Finite Group Databasebeta

← #13092601

Subgroups — #13092601

Order 1472.

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

normal subgroups only

This group has 142 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#10625161C211yesmaximal, characteristic
2#10625122C211yesmaximal, characteristic, complemented
3#10625080C211yesmaximal, characteristic, complemented
4#10625040C211yesmaximal, characteristic, complemented
5C23×#104C211yesmaximal, characteristic, complemented
6#10625006C211yesmaximal, characteristic, complemented
7#10624987C211yesmaximal, characteristic, complemented
8#41×C23C2211yescharacteristic
9Q8×D23—21no—
10#67290—21no—
11#67290—22no—
12#67288—21no—
13#67288C2211yescharacteristic
14C2×Dic46—21no—
15C2×Dic46C2211yescharacteristic
16C2×Dic46C2211yescharacteristic
17M16×C23C2211yescharacteristic
18C42×C23C2211yescharacteristic
19#67275—21no—
20#67273—21no—
21C4⋊Dic23—22no—
22#67267C2211yescharacteristic
23Dic92—21no—
24#67263—21no—
25Q8×C23D411yescharacteristic
26D4×C23—21no—
27D4×C23D411yescharacteristic
28C2×C4×C23—21no—
29C2×C4×C23—21no—
30C2×C4×C23C2311yescharacteristic
31C22⋊D23—22no—
32C22⋊D23—21no—
33C2×Dic23—22no—
34C2×Dic23—21no—
35C2×Dic23D412yes—
36D92D411yescharacteristic
37C4×D23—22no—
38C4×D23—21no—
39Dic46—22no—
40Dic46—21no—
41Dic46—21no—
42Dic46—21no—
43Dic46—21no—
44Dic46D411yescharacteristic
45C8×C23—21no—
46C23⋊C8—21no—
47C22×C23—21no—
48C22×C23C2×D411yescharacteristic
49C2×D23—21no—
50C4×C23—22no—
51C4×C23—21no—
52C4×C23C2×D411yescharacteristic
53C4×C23C2×D411yescharacteristic
54Dic23—22no—
55Dic23—21no—
56Dic23—41no—
57#456—231nomaximal, Sylow
58C2×C23—21no—
59C2×C23—41no—
60C2×C23#12011yescharacteristic
61D23—41no—
622−1+4—231no—
63#137—231no—
64#137—231no—
65C4⋊Q8—231no—
66#104—231no—
67#104D2311yescharacteristic, complemented
68#101—231no—
69C23#45611yescharacteristic, complemented, Sylow
70#41—231no—
71#41—461no—
72#41—462no—
73#41—461no—
74#41C2×D2311yescharacteristic
75C2×Q8—231no—
76C2×Q8—231no—
77C2×Q8—461no—
78C2×Q8—461no—
79Q16—461no—
80Q16—461no—
81SD16—461no—
82SD16—461no—
83M16—231no—
84M16C2×D2311yescharacteristic
85C4⋊C4—462no—
86C42C2×D2311yescharacteristic
87Q8—231no—
88Q8—462no—
89Q8—461no—
90Q8—461no—
91Q8—461no—
92Q8—461no—
93Q8D9211yescharacteristic
94D4—21no—
95D4—231no—
96D4—462no—
97D4—461no—
98D4D9211yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—232no—
102C2×C4—462no—
103C2×C4—462no—
104C2×C4—461no—
105C2×C4—461no—
106C2×C4C22×D2311yescharacteristic
107C8—21no—
108C8—461no—
109C22—21no—
110C22—461no—
111C22D4×D2311yescharacteristic
112C4—22no—
113C4—21no—
114C4—462no—
115C4—461no—
116C4—921no—
117C4C2×D9211yescharacteristic
118C4D4×D2311yescharacteristic
119C2—21no—
120C2—41no—
121C2—921no—
122C2#1062505311yescharacteristic
subgroupG/H
centerC2#10625053
commutator, cosocleC2×C4×C23C23
FrattiniC2×C4C22×D23
FittingC23×#104C2
socleC2×C23#120
prime radical#10625161C2
hypercenter#104D23
hypocenterC23#456
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #10625122C2semidirect
3. #10625080C2semidirect
4. #10625040C2semidirect
5. C23×#104C2semidirect
6. #10625006C2semidirect
7. #10624987C2semidirect
67. #104D23semidirect
69. C23#456semidirect

Maximal subgroups

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

subgroupindex
#106251612
#106251222
#106250802
#106250402
C23×#1042
#106250062
#106249872
#45623