Finite Group Databasebeta

← #16070084

Subgroups — #16070084

Order 3328.

1854 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123123C212yesmaximal
2#13122031C214yesmaximal, complemented
3#13121741C214yesmaximal, complemented
4#13121494C214yesmaximal, complemented
5#13121302C214yesmaximal, complemented
6#13120950C211yesmaximal, characteristic, complemented
7#13120806C211yesmaximal, characteristic, complemented
8#13119076C214yesmaximal
9#13118971C214yesmaximal, complemented
10#13117569C212yesmaximal, complemented
11C2×C13×#380C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2212yes—
14C22×C13×C22⋊C4C2212yes—
15C2×#88178C2212yes—
16C2×#88178C2212yes—
17C2×#88178C2212yes—
18C2×#88143C2214yescomplemented
19C2×#88133C2214yes—
20C13×#380C2214yes—
21C13×#380C2214yes—
22C2×C13×#95C2211yescharacteristic
23C2×C13×#95C2211yescharacteristic
24#11718908C2214yes—
25#11718873C2212yes—
26#11718873C2212yes—
27#11718873C2212yes—
28#11718873C2214yes—
29#11718871C2214yes—
30#11718871C2214yes—
31#11718871C2214yes—
32#11718871C2214yes—
33#11718871C2214yes—
34C4×C22⋊Dic13C2214yes—
35#11718645C2214yescomplemented
36#11718644C2214yescomplemented
37#11718643C2214yescomplemented
38#11718642C2214yescomplemented
39#11718641C2214yescomplemented
40#11718639C2214yescomplemented
41#11718633C2214yescomplemented
42#11718614C2214yes—
43#11718613C2214yes—
44#11718613C2214yes—
45#11718612C2214yes—
46#11718609C2214yes—
47#11718606C2214yes—
48#11718605C2214yes—
49#11718322C2214yescomplemented
50#11718321C2214yescomplemented
51#11718318C2214yescomplemented
52#11718317C2214yescomplemented
53#11718316C2214yescomplemented
54#11718315C2214yescomplemented
55#11718308C2214yescomplemented
56#11718307C2214yescomplemented
57C25×C13C2311yescharacteristic
58C23×C4×C13—24no—
59C23×C4×C13—44no—
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2312yes—
62C23×C4×C13C2312yes—
63C23×C4×C13C2312yes—
64C23×C4×C13C2312yes—
65C23×C4×C13C2311yescharacteristic
66C22×Dic26C2312yes—
67C2×C13×C4⋊C4—44no—
68C2×C13×C4⋊C4C2314yes—
69C2×C13×C4⋊C4C2314yes—
70C2×C13×C22⋊C4—44no—
71C2×C13×C22⋊C4C2314yes—
72C2×C13×C22⋊C4C2314yes—
73C2×C22⋊Dic13C2314yes—
74C2×C22⋊Dic13C2314yes—
75C2×C22⋊Dic13C2314yes—
76C2×C22⋊Dic13C2314yes—
77C2×C22⋊Dic13C2314yes—
78C2×C22⋊Dic13C2314yes—
79C2×C4⋊Dic13C2312yes—
80C2×C4⋊Dic13C2314yes—
81C2×C4⋊Dic13C2314yes—
82C2×C4⋊Dic13C2312yes—
83C2×C4⋊Dic13C2312yes—
84#88178—28no—
85#88178—44no—
86#88178—44no—
87C2×#6101C2314yes—
88C2×#6101C2314yes—
89C2×#6101C2314yes—
90C2×#6101C2314yes—
91C2×#6101C2314yes—
92C2×#6101C2314yes—
93C2×#6101C2314yes—
94C2×C4×Dic13C2314yes—
95C2×C4×Dic13C2314yes—
96#88143—48no—
97#88133—48no—
98C13×#95C2314yes—
99C13×#95C2314yes—
100#88071C2314yes—
101#88071C2314yes—
102#88071C2314yes—
103#88071C2314yes—
104#88071C2314yes—
105#88071C2314yes—
106#88071C2314yes—
