Finite Group Databasebeta

← #15848157

Subgroups — #15848157

Order 3328.

728 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125954C211yesmaximal, characteristic, complemented
2C2×#11718680C211yesmaximal, characteristic, complemented
3#13123860C211yesmaximal, characteristic, complemented
4#13114271C214yesmaximal, complemented
5#13114223C214yesmaximal, complemented
6#13113612C211yesmaximal, characteristic, complemented
7#13113509C211yesmaximal, characteristic, complemented
8#13113485C211yesmaximal, characteristic, complemented
9C13×#3036C211yesmaximal, characteristic
10C2×C13×AGL(1,ℤ/8)—21no—
11C13×#532C2211yescharacteristic
12C2×C4×D4×C13C2211yescharacteristic
13C22×#6105—21no—
14C2×#88123C2211yescharacteristic
15C13×#463—22no—
16C13×#461C2212yes—
17C13×#459C2212yes—
18C13×#423C2211yescharacteristic
19C13×#417—21no—
20C2×C22⋊#1055—22no—
21#11718739C2212yescomplemented
22#11718731C2212yescomplemented
23#11718694—22no—
24#11718680—22no—
25#11718680C2214yes—
26D4×#1055—22no—
27D4×#1055C2214yes—
28#11718668—22no—
29C2×#88050—21no—
30#11718586C2211yescharacteristic
31#11718586C2211yescharacteristic
32C2×C4⋊#1055C2211yescharacteristic
33#11718139C2212yescomplemented
34#11718136C2212yescomplemented
35#11718074C2214yescomplemented
36#11718071C2214yescomplemented
37C2×C13×#41—21no—
38C22×D4×C13D411yescharacteristic
39C23×C4×C13—21no—
40C22×Dic26—21no—
41C13×AGL(1,ℤ/8)—44no—
42C2×C13×SD16—22no—
43C2×C13×D8—22no—
44C2×C13×M16—21no—
45C13×C4⋊Q8C2311yescharacteristic
46C13×#127C2311yescharacteristic
47C13×#124—21no—
48C13×#121—21no—
49C13×#121—21no—
50C4×D4×C13—21no—
51C4×D4×C13—21no—
52C4×D4×C13—21no—
53C4×D4×C13—21no—
54C4×D4×C13D412yes—
55C4×D4×C13C2312yes—
56C2×C13×C4⋊C4D411yescharacteristic
57C2×C13×C22⋊C4—21no—
58C2×C42×C13C2311yescharacteristic
59C2×#6105—24no—
60C2×#6105—44no—
61C2×C4⋊Dic13—21no—
62C2×C4⋊Dic13—21no—
63C22×#1055—21no—
64C22×#1055—24no—
65#88123—21no—
66#88123—21no—
67#88123—21no—
68#88123C2312yes—
69C13×C4⋊C8—21no—
70C13×C4⋊C8C2312yes—
71C13×#103—22no—
72C13×#102—22no—
73#88072—24no—
74C22⋊#1055—21no—
75C22⋊#1055—24no—
76C22⋊#1055D412yes—
77#88050—24no—
78#88047—24no—
79C4⋊#1055—21no—
80C4⋊#1055D412yes—
81C4⋊#1055C2312yes—
82C4⋊#1055C2312yes—
83C4×#1055—21no—
84C4×#1055C2312yes—
85#19392—131nomaximal, Sylow
86C24×C13—21no—
87C13×#41—42no—
88C13×#41—42no—
89C2×Q8×C13—21no—
90C2×D4×C13—21no—
91C2×D4×C13—22no—
92C2×D4×C13—21no—
93C2×D4×C13—21no—
94C2×D4×C13—21no—
95C2×D4×C13—41no—
96C2×D4×C13D814yes—
97C2×D4×C13C2×D412yes—
98C22×C4×C13—21no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—41no—
102C22×C4×C13—82no—
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13#4111yescharacteristic
106C22×Dic13—41no—
107C2×Dic26—22no—
108C2×Dic26—42no—
109C2×Dic26—42no—
110C2×Dic26—41no—
111C13×SD16—44no—
112C13×D8—44no—
113C13×M16—42no—
114C2×C8×C13—22no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4C2×D412yes—
119C13×C22⋊C4—22no—
120C13×C22⋊C4—22no—
121C13×C22⋊C4—41no—
122C13×C22⋊C4—41no—
123C42×C13C2×D411yescharacteristic
124C42×C13C2×D411yescharacteristic
125C42×C13#4111yescharacteristic
126C42×C13C2411yescharacteristic
