Finite Group Databasebeta

← #15830629

Subgroups — #15830629

Order 3328.

1070 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
1#13128637C211yesmaximal, characteristic
2#13123859C211yesmaximal, characteristic
3#13117747C211yesmaximal, characteristic
4#13113406C214yesmaximal, complemented
5#13113401C211yesmaximal, characteristic, complemented
6#13113400C211yesmaximal, characteristic, complemented
7#13113334C211yesmaximal, characteristic, complemented
8D13×#328C214yesmaximal, complemented
9C13×#1503C211yesmaximal, characteristic, complemented
10C13×#533C2211yescharacteristic
11#11719435C412yescomplemented
12#11719432C412yescomplemented
13#11719395—22no—
14#11719339—22no—
15D13×C22⋊Q8C2214yes—
16#11719284—22no—
17#11719284C412yescomplemented
18Q8×D52C412yescomplemented
19#11719226—21no—
20#11719224—21no—
21C2×C4×D52—21no—
22C2×C4×D52C2211yescharacteristic
23#11719175C2211yescharacteristic
24C13×#431C2211yescharacteristic
25C4×C13×C4⋊C4C2211yescharacteristic
26#11718650—22no—
27#11718597C2211yescharacteristic
28#11718589—21no—
29#11718586C2211yescharacteristic
30#11718495—22no—
31D13×C22⋊C8C2214yes—
32C8×D52—22no—
33#11718328C2212yes—
34D13×#95C2212yes—
35C13×#328C2212yes—
36C13×#328C2212yes—
37#11718130C2214yes—
38#11718059C2214yes—
39#11718044C2212yes—
40#11718044C2212yes—
41C2×Q8×D13C2×C414yescomplemented
42C22×D52D411yescharacteristic
43C22×C4×D13—22no—
44C22×C4×D13C2312yes—
45C13×C4⋊Q8C2×C411yescharacteristic, complemented
46C13×C4⋊Q8C2×C411yescharacteristic, complemented
47C13×#125—21no—
48C13×C22⋊Q8—21no—
49C13×C22⋊Q8C2312yes—
50C4×Q8×C13—21no—
51C4×Q8×C13C2×C412yescomplemented
52C13×#117—21no—
53C2×C13×C4⋊C4—21no—
54C2×C42×C13—21no—
55C2×C42×C13C2311yescharacteristic
56#88200—24no—
57#88200C2×C414yescomplemented
58C2×#6103—22no—
59C2×#6103D412yes—
60#88180—21no—
61C2×C4⋊Dic13—21no—
62C2×C4⋊Dic13D411yescharacteristic
63#88178—21no—
64#88178C2312yes—
65C2×#6101—22no—
66C2×C8×D13—24no—
67#88151—24no—
68#88151C2×C414yescomplemented
69#88150—24no—
70#88150—24no—
71#88150—24no—
72#88147—22no—
73#88147—22no—
74C4⋊C4×D13—24no—
75C4⋊C4×D13C2×C414yescomplemented
76#88144—22no—
77#88142—22no—
78C22⋊C4×D13—24no—
79#88132—24no—
80C4×D52—22no—
81C4×D52—22no—
82C4×D52—44no—
83C4×D52C2×C412yes—
84C4×D52C2×C412yes—
85C4×D52D412yes—
86C4×D52D412yes—
87#88124—21no—
88#88124—22no—
89#88123—22no—
90#88123C2×C411yescharacteristic, complemented
91#88123C2×C411yescharacteristic, complemented
92C4×Dic26—21no—
93C4×Dic26C2×C412yescomplemented
94C13×C4⋊C8—21no—
95C13×C22⋊C8C2312yes—
96C4×C8×C13—21no—
97C13×#95C2311yescharacteristic
98C13×#95C2311yescharacteristic
99#88071—21no—
100#88071—22no—
101#88071C2312yes—
102C22⋊#1055C2312yes—
103#88060—24no—
104C4⋊#1055—21no—
105C4×#1055—21no—
106#17614—131nomaximal, Sylow
