Finite Group Databasebeta

← #44506773

Subgroups — #44506773

Order 30848.

172 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 49 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#29508127C212yesmaximal
2#29508087C211yesmaximal, characteristic
3#29507459C212yesmaximal
4#29507459C211yesmaximal, characteristic
5#564×C241C211yesmaximal, characteristic
6#21440642C2211yescharacteristic
7#21440575—22no—
8#21440573—22no—
9#21440565—22no—
10#21440553C2212yes—
11#21440553C2211yescharacteristic
12#125×C241—22no—
13#125×C241—22no—
14#125×C241—22no—
15#125×C241C2212yes—
16#125×C241C2211yescharacteristic
17C2×Dic482—21no—
18C2×#14515349—22no—
19C2×#14515349—21no—
20C4⋊Dic241—22no—
21C4⋊C4×C241—22no—
22C4⋊C4×C241—22no—
23C4⋊C4×C241—22no—
24C4⋊C4×C241—22no—
25C4⋊C4×C241—22no—
26C4⋊C4×C241—22no—
27C4⋊C4×C241D412yes—
28C4⋊C4×C241D412yes—
29C4⋊C4×C241D412yes—
30C42×C241—22no—
31C42×C241C2311yescharacteristic
32Dic482—42no—
33C2×Dic241—41no—
34#14515349—24no—
35#14515349—41no—
36C2×C4×C241—22no—
37C2×C4×C241—22no—
38C2×C4×C241—22no—
39C2×C4×C241C2×D412yes—
40C2×C4×C241C2×D411yescharacteristic
41C22×C241#12011yescharacteristic
42C4×C241—21no—
43C4×C241—22no—
44C4×C241—42no—
45C4×C241—42no—
46C4×C241—42no—
47Dic241—81no—
48C2×C241#45411yescharacteristic
49C2×C241#45612yes—
50C241#166311yescharacteristic, complemented, Sylow
51#1663—2411nomaximal, Sylow
52#564D24111yescharacteristic
53#501—2412no—
54#491—2411no—
55#330—2412no—
56#330—2411no—
57C4⋊Q8—2411no—
58#125—22no—
59#125—22no—
60#125—22no—
61#125C2×D24111yescharacteristic
62#125C2×D24112yes—
63#107—4822no—
64#106—4822no—
65#103—4822no—
66#97—2411no—
67#97—2412no—
68C2×Q8—4821no—
69C2×C8—4821no—
70C2×C8—4822no—
71C4⋊C4—22no—
72C4⋊C4—22no—
73C4⋊C4—22no—
74C4⋊C4—22no—
75C4⋊C4—22no—
76C4⋊C4—22no—
77C4⋊C4—4822no—
78C4⋊C4C22⋊D24112yes—
79C4⋊C4C22⋊D24112yes—
80C4⋊C4C22⋊D24112yes—
81C42—22no—
82C42C22×D24111yescharacteristic
83Q8—9642no—
84C2×C4—22no—
85C2×C4—22no—
86C2×C4—22no—
87C2×C4—9641no—
88C2×C4C2×C22⋊D24112yes—
89C2×C4C2×C22⋊D24111yescharacteristic
90C8—9641no—
91C8—4824no—
92C22#2144061111yescharacteristic
93C4—21no—
94C4—22no—
95C4—42no—
96C4—42no—
97C4—42no—
98C4—19281no—
99C2#2950789011yescharacteristic
100C2#2950790012yes—
subgroupG/H
centerC22#21440611
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#564×C241C2
socle, prime radicalC22×C241#120
hypercenter#564D241
hypocenterC241#1663
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #564

Complements

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

NH ≅ G/Ntype
50. C241#1663semidirect

Maximal subgroups

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

subgroupindex
#295081272
#295080872
#295074592
#564×C2412
#1663241