dic13—41no—
209C2×Dic13C2×C22⋊C414yes—
210C2×Dic13C2×C22⋊C414yes—
211D52—22no—
212D52—22no—
213D52—22no—
214D52C4×Q814yes—
215C4×D13—48no—
216C4×D13—88no—
217Dic26—28no—
218C8×C13—22no—
219C8×C13—41no—
220#1055—42no—
221#554—138no—
222#554—264no—
223C2×C4⋊Q8C2×D1311yescharacteristic
224C2×#125—132no—
225C2×C22⋊Q8—261no—
226C2×C22⋊Q8—262no—
227C2×C4×Q8—131no—
228C2×C4×D4—132no—
229C2×C4×D4—131no—
230C22×C4⋊C4—261no—
231C8×Q8—264no—
232C2×C4⋊C8—132no—
233C2×C4⋊C8—131no—
234C2×#102—131no—
235C2×#102—131no—
236C2×#102—132no—
237C2×C4×C8—132no—
238C2×C4×C8C2×D1311yescharacteristic
239#391—261no—
240#387—262no—
241#384C2×D1311yescharacteristic
242#382—132no—
243C4×C4⋊C4—132no—
244C4×C4⋊C4—131no—
245C4×C4⋊C4—261no—
246#340—131no—
247#340—131no—
248#340—132no—
249#340—132no—
250#340—132no—
251#340C2×D1312yes—
252#340C2×D1312yes—
253C22×C13C22×C22⋊C411yescharacteristic
254C22×C13#54811yescharacteristic
255C22×C13D4×Q811yescharacteristic
256C22×C13C2×#13511yescharacteristic
257C22×C13C2×#13511yescharacteristic
258C22×C13#57611yescharacteristic
259C22×C13#57711yescharacteristic
260C2×D13—24no—
261C2×D13—42no—
262C2×D13—42no—
263C2×D13—42no—
264C2×D13—42no—
265C2×D13—42no—
266C2×D13—42no—
267C4×C13—22no—
268C4×C13—44no—
269C4×C13—82no—
270C4×C13#41614yes—
271C4×C13C2×C4×Q811yescharacteristic
272C4×C13#51911yescharacteristic
273C4×C13#54811yescharacteristic
274C4×C13D4×Q811yescharacteristic
275Dic13—24no—
276Dic13—24no—
277Dic13—42no—
278Dic13—42no—
279Dic13—81no—
280C22×Q8—21no—
281C22×Q8—131no—
282C22×D4—131no—
283C23×C4—262no—
284C23×C4—261no—
285C22×C8—132no—
286C22×C8C22×D1311yescharacteristic
287C22×C8C22×D1311yescharacteristic
288C4⋊Q8—22no—
289C4⋊Q8C4×D1314yes—
290#125—138no—
291#125—264no—
292C22⋊Q8—268no—
293C22⋊Q8—2616no—
294C4×Q8—134no—
295C4×Q8—134no—
296C4×D4—138no—
297C4×D4—134no—
298C4×D4—264no—
299C4×D4—262no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—131no—
304C2×C4⋊C4—132no—
305C2×C4⋊C4—131no—
306C2×C4⋊C4—131no—
307C2×C4⋊C4—131no—
308C2×C4⋊C4—268no—
309C2×C4⋊C4—262no—
310C2×C4⋊C4—262no—
311C2×C4⋊C4C22×D1312yes—
312C2×C4⋊C4C22×D1312yes—
313C2×C22⋊C4—262no—
314C2×C22⋊C4—261no—
315C2×C42—132no—
316C2×C42—261no—
317C2×C42—262no—
318C2×C42C22×D1311yescharacteristic
319C4⋊C8—264no—
320C4⋊C8—262no—
321#102—134no—
322#102—264no—
323#102—262no—
324C4×C8—22no—
325C4×C8—264no—
326#95—262no—
327#95—262no—
328#95—262no—
329#95—261no—
330C2×C13Q8×C22⋊C411yescharacteristic
331C2×C13C2×#41611yescharacteristic
332C2×C13#289711yescharacteristic
333C2×C13#336011yescharacteristic
334C2×C13#336111yescharacteristic
335C2×C13#338011yescharacteristic
336C2×C13#338111yescharacteristic
337D13—44no—
338C24—261no—
339C2×Q8—24no—
340C2×Q8—81no—
341C2×Q8—81no—
342C2×Q8—134no—
343C2×Q8—262no—
344C2×Q8—262no—
345C2×D4—132no—
346C2×D4—132no—
347C2×D4—132no—
348C2×D4—261no—
349C2×D4—261no—
350C2×D4—261no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—132no—
354C22×C4—132no—
355C22×C4—268no—
356C22×C4—261no—
357C22×C4—261no—
358C22×C4—264no—
359C22×C4—261no—
360C22×C4—522no—
361C22×C4—522no—
362C22×C4—1042no—
363C22×C4—1042no—
