Finite Group Databasebeta

← #21461564

Subgroups — #21461564

Order 7808.

412 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 94 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×#14519836C212yesmaximal
2C4×C22⋊#6923C212yesmaximal, complemented
3#16840640C212yesmaximal, complemented
4C2×#14519739C211yesmaximal, characteristic
5C2×C22⋊#6923C2214yes—
6C2×C4×#6923—22no—
7#14519836C418yescomplemented
8(C2×#6923)⋊C4—22no—
9C22×D244C2211yescharacteristic
10C22×C4×D61C411yescharacteristic, complemented
11C22×C4×D61C2211yescharacteristic
12#14519739—22no—
13#14519739—22no—
14C2×#11758198C411yescharacteristic, complemented
15C2×#11758198C2211yescharacteristic
16C2×C4×Dic61C411yescharacteristic, complemented
17C2×C4⋊C4×C61C411yescharacteristic, complemented
18C23×D61C2×C411yescharacteristic
19C23×D61C2311yescharacteristic
20C22×#6923—24no—
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61C2×C411yescharacteristic
23C22×C4×C61C2×C411yescharacteristic
24C22×Dic61C2×C411yescharacteristic
25C22×Dic61C2×C411yescharacteristic
26C2×D244—22no—
27C2×D244—22no—
28C2×D244C2×C414yes—
29C2×C4×D61—21no—
30C2×C4×D61—21no—
31C2×C4×D61—42no—
32C2×C4×D61—42no—
33C2×C4×D61D412yes—
34C2×C4×D61D412yes—
35C22⋊#6923—24no—
36C22⋊#6923C2×C418yescomplemented
37C4×#6923—44no—
38C4⋊C4×C61—22no—
39#11758198—22no—
40#11758198—22no—
41C4×Dic61—21no—
42C4×Dic61—21no—
43C23×C61C22×C411yescharacteristic
44C22×D61—21no—
45C22×D61—21no—
46C22×D61—41no—
47C22×D61—41no—
48C22×D61—41no—
49C22×D61—41no—
50C22×D61C4212yescomplemented
51C22×D61C22×C412yes—
52C22×D61C2×D412yes—
53C22×D61#4112yes—
54C2×#6923—28no—
55C2×#6923—44no—
56C2×#6923—44no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61C4212yescomplemented
63C2×C4×C61C22⋊C412yes—
64C2×Dic61—22no—
65C2×Dic61—21no—
66C2×Dic61—41no—
67C2×Dic61C22⋊C411yescharacteristic
68C2×Dic61C22⋊C411yescharacteristic
69D244—28no—
70C4×D61—24no—
71C4×D61—42no—
72C4×D61—42no—
73C4×D61—42no—
74C22×C61—21no—
75C22×C61—21no—
76C22×C61C2×C4211yescharacteristic
77C22×C61C2×C22⋊C411yescharacteristic
78C22×C61#11711yescharacteristic
79C2×D61—22no—
80C2×D61—22no—
81C2×D61—22no—
82C2×D61—42no—
83C2×D61—42no—
84C2×D61—42no—
85C2×D61—41no—
86C2×D61—41no—
87C2×D61—42no—
88C2×D61C4×D414yes—
89#6923—48no—
90C4×C61—22no—
91C4×C61—22no—
92C4×C61—41no—
93Dic61—21no—
94Dic61—41no—
95Dic61#9912yescomplemented
96C4×#99—611nomaximal, Sylow
97C2×C61—21no—
98C2×C61—21no—
99C2×C61C4×C22⋊C411yescharacteristic
100C2×C61C2×#9911yescharacteristic
101C2×C61#41011yescharacteristic
102D61—24no—
103D61—42no—
104C2×C4×D4—611no—
105C2×#99—612no—
106C4×C22⋊C4—612no—
107#342—612no—
108C61C4×#9911yescharacteristic, complemented, Sylow
109C22×D4—611no—
110C23×C4—611no—
111C23×C4—611no—
112C4×D4—1222no—
113C4×D4—1222no—
114C2×C4⋊C4#692311yescharacteristic, complemented
115C2×C22⋊C4—614no—
116C2×C22⋊C4—611no—
117C2×C22⋊C4—611no—
118C2×C42—611no—
119C2×C42—1222no—
120#99—618no—
121#95—1222no—
122C24—611no—
123C24—611no—
124C2×D4—614no—
125C2×D4—1222no—
126C2×D4—1222no—
127C22×C4—611no—
128C22×C4—612no—
129C22×C4—612no—
130C22×C4—611no—
131C22×C4—1221no—
132C22×C4—1221no—
133C22×C4—1224no—
134C22×C4—2442no—
135C22×C4—2442no—
136C22×C4C2×#692311yescharacteristic
137C22×C4C2×#692311yescharacteristic
138C22×C4C2×#692311yescharacteristic
139C4⋊C4—22no—
140C22⋊C4—618no—
141C22⋊C4—1222no—
142C22⋊C4—1224no—
143C22⋊C4—1222no—
144C42—1221no—
145C42—1221no—
146C42—2444no—
147C23—612no—
148C23—612no—
149C23—612no—
150C23—612no—
151C23—1221no—
152C23—1221no—
153C23—2441no—
154C23—2441no—
155C23—2441no—
156C23—2441no—
157C23C22×#692311yescharacteristic
158D4—1228no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—611no—
165C2×C4—611no—
166C2×C4—1224no—
167C2×C4—1222no—
168C2×C4—1228no—
169C2×C4—1221no—
170C2×C4—2442no—
171C2×C4—2442no—
172C2×C4—2442no—
173C2×C4—2444no—
174C2×C4—2444no—
175C2×C4—2441no—
176C2×C4C4×#692312yescomplemented
177C2×C4C22⋊#692312yes—
178C22—21no—
179C22—21no—
180C22—614no—
181C22—1222no—
182C22—1222no—
183C22—1222no—
184C22—2442no—
185C22—2442no—
186C22—2442no—
187C22—2442no—
188C22—2441no—
189C22—2441no—
190C22C2×C4×#692311yescharacteristic
191C22C2×C22⋊#692311yescharacteristic
192C22#1451985611yescharacteristic
193C4—22no—
194C4—22no—
195C4—41no—
196C4—612no—
197C4—1221no—
198C4—2448no—
199C4—2441no—
200C2—21no—
201C2—21no—
202C2—1224no—
203C2—2442no—
204C2C4×C22⋊#692311yescharacteristic
205C2D61⋊#9911yescharacteristic
206C2#1684074311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC22×C61C2×C42
FrattiniC23C22×#6923
FittingC2×C4⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61C4×#99
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊#6923C2semidirect
3. #16840640C2semidirect
7. #14519836C4semidirect
10. C22×C4×D61C4semidirect
14. C2×#11758198C4semidirect
16. C2×C4×Dic61C4semidirect
17. C2×C4⋊C4×C61C4semidirect
36. C22⋊#6923C2×C4semidirect
50. C22×D61C42semidirect
62. C2×C4×C61C42semidirect
95. Dic61#99semidirect
108. C61C4×#99semidirect
114. C2×C4⋊C4#6923semidirect
176. C2×C4C4×#6923semidirect