Finite Group Databasebeta

← #44506452

Subgroups — #44506452

Order 30848.

210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 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#29508348C211yesmaximal, characteristic
2#29508047C212yesmaximal
3#29507453C212yesmaximal
4#29507443C211yesmaximal, characteristic
5#398×C241C211yesmaximal, characteristic
6#21440641—22no—
7#21440633—22no—
8#21440621—21no—
9#21440621C2212yes—
10#21440601—21no—
11#21440573—22no—
12#21440565—22no—
13C22⋊#14515349C2212yes—
14C2×C4⋊C4×C241—21no—
15C2×C4⋊C4×C241C2211yescharacteristic
16C2×C4⋊C4×C241C2211yescharacteristic
17#95×C241—21no—
18#95×C241C2211yescharacteristic
19C2×Dic482—21no—
20C2×Dic482D412yes—
21C2×#14515349—22no—
22C4⋊Dic241—21no—
23C4⋊Dic241—21no—
24C4⋊Dic241—21no—
25C4⋊Dic241D412yes—
26#16838749—22no—
27#16838749—22no—
28C22⋊Dic241—22no—
29C4×Dic241—22no—
30C22×C4×C241—21no—
31C22×C4×C241—21no—
32C22×C4×C241D411yescharacteristic
33C22×C4×C241D411yescharacteristic
34C22×C4×C241C2311yescharacteristic
35C4⋊C4×C241—22no—
36C4⋊C4×C241—22no—
37C4⋊C4×C241—42no—
38Dic482—42no—
39Dic482—81no—
40C2×Dic241—22no—
41C2×Dic241—22no—
42#14515349—42no—
43C23×C241C2×D411yescharacteristic
44C2×C4×C241—21no—
45C2×C4×C241—21no—
46C2×C4×C241—22no—
47C2×C4×C241—21no—
48C2×C4×C241—41no—
49C2×C4×C241—41no—
50C2×C4×C241—41no—
51C2×C4×C241—41no—
52C2×C4×C241—41no—
53C2×C4×C241—41no—
54C2×C4×C241—41no—
55C2×C4×C241SD1612yes—
56C2×C4×C241C2×D412yes—
57C22×C241—21no—
58C22×C241—21no—
59C22×C241#12011yescharacteristic
60C22×C241C2×SD1611yescharacteristic
61C22×C241#13711yescharacteristic
62C4×C241—22no—
63C4×C241—22no—
64C4×C241—42no—
65C4×C241—41no—
66C4×C241—81no—
67Dic241—42no—
68Dic241—42no—
69C2×C241—21no—
70C2×C241—21no—
71C2×C241#44811yescharacteristic
72C2×C241#45611yescharacteristic
73C2×C241#45811yescharacteristic
74C241#161111yescharacteristic, complemented, Sylow
75#1611—2411nomaximal, Sylow
76#544—2411no—
77#483—2412no—
78#398D24111yescharacteristic
79#328—2412no—
80#324—2411no—
81C4⋊Q8—4822no—
82#125—4822no—
83C22⋊Q8—4821no—
84C22⋊Q8—2412no—
85#117—4821no—
86C2×C4⋊C4—21no—
87C2×C4⋊C4C2×D24111yescharacteristic
88C2×C4⋊C4C2×D24111yescharacteristic
89#106—4822no—
90#103—4822no—
91C22⋊C8—2412no—
92#95—21no—
93#95C2×D24111yescharacteristic
94C2×Q8—4821no—
95C2×Q8—2412no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4C22⋊D24111yescharacteristic
99C22×C4C22⋊D24111yescharacteristic
100C22×C4C22×D24111yescharacteristic
101C2×C8—4822no—
102C4⋊C4—22no—
103C4⋊C4—22no—
104C4⋊C4—42no—
105C4⋊C4—4822no—
106C4⋊C4—4821no—
107C4⋊C4—4821no—
108C4⋊C4—4821no—
109C4⋊C4—4822no—
110C4⋊C4—2412no—
111C22⋊C4—4822no—
112C42—4822no—
113C23C2×C22⋊D24111yescharacteristic
114Q8—19281no—
115Q8—9642no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—21no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—4822no—
128C2×C4—4822no—
129C2×C4#1683875812yes—
130C2×C4D4×D24112yes—
131C8—9642no—
132C22—21no—
133C22—21no—
134C22#2144061011yescharacteristic
135C22C2×#1683875811yescharacteristic
136C22#2144067211yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—41no—
141C4—81no—
142C4—9642no—
143C4—9642no—
144C2—21no—
145C2—21no—
146C2#2950785511yescharacteristic
147C2#2950789911yescharacteristic
148C2#2950790611yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#398×C241C2
socleC22×C241#120
prime radicalC23×C241C2×D4
hypercenter#398D241
hypocenterC241#1611
LCSG ▷ C22×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
74. C241#1611semidirect

Maximal subgroups

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

subgroupindex
#295083482
#295080472
#295074532
#295074432
#398×C2412
#1611241