127#6105—48no—
128C4⋊Dic13—22no—
129C4⋊Dic13—22no—
130C4⋊Dic13—41no—
131C4⋊Dic13—41no—
132C2×#1055—22no—
133C2×#1055—22no—
134C2×#1055—42no—
135C2×#1055—84no—
136C2×#1055C2×D414yes—
137#3226—131no—
138#3036D1311yescharacteristic
139C2×#461—131no—
140#2972—131no—
141#1681—134no—
142#1673—134no—
143#1571—131no—
144#1546—131no—
145#1540—131no—
146C23×C13—22no—
147C23×C13—24no—
148C23×C13—41no—
149C23×C13—81no—
150C23×C13—81no—
151C23×C13#12111yescharacteristic
152Q8×C13—41no—
153Q8×C13—41no—
154D4×C13—22no—
155D4×C13—24no—
156D4×C13—41no—
157D4×C13—41no—
158D4×C13—42no—
159D4×C13—81no—
160D4×C13—82no—
161D4×C13C2×D814yes—
162C2×C4×C13—22no—
163C2×C4×C13—22no—
164C2×C4×C13—41no—
165C2×C4×C13—44no—
166C2×C4×C13—41no—
167C2×C4×C13—82no—
168C2×C4×C13—81no—
169C2×C4×C13—82no—
170C2×C4×C13#12111yescharacteristic
171C2×C4×C13#12111yescharacteristic
172C2×C4×C13#12111yescharacteristic
173C2×C4×C13C2×D812yes—
174C2×C4×C13#13512yes—
175C2×C4×C13C22×D411yescharacteristic
176C2×C4×C13C22×D411yescharacteristic
177C2×C4×C13C2×#4111yescharacteristic
178C2×Dic13—42no—
179C2×Dic13—82no—
180Dic26—42no—
181Dic26—42no—
182Dic26—82no—
183C8×C13—42no—
184#1055—24no—
185#1055—42no—
186#1055—42no—
187C2×AGL(1,ℤ/8)—21no—
188C22×SD16—261no—
189#532C2×D1311yescharacteristic
190C2×C4⋊Q8—131no—
191C2×C4×D4C2×D1311yescharacteristic
192#500—132no—
193#486—132no—
194#480—262no—
195#474—262no—
196#463—22no—
197#461—134no—
198#461—262no—
199#461C2×D1312yes—
200#459C2×D1312yes—
201C8×D4—134no—
202C8×D4—262no—
203#431—131no—
204#431—131no—
205#423C2×D1311yescharacteristic
206C2×C4⋊C8—131no—
207#417—21no—
208C2×#103—261no—
209C2×C22⋊C8—262no—
210#335—134no—
211#332—132no—
212#332—134no—
213#331—132no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—24no—
217C22×C13—42no—
218C22×C13—42no—
219C22×C13—84no—
220C22×C13—81no—
221C22×C13—81no—
222C22×C13—81no—
223C22×C13#46612yes—
224C22×C13C2×#12111yescharacteristic
225C4×C13—21no—
226C4×C13—21no—
227C4×C13—21no—
228C4×C13—42no—
229C4×C13—81no—
230C4×C13#46612yes—
231C4×C13C22×D811yescharacteristic
232C4×C13C2×#13511yescharacteristic
233C4×C13#57712yes—
234Dic13—82no—
235C2×#41—21no—
236C22×Q8—261no—
237C22×D4C22⋊D1311yescharacteristic
238C23×C4—21no—
239AGL(1,ℤ/8)—44no—
240C2×SD16—22no—
241C2×SD16—264no—
242C2×SD16—524no—
243C2×D8—22no—
244C2×M16—21no—
245C22×C8—264no—
246C22×C8—261no—
247C4⋊Q8—132no—
248C4⋊Q8—261no—
249C4⋊Q8—261no—
250C4⋊Q8—261no—
251C4⋊Q8C22×D1311yescharacteristic
252#127C22×D1311yescharacteristic
253#124—21no—
254#121—21no—
255#121—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4C22⋊D1312yes—
261C4×D4C22×D1312yes—
262C2×C4⋊C4—261no—
263C2×C4⋊C4—261no—
264C2×C4⋊C4C22⋊D1311yescharacteristic
265C2×C22⋊C4—21no—
266C2×C42C22×D1311yescharacteristic
267#107—264no—
268C4⋊C8—21no—
269C4⋊C8—132no—
270C4⋊C8—132no—
271C4⋊C8—132no—
272C4⋊C8—261no—
273C4⋊C8C22×D1312yes—
274#103—22no—
275#103—264no—
276#102—22no—
277#102—264no—
278C22⋊C8—132no—
279C22⋊C8—264no—
280C22⋊C8—261no—
281C4×C8—132no—
282C4×C8—261no—
283C2×C13—22no—
284C2×C13—44no—
285C2×C13—161no—
286C2×C13#304211yescharacteristic
