Finite Group Databasebeta

← #44506529

Subgroups — #44506529

Order 30848.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#29508433C211yesmaximal, characteristic, complemented
2#29508091C211yesmaximal, characteristic, complemented
3#29507913C212yesmaximal, complemented
4#29507444C212yesmaximal, complemented
5#333×C241C211yesmaximal, characteristic, complemented
6C2×#16838757—22no—
7C2×D1928—22no—
8#21440639C2211yescharacteristic
9#21440631—22no—
10#21440617—22no—
11C4×D964C2212yes—
12#21440600—22no—
13#21440564—22no—
14C4×#14515349C2211yescharacteristic
15C4⋊Q8×C241C2211yescharacteristic
16C4⋊C8×C241C2212yes—
17C2×D964—22no—
18C2×D964—22no—
19C2×D964—21no—
20C2×D964D412yes—
21C2×C4×D241—22no—
22#16838757—44no—
23D1928—44no—
24C2×#14515349—21no—
25C4⋊Dic241D412yes—
26#16838747—24no—
27#16838747—22no—
28C4×Dic241—22no—
29C2×Q8×C241D412yes—
30C2×C8×C241—22no—
31C4⋊C4×C241—22no—
32C42×C241C2311yescharacteristic
33C22×D241—22no—
34C22×D241—41no—
35D964—22no—
36D964—22no—
37D964—42no—
38D964—42no—
39D964—42no—
40D964—82no—
41C2×Dic241—22no—
42C4×D241—42no—
43C4×D241—42no—
44#14515349—22no—
45Q8×C241—42no—
46C2×C4×C241—22no—
47C2×C4×C241C2×D412yes—
48C2×C4×C241C2×D411yescharacteristic
49C8×C241—42no—
50C22×C241#12011yescharacteristic
51C2×D241—42no—
52C2×D241—42no—
53C2×D241—42no—
54C2×D241—82no—
55C2×D241—81no—
56C4×C241—21no—
57C4×C241—42no—
58C4×C241#13512yes—
59C4×C241AGL(1,ℤ/8)12yes—
60Dic241—42no—
61C2×C241#44912yes—
62C2×C241#45311yescharacteristic
63D241—82no—
64D241—161no—
65C241#162411yescharacteristic, complemented, Sylow
66#1624—2411nomaximal, Sylow
67#555—2411no—
68#492—2411no—
69#459—2412no—
70#333D24111yescharacteristic, complemented
71D4⋊C8—2412no—
72C2×SD16—4822no—
73C2×D8—4822no—
74C4⋊Q8C2×D24111yescharacteristic
75#127—2411no—
76#124—4822no—
77#121—4822no—
78C4×D4—2412no—
79#117—4822no—
80C4⋊C8C2×D24112yes—
81#102—4822no—
82C4×C8—2411no—
83C2×Q8D96412yes—
84C2×D4—4822no—
85C2×D4—4822no—
86C2×D4—4821no—
87C2×D4—2412no—
88C22×C4—4822no—
89SD16—9644no—
90D8—9644no—
91C2×C8—22no—
92C2×C8—4821no—
93C4⋊C4—22no—
94C4⋊C4—2412no—
95C22⋊C4—4824no—
96C22⋊C4—4822no—
97C42—4822no—
98C42C22×D24111yescharacteristic
99C23—9641no—
100C23—4822no—
101Q8—42no—
102D4—19282no—
103D4—9642no—
104D4—9642no—
105D4—9642no—
106D4—4822no—
107D4—4822no—
108C2×C4—22no—
109C2×C4—9642no—
110C2×C4—9642no—
111C2×C4—4822no—
112C2×C4D4×D24112yes—
113C2×C4C2×D96411yescharacteristic
114C8—42no—
115C8—4822no—
116C22—19282no—
117C22—19281no—
118C22—9642no—
119C22—9642no—
120C22—9642no—
121C22#2144061211yescharacteristic
122C4—21no—
123C4—42no—
124C4—9642no—
125C4#2144066512yes—
126C4#2144066912yes—
127C2—38561no—
128C2—19282no—
129C2#2950786512yes—
130C2#2950788711yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#333×C241C2
socleC22×C241#120
hypercenter#333D241
hypocenterC241#1624
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #29508433C2semidirect
2. #29508091C2semidirect
3. #29507913C2semidirect
4. #29507444C2semidirect
5. #333×C241C2semidirect
65. C241#1624semidirect
70. #333D241semidirect

Maximal subgroups

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

subgroupindex
#295084332
#295080912
#295079132
#295074442
#333×C2412
#1624241