Finite Group Databasebeta

← #15761912

Subgroups — #15761912

Order 3328.

700 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
1#13114598C211yesmaximal, characteristic, complemented
2C2×#11718130C212yesmaximal, complemented
3C2×#11718129C212yesmaximal
4#13113066C211yesmaximal, characteristic, complemented
5C13×#2850C211yesmaximal, characteristic
6C2×C13×#124C411yescharacteristic, complemented
7C2×C13×C22⋊Q8C2211yescharacteristic
8C2×C13×#121C2211yescharacteristic
9C22×C42×C13C2211yescharacteristic
10C22×C4⋊Dic13—21no—
11C13×#391C411yescharacteristic, complemented
12C13×#390C411yescharacteristic, complemented
13C13×#388—21no—
14C13×#388—21no—
15C13×#386—21no—
16C13×#386—21no—
17C13×#382C411yescharacteristic, complemented
18C2×#88071—21no—
19C2×#88071C2212yes—
20C2×C22⋊#1055C2212yes—
21C2×#88043—21no—
22#11718130—24no—
23#11718129—24no—
24#11718116—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×D4×C13—21no—
27C22×D4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C23×C4×C13C2311yescharacteristic
31C23×Dic13—22no—
32C13×#124—42no—
33C13×C22⋊Q8—22no—
34C13×C22⋊Q8—22no—
35C13×#121—22no—
36C13×#121—22no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C4⋊C4C2×C411yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C42×C13—42no—
47C2×C42×C13C2×C411yescharacteristic
48C2×C42×C13C2×C411yescharacteristic
49C2×C42×C13D411yescharacteristic
50C2×C42×C13D411yescharacteristic
51C2×C4⋊Dic13—24no—
52C2×C4⋊Dic13—42no—
53C2×C4⋊Dic13—42no—
54C22×#1055—22no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59#88071—22no—
60#88071—22no—
61#88071—42no—
62C22⋊#1055—22no—
63C22⋊#1055D414yes—
64#88043—42no—
65#9682—131nomaximal, Sylow
66C24×C13—21no—
67C24×C13C2×D411yescharacteristic
68C2×Q8×C13—22no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×D4×C13—22no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—41no—
79C2×D4×C13—41no—
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—21no—
88C22×C4×C13—21no—
89C22×C4×C13—41no—
90C22×C4×C13—41no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13C22⋊C411yescharacteristic
94C22×C4×C13C22⋊C411yescharacteristic
95C22×C4×C13C22⋊C411yescharacteristic
96C22×C4×C13C22⋊C411yescharacteristic
97C22×C4×C13C22×C411yescharacteristic
98C22×C4×C13C2×D412yes—
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13#4112yes—
101C22×Dic13—24no—
102C22×Dic13—42no—
103C22×Dic13—42no—
104C22×Dic13—42no—
105C22×Dic13—42no—
106C22×Dic13—42no—
107C22×Dic13—42no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—22no—
110C13×C4⋊C4—42no—
111C13×C22⋊C4—42no—
112C13×C22⋊C4—42no—
113C13×C22⋊C4—41no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—42no—
116C13×C22⋊C4—42no—
117C13×C22⋊C4—42no—
118C42×C13—22no—
119C42×C13—22no—
120C42×C13—41no—
121C42×C13—41no—
122C4⋊Dic13—48no—
123C2×#1055—24no—
124C2×#1055—42no—
125C2×#1055—42no—
126#2850D1311yescharacteristic
127#1749—131no—
128C2×#328—132no—
129C2×#327—132no—
130C4⋊#95—131no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—21no—
134C23×C13—21no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13C2×C22⋊C411yescharacteristic
143C23×C13#12411yescharacteristic
144C23×C13#12711yescharacteristic
145C23×C13AGL(1,ℤ/8)11yescharacteristic
146C23×C13AGL(1,ℤ/8)11yescharacteristic
147C23×C13#13711yescharacteristic
148C23×C13#13711yescharacteristic
149Q8×C13—82no—
150D4×C13—82no—
151D4×C13—81no—
152D4×C13—81no—
153D4×C13—81no—
154D4×C13—81no—
155C2×C4×C13—24no—
156C2×C4×C13—24no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13—42no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13#9912yes—
185C2×C4×C13#10412yes—
186C2×C4×C13C4×D412yes—
187C2×C4×C13#12112yes—
188C2×Dic13—44no—
189C2×Dic13—44no—
190C2×Dic13—44no—
191C2×Dic13—82no—
192C2×Dic13—82no—
193C2×Dic13—82no—
194C2×Dic13—82no—
195#1055—44no—
196C2×#124Dic1311yescharacteristic, complemented
197C2×C22⋊Q8C2×D1311yescharacteristic
198C2×#121C2×D1311yescharacteristic
199C22×C4⋊C4—261no—
200C22×C42C2×D1311yescharacteristic
201C2×C22⋊C8—132no—
202C2×#97—261no—
203#391Dic1311yescharacteristic, complemented
204#390Dic1311yescharacteristic, complemented
205#388—21no—
206#388—21no—
207#386—21no—
208#386—21no—
209#382Dic1311yescharacteristic, complemented
210C2×#95—132no—
211C2×#95—261no—
212#336—261no—
213#328—264no—
214#327—264no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13—81no—
228C22×C13—81no—
229C22×C13—81no—
230C22×C13—81no—
231C22×C13—81no—
232C22×C13—81no—
233C22×C13—81no—
234C22×C13#39011yescharacteristic
235C22×C13C2×#9911yescharacteristic
236C22×C13#41011yescharacteristic
237C22×C13#41711yescharacteristic
238C22×C13#41711yescharacteristic
239C22×C13C2×#10411yescharacteristic
