Finite Group Databasebeta

← #11771109

Subgroups — #11771109

Order 1152.

380 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 48 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#10593800C212yesmaximal
2#10592825C211yesmaximal, characteristic
3C22×C4×C3⋊D3C2211yescharacteristic
4C2×#3787—22no—
5C2×C32×M16C411yescharacteristic
6C2×#3748C411yescharacteristic
7C22⋊#622—22no—
8#63778C414yes—
9#63647—22no—
10#5126—62no—
11C23×C3⋊D3Q811yescharacteristic
12C22×C32×C4C2×C411yescharacteristic
13C22×C3⋊Dic3D411yescharacteristic
14C2×C4×C3⋊D3—41no—
15C2×C4×C3⋊D3—41no—
16C2×C4×C3⋊D3C2×C412yes—
17C2×C4×C3⋊D3D412yes—
18C2×#622—24no—
19#3787—42no—
20#3787—42no—
21C32×M16—41no—
22C2×C32×C8—21no—
23#3748—41no—
24C2×C3⋊(C3⋊C8)—21no—
25#1298—91nomaximal, Sylow
26C22×C4×D3—62no—
27C2×C3×M16—22no—
28C2×#208—62no—
29(C2×D3)⋊C8—68no—
30C23×C32C4⋊C411yescharacteristic
31C22×C3⋊D3—24no—
32C22×C3⋊D3—41no—
33C22×C3⋊D3C4⋊C412yes—
34C2×C32×C4—21no—
35C2×C32×C4—21no—
36C2×C32×C4C4211yescharacteristic
37C2×C32×C4C22⋊C411yescharacteristic
38C2×C3⋊Dic3—41no—
39C2×C3⋊Dic3C22⋊C412yes—
40C4×C3⋊D3—22no—
41C4×C3⋊D3—22no—
42C4×C3⋊D3—42no—
43#622—44no—
44C32×C8—41no—
45C3⋊(C3⋊C8)—41no—
46#407—91no—
47C2×C22⋊C8—92no—
48C23×D3—62no—
49C22×C3×C4—22no—
50C22×Dic3—62no—
51C2×C4×D3—64no—
52C2×C4×D3—64no—
53C2×C4×D3—124no—
54C2×C4×D3—124no—
55C3×M16—44no—
56C2×C3×C8—24no—
57#208—124no—
58C2×C3⋊C8—64no—
59C22×C32—21no—
60C22×C32—22no—
61C22×C32#9511yescharacteristic
62C2×C3⋊D3—22no—
63C2×C3⋊D3—22no—
64C2×C3⋊D3—44no—
65C2×C3⋊D3#10814yes—
66C32×C4—21no—
67C32×C4#9911yescharacteristic
68C32×C4#9911yescharacteristic
69C3⋊Dic3—22no—
70C23×C4—91no—
71C2×M16—91no—
72C2×M16#15711yescharacteristic
73C22×C8—182no—
74C22⋊C8—94no—
75C22⋊C8—182no—
76C22⋊C8—182no—
77C23×C3—22no—
78C22×D3—64no—
79C22×D3—128no—
80C22×D3—124no—
81C2×C3×C4—24no—
82C2×C3×C4—24no—
83C2×C3×C4—22no—
84C2×C3×C4—22no—
85C2×Dic3—64no—
86C2×Dic3—124no—
87C4×D3—124no—
88C4×D3—124no—
89C4×D3—128no—
90C3×C8—44no—
91C3⋊C8—124no—
92C2×C32—41no—
93C2×C32#34112yes—
94C2×C32#34211yescharacteristic
95C3⋊D3—24no—
96C24—91no—
97C22×C4—91no—
98C22×C4—92no—
99C22×C4—92no—
100C22×C4—361no—
101C22×C4—361no—
102C22×C4C2×#15711yescharacteristic
103M16—41no—
104M16—361no—
105C2×C8—21no—
106C2×C8—184no—
107C2×C8—181no—
108C2×C8—362no—
109C2×C8—362no—
110C22×C3—24no—
111C22×C3—22no—
112C22×C3—44no—
113C2×D3—68no—
114C2×D3—124no—
115C2×D3—124no—
116C2×D3—1216no—
117C3×C4—24no—
118C3×C4—22no—
119C3×C4—22no—
120Dic3—124no—
121C32#129811yescharacteristic, complemented, Sylow
122C23—92no—
123C23—184no—
124C23—361no—
125C23C4⋊#15711yescharacteristic
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—92no—
129C2×C4—182no—
130C2×C4—182no—
131C2×C4—362no—
132C2×C4—361no—
133C2×C4C4×#15711yescharacteristic
134C2×C4C22⋊#15711yescharacteristic
135C8—41no—
136C8—364no—
137C8—361no—
138C2×C3—24no—
139C2×C3—22no—
140C2×C3—44no—
141D3—128no—
142C22—22no—
143C22—21no—
144C22—94no—
145C22—182no—
146C22—182no—
147C22—364no—
148C22#6378111yescharacteristic
149C4—21no—
150C4—182no—
151C4#6377411yescharacteristic
152C4#6378611yescharacteristic
153C3—22no—
154C2—41no—
155C2—184no—
156C2#1059019012yes—
157C2#1059020611yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC2×C32×C4C42
FrattiniC22×C4C2×#157
FittingC2×C32×M16C4
socleC22×C32#95
prime radicalC23×C3⋊D3Q8
cosocleC22×C4×C3⋊D3C22
hypercenterC2×M16#157
hypocenterC32#1298
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
121. C32#1298semidirect

Maximal subgroups

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

subgroupindex
#105938002
#105928252
#12989