Finite Group Databasebeta

← #21455752

Subgroups — #21455752

Order 7808.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14519736C211yesmaximal, characteristic, complemented
3#16840104C214yesmaximal, complemented
4#16840087C214yesmaximal, complemented
5#16839804C212yesmaximal, complemented
6#16839764C212yesmaximal, complemented
7C61×#407C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519760—21no—
10#14519756C2212yes—
11#14519751C2212yes—
12#14519746—21no—
13C4×C22⋊D61—22no—
14#14519736—22no—
15#14519736C2214yes—
16#14519736C2211yescharacteristic
17C2×C4⋊Dic61C2212yes—
18C2×C22⋊Dic61—21no—
19C2×C4×Dic61—21no—
20#14519711C2214yescomplemented
21#14519709C2214yescomplemented
22#14519702C2214yescomplemented
23#14519699C2214yescomplemented
24C23×C4×C61C2211yescharacteristic
25C2×M16×C61C2212yes—
26C22⋊C8×C61C2214yes—
27C24×C61D411yescharacteristic
28C22×C4×C61—24no—
29C22×C4×C61D411yescharacteristic
30C22×C4×C61D412yes—
31C22×C4×C61C2312yes—
32C22×C4×C61C2311yescharacteristic
33C2×C22⋊D61—21no—
34C2×C22⋊D61—22no—
35C22×Dic61—22no—
36#11758222—24no—
37C2×D244C2311yescharacteristic
38C2×C4×D61—21no—
39C2×Dic122C2311yescharacteristic
40M16×C61—24no—
41C2×C8×C61C2314yes—
42C22⋊Dic61—24no—
43C22⋊Dic61—21no—
44C22⋊Dic61—22no—
45#11758198—22no—
46C4⋊Dic61—22no—
47C4⋊Dic61C2314yes—
48C4⋊Dic61C2312yes—
49#11758196—22no—
50C4×Dic61—24no—
51C4×Dic61—21no—
52C23×C61—22no—
53C23×C61—42no—
54C23×C61C2×D412yes—
55C23×C61C2×D411yescharacteristic
56C22×D61—21no—
57C2×C4×C61—22no—
58C2×C4×C61—24no—
59C2×C4×C61—24no—
60C2×C4×C61C2×D412yes—
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61#4114yes—
63C2×C4×C61C2411yescharacteristic
64C22⋊D61—44no—
65C22⋊D61—42no—
66C2×Dic61—24no—
67C2×Dic61—22no—
68C2×Dic61—21no—
69C2×Dic61—44no—
70D244—22no—
71C4×D61—42no—
72Dic122—22no—
73C8×C61—24no—
74C22×C61—22no—
75C22×C61—22no—
76C22×C61—22no—
77C22×C61—22no—
78C22×C61—44no—
79C22×C61#12312yes—
80C22×C61C22×D411yescharacteristic
81C2×D61—41no—
82C2×D61—42no—
83C4×C61—22no—
84C4×C61#12312yes—
85C4×C61C2×#4112yes—
86Dic61—41no—
87Dic61—44no—
88Dic61—42no—
89#3093—611nomaximal, Sylow
90C2×C61—22no—
91C2×C61—42no—
92C2×C61C2×#12311yescharacteristic
93C2×C61#57512yes—
94D61—81no—
95#525—611no—
96C2×#117—611no—
97#485—614no—
98#482—614no—
99#428—612no—
100#417—612no—
101#407D6111yescharacteristic, complemented
102C61#309311yescharacteristic, complemented, Sylow
103C2×#41—611no—
104C23×C4C2×D6111yescharacteristic
105C2×M16C2×D6112yes—
106#123—1221no—
107C22⋊Q8—612no—
108#121—612no—
109#120—1221no—
110C4×D4—1222no—
111#117—614no—
112#117—611no—
113#117—1222no—
114C2×C4⋊C4—612no—
115C2×C22⋊C4—1221no—
116C2×C42—1221no—
117#107—614no—
118#106—614no—
119#103—614no—
120#102—614no—
121C22⋊C8C2×D6114yes—
122C24D24411yescharacteristic
123#41—1224no—
124C2×Q8—611no—
125C2×D4—611no—
126C2×D4—1222no—
127C2×D4—1221no—
128C22×C4—24no—
129C22×C4—1222no—
130C22×C4—1221no—
131C22×C4D24411yescharacteristic
132C22×C4D24412yes—
133C22×C4C22×D6112yes—
134C22×C4C22×D6111yescharacteristic
135M16—24no—
136C2×C8C22×D6114yes—
137C4⋊C4—614no—
138C4⋊C4—612no—
139C4⋊C4—1222no—
140C4⋊C4—1222no—
141C22⋊C4—1224no—
142C22⋊C4—1221no—
143C22⋊C4—1222no—
144C22⋊C4—1222no—
145C42—1224no—
146C42—1221no—
147C23—22no—
148C23—42no—
149C23—1221no—
150C23C2×D24412yes—
151C23C2×D24411yescharacteristic
152Q8—1222no—
153D4—1222no—
154D4—2444no—
155D4—2442no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—1224no—
160C2×C4—1222no—
161C2×C4—1221no—
162C2×C4—2444no—
163C2×C4—2442no—
164C2×C4C2×D24412yes—
165C2×C4C2×D24411yescharacteristic
166C2×C4#1175822414yes—
167C2×C4C23×D6111yescharacteristic
168C8—24no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—2441no—
175C22—2442no—
176C22#1451976112yes—
177C22C22×D24411yescharacteristic
178C4—22no—
179C4—2441no—
180C4—2444no—
181C4—2442no—
182C4#1451976112yes—
183C4C2×#1175822412yes—
184C2—22no—
185C2—42no—
186C2—4881no—
187C2C2×#1451976111yescharacteristic
188C2#1684056212yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#407C2
socleC22×C61C22×D4
hypercenter#407D61
hypocenterC61#3093
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
2. C2×#14519736C2semidirect
3. #16840104C2semidirect
4. #16840087C2semidirect
5. #16839804C2semidirect
6. #16839764C2semidirect
7. C61×#407C2semidirect
20. #14519711C22semidirect
21. #14519709C22semidirect
22. #14519702C22semidirect
23. #14519699C22semidirect
101. #407D61semidirect
102. C61#3093semidirect