Finite Group Databasebeta

← #44506453

Subgroups — #44506453

Order 30848.

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

normal subgroups only

This group has 210 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#29508045C212yesmaximal
2#29507647C211yesmaximal, characteristic
3#29507454C212yesmaximal
4#29507443C211yesmaximal, characteristic
5#544×C241C211yesmaximal, characteristic
6C2×C4⋊Dic241C2211yescharacteristic
7C2×#16838749—21no—
8#21440573—22no—
9#21440566—22no—
10C22⋊#14515349C2212yes—
11#21440549—21no—
12#21440549C2211yescharacteristic
13C4⋊Q8×C241—22no—
14#125×C241—22no—
15C22⋊Q8×C241—21no—
16C22⋊Q8×C241C2212yes—
17#117×C241—21no—
18C2×C4⋊C4×C241C2211yescharacteristic
19C22×Dic241—21no—
20C22×Dic241—21no—
21C2×#14515349—22no—
22C4⋊Dic241—22no—
23#16838749—42no—
24C2×Q8×C241—21no—
25C2×Q8×C241D412yes—
26C22×C4×C241D411yescharacteristic
27C22×C4×C241D411yescharacteristic
28C22×C4×C241C2311yescharacteristic
29C4⋊C4×C241—21no—
30C4⋊C4×C241—21no—
31C4⋊C4×C241—21no—
32C4⋊C4×C241—22no—
33C4⋊C4×C241—22no—
34C4⋊C4×C241—22no—
35C4⋊C4×C241D412yes—
36C22⋊C4×C241—22no—
37C42×C241—22no—
38C2×Dic241—22no—
39C2×Dic241—41no—
40C2×Dic241—41no—
41C2×Dic241—41no—
42C2×Dic241—41no—
43C2×Dic241—41no—
44#14515349—42no—
45C23×C241C2×D411yescharacteristic
46Q8×C241—42no—
47Q8×C241—81no—
48C2×C4×C241—21no—
49C2×C4×C241—21no—
50C2×C4×C241—22no—
51C2×C4×C241—22no—
52C2×C4×C241—21no—
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—42no—
67Dic241—42no—
68Dic241—81no—
69C2×C241—21no—
70C2×C241—21no—
71C2×C241#44811yescharacteristic
72C2×C241#45611yescharacteristic
73C2×C241#45811yescharacteristic
74C241#161111yescharacteristic, complemented, Sylow
75#1611—2411nomaximal, Sylow
76#544D24111yescharacteristic
77#483—2412no—
78#398—2411no—
79#328—2412no—
80#324—2411no—
81C4⋊Q8—22no—
82#125—22no—
83C22⋊Q8—21no—
84C22⋊Q8C2×D24112yes—
85#117—21no—
86C2×C4⋊C4—4821no—
87C2×C4⋊C4—2411no—
88C2×C4⋊C4C2×D24111yescharacteristic
89#106—4822no—
90#103—4822no—
91C22⋊C8—2412no—
92#95—4821no—
93#95—2411no—
94C2×Q8—21no—
95C2×Q8C22⋊D24112yes—
96C22×C4—4821no—
97C22×C4—4821no—
98C22×C4C22⋊D24111yescharacteristic
99C22×C4C22⋊D24111yescharacteristic
100C22×C4C22×D24111yescharacteristic
101C2×C8—4822no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—22no—
106C4⋊C4—22no—
107C4⋊C4—22no—
108C4⋊C4—9642no—
109C4⋊C4—4822no—
110C4⋊C4C22⋊D24112yes—
111C22⋊C4—22no—
112C42—22no—
113C23C2×C22⋊D24111yescharacteristic
114Q8—42no—
115Q8—81no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—21no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—9641no—
124C2×C4—9641no—
125C2×C4—9641no—
126C2×C4—9641no—
127C2×C4—9641no—
128C2×C4—4822no—
129C2×C4#1683875712yes—
130C2×C4C2×C22⋊D24112yes—
131C8—9642no—
132C22—21no—
133C22—21no—
134C22#2144061111yescharacteristic
135C22C2×#1683875711yescharacteristic
136C22#2144067311yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—41no—
141C4—42no—
142C4—19281no—
143C4—9642no—
144C2—21no—
145C2—21no—
146C2#2950785611yescharacteristic
147C2#2950790011yescharacteristic
148C2#2950790711yescharacteristic
subgroupG/H
centerC22#21440611
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#544×C241C2
socleC22×C241#120
prime radicalC23×C241C2×D4
hypercenter#544D241
hypocenterC241#1611
LCSG ▷ C22×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

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
#295080452
#295076472
#295074542
#295074432
#544×C2412
#1611241