Finite Group Databasebeta

← C2×#16839621 #21448191

Subgroups — C2×#16839621 #21448191

Order 7808.

1232 conjugacy classes of subgroups; only the 349 normal subgroups are shown.

normal subgroups only

This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 349 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
1C23×C4×D61C211yesmaximal, characteristic
2C22×#11758196C212yesmaximal, complemented
3C22×#11758198C212yesmaximal
4#16839621C218yesmaximal, direct product factor
5C2×#14519684C211yesmaximal, characteristic, complemented
6C2×#95×C61C211yesmaximal, characteristic, complemented
7C24×D61C2211yescharacteristic
8C23×Dic61C2212yes—
9C23×Dic61C2211yescharacteristic
10C22×C4×D61—28no—
11C22×C4×D61C418yescomplemented
12C22×C4×D61C2214yes—
13C2×#11758196—28no—
14C2×#11758196C2218yescomplemented
15C2×#11758198—28no—
16C2×#11758198C2218yes—
17#14519684C2214yescomplemented
18C23×C4×C61C2212yes—
19C23×C4×C61C2211yescharacteristic
20#95×C61C2214yescomplemented
21C24×C61C2311yescharacteristic
22C23×D61—24no—
23C23×D61—24no—
24C23×D61C2×C414yes—
25C23×D61D414yes—
26C23×D61Q814yes—
27C23×D61C2312yes—
28C22×C4×C61—24no—
29C22×C4×C61—24no—
30C22×C4×C61—24no—
31C22×C4×C61—24no—
32C22×C4×C61C2×C414yes—
33C22×C4×C61C2314yes—
34C22×C4×C61C2312yes—
35C22×Dic61—24no—
36C22×Dic61—24no—
37C22×Dic61—24no—
38C22×Dic61C2×C414yes—
39C22×Dic61D418yes—
40C22×Dic61C2314yes—
41C22×Dic61C2312yes—
42C2×C4×D61—232no—
43C2×C4×D61—216no—
44C2×C4×D61C2×C4116yescomplemented
45#11758198—216no—
46#11758196—216no—
47C23×C61C22×C412yes—
48C23×C61C2×D414yes—
49C23×C61C2×D412yes—
50C23×C61C2×Q812yes—
51C23×C61#4114yes—
52C23×C61C2411yescharacteristic
53C22×D61—28no—
54C22×D61—28no—
55C22×D61—216no—
56C22×D61—216no—
57C22×D61—24no—
58C22×D61—24no—
59C22×D61C4⋊C4116yescomplemented
60C22×D61C22×C414yes—
61C22×D61C2×D414yes—
62C22×D61C2×Q814yes—
63C2×C4×C61—28no—
64C2×C4×C61—24no—
65C2×C4×C61—24no—
66C2×C4×C61—24no—
67C2×C4×C61—24no—
68C2×C4×C61—48no—
69C2×C4×C61C22×C414yes—
70C2×Dic61—24no—
71C2×Dic61—24no—
72C2×Dic61—24no—
73C2×Dic61—48no—
74C2×Dic61C22⋊C4116yescomplemented
75C2×Dic61C22×C414yes—
76C2×Dic61C2×D418yes—
77C4×D61—232no—
78C22×C61C2×C22⋊C414yes—
79C22×C61C2×C4⋊C414yes—
80C22×C61#11714yes—
81C22×C61#12118yes—
82C22×C61C22⋊Q818yes—
83C22×C61C23×C411yescharacteristic
84C22×C61C22×D412yes—
85C22×C61C22×D411yescharacteristic
86C22×C61C22×Q811yescharacteristic
87C22×C61C2×#4112yes—
88C2×D61—24no—
89C2×D61—24no—
90C2×D61—28no—
91C2×D61—28no—
92C2×D61—232no—
93C2×D61C2×C4⋊C418yescomplemented
94C4×C61—24no—
95C4×C61—44no—
96Dic61—44no—
97Dic61C2×C22⋊C418yescomplemented
98C2×#380—611nomaximal, Sylow
99C2×C61#38018yescomplemented
100C2×C61C22×C22⋊C411yescharacteristic
101C2×C61C22×C4⋊C411yescharacteristic
102C2×C61C2×#11711yescharacteristic
103C2×C61C2×#12112yes—
104C2×C61C2×C22⋊Q812yes—
