Finite Group Databasebeta

← #11798025

Subgroups — #11798025

Order 1152.

228 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 74 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
1Q8×C3⋊(C3⋊C8)C211yesmaximal, characteristic
2#10590148C212yesmaximal
3C4⋊#3708C212yesmaximal
4C4⋊#3708C211yesmaximal, characteristic
5C4×#3708C211yesmaximal, characteristic
6C32×C4×Q8C411yescharacteristic
7C2×#3708C2211yescharacteristic
8C2×#3708C2212yes—
9C2×#3708C2211yescharacteristic
10C4⋊(C3⋊(C3⋊C8))C412yes—
11C4⋊(C3⋊(C3⋊C8))C411yescharacteristic
12C4×C3⋊(C3⋊C8)C2211yescharacteristic
13C4×C3⋊(C3⋊C8)C2212yes—
14Q8×C3⋊C8—62no—
15C2×C32×Q8C811yescharacteristic
16C32×C4⋊C4C812yes—
17C32×C4⋊C4C811yescharacteristic
18C32×C42C2×C412yes—
19C32×C42C2×C411yescharacteristic
20C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
21C2×C3⋊(C3⋊C8)C2×C412yes—
22C2×C3⋊(C3⋊C8)C2311yescharacteristic
23#3708—21no—
24#3708—22no—
25#3708Q812yescomplemented
26#2183—91nomaximal, Sylow
27C3×C4×Q8—22no—
28C4⋊(C3⋊C8)—64no—
29C4⋊(C3⋊C8)—62no—
30C4×C3⋊C8—62no—
31C4×C3⋊C8—64no—
32C32×Q8—22no—
33C2×C32×C4C2×C812yes—
34C2×C32×C4C2×C811yescharacteristic
35C2×C32×C4C2×C812yes—
36C2×C32×C4C2×C811yescharacteristic
37C2×C32×C4C22×C411yescharacteristic
38C3⋊(C3⋊C8)—21no—
39C3⋊(C3⋊C8)—22no—
40C3⋊(C3⋊C8)C2×Q811yescharacteristic
41C3⋊(C3⋊C8)#4111yescharacteristic
42C8×Q8—91no—
43C4⋊C16—91no—
44C4⋊C16—92no—
45#346—92no—
46C4×C16—91no—
47C2×C3×Q8—22no—
48C3×C4⋊C4—24no—
49C3×C4⋊C4—22no—
50C3×C42—24no—
51C3×C42—22no—
52C2×C3⋊C8—62no—
53C2×C3⋊C8—62no—
54C2×C3⋊C8—64no—
55C22×C32C22×C811yescharacteristic
56C32×C4—22no—
57C32×C4—22no—
58C32×C4—21no—
59C32×C4M3212yes—
60C32×C4C4×Q811yescharacteristic
61C32×C4#13111yescharacteristic
62C4×Q8#15711yescharacteristic
63C2×C16—91no—
64C2×C16—91no—
65C2×C16—92no—
66C4⋊C8—92no—
67C4⋊C8—91no—
68C4×C8—91no—
69C4×C8—92no—
70C3×Q8—28no—
71C2×C3×C4—22no—
72C2×C3×C4—24no—
73C2×C3×C4—22no—
74C2×C3×C4—24no—
75C2×C3×C4—22no—
76C3⋊C8—62no—
77C3⋊C8—62no—
78C3⋊C8—122no—
79C3⋊C8—124no—
80C2×C32C8×Q811yescharacteristic
81C2×C32C2×M3211yescharacteristic
82C2×C32#50411yescharacteristic
83C2×Q8#62211yescharacteristic
84C2×C8—91no—
85C2×C8—91no—
86C2×C8—92no—
87C4⋊C4#62212yes—
88C4⋊C4#62211yescharacteristic
89C42C2×#15712yes—
90C42C2×#15711yescharacteristic
91C16—92no—
92C16—181no—
93C16—182no—
94C22×C3—22no—
95C3×C4—28no—
96C3×C4—24no—
97C3×C4—22no—
98C3×C4—22no—
99C3×C4—44no—
100C3×C4—42no—
101C32#218311yescharacteristic, complemented, Sylow
102Q8—22no—
103C2×C4C2×#62212yes—
104C2×C4C2×#62211yescharacteristic
105C2×C4C2×#62212yes—
106C2×C4C2×#62211yescharacteristic
107C2×C4C22×#15711yescharacteristic
108C8—91no—
109C8—91no—
110C8—181no—
111C8—182no—
112C2×C3—22no—
113C2×C3—22no—
114C2×C3—22no—
115C22C22×#62211yescharacteristic
116C4—22no—
117C4—21no—
118C4—22no—
119C4#6377312yes—
120C4#6428911yescharacteristic
121C4Q8×#15711yescharacteristic
122C3—22no—
123C2C2×#6377311yescharacteristic
124C2Q8×#62211yescharacteristic
125C2#1059383811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#157
commutator, socle, prime radicalC22×C32C22×C8
FittingC32×C4×Q8C4
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC4×Q8#157
hypocenterC32#2183
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
25. #3708Q8semidirect
101. C32#2183semidirect

Maximal subgroups

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

subgroupindex
Q8×C3⋊(C3⋊C8)2
#105901482
C4⋊#37082
C4×#37082
#21839