Finite Group Databasebeta

← #15758210

Subgroups — #15758210

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718746C211yesmaximal, characteristic
2#13117900C211yesmaximal, characteristic
3#13115785C211yesmaximal, characteristic, complemented
4C2×#11718077C211yesmaximal, characteristic
5#13112677C211yesmaximal, characteristic, complemented
6#13112675C211yesmaximal, characteristic, complemented
7C13×#1987C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C22×#6106—22no—
10C2×#88147—21no—
11C2×#88128C2211yescharacteristic
12C2×C4×D52—21no—
13C2×C13×C4⋊C8C2211yescharacteristic
14C4×C13×C4⋊C4C2211yescharacteristic
15#11718746—22no—
16#11718746C414yescomplemented
17#11718649—21no—
18#11718600—21no—
19C4×C4⋊Dic13C2211yescharacteristic
20C2×C4⋊#1055C2211yescharacteristic
21C2×C4×#1055C2211yescharacteristic
22#11718326—22no—
23C13×#340—21no—
24C13×#340—21no—
25#11718121—21no—
26#11718121—21no—
27#11718077—22no—
28C22×Q8×C13—21no—
29C22×D52—21no—
30C22×D52—21no—
31C22×D52D412yes—
32C22×C4×D13—22no—
33C22×C8×C13—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8C2×C412yescomplemented
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4D411yescharacteristic
41C2×C13×C4⋊C4D411yescharacteristic
42C2×C42×C13—21no—
43C2×C42×C13C2311yescharacteristic
44C2×#6106—28no—
45C2×#6106—44no—
46C2×#6106—44no—
47C2×#6103—22no—
48C2×#6103—22no—
49C2×#6103—22no—
50C2×C4⋊Dic13D411yescharacteristic
51C2×C4⋊Dic13D411yescharacteristic
52C2×C4×Dic13—21no—
53C22×#1055—21no—
54C22×#1055—21no—
55#88147—42no—
56#88147—42no—
57#88128—21no—
58#88128—21no—
59#88128C2×C412yes—
60#88128D412yes—
61C4×D52—42no—
62C4×D52—42no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C13×#95—21no—
66#88071—21no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4×#1055—21no—
70C4×#1055C2×C412yescomplemented
71#9064—131nomaximal, Sylow
72C23×D13—22no—
73C2×Q8×C13—22no—
74C2×Q8×C13—42no—
75C2×Q8×C13—42no—
76C2×Q8×C13—41no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—41no—
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×Dic13—21no—
84C22×Dic13—21no—
85C2×D52—22no—
86C2×D52—22no—
87C2×D52—22no—
88C2×D52—22no—
89C2×D52—22no—
90C2×D52—41no—
91C2×D52—41no—
92C2×D52—41no—
93C2×D52—41no—
94C2×D52—41no—
95C2×D52—41no—
96C2×D52—41no—
97C2×D52—41no—
98C2×D52—42no—
99C2×D52—42no—
100C2×D52C22⋊C414yes—
101C2×C4×D13—44no—
102C2×C4×D13—44no—
103C2×C4×D13—82no—
104C2×C8×C13—41no—
105C2×C8×C13—41no—
106C2×C8×C13—41no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—22no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4SD1612yescomplemented
115C42×C13—41no—
116C42×C13—41no—
117C42×C13C22×C411yescharacteristic
118C42×C13C2×D411yescharacteristic
119C42×C13#4111yescharacteristic
120C42×C13#4111yescharacteristic
121#6106—416no—
122#6103—44no—
123#6103—44no—
124#6103—82no—
125C4⋊Dic13—21no—
126C4⋊Dic13—21no—
127C4⋊Dic13—21no—
128C4⋊Dic13SD1612yescomplemented
129C4×Dic13—41no—
130C4×Dic13—41no—
131C2×#1055—22no—
132C2×#1055—22no—
133C2×#1055—22no—
134C2×#1055—41no—
135C2×#1055—41no—
136C2×#1055—41no—
137C2×#492—131no—
138#2366—131no—
139#1987—131no—
140#1987D1311yescharacteristic, complemented
141C2×#331—131no—
142#1279—131no—
143#1279—131no—
144C23×C13#12011yescharacteristic
145C22×D13—24no—
146C22×D13—42no—
147C22×D13—42no—
148C22×D13—42no—
149C22×D13—42no—
150C22×D13—42no—
151C22×D13—42no—
152Q8×C13—44no—
153Q8×C13—82no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—22no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—42no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—81no—