364C22×C4D4×D1311yescharacteristic
365C22×C4D4×D1311yescharacteristic
366C22×C4C23×D1311yescharacteristic
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—262no—
373C2×C8—262no—
374C2×C8—262no—
375C2×C8Q8×D1312yes—
376C4⋊C4—24no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—42no—
381C4⋊C4—81no—
382C4⋊C4—134no—
383C4⋊C4—138no—
384C4⋊C4—132no—
385C4⋊C4—132no—
386C4⋊C4—268no—
387C4⋊C4—268no—
388C4⋊C4—261no—
389C4⋊C4—261no—
390C4⋊C4—261no—
391C4⋊C4—261no—
392C4⋊C4C2×C4×D1314yes—
393C22⋊C4—268no—
394C22⋊C4—264no—
395C42—134no—
396C42—134no—
397C42—522no—
398C42—1042no—
399C42C2×C4×D1312yes—
400C42D4×D1312yes—
401C13#2251911yescharacteristic, complemented, Sylow
402C23—262no—
403C23—262no—
404C23—262no—
405C23—521no—
406C23—521no—
407C23—521no—
408C23—521no—
409C23C2×D4×D1311yescharacteristic
410Q8—84no—
411Q8—268no—
412D4—134no—
413D4—262no—
414D4—262no—
415D4—262no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—24no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—134no—
425C2×C4—134no—
426C2×C4—262no—
427C2×C4—262no—
428C2×C4—262no—
429C2×C4—262no—
430C2×C4—262no—
431C2×C4—262no—
432C2×C4—521no—
433C2×C4—521no—
434C2×C4—521no—
435C2×C4—521no—
436C2×C4—528no—
437C2×C4—521no—
438C2×C4—521no—
439C2×C4—521no—
440C2×C4—1048no—
441C2×C4C22⋊C4×D1312yes—
442C2×C4C22⋊C4×D1312yes—
443C2×C4#8817012yes—
444C2×C4#8817312yes—
445C2×C4C22×C4×D1311yescharacteristic
446C2×C4C2×D4×D1311yescharacteristic
447C2×C4C2×Q8×D1311yescharacteristic
448C2×C4#8825411yescharacteristic
449C2×C4#41×D1311yescharacteristic
450C2×C4#8825711yescharacteristic
451C8—22no—
452C8—41no—
453C8—522no—
454C22—264no—
455C22—522no—
456C22—522no—
457C22—522no—
458C22—522no—
459C22—522no—
460C22—522no—
461C22C2×C22⋊C4×D1311yescharacteristic
462C22#1171938211yescharacteristic
463C22#1171943211yescharacteristic
464C22#1171946211yescharacteristic
465C22C2×#8817011yescharacteristic
466C22#1171946711yescharacteristic
467C22C2×#8817311yescharacteristic
468C4—22no—
469C4—44no—
470C4—82no—
471C4—264no—
472C4—264no—
473C4—522no—
474C4—522no—
475C4—1041no—
476C4#1171846514yes—
477C4C4×Q8×D1311yescharacteristic
478C4#1171927711yescharacteristic
479C4#1171933711yescharacteristic
480C4#1171933811yescharacteristic
481C2—524no—
482C2#1311767011yescharacteristic
483C2C2×#1171846511yescharacteristic
484C2#1312335711yescharacteristic
485C2#1312749011yescharacteristic
486C2#1312750111yescharacteristic
487C2#1312770511yescharacteristic
488C2#1312771611yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1990C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1990D13
hypocenterC13#22519
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic26C2semidirect
3. #13117795C2semidirect
4. #13115799C2semidirect
5. #13115790C2semidirect
6. #13115785C2semidirect
11. C13×#1990C2semidirect
15. #11719435C4semidirect
89. #88061Q8semidirect
162. #1990D13semidirect
401. C13#22519semidirect

Maximal subgroups

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

subgroupindex
C2×#117194352
C2×C8×Dic262
#131177952
#131157992
#131157902
#131157852
#131148452
#131148332
C4×#880612
#131146502
C13×#19902
#2251913