Finite Group Databasebeta

← #15848160

Subgroups — #15848160

Order 3328.

642 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124629C211yesmaximal, characteristic
2C2×#11718745C211yesmaximal, characteristic
3#13123859C211yesmaximal, characteristic
4#13114284C214yesmaximal, complemented
5#13114232C214yesmaximal, complemented
6#13113611C211yesmaximal, characteristic, complemented
7#13113517C211yesmaximal, characteristic, complemented
8#13113493C211yesmaximal, characteristic, complemented
9C13×#3230C211yesmaximal, characteristic, complemented
10C13×#533C2211yescharacteristic
11C2×C13×C4⋊Q8C2211yescharacteristic
12C2×C4×D52C2211yescharacteristic
13C13×#500C2212yescomplemented
14C13×#487C2212yescomplemented
15C13×#484—22no—
16C13×#477—22no—
17C13×#431C2211yescharacteristic
18#11718748C2212yes—
19#11718745—22no—
20#11718745C2212yes—
21#11718745C2214yes—
22#11718727—22no—
23#11718662—21no—
24#11718656—21no—
25C2×#88049—21no—
26C2×#88048—21no—
27#11718586C2211yescharacteristic
28#11718585C2211yescharacteristic
29C2×C4⋊#1055C2211yescharacteristic
30#11718495—22no—
31D13×C22⋊C8—22no—
32C8×D52C2214yes—
33#11718139C2212yescomplemented
34#11718138C2212yescomplemented
35#11718138C2214yescomplemented
36#11718050C2214yescomplemented
37C22×Q8×C13—21no—
38C22×D52D411yescharacteristic
39C22×C4×D13—21no—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8C2312yes—
44C13×C4⋊Q8C2311yescharacteristic
45C13×C4⋊Q8C2311yescharacteristic
46C13×#125—21no—
47C13×C22⋊Q8—21no—
48C13×C22⋊Q8—21no—
49C4×Q8×C13—21no—
50C4×Q8×C13—21no—
51C13×#117—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C42×C13C2311yescharacteristic
55C2×#6103—21no—
56C2×C4⋊Dic13D411yescharacteristic
57C2×#6099—21no—
58C22×#1055—21no—
59C2×C8×D13—24no—
60C4×D52—21no—
61C4×D52—21no—
62C4×D52D412yes—
63C4×D52C2312yes—
64C13×#107—24no—
65C13×C4⋊C8D412yes—
66C13×#103—24no—
67C13×C22⋊C8D412yes—
68C4×C8×C13C2312yes—
69C22⋊#1055—21no—
70#88060—24no—
71#88049—22no—
72#88049—22no—
73#88049—24no—
74#88048—22no—
75#88048—24no—
76#88047—22no—
77C4⋊#1055—21no—
78C4⋊#1055—21no—
79C4⋊#1055C2312yes—
80C4⋊#1055C2312yes—
81C4⋊#1055C2312yes—
82C4×#1055—21no—
83#19393—131nomaximal, Sylow
84C23×D13—21no—
85C2×Q8×C13—21no—
86C2×Q8×C13—21no—
87C2×Q8×C13—22no—
88C2×Q8×C13—41no—
89C2×Q8×C13—82no—
90C22×C4×C13—41no—
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13#4111yescharacteristic
94C22×Dic13—21no—
95C2×D52—21no—
96C2×D52—22no—
97C2×D52Q1614yes—
98C2×D52C2×D412yes—
99C2×C4×D13—22no—
100C2×C4×D13—22no—
101C2×C4×D13—82no—
102C2×C8×C13C2×D414yes—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C22⋊C4—41no—
114C42×C13—41no—
115C42×C13C2×D411yescharacteristic
116C42×C13C2×D411yescharacteristic
117C42×C13#4111yescharacteristic
118C42×C13C2411yescharacteristic
119#6103—22no—
120#6103—22no—
121C4⋊Dic13—21no—
122C4⋊Dic13C2×D412yes—
123#6099—42no—
124C2×#1055—22no—
125C2×#1055—22no—
126C2×#1055—22no—
127C2×#1055—42no—
128C8×D13—84no—
129#3230D1311yescharacteristic, complemented
130#3077—131no—
131C2×#476—131no—
132#2972—131no—
133#1683—134no—
134#1675—134no—
135#1571—131no—
136#1548—131no—
137#1542—131no—
138C23×C13#12111yescharacteristic
139C22×D13—22no—
140C22×D13—24no—
141C22×D13—81no—
142C22×D13—81no—
143Q8×C13—42no—
144Q8×C13—82no—
145Q8×C13—81no—
146Q8×C13—82no—
147C2×C4×C13—22no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—42no—
152C2×C4×C13—82no—
153C2×C4×C13#12111yescharacteristic
154C2×C4×C13#12111yescharacteristic
155C2×C4×C13#12111yescharacteristic
156C2×C4×C13C2×Q1612yes—
157C2×C4×C13#13512yes—
158C2×C4×C13C22×D411yescharacteristic
159C2×C4×C13C22×D411yescharacteristic
160C2×C4×C13C2×#4111yescharacteristic
161C2×Dic13—22no—
162C2×Dic13—81no—
163D52—22no—
164D52—24no—
165D52C2×Q1614yes—
166C4×D13—44no—
167C4×D13—82no—
168C8×C13—24no—
169#1055—42no—
170#1055—42no—
171#1055—42no—
172#533C2×D1311yescharacteristic
173C2×C4⋊Q8C2×D1311yescharacteristic
174C2×C4×D4—131no—
175#500C2×D1312yescomplemented
176#487C2×D1312yescomplemented
177#484—22no—
178#478—262no—
179#477—22no—
180#476—132no—
181#476—134no—
182#476—262no—
183#474—132no—
184C8×D4—134no—
185C8×D4—262no—
186#431—131no—
187#431C2×D1311yescharacteristic
188#428—261no—
189C2×#106—261no—