164C2×C4×C13—81no—
165C2×C4×C13C2×C22⋊C411yescharacteristic
166C2×C4×C13C4×D411yescharacteristic
167C2×C4×C13C4×D411yescharacteristic
168C2×C4×C13#12111yescharacteristic
169C2×C4×C13#12111yescharacteristic
170C2×C4×C13#12311yescharacteristic
171C2×C4×C13C2×SD1611yescharacteristic
172C2×C4×C13C2×SD1611yescharacteristic
173C2×C4×C13#13511yescharacteristic
174C2×C4×C13#13511yescharacteristic
175C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C13#13711yescharacteristic
178C2×C4×C13#13711yescharacteristic
179C2×Dic13—22no—
180C2×Dic13—41no—
181C2×Dic13—41no—
182C2×Dic13—41no—
183C2×Dic13—41no—
184C2×Dic13—41no—
185D52—44no—
186D52—42no—
187D52—42no—
188D52—42no—
189D52—42no—
190D52—42no—
191D52—42no—
192D52—42no—
193D52—42no—
194D52—82no—
195C4×D13—88no—
196C8×C13—81no—
197#1055—24no—
198#1055—81no—
199C22×SD16—262no—
200C2×C4⋊Q8C2×D1311yescharacteristic
201C2×#127—131no—
202C2×C4×D4—261no—
203C2×C4×D4—261no—
204#492—134no—
205#492—262no—
206C2×C4⋊C8—131no—
207C2×C4⋊C8C2×D1311yescharacteristic
208C2×C4×C8—131no—
209#390—261no—
210#390—261no—
211#386—262no—
212C4×C4⋊C4—131no—
213C4×C4⋊C4C2×D1311yescharacteristic
214#340—21no—
215#340—21no—
216#340—261no—
217#340—261no—
218#331—262no—
219C22×C13#38611yescharacteristic
220C22×C13#45011yescharacteristic
221C22×C13#45011yescharacteristic
222C22×C13#45211yescharacteristic
223C22×C13#45211yescharacteristic
224C22×C13#45311yescharacteristic
225C22×C13#45311yescharacteristic
226C2×D13—44no—
227C2×D13—44no—
228C2×D13—44no—
229C2×D13—82no—
230C2×D13—82no—
231C2×D13—82no—
232C2×D13—82no—
233C4×C13—21no—
234C4×C13—21no—
235C4×C13—42no—
236C4×C13—81no—
237C4×C13—82no—
238C4×C13C4×SD1611yescharacteristic
239C4×C13C4×SD1611yescharacteristic
240C4×C13#44011yescharacteristic
241C4×C13#44011yescharacteristic
242C4×C13#46111yescharacteristic
243C4×C13#46111yescharacteristic
244C4×C13#46311yescharacteristic
245C4×C13#46311yescharacteristic
246Dic13—42no—
247Dic13—81no—
248C22×Q8—21no—
249C22×D4—132no—
250C22×D4—261no—
251C22×D4—261no—
252C23×C4—262no—
253C2×SD16—268no—
254C2×SD16—524no—
255C2×SD16—524no—
256C22×C8—21no—
257C22×C8—261no—
258C22×C8—261no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8C4×D1312yescomplemented
263#127—132no—
264#127—132no—
265#127—261no—
266#127—261no—
267C4×D4—522no—
268C4×D4—522no—
269C4×D4—522no—
270C4×D4—522no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—131no—
274C2×C4⋊C4—131no—
275C2×C4⋊C4C22⋊D1311yescharacteristic
276C2×C4⋊C4C22⋊D1311yescharacteristic
277C2×C22⋊C4—262no—
278C2×C22⋊C4—262no—
279C2×C22⋊C4—262no—
280C2×C42—21no—
281C2×C42—261no—
282C2×C42C22×D1311yescharacteristic
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—261no—
286C4⋊C8—261no—
287C4×C8—132no—
288C4×C8—261no—
289#95—21no—
290#95—261no—
291C2×C13#162911yescharacteristic
292C2×C13#163011yescharacteristic
293C2×C13#163111yescharacteristic
294C2×C13#163111yescharacteristic
295C2×C13#187711yescharacteristic
296C2×C13#187711yescharacteristic
297C2×C13#188711yescharacteristic
298D13—84no—
299C24—262no—
300C2×Q8—22no—
301C2×Q8—42no—
302C2×Q8—42no—
303C2×Q8—41no—
304C2×D4—134no—
305C2×D4—262no—
306C2×D4—262no—
307C2×D4—262no—
308C2×D4—262no—
309C2×D4—262no—
310C2×D4—522no—
311C2×D4—522no—
312C2×D4—521no—
313C2×D4—521no—
314C2×D4—521no—
315C2×D4—521no—
316C2×D4—521no—
317C2×D4—521no—
318C2×D4—521no—
319C2×D4—521no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—41no—
323C22×C4—261no—