107#88071C2314yes—
108#88071C2314yes—
109#88071C2314yes—
110#88071C2314yes—
111#36728—131nomaximal, Sylow
112C24×C13—22no—
113C24×C13—22no—
114C24×C13—22no—
115C24×C13—24no—
116C24×C13—42no—
117C24×C13C2411yescharacteristic
118C24×C13C2411yescharacteristic
119C24×C13C2411yescharacteristic
120C22×C4×C13—22no—
121C22×C4×C13—24no—
122C22×C4×C13—24no—
123C22×C4×C13—24no—
124C22×C4×C13—24no—
125C22×C4×C13—24no—
126C22×C4×C13—24no—
127C22×C4×C13—24no—
128C22×C4×C13—42no—
129C22×C4×C13—42no—
130C22×C4×C13—42no—
131C22×C4×C13—42no—
132C22×C4×C13—42no—
133C22×C4×C13—42no—
134C22×C4×C13—42no—
135C22×C4×C13—416no—
136C22×C4×C13#4114yes—
137C22×C4×C13C2414yes—
138C22×C4×C13C2414yes—
139C22×C4×C13C2412yes—
140C22×C4×C13C2412yes—
141C22×Dic13C2414yes—
142C22×Dic13C2414yes—
143C22×Dic13C2414yes—
144C22×Dic13C2414yes—
145C2×Dic26—24no—
146C2×Dic26—42no—
147C2×Dic26—42no—
148C13×C4⋊C4—28no—
149C13×C4⋊C4—44no—
150C13×C22⋊C4—28no—
151C13×C22⋊C4—44no—
152C22⋊Dic13—28no—
153C22⋊Dic13—28no—
154C22⋊Dic13—28no—
155C22⋊Dic13—28no—
156C22⋊Dic13—44no—
157C22⋊Dic13—44no—
158C4⋊Dic13—24no—
159C4⋊Dic13—44no—
160C4⋊Dic13—44no—
161C4⋊Dic13—42no—
162C4⋊Dic13—42no—
163#6101—28no—
164#6101—28no—
165#6101—28no—
166#6101—44no—
167#6101—44no—
168#6101—44no—
169#6101—44no—
170C4×Dic13—44no—
171C4×Dic13—44no—
172#2848—132no—
173#2747—134no—
174#2722—134no—
175#2704—134no—
176#2690—134no—
177#2659—131no—
178#2646—131no—
179#2480—134no—
180#2473—134no—
181#2329—132no—
182C2×#380D1311yescharacteristic
183C23×C13—22no—
184C23×C13—21no—
185C23×C13—21no—
186C23×C13—28no—
187C23×C13—21no—
188C23×C13—21no—
189C23×C13—22no—
190C23×C13—22no—
191C23×C13—21no—
192C23×C13—21no—
193C23×C13—22no—
194C23×C13—22no—
195C23×C13—48no—
196C23×C13—48no—
197C23×C13—44no—
198C23×C13—44no—
199C23×C13C2×#4112yes—
200C23×C13H(5,𝔽2)12yes—
201C23×C132−1+412yes—
202C23×C132−1+414yes—
203C23×C13C2511yescharacteristic
204C2×C4×C13—28no—
205C2×C4×C13—22no—
206C2×C4×C13—22no—
207C2×C4×C13—22no—
208C2×C4×C13—22no—
209C2×C4×C13—24no—
210C2×C4×C13—24no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—24no—
215C2×C4×C13—44no—
216C2×C4×C13—48no—
217C2×C4×C13—48no—
218C2×C4×C13—84no—
219C2×C4×C13—84no—
220C2×C4×C13C2×#4114yes—
221C2×C4×C13H(5,𝔽2)14yes—
222C2×Dic13—24no—
223C2×Dic13—24no—
224C2×Dic13—24no—
225C2×Dic13—24no—
226C2×Dic13—24no—
227C2×Dic13—24no—
228C2×Dic13—24no—
229C2×Dic13—24no—
230C2×Dic13—24no—
231C2×Dic13—24no—
232C2×Dic13—24no—
233C2×Dic13—24no—
234Dic26—84no—
235C24×C4C2×D1311yescharacteristic
236C2×#126—134no—
237C2×#125—134no—
238C2×C22⋊Q8—132no—
239C2×C22⋊Q8—132no—
240C2×C22⋊Q8—132no—
241C22×C4⋊C4C2×D1312yes—
242C22×C22⋊C4C2×D1312yes—
243#400—134no—
244#400—134no—
245#398—134no—
246#398—134no—
247#398—134no—
248#398—134no—
249#398—134no—
250#397—134no—
251#397—134no—
252#397—134no—
253#396—134no—
