Finite Group Databasebeta

← #44506744

Subgroups — #44506744

Order 30848.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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#29508467C211yesmaximal, characteristic, complemented
2#29508107C211yesmaximal, characteristic
3#29508082C212yesmaximal, complemented
4#29507458C212yesmaximal, complemented
5#329×C241C211yesmaximal, characteristic, complemented
6C2×#16838757—21no—
7C2×#16838755—21no—
8#21440640—21no—
9#21440639C2211yescharacteristic
10#21440635—22no—
11#21440634C2212yes—
12#21440623—21no—
13#21440619—22no—
14#21440564—22no—
15#21440564—22no—
16#21440553C2211yescharacteristic
17#124×C241C2211yescharacteristic
18#97×C241C2212yes—
19C2×Dic482—21no—
20C2×D964—22no—
21C2×D964—21no—
22C22×Dic241—21no—
23#16838757—42no—
24#16838755—42no—
25C2×#14515349—21no—
26C4⋊Dic241D412yes—
27C4⋊Dic241D412yes—
28#16838749—22no—
29#16838749—22no—
30#16838749—22no—
31C22⋊Dic241—22no—
32C22⋊Dic241—21no—
33C4×Dic241—21no—
34C2×Q8×C241D411yescharacteristic
35C2×D4×C241D411yescharacteristic
36C2×C8×C241—22no—
37C22⋊C4×C241—22no—
38C42×C241C2311yescharacteristic
39C22×D241—41no—
40Dic482—81no—
41D964—41no—
42D964—41no—
43D964—44no—
44C2×Dic241—22no—
45C2×Dic241—22no—
46C2×Dic241—81no—
47#14515349—22no—
48C23×C241—21no—
49Q8×C241—41no—
50D4×C241—41no—
51C2×C4×C241—21no—
52C2×C4×C241C2×D412yes—
53C2×C4×C241C2×D411yescharacteristic
54C8×C241—42no—
55C22×C241—41no—
56C22×C241—42no—
57C22×C241#12011yescharacteristic
58C2×D241—81no—
59C2×D241—82no—
60C4×C241—21no—
61C4×C241—22no—
62C4×C241—41no—
63Dic241—42no—
64Dic241—42no—
65C2×C241—81no—
66C2×C241#45311yescharacteristic
67C2×C241#45412yes—
68D241—161no—
69C241#165711yescharacteristic, complemented, Sylow
70#1657—2411nomaximal, Sylow
71#563—2411no—
72#496—2411no—
73#490—2412no—
74#330—2412no—
75#329D24111yescharacteristic, complemented
76C2×SD16—4821no—
77C2×D8—4821no—
78C4⋊Q8—4821no—
79#127—2411no—
80#126—4822no—
81#125—2412no—
82#124C2×D24111yescharacteristic
83#123—4821no—
84C22⋊Q8—4822no—
85#102—4822no—
86#102—4822no—
87#97—2411no—
88#97C2×D24112yes—
89C2×Q8—4821no—
90C2×Q8D96411yescharacteristic
91C2×D4—4822no—
92C2×D4—4821no—
93C2×D4D96411yescharacteristic
94C22×C4—4821no—
95SD16—9642no—
96D8—9642no—
97C2×C8—22no—
98C2×C8—4821no—
99C4⋊C4—4822no—
100C4⋊C4—4822no—
101C4⋊C4—4822no—
102C4⋊C4—2412no—
103C4⋊C4—2412no—
104C22⋊C4—22no—
105C22⋊C4—4822no—
106C22⋊C4—4821no—
107C42—4821no—
108C42C22×D24111yescharacteristic
109C23—21no—
110C23—9641no—
111Q8—41no—
112Q8—19281no—
113D4—41no—
114D4—9641no—
115D4—9641no—
116D4—9644no—
117C2×C4—21no—
118C2×C4—19281no—
119C2×C4—4822no—
120C2×C4—4822no—
121C2×C4D4×D24112yes—
122C2×C4C2×D96411yescharacteristic
123C8—42no—
124C8—4822no—
125C22—41no—
126C22—42no—
127C22—19281no—
128C22—19282no—
129C22#2144061211yescharacteristic
130C4—21no—
131C4—22no—
132C4—41no—
133C4—9642no—
134C4—9642no—
135C2—81no—
136C2—38561no—
137C2#2950788711yescharacteristic
138C2#2950789112yes—
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#329×C241C2
socleC22×C241#120
prime radical#29508107C2
hypercenter#329D241
hypocenterC241#1657
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
1. #29508467C2semidirect
3. #29508082C2semidirect
4. #29507458C2semidirect
5. #329×C241C2semidirect
69. C241#1657semidirect
75. #329D241semidirect

Maximal subgroups

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

subgroupindex
#295084672
#295081072
#295080822
#295074582
#329×C2412
#1657241