Finite Group Databasebeta

← #11771353

Subgroups — #11771353

Order 1152.

274 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 36 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#10592933C211yesmaximal, characteristic
2C22⋊#3708C212yesmaximal, complemented
3C2×C32×#41C411yescharacteristic
4C2×#3748C411yescharacteristic
5C22×C3⋊(C3⋊C8)C2211yescharacteristic
6C2×#3708—22no—
7#63657—22no—
8#5234—62no—
9C32×#41—41no—
10C32×#41—41no—
11C2×C32×Q8C811yescharacteristic
12C2×C32×D4—21no—
13C2×C32×D4C811yescharacteristic
14C22×C32×C4—21no—
15C22×C32×C4C2×C411yescharacteristic
16#3748—41no—
17C2×C3⋊(C3⋊C8)—21no—
18C2×C3⋊(C3⋊C8)—41no—
19C2×C3⋊(C3⋊C8)D412yes—
20#3708—42no—
21#1315—91nomaximal, Sylow
22C2×C3×#41—22no—
23C2×#208—62no—
24C22×C3⋊C8—62no—
25#830—68no—
26C23×C32—21no—
27C23×C32M1611yescharacteristic
28C32×Q8—41no—
29C32×D4—41no—
30C32×D4—42no—
31C2×C32×C4—21no—
32C2×C32×C4—21no—
33C2×C32×C4—21no—
34C2×C32×C4—41no—
35C2×C32×C4—41no—
36C2×C32×C4C22⋊C411yescharacteristic
37C2×C32×C4C2×C811yescharacteristic
38C3⋊(C3⋊C8)—22no—
39C3⋊(C3⋊C8)—41no—
40#408—91no—
41C22⋊C16—92no—
42C3×#41—44no—
43C3×#41—44no—
44C2×C3×Q8—22no—
45C2×C3×D4—24no—
46C2×C3×D4—22no—
47C22×C3×C4—24no—
48C22×C3×C4—22no—
49#208—124no—
50C2×C3⋊C8—64no—
51C2×C3⋊C8—64no—
52C2×C3⋊C8—124no—
53C22×C32—21no—
54C22×C32—22no—
55C22×C32—41no—
56C22×C32—42no—
57C22×C32C22⋊C811yescharacteristic
58C32×C4—21no—
59C32×C4—41no—
60C32×C4#9911yescharacteristic
61C32×C4#10011yescharacteristic
62C2×#41#15711yescharacteristic
63C2×M16—91no—
64C22×C8—91no—
65C2×C16—182no—
66C22⋊C8—182no—
67C23×C3—24no—
68C23×C3—22no—
69C3×Q8—44no—
70C3×D4—44no—
71C3×D4—48no—
72C2×C3×C4—24no—
73C2×C3×C4—24no—
74C2×C3×C4—24no—
75C2×C3×C4—22no—
76C2×C3×C4—22no—
77C2×C3×C4—44no—
78C2×C3×C4—44no—
79C3⋊C8—124no—
80C3⋊C8—124no—
81C2×C32—41no—
82C2×C32—81no—
83C2×C32#32311yescharacteristic
84C2×C32#35012yes—
85#41—41no—
86#41—41no—
87C2×Q8#62211yescharacteristic
88C2×D4—21no—
89C2×D4#62211yescharacteristic
90C22×C4—21no—
91C22×C4C2×#15711yescharacteristic
92M16—361no—
93C2×C8—92no—
94C2×C8—181no—
95C2×C8—361no—
96C16—362no—
97C22×C3—24no—
98C22×C3—22no—
99C22×C3—44no—
100C22×C3—44no—
101C22×C3—48no—
102C3×C4—24no—
103C3×C4—22no—
104C3×C4—22no—
105C3×C4—44no—
106C32#131511yescharacteristic, complemented, Sylow
107C23—21no—
108C23#379211yescharacteristic
109Q8—41no—
110D4—41no—
111D4—42no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4C2×#62211yescharacteristic
118C2×C4C22⋊#15711yescharacteristic
119C8—182no—
120C8—361no—
121C2×C3—24no—
122C2×C3—22no—
123C2×C3—44no—
124C2×C3—84no—
125C22—22no—
126C22—21no—
127C22—42no—
128C22—41no—
129C22C22⋊#62211yescharacteristic
130C4—21no—
131C4—41no—
132C4#6378611yescharacteristic
133C4#6378811yescharacteristic
134C3—22no—
135C2—41no—
136C2—81no—
137C2#1059022112yes—
138C2#1059022211yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC2×C32×C4C2×C8
FrattiniC22×C4C2×#157
Fitting, prime radicalC2×C32×#41C4
socleC22×C32C22⋊C8
cosocleC22×C3⋊(C3⋊C8)C22
hypercenterC2×#41#157
hypocenterC32#1315
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C22⋊#3708C2semidirect
106. C32#1315semidirect

Maximal subgroups

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

subgroupindex
#105929332
C22⋊#37082
#13159