287C2×C13C2×#46611yescharacteristic
288C2×C13#306911yescharacteristic
289C24—21no—
290#41—42no—
291#41—42no—
292C2×Q8—21no—
293C2×Q8—262no—
294C2×Q8—521no—
295C2×Q8—522no—
296C2×Q8—522no—
297C2×D4—21no—
298C2×D4—22no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—41no—
303C2×D4#610414yes—
304C2×D4C2×C22⋊D1312yes—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—41no—
309C22×C4—82no—
310C22×C4—521no—
311C22×C4D4×D1311yescharacteristic
312C22×C4#612911yescharacteristic
313C22×C4C2×C22⋊D1311yescharacteristic
314SD16—44no—
315SD16—528no—
316D8—44no—
317M16—42no—
318C2×C8—22no—
319C2×C8—134no—
320C2×C8—262no—
321C2×C8—262no—
322C2×C8—522no—
323C2×C8—1044no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—262no—
328C4⋊C4—262no—
329C4⋊C4—521no—
330C4⋊C4—521no—
331C4⋊C4C2×C22⋊D1312yes—
332C22⋊C4—22no—
333C22⋊C4—22no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C42D4×D1311yescharacteristic
337C42#612911yescharacteristic
338C42C2×C22⋊D1311yescharacteristic
339C42C23×D1311yescharacteristic
340C13#1939211yescharacteristic, complemented, Sylow
341C23—22no—
342C23—24no—
343C23—41no—
344C23—81no—
345C23—81no—
346C23#8819311yescharacteristic
347Q8—41no—
348Q8—41no—
349Q8—522no—
350Q8—522no—
351Q8—1042no—
352D4—24no—
353D4—22no—
354D4—42no—
355D4—41no—
356D4—41no—
357D4—81no—
358D4—82no—
359D4C2×#610414yes—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—44no—
364C2×C4—41no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4—82no—
368C2×C4—522no—
369C2×C4—1042no—
370C2×C4C2×#610412yes—
371C2×C4#8819311yescharacteristic
372C2×C4#8819311yescharacteristic
373C2×C4#8819311yescharacteristic
374C2×C4#8820412yes—
375C2×C4C2×D4×D1311yescharacteristic
376C2×C4C2×#612911yescharacteristic
377C2×C4C22×C22⋊D1311yescharacteristic
378C8—42no—
379C8—264no—
380C8—522no—
381C8—522no—
382C22—21no—
383C22—21no—
384C22—24no—
385C22—42no—
386C22—42no—
387C22—84no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22#1171869912yes—
392C22C2×#8819311yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—81no—
398C4—1042no—
399C4#1171869912yes—
400C4#1171948012yes—
401C4C22×#610411yescharacteristic
402C4C2×#8820411yescharacteristic
403C2—22no—
404C2—44no—
405C2—161no—
406C2#1312435011yescharacteristic
407C2C2×#1171869911yescharacteristic
408C2#1312457511yescharacteristic
subgroupG/H
centerC22C2×#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
Fitting, prime radicalC13×#3036C2
socleC22×C13C2×#121
hypercenter#3036D13
hypocenterC13#19392
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13125954C2semidirect
2. C2×#11718680C2semidirect
3. #13123860C2semidirect
4. #13114271C2semidirect
5. #13114223C2semidirect
6. #13113612C2semidirect
7. #13113509C2semidirect
8. #13113485C2semidirect
21. #11718739C22semidirect
22. #11718731C22semidirect
33. #11718139C22semidirect
34. #11718136C22semidirect
35. #11718074C22semidirect
36. #11718071C22semidirect
340. C13#19392semidirect

Maximal subgroups

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

subgroupindex
#131259542
C2×#117186802
#131238602
#131142712
#131142232
#131136122
#131135092
#131134852
C13×#30362
#1939213