Finite Group Databasebeta

← #21444326

Subgroups — #21444326

Order 7808.

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

normal subgroups only

This group has 272 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
1#16840312C211yesmaximal, characteristic
2#16839819C211yesmaximal, characteristic, complemented
3#16839495C214yesmaximal, complemented
4C61×#376C211yesmaximal, characteristic, complemented
5C2×#11758222—21no—
6#14519777C411yescharacteristic, complemented
7#14519774C411yescharacteristic, complemented
8#14519765—21no—
9#14519751—21no—
10#14519751C2212yes—
11C4×D244—21no—
12C4×D244C412yescomplemented
13C4⋊#92418—21no—
14C22⋊#92418C2212yes—
15#14519688—21no—
16C2×C42×C61—21no—
17C2×C42×C61C2211yescharacteristic
18#95×C61—21no—
19#95×C61C2212yes—
20C22×C4×C61—22no—
21C22×C4×C61D411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61C2311yescharacteristic
24C2×C22⋊D61—22no—
25#11758222—44no—
26C2×D244—21no—
27C2×D244—21no—
28C2×D244C2×C412yes—
29C2×C4×D61—22no—
30C2×Dic122—21no—
31C42×C61—24no—
32C42×C61C2×C411yescharacteristic
33C42×C61C2×C411yescharacteristic
34C42×C61D411yescharacteristic
35C42×C61D411yescharacteristic
36#11758198—22no—
37#11758198—22no—
38C4⋊Dic61—21no—
39C4⋊Dic61C2×C412yes—
40C2×#92418—22no—
41C23×C61C2×D411yescharacteristic
42C22×D61—22no—
43C2×C4×C61—22no—
44C2×C4×C61—22no—
45C2×C4×C61—24no—
46C2×C4×C61—41no—
47C2×C4×C61—42no—
48C2×C4×C61—42no—
49C2×C4×C61C22⋊C411yescharacteristic
50C2×C4×C61C22⋊C411yescharacteristic
51C2×C4×C61C22⋊C411yescharacteristic
52C2×C4×C61C22⋊C411yescharacteristic
53C2×C4×C61C22×C411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C22⋊D61—44no—
56C2×Dic61—22no—
57D244—42no—
58D244—42no—
59D244—42no—
60C4×D61—44no—
61Dic122—42no—
62#92418—42no—
63C22×C61—21no—
64C22×C61—21no—
65C22×C61C2×C22⋊C411yescharacteristic
66C22×C61AGL(1,ℤ/8)12yes—
67C2×D61—42no—
68C2×D61—42no—
69C2×D61—42no—
70C4×C61—21no—
71C4×C61—21no—
72C4×C61—21no—
73C4×C61—21no—
74C4×C61—21no—
75C4×C61—44no—
76C4×C61#10412yes—
77Dic61—42no—
78#1505—611nomaximal, Sylow
79C2×C61—22no—
80C2×C61#41011yescharacteristic
81C2×C61#41811yescharacteristic
82C2×C61C2×#10411yescharacteristic
83D61—82no—
84#532—611no—
85#432—611no—
86#376D6111yescharacteristic, complemented
87#327—614no—
88C61#150511yescharacteristic, complemented, Sylow
89C2×#41—1221no—
90C4⋊Q8—611no—
91#127—611no—
92#124—1221no—
93#121—612no—
94#121—1221no—
95C4×D4—612no—
96C4×D4—1221no—
97C2×C42—21no—
98C2×C42C2×D6111yescharacteristic
99C4⋊C8—1221no—
100C22⋊C8—612no—
101#97—1221no—
102#95—21no—
103#95C2×D6112yes—
104#41—2444no—
105C2×Q8—1221no—
106C2×D4—612no—
107C2×D4—1222no—
108C2×D4—1221no—
109C2×D4—1221no—
110C22×C4—22no—
111C22×C4—1222no—
112C22×C4C22⋊D6111yescharacteristic
113C22×C4C22⋊D6111yescharacteristic
114C22×C4C22×D6111yescharacteristic
115C2×C8—1222no—
116C4⋊C4—612no—
117C4⋊C4—1221no—
118C22⋊C4—1222no—
119C22⋊C4—1222no—
120C42—24no—
121C42C4×D6111yescharacteristic
122C42C4×D6111yescharacteristic
123C42D24411yescharacteristic
124C42D24411yescharacteristic
125C23—1222no—
126C23C2×C22⋊D6111yescharacteristic
127Q8—2442no—
128D4—2442no—
129D4—2442no—
130D4—2444no—
131D4—2442no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—24no—
135C2×C4—41no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—1222no—
139C2×C4—2444no—
140C2×C4#1175819811yescharacteristic
141C2×C4#1175819811yescharacteristic
142C2×C4#1175819811yescharacteristic
143C2×C4#1175819811yescharacteristic
144C2×C4C2×C4×D6111yescharacteristic
145C2×C4C2×D24411yescharacteristic
146C8—2442no—
147C22—21no—
148C22—21no—
149C22—2442no—
150C22—2442no—
151C22—2442no—
152C22C2×#1175819811yescharacteristic
153C22#1451980212yes—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—44no—
160C4—2442no—
161C4#1451970512yes—
162C2—22no—
163C2—4882no—
164C2#1683973511yescharacteristic
165C2#1683976611yescharacteristic
166C2C2×#1451970511yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#376C2
socleC22×C61C2×C22⋊C4
hypercenter#376D61
hypocenterC61#1505
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #16839819C2semidirect
3. #16839495C2semidirect
4. C61×#376C2semidirect
6. #14519777C4semidirect
7. #14519774C4semidirect
12. C4×D244C4semidirect
86. #376D61semidirect
88. C61#1505semidirect