Finite Group Databasebeta

← #21445848

Subgroups — #21445848

Order 7808.

336 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519711C212yesmaximal, complemented
2#16839622C212yesmaximal
3#16839525C212yesmaximal, complemented
4C23×C8×C61C211yesmaximal, characteristic
5C2×C4⋊Dic61C2214yes—
6C2×C22⋊Dic61—22no—
7#14519711—24no—
8#14519684—22no—
9C23×C4×C61C2211yescharacteristic
10C22×C8×C61—24no—
11C22×C8×C61C414yescomplemented
12C22×C8×C61C2211yescharacteristic
13C22×C8×C61C2211yescharacteristic
14C24×C61D411yescharacteristic
15C22×C4×C61—22no—
16C22×C4×C61—22no—
17C22×C4×C61C2×C412yes—
18C22×C4×C61D411yescharacteristic
19C22×C4×C61Q812yes—
20C22×C4×C61C2311yescharacteristic
21C22×Dic61—24no—
22C2×C8×C61—22no—
23C2×C8×C61—28no—
24C2×C8×C61C2×C412yes—
25C2×C8×C61C2×C412yes—
26C2×C8×C61D414yes—
27C22⋊Dic61—44no—
28C4⋊Dic61—24no—
29C4⋊Dic61—24no—
30C23×C61—22no—
31C23×C61—22no—
32C23×C61C4⋊C412yes—
33C23×C61D812yes—
34C23×C61Q1612yes—
35C23×C61C2×D411yescharacteristic
36C2×C4×C61—22no—
37C2×C4×C61—22no—
38C2×C4×C61—22no—
39C2×C4×C61—24no—
40C2×C4×C61C4⋊C412yes—
41C2×C4×C61C22×C411yescharacteristic
42C2×C4×C61C2×D412yes—
43C2×C4×C61C2×Q811yescharacteristic
44C2×C4×C61#4112yes—
45C2×Dic61—44no—
46C2×Dic61—44no—
47C2×Dic61—44no—
48C8×C61—22no—
49C8×C61C22⋊C414yescomplemented
50C22×C61—22no—
51C22×C61—22no—
52C22×C61—24no—
53C22×C61—24no—
54C22×C61#10714yescomplemented
55C22×C61C2×C4⋊C411yescharacteristic
56C22×C61#12112yes—
57C22×C61C2×D811yescharacteristic
58C22×C61C2×Q1611yescharacteristic
59C22×C61#13512yes—
60C4×C61—22no—
61C4×C61C2×C22⋊C411yescharacteristic
62C4×C61#11711yescharacteristic
63C4×C61C22⋊Q812yes—
64Dic61—84no—
65#1808—611nomaximal, Sylow
66C2×C61—24no—
67C2×C61#38011yescharacteristic
68C2×C61C2×#10711yescharacteristic
69C2×C61#42711yescharacteristic
70C2×C61#46612yes—
71C2×C61#46712yes—
72C23×C8D6111yescharacteristic
73C2×#107—612no—
74#380—612no—
75#340—612no—
76C61#180811yescharacteristic, complemented, Sylow
77C23×C4C2×D6111yescharacteristic
78C22×C8—24no—
79C22×C8Dic6114yescomplemented
80C22×C8C2×D6111yescharacteristic
81C22×C8C2×D6111yescharacteristic
82C2×C4⋊C4—614no—
83C2×C22⋊C4—1222no—
84#107—1224no—
85#95—1222no—
86C24D24411yescharacteristic
87C22×C4—22no—
88C22×C4—22no—
89C22×C4—1224no—
90C22×C4Dic12212yes—
91C22×C4D24411yescharacteristic
92C22×C4C2×Dic6112yes—
93C22×C4C22×D6111yescharacteristic
94C2×C8—22no—
95C2×C8—28no—
96C2×C8C2×Dic6112yes—
97C2×C8C2×Dic6112yes—
98C2×C8C22⋊D6114yes—
99C4⋊C4—1224no—
100C4⋊C4—1224no—
101C22⋊C4—2444no—
102C23—22no—
103C23—22no—
104C23D48812yes—
105C23Dic24412yes—
106C23C4⋊Dic6112yes—
107C23C2×D24411yescharacteristic
108C2×C4—22no—
109C2×C4—22no—
110C2×C4—22no—
111C2×C4—24no—
112C2×C4—2444no—
113C2×C4—2444no—
114C2×C4—2444no—
115C2×C4C4⋊Dic6112yes—
116C2×C4C2×Dic12211yescharacteristic
117C2×C4#1175822212yes—
118C2×C4C22×Dic6111yescharacteristic
119C2×C4C2×C22⋊D6112yes—
120C8—22no—
121C8C22⋊Dic6114yescomplemented
122C22—24no—
123C22—24no—
124C22—22no—
125C22—22no—
126C22#1451971114yescomplemented
127C22C2×C4⋊Dic6111yescharacteristic
128C22#1451975112yes—
129C22C2×D48811yescharacteristic
130C22C2×Dic24411yescharacteristic
131C22#1451979912yes—
132C4—22no—
133C4—4884no—
134C4C2×C22⋊Dic6111yescharacteristic
135C4#1451973611yescharacteristic
136C4#1451975612yes—
137C2—24no—
138C2#1683962211yescharacteristic
139C2C2×#1451971111yescharacteristic
140C2#1683980011yescharacteristic
141C2#1683999812yes—
142C2#1684000312yes—
subgroupG/H
centerC23C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC23×C8×C61C2
socleC23×C61C2×D4
hypercenterC23×C8D61
hypocenterC61#1808
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. C2×#14519711C2semidirect
3. #16839525C2semidirect
11. C22×C8×C61C4semidirect
49. C8×C61C22⋊C4semidirect
54. C22×C61#107semidirect
76. C61#1808semidirect
79. C22×C8Dic61semidirect
121. C8C22⋊Dic61semidirect
126. C22#14519711semidirect