Finite Group Databasebeta

← #11797830

Subgroups — #11797830

Order 1152.

306 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 49 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×#63734C211yesmaximal, characteristic
2#10590740C212yesmaximal, complemented
3#10590175C211yesmaximal, characteristic, complemented
4#10590069C211yesmaximal, characteristic, complemented
5#10590061C212yesmaximal, complemented
6#63898—22no—
7C2×#3713C2212yes—
8C2×#3708C2211yescharacteristic
9C2×#3708C2211yescharacteristic
10#63734C414yescomplemented
11C8×C3⋊Dic3C2211yescharacteristic
12C3×#821—22no—
13#63576C2212yes—
14#4756—62no—
15C2×C3×D12—22no—
16C2×D3×Dic3—42no—
17C2×C32×C8D411yescharacteristic
18C4×C3⋊Dic3D411yescharacteristic
19C2×C3⋊(C3⋊C8)C2311yescharacteristic
20C3×C4⋊Dic3—22no—
21(C2×D3)⋊Dic3—42no—
22#3713—22no—
23#3713C2×C414yescomplemented
24#3708—21no—
25#3708C2×C412yescomplemented
26#2177—91nomaximal, Sylow
27D4×Dic3—62no—
28C2×#213—62no—
29#893—62no—
30C3×#102—62no—
31#821—22no—
32C8×Dic3—62no—
33#807—62no—
34C22×C3×D3—42no—
35C2×C32×C4C2×D411yescharacteristic
36C2×C3⋊Dic3D812yes—
37C2×C3×Dic3—42no—
38C3×D12—24no—
39C3×D12—42no—
40D3×Dic3—84no—
41C32×C8—21no—
42C3⋊(C3⋊C8)C22×C411yescharacteristic
43C3⋊(C3⋊C8)#4111yescharacteristic
44C2×D16—91no—
45C4×D8—92no—
46#367—91no—
47#357—92no—
48#346—91no—
49C2×C3×D4—62no—
50C22×Dic3—122no—
51C2×D12—22no—
52C2×C4×D3—122no—
53C2×C3×C8—22no—
54C3×C4⋊C4—62no—
55#217—122no—
56#213—64no—
57#213—64no—
58(C2×D3)⋊C4—122no—
59C4⋊Dic3—22no—
60C4×Dic3—62no—
61C2×C3⋊C8—62no—
62C22×C32C2×D811yescharacteristic
63C2×C3×D3—44no—
64C2×C3×D3—82no—
65C2×C3×D3—82no—
66C32×C4C4×D411yescharacteristic
67C32×C4#13511yescharacteristic
68C3⋊Dic3—22no—
69C3×Dic3—82no—
70C2×D8—92no—
71C4×D4—182no—
72D16—94no—
73C2×C16—91no—
74C2×C16—91no—
75#107—92no—
76#102—62no—
77C4×C8—91no—
78C23×C3—122no—
79C22×D3—42no—
80C3×D4—64no—
81C3×D4—122no—
82C2×C3×C4—22no—
83C2×C3×C4—122no—
84C2×Dic3—42no—
85C2×Dic3—62no—
86C2×Dic3—62no—
87C2×Dic3—244no—
88D12—24no—
89D12—42no—
90C4×D3—244no—
91C3×C8—42no—
92C3⋊C8—62no—
93C3⋊C8—62no—
94C2×C32C4×D811yescharacteristic
95C2×C32#50912yes—
96C3×D3—84no—
97C2×D4—62no—
98C22×C4—362no—
99D8—94no—
100D8—182no—
101C2×C8—91no—
102C2×C8GO+(4,𝔽2)11yescharacteristic
103C4⋊C4—62no—
104C22⋊C4—362no—
105C42—91no—
106C16—92no—
107C16—181no—
108C22×C3—22no—
109C22×C3—124no—
110C22×C3—242no—
111C22×C3—242no—
112C2×D3—44no—
113C2×D3—82no—
114C2×D3—82no—
115C3×C4—22no—
116C3×C4—22no—
117C3×C4—242no—
118Dic3—64no—
119Dic3—82no—
120Dic3—122no—
121C32#217711yescharacteristic, complemented, Sylow
122C23—122no—
123D4—64no—
124D4—122no—
125C2×C4—92no—
126C2×C4—122no—
127C2×C4—724no—
128C2×C4C2×GO+(4,𝔽2)11yescharacteristic
129C8—21no—
130C8—91no—
131C8—91no—
132C2×C3—22no—
133C2×C3—22no—
134C2×C3—22no—
135C2×C3—244no—
136D3—84no—
137C22—124no—
138C22—242no—
139C22—242no—
140C22#6422511yescharacteristic
141C4—182no—
142C4—242no—
143C4C4×GO+(4,𝔽2)11yescharacteristic
144C4#6423711yescharacteristic
145C3—22no—
146C2—244no—
147C2#1059327712yes—
148C2#1059342011yescharacteristic
subgroupG/H
centerC22#64225
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32C2×D8
prime radicalC2×#63734C2
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2177
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10590740C2semidirect
3. #10590175C2semidirect
4. #10590069C2semidirect
5. #10590061C2semidirect
10. #63734C4semidirect
23. #3713C2×C4semidirect
25. #3708C2×C4semidirect
121. C32#2177semidirect

Maximal subgroups

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

subgroupindex
C2×#637342
#105907402
#105901752
#105900692
#105900612
#21779