Finite Group Databasebeta

← #44506562

Subgroups — #44506562

Order 30848.

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

normal subgroups only

This group has 314 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#29508352C211yesmaximal, characteristic
2#29508089C211yesmaximal, characteristic, complemented
3#29508008C212yesmaximal, complemented
4#29507444C212yesmaximal, complemented
5#331×C241C211yesmaximal, characteristic, complemented
6C2×D4×D241—22no—
7C2×#16838758—22no—
8#21440642C2211yescharacteristic, complemented
9#21440613—22no—
10#21440610—22no—
11C4×D964C2212yes—
12#21440574—22no—
13#21440564—22no—
14C4×#14515349C2211yescharacteristic, complemented
15#127×C241C2211yescharacteristic
16C4⋊C8×C241C2212yescomplemented
17C23×D241—22no—
18C2×Dic482—21no—
19C2×D964D412yes—
20C2×C22⋊D241—24no—
21D4×D241—44no—
22D4×D241—44no—
23C2×C4×D241—22no—
24#16838758—44no—
25C2×#14515349—21no—
26C4⋊Dic241—22no—
27C4⋊Dic241D412yes—
28C22⋊Dic241—22no—
29#16838747—22no—
30C2×D4×C241—22no—
31C2×D4×C241D412yes—
32C2×C8×C241—22no—
33C42×C241C2311yescharacteristic
34C22×D241—22no—
35C22×D241—48no—
36C22×D241—82no—
37Dic482—42no—
38D964—22no—
39D964SD1614yescomplemented
40C22⋊D241—48no—
41C2×Dic241—22no—
42C2×Dic241—41no—
43C4×D241—42no—
44C4×D241—42no—
45#14515349—22no—
46C23×C241—22no—
47D4×C241—42no—
48D4×C241—42no—
49D4×C241—42no—
50C2×C4×C241C2×D412yes—
51C2×C4×C241C2×D411yescharacteristic
52C8×C241—42no—
53C22×C241—44no—
54C22×C241—42no—
55C22×C241#12011yescharacteristic
56C2×D241—24no—
57C2×D241—42no—
58C2×D241—42no—
59C2×D241—88no—
60C4×C241—21no—
61C4×C241C2×SD1612yes—
62C4×C241AGL(1,ℤ/8)12yes—
63Dic241—42no—
64Dic241—81no—
65C2×C241—82no—
66C2×C241#45012yes—
67C2×C241#45311yescharacteristic
68D241—44no—
69C241#162911yescharacteristic, complemented, Sylow
70#1629—2411nomaximal, Sylow
71D42—2411no—
72#492—2411no—
73#476—2412no—
74#331D24111yescharacteristic, complemented
75D4⋊C8—2412no—
76C22×D4—4822no—
77C2×SD16—4822no—
78C4⋊Q8—2411no—
79#127C2×D24111yescharacteristic
80#121—4822no—
81#120—4822no—
82C4×D4—2412no—
83#106—4822no—
84C4⋊C8C2×D24112yescomplemented
85#102—4822no—
86C4×C8—2411no—
87C24—4822no—
88C2×Q8—4821no—
89C2×D4—22no—
90C2×D4—9644no—
91C2×D4—9644no—
92C2×D4—4824no—
93C2×D4—2412no—
94C2×D4D96412yes—
95C22×C4—4822no—
96SD16—9644no—
97C2×C8—22no—
98C2×C8—4821no—
99C4⋊C4—4822no—
100C4⋊C4—2412no—
101C22⋊C4—4822no—
102C22⋊C4—4822no—
103C42C22×D24111yescharacteristic
104C23—22no—
105C23—19282no—
106C23—9648no—
107C23—4822no—
108Q8—9642no—
109D4—42no—
110D4—42no—
111D4—42no—
112D4—9648no—
113D4—4822no—
114D4—2414no—
115C2×C4—9641no—
116C2×C4—9642no—
117C2×C4—9642no—
118C2×C4—4822no—
119C2×C4D4×D24112yes—
120C2×C4C2×D96411yescharacteristic
121C8—42no—
122C8—4822no—
123C22—44no—
124C22—42no—
125C22—19288no—
126C22—9642no—
127C22—9642no—
128C22—4824no—
129C22#2144061211yescharacteristic
130C4—21no—
131C4—19281no—
132C4—9642no—
133C4SD16×D24112yes—
134C4#2144066612yes—
135C2—82no—
136C2—9644no—
137C2#2950786912yes—
138C2#2950788711yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#331×C241C2
socleC22×C241#120
prime radical#29508352C2
hypercenter#331D241
hypocenterC241#1629
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #29508089C2semidirect
3. #29508008C2semidirect
4. #29507444C2semidirect
5. #331×C241C2semidirect
8. #21440642C22semidirect
14. C4×#14515349C22semidirect
16. C4⋊C8×C241C22semidirect
39. D964SD16semidirect
69. C241#1629semidirect
74. #331D241semidirect
84. C4⋊C8C2×D241semidirect

Maximal subgroups

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

subgroupindex
#295083522
#295080892
#295080082
#295074442
#331×C2412
#1629241