Finite Group Databasebeta

← #16791260

Subgroups — #16791260

Order 3328.

474 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 60 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×#11718225C212yesmaximal, complemented
2#13129969C212yesmaximal, complemented
3#13129967C212yesmaximal, complemented
4#13125289C211yesmaximal, characteristic
5C13×#532C411yescharacteristic, complemented
6C2×#88203—22no—
7C2×#88128C2211yescharacteristic
8C2×#88107—22no—
9#11718746C411yescharacteristic, complemented
10#11718746C2211yescharacteristic
11#11718734C411yescharacteristic, complemented
12#11718734C2211yescharacteristic
13#11718719—22no—
14C4×#6099C411yescharacteristic, complemented
15#11718225—22no—
16#11718225C2214yes—
17C2×C13×#41—21no—
18C22×D52—41no—
19C22×D52D412yes—
20C2×C22⋊#261—42no—
21C13×C4⋊Q8C2×C411yescharacteristic, complemented
22C13×#127C2×C411yescharacteristic, complemented
23C13×#124—21no—
24C13×#121—41no—
25C4×D4×C13—41no—
26C2×C42×C13C2×C411yescharacteristic
27#88203—44no—
28#88203—44no—
29C2×#6106—22no—
30C2×#6106—22no—
31C2×#6104—22no—
32C2×#6104—22no—
33C2×#6099—21no—
34#88128—41no—
35#88128C2×C411yescharacteristic
36#88128D412yes—
37#88128C2311yescharacteristic
38#88107—24no—
39#88107—42no—
40#88043—21no—
41C4×#1055C2×C411yescharacteristic, complemented
42C4×#1055C2×C411yescharacteristic, complemented
43#13584—131nomaximal, Sylow
44C23×D13—22no—
45C22×#261—82no—
46C13×#41—42no—
47C13×#41—42no—
48C2×Q8×C13—21no—
49C2×D4×C13—21no—
50C2×D4×C13—41no—
51C2×D4×C13—41no—
52C22×C4×C13—21no—
53C22×C4×C13—41no—
54C22×C4×C13C22⋊C411yescharacteristic
55C2×D52—22no—
56C2×D52—42no—
57C2×D52—42no—
58C2×D52—41no—
59C2×D52—42no—
60C2×D52—41no—
61C2×D52—84no—
62C2×D52C22⋊C412yes—
63C2×D52C2×D412yes—
64C22⋊#261—44no—
65C22⋊#261—82no—
66C13×C4⋊C4—41no—
67C13×C22⋊C4—42no—
68C42×C13—21no—
69C42×C13C22⋊C411yescharacteristic
70C42×C13C22×C411yescharacteristic
71#6106—44no—
72#6106—44no—
73#6104—44no—
74#6104—44no—
75#6099—24no—
76C2×#1055—21no—
77C2×#1055—21no—
78#3151—131no—
79C2×#353—132no—
80#1409—132no—
81#1408—132no—
82C23×C13—41no—
83C23×C13#9911yescharacteristic
84C22×D13—22no—
85C22×D13—22no—
86C22×D13—42no—
87C22×D13—42no—
88C22×D13—84no—
89C2×#261—84no—
90C2×#261—164no—
91Q8×C13—42no—
92D4×C13—42no—
93D4×C13—82no—
94D4×C13—82no—
95C2×C4×C13—22no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—42no—
99C2×C4×C13—41no—
100C2×C4×C13—81no—
101C2×C4×C13—81no—
102C2×C4×C13#9911yescharacteristic
103C2×C4×C13C2×C22⋊C411yescharacteristic
104D52—42no—
105D52—42no—
106D52—82no—
107D52—82no—
108D52—82no—
109D52—84no—
110#1055—22no—
111#1055—22no—
112C2×AGL(1,ℤ/8)—262no—
113#532#26111yescharacteristic, complemented
114C2×#127—131no—
115#496—262no—
116#493—131no—
117#493—131no—
118#492—131no—
119#492—131no—
120C2×#99—262no—
121C4×M16—131no—
122#353—134no—
123#353—262no—
124C22×C13—41no—
125C22×C13—82no—
126C22×C13—81no—
127C22×C13#35312yes—
128C22×C13C2×#9911yescharacteristic
129C2×D13—42no—
130C2×D13—42no—
131C2×D13—84no—
132C2×D13—82no—
133C2×D13—82no—