107C23×D13C2×D412yes—
108C2×Q8×C13—21no—
109C2×Q8×C13C22×C412yes—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2411yescharacteristic
115C22×Dic13—22no—
116C22×Dic13C2×D412yes—
117Q8×D13—84no—
118C2×D52C22⋊C412yes—
119C2×D52C22⋊C412yes—
120C2×D52SD1614yes—
121C2×D52Q1614yes—
122C2×C4×D13—24no—
123C2×C4×D13—24no—
124C2×C4×D13—44no—
125C2×C4×D13—44no—
126C2×C4×D13—82no—
127C2×C4×D13—82no—
128C2×C4×D13C22×C414yes—
129C2×C4×D13C2×D414yes—
130C2×Dic26—21no—
131C2×Dic26—24no—
132C2×Dic26C22×C412yes—
133C2×C8×C13—22no—
134C13×C4⋊C4—21no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4—21no—
137C13×C4⋊C4—22no—
138C13×C4⋊C4—22no—
139C13×C4⋊C4—42no—
140C13×C4⋊C4C22×C412yes—
141C13×C22⋊C4—22no—
142C42×C13—22no—
143C42×C13—42no—
144C42×C13C22×C411yescharacteristic
145C42×C13C22×C411yescharacteristic
146C42×C13C2×D411yescharacteristic
147C42×C13C2×D411yescharacteristic
148C22⋊Dic13—22no—
149#6103—24no—
150#6103—24no—
151#6103—44no—
152#6103C22⋊C414yes—
153#6103C22⋊C414yes—
154C4⋊Dic13—21no—
155C4⋊Dic13—21no—
156C4⋊Dic13—21no—
157C4⋊Dic13—24no—
158C4⋊Dic13—42no—
159C4⋊Dic13C22⋊C412yes—
160C4⋊Dic13C22⋊C412yes—
161C4⋊Dic13C22×C412yes—
162#6101—22no—
163#6101—22no—
164#6101—24no—
165#6101—24no—
166#6101—82no—
167C4×Dic13—22no—
168C2×#1055—22no—
169C8×D13—84no—
170#3501—131no—
171#2972—131no—
172#2349—131no—
173#1520—134no—
174#1518—131no—
175#1518—131no—
176#1503—131no—
177#1503D1311yescharacteristic, complemented
178C2×#328—134no—
179C23×C13C22×D411yescharacteristic
180C22×D13—42no—
181C22×D13—42no—
182C22×D13C2×C22⋊C414yes—
183C22×D13C2×SD1614yes—
184C22×D13C2×Q1614yes—
185Q8×C13—42no—
186Q8×C13—81no—
187C2×C4×C13—22no—
188C2×C4×C13—22no—
189C2×C4×C13—22no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13C2×C22⋊C411yescharacteristic
198C2×C4×C13C2×C22⋊C411yescharacteristic
199C2×C4×C13C2×C22⋊C411yescharacteristic
200C2×C4×C13C2×C22⋊C411yescharacteristic
201C2×C4×C13C2×SD1612yes—
202C2×C4×C13C2×Q1612yes—
203C2×C4×C13C23×C411yescharacteristic
204C2×C4×C13C22×D411yescharacteristic
205C2×Dic13—22no—
206C2×Dic13—22no—
207C2×Dic13—42no—
208C2×Dic13—42no—
209C2×Dic13—42no—
210C2×Dic13—42no—
211C2×Dic13C2×C22⋊C414yes—
212D52#10318yes—
213D52#10318yes—
214C4×D13—44no—
215C4×D13—44no—
216C4×D13—84no—
217C4×D13—84no—
218C4×D13—88no—
219Dic26—42no—
220Dic26—84no—
221Dic26—81no—
222C8×C13—42no—
223#1055—42no—
224#554—132no—
225#554—132no—
226#554—262no—
227#554—262no—
228D4×Q8—132no—
229D4×Q8—132no—
230#544—261no—
231#543—262no—
232#533—131no—
233#533C2×D1311yescharacteristic
234C2×C22⋊Q8—134no—
235#518—261no—
236C2×C4×D4—131no—
237C2×C4×D4—261no—
238C8×D4—262no—
239C8×D4—262no—
240#431—131no—
241#431C2×D1311yescharacteristic
242C2×C22⋊C8—134no—
243#389—261no—
244#385—262no—
245#382—131no—
246#380—132no—
