Finite Group Databasebeta

← #21446260

Subgroups — #21446260

Order 7808.

442 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 97 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
2C22×C4×Dic61C211yesmaximal, characteristic, complemented
3C2×#14519703C212yesmaximal, complemented
4#16839523C212yesmaximal, complemented
5C61×#407C211yesmaximal, characteristic, complemented
6C2×#11758222C2211yescharacteristic
7C23×Dic61—21no—
8#14519760—21no—
9#14519756C412yescomplemented
10#14519751C412yescomplemented
11#14519746—21no—
12C4×C22⋊D61—22no—
13#14519736C2211yescharacteristic
14C2×C4×Dic61—21no—
15C2×C4×Dic61—24no—
16C2×C4×Dic61C2212yes—
17#14519703—24no—
18C23×C4×C61C2211yescharacteristic
19C2×M16×C61C2212yes—
20C22⋊C8×C61—22no—
21C24×C61D411yescharacteristic
22C22×C4×C61—22no—
23C22×C4×C61—22no—
24C22×C4×C61C2×C412yes—
25C22×C4×C61D411yescharacteristic
26C22×C4×C61D412yes—
27C22×C4×C61C2311yescharacteristic
28C2×C22⋊D61—22no—
29C2×C22⋊D61—21no—
30C22×Dic61—28no—
31C22×Dic61—24no—
32C22×Dic61—22no—
33#11758222—22no—
34#11758222—22no—
35C2×D244C2×C411yescharacteristic, complemented
36C2×C4×D61—21no—
37C2×Dic122C2×C411yescharacteristic, complemented
38M16×C61—22no—
39M16×C61—22no—
40C2×C8×C61—22no—
41C22⋊Dic61—22no—
42C22⋊Dic61—21no—
43#11758198—22no—
44C4⋊Dic61C2×C412yescomplemented
45#11758196—22no—
46C4×Dic61—24no—
47C4×Dic61—22no—
48C4×Dic61—21no—
49C4×Dic61D414yescomplemented
50C23×C61—24no—
51C23×C61—21no—
52C23×C61—21no—
53C23×C61C22⋊C412yes—
54C23×C61C2×D411yescharacteristic
55C22×D61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—24no—
59C2×C4×C61—24no—
60C2×C4×C61C22⋊C412yes—
61C2×C4×C61C22×C411yescharacteristic
62C2×C4×C61C2×D412yes—
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61#4112yes—
65C22⋊D61—44no—
66C22⋊D61—41no—
67C22⋊D61—41no—
68C2×Dic61—216no—
69C2×Dic61—28no—
70C2×Dic61—24no—
71C2×Dic61—22no—
72C2×Dic61—21no—
73D244—22no—
74C4×D61—42no—
75Dic122—22no—
76C8×C61—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—22no—
89C4×C61C4×D412yes—
90C4×C61#12112yes—
91Dic61—28no—
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×C42—611no—
103C2×#104—612no—
104#407D6111yescharacteristic, complemented
105#339—612no—
106C61#189611yescharacteristic, complemented, Sylow
107C2×#41—611no—
108C23×C4—1221no—
109C23×C4C2×D6111yescharacteristic
110C2×M16C2×D6112yes—
111#123—1221no—
112C22⋊Q8—612no—
113#121—612no—
114#120—1221no—
115C4×D4—1222no—
116#117—611no—
117C2×C42—612no—
118C2×C42—1224no—
119C2×C42—1221no—
120#104—1224no—
121C22⋊C8—22no—
122C24D24411yescharacteristic
123#41—1222no—
124#41—1222no—
125C2×Q8—611no—
126C2×D4—611no—
127C2×D4—1222no—
128C2×D4—1221no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—1224no—
132C22×C4—1228no—
133C22×C4—1222no—
134C22×C4—1221no—
135C22×C4C4×D6112yes—
136C22×C4D24411yescharacteristic
137C22×C4C22⋊D6112yes—
138C22×C4C22×D6111yescharacteristic
139M16—22no—
140M16—22no—
141C2×C8—22no—
142C4⋊C4—612no—
143C4⋊C4—1222no—
144C22⋊C4—1222no—
145C22⋊C4—1221no—
146C22⋊C4—1222no—
147C42—614no—
148C42—1224no—
149C42—1222no—
150C42—1221no—
151C23—24no—
152C23—21no—
153C23—21no—
154C23—1221no—
155C23#1175819812yes—
156C23C2×D24411yescharacteristic
157Q8—1222no—
158D4—1222no—
159D4—2444no—
160D4—2441no—
161D4—2441no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—12216no—
167C2×C4—1228no—
168C2×C4—1224no—
169C2×C4—1222no—
170C2×C4—1221no—
171C2×C4—2442no—
172C2×C4#1175819812yes—
173C2×C4C2×C4×D6111yescharacteristic
174C2×C4D4×D6112yes—
175C2×C4#1175822412yes—
176C2×C4C2×C22⋊D6111yescharacteristic
177C8—42no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—2442no—
184C22—2441no—
185C22#1451970314yescomplemented
186C22C2×#1175819811yescharacteristic
187C22#1451974711yescharacteristic
188C22#1451976111yescharacteristic
189C4—22no—
190C4—1228no—
191C4—2442no—
192C4—2441no—
193C4#1451973712yes—
194C4#1451974912yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—4881no—
199C2#1683963911yescharacteristic
200C2C2×#1451970312yes—
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#407C2
socleC22×C61C2×C22⋊C4
hypercenter#407D61
hypocenterC61#1896
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic61C2semidirect
3. C2×#14519703C2semidirect
4. #16839523C2semidirect
5. C61×#407C2semidirect
9. #14519756C4semidirect
10. #14519751C4semidirect
35. C2×D244C2×C4semidirect
37. C2×Dic122C2×C4semidirect
44. C4⋊Dic61C2×C4semidirect
49. C4×Dic61D4semidirect
82. C22×C61#104semidirect
104. #407D61semidirect
106. C61#1896semidirect
185. C22#14519703semidirect