Finite Group Databasebeta

← #44507092

Subgroups — #44507092

Order 30848.

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

normal subgroups only

This group has 164 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#29508120C211yesmaximal, characteristic
2#29508113C211yesmaximal, characteristic
3#29508069C211yesmaximal, characteristic
4#29508068C211yesmaximal, characteristic
5#29508067C211yesmaximal, characteristic
6#29507438C211yesmaximal, characteristic
7#487×C241C211yesmaximal, characteristic
8#21440642C2211yescharacteristic
9#21440642C2211yescharacteristic
10#21440575—22no—
11#21440573—22no—
12#21440567—22no—
13#21440566—22no—
14#21440565—22no—
15C4×#14515349C2211yescharacteristic
16C4×#14515349C2211yescharacteristic
17C4⋊Q8×C241C2211yescharacteristic
18C4⋊Q8×C241C2211yescharacteristic
19#103×C241—22no—
20C4×C8×C241C2211yescharacteristic
21C2×Dic482—21no—
22C2×Dic482—21no—
23C2×#14515349D412yes—
24C2×#14515349D412yes—
25C4⋊Dic241—21no—
26C4⋊Dic241—21no—
27C4⋊Dic241—21no—
28C4⋊Dic241—21no—
29C2×Q8×C241—21no—
30C2×Q8×C241—21no—
31C2×C8×C241D412yes—
32C4⋊C4×C241—21no—
33C4⋊C4×C241—21no—
34C4⋊C4×C241—21no—
35C4⋊C4×C241—21no—
36C42×C241C2311yescharacteristic
37Dic482—42no—
38Dic482—42no—
39C2×Dic241—41no—
40C2×Dic241—41no—
41#14515349—22no—
42#14515349—22no—
43Q8×C241—42no—
44Q8×C241—42no—
45C2×C4×C241—41no—
46C2×C4×C241—41no—
47C2×C4×C241C2×D411yescharacteristic
48C2×C4×C241C2×D411yescharacteristic
49C2×C4×C241C2×D411yescharacteristic
50C8×C241—22no—
51C22×C241#12711yescharacteristic
52C4×C241—81no—
53C4×C241—81no—
54C4×C241#13512yes—
55C4×C241#13712yes—
56C4×C241#13712yes—
57Dic241—81no—
58Dic241—81no—
59C2×C241#49511yescharacteristic
60C2×C241#49711yescharacteristic
61C2×C241#49711yescharacteristic
62C241#171811yescharacteristic, complemented, Sylow
63#1718—2411nomaximal, Sylow
64#500—2411no—
65#498—2411no—
66#487—2411no—
67#487—2411no—
68#487—2411no—
69#487D24111yescharacteristic
70#322—2411no—
71C4⋊Q8—2411no—
72C4⋊Q8—2411no—
73C4⋊Q8C2×D24111yescharacteristic
74C4⋊Q8C2×D24111yescharacteristic
75#107—4822no—
76#106—4822no—
77#103—22no—
78#103—4822no—
79#103—4822no—
80#103—4822no—
81C4×C8—2411no—
82C4×C8—2411no—
83C4×C8C2×D24111yescharacteristic
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—4821no—
87C2×Q8—4821no—
88C2×C8—2412no—
89C2×C8—2412no—
90C2×C8C22⋊D24112yes—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—4821no—
96C4⋊C4—4821no—
97C4⋊C4—4821no—
98C4⋊C4—4821no—
99C42C22×D24111yescharacteristic
100Q8—42no—
101Q8—42no—
102Q8—9642no—
103Q8—9642no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—9641no—
107C2×C4—9641no—
108C2×C4D4×D24111yescharacteristic
109C2×C4D4×D24111yescharacteristic
110C2×C4C2×C22⋊D24111yescharacteristic
111C8—22no—
112C8—4822no—
113C8—4822no—
114C22#2144063811yescharacteristic
115C4—81no—
116C4—81no—
117C4—19281no—
118C4—19281no—
119C4#2144066212yes—
120C4#2144067112yes—
121C4#2144067412yes—
122C2#2950809911yescharacteristic
123C2#2950810811yescharacteristic
124C2#2950811011yescharacteristic
subgroupG/H
centerC22#21440638
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#487×C241C2
socle, prime radicalC22×C241#127
hypercenter#487D241
hypocenterC241#1718
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
62. C241#1718semidirect

Maximal subgroups

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

subgroupindex
#295081202
#295081132
#295080692
#295080682
#295080672
#295074382
#487×C2412
#1718241