247C4×C4⋊C4C2×D1311yescharacteristic
248C2×#95—132no—
249#328—134no—
250#328—134no—
251#328—132no—
252#328—132no—
253#328C2×D1312yes—
254#328C2×D1312yes—
255C22×C13—21no—
256C22×C13—21no—
257C22×C13C22×C22⋊C411yescharacteristic
258C22×C13C22×SD1611yescharacteristic
259C22×C13C22×Q1611yescharacteristic
260C2×D13—24no—
261C2×D13—24no—
262C2×D13—44no—
263C2×D13—44no—
264C2×D13C2×#10318yes—
265C4×C13—21no—
266C4×C13—21no—
267C4×C13—21no—
268C4×C13—21no—
269C4×C13—42no—
270C4×C13—42no—
271C4×C13—42no—
272C4×C13—81no—
273C4×C13C2×#10312yes—
274C4×C13C2×#10312yes—
275Dic13—24no—
276Dic13—42no—
277Dic13—42no—
278Dic13—82no—
279C22×Q8—134no—
280C22×D4—131no—
281C23×C4—132no—
282C23×C4—262no—
283C22×C8—264no—
284C4⋊Q8—131no—
285C4⋊Q8—131no—
286C4⋊Q8—262no—
287C4⋊Q8—262no—
288C4⋊Q8C4×D1311yescharacteristic, complemented
289C4⋊Q8C4×D1311yescharacteristic, complemented
290#125—21no—
291#125—262no—
292#125—262no—
293#125—261no—
294C22⋊Q8—21no—
295C22⋊Q8—134no—
296C22⋊Q8—132no—
297C22⋊Q8—134no—
298C22⋊Q8—264no—
299C22⋊Q8—264no—
300C22⋊Q8—264no—
301C22⋊Q8—264no—
302C22⋊Q8—264no—
303C22⋊Q8—264no—
304C22⋊Q8—261no—
305C22⋊Q8C22×D1312yes—
306C4×Q8—21no—
307C4×Q8—132no—
308C4×Q8—261no—
309C4×Q8C4×D1312yescomplemented
310C4×D4—132no—
311C4×D4—132no—
312C4×D4—132no—
313C4×D4—132no—
314C4×D4—262no—
315C4×D4—262no—
316C4×D4—262no—
317C4×D4—262no—
318C4×D4—524no—
319#117—21no—
320#117—261no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—131no—
323C2×C4⋊C4—134no—
324C2×C4⋊C4—264no—
325C2×C4⋊C4—261no—
326C2×C4⋊C4—262no—
327C2×C22⋊C4—132no—
328C2×C22⋊C4—264no—
329C2×C22⋊C4—262no—
330C2×C42—21no—
331C2×C42C22×D1311yescharacteristic
332C4⋊C8—21no—
333C4⋊C8—261no—
334C22⋊C8—132no—
335C22⋊C8—264no—
336C22⋊C8C22×D1312yes—
337C4×C8—21no—
338C4×C8—261no—
339#95—132no—
340#95—262no—
341#95—261no—
342#95C22×D1311yescharacteristic
343#95C22×D1311yescharacteristic
344C2×C13—21no—
345C2×C13—21no—
346C2×C13#288311yescharacteristic
347C2×C13C22×#10311yescharacteristic
348C2×C13#290111yescharacteristic
349D13—28no—
350C24—132no—
351C2×Q8—21no—
352C2×Q8—132no—
353C2×Q8—264no—
354C2×Q8—261no—
355C2×Q8—1044no—
356C2×Q8C2×C4×D1312yes—
357C2×D4—132no—
358C2×D4—132no—
359C2×D4—134no—
360C2×D4—134no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—132no—
364C22×C4—134no—
365C22×C4—134no—
366C22×C4—264no—
367C22×C4—264no—
368C22×C4—262no—
369C22×C4—524no—
370C22×C4—524no—
371C22×C4—1042no—
372C22×C4—1042no—
373C22×C4D4×D1311yescharacteristic
374C22×C4D4×D1311yescharacteristic
375C22×C4C23×D1311yescharacteristic
376C2×C8—22no—
377C2×C8—262no—
378C2×C8—1044no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—42no—
385C4⋊C4—132no—
386C4⋊C4—132no—
387C4⋊C4—132no—
388C4⋊C4—264no—
389C4⋊C4—264no—
390C4⋊C4—264no—
391C4⋊C4—261no—
392C4⋊C4—261no—
393C4⋊C4—262no—
