Finite Group Databasebeta

← #15758087

Subgroups — #15758087

Order 3328.

678 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718629C211yesmaximal, characteristic
2#13117539C211yesmaximal, characteristic
3#13114926C211yesmaximal, characteristic, complemented
4C2×#11718043C211yesmaximal, characteristic
5#13112715C211yesmaximal, characteristic, complemented
6#13112679C211yesmaximal, characteristic, complemented
7C13×#1445C211yesmaximal, characteristic, complemented
8C22×C13×C4⋊C4C2211yescharacteristic
9C2×#88184C2211yescharacteristic
10C2×C4×C22⋊D13—21no—
11C2×C13×#95—21no—
12C2×C13×#95—21no—
13C2×C13×#95C2211yescharacteristic
14C2×C13×#95C2211yescharacteristic
15#11718874—21no—
16#11718873C2211yescharacteristic
17C2×C22⋊#1055C2211yescharacteristic
18C2×C22⋊#1055C2211yescharacteristic
19#11718629—22no—
20#11718629C414yescomplemented
21C2×#88049—21no—
22C2×#88048—21no—
23#11718331—21no—
24#11718329—21no—
25#11718326—21no—
26#11718314—21no—
27#11718121—21no—
28#11718121—21no—
29#11718043—22no—
30C23×C4×C13—21no—
31C23×C4×C13—21no—
32C23×C4×C13D411yescharacteristic
33C23×C4×C13D411yescharacteristic
34C23×C4×C13C2311yescharacteristic
35C22×C22⋊D13—21no—
36C22×D52D411yescharacteristic
37C22×C4×D13—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4C2×C412yescomplemented
44C2×C22⋊Dic13—21no—
45#88184—21no—
46#88184—21no—
47#88184C2×C412yes—
48#88184D412yes—
49C4×C22⋊D13—42no—
50C4×C22⋊D13—42no—
51C2×#6103—21no—
52C2×#6103—21no—
53C2×#6103—21no—
54C2×#6103—21no—
55C2×C4⋊Dic13D411yescharacteristic
56C2×C4⋊Dic13D411yescharacteristic
57C2×C4⋊Dic13D411yescharacteristic
58C2×#6101—21no—
59C2×C4×Dic13—21no—
60C22×#1055—21no—
61C22×#1055—21no—
62C13×#95—21no—
63C13×#95—21no—
64C13×#95—21no—
65C13×#95—21no—
66C13×#95—42no—
67C13×#95—42no—
68#88071—21no—
69#88071—21no—
70#88071—21no—
71C22⋊#1055—21no—
72C22⋊#1055—21no—
73C22⋊#1055—21no—
74C22⋊#1055C2×C412yescomplemented
75#88049—24no—
76#88048—24no—
77#9045—131nomaximal, Sylow
78C24×C13C2×D411yescharacteristic
79C23×D13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—22no—
83C22×C4×C13—22no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13—41no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13—41no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13—41no—
99C22×C4×C13—41no—
100C22×C4×C13—41no—
101C22×C4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13—41no—
104C22×C4×C13—41no—
105C22×C4×C13SD1612yes—
106C22×C4×C13C22×C411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13#4111yescharacteristic
111C22×C4×C13#4111yescharacteristic
112C2×C22⋊D13—22no—
113C2×C22⋊D13—22no—
114C2×C22⋊D13—41no—
115C2×C22⋊D13—41no—
116C2×C22⋊D13—41no—
117C2×C22⋊D13—41no—
118C22×Dic13—21no—
119C22×Dic13—21no—
120C22×Dic13—21no—
121C2×D52—21no—
122C2×D52—41no—
123C2×D52—41no—
124C2×D52C22⋊C412yes—
125C2×C4×D13—42no—
126C2×C4×D13—81no—
127C2×C4×D13—81no—
128C13×C4⋊C4—22no—
129C13×C4⋊C4—22no—
130C13×C4⋊C4—41no—
131C13×C4⋊C4—41no—
132C22⋊Dic13—41no—
133C22⋊Dic13—41no—
134#6103—22no—
135#6103—22no—
136#6103—42no—
137#6103—81no—
138#6103—81no—
139C4⋊Dic13—21no—
140C4⋊Dic13—41no—
141C4⋊Dic13—41no—
142C4⋊Dic13C22⋊C412yes—
143#6101—42no—
144C4×Dic13—42no—
145C2×#1055—22no—
146C2×#1055—41no—
147C2×#1055—41no—
148C2×#1055—41no—
149C2×#1055—41no—
150C2×#1055—41no—
151C2×#481—131no—
152#2325—131no—
153#1824—131no—
154C2×#327—131no—
155#1445D1311yescharacteristic, complemented
156#1294—131no—
157#1280—131no—
158C23×C13—21no—
159C23×C13—21no—
160C23×C13—21no—
161C23×C13—21no—
162C23×C13C4×D411yescharacteristic
163C23×C13#12011yescharacteristic
164C23×C13#12111yescharacteristic
165C23×C13C2×SD1611yescharacteristic
