Finite Group Databasebeta

← #11776050

Subgroups — #11776050

Order 1152.

582 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 119 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#10596159C211yesmaximal, characteristic
2#10592404C212yesmaximal
3C32×#330C211yesmaximal, characteristic, complemented
4#10589409C211yesmaximal, characteristic, complemented
5#10589331C212yesmaximal, complemented
6#68369—34nomaximal
7C32×#125C2211yescharacteristic
8#64105—22no—
9#64101C412yes—
10#64097C412yes—
11#64096—22no—
12C42×C3⋊D3C2211yescharacteristic
13#64079C2211yescharacteristic
14C32×#97C2212yes—
15#63647—22no—
16#63641—22no—
17#63630C2212yes—
18#5688—34no—
19#4705—38no—
20C3×#330D314yescomplemented
21#4543—34no—
22#4465—38no—
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3D412yes—
25C2×#634—22no—
26C2×C32×C8—22no—
27C32×C4⋊C4—22no—
28C32×C4⋊C4C2×C412yes—
29C32×C42C2311yescharacteristic
30#3752—22no—
31C4⋊(C3⋊Dic3)C2×C412yes—
32#3750—22no—
33#3750—22no—
34C4×C3⋊Dic3—22no—
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D412yes—
37C2×C3⋊(C3⋊C8)—22no—
38#1537—91noSylow
39C3×#125C2×D314yes—
40#896—68no—
41#892—38no—
42#888—38no—
43#887—68no—
44C42×D3—34no—
45#870—34no—
46C3×#97C2×D318yes—
47(C2×D3)⋊C8—68no—
48Dic3⋊C8—68no—
49#803—38no—
50C22×C3⋊D3C22⋊C411yescharacteristic
51C2×C32×C4—22no—
52C2×C32×C4C22×C411yescharacteristic
53C2×C32×C4C2×D412yes—
54C2×C3⋊Dic3—22no—
55C2×C3⋊Dic3C22⋊C412yes—
56C2×C3⋊Dic3C22⋊C411yescharacteristic
57C4×C3⋊D3—22no—
58C4×C3⋊D3—42no—
59#634—44no—
60C32×C8—42no—
61C3⋊(C3⋊C8)—42no—
62#533—91no—
63#432—92no—
64#330—91no—
65#330—92no—
66#330C3⋊D311yescharacteristic, complemented
67C2×C4×D3—34no—
68C2×C4×D3—38no—
69C2×Dic6—68no—
70C2×C3×C8—28no—
71C3×C4⋊C4—28no—
72C3×C4⋊C4C4×D318yes—
73C3×C42C22×D314yes—
74(C2×D3)⋊C4—68no—
75C4⋊Dic3—38no—
76Dic3⋊C4—68no—
77Dic3⋊C4—68no—
78C4×Dic3—34no—
79C4×Dic3—38no—
80C4×Dic3—68no—
81C2×C3⋊C8—68no—
82C22×C32C2×C22⋊C411yescharacteristic
83C2×C3⋊D3—21no—
84C2×C3⋊D3—22no—
85C32×C4—21no—
86C32×C4—22no—
87C32×C4—42no—
88C3⋊Dic3—22no—
89C3⋊Dic3—42no—
90C3⋊Dic3#10112yes—
91C4⋊Q8—92no—
92#125—91no—
93#125C2×C3⋊D311yescharacteristic
94C22⋊Q8—182no—
95C4×Q8—182no—
96#117—92no—
97C2×C42—91no—
98C4⋊C8—182no—
99C22⋊C8—182no—
100#97—92no—
101#97C2×C3⋊D312yes—
102C22×D3—34no—
103C2×C3×C4—28no—
104C2×C3×C4C2×C4×D314yes—
105C2×C3×C4D3×D418yes—
106C2×Dic3—34no—
107C2×Dic3—38no—
108C2×Dic3—68no—
109C4×D3—68no—
110C4×D3—128no—
111Dic6—1216no—
112C3×C8—48no—
113C3⋊C8—128no—
114C2×C32C2×#10111yescharacteristic
115C2×C32#42112yes—
116C3⋊D3—41no—
117C2×Q8—182no—
118C22×C4—91no—
119C22×C4—92no—
120C2×C8—22no—
121C2×C8—182no—
122C4⋊C4—22no—
123C4⋊C4—92no—
124C4⋊C4—182no—
125C4⋊C4—182no—
126C4⋊C4C4×C3⋊D312yes—
127C22⋊C4—182no—
128C42—91no—
129C42—92no—
130C42—182no—
131C42C22×C3⋊D311yescharacteristic
132C22×C3D3×C22⋊C414yes—
133C2×D3—64no—
134C2×D3—68no—
135C3×C4—24no—
136C3×C4—28no—
137C3×C4—48no—
138Dic3—38no—
139Dic3—68no—
140Dic3—128no—
141C32#153711yescharacteristic, complemented, Sylow
142C23—91no—
143Q8—364no—
144C2×C4—22no—
145C2×C4—91no—
146C2×C4—92no—
147C2×C4—182no—
148C2×C4—182no—
149C2×C4—362no—
150C2×C4C2×C4×C3⋊D311yescharacteristic
151C2×C4D4×C3⋊D312yes—
152C8—42no—
153C8—362no—
154C2×C3D3×#10114yes—
155C2×C3#482118yes—
156D3—124no—
157C22—182no—
158C22—181no—
159C22C22⋊C4×C3⋊D311yescharacteristic
160C4—22no—
161C4—21no—
162C4—42no—
163C4—92no—
164C4—182no—
165C4—362no—
166C3#6836914yescomplemented
167C2—361no—
168C2C3⋊D3×#10111yescharacteristic
169C2#1059252012yes—
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×#330C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenter#330C3⋊D3
hypocenterC32#1537
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. C32×#330C2semidirect
4. #10589409C2semidirect
5. #10589331C2semidirect
20. C3×#330D3semidirect
66. #330C3⋊D3semidirect
141. C32#1537semidirect
166. C3#68369semidirect

Maximal subgroups

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

subgroupindex
#105961592
#105924042
C32×#3302
#105894092
#105893312
#683693