Finite Group Databasebeta

← #11771409

Subgroups — #11771409

Order 1152.

384 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 85 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#10592825C211yesmaximal, characteristic
2C32×#349C211yesmaximal, characteristic, complemented
3#10589419C211yesmaximal, characteristic, complemented
4#67530—34nomaximal
5C22×C4×C3⋊D3C411yescharacteristic
6C2×C32×M16C2211yescharacteristic
7C2×#3748C411yescharacteristic
8C32×M32—21no—
9#63647—21no—
10#63647—21no—
11#63639—21no—
12#5126—34no—
13C3×#349D314yescomplemented
14#4553—34no—
15C23×C3⋊D3C811yescharacteristic
16C22×C32×C4C2×C411yescharacteristic
17C22×C3⋊Dic3C811yescharacteristic
18C2×C4×C3⋊D3—21no—
19C2×C4×C3⋊D3—21no—
20C2×C4×C3⋊D3—41no—
21C2×C4×C3⋊D3—41no—
22C32×M16—41no—
23C2×C32×C8D411yescharacteristic
24C2×C32×C8D411yescharacteristic
25#3748—41no—
26C2×C3⋊(C3⋊C8)—21no—
27C32×C16—41no—
28C3⋊(C3⋊C16)—41no—
29#1320—91noSylow
30C22×C4×D3—34no—
31C2×C3×M16C2×D314yes—
32C2×#208—34no—
33C3×M32—24no—
34(C2×D3)⋊C8—64no—
35(C2×D3)⋊C8—64no—
36#812—64no—
37C23×C32C2×C811yescharacteristic
38C22×C3⋊D3—21no—
39C22×C3⋊D3—42no—
40C22×C3⋊D3—41no—
41C2×C32×C4—21no—
42C2×C32×C4—21no—
43C2×C32×C4C22⋊C411yescharacteristic
44C2×C32×C4M1611yescharacteristic
45C2×C3⋊Dic3—21no—
46C2×C3⋊Dic3—41no—
47C4×C3⋊D3—42no—
48C4×C3⋊D3—41no—
49C4×C3⋊D3—41no—
50C32×C8—21no—
51C32×C8—21no—
52C3⋊(C3⋊C8)—41no—
53#407—91no—
54#349—91no—
55#349C3⋊D311yescharacteristic, complemented
56C23×D3—34no—
57C22×C3×C4C4×D314yes—
58C22×Dic3—34no—
59C2×C4×D3—64no—
60C2×C4×D3—64no—
61C2×C4×D3—124no—
62C2×C4×D3—124no—
63C3×M16—44no—
64C2×C3×C8D1214yes—
65C2×C3×C8#6714yes—
66#208—124no—
67C2×C3⋊C8—64no—
68C3×C16—44no—
69C3⋊C16—124no—
70C22×C32—21no—
71C22×C32—41no—
72C22×C32C22⋊C811yescharacteristic
73C2×C3⋊D3—22no—
74C2×C3⋊D3—41no—
75C2×C3⋊D3—42no—
76C2×C3⋊D3—41no—
77C2×C3⋊D3—42no—
78C32×C4—21no—
79C32×C4#9911yescharacteristic
80C32×C4#10011yescharacteristic
81C3⋊Dic3—41no—
82C23×C4—91no—
83C2×M16—91no—
84C2×M16C2×C3⋊D311yescharacteristic
85M32—21no—
86M32—181no—
87C22⋊C8—181no—
88C22⋊C8—181no—
89C23×C3D3×C814yes—
90C22×D3—64no—
91C22×D3—128no—
92C22×D3—124no—
93C2×C3×C4—24no—
94C2×C3×C4—24no—
95C2×C3×C4ΓL(1,𝔽25)14yes—
96C2×C3×C4(C2×D3)⋊C414yes—
97C2×Dic3—64no—
98C2×Dic3—124no—
99C4×D3—128no—
100C4×D3—124no—
101C4×D3—124no—
102C3×C8—24no—
103C3×C8—24no—
104C3⋊C8—124no—
105C2×C32—21no—
106C2×C32—41no—
107C2×C32#32311yescharacteristic
108C3⋊D3—42no—
109C24—91no—
110C22×C4—91no—
111C22×C4—181no—
112C22×C4—181no—
113C22×C4—361no—
114C22×C4—361no—
115C22×C4C4×C3⋊D311yescharacteristic
116M16—41no—
117M16—361no—
118C2×C8—181no—
119C2×C8C4⋊(C3⋊D3)11yescharacteristic
120C2×C8#63811yescharacteristic
121C16—41no—
122C16—361no—
123C22×C3—24no—
124C22×C3—44no—
125C22×C3(C2×D3)⋊C814yes—
126C2×D3—68no—
127C2×D3—124no—
128C2×D3—128no—
129C2×D3—124no—
130C2×D3—128no—
131C3×C4—24no—
132C3×C4#80614yes—
133C3×C4#82314yes—
134Dic3—124no—
135C32#132011yescharacteristic, complemented, Sylow
136C23—181no—
137C23—361no—
138C23—362no—
139C23C8×C3⋊D311yescharacteristic
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—181no—
143C2×C4—362no—
144C2×C4—361no—
145C2×C4—361no—
146C2×C4—361no—
147C2×C4#374311yescharacteristic
148C2×C4#375211yescharacteristic
149C8—21no—
150C8—21no—
151C8—361no—
152C2×C3—24no—
153C2×C3—44no—
154C2×C3#446814yes—
155D3—128no—
156C22—21no—
157C22—41no—
158C22—182no—
159C22—361no—
160C22—362no—
161C22—362no—
162C22—361no—
163C22#6364711yescharacteristic
164C4—21no—
165C4—361no—
166C4#6363311yescharacteristic
167C4#6365011yescharacteristic
168C3#6753014yescomplemented
169C2—21no—
170C2—41no—
171C2—362no—
172C2#1058933411yescharacteristic
subgroupG/H
centerC4#63633
commutatorC23×C32C2×C8
FrattiniC2×M16C2×C3⋊D3
FittingC32×#349C2
socleC2×C32#323
prime radicalC23×C3⋊D3C8
cosocleC2×C32×M16C22
hypercenter#349C3⋊D3
hypocenterC32#1320
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. C32×#349C2semidirect
3. #10589419C2semidirect
13. C3×#349D3semidirect
55. #349C3⋊D3semidirect
135. C32#1320semidirect
168. C3#67530semidirect

Maximal subgroups

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

subgroupindex
#105928252
C32×#3492
#105894192
#675303