240C22×C13#42111yescharacteristic
241C22×C13#48911yescharacteristic
242C22×C13#48911yescharacteristic
243C22×C13#49611yescharacteristic
244C22×C13#49711yescharacteristic
245C4×C13—22no—
246C4×C13—22no—
247C4×C13—22no—
248C4×C13—22no—
249C4×C13—41no—
250C4×C13—41no—
251C4×C13—81no—
252C4×C13—81no—
253C4×C13—81no—
254Dic13—84no—
255C22×Q8C2×Dic1311yescharacteristic
256C22×D4—21no—
257C22×D4C2×Dic1311yescharacteristic
258C23×C4—262no—
259C23×C4C22⋊D1311yescharacteristic
260C23×C4C22⋊D1311yescharacteristic
261C23×C4C22×D1311yescharacteristic
262C22×C8—262no—
263#124—42no—
264C22⋊Q8—22no—
265C22⋊Q8—22no—
266#121—22no—
267#121—22no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—264no—
270C2×C4⋊C4—522no—
271C2×C4⋊C4—522no—
272C2×C4⋊C4C2×Dic1311yescharacteristic
273C2×C4⋊C4C2×Dic1311yescharacteristic
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C42—42no—
281C2×C42C2×Dic1311yescharacteristic
282C2×C42C2×Dic1311yescharacteristic
283C2×C42C22⋊D1311yescharacteristic
284C2×C42C22⋊D1311yescharacteristic
285C22⋊C8—134no—
286C22⋊C8—262no—
287#97—522no—
288#95—21no—
289#95—21no—
290#95—21no—
291#95—21no—
292#95—262no—
293#95—262no—
294#95—522no—
295C2×C13—21no—
296C2×C13—21no—
297C2×C13—21no—
298C2×C13—21no—
299C2×C13—161no—
300C2×C13#150411yescharacteristic
301C2×C13#150911yescharacteristic
302C2×C13#151211yescharacteristic
303C2×C13#151311yescharacteristic
304C2×C13#195911yescharacteristic
305C2×C13#196411yescharacteristic
306C2×C13#198011yescharacteristic
307C24—21no—
308C24C2×C22⋊D1311yescharacteristic
309C2×Q8—22no—
310C2×Q8—41no—
311C2×Q8—41no—
312C2×D4—22no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—264no—
335C22×C4—522no—
336C22×C4—522no—
337C22×C4—522no—
338C22×C4—522no—
339C22×C4—522no—
340C22×C4—522no—
341C22×C4C22⋊Dic1311yescharacteristic
342C22×C4C22⋊Dic1311yescharacteristic
343C22×C4C22⋊Dic1311yescharacteristic
344C22×C4C22⋊Dic1311yescharacteristic
345C22×C4D4×D1312yes—
346C22×C4#612912yes—
347C22×C4C22×Dic1311yescharacteristic
348C22×C4C2×C22⋊D1311yescharacteristic
349C2×C8—264no—
350C2×C8—522no—
351C2×C8—522no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—42no—
355C4⋊C4—528no—
356C22⋊C4—42no—
357C22⋊C4—42no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—42no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C42—22no—
364C42—22no—
365C42—41no—
366C42—41no—
367C13#968211yescharacteristic, complemented, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23#8819011yescharacteristic
380C23#8819411yescharacteristic
381C23#8820311yescharacteristic
382C23#8820311yescharacteristic
383C23#8820511yescharacteristic
384C23#8820511yescharacteristic
385C23C2×C22⋊Dic1311yescharacteristic
386Q8—82no—
387D4—82no—
388D4—81no—
389D4—81no—
390D4—81no—
391D4—81no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—524no—
422C2×C4—524no—
423C2×C4—524no—
424C2×C4—1042no—
425C2×C4—1042no—
426C2×C4—1042no—
427C2×C4—1042no—
428C2×C4#8807412yes—
429C2×C4#8807712yes—
430C2×C4D4×Dic1312yes—
431C2×C4#8819212yes—
432C8—524no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22#1171871611yescharacteristic
453C22#1171871611yescharacteristic
454C22#1171871911yescharacteristic
455C22#1171872111yescharacteristic
456C22C2×#8807411yescharacteristic
457C22#1171888211yescharacteristic
458C22#1171889311yescharacteristic
459C22#1171889311yescharacteristic
460C22C2×#8807711yescharacteristic
461C22#1171889711yescharacteristic
462C22#1171890111yescharacteristic
463C4—22no—
464C4—22no—
465C4—22no—
466C4—22no—
467C4—41no—
468C4—41no—
469C4—81no—
470C4—81no—
471C4—81no—
472C4—1044no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2—21no—
477C2—161no—
478C2#1311334011yescharacteristic
479C2#1311336111yescharacteristic
480C2#1311337411yescharacteristic
481C2#1311337911yescharacteristic
482C2#1311565311yescharacteristic
483C2#1311567311yescharacteristic
484C2#1311575611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2850C2
socleC23×C13C2×C22⋊C4
prime radicalC2×C13×#121C22
cosocleC23×C4×C13C23
hypercenter#2850D13
hypocenterC13#9682
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2850

Complements

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

NH ≅ G/Ntype
1. #13114598C2semidirect
2. C2×#11718130C2semidirect
4. #13113066C2semidirect
6. C2×C13×#124C4semidirect
11. C13×#391C4semidirect
12. C13×#390C4semidirect
17. C13×#382C4semidirect
196. C2×#124Dic13semidirect
203. #391Dic13semidirect
204. #390Dic13semidirect
209. #382Dic13semidirect
367. C13#9682semidirect

Maximal subgroups

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

subgroupindex
#131145982
C2×#117181302
C2×#117181292
#131130662
C13×#28502
#968213