Finite Group Databasebeta

← #21444145

Subgroups — #21444145

Order 7808.

440 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C22×#11758198C211yesmaximal, characteristic
2#16839726C211yesmaximal, characteristic, complemented
3#16839485C214yesmaximal, complemented
4C61×#407C211yesmaximal, characteristic, complemented
5C24×D61C411yescharacteristic
6C23×Dic61C411yescharacteristic
7C2×#11758194—21no—
8C2×#11758198—21no—
9C2×#11758198—21no—
10C2×#11758198—21no—
11C2×#11758198—21no—
12C2×#11758198C412yes—
13C2×#11758198C2212yes—
14C22⋊#92418—21no—
15C22⋊#92418C2212yescomplemented
16C23×C4×C61C2211yescharacteristic
17C2×M16×C61—21no—
18C22⋊C8×C61—21no—
19C22⋊C8×C61C2212yescomplemented
20C24×C61C2×C411yescharacteristic
21C23×D61—21no—
22C23×D61—21no—
23C23×D61—24no—
24C23×D61—42no—
25C23×D61—42no—
26C23×D61C2×C412yes—
27C22×C4×C61—42no—
28C22×C4×C61C2×C411yescharacteristic
29C22×C4×C61D411yescharacteristic
30C22×C4×C61D411yescharacteristic
31C22×C4×C61D411yescharacteristic
32C22×C4×C61D411yescharacteristic
33C22×C4×C61C2311yescharacteristic
34C22×Dic61—21no—
35C22×Dic61—21no—
36C22×Dic61—42no—
37C22×Dic61C2×C412yes—
38M16×C61—42no—
39C2×C8×C61—22no—
40#11758198—22no—
41#11758198—22no—
42#11758198—22no—
43#11758198—22no—
44#11758194—42no—
45C2×#92418—22no—
46C23×C61—22no—
47C23×C61—22no—
48C23×C61—22no—
49C23×C61C22⋊C411yescharacteristic
50C23×C61C22⋊C411yescharacteristic
51C23×C61C22×C411yescharacteristic
52C22×D61—24no—
53C22×D61—24no—
54C22×D61—22no—
55C22×D61—22no—
56C22×D61—416no—
57C22×D61—42no—
58C22×D61—42no—
59C22×D61—42no—
60C22×D61—42no—
61C22×D61—42no—
62C22×D61—42no—
63C22×D61M1614yescomplemented
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61C22⋊C411yescharacteristic
71C2×C4×C61C22⋊C411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×Dic61—22no—
75C2×Dic61—42no—
76C2×Dic61—42no—
77C2×Dic61—42no—
78C8×C61—42no—
79#92418—42no—
80C22×C61—28no—
81C22×C61—21no—
82C22×C61—21no—
83C22×C61—21no—
84C22×C61—21no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61#9912yes—
88C22×C61#10012yes—
89C22×C61C2×C22⋊C411yescharacteristic
90C22×C61C2×M1612yes—
91C2×D61—24no—
92C2×D61—48no—
93C2×D61—48no—
94C2×D61—44no—
95C2×D61—42no—
96C2×D61—42no—
97C2×D61—44no—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—21no—
101C4×C61—21no—
102Dic61—42no—
103#1462—611nomaximal, Sylow
104C2×C61—22no—
105C2×C61—22no—
106C2×C61—22no—
107C2×C61#40711yescharacteristic
108C2×C61C2×#9911yescharacteristic
109C2×C61C2×#10011yescharacteristic
110D61—44no—
111C22×C22⋊C4—611no—
112#407—611no—
113#407D6111yescharacteristic, complemented
114#323—614no—
115C61#146211yescharacteristic, complemented, Sylow
116C25—611no—
117C23×C4—611no—
118C23×C4C2×D6111yescharacteristic
119C2×M16—21no—
120C2×M16—1221no—
121C2×C22⋊C4—612no—
122C2×C22⋊C4—612no—
123C2×C22⋊C4—1221no—
124C2×C22⋊C4—1221no—
125C2×C22⋊C4—1221no—
126C2×C22⋊C4—1221no—
127C22⋊C8—21no—
128C22⋊C8—612no—
129C22⋊C8—1221no—
130C22⋊C8C2×D6112yescomplemented
131C24—612no—
132C24—1224no—
133C24—1221no—
134C24—1221no—
135C24—2442no—
136C24—2442no—
137C24C4×D6111yescharacteristic
138C22×C4—42no—
139C22×C4—612no—
140C22×C4—1221no—
141C22×C4—1221no—
142C22×C4—2442no—
143C22×C4C4×D6111yescharacteristic
144C22×C4D24411yescharacteristic
145C22×C4D24411yescharacteristic
146C22×C4C22⋊D6111yescharacteristic
147C22×C4C22⋊D6111yescharacteristic
148C22×C4C22×D6111yescharacteristic
149M16—42no—
150M16—2442no—
151C2×C8—22no—
152C2×C8—1222no—
153C22⋊C4—1222no—
154C22⋊C4—1222no—
155C22⋊C4—1222no—
156C22⋊C4—1222no—
157C23—22no—
158C23—22no—
159C23—22no—
160C23—614no—
161C23—1224no—
162C23—1224no—
163C23—1222no—
164C23—1222no—
165C23—2442no—
166C23—2442no—
167C23—24416no—
168C23—2442no—
169C23—2442no—
170C23—2442no—
171C23—2442no—
172C23#1175819811yescharacteristic
173C23#1175819811yescharacteristic
174C23C2×C4×D6111yescharacteristic
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—1222no—
182C2×C4—2442no—
183C2×C4—2442no—
184C2×C4—2442no—
185C2×C4#1175819811yescharacteristic
186C2×C4#1175819811yescharacteristic
187C2×C4C2×D24411yescharacteristic
188C2×C4C2×C22⋊D6111yescharacteristic
189C8—42no—
190C8—2442no—
191C22—28no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—1224no—
199C22—2444no—
200C22—2448no—
201C22—2448no—
202C22—2444no—
203C22—2442no—
204C22—2442no—
205C22#1451969112yes—
206C22#1451969312yes—
207C22C2×#1175819811yescharacteristic
208C22M16×D6112yes—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—2442no—
214C2—22no—
215C2—22no—
216C2—22no—
217C2—2444no—
218C2#1683972511yescharacteristic
219C2C2×#1451969111yescharacteristic
220C2C2×#1451969311yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#407C2
socleC22×C61C2×C22⋊C4
hypercenter#407D61
hypocenterC61#1462
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. #16839726C2semidirect
3. #16839485C2semidirect
4. C61×#407C2semidirect
15. C22⋊#92418C22semidirect
19. C22⋊C8×C61C22semidirect
63. C22×D61M16semidirect
113. #407D61semidirect
115. C61#1462semidirect
130. C22⋊C8C2×D61semidirect