394C4⋊C4—261no—
395C4⋊C4—262no—
396C4⋊C4—522no—
397C4⋊C4—1042no—
398C4⋊C4C2×C4×D1312yes—
399C22⋊C4—22no—
400C22⋊C4—134no—
401C22⋊C4—134no—
402C22⋊C4—264no—
403C22⋊C4—264no—
404C22⋊C4—262no—
405C22⋊C4—524no—
406C42—22no—
407C42—42no—
408C42—262no—
409C42C2×C4×D1311yescharacteristic
410C42C2×C4×D1311yescharacteristic
411C42D4×D1311yescharacteristic
412C42D4×D1311yescharacteristic
413C13#1761411yescharacteristic, complemented, Sylow
414C23—134no—
415C23—134no—
416C23—134no—
417C23—522no—
418C23—522no—
419C23C2×D4×D1311yescharacteristic
420Q8—42no—
421Q8—81no—
422Q8—522no—
423Q8—1041no—
424Q8—1044no—
425D4—138no—
426D4—138no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—134no—
438C2×C4—262no—
439C2×C4—262no—
440C2×C4—524no—
441C2×C4—524no—
442C2×C4—522no—
443C2×C4—522no—
444C2×C4—522no—
445C2×C4—522no—
446C2×C4—1044no—
447C2×C4—1044no—
448C2×C4—1048no—
449C2×C4C22⋊C4×D1311yescharacteristic
450C2×C4C22⋊C4×D1311yescharacteristic
451C2×C4C22⋊C4×D1311yescharacteristic
452C2×C4C22⋊C4×D1311yescharacteristic
453C2×C4SD16×D1312yes—
454C2×C4Q16×D1312yes—
455C2×C4C22×C4×D1311yescharacteristic
456C2×C4C2×D4×D1311yescharacteristic
457C8—42no—
458C8—522no—
459C22—21no—
460C22—21no—
461C22—138no—
462C22—264no—
463C22—264no—
464C22—524no—
465C22—524no—
466C22C2×C22⋊C4×D1311yescharacteristic
467C22C2×SD16×D1311yescharacteristic
468C22C2×Q16×D1311yescharacteristic
469C4—21no—
470C4—21no—
471C4—21no—
472C4—21no—
473C4—42no—
474C4—42no—
475C4—42no—
476C4—81no—
477C4—264no—
478C4—522no—
479C4—522no—
480C4—1042no—
481C4D13×#10312yes—
482C4D13×#10312yes—
483C2—21no—
484C2—21no—
485C2—268no—
486C2#1312329511yescharacteristic
487C2C2×D13×#10311yescharacteristic
488C2#1312338011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1503C2
socleC22×C13C22×C22⋊C4
prime radicalC22×D52D4
cosocleC22×C4×C13C24
hypercenter#1503D13
hypocenterC13#17614
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
4. #13113406C2semidirect
5. #13113401C2semidirect
6. #13113400C2semidirect
7. #13113334C2semidirect
8. D13×#328C2semidirect
9. C13×#1503C2semidirect
11. #11719435C4semidirect
12. #11719432C4semidirect
17. #11719284C4semidirect
18. Q8×D52C4semidirect
41. C2×Q8×D13C2×C4semidirect
45. C13×C4⋊Q8C2×C4semidirect
46. C13×C4⋊Q8C2×C4semidirect
51. C4×Q8×C13C2×C4semidirect
57. #88200C2×C4semidirect
68. #88151C2×C4semidirect
75. C4⋊C4×D13C2×C4semidirect
90. #88123C2×C4semidirect
91. #88123C2×C4semidirect
93. C4×Dic26C2×C4semidirect
177. #1503D13semidirect
288. C4⋊Q8C4×D13semidirect
289. C4⋊Q8C4×D13semidirect
309. C4×Q8C4×D13semidirect
413. C13#17614semidirect

Maximal subgroups

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

subgroupindex
#131286372
#131238592
#131177472
#131134062
#131134012
#131134002
#131133342
D13×#3282
C13×#15032
#1761413