166C23×C13#13511yescharacteristic
167C23×C13AGL(1,ℤ/8)11yescharacteristic
168C23×C13#13711yescharacteristic
169C22×D13—22no—
170C22×D13—41no—
171C22×D13—41no—
172C22×D13—41no—
173C22×D13—41no—
174C22×D13—41no—
175C22×D13—41no—
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—21no—
180C2×C4×C13—22no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—42no—
188C2×C4×C13—42no—
189C2×C4×C13—42no—
190C2×C4×C13—42no—
191C2×C4×C13—42no—
192C2×C4×C13—42no—
193C2×C4×C13—42no—
194C2×C4×C13—42no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
198C2×C4×C13—81no—
199C2×C4×C13—81no—
200C2×C4×C13—81no—
201C2×C4×C13—81no—
202C2×C4×C13—81no—
203C2×C4×C13—81no—
204C2×C4×C13—81no—
205C2×C4×C13—81no—
206C2×C4×C13—81no—
207C2×C4×C13—81no—
208C2×C4×C13C2×C22⋊C411yescharacteristic
209C2×C4×C13C4×D411yescharacteristic
210C2×C4×C13#12111yescharacteristic
211C2×C4×C13#12311yescharacteristic
212C22⋊D13—42no—
213C22⋊D13—42no—
214C22⋊D13—42no—
215C22⋊D13—42no—
216C2×Dic13—22no—
217C2×Dic13—41no—
218C2×Dic13—41no—
219C2×Dic13—41no—
220C2×Dic13—41no—
221C2×Dic13—41no—
222C2×Dic13—41no—
223C2×Dic13—41no—
224C2×Dic13—41no—
225D52—42no—
226D52—81no—
227C4×D13—84no—
228#1055—42no—
229#1055—81no—
230C2×#121—131no—
231C2×C4×D4—261no—
232C22×C4⋊C4C2×D1311yescharacteristic
233#481—134no—
234#481—262no—
235C2×#106—261no—
236C2×#102—261no—
237C2×C22⋊C8—131no—
238C2×C22⋊C8—131no—
239#388—261no—
240#387—261no—
241#386—261no—
242#386—261no—
243#385—261no—
244#380—131no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95C2×D1311yescharacteristic
248C2×#95C2×D1311yescharacteristic
249#340—261no—
250#340—261no—
251#327—262no—
252C22×C13—21no—
253C22×C13—21no—
254C22×C13—21no—
255C22×C13—21no—
256C22×C13—21no—
257C22×C13—21no—
258C22×C13—21no—
259C22×C13—21no—
260C22×C13—21no—
261C22×C13—21no—
262C22×C13—21no—
263C22×C13—21no—
264C22×C13#38611yescharacteristic
265C22×C13C4×SD1611yescharacteristic
266C22×C13#44011yescharacteristic
267C22×C13#45011yescharacteristic
268C22×C13#45211yescharacteristic
269C22×C13#45311yescharacteristic
270C22×C13#45411yescharacteristic
271C22×C13#45811yescharacteristic
272C22×C13#45811yescharacteristic
273C22×C13#46111yescharacteristic
274C22×C13#46311yescharacteristic
275C2×D13—42no—
276C2×D13—42no—
277C2×D13—42no—
278C2×D13—81no—
279C2×D13—81no—
280C2×D13—81no—
281C2×D13—81no—
282C4×C13—21no—
283C4×C13—21no—
284C4×C13—21no—
285C4×C13—21no—
286C4×C13—42no—
287C4×C13—82no—
288C4×C13—81no—
289C4×C13—82no—
290Dic13—42no—
291Dic13—81no—
292Dic13—81no—
293C22×D4—131no—
294C22×D4—261no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—261no—
298C23×C4C22⋊D1311yescharacteristic
299C23×C4C22⋊D1311yescharacteristic
300C23×C4C22×D1311yescharacteristic
301C22×C8—261no—
302C22×C8—261no—
303#121—132no—
304#121—132no—
305#121—261no—
306#121—261no—
307C4×D4—522no—
308C4×D4—522no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—131no—
315C2×C4⋊C4—131no—
316C2×C4⋊C4—131no—
317C2×C4⋊C4—261no—
318C2×C4⋊C4C4×D1312yescomplemented
319C2×C22⋊C4—261no—
320C2×C22⋊C4—261no—
321C2×C22⋊C4—261no—
322C2×C22⋊C4—261no—
323C2×C22⋊C4—261no—
324C2×C42—261no—
325#106—264no—
326#102—264no—
327C22⋊C8—132no—
328C22⋊C8—261no—
329C22⋊C8—261no—
330C22⋊C8—261no—
331#95—21no—
332#95—21no—
333#95—21no—
334#95—21no—
335#95—42no—
336#95—42no—
337#95—261no—
338#95—261no—
339#95—261no—
340C2×C13—21no—
341C2×C13—21no—
342C2×C13—21no—
343C2×C13—21no—
344C2×C13#161311yescharacteristic
345C2×C13#161511yescharacteristic
346C2×C13#161611yescharacteristic
347C2×C13#161811yescharacteristic
348C2×C13#187711yescharacteristic
349C2×C13#188311yescharacteristic
350C2×C13#189011yescharacteristic
351D13—82no—
352C24—261no—
