Finite Group Databasebeta

← #44506590

Subgroups — #44506590

Order 30848.

218 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 57 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#29508096C211yesmaximal, characteristic, complemented
2#29508007C212yesmaximal, complemented
3#29507466C211yesmaximal, characteristic, complemented
4D4⋊#14515349C212yesmaximal, complemented
5#555×C241C211yesmaximal, characteristic
6C2×#16838760—22no—
7#21440642C2211yescharacteristic
8#21440573—22no—
9C4⋊#14515349C2212yes—
10#21440563—22no—
11C4×#14515349C2211yescharacteristic
12C4⋊Q8×C241C2211yescharacteristic
13#124×C241—22no—
14#121×C241—22no—
15C4×D4×C241C2212yes—
16#117×C241—22no—
17C2×Dic482—21no—
18#16838760—44no—
19C2×#14515349—21no—
20C2×#14515349—22no—
21C4⋊Dic241—22no—
22C2×Q8×C241D412yes—
23C2×D4×C241—22no—
24C2×D4×C241D412yes—
25C22×C4×C241—22no—
26C4⋊C4×C241—22no—
27C4⋊C4×C241D412yes—
28C22⋊C4×C241—24no—
29C22⋊C4×C241—22no—
30C42×C241—22no—
31C42×C241C2311yescharacteristic
32Dic482—42no—
33C2×Dic241—41no—
34#14515349—22no—
35#14515349—42no—
36C23×C241—22no—
37Q8×C241—42no—
38D4×C241—22no—
39D4×C241—22no—
40D4×C241—82no—
41C2×C4×C241—22no—
42C2×C4×C241—22no—
43C2×C4×C241—42no—
44C2×C4×C241—42no—
45C2×C4×C241C2×D411yescharacteristic
46C2×C4×C241C2×D412yes—
47C22×C241—42no—
48C22×C241—42no—
49C22×C241—42no—
50C22×C241#12011yescharacteristic
51C4×C241—21no—
52C4×C241—42no—
53C4×C241—42no—
54C4×C241#13512yes—
55C4×C241#13712yes—
56Dic241—81no—
57C2×C241—82no—
58C2×C241#45212yes—
59C2×C241#45311yescharacteristic
60C241#163411yescharacteristic, complemented, Sylow
61#1634—2411nomaximal, Sylow
62#555D24111yescharacteristic
63#494—2411no—
64#476—2412no—
65#333—2411no—
66D4⋊C8—2412no—
67C2×Q16—4822no—
68C4⋊Q8—2411no—
69C4⋊Q8C2×D24111yescharacteristic
70#124—22no—
71#121—22no—
72C4×D4C2×D24112yes—
73#117—22no—
74#106—4822no—
75C4⋊C8—2412no—
76#102—4822no—
77C4×C8—2411no—
78C2×Q8—4821no—
79C2×Q8C22⋊D24112yes—
80C2×D4—22no—
81C2×D4C22⋊D24112yes—
82C22×C4—22no—
83Q16—9644no—
84C2×C8—4822no—
85C2×C8—4821no—
86C4⋊C4—22no—
87C4⋊C4—4822no—
88C4⋊C4C22⋊D24112yes—
89C22⋊C4—24no—
90C22⋊C4—22no—
91C42—22no—
92C42C22×D24111yescharacteristic
93C23—22no—
94Q8—42no—
95Q8—9642no—
96D4—22no—
97D4—22no—
98D4—82no—
99C2×C4—22no—
100C2×C4—22no—
101C2×C4—42no—
102C2×C4—42no—
103C2×C4—9641no—
104C2×C4C2×C22⋊D24111yescharacteristic
105C2×C4C2×C22⋊D24112yes—
106C8—9642no—
107C8—4822no—
108C22—42no—
109C22—42no—
110C22—42no—
111C22#2144061111yescharacteristic
112C4—21no—
113C4—42no—
114C4—42no—
115C4—19281no—
116C4#2144066212yes—
117C4#2144067212yes—
118C2—82no—
119C2#2950787912yes—
120C2#2950788511yescharacteristic
subgroupG/H
centerC22#21440611
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting, prime radical#555×C241C2
socleC22×C241#120
hypercenter#555D241
hypocenterC241#1634
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #29508096C2semidirect
2. #29508007C2semidirect
3. #29507466C2semidirect
4. D4⋊#14515349C2semidirect
60. C241#1634semidirect

Maximal subgroups

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

subgroupindex
#295080962
#295080072
#295074662
D4⋊#145153492
#555×C2412
#1634241