Finite Group Databasebeta

← #13092583

Subgroups — #13092583

Order 1472.

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

normal subgroups only

This group has 168 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#10625160C211yesmaximal, characteristic, complemented
2C23×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
3#10625111C211yesmaximal, characteristic, complemented
4#10625103C211yesmaximal, characteristic, complemented
5#10625019C211yesmaximal, characteristic, complemented
6#10625007C211yesmaximal, characteristic, complemented
7#10625005C211yesmaximal, characteristic, complemented
8#41×C23C2211yescharacteristic
9C2×D4×C23C2211yescharacteristic, complemented
10C2×C22⋊D23—22no—
11#67292—21no—
12D4×D23—22no—
13D4×D23—21no—
14#67288—21no—
15#67288C2211yescharacteristic
16C2×D92—21no—
17C2×D92C2211yescharacteristic
18SD16×C23—21no—
19D8×C23—21no—
20M16×C23C2211yescharacteristic, complemented
21#67273—21no—
22#67272—21no—
23C4×Dic23C2211yescharacteristic, complemented
24#67267C2211yescharacteristic, complemented
25C23×C23—21no—
26C22×D23—22no—
27C22×D23D412yes—
28Q8×C23D411yescharacteristic, complemented
29D4×C23—21no—
30D4×C23—21no—
31D4×C23—21no—
32D4×C23D411yescharacteristic, complemented
33C2×C4×C23—21no—
34C2×C4×C23C2311yescharacteristic
35C22⋊D23—22no—
36C22⋊D23—21no—
37C22⋊D23—44no—
38C2×Dic23—21no—
39D92—22no—
40D92—21no—
41D92—21no—
42D92D411yescharacteristic, complemented
43C4×D23—22no—
44C4×D23—21no—
45Dic46D411yescharacteristic, complemented
46C8×C23—21no—
47C23⋊C8—21no—
48C22×C23—21no—
49C22×C23—42no—
50C22×C23—41no—
51C22×C23C2×D411yescharacteristic
52C2×D23—22no—
53C2×D23—21no—
54C2×D23—42no—
55C2×D23—82no—
56C4×C23—21no—
57C4×C23C2×D411yescharacteristic
58C4×C23C2×D411yescharacteristic
59Dic23—22no—
60Dic23—21no—
61#453—231nomaximal, Sylow
62C2×C23—21no—
63C2×C23—41no—
64C2×C23—81no—
65C2×C23#12011yescharacteristic
66D23—42no—
67D23—41no—
68H(5,𝔽2)—231no—
69AGL(1,ℤ/8)—231no—
70AGL(1,ℤ/8)D2311yescharacteristic, complemented
71#127—231no—
72#104—231no—
73#104—231no—
74#100—231no—
75C23#45311yescharacteristic, complemented, Sylow
76#41—231no—
77#41—461no—
78#41—461no—
79#41C2×D2311yescharacteristic
80C2×D4—231no—
81C2×D4—461no—
82C2×D4—462no—
83C2×D4—461no—
84C2×D4—462no—
85C2×D4C2×D2311yescharacteristic, complemented
86SD16—21no—
87SD16—461no—
88D8—21no—
89D8—461no—
90M16—231no—
91M16C2×D2311yescharacteristic, complemented
92C42—231no—
93C23—21no—
94C23—232no—
95C23—462no—
96Q8—231no—
97Q8C22⋊D2311yescharacteristic, complemented
98D4—21no—
99D4—21no—
100D4—21no—
101D4—231no—
102D4—462no—
103D4—462no—
104D4—461no—
105D4—461no—
106D4—461no—
107D4—924no—
108D4C22⋊D2311yescharacteristic, complemented
109C2×C4—21no—
110C2×C4—462no—
111C2×C4—461no—
112C2×C4—461no—
113C2×C4C22×D2311yescharacteristic
114C8—21no—
115C8—461no—
116C22—21no—
117C22—42no—
118C22—41no—
119C22—461no—
120C22—462no—
121C22—922no—
122C22—1842no—
123C22D4×D2311yescharacteristic
124C4—21no—
125C4—462no—
126C4—461no—
127C4D4×D2311yescharacteristic
128C4C2×C22⋊D2311yescharacteristic
129C2—21no—
130C2—41no—
131C2—81no—
132C2—922no—
133C2—921no—
134C2#1062510811yescharacteristic
subgroupG/H
centerC2#10625108
commutator, cosocleC2×C4×C23C23
FrattiniC2×C4C22×D23
FittingC23×AGL(1,ℤ/8)C2
socleC2×C23#120
hypercenterAGL(1,ℤ/8)D23
hypocenterC23#453
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #10625160C2semidirect
2. C23×AGL(1,ℤ/8)C2semidirect
3. #10625111C2semidirect
4. #10625103C2semidirect
5. #10625019C2semidirect
6. #10625007C2semidirect
7. #10625005C2semidirect
9. C2×D4×C23C22semidirect
20. M16×C23C22semidirect
23. C4×Dic23C22semidirect
24. #67267C22semidirect
28. Q8×C23D4semidirect
32. D4×C23D4semidirect
42. D92D4semidirect
45. Dic46D4semidirect
70. AGL(1,ℤ/8)D23semidirect
75. C23#453semidirect
85. C2×D4C2×D23semidirect
91. M16C2×D23semidirect
97. Q8C22⋊D23semidirect
108. D4C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
#106251602
C23×AGL(1,ℤ/8)2
#106251112
#106251032
#106250192
#106250072
#106250052
#45323