254#395—134no—
255#391—134no—
256#389—134no—
257#389—134no—
258#388—134no—
259#388—134no—
260#388—134no—
261#387—134no—
262#387—134no—
263#387—134no—
264#387—134no—
265#385—134no—
266#385—134no—
267#385—134no—
268#385—134no—
269#385—134no—
270#380—132no—
271#380—132no—
272#380—132no—
273#380—134no—
274#380C2×D1314yes—
275#380C2×D1314yes—
276#379—134no—
277C4×C22⋊C4—134no—
278C2×#95C2×D1311yescharacteristic
279C2×#95C2×D1311yescharacteristic
280C22×C13—22no—
281C22×C13—22no—
282C22×C13—24no—
283C22×C13—24no—
284C22×C13—22no—
285C22×C13—22no—
286C22×C13—24no—
287C22×C13—24no—
288C22×C13—416no—
289C22×C13—41no—
290C22×C13—41no—
291C22×C13—41no—
292C22×C13—41no—
293C22×C13—42no—
294C22×C13—42no—
295C22×C13#54114yes—
296C22×C13C22×#4111yescharacteristic
297C22×C13C2×H(5,𝔽2)12yes—
298C22×C13C2×H(5,𝔽2)11yescharacteristic
299C22×C13C2×2−1+411yescharacteristic
300C22×C13C2×2−1+412yes—
301C4×C13—24no—
302C4×C13—24no—
303C4×C13—44no—
304C4×C13—44no—
305Dic13—44no—
306Dic13—44no—
307Dic13—44no—
308Dic13—44no—
309C25C22×D1311yescharacteristic
310C22×Q8—132no—
311C23×C4—24no—
312C23×C4—44no—
313C23×C4C22×D1311yescharacteristic
314C23×C4C22×D1312yes—
315C23×C4C22×D1312yes—
316C23×C4C22×D1312yes—
317C23×C4C22×D1312yes—
318C23×C4C22×D1311yescharacteristic
319#126—528no—
320#125—528no—
321C22⋊Q8—268no—
322C22⋊Q8—524no—
323C22⋊Q8—524no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—134no—
326C2×C4⋊C4—134no—
327C2×C4⋊C4—134no—
328C2×C4⋊C4—132no—
329C2×C4⋊C4—132no—
330C2×C4⋊C4—132no—
331C2×C4⋊C4—134no—
332C2×C4⋊C4—134no—
333C2×C4⋊C4—134no—
334C2×C4⋊C4—134no—
335C2×C4⋊C4—134no—
336C2×C4⋊C4—134no—
337C2×C4⋊C4C22×D1314yes—
338C2×C4⋊C4C22×D1314yes—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—134no—
341C2×C22⋊C4—134no—
342C2×C22⋊C4—134no—
343C2×C22⋊C4—134no—
344C2×C22⋊C4—134no—
345C2×C22⋊C4—134no—
346C2×C22⋊C4C22×D1314yes—
347C2×C22⋊C4C22×D1314yes—
348C2×C42—134no—
349C2×C42—134no—
350#95—134no—
351#95—134no—
352#95—134no—
353#95—134no—
354#95—134no—
355#95—134no—
356#95—134no—
357#95—134no—
358#95—134no—
359#95—134no—
360#95—134no—
361#95C22×D1314yes—
362#95C22×D1314yes—
363C2×C13—24no—
364C2×C13—42no—
365C2×C13—42no—
366C2×C13C2×#54111yescharacteristic
367C2×C13#349011yescharacteristic
368C2×C13#349211yescharacteristic
369C2×C13#353612yes—
370C2×C13#353812yes—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—24no—
375C24—42no—
376C24C23×D1311yescharacteristic
377C24C23×D1311yescharacteristic
378C24C23×D1311yescharacteristic
379C2×Q8—264no—
380C2×Q8—522no—
381C2×Q8—522no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—416no—
398C22×C4—134no—
399C22×C4—134no—
400C22×C4—134no—
401C22×C4—134no—
402C22×C4#612714yes—
403C22×C4C23×D1314yes—
404C22×C4C23×D1314yes—
405C22×C4C23×D1312yes—
406C22×C4C23×D1312yes—
407C4⋊C4—28no—
408C4⋊C4—44no—
409C4⋊C4—268no—