353C24C2×C22⋊D1311yescharacteristic
354C2×D4—132no—
355C2×D4—262no—
356C2×D4—262no—
357C2×D4—261no—
358C2×D4—521no—
359C2×D4—521no—
360C2×D4—521no—
361C2×D4—521no—
362C2×D4—521no—
363C2×D4—521no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—261no—
390C22×C4—261no—
391C22×C4—261no—
392C22×C4—522no—
393C22×C4—1041no—
394C22×C4—1041no—
395C22×C4#610612yes—
396C22×C4C2×C4×D1311yescharacteristic
397C22×C4#612711yescharacteristic
398C22×C4D4×D1311yescharacteristic
399C22×C4D4×D1311yescharacteristic
400C22×C4D4×D1311yescharacteristic
401C22×C4#612911yescharacteristic
402C2×C8—262no—
403C2×C8—521no—
404C2×C8—521no—
405C2×C8—521no—
406C2×C8—521no—
407C2×C8—521no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—132no—
413C4⋊C4—261no—
414C4⋊C4—521no—
415C4⋊C4—521no—
416C4⋊C4—522no—
417C22⋊C4—262no—
418C22⋊C4—262no—
419C22⋊C4—522no—
420C22⋊C4—521no—
421C22⋊C4—521no—
422C22⋊C4—1041no—
423C22⋊C4—1041no—
424C42—522no—
425C13#904511yescharacteristic, complemented, Sylow
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—262no—
431C23—521no—
432C23—521no—
433C23—521no—
434C23—521no—
435C23—521no—
436C23—521no—
437C23C4×C22⋊D1311yescharacteristic
438C23#8819111yescharacteristic
439C23#8819211yescharacteristic
440C23C2×#610611yescharacteristic
441C23#8819611yescharacteristic
442C23#8820311yescharacteristic
443C23#8820411yescharacteristic
444D4—522no—
445D4—522no—
446D4—522no—
447D4—522no—
448D4—522no—
449D4—1041no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—81no—
473C2×C4—81no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4—81no—
482C2×C4—262no—
483C2×C4—521no—
484C2×C4—521no—
485C2×C4—521no—
486C2×C4—521no—
487C2×C4—521no—
488C2×C4—521no—
489C2×C4—521no—
490C2×C4—521no—
491C2×C4—1044no—
492C2×C4C22⋊C4×D1311yescharacteristic
493C2×C4#8813511yescharacteristic
494C2×C4#8813711yescharacteristic
495C2×C4#8813811yescharacteristic
496C8—522no—
497C8—1041no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—522no—
511C22—522no—
512C22—522no—
513C22—1041no—
514C22—1041no—
515C22—1041no—
516C22—1041no—
517C22#1171861711yescharacteristic
518C22C4×#610611yescharacteristic
519C22#1171868711yescharacteristic
520C22#1171870711yescharacteristic
521C22#1171870811yescharacteristic
522C22#1171871411yescharacteristic
523C22#1171871411yescharacteristic
524C22#1171871811yescharacteristic
525C22#1171872311yescharacteristic
526C22#1171873811yescharacteristic
527C22#1171874411yescharacteristic
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—42no—
533C4—82no—
534C4—81no—
535C4—82no—
536C4—522no—
537C4—1041no—
538C4—1041no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—1042no—
544C2#1311385511yescharacteristic
545C2#1311386511yescharacteristic
546C2#1311387211yescharacteristic
547C2#1311388211yescharacteristic
548C2#1311517311yescharacteristic
549C2#1311521511yescharacteristic
550C2#1311524611yescharacteristic
subgroupG/H
centerC23#88191
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1445C2
socleC23×C13#120
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenter#1445D13
hypocenterC13#9045
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1445

Complements

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

NH ≅ G/Ntype
3. #13114926C2semidirect
5. #13112715C2semidirect
6. #13112679C2semidirect
7. C13×#1445C2semidirect
20. #11718629C4semidirect
43. C2×C13×C4⋊C4C2×C4semidirect
74. C22⋊#1055C2×C4semidirect
155. #1445D13semidirect
318. C2×C4⋊C4C4×D13semidirect
425. C13#9045semidirect

Maximal subgroups

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

subgroupindex
C2×#117186292
#131175392
#131149262
C2×#117180432
#131127152
#131126792
C13×#14452
#904513