Finite Group Databasebeta

← #29507901

Subgroups — #29507901

Order 15424.

142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 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#21440689C211yesmaximal, characteristic
2#21440675C211yesmaximal, characteristic, complemented
3#21440672C211yesmaximal, characteristic, complemented
4#21440642C211yesmaximal, characteristic, complemented
5#21440570C211yesmaximal, characteristic, complemented
6#21440560C211yesmaximal, characteristic, complemented
7#104×C241C211yesmaximal, characteristic, complemented
8#16838770—21no—
9#16838770C2211yescharacteristic
10#16838769—22no—
11#16838769—21no—
12C2×Dic482—21no—
13C2×Dic482C2211yescharacteristic
14C2×Dic482C2211yescharacteristic
15Q8×D241—21no—
16Dic964—21no—
17#16838760—21no—
18#16838759—21no—
19#16838758—21no—
20#16838754C2211yescharacteristic
21C4⋊Dic241—22no—
22#41×C241C2211yescharacteristic
23M16×C241C2211yescharacteristic
24C42×C241C2211yescharacteristic
25Dic482—22no—
26Dic482—21no—
27Dic482—21no—
28Dic482—21no—
29Dic482—21no—
30Dic482D411yescharacteristic
31D964D411yescharacteristic
32C22⋊D241—22no—
33C22⋊D241—21no—
34C2×Dic241—22no—
35C2×Dic241—21no—
36C2×Dic241D412yes—
37C4×D241—22no—
38C4×D241—21no—
39#14515349—21no—
40Q8×C241D411yescharacteristic
41D4×C241—21no—
42D4×C241D411yescharacteristic
43C2×C4×C241—21no—
44C2×C4×C241—21no—
45C2×C4×C241C2311yescharacteristic
46C8×C241—21no—
47C22×C241—21no—
48C22×C241C2×D411yescharacteristic
49C2×D241—21no—
50C4×C241—22no—
51C4×C241—21no—
52C4×C241C2×D411yescharacteristic
53C4×C241C2×D411yescharacteristic
54Dic241—21no—
55Dic241—22no—
56Dic241—41no—
57C2×C241—21no—
58C2×C241—41no—
59C2×C241#12011yescharacteristic
60D241—41no—
61C241#45611yescharacteristic, complemented, Sylow
62#456—2411nomaximal, Sylow
632−1+4—2411no—
64#137—2411no—
65#137—2411no—
66C4⋊Q8—2411no—
67#104—2411no—
68#104D24111yescharacteristic, complemented
69#101—2411no—
70#41—4821no—
71#41—4821no—
72#41—4822no—
73#41—2411no—
74#41C2×D24111yescharacteristic
75C2×Q8—4821no—
76C2×Q8—4821no—
77C2×Q8—2411no—
78C2×Q8—2411no—
79Q16—4821no—
80Q16—4821no—
81SD16—4821no—
82SD16—4821no—
83M16—2411no—
84M16C2×D24111yescharacteristic
85C4⋊C4—4822no—
86C42C2×D24111yescharacteristic
87Q8—4822no—
88Q8—4821no—
89Q8—4821no—
90Q8—4821no—
91Q8—4821no—
92Q8—2411no—
93Q8D96411yescharacteristic
94D4—21no—
95D4—4822no—
96D4—4821no—
97D4—2411no—
98D4D96411yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—4822no—
102C2×C4—4821no—
103C2×C4—4822no—
104C2×C4—4821no—
105C2×C4—2412no—
106C2×C4C22×D24111yescharacteristic
107C8—21no—
108C8—4821no—
109C22—21no—
110C22—4821no—
111C22D4×D24111yescharacteristic
112C4—22no—
113C4—21no—
114C4—9641no—
115C4—4821no—
116C4—4822no—
117C4D4×D24111yescharacteristic
118C4C2×D96411yescharacteristic
119C2—21no—
120C2—41no—
121C2—9641no—
122C2#2144061211yescharacteristic
subgroupG/H
centerC2#21440612
commutator, cosocleC2×C4×C241C23
FrattiniC2×C4C22×D241
Fitting#104×C241C2
socleC2×C241#120
prime radical#21440689C2
hypercenter#104D241
hypocenterC241#456
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #21440675C2semidirect
3. #21440672C2semidirect
4. #21440642C2semidirect
5. #21440570C2semidirect
6. #21440560C2semidirect
7. #104×C241C2semidirect
61. C241#456semidirect
68. #104D241semidirect

Maximal subgroups

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

subgroupindex
#214406892
#214406752
#214406722
#214406422
#214405702
#214405602
#104×C2412
#456241