Finite Group Databasebeta

← C2×#11718306 #13131081

Subgroups — C2×#11718306 #13131081

Order 1664.

438 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 58 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×#88207C211yesmaximal, characteristic
2C2×#88121C211yesmaximal, characteristic, complemented
3C2×#88119C211yesmaximal, characteristic, complemented
4#11718306C214yesmaximal, direct product factor
5C25×C13C411yescharacteristic, complemented
6C22×C22⋊D13—21no—
7C22×C22⋊D13C2211yescharacteristic
8C2×C22⋊#261—21no—
9C2×#6122—21no—
10#88207—21no—
11#88207—21no—
12#88207C412yescomplemented
13#88207C2212yes—
14C2×C22⋊Dic13—21no—
15C2×C22⋊Dic13C411yescharacteristic, complemented
16#88121—21no—
17#88121C2212yescomplemented
18#88119—21no—
19#88119C2212yescomplemented
20C24×C13—21no—
21C24×C13—21no—
22C24×C13—44no—
23C24×C13—41no—
24C24×C13—41no—
25C24×C13C2×C411yescharacteristic
26C24×C13C2×C412yescomplemented
27C23×D13D411yescharacteristic
28C22×#261—41no—
29C2×C22⋊D13—22no—
30C2×C22⋊D13—22no—
31C2×C22⋊D13—41no—
32C2×C22⋊D13—41no—
33C2×C22⋊D13—44no—
34C2×C22⋊D13C2×C411yescharacteristic
35C2×C22⋊D13D411yescharacteristic
36C2×C22⋊D13D411yescharacteristic
37C2×C22⋊D13C2311yescharacteristic
38C22×Dic13—21no—
39C22×Dic13D411yescharacteristic
40C22⋊#261—22no—
41C22⋊#261—41no—
42#6122—22no—
43#6122—41no—
44C2×#1057—41no—
45C22⋊Dic13—21no—
46C22⋊Dic13—22no—
47C22⋊Dic13—22no—
48C22⋊Dic13C2×C412yescomplemented
49C2×AΣL(1,𝔽16)—131nomaximal, Sylow
50C23×C13—24no—
51C23×C13—21no—
52C23×C13—21no—
53C23×C13—22no—
54C23×C13—42no—
55C23×C13—44no—
56C23×C13—42no—
57C23×C13—42no—
58C23×C13—44no—
59C23×C13—42no—
60C23×C13—48no—
61C23×C13—44no—
62C23×C13—41no—
63C23×C13—41no—
64C23×C13—44no—
65C23×C13C22⋊C411yescharacteristic
66C23×C13C22⋊C411yescharacteristic
67C23×C13C22×C411yescharacteristic
68C22×D13—21no—
69C22×D13—21no—
70C22×D13—42no—
71C22×D13C22⋊C411yescharacteristic
72C22×D13C2×D411yescharacteristic
73C2×#261—42no—
74C2×#261—82no—
75C22⋊D13—41no—
76C22⋊D13—41no—
77C22⋊D13—41no—
78C22⋊D13—41no—
79C22⋊D13—44no—
80C22⋊D13—44no—
81C2×Dic13—21no—
82C2×Dic13—21no—
83C2×Dic13—22no—
84C2×Dic13—42no—
85C2×Dic13C22⋊C411yescharacteristic
86C2×Dic13C2×D411yescharacteristic
87#1057—42no—
88C2×#120—131no—
89C2×#100—131no—
90C2×#99—131no—
91AΣL(1,𝔽16)—134no—
92C22×C13—22no—
93C22×C13—24no—
94C22×C13—21no—
95C22×C13—21no—
96C22×C13—41no—
97C22×C13—41no—
98C22×C13—42no—
99C22×C13—44no—
100C22×C13—42no—
101C22×C13—44no—
102C22×C13—48no—
103C22×C13—44no—
104C22×C13—44no—
105C22×C13—42no—
106C22×C13—42no—
107C22×C13#9911yescharacteristic
108C22×C13#9911yescharacteristic
109C22×C13C2×C22⋊C411yescharacteristic
110C2×D13—21no—
111C2×D13—21no—
112C2×D13—42no—
113C2×D13—41no—
114C2×D13—41no—
115C2×D13—81no—
116#261—82no—
117Dic13—21no—
118Dic13—21no—
119Dic13—42no—
120C25#26111yescharacteristic, complemented
121C22×D4—131no—
122C22×D4—261no—