105D61—28no—
106C24×C4—611no—
107C22×C4⋊C4—612no—
108C22×C22⋊C4—612no—
109#380—618no—
110C2×#95—611no—
111C2×#95D6111yescharacteristic, complemented
112C61C2×#38011yescharacteristic, complemented, Sylow
113C25—611no—
114C23×C4—611no—
115C23×C4—618no—
116C23×C4—614no—
117C23×C4—612no—
118C23×C4—1228no—
119C23×C4C2×D6112yes—
120C23×C4C2×D6111yescharacteristic
121C2×C4⋊C4—618no—
122C2×C4⋊C4—1228no—
123C2×C22⋊C4—618no—
124C2×C22⋊C4—1228no—
125#95—614no—
126#95C2×D6114yescomplemented
127C24—614no—
128C24—614no—
129C24—614no—
130C24—612no—
131C24—1224no—
132C24—1224no—
133C24C22×D6111yescharacteristic
134C22×C4—24no—
135C22×C4—24no—
136C22×C4—24no—
137C22×C4—24no—
138C22×C4—614no—
139C22×C4—618no—
140C22×C4—612no—
141C22×C4—6116no—
142C22×C4—614no—
143C22×C4—12216no—
144C22×C4—12232no—
145C22×C4—1224no—
146C22×C4—1224no—
147C22×C4—1224no—
148C22×C4C4×D6114yes—
149C22×C4C22×D6114yes—
150C22×C4C22×D6112yes—
151C4⋊C4—12216no—
152C22⋊C4—12216no—
153C23—614no—
154C23—614no—
155C23—614no—
156C23—6116no—
157C23—1224no—
158C23—1224no—
159C23—1228no—
160C23—1228no—
161C23—12216no—
162C23—12216no—
163C23C2×C4×D6112yes—
164C23#1175822214yes—
165C23D4×D6114yes—
166C23D4×D6112yes—
167C23Q8×D6112yes—
168C23C23×D6111yescharacteristic
169C2×C4—24no—
170C2×C4—28no—
171C2×C4—24no—
172C2×C4—24no—
173C2×C4—24no—
174C2×C4—48no—
175C2×C4—614no—
176C2×C4—618no—
177C2×C4—6116no—
178C2×C4—12232no—
179C2×C4—1224no—
180C2×C4—1224no—
181C2×C4—1224no—
182C2×C4—2448no—
183C2×C4C2×C4×D6114yes—
184C22—618no—
185C22—1224no—
186C22—1224no—
187C22—1228no—
188C22—1228no—
189C22—12232no—
190C22C22⋊C4×D6114yes—
191C22C4⋊C4×D6114yes—
192C22#1451973414yes—
193C22#1451975018yes—
194C22#1451975518yes—
195C22C22×C4×D6111yescharacteristic
196C22C2×D4×D6112yes—
197C22C2×D4×D6111yescharacteristic
198C22C2×Q8×D6111yescharacteristic
199C22C2×#1175822212yes—
200C4—24no—
201C4—44no—
202C4—618no—
203C4—2444no—
204C2—1228no—
205C2#1683962118yesdirect product factor
206C2C2×C22⋊C4×D6111yescharacteristic
207C2C2×C4⋊C4×D6111yescharacteristic
208C2C2×#1451973411yescharacteristic
209C2C2×#1451975012yes—
210C2C2×#1451975512yes—
subgroupG/H
centerC24C22×D61
commutatorC22×C61C23×C4
FrattiniC23C23×D61
FittingC2×#95×C61C2
socleC24×C61C23
hypercenterC2×#95D61
hypocenterC61C2×#380
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
2. C22×#11758196C2semidirect
4. #16839621C2direct (N × H)
5. C2×#14519684C2semidirect
6. C2×#95×C61C2semidirect
11. C22×C4×D61C4semidirect
14. C2×#11758196C22semidirect
17. #14519684C22semidirect
20. #95×C61C22semidirect
44. C2×C4×D61C2×C4semidirect
59. C22×D61C4⋊C4semidirect
74. C2×Dic61C22⋊C4semidirect
93. C2×D61C2×C4⋊C4semidirect
97. Dic61C2×C22⋊C4semidirect
99. C2×C61#380semidirect
111. C2×#95D61semidirect
112. C61C2×#380semidirect
126. #95C2×D61semidirect
205. C2#16839621direct (N × H)