Finite Group Databasebeta

← #21444349

Subgroups — #21444349

Order 7808.

326 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#14519751C211yesmaximal, characteristic
2#16839625C211yesmaximal, characteristic, complemented
3#16839497C214yesmaximal, complemented
4C61×#407C211yesmaximal, characteristic, complemented
5C22×D244C411yescharacteristic, complemented
6C22×C22⋊D61—21no—
7#14519751—21no—
8#14519751—21no—
9#14519751C412yescomplemented
10#14519751C2212yes—
11C2×C4⋊Dic61C411yescharacteristic, complemented
12C2×C22⋊Dic61—21no—
13C2×#11758198—21no—
14#14519684—21no—
15#14519684C2212yescomplemented
16C23×C4×C61C2211yescharacteristic
17C2×M16×C61—21no—
18C22⋊C8×C61—21no—
19C22⋊C8×C61C2212yescomplemented
20C24×C61D411yescharacteristic
21C23×D61—21no—
22C22×C4×C61—42no—
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61C2×C411yescharacteristic
25C22×C4×C61D411yescharacteristic
26C22×C4×C61D411yescharacteristic
27C22×C4×C61D411yescharacteristic
28C22×C4×C61C2311yescharacteristic
29C2×C22⋊D61—22no—
30C2×C22⋊D61—22no—
31C2×C22⋊D61—44no—
32C22×Dic61—21no—
33C22×Dic61—22no—
34C2×D244—21no—
35C2×D244—42no—
36C2×D244C2×C412yes—
37M16×C61—42no—
38C2×C8×C61—22no—
39C22⋊Dic61—42no—
40#11758198—22no—
41#11758198—22no—
42C4⋊Dic61—21no—
43C4⋊Dic61C2×C412yes—
44C23×C61—22no—
45C23×C61—22no—
46C23×C61—41no—
47C23×C61C22⋊C411yescharacteristic
48C23×C61C22⋊C411yescharacteristic
49C23×C61C2×D411yescharacteristic
50C22×D61—22no—
51C22×D61—42no—
52C22×D61—42no—
53C22×D61—42no—
54C2×C4×C61—22no—
55C2×C4×C61—22no—
56C2×C4×C61—41no—
57C2×C4×C61—41no—
58C2×C4×C61—41no—
59C2×C4×C61—41no—
60C2×C4×C61C22⋊C411yescharacteristic
61C2×C4×C61C22⋊C411yescharacteristic
62C2×C4×C61C22×C411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C22⋊D61—44no—
65C22⋊D61—44no—
66C2×Dic61—22no—
67C2×Dic61—42no—
68C2×Dic61—42no—
69C2×Dic61—42no—
70C2×Dic61—42no—
71D244—42no—
72D244—42no—
73C8×C61—42no—
74C22×C61—21no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61—21no—
78C22×C61—21no—
79C22×C61—21no—
80C22×C61—21no—
81C22×C61—44no—
82C22×C61#9912yes—
83C22×C61C2×C22⋊C411yescharacteristic
84C22×C61AGL(1,ℤ/8)12yes—
85C2×D61—42no—
86C2×D61—42no—
87C2×D61—42no—
88C2×D61—84no—
89C4×C61—21no—
90C4×C61—21no—
91C4×C61—21no—
92C4×C61—21no—
93Dic61—42no—
94Dic61—82no—
95#1510—611nomaximal, Sylow
96C2×C61—22no—
97C2×C61—22no—
98C2×C61—41no—
99C2×C61C2×#9911yescharacteristic
100C2×C61#41811yescharacteristic
101C2×C61#42111yescharacteristic
102D61—82no—
103C2×#121—611no—
104#407D6111yescharacteristic, complemented
105#381—611no—
106#327—614no—
107C61#151011yescharacteristic, complemented, Sylow
108C22×D4—611no—
109C22×D4—1221no—
110C23×C4C2×D6111yescharacteristic
111C2×M16—21no—
112#121—612no—
113#121—612no—
114#121—1221no—
115#121—1221no—
116C2×C4⋊C4—611no—
117C2×C22⋊C4—1221no—
118C2×C22⋊C4—1221no—
119C22⋊C8—21no—
120C22⋊C8C2×D6112yescomplemented
121#95—612no—
122#95—1221no—
123C24—1221no—
124C24D24411yescharacteristic
125C2×D4—612no—
126C2×D4—1222no—
127C2×D4—1222no—
128C2×D4—1221no—
129C2×D4—2442no—
130C2×D4—2444no—
131C22×C4—42no—
132C22×C4—1221no—
133C22×C4—1222no—
134C22×C4C4×D6111yescharacteristic
135C22×C4C4×D6111yescharacteristic
136C22×C4D24411yescharacteristic
137C22×C4C22⋊D6111yescharacteristic
138C22×C4C22⋊D6111yescharacteristic
139C22×C4C22×D6111yescharacteristic
140M16—42no—
141C2×C8—22no—
142C4⋊C4—612no—
143C4⋊C4—1221no—
144C22⋊C4—1222no—
145C22⋊C4—1222no—
146C22⋊C4—2442no—
147C23—22no—
148C23—22no—
149C23—41no—
150C23—1222no—
151C23—2442no—
152C23—2442no—
153C23—2442no—
154C23#1175819811yescharacteristic
155C23#1175819811yescharacteristic
156C23C2×D24411yescharacteristic
157D4—2442no—
158D4—2442no—
159D4—2444no—
160D4—2444no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—1222no—
168C2×C4—2442no—
169C2×C4—2442no—
170C2×C4—2442no—
171C2×C4—2442no—
172C2×C4#1175819811yescharacteristic
173C2×C4#1175819811yescharacteristic
174C2×C4C2×C4×D6111yescharacteristic
175C2×C4C2×C22⋊D6111yescharacteristic
176C8—42no—
177C22—21no—
178C22—21no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—44no—
185C22—4884no—
186C22—2442no—
187C22—2442no—
188C22—2442no—
189C22#1451969112yes—
190C22C2×#1175819811yescharacteristic
191C22#1451980512yes—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—21no—
196C4—4882no—
197C4—2442no—
198C2—22no—
199C2—22no—
200C2—41no—
201C2—4882no—
202C2C2×#1451969111yescharacteristic
203C2#1683976811yescharacteristic
204C2#1683977811yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#407C2
socleC22×C61C2×C22⋊C4
hypercenter#407D61
hypocenterC61#1510
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. #16839625C2semidirect
3. #16839497C2semidirect
4. C61×#407C2semidirect
5. C22×D244C4semidirect
9. #14519751C4semidirect
11. C2×C4⋊Dic61C4semidirect
15. #14519684C22semidirect
19. C22⋊C8×C61C22semidirect
104. #407D61semidirect
107. C61#1510semidirect
120. C22⋊C8C2×D61semidirect