410C4⋊C4—264no—
411C4⋊C4—268no—
412C4⋊C4—268no—
413C4⋊C4—522no—
414C4⋊C4—522no—
415C4⋊C4—524no—
416C4⋊C4—524no—
417C4⋊C4—524no—
418C4⋊C4—524no—
419C4⋊C4—524no—
420C4⋊C4—524no—
421C22⋊C4—28no—
422C22⋊C4—44no—
423C22⋊C4—268no—
424C22⋊C4—268no—
425C22⋊C4—268no—
426C22⋊C4—268no—
427C22⋊C4—524no—
428C22⋊C4—524no—
429C42—524no—
430C42—524no—
431C13#3672811yescharacteristic, complemented, Sylow
432C23—22no—
433C23—21no—
434C23—21no—
435C23—28no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—22no—
440C23—22no—
441C23—21no—
442C23—22no—
443C23—22no—
444C23—48no—
445C23—48no—
446C23—44no—
447C23—44no—
448C23C2×#612712yes—
449C23#8825112yes—
450C23#8825412yes—
451C23#8825714yes—
452C23C24×D1311yescharacteristic
453Q8—1044no—
454C2×C4—28no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—44no—
466C2×C4—48no—
467C2×C4—48no—
468C2×C4—84no—
469C2×C4—84no—
470C2×C4—264no—
471C2×C4—264no—
472C2×C4—264no—
473C2×C4—264no—
474C2×C4—264no—
475C2×C4—264no—
476C2×C4—264no—
477C2×C4—264no—
478C2×C4—264no—
479C2×C4—264no—
480C2×C4—264no—
481C2×C4—264no—
482C2×C4C2×#612714yes—
483C2×C4#8825114yes—
484C22—22no—
485C22—22no—
486C22—24no—
487C22—24no—
488C22—22no—
489C22—22no—
490C22—24no—
491C22—24no—
492C22—416no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—42no—
498C22—42no—
499C22#1171922314yes—
500C22C22×#612711yescharacteristic
501C22C2×#8825112yes—
502C22C2×#8825111yescharacteristic
503C22C2×#8825411yescharacteristic
504C22C2×#8825712yes—
505C4—24no—
506C4—24no—
507C4—44no—
508C4—44no—
509C4—524no—
510C4—524no—
511C4—524no—
512C4—524no—
513C2—24no—
514C2—42no—
515C2—42no—
516C2C2×#1171922311yescharacteristic
517C2#1312852511yescharacteristic
518C2#1312854511yescharacteristic
519C2#1312905812yes—
520C2#1312908112yes—
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC2×C13×#380C2
prime radicalC25×C13C23
hypercenterC2×#380D13
hypocenterC13#36728
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. #13122031C2semidirect
3. #13121741C2semidirect
4. #13121494C2semidirect
5. #13121302C2semidirect
6. #13120950C2semidirect
7. #13120806C2semidirect
9. #13118971C2semidirect
10. #13117569C2semidirect
18. C2×#88143C22semidirect
35. #11718645C22semidirect
36. #11718644C22semidirect
37. #11718643C22semidirect
38. #11718642C22semidirect
39. #11718641C22semidirect
40. #11718639C22semidirect
41. #11718633C22semidirect
49. #11718322C22semidirect
50. #11718321C22semidirect
51. #11718318C22semidirect
52. #11718317C22semidirect
53. #11718316C22semidirect
54. #11718315C22semidirect
55. #11718308C22semidirect
56. #11718307C22semidirect
431. C13#36728semidirect

Maximal subgroups

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

subgroupindex
#131231232
#131220312
#131217412
#131214942
#131213022
#131209502
#131208062
#131190762
#131189712
#131175692
C2×C13×#3802
#3672813