Finite Group Databasebeta

← C2×#16840662 #21462064

Subgroups — C2×#16840662 #21462064

Order 7808.

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×#14519837C211yesmaximal, characteristic, complemented
2C2×#14519835C211yesmaximal, characteristic, complemented
3#16840662C214yesmaximal, direct product factor
4C2×#14519746C211yesmaximal, characteristic
5C2×#11758217—21no—
6C2×C22⋊#6923—21no—
7#14519837—21no—
8#14519837C2212yescomplemented
9#14519835—21no—
10#14519835C2212yescomplemented
11C22×C22⋊D61—21no—
12C22×C22⋊D61C2211yescharacteristic
13#14519746—21no—
14#14519746—21no—
15#14519746C412yescomplemented
16#14519746C2212yes—
17C2×C22⋊Dic61—21no—
18C2×C22⋊Dic61C411yescharacteristic, complemented
19C25×C61C411yescharacteristic, complemented
20C24×C61—21no—
21C24×C61—21no—
22C24×C61—44no—
23C24×C61—41no—
24C24×C61—41no—
25C24×C61C2×C411yescharacteristic
26C24×C61C2×C412yescomplemented
27C23×D61D411yescharacteristic
28C22×#6923—41no—
29C2×C22⋊D61—22no—
30C2×C22⋊D61—22no—
31C2×C22⋊D61—41no—
32C2×C22⋊D61—41no—
33C2×C22⋊D61—44no—
34C2×C22⋊D61C2×C411yescharacteristic
35C2×C22⋊D61D411yescharacteristic
36C2×C22⋊D61D411yescharacteristic
37C2×C22⋊D61C2311yescharacteristic
38C22×Dic61—21no—
39C22×Dic61D411yescharacteristic
40C22⋊#6923—22no—
41C22⋊#6923—41no—
42#11758217—22no—
43#11758217—41no—
44C2×#92420—41no—
45C22⋊Dic61—21no—
46C22⋊Dic61—22no—
47C22⋊Dic61—22no—
48C22⋊Dic61C2×C412yescomplemented
49C23×C61—24no—
50C23×C61—21no—
51C23×C61—21no—
52C23×C61—22no—
53C23×C61—42no—
54C23×C61—44no—
55C23×C61—42no—
56C23×C61—42no—
57C23×C61—44no—
58C23×C61—42no—
59C23×C61—48no—
60C23×C61—44no—
61C23×C61—41no—
62C23×C61—41no—
63C23×C61—44no—
64C23×C61C22⋊C411yescharacteristic
65C23×C61C22⋊C411yescharacteristic
66C23×C61C22×C411yescharacteristic
67C22×D61—21no—
68C22×D61—21no—
69C22×D61—42no—
70C22×D61C22⋊C411yescharacteristic
71C22×D61C2×D411yescharacteristic
72C2×#6923—42no—
73C2×#6923—82no—
74C22⋊D61—41no—
75C22⋊D61—41no—
76C22⋊D61—41no—
77C22⋊D61—41no—
78C22⋊D61—44no—
79C22⋊D61—44no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—22no—
83C2×Dic61—42no—
84C2×Dic61C22⋊C411yescharacteristic
85C2×Dic61C2×D411yescharacteristic
86#92420—42no—
87C22×C61—22no—
88C22×C61—24no—
89C22×C61—21no—
90C22×C61—21no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61—42no—
94C22×C61—44no—
95C22×C61—42no—
96C22×C61—44no—
97C22×C61—48no—
98C22×C61—44no—
99C22×C61—44no—
100C22×C61—42no—
101C22×C61—42no—
102C22×C61#9911yescharacteristic
103C22×C61#9911yescharacteristic
104C22×C61C2×C22⋊C411yescharacteristic
105C2×D61—21no—
106C2×D61—21no—
107C2×D61—42no—
108C2×D61—41no—
109C2×D61—41no—
110C2×D61—81no—
111#6923—82no—
112Dic61—21no—
113Dic61—21no—
114Dic61—42no—
115C2×AΣL(1,𝔽16)—611nomaximal, Sylow
