Finite Group Databasebeta

← #44506746

Subgroups — #44506746

Order 30848.

182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C241⋊#564C211yesmaximal, characteristic, complemented
2#29508081C212yesmaximal
3#29507459C211yesmaximal, characteristic, complemented
4#29507458C212yesmaximal, complemented
5#490×C241C211yesmaximal, characteristic
6#21440634C2212yes—
7#21440633—22no—
8#21440632—22no—
9#21440632—22no—
10#21440563—22no—
11#21440563—22no—
12#21440553C2212yes—
13#127×C241C2211yescharacteristic
14#125×C241C2211yescharacteristic
15#102×C241—22no—
16#97×C241C2211yescharacteristic
17C2×#14515349—22no—
18C4⋊Dic241—22no—
19C4⋊Dic241D412yes—
20C4⋊Dic241D412yes—
21#16838749—22no—
22#16838749—22no—
23#16838749—22no—
24#16838749—22no—
25C4×Dic241—22no—
26C2×D4×C241—22no—
27C2×D4×C241—21no—
28C2×C8×C241—21no—
29C4⋊C4×C241—22no—
30C4⋊C4×C241D412yes—
31C42×C241C2311yescharacteristic
32C2×Dic241—22no—
33C2×Dic241—22no—
34#14515349—42no—
35C23×C241—41no—
36D4×C241—42no—
37D4×C241—44no—
38C2×C4×C241—22no—
39C2×C4×C241C2×D412yes—
40C2×C4×C241C2×D411yescharacteristic
41C8×C241—41no—
42C22×C241—82no—
43C22×C241—81no—
44C22×C241#12011yescharacteristic
45C4×C241—21no—
46C4×C241—22no—
47C4×C241—42no—
48Dic241—42no—
49Dic241—42no—
50C2×C241—161no—
51C2×C241#45412yes—
52C2×C241#45411yescharacteristic
53C241#165811yescharacteristic, complemented, Sylow
54#1658—2411nomaximal, Sylow
55#564—2411no—
56#490—2412no—
57#490D24111yescharacteristic
58#330—2411no—
59#330—2412no—
60#127C2×D24111yescharacteristic
61#125—4822no—
62#125—4822no—
63#125—4822no—
64#125—2412no—
65#125C2×D24111yescharacteristic
66#102—22no—
67#102—4822no—
68#102—4822no—
69#97—2412no—
70#97C2×D24111yescharacteristic
71C2×D4—22no—
72C2×D4—21no—
73C2×C8—21no—
74C2×C8—4822no—
75C4⋊C4—22no—
76C4⋊C4—4822no—
77C4⋊C4—4822no—
78C4⋊C4—4822no—
79C4⋊C4—4822no—
80C4⋊C4—4822no—
81C4⋊C4—2412no—
82C4⋊C4—2412no—
83C4⋊C4C22⋊D24112yes—
84C42—4822no—
85C42C22×D24111yescharacteristic
86C23—41no—
87D4—44no—
88D4—42no—
89C2×C4—22no—
90C2×C4—4822no—
91C2×C4—4822no—
92C2×C4D4×D24112yes—
93C2×C4C2×C22⋊D24111yescharacteristic
94C8—41no—
95C8—9642no—
96C22—82no—
97C22—81no—
98C22#2144061011yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—9642no—
103C4—9642no—
104C2—161no—
105C2#2950788812yes—
106C2#2950788911yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#490×C241C2
socleC22×C241#120
prime radical#127×C241C22
hypercenter#490D241
hypocenterC241#1658
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. C241⋊#564C2semidirect
3. #29507459C2semidirect
4. #29507458C2semidirect
53. C241#1658semidirect

Maximal subgroups

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

subgroupindex
C241⋊#5642
#295080812
#295074592
#295074582
#490×C2412
#1658241