190#423—131no—
191C2×C4⋊C8—131no—
192#418—261no—
193C2×#102—261no—
194C2×C22⋊C8—262no—
195#335—134no—
196#333—132no—
197#333—134no—
198#332—132no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13#46712yes—
202C22×C13C2×#12111yescharacteristic
203C2×D13—24no—
204C2×D13—42no—
205C2×D13—42no—
206C2×D13—84no—
207C4×C13—21no—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—81no—
211C4×C13—82no—
212C4×C13—81no—
213C4×C13#46712yes—
214C4×C13C22×Q1611yescharacteristic
215C4×C13C2×#13511yescharacteristic
216C4×C13#57712yes—
217Dic13—42no—
218C22×Q8—21no—
219C22×D4—131no—
220C23×C4—261no—
221C2×M16—261no—
222C22×C8—261no—
223C22×C8—264no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8C22×D1312yes—
228C4⋊Q8C22×D1311yescharacteristic
229C4⋊Q8C22×D1311yescharacteristic
230#125—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—132no—
236C4×D4—132no—
237C4×D4—261no—
238C4×D4—261no—
239#117—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—131no—
243C2×C22⋊C4—261no—
244C2×C42C22×D1311yescharacteristic
245#107—24no—
246#107—262no—
247#106—264no—
248#106—262no—
249C4⋊C8—132no—
250C4⋊C8—132no—
251C4⋊C8—132no—
252C4⋊C8—261no—
253C4⋊C8—261no—
254C4⋊C8C22⋊D1312yes—
255#103—24no—
256#102—264no—
257#102—262no—
258#102—262no—
259C22⋊C8—261no—
260C22⋊C8—264no—
261C22⋊C8C22⋊D1312yes—
262C4×C8—261no—
263C4×C8C22×D1312yes—
264C2×C13—22no—
265C2×C13#304211yescharacteristic
266C2×C13C2×#46711yescharacteristic
267C2×C13#306811yescharacteristic
268D13—44no—
269C24—261no—
270C2×Q8—21no—
271C2×Q8—22no—
272C2×Q8—21no—
273C2×Q8—41no—
274C2×Q8—82no—
275C2×D4—134no—
276C2×D4—132no—
277C2×D4—262no—
278C2×D4—261no—
279C22×C4—41no—
280C22×C4—261no—
281C22×C4—262no—
282C22×C4—262no—
283C22×C4—1042no—
284C22×C4D4×D1311yescharacteristic
285C22×C4#612911yescharacteristic
286C22×C4C2×C22⋊D1311yescharacteristic
287M16—522no—
288C2×C8—262no—
289C2×C8—262no—
290C2×C8—262no—
291C2×C8—522no—
292C2×C8—1044no—
293C2×C8C2×C22⋊D1314yes—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—132no—
305C4⋊C4—261no—
306C22⋊C4—41no—
307C22⋊C4—262no—
308C22⋊C4—262no—
309C42—41no—
310C42D4×D1311yescharacteristic
311C42#612911yescharacteristic
312C42C2×C22⋊D1311yescharacteristic
313C42C23×D1311yescharacteristic
314C13#1939311yescharacteristic, complemented, Sylow
315C23—262no—
316C23—264no—
317C23—1041no—
318C23—1041no—
319C23#8819211yescharacteristic
320Q8—42no—
321Q8—82no—
322Q8—81no—
323Q8—82no—
324D4—134no—
325D4—262no—
326D4—264no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—82no—
333C2×C4—262no—
334C2×C4—524no—
335C2×C4—1042no—
336C2×C4—1041no—
337C2×C4Q16×D1312yes—
338C2×C4#8817312yes—
339C2×C4#8819211yescharacteristic
340C2×C4#8819211yescharacteristic
341C2×C4#8819211yescharacteristic
342C2×C4C2×D4×D1311yescharacteristic
343C2×C4C2×#612911yescharacteristic
344C2×C4C22×C22⋊D1311yescharacteristic
345C8—24no—
346C8—522no—
347C8—522no—
348C8—522no—
349C22—21no—
350C22—21no—
351C22—264no—
352C22—522no—
353C22—522no—
354C22—1044no—
355C22#1171884912yes—
356C22C2×#8819211yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—82no—
361C4—81no—
362C4—81no—
363C4—522no—
364C4#1171884912yes—
365C4C2×Q16×D1311yescharacteristic
366C4C2×#8817311yescharacteristic
367C4#1171954212yes—
368C2—22no—
369C2—524no—
370C2#1312434411yescharacteristic
371C2C2×#1171884911yescharacteristic
372C2#1312456011yescharacteristic
subgroupG/H
centerC22C2×#88192
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#3230C2
socleC22×C13C2×#121
prime radicalC22×D52D4
hypercenter#3230D13
hypocenterC13#19393
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
4. #13114284C2semidirect
5. #13114232C2semidirect
6. #13113611C2semidirect
7. #13113517C2semidirect
8. #13113493C2semidirect
9. C13×#3230C2semidirect
13. C13×#500C22semidirect
14. C13×#487C22semidirect
33. #11718139C22semidirect
34. #11718138C22semidirect
35. #11718138C22semidirect
36. #11718050C22semidirect
129. #3230D13semidirect
175. #500C2×D13semidirect
176. #487C2×D13semidirect
314. C13#19393semidirect

Maximal subgroups

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

subgroupindex
#131246292
C2×#117187452
#131238592
#131142842
#131142322
#131136112
#131135172
#131134932
C13×#32302
#1939313