Finite Group Databasebeta

← #44506743

Subgroups — #44506743

Order 30848.

206 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 49 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#29508107C211yesmaximal, characteristic
2#29508083C212yesmaximal, complemented
3#29507459C212yesmaximal, complemented
4#29507457C211yesmaximal, characteristic, complemented
5#563×C241C211yesmaximal, characteristic, complemented
6C2×#16838757—21no—
7C2×#16838755—21no—
8#21440639C2211yescharacteristic
9#21440562—22no—
10#21440562—22no—
11#21440553C2211yescharacteristic
12#21440553C2212yes—
13C4⋊Q8×C241—21no—
14#126×C241—22no—
15#125×C241C2212yes—
16#124×C241C2211yescharacteristic
17#123×C241—21no—
18C22⋊Q8×C241—22no—
19C2×D964—22no—
20C2×D964—21no—
21#16838757—42no—
22#16838755—42no—
23C2×#14515349—21no—
24C2×#14515349—22no—
25C2×Q8×C241—21no—
26C2×Q8×C241D411yescharacteristic
27C2×D4×C241D411yescharacteristic
28C22×C4×C241—21no—
29C4⋊C4×C241—22no—
30C4⋊C4×C241—22no—
31C4⋊C4×C241—22no—
32C4⋊C4×C241D412yes—
33C4⋊C4×C241D412yes—
34C22⋊C4×C241—22no—
35C22⋊C4×C241—21no—
36C22⋊C4×C241—22no—
37C42×C241—21no—
38C42×C241C2311yescharacteristic
39C22×D241—41no—
40D964—41no—
41D964—41no—
42D964—44no—
43#14515349—22no—
44#14515349—42no—
45C23×C241—21no—
46Q8×C241—41no—
47Q8×C241—81no—
48D4×C241—41no—
49C2×C4×C241—22no—
50C2×C4×C241—21no—
51C2×C4×C241—22no—
52C2×C4×C241—81no—
53C2×C4×C241C2×D412yes—
54C2×C4×C241C2×D411yescharacteristic
55C22×C241—41no—
56C22×C241—42no—
57C22×C241#12011yescharacteristic
58C2×D241—81no—
59C2×D241—82no—
60C4×C241—21no—
61C4×C241—22no—
62C4×C241—42no—
63C4×C241—41no—
64C4×C241—42no—
65C2×C241—81no—
66C2×C241#45311yescharacteristic
67C2×C241#45412yes—
68D241—161no—
69C241#165711yescharacteristic, complemented, Sylow
70#1657—2411nomaximal, Sylow
71#563D24111yescharacteristic, complemented
72#496—2411no—
73#490—2412no—
74#330—2412no—
75#329—2411no—
76C2×SD16—4821no—
77C2×D8—4821no—
78C4⋊Q8—21no—
79#127—2411no—
80#126—22no—
81#125C2×D24112yes—
82#124C2×D24111yescharacteristic
83#123—21no—
84C22⋊Q8—22no—
85#102—4822no—
86#102—4822no—
87#97—2412no—
88#97—2411no—
89C2×Q8—21no—
90C2×Q8C22⋊D24111yescharacteristic
91C2×D4—4822no—
92C2×D4—4821no—
93C2×D4C22⋊D24111yescharacteristic
94C22×C4—21no—
95SD16—9642no—
96D8—9642no—
97C2×C8—4822no—
98C2×C8—4821no—
99C4⋊C4—22no—
100C4⋊C4—22no—
101C4⋊C4—22no—
102C4⋊C4C22⋊D24112yes—
103C4⋊C4C22⋊D24112yes—
104C22⋊C4—22no—
105C22⋊C4—21no—
106C22⋊C4—22no—
107C42—21no—
108C42C22×D24111yescharacteristic
109C23—21no—
110C23—9641no—
111Q8—41no—
112Q8—81no—
113D4—41no—
114D4—9641no—
115D4—9641no—
116D4—9644no—
117C2×C4—22no—
118C2×C4—21no—
119C2×C4—22no—
120C2×C4—81no—
121C2×C4C2×C22⋊D24112yes—
122C2×C4C2×C22⋊D24111yescharacteristic
123C8—9642no—
124C8—4822no—
125C22—41no—
126C22—42no—
127C22—19281no—
128C22—19282no—
129C22#2144061111yescharacteristic
130C4—21no—
131C4—22no—
132C4—42no—
133C4—41no—
134C4—42no—
135C2—81no—
136C2—38561no—
137C2#2950788511yescharacteristic
138C2#2950789012yes—
subgroupG/H
centerC22#21440611
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#563×C241C2
socleC22×C241#120
prime radical#29508107C2
hypercenter#563D241
hypocenterC241#1657
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
2. #29508083C2semidirect
3. #29507459C2semidirect
4. #29507457C2semidirect
5. #563×C241C2semidirect
69. C241#1657semidirect
71. #563D241semidirect

Maximal subgroups

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

subgroupindex
#295081072
#295080832
#295074592
#295074572
#563×C2412
#1657241