Finite Group Databasebeta

← #21461714

Subgroups — #21461714

Order 7808.

504 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 74 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
1#16840703C212yesmaximal
2#16840640C214yesmaximal, complemented
3C22×#11758198C211yesmaximal, characteristic
4C2×C22⋊#6923—22no—
5C2×C22⋊#6923—22no—
6C2×C22⋊#6923C2214yes—
7C24×D61C2211yescharacteristic
8C23×Dic61C411yescharacteristic, complemented
9C2×#11758198—22no—
10C2×#11758198—22no—
11C2×#11758198C412yescomplemented
12C2×#11758198C2212yes—
13C23×C4×C61C411yescharacteristic, complemented
14C24×C61C2×C411yescharacteristic
15C23×D61—24no—
16C23×D61—42no—
17C23×D61—42no—
18C23×D61C2×C411yescharacteristic
19C23×D61D412yes—
20C23×D61D412yes—
21C23×D61C2311yescharacteristic
22C22×#6923—24no—
23C22×C4×C61—21no—
24C22×C4×C61—21no—
25C22×C4×C61—42no—
26C22×C4×C61C2×C412yes—
27C22×Dic61—21no—
28C22×Dic61—21no—
29C22×Dic61—42no—
30C22×Dic61C2×C412yes—
31C22⋊#6923—28no—
32C22⋊#6923—44no—
33C22⋊#6923—44no—
34#11758198—24no—
35#11758198—24no—
36C23×C61—22no—
37C23×C61—22no—
38C23×C61—22no—
39C23×C61C22⋊C411yescharacteristic
40C23×C61C22⋊C411yescharacteristic
41C23×C61C22×C411yescharacteristic
42C22×D61—24no—
43C22×D61—24no—
44C22×D61—22no—
45C22×D61—24no—
46C22×D61—24no—
47C22×D61—41no—
48C22×D61—41no—
49C22×D61—42no—
50C22×D61—42no—
51C22×D61—41no—
52C22×D61—41no—
53C22×D61—416no—
54C22×D61C22⋊C412yes—
55C22×D61C2×D412yes—
56C22×D61#4114yes—
57C2×#6923—44no—
58C2×#6923—44no—
59C2×#6923—44no—
60C2×C4×C61—22no—
61C2×C4×C61—42no—
62C2×C4×C61—42no—
63C2×C4×C61—42no—
64C2×Dic61—22no—
65C2×Dic61—42no—
66C2×Dic61—42no—
67C2×Dic61—42no—
68C22×C61—28no—
69C22×C61—21no—
70C22×C61—21no—
71C22×C61—21no—
72C22×C61—21no—
73C22×C61—21no—
74C22×C61—21no—
75C22×C61#9912yes—
76C22×C61#9912yes—
77C22×C61C2×C22⋊C411yescharacteristic
78C22×C61#11712yes—
79C2×D61—22no—
80C2×D61—22no—
81C2×D61—22no—
82C2×D61—22no—
83C2×D61—22no—
84C2×D61—44no—
85C2×D61—48no—
86C2×D61—48no—
87C2×D61—44no—
88C2×D61#12314yes—
89#6923—84no—
90C4×C61—42no—
91Dic61—42no—
92#1819—611nomaximal, Sylow
93C2×C61—22no—
94C2×C61—22no—
95C2×C61—22no—
96C2×C61#38111yescharacteristic
97C2×C61C2×#9911yescharacteristic
98C2×C61C2×#9911yescharacteristic
99D61—24no—
100D61—42no—
101C22×C22⋊C4—611no—
102#379—612no—
103#342—614no—
104C61#181911yescharacteristic, complemented, Sylow
105C25—611no—
106C23×C4—611no—
107C23×C4#692311yescharacteristic, complemented
108C2×C22⋊C4—612no—
109C2×C22⋊C4—612no—
110C2×C22⋊C4—614no—
111C2×C22⋊C4—1222no—
112C2×C22⋊C4—1222no—
113C2×C22⋊C4—1222no—
114C2×C22⋊C4—1222no—
115C24—611no—
116C24—612no—
117C24—612no—
118C24—611no—
119C24—1224no—
120C24—2442no—
121C24—2442no—
122C24C2×#692311yescharacteristic
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—42no—
126C22×C4—612no—
127C22×C4—1221no—
128C22×C4—1221no—
129C22×C4—1224no—
130C22×C4—2442no—
131C22×C4C2×#692312yes—
132C22⋊C4—1224no—
133C22⋊C4—1224no—
134C22⋊C4—1228no—
135C22⋊C4—2444no—
136C22⋊C4—2444no—
137C23—22no—
138C23—22no—
139C23—22no—
140C23—612no—
141C23—614no—
142C23—612no—
143C23—1224no—
144C23—1224no—
145C23—1224no—
146C23—1224no—
147C23—1222no—
148C23—2442no—
149C23—2441no—
150C23—2441no—
151C23—2442no—
152C23—2441no—
153C23—2441no—
154C23—24416no—
155C23C22⋊#692311yescharacteristic
156C23C22⋊#692311yescharacteristic
157C23C22×#692311yescharacteristic
158C2×C4—22no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—1222no—
163C2×C4—2444no—
164C2×C4—2444no—
165C2×C4—2444no—
166C2×C4—2442no—
167C2×C4—2442no—
168C2×C4—2442no—
169C22—28no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—614no—
177C22—1222no—
178C22—1222no—
179C22—1222no—
180C22—1222no—
181C22—1222no—
182C22—2444no—
183C22—2448no—
184C22—2448no—
185C22—2444no—
186C22#1451983512yes—
187C22#1451983612yes—
188C22C2×C22⋊#692311yescharacteristic
189C22#1451985612yes—
190C4—42no—
191C4—4884no—
192C4—2442no—
193C2—22no—
194C2—22no—
195C2—22no—
196C2—1224no—
197C2—2442no—
198C2#1684070511yescharacteristic
199C2C2×#1451983511yescharacteristic
200C2C2×#1451983611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC23×C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC23×C4#6923
hypocenterC61#1819
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #16840640C2semidirect
8. C23×Dic61C4semidirect
11. C2×#11758198C4semidirect
13. C23×C4×C61C4semidirect
104. C61#1819semidirect
107. C23×C4#6923semidirect