116C2×C61—21no—
117C2×C61—21no—
118C2×C61—44no—
119C2×C61—41no—
120C2×C61—41no—
121C2×C61AΣL(1,𝔽16)12yescomplemented
122C2×C61C2×#9911yescharacteristic
123D61—41no—
124D61—41no—
125C2×#120—611no—
126C2×#100—611no—
127C2×#99—611no—
128AΣL(1,𝔽16)—614no—
129C61C2×AΣL(1,𝔽16)11yescharacteristic, complemented, Sylow
130C25#692311yescharacteristic, complemented
131C22×D4—611no—
132C22×D4—1221no—
133C2×M16—1221no—
134#120—612no—
135#120—612no—
136#120—1221no—
137#120—1221no—
138C2×C22⋊C4—611no—
139C2×C22⋊C4—1221no—
140C2×C22⋊C4—1221no—
141#100—612no—
142#100—1221no—
143#99—612no—
144#99—1221no—
145C24—21no—
146C24—21no—
147C24—44no—
148C24—41no—
149C24—41no—
150C24—611no—
151C24C2×#692311yescharacteristic
152C24C2×#692312yescomplemented
153C2×D4—611no—
154C2×D4—611no—
155C2×D4—611no—
156C2×D4—611no—
157C2×D4—1222no—
158C2×D4—1222no—
159C2×D4—2441no—
160C2×D4—2441no—
161C2×D4—2444no—
162C22×C4—611no—
163C22×C4—1221no—
164C22×C4—2441no—
165M16—1222no—
166M16—2441no—
167C2×C8—2441no—
168C22⋊C4—612no—
169C22⋊C4—1222no—
170C22⋊C4—1222no—
171C22⋊C4—1221no—
172C22⋊C4—1222no—
173C22⋊C4—2441no—
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—611no—
190C23—611no—
191C23—1221no—
192C23—1221no—
193C23—2442no—
194C23C22⋊#692311yescharacteristic
195C23C22⋊#692311yescharacteristic
196C23C22×#692311yescharacteristic
197D4—2441no—
198D4—2441no—
199D4—2441no—
200D4—2441no—
201D4—2444no—
202D4—2444no—
203C2×C4—611no—
204C2×C4—611no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—1222no—
208C2×C4—4882no—
209C2×C4—2442no—
210C2×C4—2442no—
211C8—2442no—
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—42no—
225C22—44no—
226C22—42no—
227C22—1221no—
228C22—1221no—
229C22—4881no—
230C22—2441no—
231C22—2441no—
232C22—2442no—
233C22#1451983511yescharacteristic
234C22#1451983511yescharacteristic
235C22C2×C22⋊#692311yescharacteristic
236C4—1221no—
237C4—1221no—
238C4—4882no—
239C4—2442no—
240C2—21no—
241C2—21no—
242C2—44no—
243C2—41no—
244C2—41no—
245C2—2441no—
246C2—2441no—
247C2#1684066212yesdirect product factor
248C2C2×#1451983511yescharacteristic
subgroupG/H
centerC22#14519835
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC25×C61C4
socleC22×C61#99
hypercenterC25#6923
hypocenterC61C2×AΣL(1,𝔽16)
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C2×#14519837C2semidirect
2. C2×#14519835C2semidirect
3. #16840662C2direct (N × H)
8. #14519837C22semidirect
10. #14519835C22semidirect
15. #14519746C4semidirect
18. C2×C22⋊Dic61C4semidirect
19. C25×C61C4semidirect
26. C24×C61C2×C4semidirect
48. C22⋊Dic61C2×C4semidirect
121. C2×C61AΣL(1,𝔽16)semidirect
129. C61C2×AΣL(1,𝔽16)semidirect
130. C25#6923semidirect
152. C24C2×#6923semidirect
247. C2#16840662direct (N × H)