134C2×D13—162no—
135#261—164no—
136C4×C13—22no—
137C4×C13—21no—
138C4×C13—21no—
139C4×C13—41no—
140C4×C13—81no—
141C2×#41—21no—
142C22×D4—132no—
143C22×D4—521no—
144AGL(1,ℤ/8)—524no—
145AGL(1,ℤ/8)—524no—
146C2×SD16—262no—
147C2×SD16—262no—
148C2×D8—262no—
149C2×D8—262no—
150C2×M16—261no—
151C4⋊Q8C2×#26111yescharacteristic, complemented
152#127—132no—
153#127—131no—
154#127—131no—
155#127—521no—
156#127C2×#26111yescharacteristic, complemented
157#124—21no—
158#121—41no—
159C4×D4—41no—
160C2×C22⋊C4—522no—
161C2×C42C2×#26111yescharacteristic
162#99—264no—
163#99—522no—
164#97—261no—
165C4×C8—131no—
166C4×C8—131no—
167C2×C13—21no—
168C2×C13—22no—
169C2×C13—161no—
170C2×C13C2×#35311yescharacteristic
171D13—82no—
172D13—82no—
173C24—262no—
174#41—42no—
175#41—42no—
176C2×Q8—21no—
177C2×D4—21no—
178C2×D4—41no—
179C2×D4—41no—
180C2×D4—132no—
181C2×D4—132no—
182C2×D4—262no—
183C2×D4—522no—
184C2×D4—522no—
185C2×D4—521no—
186C2×D4—521no—
187C2×D4—522no—
188C2×D4—1044no—
189C22×C4—21no—
190C22×C4—41no—
191C22×C4—1042no—
192C22×C4C22⋊#26111yescharacteristic
193SD16—524no—
194SD16—524no—
195D8—524no—
196D8—524no—
197M16—264no—
198C2×C8—261no—
199C2×C8—261no—
200C4⋊C4—41no—
201C22⋊C4—42no—
202C22⋊C4—524no—
203C22⋊C4—1042no—
204C42—21no—
205C42C22⋊#26111yescharacteristic
206C42C22×#26111yescharacteristic
207C13#1358411yescharacteristic, complemented, Sylow
208C23—41no—
209C23—262no—
210C23—262no—
211C23—522no—
212C23—522no—
213C23—1044no—
214C23#8811911yescharacteristic
215Q8—42no—
216D4—42no—
217D4—82no—
218D4—82no—
219D4—522no—
220D4—522no—
221D4—1042no—
222D4—1042no—
223D4—1042no—
224D4—1044no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—41no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—1044no—
233C2×C4—2084no—
234C2×C4#8811911yescharacteristic
235C2×C4C2×C22⋊#26111yescharacteristic
236C8—262no—
237C8—262no—
238C22—41no—
239C22—82no—
240C22—81no—
241C22—522no—
242C22—522no—
243C22—1042no—
244C22—1042no—
245C22—1044no—
246C22—2082no—
247C22#1171829412yes—
248C22C2×#8811911yescharacteristic
249C4—22no—
250C4—21no—
251C4—21no—
252C4—41no—
253C4—81no—
254C4—2084no—
255C2—21no—
256C2—22no—
257C2—161no—
258C2—1042no—
259C2—1042no—
260C2C2×#1171829411yescharacteristic
subgroupG/H
centerC2C2×#11718294
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC13×#532C4
socleC2×C13C2×#353
prime radical#13125289C2
cosocle#88128C23
hypercenter#532#261
hypocenterC13#13584
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×#11718225C2semidirect
2. #13129969C2semidirect
3. #13129967C2semidirect
5. C13×#532C4semidirect
9. #11718746C4semidirect
11. #11718734C4semidirect
14. C4×#6099C4semidirect
21. C13×C4⋊Q8C2×C4semidirect
22. C13×#127C2×C4semidirect
41. C4×#1055C2×C4semidirect
42. C4×#1055C2×C4semidirect
113. #532#261semidirect
151. C4⋊Q8C2×#261semidirect
156. #127C2×#261semidirect
207. C13#13584semidirect

Maximal subgroups

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

subgroupindex
C2×#117182252
#131299692
#131299672
#131252892
#1358413