Finite Group Databasebeta

← #44506769

Subgroups — #44506769

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#29508087C211yesmaximal, characteristic, complemented
3#29508077C212yesmaximal, complemented
4#29507456C212yesmaximal, complemented
5#330×C241C211yesmaximal, characteristic, complemented
6#21440642C2211yescharacteristic
7#21440630C2212yes—
8#21440627—22no—
9#21440620—22no—
10#21440617—22no—
11#21440567—22no—
12#21440565—22no—
13#21440564—22no—
14#21440553C2211yescharacteristic
15#125×C241C2211yescharacteristic
16#97×C241C2212yes—
17C2×Dic482—21no—
18C2×Dic482D412yes—
19C2×D964—22no—
20C2×D964D412yes—
21C2×C4×D241—22no—
22C2×#14515349—21no—
23C4⋊Dic241—22no—
24#16838749—22no—
25#16838747—22no—
26#16838747—22no—
27#16838747—22no—
28C2×C8×C241—22no—
29C4⋊C4×C241—22no—
30C4⋊C4×C241D412yes—
31C42×C241C2311yescharacteristic
32C22×D241—22no—
33Dic482—42no—
34Dic482—42no—
35D964—42no—
36D964—82no—
37C2×Dic241—22no—
38C2×Dic241—41no—
39C4×D241—82no—
40#14515349—41no—
41C2×C4×C241—22no—
42C2×C4×C241C2×D412yes—
43C2×C4×C241C2×D411yescharacteristic
44C8×C241—42no—
45C22×C241#12011yescharacteristic
46C2×D241—42no—
47C2×D241—42no—
48C2×D241—42no—
49C4×C241—21no—
50C4×C241—22no—
51C4×C241—42no—
52Dic241—42no—
53Dic241—81no—
54C2×C241#45411yescharacteristic
55C2×C241#45512yes—
56D241—82no—
57C241#166211yescharacteristic, complemented, Sylow
58#1662—2411nomaximal, Sylow
59#562—2411no—
60#491—2411no—
61#489—2412no—
62#330D24111yescharacteristic, complemented
63#329—2412no—
64C4⋊Q8—2411no—
65#125C2×D24111yescharacteristic
66#124—2412no—
67#123—4822no—
68C22⋊Q8—4822no—
69#121—4822no—
70#103—4822no—
71#103—4822no—
72#102—4822no—
73#97—2411no—
74#97C2×D24112yes—
75C2×Q8—4821no—
76C2×Q8—2412no—
77C2×D4—4822no—
78C2×D4—2412no—
79C22×C4—4822no—
80C2×C8—22no—
81C2×C8—4821no—
82C4⋊C4—22no—
83C4⋊C4—4822no—
84C4⋊C4—4822no—
85C4⋊C4D96412yes—
86C22⋊C4—4822no—
87C22⋊C4—4822no—
88C22⋊C4—4822no—
89C42C22×D24111yescharacteristic
90C23—4822no—
91Q8—9642no—
92Q8—9642no—
93D4—19282no—
94D4—9642no—
95C2×C4—22no—
96C2×C4—19282no—
97C2×C4—9641no—
98C2×C4—4822no—
99C2×C4D4×D24112yes—
100C2×C4C2×D96411yescharacteristic
101C8—42no—
102C8—9641no—
103C22—9642no—
104C22—9642no—
105C22—9642no—
106C22#2144061211yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—19281no—
111C4—9642no—
112C2—19282no—
113C2#2950789211yescharacteristic
114C2#2950789612yes—
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#330×C241C2
socleC22×C241#120
prime radical#29508465C2
hypercenter#330D241
hypocenterC241#1662
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #29508087C2semidirect
3. #29508077C2semidirect
4. #29507456C2semidirect
5. #330×C241C2semidirect
57. C241#1662semidirect
62. #330D241semidirect

Maximal subgroups

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

subgroupindex
#295084652
#295080872
#295080772
#295074562
#330×C2412
#1662241