Finite Group Databasebeta

← #21446262

Subgroups — #21446262

Order 7808.

442 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 101 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#16840273C211yesmaximal, characteristic
2C2×#14519705C212yesmaximal, complemented
3#16839726C211yesmaximal, characteristic, complemented
4#16839522C212yesmaximal, complemented
5C22×C42×C61C211yesmaximal, characteristic, complemented
6C2×#11758222C2211yescharacteristic
7C2×#11758194C2212yes—
8#14519760—21no—
9#14519756C412yescomplemented
10#14519751C412yescomplemented
11#14519746—21no—
12C4×C22⋊D61—22no—
13#14519736C2211yescharacteristic
14#14519705—24no—
15C22⋊#92418—22no—
16C23×C4×C61—21no—
17C23×C4×C61C2211yescharacteristic
18C2×C42×C61—21no—
19C2×C42×C61—24no—
20C2×C42×C61C2212yes—
21C24×C61D411yescharacteristic
22C22×C4×C61—24no—
23C22×C4×C61—28no—
24C22×C4×C61—22no—
25C22×C4×C61—22no—
26C22×C4×C61—22no—
27C22×C4×C61C2×C412yes—
28C22×C4×C61D411yescharacteristic
29C22×C4×C61D412yes—
30C22×C4×C61C2311yescharacteristic
31C2×C22⋊D61—22no—
32C2×C22⋊D61—21no—
33#11758222—22no—
34#11758222—22no—
35C2×D244C2×C411yescharacteristic, complemented
36C2×C4×D61—21no—
37C2×Dic122C2×C411yescharacteristic, complemented
38C42×C61—24no—
39C42×C61—22no—
40C42×C61D414yescomplemented
41C22⋊Dic61—22no—
42C22⋊Dic61—21no—
43#11758198—22no—
44C4⋊Dic61C2×C412yescomplemented
45#11758196—22no—
46C4×Dic61—21no—
47#11758194—22no—
48#11758194—22no—
49C2×#92418—22no—
50C23×C61—24no—
51C23×C61—21no—
52C23×C61—21no—
53C23×C61C22⋊C412yes—
54C23×C61C2×D411yescharacteristic
55C22×D61—21no—
56C2×C4×C61—216no—
57C2×C4×C61—28no—
58C2×C4×C61—21no—
59C2×C4×C61—24no—
60C2×C4×C61—21no—
61C2×C4×C61—24no—
62C2×C4×C61—24no—
63C2×C4×C61C22⋊C412yes—
64C2×C4×C61C22×C411yescharacteristic
65C2×C4×C61C2×D412yes—
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61#4112yes—
68C22⋊D61—44no—
69C22⋊D61—41no—
70C22⋊D61—41no—
71C2×Dic61—22no—
72C2×Dic61—21no—
73D244—22no—
74C4×D61—42no—
75Dic122—22no—
76#92418—42no—
77C22×C61—24no—
78C22×C61—24no—
79C22×C61—22no—
80C22×C61—22no—
81C22×C61—22no—
82C22×C61#10414yescomplemented
83C22×C61C2×C22⋊C411yescharacteristic
84C22×C61#12011yescharacteristic
85C22×C61#12311yescharacteristic
86C2×D61—41no—
87C2×D61—42no—
88C4×C61—28no—
89C4×C61—22no—
90C4×C61C4×D412yes—
91C4×C61#12112yes—
92Dic61—41no—
93Dic61—42no—
94#1896—611nomaximal, Sylow
95C2×C61—21no—
96C2×C61—24no—
97C2×C61—21no—
98C2×C61#38611yescharacteristic
99C2×C61C2×#10412yes—
100D61—81no—
101#525—611no—
102C22×C42D6111yescharacteristic, complemented
103C2×#104—612no—
104#407—611no—
105#339—612no—
106C61#189611yescharacteristic, complemented, Sylow
107C2×#41—611no—
108C23×C4—21no—
109C23×C4C2×D6111yescharacteristic
110C2×M16—612no—
111#123—1221no—
112C22⋊Q8—612no—
113#121—612no—
114#120—1221no—
115C4×D4—1222no—
116#117—611no—
117C2×C42—21no—
118C2×C42—24no—
119C2×C42C2×D6112yes—
120#104—1224no—
121C22⋊C8—1222no—
122C24C22⋊D6111yescharacteristic
123#41—1222no—
124#41—1222no—
125C2×Q8—611no—
126C2×D4—611no—
127C2×D4—1222no—
128C2×D4—1221no—
129C22×C4—24no—
130C22×C4—28no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—1221no—
135C22×C4C4×D6112yes—
136C22×C4D24412yes—
137C22×C4C22⋊D6111yescharacteristic
138C22×C4C22×D6111yescharacteristic
139M16—1222no—
140M16—1222no—
141C2×C8—1222no—
142C4⋊C4—612no—
143C4⋊C4—1222no—
144C22⋊C4—1222no—
145C22⋊C4—1221no—
146C22⋊C4—1222no—
147C42—24no—
148C42—22no—
149C42—1221no—
150C42C22⋊D6114yescomplemented
151C23—24no—
152C23—21no—
153C23—21no—
154C23—1221no—
155C23#1175819812yes—
156C23C2×C22⋊D6111yescharacteristic
157Q8—1222no—
158D4—1222no—
159D4—2444no—
160D4—2441no—
161D4—2441no—
162C2×C4—216no—
163C2×C4—28no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—24no—
168C2×C4—24no—
169C2×C4—1222no—
170C2×C4—1221no—
171C2×C4—2442no—
172C2×C4#1175819812yes—
173C2×C4C2×C4×D6111yescharacteristic
174C2×C4C2×D24411yescharacteristic
175C2×C4#1175822212yes—
176C2×C4C2×C22⋊D6112yes—
177C8—2442no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—2442no—
184C22—2441no—
185C22#1451970514yescomplemented
186C22C2×#1175819811yescharacteristic
187C22#1451974611yescharacteristic
188C22#1451976011yescharacteristic
189C4—28no—
190C4—22no—
191C4—2442no—
192C4—2441no—
193C4C4×C22⋊D6112yes—
194C4#1451975112yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—4881no—
199C2#1683964111yescharacteristic
200C2C2×#1451970512yes—
subgroupG/H
centerC2×C4C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC22×C42×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC22×C42D61
hypocenterC61#1896
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C2×#14519705C2semidirect
3. #16839726C2semidirect
4. #16839522C2semidirect
5. C22×C42×C61C2semidirect
9. #14519756C4semidirect
10. #14519751C4semidirect
35. C2×D244C2×C4semidirect
37. C2×Dic122C2×C4semidirect
40. C42×C61D4semidirect
44. C4⋊Dic61C2×C4semidirect
82. C22×C61#104semidirect
102. C22×C42D61semidirect
106. C61#1896semidirect
150. C42C22⋊D61semidirect
185. C22#14519705semidirect