Finite Group Databasebeta

← #21455056

Subgroups — #21455056

Order 7808.

738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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×Dic122C211yesmaximal, characteristic, complemented
2C2×#14519810C212yesmaximal, complemented
3#16840273C211yesmaximal, characteristic
4#16839920C214yesmaximal, complemented
5#16839903C214yesmaximal, complemented
6#16839772C212yesmaximal, complemented
7C61×#407C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×Dic122—22no—
10C22×Dic122—21no—
11C22×Dic122—28no—
12C22×Dic122C2214yes—
13C22×Dic122C2212yes—
14C23×Dic61—21no—
15#14519810—28no—
16C2×Dic244C2214yescomplemented
17C2×#11758190C2214yescomplemented
18#14519760—21no—
19#14519756C2212yes—
20#14519751C2212yes—
21#14519746—21no—
22C4×C22⋊D61—22no—
23#14519736C2211yescharacteristic
24#14519702C2218yescomplemented
25C23×C4×C61C2211yescharacteristic
26C2×M16×C61C2212yes—
27C22⋊C8×C61C2214yes—
28C24×C61D411yescharacteristic
29C22×C4×C61—24no—
30C22×C4×C61D412yes—
31C22×C4×C61D411yescharacteristic
32C22×C4×C61C2312yes—
33C22×C4×C61C2311yescharacteristic
34C2×C22⋊D61—21no—
35C2×C22⋊D61—22no—
36C22×Dic61—28no—
37C22×Dic61—24no—
38C22×Dic61—22no—
39#11758222—24no—
40C2×D244C2311yescharacteristic
41C2×C4×D61—21no—
42C2×Dic122—28no—
43C2×Dic122—216no—
44C2×Dic122—24no—
45C2×Dic122—22no—
46C2×Dic122—24no—
47C2×Dic122—216no—
48C2×Dic122D418yescomplemented
49C2×Dic122C2311yescharacteristic
50C2×Dic122C2314yes—
51M16×C61—24no—
52C2×C8×C61C2314yes—
53C22⋊Dic61—21no—
54C22⋊Dic61—22no—
55#11758198—22no—
56C4⋊Dic61C2312yes—
57#11758196—22no—
58C4×Dic61—21no—
59Dic244—28no—
60#11758190—28no—
61C23×C61—22no—
62C23×C61—24no—
63C23×C61C2×D411yescharacteristic
64C23×C61C2×D412yes—
65C22×D61—21no—
66C2×C4×C61—22no—
67C2×C4×C61—24no—
68C2×C4×C61—24no—
69C2×C4×C61C2×D412yes—
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D414yes—
72C2×C4×C61C2411yescharacteristic
73C22⋊D61—42no—
74C22⋊D61—44no—
75C2×Dic61—216no—
76C2×Dic61—28no—
77C2×Dic61—24no—
78C2×Dic61—22no—
79C2×Dic61—21no—
80D244—22no—
81C4×D61—42no—
82Dic122—216no—
83Dic122—28no—
84Dic122—24no—
85Dic122—22no—
86Dic122C2×D418yes—
87C8×C61—24no—
88C22×C61—28no—
89C22×C61—22no—
90C22×C61—22no—
91C22×C61—22no—
92C22×C61#12012yes—
93C22×C61#13714yescomplemented
94C22×C61C22×D411yescharacteristic
95C2×D61—41no—
96C2×D61—42no—
97C4×C61—22no—
98C4×C61#12012yes—
99C4×C61C22×D412yes—
100Dic61—28no—
101Dic61—41no—
102Dic61—42no—
103#3004—611nomaximal, Sylow
104C2×C61—22no—
105C2×C61—24no—
106C2×C61C2×#12011yescharacteristic
107C2×C61C2×#13712yes—
108D61—81no—
109C23×Q8—611no—
110C2×#137—612no—
111#525—611no—
112#451—614no—
113#448—614no—
114#419—612no—
115#407D6111yescharacteristic, complemented
116C61#300411yescharacteristic, complemented, Sylow
117C2×#41—611no—
118C22×Q8—612no—
119C22×Q8—614no—
120C22×Q8—1228no—
121C22×Q8—1222no—
122C22×Q8—1221no—
123C23×C4—1221no—
124C23×C4C2×D6111yescharacteristic
125#137—1228no—
126C2×Q16—614no—
127C2×SD16—614no—
128C2×M16C2×D6112yes—
129#123—1221no—
130C22⋊Q8—612no—
131#121—612no—
132#120—1221no—
133C4×D4—1222no—
134#117—611no—
135#103—618no—
136C22⋊C8C2×D6114yes—
137C24D24411yescharacteristic
138#41—1224no—
139C2×Q8—618no—
140C2×Q8—614no—
141C2×Q8—611no—
142C2×Q8—12216no—
143C2×Q8—1228no—
144C2×Q8—12216no—
145C2×Q8—1224no—
146C2×Q8—1222no—
147C2×Q8—1224no—
148C2×D4—611no—
149C2×D4—1222no—
150C2×D4—1221no—
151C22×C4—24no—
152C22×C4—1228no—
153C22×C4—1224no—
154C22×C4—1222no—
155C22×C4—1221no—
156C22×C4D24412yes—
157C22×C4D24411yescharacteristic
158C22×C4C22×D6112yes—
159C22×C4C22×D6111yescharacteristic
160Q16—1228no—
161SD16—1228no—
162M16—24no—
163C2×C8C22×D6114yes—
164C4⋊C4—612no—
165C4⋊C4—1222no—
166C22⋊C4—1221no—
167C22⋊C4—1222no—
168C22⋊C4—1222no—
169C42—1221no—
170C23—24no—
171C23—22no—
172C23—1221no—
173C23C2×D24412yes—
174C23C2×D24411yescharacteristic
175Q8—618no—
176Q8—12216no—
177Q8—1224no—
178Q8—1228no—
179Q8—1222no—
180D4—1222no—
181D4—2444no—
182D4—2442no—
183C2×C4—22no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—12216no—
187C2×C4—1224no—
188C2×C4—1228no—
189C2×C4—1222no—
190C2×C4—1221no—
191C2×C4—2442no—
192C2×C4C2×D24412yes—
193C2×C4C2×D24411yescharacteristic
194C2×C4D4×D6114yes—
195C2×C4C23×D6111yescharacteristic
196C8—24no—
197C22—28no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22—2441no—
202C22—2442no—
203C22#1451974712yes—
204C22#1451981014yescomplemented
205C22C22×D24411yescharacteristic
206C4—22no—
207C4—1228no—
208C4—2441no—
209C4—2442no—
210C4#1451974712yes—
211C4C2×D4×D6112yes—
212C2—24no—
213C2—22no—
214C2—4881no—
215C2C2×#1451974711yescharacteristic
216C2C2×#1451981012yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#407C2
socleC22×C61C22×D4
hypercenter#407D61
hypocenterC61#3004
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C23×Dic122C2semidirect
2. C2×#14519810C2semidirect
4. #16839920C2semidirect
5. #16839903C2semidirect
6. #16839772C2semidirect
7. C61×#407C2semidirect
16. C2×Dic244C22semidirect
17. C2×#11758190C22semidirect
24. #14519702C22semidirect
48. C2×Dic122D4semidirect
93. C22×C61#137semidirect
115. #407D61semidirect
116. C61#3004semidirect
204. C22#14519810semidirect