Finite Group Databasebeta

← #11796063

Subgroups — #11796063

Order 1152.

302 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C2×#64287C211yesmaximal, characteristic
2#10596481C212yesmaximal, complemented
3#10593274C214yesmaximal, complemented
4C2×#3830C411yescharacteristic
5C2×#3792C2212yes—
6C22×#622C412yes—
7#64287—22no—
8#64287—22no—
9C2×#3788C411yescharacteristic
10C2×#3787C2211yescharacteristic
11#64218C2214yes—
12#64214—22no—
13#64213—22no—
14C2×C32×D4C811yescharacteristic
15C2×#638C812yes—
16C22×C3⋊Dic3C2×C412yes—
17#3830—22no—
18#3830—22no—
19C2×C4×C3⋊D3C2×C411yescharacteristic
20C2×#634C811yescharacteristic
21#3792—24no—
22C2×#622—22no—
23C2×#622—22no—
24C2×#622C2×C412yes—
25C2×#622C2×C411yescharacteristic
26C2×#622C2311yescharacteristic
27#3788—22no—
28#3787D412yes—
29#3787D412yes—
30#3771—24no—
31#2115—91nomaximal, Sylow
32C2×#237—121no—
33C23×C32C2×C812yes—
34C22×C3⋊D3C2×C811yescharacteristic
35C32×D4—22no—
36C2×C32×C4C2×C811yescharacteristic
37#638—24no—
38C2×C3⋊Dic3—22no—
39C2×C3⋊Dic3—22no—
40C2×C3⋊Dic3C2×C812yes—
41C2×C3⋊Dic3C22×C411yescharacteristic
42C4×C3⋊D3C22⋊C412yes—
43C4×C3⋊D3M1612yes—
44#634—22no—
45#622—22no—
46#622C22⋊C411yescharacteristic
47#622C22⋊C411yescharacteristic
48#622C2×D412yes—
49C2×#131—91no—
50C2×M32—92no—
51#349—94no—
52C2×C3×D4—41no—
53C2×#67—122no—
54C22×Dic3—122no—
55#237—124no—
56#237—124no—
57C2×C4×D3—121no—
58C2×Dic6—121no—
59C22×C32—22no—
60C22×C32—42no—
61C22×C32C22×C811yescharacteristic
62C2×C3⋊D3—41no—
63C2×C3⋊D3C22⋊C812yes—
64C32×C4C22⋊C812yes—
65C3⋊Dic3—22no—
66C3⋊Dic3C2×C22⋊C411yescharacteristic
67C3⋊Dic3C2×M1611yescharacteristic
68C2×#41—91no—
69#131—182no—
70#131—182no—
71C2×M16—91no—
72C2×M16—92no—
73C22×C8—91no—
74C22×C8—92no—
75M32—94no—
76M32—182no—
77C2×C16—182no—
78C23×C3—42no—
79C22×D3—121no—
80C3×D4—44no—
81C2×C3×C4—41no—
82#67—128no—
83C2×Dic3—122no—
84C2×Dic3—121no—
85C2×Dic3—124no—
86C2×Dic3—124no—
87C4×D3—122no—
88C4×D3—122no—
89Dic6—124no—
90C2×C32—21no—
91C2×C32—42no—
92C2×C32C2×C22⋊C811yescharacteristic
93C3⋊D3—22no—
94#41—182no—
95#41—182no—
96C2×Q8—91no—
97C2×D4—92no—
98C2×D4AGL(1,𝔽9)11yescharacteristic
99C22×C4—91no—
100C22×C4—92no—
101M16—184no—
102M16—182no—
103C2×C8—92no—
104C2×C8—91no—
105C2×C8—92no—
106C2×C8—91no—
107C2×C8—92no—
108C2×C8—182no—
109C2×C8—182no—
110C16—184no—
111C22×C3—44no—
112C22×C3—41no—
113C22×C3—84no—
114C2×D3—122no—
115C2×D3—242no—
116C3×C4—42no—
117Dic3—121no—
118Dic3—121no—
119Dic3—124no—
120C32#211511yescharacteristic, complemented, Sylow
121C23—91no—
122C23C2×AGL(1,𝔽9)12yes—
123Q8—182no—
124D4—22no—
125D4—184no—
126C2×C4—91no—
127C2×C4—92no—
128C2×C4—92no—
129C2×C4—92no—
130C2×C4—182no—
131C2×C4—182no—
132C2×C4C2×AGL(1,𝔽9)11yescharacteristic
133C8—92no—
134C8—91no—
135C8—91no—
136C8—182no—
137C2×C3—42no—
138C2×C3—41no—
139C2×C3—84no—
140D3—242no—
141C22—22no—
142C22—42no—
143C22—92no—
144C22—361no—
145C22C22×AGL(1,𝔽9)11yescharacteristic
146C4—91no—
147C4—91no—
148C4—182no—
149C4C22⋊AGL(1,𝔽9)12yes—
150C3—41no—
151C2—21no—
152C2—42no—
153C2—182no—
154C2C2×C22⋊AGL(1,𝔽9)11yescharacteristic
subgroupG/H
centerC2C2×C22⋊AGL(1,𝔽9)
commutatorC22×C32C22×C8
FrattiniC22C22×AGL(1,𝔽9)
FittingC2×C32×D4C8
socleC2×C32C2×C22⋊C8
prime radicalC2×#3830C4
cosocleC2×#622C23
hypercenterC2×D4AGL(1,𝔽9)
hypocenterC32#2115
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #10596481C2semidirect
3. #10593274C2semidirect
120. C32#2115semidirect

Maximal subgroups

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

subgroupindex
C2×#642872
#105964812
#105932742
#21159