Finite Group Databasebeta

← #44506768

Subgroups — #44506768

Order 30848.

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

normal subgroups only

This group has 196 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#29508087C211yesmaximal, characteristic, complemented
2#29508076C212yesmaximal, complemented
3#29507459C211yesmaximal, characteristic, complemented
4#29507457C212yesmaximal, complemented
5#562×C241C211yesmaximal, characteristic
6#21440642C2211yescharacteristic
7#21440566—22no—
8#21440565—22no—
9#21440563—22no—
10#21440553C2211yescharacteristic
11#21440553C2212yes—
12#125×C241C2211yescharacteristic
13#124×C241C2212yes—
14#123×C241—22no—
15C22⋊Q8×C241—22no—
16#121×C241—22no—
17C2×Dic482—21no—
18C2×#14515349—22no—
19C2×#14515349—21no—
20C4⋊Dic241—22no—
21C2×Q8×C241D412yes—
22C2×D4×C241—22no—
23C2×D4×C241D412yes—
24C22×C4×C241—22no—
25C4⋊C4×C241—22no—
26C4⋊C4×C241—22no—
27C4⋊C4×C241D412yes—
28C22⋊C4×C241—22no—
29C22⋊C4×C241—22no—
30C22⋊C4×C241—22no—
31C42×C241C2311yescharacteristic
32Dic482—42no—
33C2×Dic241—41no—
34#14515349—41no—
35#14515349—42no—
36C23×C241—22no—
37Q8×C241—42no—
38D4×C241—42no—
39D4×C241—82no—
40C2×C4×C241—22no—
41C2×C4×C241—22no—
42C2×C4×C241—82no—
43C2×C4×C241C2×D411yescharacteristic
44C2×C4×C241C2×D412yes—
45C22×C241—42no—
46C22×C241—42no—
47C22×C241—42no—
48C22×C241#12011yescharacteristic
49C4×C241—21no—
50C4×C241—22no—
51C4×C241—42no—
52C4×C241—42no—
53Dic241—81no—
54C2×C241—82no—
55C2×C241#45411yescharacteristic
56C2×C241#45512yes—
57C241#166211yescharacteristic, complemented, Sylow
58#1662—2411nomaximal, Sylow
59#562D24111yescharacteristic
60#491—2411no—
61#489—2412no—
62#330—2411no—
63#329—2412no—
64C4⋊Q8—2411no—
65#125C2×D24111yescharacteristic
66#124C2×D24112yes—
67#123—22no—
68C22⋊Q8—22no—
69#121—22no—
70#103—4822no—
71#103—4822no—
72#102—4822no—
73#97—2411no—
74#97—2412no—
75C2×Q8—4821no—
76C2×Q8C22⋊D24112yes—
77C2×D4—22no—
78C2×D4C22⋊D24112yes—
79C22×C4—22no—
80C2×C8—4822no—
81C2×C8—4821no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—4822no—
85C4⋊C4C22⋊D24112yes—
86C22⋊C4—22no—
87C22⋊C4—22no—
88C22⋊C4—22no—
89C42C22×D24111yescharacteristic
90C23—22no—
91Q8—42no—
92Q8—9642no—
93D4—42no—
94D4—82no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—82no—
98C2×C4—9641no—
99C2×C4C2×C22⋊D24111yescharacteristic
100C2×C4C2×C22⋊D24112yes—
101C8—9641no—
102C8—9642no—
103C22—42no—
104C22—42no—
105C22—42no—
106C22#2144061111yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—42no—
111C4—19281no—
112C2—82no—
113C2#2950789011yescharacteristic
114C2#2950789512yes—
subgroupG/H
centerC22#21440611
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting, prime radical#562×C241C2
socleC22×C241#120
hypercenter#562D241
hypocenterC241#1662
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #29508087C2semidirect
2. #29508076C2semidirect
3. #29507459C2semidirect
4. #29507457C2semidirect
57. C241#1662semidirect

Maximal subgroups

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

subgroupindex
#295080872
#295080762
#295074592
#295074572
#562×C2412
#1662241