Finite Group Databasebeta

← #44506528

Subgroups — #44506528

Order 30848.

240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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#29508091C211yesmaximal, characteristic, complemented
2#29507912C212yesmaximal, complemented
3#29507466C211yesmaximal, characteristic, complemented
4D4⋊#14515349C212yesmaximal, complemented
5#555×C241C211yesmaximal, characteristic, complemented
6C2×#16838757—22no—
7C2×#16838755—22no—
8#21440639C2211yescharacteristic
9C4⋊#14515349C2212yes—
10#21440562—22no—
11C4×#14515349C2211yescharacteristic
12C4⋊Q8×C241C2211yescharacteristic
13#124×C241—22no—
14#121×C241—22no—
15C4×D4×C241C2212yes—
16#117×C241—22no—
17C2×D964—22no—
18C2×D964—21no—
19#16838757—44no—
20#16838755—44no—
21C2×#14515349—21no—
22C2×#14515349—22no—
23C2×Q8×C241D412yes—
24C2×D4×C241—22no—
25C2×D4×C241D412yes—
26C22×C4×C241—22no—
27C4⋊C4×C241—22no—
28C4⋊C4×C241D412yes—
29C22⋊C4×C241—24no—
30C22⋊C4×C241—22no—
31C42×C241—22no—
32C42×C241C2311yescharacteristic
33C22×D241—41no—
34D964—42no—
35D964—42no—
36D964—42no—
37#14515349—22no—
38#14515349—42no—
39C23×C241—22no—
40Q8×C241—42no—
41D4×C241—22no—
42D4×C241—22no—
43D4×C241—82no—
44C2×C4×C241—22no—
45C2×C4×C241—22no—
46C2×C4×C241—42no—
47C2×C4×C241—42no—
48C2×C4×C241C2×D411yescharacteristic
49C2×C4×C241C2×D412yes—
50C22×C241—42no—
51C22×C241—42no—
52C22×C241—42no—
53C22×C241#12011yescharacteristic
54C2×D241—82no—
55C2×D241—81no—
56C4×C241—21no—
57C4×C241—42no—
58C4×C241—42no—
59C4×C241#13512yes—
60C4×C241AGL(1,ℤ/8)12yes—
61C2×C241—82no—
62C2×C241#44912yes—
63C2×C241#45311yescharacteristic
64D241—161no—
65C241#162411yescharacteristic, complemented, Sylow
66#1624—2411nomaximal, Sylow
67#555D24111yescharacteristic, complemented
68#492—2411no—
69#459—2412no—
70#333—2411no—
71D4⋊C8—2412no—
72C2×SD16—4822no—
73C2×D8—4822no—
74C4⋊Q8C2×D24111yescharacteristic
75#127—2411no—
76#124—22no—
77#121—22no—
78C4×D4C2×D24112yes—
79#117—22no—
80C4⋊C8—2412no—
81#102—4822no—
82C4×C8—2411no—
83C2×Q8C22⋊D24112yes—
84C2×D4—22no—
85C2×D4—4822no—
86C2×D4—4821no—
87C2×D4C22⋊D24112yes—
88C22×C4—22no—
89SD16—9644no—
90D8—9644no—
91C2×C8—4822no—
92C2×C8—4821no—
93C4⋊C4—22no—
94C4⋊C4C22⋊D24112yes—
95C22⋊C4—24no—
96C22⋊C4—22no—
97C42—22no—
98C42C22×D24111yescharacteristic
99C23—22no—
100C23—9641no—
101Q8—42no—
102D4—22no—
103D4—22no—
104D4—82no—
105D4—9642no—
106D4—9642no—
107D4—9642no—
108C2×C4—22no—
109C2×C4—22no—
110C2×C4—42no—
111C2×C4—42no—
112C2×C4C2×C22⋊D24111yescharacteristic
113C2×C4C2×C22⋊D24112yes—
114C8—9642no—
115C8—4822no—
116C22—42no—
117C22—42no—
118C22—42no—
119C22—19282no—
120C22—19281no—
121C22#2144061111yescharacteristic
122C4—21no—
123C4—42no—
124C4—42no—
125C4#2144066212yes—
126C4#2144066712yes—
127C2—82no—
128C2—38561no—
129C2#2950786212yes—
130C2#2950788511yescharacteristic
subgroupG/H
centerC22#21440611
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#555×C241C2
socleC22×C241#120
hypercenter#555D241
hypocenterC241#1624
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #29508091C2semidirect
2. #29507912C2semidirect
3. #29507466C2semidirect
4. D4⋊#14515349C2semidirect
5. #555×C241C2semidirect
65. C241#1624semidirect
67. #555D241semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#295080912
#295079122
#295074662
D4⋊#145153492
#555×C2412
#1624241