123C2×M16—261no—
124#120—132no—
125#120—132no—
126#120—261no—
127#120—261no—
128C2×C22⋊C4—131no—
129C2×C22⋊C4—261no—
130C2×C22⋊C4—261no—
131#100—132no—
132#100—261no—
133#99—132no—
134#99—261no—
135C2×C13—21no—
136C2×C13—21no—
137C2×C13—44no—
138C2×C13—41no—
139C2×C13—41no—
140C2×C13AΣL(1,𝔽16)12yescomplemented
141C2×C13C2×#9911yescharacteristic
142D13—41no—
143D13—41no—
144C24—21no—
145C24—21no—
146C24—44no—
147C24—41no—
148C24—41no—
149C24—131no—
150C24C2×#26111yescharacteristic
151C24C2×#26112yescomplemented
152C2×D4—131no—
153C2×D4—131no—
154C2×D4—131no—
155C2×D4—131no—
156C2×D4—262no—
157C2×D4—262no—
158C2×D4—521no—
159C2×D4—521no—
160C2×D4—524no—
161C22×C4—131no—
162C22×C4—261no—
163C22×C4—521no—
164M16—262no—
165M16—521no—
166C2×C8—521no—
167C22⋊C4—132no—
168C22⋊C4—262no—
169C22⋊C4—262no—
170C22⋊C4—261no—
171C22⋊C4—262no—
172C22⋊C4—521no—
173C13C2×AΣL(1,𝔽16)11yescharacteristic, complemented, Sylow
174C23—24no—
175C23—21no—
176C23—21no—
177C23—22no—
178C23—42no—
179C23—44no—
180C23—42no—
181C23—42no—
182C23—44no—
183C23—42no—
184C23—44no—
185C23—48no—
186C23—44no—
187C23—41no—
188C23—41no—
189C23—131no—
190C23—131no—
191C23—261no—
192C23—261no—
193C23—522no—
194C23C22⋊#26111yescharacteristic
195C23C22⋊#26111yescharacteristic
196C23C22×#26111yescharacteristic
197D4—521no—
198D4—521no—
199D4—521no—
200D4—521no—
201D4—524no—
202D4—524no—
203C2×C4—131no—
204C2×C4—131no—
205C2×C4—261no—
206C2×C4—261no—
207C2×C4—262no—
208C2×C4—522no—
209C2×C4—522no—
210C2×C4—1042no—
211C8—522no—
212C22—22no—
213C22—24no—
214C22—21no—
215C22—21no—
216C22—41no—
217C22—41no—
218C22—42no—
219C22—44no—
220C22—42no—
221C22—44no—
222C22—44no—
223C22—48no—
224C22—44no—
225C22—42no—
226C22—42no—
227C22—261no—
228C22—261no—
229C22—521no—
230C22—521no—
231C22—522no—
232C22—1041no—
233C22#8811911yescharacteristic
234C22#8811911yescharacteristic
235C22C2×C22⋊#26111yescharacteristic
236C4—261no—
237C4—261no—
238C4—522no—
239C4—1042no—
240C2—21no—
241C2—21no—
242C2—44no—
243C2—41no—
244C2—41no—
245C2—521no—
246C2—521no—
247C2#1171830612yesdirect product factor
248C2C2×#8811911yescharacteristic
subgroupG/H
centerC22#88119
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC25×C13C4
socleC22×C13#99
prime radicalC2×#88207C2
cosocleC2×C22⋊D13C23
hypercenterC25#261
hypocenterC13C2×AΣL(1,𝔽16)
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
2. C2×#88121C2semidirect
3. C2×#88119C2semidirect
4. #11718306C2direct (N × H)
5. C25×C13C4semidirect
12. #88207C4semidirect
15. C2×C22⋊Dic13C4semidirect
17. #88121C22semidirect
19. #88119C22semidirect
26. C24×C13C2×C4semidirect
48. C22⋊Dic13C2×C4semidirect
120. C25#261semidirect
140. C2×C13AΣL(1,𝔽16)semidirect
151. C24C2×#261semidirect
173. C13C2×AΣL(1,𝔽16)semidirect
247. C2#11718306direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#882072
C2×#881212
C2×#881192
#117183062
C2×AΣL(1,𝔽16)13