Finite Group Databasebeta

← #16789453

Subgroups — #16789453

Order 3328.

628 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718294C212yesmaximal
2#13130581C212yesmaximal, complemented
3#13129930C212yesmaximal, complemented
4#13117560C211yesmaximal, characteristic
5C2×#88194C2211yescharacteristic
6C2×D4×Dic13C411yescharacteristic, complemented
7C2×#88147C2211yescharacteristic
8C4×C22⋊#261—22no—
9C2×#88107C2214yes—
10C13×#390C411yescharacteristic, complemented
11#11718638C411yescharacteristic, complemented
12#11718619—22no—
13#11718617—22no—
14#11718600C2211yescharacteristic
15#11718593C411yescharacteristic, complemented
16#11718294C418yescomplemented
17#11718289—22no—
18C22×D4×C13C2×C411yescharacteristic
19C22×C22⋊D13—22no—
20C23×Dic13—21no—
21C22×D52C2311yescharacteristic
22C22×C4×D13D412yes—
23C2×C22⋊#261—24no—
24C2×C4×#261—42no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C13×C22⋊C4—22no—
27C2×C42×C13C2×C411yescharacteristic
28C2×C22⋊Dic13—21no—
29#88194—22no—
30#88194C2×C414yes—
31D4×Dic13—42no—
32C2×#6103—22no—
33C2×#6103D412yes—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C4×Dic13C2×C411yescharacteristic
37#88147—42no—
38(C2×#261)⋊C4—42no—
39#88107—24no—
40#88107C2×C418yescomplemented
41#88071—22no—
42#88071—21no—
43#88071—21no—
44#12628—131nomaximal, Sylow
45C24×C13—21no—
46C23×D13C2×D412yes—
47C22×#261—44no—
48C2×D4×C13—21no—
49C2×D4×C13—41no—
50C2×D4×C13—41no—
51C2×D4×C13C4212yescomplemented
52C22×C4×C13—21no—
53C22×C4×C13C22⋊C412yes—
54C22×C4×C13C22×C411yescharacteristic
55C2×C22⋊D13—28no—
56C2×C22⋊D13—82no—
57C2×C22⋊D13—82no—
58C22×Dic13—21no—
59C22×Dic13—21no—
60C22×Dic13—42no—
61C22×Dic13—82no—
62C22×Dic13C22⋊C411yescharacteristic
63C22×Dic13C22⋊C411yescharacteristic
64C2×D52—41no—
65C2×D52—41no—
66C2×D52C22×C412yes—
67C2×D52#4112yes—
68C2×C4×D13—22no—
69C2×C4×D13—22no—
70C2×C4×D13—82no—
71C22⋊#261—28no—
72C22⋊#261—44no—
73C4×#261—84no—
74C13×C4⋊C4—41no—
75C13×C22⋊C4—82no—
76C42×C13—41no—
77C22⋊Dic13—42no—
78#6103—42no—
79#6103—82no—
80C4⋊Dic13—41no—
81C4×Dic13—21no—
82C4×Dic13—22no—
83C4×Dic13C4212yescomplemented
84#2328—131no—
85C2×#353—132no—
86C4×#99—132no—
87#1393—132no—
88C23×C13—22no—
89C23×C13—42no—
90C23×C13—42no—
91C23×C13—41no—
92C23×C13—41no—
93C23×C13C2×C22⋊C411yescharacteristic
94C22×D13—22no—
95C22×D13—22no—
96C22×D13—42no—
97C22×D13—42no—
98C22×D13C4×D414yes—
99C2×#261—48no—
100C2×#261—84no—
101C2×#261—84no—
102D4×C13—42no—
103D4×C13—42no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—42no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13C2×C4211yescharacteristic
112C2×C4×C13#11711yescharacteristic
113C22⋊D13—88no—
114C2×Dic13—22no—
115C2×Dic13—21no—
116C2×Dic13—41no—
117C2×Dic13—41no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—42no—
121C2×Dic13—41no—
122C2×Dic13—84no—
123C2×Dic13#9912yes—
124D52—42no—
125D52—42no—
126C4×D13—44no—
127C4×D13—82no—
128C2×#127—131no—
129C2×C4×D4—131no—
130C2×C4×D4—131no—
131C2×#99—134no—
132#390—131no—
133#390#26111yescharacteristic, complemented
134#386—262no—
135#386—262no—
136#382—131no—
137C4×C22⋊C4—262no—
138#376—131no—
139#353—138no—
140#342—262no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—44no—
144C22×C13—42no—
145C22×C13—82no—
146C22×C13—81no—
147C22×C13—81no—
148C22×C13C4×C22⋊C411yescharacteristic
149C22×C13C2×#9911yescharacteristic
150C22×C13#41011yescharacteristic
151C2×D13—24no—
152C2×D13—42no—
153C2×D13—42no—
154C2×D13—44no—
