Finite Group Databasebeta

← #44506104

Subgroups — #44506104

Order 30848.

246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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#29508265C211yesmaximal, characteristic
2#29507769C212yesmaximal, complemented
3#29507465C212yesmaximal, complemented
4#29507461C211yesmaximal, characteristic, complemented
5#331×C241C211yesmaximal, characteristic, complemented
6C2×#16838769C412yes—
7#21440642C2211yescharacteristic
8#21440629C412yes—
9#21440613—22no—
10D4×Dic241—22no—
11C42×D241C2211yescharacteristic
12C4⋊#14515349C2212yes—
13#21440554—22no—
14C8×Dic241—22no—
15#127×C241C2211yescharacteristic
16C4⋊C8×C241C2212yes—
17#16838769—44no—
18C2×Dic482C2×C412yes—
19C2×C22⋊D241—22no—
20C22×Dic241—22no—
21C2×C4×D241C2×C411yescharacteristic
22C2×C4×D241D412yes—
23C2×#14515349—22no—
24C4⋊Dic241—22no—
25C22⋊Dic241—24no—
26C4×Dic241C2×C411yescharacteristic
27C4×Dic241D412yes—
28C2×D4×C241—22no—
29C2×D4×C241C2×C412yes—
30C2×C8×C241—22no—
31C42×C241C2311yescharacteristic
32C22×D241C22⋊C411yescharacteristic
33Dic482—42no—
34C22⋊D241—44no—
35C2×Dic241—22no—
36C2×Dic241—44no—
37C2×Dic241C22⋊C412yes—
38C2×Dic241C22⋊C411yescharacteristic
39C4×D241—22no—
40C4×D241—22no—
41C4×D241—22no—
42#14515349—42no—
43C23×C241—22no—
44D4×C241—42no—
45D4×C241—42no—
46D4×C241—42no—
47C2×C4×C241C22×C411yescharacteristic
48C2×C4×C241C2×D412yes—
49C8×C241—42no—
50C22×C241—42no—
51C22×C241—44no—
52C22×C241C2×C22⋊C411yescharacteristic
53C2×D241—21no—
54C2×D241—22no—
55C4×C241—21no—
56C4×C241#13512yes—
57C4×C241#13512yes—
58Dic241—22no—
59Dic241—42no—
60Dic241#10012yes—
61C2×C241—82no—
62C2×C241C2×#10011yescharacteristic
63C2×C241#41612yes—
64D241—41no—
65C241#154311yescharacteristic, complemented, Sylow
66#1543—2411nomaximal, Sylow
67#532—2411no—
68#431—2412no—
69#333—2412no—
70#331—2411no—
71#331D24111yescharacteristic, complemented
72C2×#41—2412no—
73C4⋊Q8—2411no—
74#127C2×D24111yescharacteristic
75#124—2412no—
76#121—4822no—
77C4×D4—4822no—
78C2×C42—2411no—
79C4⋊C8—2412no—
80C4⋊C8C2×D24112yes—
81C22⋊C8—4822no—
82C4×C8—4822no—
83#41—9644no—
84C2×Q8—2412no—
85C2×D4—22no—
86C2×D4—4822no—
87C2×D4C4×D24112yes—
88C22×C4—4822no—
89C22×C4—2411no—
90C22×C4—2412no—
91C2×C8—22no—
92C2×C8—4822no—
93C4⋊C4—4822no—
94C22⋊C4—4824no—
95C42—2411no—
96C42—2412no—
97C42C22×D24111yescharacteristic
98C23—22no—
99C23—2411no—
100Q8—9642no—
101D4—42no—
102D4—42no—
103D4—42no—
104D4—9644no—
105C2×C4—9644no—
106C2×C4—4822no—
107C2×C4—4822no—
108C2×C4—4822no—
109C2×C4—4822no—
110C2×C4—2412no—
111C2×C4—2411no—
112C2×C4C2×C4×D24111yescharacteristic
113C2×C4D4×D24112yes—
114C8—42no—
115C8—9642no—
116C22—42no—
117C22—44no—
118C22—4821no—
119C22—4822no—
120C22C22⋊C4×D24111yescharacteristic
121C4—21no—
122C4—9642no—
123C4—4822no—
124C4—2412no—
125C4#2144066112yes—
126C4#2144066312yes—
127C2—82no—
128C2—9641no—
129C2#100×D24111yescharacteristic
130C2#2950771012yes—
subgroupG/H
centerC22C22⋊C4×D241
commutatorC2×C4×C241C22×C4
FrattiniC42C22×D241
Fitting#331×C241C2
socleC22×C241C2×C22⋊C4
prime radical#29508265C2
cosocleC42×C241C23
hypercenter#331D241
hypocenterC241#1543
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #29507769C2semidirect
3. #29507465C2semidirect
4. #29507461C2semidirect
5. #331×C241C2semidirect
65. C241#1543semidirect
71. #331D241semidirect

Maximal subgroups

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

subgroupindex
#295082652
#295077692
#295074652
#295074612
#331×C2412
#1543241