Finite Group Databasebeta

← #11771472

Subgroups — #11771472

Order 1152.

402 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 97 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#10592674C211yesmaximal, characteristic
2C32×#324C211yesmaximal, characteristic
3#10589394C211yesmaximal, characteristic
4#67453—34nomaximal
5C2×C32×C4⋊C4C2211yescharacteristic
6C2×C4⋊(C3⋊Dic3)C411yescharacteristic
7C2×#3750—21no—
8C2×#3750—21no—
9C2×C4×C3⋊Dic3C411yescharacteristic
10C32×C22⋊C8—21no—
11#63657—21no—
12#4975—34no—
13C3×#324D314yes—
14#4528—34no—
15C22×C32×C4C2×C411yescharacteristic
16C22×C32×C4D411yescharacteristic
17C22×C32×C4D411yescharacteristic
18C22×C3⋊Dic3—21no—
19C22×C3⋊Dic3—21no—
20C2×C32×C8—41no—
21C32×C4⋊C4—41no—
22C4⋊(C3⋊Dic3)—41no—
23#3750—42no—
24#3750—42no—
25C4×C3⋊Dic3—21no—
26C4×C3⋊Dic3C812yescomplemented
27C2×C3⋊(C3⋊C8)—41no—
28#1325—91noSylow
29C2×C3×C4⋊C4C2×D314yes—
30C2×C4⋊Dic3—34no—
31C2×Dic3⋊C4—64no—
32C2×Dic3⋊C4—64no—
33C2×C4×Dic3—34no—
34C3×C22⋊C8—24no—
35#830—64no—
36C23×C32C22⋊C411yescharacteristic
37C2×C32×C4—21no—
38C2×C32×C4—21no—
39C2×C32×C4—21no—
40C2×C32×C4—21no—
41C2×C32×C4—41no—
42C2×C32×C4—41no—
43C2×C32×C4C2×C811yescharacteristic
44C2×C32×C4M1611yescharacteristic
45C2×C3⋊Dic3—22no—
46C2×C3⋊Dic3—22no—
47C2×C3⋊Dic3—22no—
48C2×C3⋊Dic3—41no—
49C2×C3⋊Dic3—41no—
50C2×C3⋊Dic3—41no—
51C32×C8—81no—
52C3⋊(C3⋊C8)—81no—
53#384—91no—
54#324—91no—
55#324C3⋊D311yescharacteristic
56C22×C3×C4C4×D314yes—
57C22×C3×C4D1214yes—
58C22×C3×C4#6714yes—
59C22×Dic3—64no—
60C22×Dic3—64no—
61C2×C3×C8—44no—
62C3×C4⋊C4—44no—
63C4⋊Dic3—124no—
64Dic3⋊C4—128no—
65Dic3⋊C4—128no—
66C4×Dic3—38no—
67C4×Dic3—64no—
68C2×C3⋊C8—124no—
69C22×C32—21no—
70C22×C32—21no—
71C22×C32C22⋊C811yescharacteristic
72C22×C32#9911yescharacteristic
73C22×C32#10111yescharacteristic
74C32×C4—21no—
75C32×C4—21no—
76C32×C4—41no—
77C32×C4—41no—
78C3⋊Dic3—24no—
79C3⋊Dic3—81no—
80C2×C4⋊C4—91no—
81C2×C4⋊C4—181no—
82C2×C4⋊C4—181no—
83C2×C4⋊C4C2×C3⋊D311yescharacteristic
84C2×C42—91no—
85C22⋊C8—21no—
86C22⋊C8—181no—
87C23×C3(C2×D3)⋊C414yes—
88C2×C3×C4—24no—
89C2×C3×C4—24no—
90C2×C3×C4—24no—
91C2×C3×C4—24no—
92C2×C3×C4—44no—
93C2×C3×C4—44no—
94C2×C3×C4D3×C814yes—
95C2×C3×C4ΓL(1,𝔽25)14yes—
96C2×Dic3—68no—
97C2×Dic3—68no—
98C2×Dic3—68no—
99C2×Dic3—124no—
100C2×Dic3—124no—
101C2×Dic3—124no—
102C3×C8—84no—
103C3⋊C8—244no—
104C2×C32—21no—
105C2×C32—21no—
106C2×C32#32411yescharacteristic
107C2×C32#35311yescharacteristic
108C2×C32#35611yescharacteristic
109C22×C4—181no—
110C22×C4—181no—
111C22×C4C4×C3⋊D311yescharacteristic
112C22×C4C4⋊(C3⋊D3)11yescharacteristic
113C22×C4#63811yescharacteristic
114C2×C8—41no—
115C2×C8—361no—
116C4⋊C4—41no—
117C4⋊C4—361no—
118C4⋊C4—362no—
119C4⋊C4—362no—
120C42—92no—
121C42—181no—
122C22×C3—24no—
123C22×C3—24no—
124C22×C3#80614yes—
125C22×C3(C2×D3)⋊C814yes—
126C22×C3#82414yes—
127C3×C4—24no—
128C3×C4—24no—
129C3×C4—44no—
130C3×C4—44no—
131Dic3—616no—
132Dic3—244no—
133C32#132511yescharacteristic, complemented, Sylow
134C23#375211yescharacteristic
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—182no—
142C2×C4—182no—
143C2×C4—182no—
144C2×C4—361no—
145C2×C4—361no—
146C2×C4—361no—
147C2×C4C8×C3⋊D311yescharacteristic
148C2×C4#374311yescharacteristic
149C8—81no—
150C8—721no—
151C2×C3—24no—
152C2×C3—24no—
153C2×C3#446914yes—
154C2×C3#447414yes—
155C2×C3#447814yes—
156C22—21no—
157C22—21no—
158C22#6363311yescharacteristic
159C22#6364711yescharacteristic
160C22#6365111yescharacteristic
161C4—21no—
162C4—21no—
163C4—41no—
164C4—41no—
165C4—184no—
166C4—721no—
167C3#6745314yescomplemented
168C2—21no—
169C2—21no—
170C2#1058933511yescharacteristic
171C2#1058934011yescharacteristic
172C2#1058934411yescharacteristic
subgroupG/H
centerC22#63633
commutatorC2×C32×C4C2×C8
FrattiniC2×C4⋊C4C2×C3⋊D3
FittingC32×#324C2
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×C32×C4⋊C4C22
hypercenter#324C3⋊D3
hypocenterC32#1325
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
26. C4×C3⋊Dic3C8semidirect
133. C32#1325semidirect
167. C3#67453semidirect

Maximal subgroups

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

subgroupindex
#105926742
C32×#3242
#105893942
#674533