Finite Group Databasebeta

← #11771391

Subgroups — #11771391

Order 1152.

428 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 34 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#10592638C211yesmaximal, characteristic
2#10590202C212yesmaximal, complemented
3C22×C4⋊(C3⋊D3)C411yescharacteristic
4C2×C32×C42C411yescharacteristic
5C2×#3752—22no—
6C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
7C22⋊#622—22no—
8#4939—62no—
9C23×C3⋊D3—21no—
10C22×C32×C4—21no—
11C22×C32×C4C2×C411yescharacteristic
12C22×C3⋊Dic3D412yes—
13C2×C4⋊(C3⋊D3)—21no—
14C2×C4⋊(C3⋊D3)—41no—
15C2×C4⋊(C3⋊D3)—41no—
16C2×C4⋊(C3⋊D3)C812yescomplemented
17C2×#622—42no—
18C32×C42—41no—
19#3752—44no—
20C4⋊(C3⋊Dic3)—41no—
21#1318—91nomaximal, Sylow
22C22×D12—62no—
23C2×C3×C42—22no—
24C2×(C2×D3)⋊C4—68no—
25C2×C4⋊Dic3—62no—
26C23×C32C22⋊C411yescharacteristic
27C22×C3⋊D3—22no—
28C22×C3⋊D3—42no—
29C22×C3⋊D3—42no—
30C22×C3⋊D3—41no—
31C22×C3⋊D3—41no—
32C2×C32×C4—21no—
33C2×C32×C4—21no—
34C2×C32×C4—22no—
35C2×C32×C4—41no—
36C2×C32×C4—41no—
37C2×C32×C4C2×C811yescharacteristic
38C2×C32×C4M1611yescharacteristic
39C2×C3⋊Dic3—22no—
40C2×C3⋊Dic3—42no—
41C4⋊(C3⋊D3)—42no—
42C4⋊(C3⋊D3)—42no—
43#622—82no—
44#390—91no—
45#324—92no—
46C23×D3—64no—
47C22×C3×C4—24no—
48C22×C3×C4—22no—
49C22×Dic3—64no—
50C2×D12—64no—
51C2×D12—64no—
52C2×D12—124no—
53C2×D12—124no—
54C3×C42—44no—
55(C2×D3)⋊C4—1216no—
56C4⋊Dic3—124no—
57C22×C32—21no—
58C22×C32—21no—
59C22×C32C22⋊C811yescharacteristic
60C22×C32#9911yescharacteristic
61C22×C32#10011yescharacteristic
62C2×C3⋊D3—44no—
63C2×C3⋊D3—42no—
64C2×C3⋊D3—82no—
65C2×C3⋊D3—81no—
66C2×C3⋊D3—81no—
67C32×C4—21no—
68C32×C4—21no—
69C32×C4—42no—
70C3⋊Dic3—42no—
71C22×D4—91no—
72C2×C4⋊C4—91no—
73C2×C22⋊C4—182no—
74C2×C42#15711yescharacteristic
75C22⋊C8—182no—
76C23×C3—22no—
77C22×D3—68no—
78C22×D3—128no—
79C22×D3—124no—
80C22×D3—124no—
81C22×D3—128no—
82C2×C3×C4—24no—
83C2×C3×C4—24no—
84C2×C3×C4—28no—
85C2×C3×C4—22no—
86C2×C3×C4—22no—
87C2×C3×C4—44no—
88C2×C3×C4—44no—
89C2×Dic3—124no—
90C2×Dic3—128no—
91D12—128no—
92D12—128no—
93C2×C32—21no—
94C2×C32—21no—
95C2×C32#32311yescharacteristic
96C2×C32#35311yescharacteristic
97C2×C32#35511yescharacteristic
98C3⋊D3—82no—
99C24—181no—
100C2×D4—92no—
101C2×D4—181no—
102C2×D4—361no—
103C2×D4—361no—
104C22×C4—21no—
105C22×C4—92no—
106C22×C4C2×#15711yescharacteristic
107C2×C8—362no—
108C4⋊C4—361no—
109C22⋊C4—364no—
110C42—41no—
111C22×C3—24no—
112C22×C3—24no—
113C22×C3—22no—
114C22×C3—22no—
115C22×C3—22no—
116C2×D3—128no—
117C2×D3—1216no—
118C2×D3—248no—
119C2×D3—244no—
120C2×D3—244no—
121C3×C4—24no—
122C3×C4—24no—
123C3×C4—48no—
124Dic3—244no—
125C32#131811yescharacteristic, complemented, Sylow
126C23—182no—
127C23—362no—
128C23—362no—
129C23—361no—
130C23—361no—
131C23C22⋊#15711yescharacteristic
132D4—362no—
133D4—362no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—22no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—182no—
140C2×C4—362no—
141C2×C4#378711yescharacteristic
142C2×C4#378811yescharacteristic
143C8—722no—
144C2×C3—24no—
145C2×C3—24no—
146C2×C3—22no—
147C2×C3—22no—
148C2×C3—22no—
149D3—248no—
150C22—21no—
151C22—21no—
152C22—364no—
153C22—362no—
154C22—722no—
155C22—721no—
156C22—721no—
157C22#6377411yescharacteristic
158C22#6377811yescharacteristic
159C22#6378811yescharacteristic
160C4—21no—
161C4—21no—
162C4—42no—
163C4—362no—
164C3—22no—
165C2—21no—
166C2—21no—
167C2—722no—
168C2#1059014211yescharacteristic
169C2#1059014511yescharacteristic
170C2#1059020411yescharacteristic
subgroupG/H
centerC22#63774
commutatorC2×C32×C4C2×C8
FrattiniC22×C4C2×#157
FittingC2×C32×C42C4
socleC22×C32#99
prime radicalC22×C4⋊(C3⋊D3)C4
cosocleC2×C4⋊(C3⋊Dic3)C22
hypercenterC2×C42#157
hypocenterC32#1318
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10590202C2semidirect
16. C2×C4⋊(C3⋊D3)C8semidirect
125. C32#1318semidirect

Maximal subgroups

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

subgroupindex
#105926382
#105902022
#13189