155C2×D13—82no—
156#261—88no—
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—42no—
160C4×C13—81no—
161Dic13—22no—
162Dic13—42no—
163Dic13—41no—
164Dic13—81no—
165C22×D4—131no—
166C22×D4—262no—
167C22×D4C2×#26111yescharacteristic
168C23×C4—132no—
169C23×C4—261no—
170#127—134no—
171#127—262no—
172C4×D4—522no—
173C4×D4—522no—
174C2×C4⋊C4—131no—
175C2×C4⋊C4C2×#26111yescharacteristic
176C2×C22⋊C4—22no—
177C2×C22⋊C4—132no—
178C2×C22⋊C4—264no—
179C2×C22⋊C4—261no—
180C2×C22⋊C4—262no—
181C2×C42—131no—
182C2×C42—131no—
183C2×C42—522no—
184C2×C42C2×#26111yescharacteristic
185#99—138no—
186#99—264no—
187#95—261no—
188#95—261no—
189#95—262no—
190#95—522no—
191C2×C13—21no—
192C2×C13—21no—
193C2×C13—82no—
194C2×C13C4×#9911yescharacteristic
195C2×C13#212711yescharacteristic
196C2×C13#212811yescharacteristic
197D13—44no—
198C24—21no—
199C24—132no—
200C2×D4—21no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4—132no—
204C2×D4—132no—
205C2×D4—268no—
206C2×D4—521no—
207C2×D4—521no—
208C2×D4—1042no—
209C2×D4—1042no—
210C2×D4C4×#26112yescomplemented
211C22×C4—21no—
212C22×C4—131no—
213C22×C4—131no—
214C22×C4—262no—
215C22×C4—262no—
216C22×C4—261no—
217C22×C4—261no—
218C22×C4—522no—
219C22×C4—524no—
220C22×C4—1042no—
221C22×C4—1042no—
222C22×C4C22⋊#26112yes—
223C22×C4C22×#26111yescharacteristic
224C4⋊C4—41no—
225C4⋊C4—521no—
226C22⋊C4—82no—
227C22⋊C4—268no—
228C22⋊C4—522no—
229C22⋊C4—522no—
230C22⋊C4—524no—
231C22⋊C4—1042no—
232C42—41no—
233C42—132no—
234C42—262no—
235C42—261no—
236C42—1044no—
237C13#1262811yescharacteristic, complemented, Sylow
238C23—22no—
239C23—42no—
240C23—42no—
241C23—41no—
242C23—41no—
243C23—134no—
244C23—262no—
245C23—262no—
246C23—522no—
247C23—522no—
248C23C2×C22⋊#26111yescharacteristic
249D4—42no—
250D4—42no—
251D4—522no—
252D4—522no—
253D4—1048no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—132no—
262C2×C4—262no—
263C2×C4—261no—
264C2×C4—524no—
265C2×C4—521no—
266C2×C4—521no—
267C2×C4—521no—
268C2×C4—521no—
269C2×C4—522no—
270C2×C4—528no—
271C2×C4—521no—
272C2×C4—1042no—
273C2×C4—1044no—
274C2×C4—1044no—
275C2×C4—1044no—
276C2×C4C2×C4×#26111yescharacteristic
277C2×C4#8823711yescharacteristic
278C22—21no—
279C22—21no—
280C22—44no—
281C22—42no—
282C22—82no—
283C22—81no—
284C22—81no—
285C22—264no—
286C22—524no—
287C22—522no—
288C22—522no—
289C22—1042no—
290C22C4×C22⋊#26111yescharacteristic
291C22D13⋊#9911yescharacteristic
292C22#1171914211yescharacteristic
293C4—21no—
294C4—21no—
295C4—42no—
296C4—81no—
297C4—262no—
298C4—522no—
299C4—521no—
300C4—1048no—
301C4—1041no—
302C2—21no—
303C2—21no—
304C2—82no—
305C2—524no—
306C2#1313058311yescharacteristic
307C2#1313111211yescharacteristic
308C2#1313111611yescharacteristic
subgroupG/H
centerC22D13⋊#99
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#390C4
socleC22×C13C2×#99
prime radicalC2×#88194C22
cosocleC22×D52C23
hypercenter#390#261
hypocenterC13#12628
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. #13130581C2semidirect
3. #13129930C2semidirect
6. C2×D4×Dic13C4semidirect
10. C13×#390C4semidirect
11. #11718638C4semidirect
15. #11718593C4semidirect
16. #11718294C4semidirect
40. #88107C2×C4semidirect
51. C2×D4×C13C42semidirect
83. C4×Dic13C42semidirect
133. #390#261semidirect
210. C2×D4C4×#261semidirect
237. C13#12628semidirect

Maximal subgroups

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

subgroupindex
C2×#117182942
#131305812
#131299302
#131175602
#1262813