324C22×C4—261no—
325C22×C4—524no—
326C22×C4—524no—
327C22×C4—1042no—
328C22×C4D4×D1311yescharacteristic
329C22×C4D4×D1311yescharacteristic
330C22×C4C2×C22⋊D1311yescharacteristic
331SD16—5216no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—262no—
336C2×C8—262no—
337C2×C8—262no—
338C2×C8—521no—
339C2×C8—521no—
340C2×C8—521no—
341C4⋊C4—21no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—132no—
349C4⋊C4—261no—
350C4⋊C4—261no—
351C4⋊C4—261no—
352C4⋊C4#610612yescomplemented
353C22⋊C4—524no—
354C22⋊C4—524no—
355C22⋊C4—1042no—
356C42—41no—
357C42—41no—
358C42—521no—
359C42—521no—
360C42C2×C4×D1311yescharacteristic
361C42#612711yescharacteristic
362C42D4×D1311yescharacteristic
363C42#612911yescharacteristic
364C13#906411yescharacteristic, complemented, Sylow
365C23—264no—
366C23—522no—
367C23—522no—
368C23—522no—
369C23—522no—
370C23—522no—
371C23—522no—
372C23#8819111yescharacteristic
373Q8—44no—
374Q8—82no—
375D4—524no—
376D4—522no—
377D4—522no—
378D4—522no—
379D4—522no—
380D4—522no—
381D4—522no—
382D4—522no—
383D4—522no—
384D4—1042no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—262no—
397C2×C4—521no—
398C2×C4—521no—
399C2×C4—521no—
400C2×C4—521no—
401C2×C4—521no—
402C2×C4—1048no—
403C2×C4C22⋊C4×D1311yescharacteristic
404C2×C4#8813511yescharacteristic
405C2×C4#8813711yescharacteristic
406C2×C4#8813811yescharacteristic
407C2×C4SD16×D1311yescharacteristic
408C2×C4#8816811yescharacteristic
409C2×C4#8817211yescharacteristic
410C2×C4#8817311yescharacteristic
411C2×C4C4×C22⋊D1311yescharacteristic
412C2×C4#8819211yescharacteristic
413C2×C4C2×#610611yescharacteristic
414C2×C4#8819611yescharacteristic
415C2×C4#8820311yescharacteristic
416C2×C4#8820411yescharacteristic
417C8—81no—
418C8—264no—
419C8—1041no—
420C22—524no—
421C22—524no—
422C22—524no—
423C22—1042no—
424C22—1042no—
425C22—1042no—
426C22—1042no—
427C22#1171861711yescharacteristic
428C22#1171870711yescharacteristic
429C22#1171870811yescharacteristic
430C22#1171883011yescharacteristic
431C22#1171884811yescharacteristic
432C22#1171885911yescharacteristic
433C22#1171885911yescharacteristic
434C4—21no—
435C4—21no—
436C4—42no—
437C4—82no—
438C4—81no—
439C4—522no—
440C4—1041no—
441C4#1171844911yescharacteristic
442C4#1171847811yescharacteristic
443C4#1171847911yescharacteristic
444C4#1171848011yescharacteristic
445C4C4×#610611yescharacteristic
446C4#1171868711yescharacteristic
447C4#1171871811yescharacteristic
448C4#1171874411yescharacteristic
449C2—1044no—
450C2#1311395111yescharacteristic
451C2#1311395611yescharacteristic
452C2#1311396111yescharacteristic
453C2#1311396211yescharacteristic
454C2#1311516711yescharacteristic
455C2#1311517311yescharacteristic
456C2#1311523111yescharacteristic
subgroupG/H
centerC23#88191
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1987C2
socleC23×C13#120
prime radicalC2×#88128C22
cosocleC2×C42×C13C23
hypercenter#1987D13
hypocenterC13#9064
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
3. #13115785C2semidirect
5. #13112677C2semidirect
6. #13112675C2semidirect
7. C13×#1987C2semidirect
16. #11718746C4semidirect
37. C13×C4⋊Q8C2×C4semidirect
70. C4×#1055C2×C4semidirect
114. C13×C4⋊C4SD16semidirect
128. C4⋊Dic13SD16semidirect
140. #1987D13semidirect
262. C4⋊Q8C4×D13semidirect
352. C4⋊C4#6106semidirect
364. C13#9064semidirect

Maximal subgroups

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

subgroupindex
C2×#117187462
#131179002
#131157852
C2×#117180772
#131126772
#131126752
C13×#19872
#906413