Finite Group Databasebeta

← #44506766

Subgroups — #44506766

Order 30848.

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

normal subgroups only

This group has 196 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
1#29508465C211yesmaximal, characteristic
2#29508079C212yesmaximal, complemented
3#29507459C211yesmaximal, characteristic, complemented
4#29507456C212yesmaximal, complemented
5#491×C241C211yesmaximal, characteristic, complemented
6#21440630C2212yes—
7#21440627—22no—
8#21440620—22no—
9#21440617—22no—
10#21440565—22no—
11#21440562—22no—
12#21440553C2212yes—
13C4⋊Q8×C241C2211yescharacteristic
14#125×C241C2211yescharacteristic
15#103×C241—22no—
16#97×C241C2211yescharacteristic
17C2×Dic482D412yes—
18C2×D964—22no—
19C2×D964D412yes—
20C2×C4×D241—22no—
21C2×#14515349—22no—
22#16838749—22no—
23#16838747—22no—
24#16838747—22no—
25#16838747—22no—
26C2×Q8×C241—21no—
27C2×C8×C241—21no—
28C4⋊C4×C241—22no—
29C4⋊C4×C241—22no—
30C4⋊C4×C241D412yes—
31C42×C241C2311yescharacteristic
32C22×D241—22no—
33Dic482—42no—
34D964—42no—
35D964—82no—
36C2×Dic241—22no—
37C4×D241—82no—
38#14515349—42no—
39Q8×C241—42no—
40C2×C4×C241—22no—
41C2×C4×C241—41no—
42C2×C4×C241C2×D412yes—
43C2×C4×C241C2×D411yescharacteristic
44C8×C241—41no—
45C22×C241#12011yescharacteristic
46C2×D241—42no—
47C2×D241—42no—
48C2×D241—42no—
49C4×C241—21no—
50C4×C241—22no—
51C4×C241—42no—
52C4×C241—81no—
53Dic241—42no—
54C2×C241#45411yescharacteristic
55C2×C241#45512yes—
56D241—82no—
57C241#166211yescharacteristic, complemented, Sylow
58#1662—2411nomaximal, Sylow
59#562—2411no—
60#491D24111yescharacteristic, complemented
61#489—2412no—
62#330—2411no—
63#329—2412no—
64C4⋊Q8C2×D24111yescharacteristic
65#125C2×D24111yescharacteristic
66#124—2412no—
67#123—4822no—
68C22⋊Q8—4822no—
69#121—4822no—
70#103—22no—
71#103—4822no—
72#102—4822no—
73#97—2412no—
74#97C2×D24111yescharacteristic
75C2×Q8—21no—
76C2×Q8—2412no—
77C2×D4—4822no—
78C2×D4—2412no—
79C22×C4—4822no—
80C2×C8—21no—
81C2×C8—4822no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—4822no—
85C4⋊C4C22⋊D24112yes—
86C22⋊C4—4822no—
87C22⋊C4—4822no—
88C22⋊C4—4822no—
89C42C22×D24111yescharacteristic
90C23—4822no—
91Q8—42no—
92Q8—9642no—
93D4—19282no—
94D4—9642no—
95C2×C4—22no—
96C2×C4—41no—
97C2×C4—19282no—
98C2×C4—4822no—
99C2×C4D4×D24112yes—
100C2×C4C2×C22⋊D24111yescharacteristic
101C8—41no—
102C8—9642no—
103C22—9642no—
104C22—9642no—
105C22—9642no—
106C22#2144061011yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—81no—
111C4—9642no—
112C2—19282no—
113C2#2950788911yescharacteristic
114C2#2950789312yes—
subgroupG/H
centerC22#21440610
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#491×C241C2
socleC22×C241#120
prime radical#29508465C2
hypercenter#491D241
hypocenterC241#1662
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #29508079C2semidirect
3. #29507459C2semidirect
4. #29507456C2semidirect
5. #491×C241C2semidirect
57. C241#1662semidirect
60. #491D241semidirect

Maximal subgroups

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

subgroupindex
#295084652
#295080792
#295074592
#295074562
#491×C2412
#1662241