Finite Group Databasebeta

← #27135433

Subgroups — #27135433

Order 12352.

146 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 39 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#20259946C211yesmaximal, characteristic, complemented
2#20259927C211yesmaximal, characteristic, complemented
3#20259924C211yesmaximal, characteristic, complemented
4#20259887C211yesmaximal, characteristic, complemented
5#20259827C211yesmaximal, characteristic, complemented
6#20259817C211yesmaximal, characteristic, complemented
7#104×C193C211yesmaximal, characteristic, complemented
8#15690555—21no—
9#15690555C2211yescharacteristic
10#15690554—22no—
11#15690554—21no—
12C2×Dic386—21no—
13C2×Dic386C2211yescharacteristic
14Q8×D193—21no—
15C2×D772C2211yescharacteristic
16#15690544—21no—
17#15690542—21no—
18D1544—21no—
19#15690540—21no—
20#15690539C2211yescharacteristic
21#15690532—22no—
22#41×C193C2211yescharacteristic
23M16×C193C2211yescharacteristic
24C42×C193C2211yescharacteristic
25C22×D193—21no—
26Dic386—22no—
27Dic386—21no—
28Dic386—21no—
29Dic386D411yescharacteristic
30D772—21no—
31D772—21no—
32D772D411yescharacteristic
33C22⋊D193—22no—
34C22⋊D193—21no—
35C2×Dic193—22no—
36C2×Dic193D412yes—
37C4×D193—22no—
38C4×D193—21no—
39#13095393—21no—
40Q8×C193D411yescharacteristic
41D4×C193—21no—
42D4×C193D411yescharacteristic
43C2×C4×C193—21no—
44C2×C4×C193—21no—
45C2×C4×C193C2311yescharacteristic
46C8×C193—21no—
47C22×C193—21no—
48C22×C193C2×D411yescharacteristic
49C2×D193—21no—
50C2×D193—42no—
51C2×D193—41no—
52C4×C193—21no—
53C4×C193—41no—
54C4×C193C2×D411yescharacteristic
55C4×C193C2×D411yescharacteristic
56Dic193—21no—
57Dic193—22no—
58C2×C193—21no—
59C2×C193—41no—
60C2×C193#12011yescharacteristic
61D193—41no—
62D193—81no—
63C193#45411yescharacteristic, complemented, Sylow
64#454—1931nomaximal, Sylow
652−1+4—1931no—
66AGL(1,ℤ/8)—1931no—
67AGL(1,ℤ/8)—1931no—
68#124—1931no—
69#104—1931no—
70#104D19311yescharacteristic, complemented
71#101—1931no—
72#41—3861no—
73#41—3861no—
74#41—3862no—
75#41—1931no—
76#41C2×D19311yescharacteristic
77C2×Q8—3861no—
78C2×Q8—3861no—
79C2×Q8—1931no—
80C2×D4—1931no—
81SD16—3861no—
82SD16—3861no—
83D8—3861no—
84D8—3861no—
85M16—1931no—
86M16C2×D19311yescharacteristic
87C22⋊C4—3862no—
88C42C2×D19311yescharacteristic
89C23—3861no—
90Q8—3862no—
91Q8—3861no—
92Q8—3861no—
93Q8—1931no—
94Q8D77211yescharacteristic
95D4—21no—
96D4—3862no—
97D4—3861no—
98D4—3861no—
99D4—3861no—
100D4—1931no—
101D4D77211yescharacteristic
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—3862no—
105C2×C4—3862no—
106C2×C4—3861no—
107C2×C4—1932no—
108C2×C4C22×D19311yescharacteristic
109C8—21no—
110C8—3861no—
111C22—21no—
112C22—7722no—
113C22—7721no—
114C22—3861no—
115C22D4×D19311yescharacteristic
116C4—21no—
117C4—41no—
118C4—3861no—
119C4—3862no—
120C4D4×D19311yescharacteristic
121C4C2×D77211yescharacteristic
122C2—21no—
123C2—41no—
124C2—7721no—
125C2—15441no—
126C2#2025986911yescharacteristic
subgroupG/H
centerC2#20259869
commutator, cosocleC2×C4×C193C23
FrattiniC2×C4C22×D193
Fitting#104×C193C2
socleC2×C193#120
hypercenter#104D193
hypocenterC193#454
LCSG ▷ C2×C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
1. #20259946C2semidirect
2. #20259927C2semidirect
3. #20259924C2semidirect
4. #20259887C2semidirect
5. #20259827C2semidirect
6. #20259817C2semidirect
7. #104×C193C2semidirect
63. C193#454semidirect
70. #104D193semidirect

Maximal subgroups

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

subgroupindex
#202599462
#202599272
#202599242
#202598872
#202598272
#202598172
#104×C1932
#454193