Finite Group Databasebeta

← #11785475

Subgroups — #11785475

Order 1152.

390 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C22×#3788C211yesmaximal, characteristic
2#10593802C212yesmaximal
3C2×#63748C212yesmaximal, complemented
4#10590097C212yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3792C2214yes—
7C22×#622C2211yescharacteristic
8C22×#622C2211yescharacteristic
9C2×#3788—24no—
10C2×#3788C414yes—
11#63778—24no—
12#63748—24no—
13C23×C3⋊D3Q811yescharacteristic
14C22×C32×C4Q811yescharacteristic
15C22×C3⋊Dic3C2311yescharacteristic
16C2×C4×C3⋊D3—22no—
17C2×C4×C3⋊D3—22no—
18C2×C4×C3⋊D3C2×C412yes—
19C2×C4×C3⋊D3D412yes—
20#3792—24no—
21#3792—24no—
22C2×#622—22no—
23C2×#622—24no—
24C2×#622C2×C412yes—
25C2×#622C2×C412yes—
26C2×#622D414yes—
27#3788—28no—
28#1811—91nomaximal, Sylow
29C22×C4×D3—121no—
30C23×C32C2×Q811yescharacteristic
31C22×C3⋊D3—22no—
32C22×C3⋊D3—42no—
33C22×C3⋊D3C4⋊C412yes—
34C2×C32×C4—22no—
35C2×C32×C4C4⋊C412yes—
36C2×C3⋊Dic3C22×C411yescharacteristic
37C2×C3⋊Dic3C2×D412yes—
38C2×C3⋊Dic3C2×D411yescharacteristic
39C2×C3⋊Dic3#4112yes—
40C4×C3⋊D3—22no—
41C4×C3⋊D3—22no—
42C4×C3⋊D3—24no—
43#622—22no—
44#622—44no—
45#622C22⋊C414yes—
46C22×M16—91no—
47C2×#108—92no—
48#407—92no—
49#341—92no—
50C23×D3—121no—
51C22×C3×C4—41no—
52C22×Dic3—121no—
53C2×C4×D3—122no—
54C2×C4×D3—122no—
55C2×C4×D3—124no—
56C2×C4×D3—124no—
57C22×C32—22no—
58C22×C32C2×C4⋊C411yescharacteristic
59C22×C32C22⋊Q812yes—
60C2×C3⋊D3—22no—
61C2×C3⋊D3—24no—
62C2×C3⋊D3—44no—
63C32×C4—22no—
64C3⋊Dic3C2×C22⋊C411yescharacteristic
65C3⋊Dic3#11711yescharacteristic
66C3⋊Dic3#12112yes—
67C23×C4—91no—
68C2×M16—94no—
69C2×M16—94no—
70C2×M16—184no—
71C22×C8—91no—
72C22×C8—91no—
73#108—184no—
74C22⋊C8—184no—
75C23×C3—41no—
76C22×D3—122no—
77C22×D3—124no—
78C22×D3—128no—
79C2×C3×C4—44no—
80C2×C3×C4—42no—
81C2×Dic3—121no—
82C2×Dic3—121no—
83C2×Dic3—122no—
84C2×Dic3—122no—
85C4×D3—124no—
86C4×D3—124no—
87C4×D3—128no—
88C2×C32—22no—
89C2×C32#38011yescharacteristic
90C2×C32#43012yes—
91C3⋊D3—42no—
92C24—91no—
93C22×C4—91no—
94C22×C4—92no—
95C22×C4—92no—
96C22×C4—182no—
97C22×C4—182no—
98C22×C4PSU(3,𝔽2)11yescharacteristic
99M16—188no—
100M16—184no—
101M16—184no—
102C2×C8—94no—
103C2×C8—92no—
104C2×C8—92no—
105C2×C8—182no—
106C2×C8—184no—
107C22×C3—44no—
108C22×C3—41no—
109C22×C3—42no—
110C2×D3—124no—
111C2×D3—128no—
112C2×D3—1216no—
113C3×C4—44no—
114Dic3—121no—
115Dic3—121no—
116Dic3—122no—
117C32#181111yescharacteristic, complemented, Sylow
118C23—92no—
119C23—182no—
120C23—362no—
121C23C2×PSU(3,𝔽2)11yescharacteristic
122C2×C4—22no—
123C2×C4—91no—
124C2×C4—91no—
125C2×C4—92no—
126C2×C4—92no—
127C2×C4—182no—
128C2×C4—184no—
129C2×C4—182no—
130C2×C4#377712yes—
131C8—94no—
132C8—182no—
133C8—364no—
134C2×C3—44no—
135C2×C3—42no—
136C2×C3—41no—
137D3—128no—
138C22—22no—
139C22—184no—
140C22—182no—
141C22—364no—
142C22C2×#377711yescharacteristic
143C22C22⋊PSU(3,𝔽2)12yes—
144C4—22no—
145C4—91no—
146C4—92no—
147C4—91no—
148C3—41no—
149C2—22no—
150C2—362no—
151C2#1059354712yes—
152C2#1059356811yescharacteristic
subgroupG/H
centerC22C2×#3777
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×PSU(3,𝔽2)
FittingC22×C32×C4Q8
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3Q8
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4PSU(3,𝔽2)
hypocenterC32#1811
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C2×#63748C2semidirect
4. #10590097C2semidirect
117. C32#1811semidirect

Maximal subgroups

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

subgroupindex
C22×#37882
#105938022
C2×#637482
#105900972
#18119