Finite Group Databasebeta

← #11776870

Subgroups — #11776870

Order 1152.

346 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 78 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#10593805C212yesmaximal
2C2×C8×C3⋊Dic3C211yesmaximal, characteristic
3#10590172C212yesmaximal, complemented
4#10590170C212yesmaximal, complemented
5C2×#3792—22no—
6C22×C32×C8C411yescharacteristic
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C22×C3⋊(C3⋊C8)C411yescharacteristic
9#63779—22no—
10C4⋊#622C2214yes—
11C8×C3⋊Dic3C411yescharacteristic
12C8×C3⋊Dic3C411yescharacteristic
13C8×C3⋊Dic3C2211yescharacteristic
14C8×C3⋊Dic3C2211yescharacteristic
15C2×C8×Dic3—62no—
16C22×C32×C4C2×C411yescharacteristic
17C22×C3⋊Dic3D411yescharacteristic
18C22×C3⋊Dic3Q811yescharacteristic
19#3792—44no—
20C2×#622—24no—
21C2×C32×C8—22no—
22C2×C32×C8C2×C411yescharacteristic
23C2×C32×C8C2×C411yescharacteristic
24C4×C3⋊Dic3C2×C411yescharacteristic
25C4×C3⋊Dic3D411yescharacteristic
26C4×C3⋊Dic3Q811yescharacteristic
27C4×C3⋊Dic3C2311yescharacteristic
28C2×C3⋊(C3⋊C8)—22no—
29C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
30C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
31#1566—91nomaximal, Sylow
32C22×C3×C8—22no—
33C2×C4×Dic3—62no—
34C22×C3⋊C8—62no—
35C8×Dic3—62no—
36C8×Dic3—62no—
37C8×Dic3—62no—
38C8×Dic3—62no—
39C23×C32C4⋊C411yescharacteristic
40C2×C32×C4—21no—
41C2×C32×C4—21no—
42C2×C32×C4C4⋊C411yescharacteristic
43C2×C32×C4C22×C411yescharacteristic
44C2×C3⋊Dic3—22no—
45C2×C3⋊Dic3C4⋊C411yescharacteristic
46C2×C3⋊Dic3C4⋊C411yescharacteristic
47C2×C3⋊Dic3SD1614yes—
48C2×C3⋊Dic3C2×D411yescharacteristic
49C2×C3⋊Dic3C2×Q811yescharacteristic
50#622—44no—
51C32×C8—21no—
52C32×C8M1612yescomplemented
53C3⋊(C3⋊C8)—21no—
54C3⋊(C3⋊C8)M1612yescomplemented
55#423—92no—
56C2×C4×C8—91no—
57#334—92no—
58#334—92no—
59C22×C3×C4—22no—
60C22×Dic3—62no—
61C22×Dic3—62no—
62C2×C3×C8—28no—
63C2×C3×C8—22no—
64C2×C3×C8—22no—
65C4×Dic3—62no—
66C4×Dic3—62no—
67C4×Dic3—62no—
68C4×Dic3—62no—
69C2×C3⋊C8—62no—
70C2×C3⋊C8—62no—
71C2×C3⋊C8—68no—
72C22×C32—21no—
73C22×C32—21no—
74C22×C32#10612yes—
75C22×C32C2×C4⋊C411yescharacteristic
76C32×C4—21no—
77C32×C4C2×M1611yescharacteristic
78C32×C4C2×M1611yescharacteristic
79C3⋊Dic3—21no—
80C3⋊Dic3#10612yes—
81C3⋊Dic3#10812yes—
82C3⋊Dic3C2×SD1612yes—
83C2×M16—182no—
84C22×C8—91no—
85C22×C8#15711yescharacteristic
86C2×C42—91no—
87C4⋊C8—94no—
88C4⋊C8—182no—
89C4×C8—91no—
90C4×C8—91no—
91C4×C8—91no—
92C4×C8—91no—
93C23×C3—22no—
94C2×C3×C4—24no—
95C2×C3×C4—24no—
96C2×C3×C4—22no—
97C2×C3×C4—22no—
98C2×Dic3—62no—
99C2×Dic3—62no—
100C2×Dic3—68no—
101C2×Dic3—62no—
102C2×Dic3—62no—
103C2×Dic3—68no—
104C3×C8—24no—
105C3×C8—24no—
106C3⋊C8—64no—
107C3⋊C8—64no—
108C2×C32—22no—
109C2×C32#42311yescharacteristic
110C2×C32C2×#10611yescharacteristic
111C2×C32C2×#10811yescharacteristic
112C22×C4—91no—
113C22×C4—91no—
114C22×C4C2×#15711yescharacteristic
115M16—364no—
116C2×C8—22no—
117C2×C8—91no—
118C2×C8—91no—
119C2×C8—182no—
120C2×C8—184no—
121C2×C8C2×#15711yescharacteristic
122C2×C8C2×#15711yescharacteristic
123C42—91no—
124C42—91no—
125C42—91no—
126C42—91no—
127C22×C3—24no—
128C22×C3—24no—
129C22×C3—24no—
130C22×C3—22no—
131C3×C4—24no—
132C3×C4—22no—
133C3×C4—22no—
134Dic3—64no—
135Dic3—64no—
136Dic3—64no—
137Dic3—64no—
138C32#156611yescharacteristic, complemented, Sylow
139C23C4⋊#15711yescharacteristic
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—94no—
143C2×C4—91no—
144C2×C4—91no—
145C2×C4—91no—
146C2×C4—91no—
147C2×C4—182no—
148C2×C4C4⋊#15711yescharacteristic
149C2×C4C22×#15711yescharacteristic
150C8—21no—
151C8—92no—
152C8—181no—
153C8—364no—
154C8#379212yescomplemented
155C2×C3—28no—
156C2×C3—22no—
157C2×C3—22no—
158C2×C3—22no—
159C22—21no—
160C22—21no—
161C22#6376812yes—
162C22C2×C4⋊#15711yescharacteristic
163C4—21no—
164C4—92no—
165C4—92no—
166C4—92no—
167C4—181no—
168C4#6428311yescharacteristic
169C4C2×#379211yescharacteristic
170C3—22no—
171C2—22no—
172C2C2×#6376811yescharacteristic
173C2#1059377111yescharacteristic
174C2#1059380511yescharacteristic
subgroupG/H
centerC22C2×C4⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC22×C32×C8C4
socleC22×C32C2×C4⋊C4
prime radicalC23×C32C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C8#157
hypocenterC32#1566
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. #10590172C2semidirect
4. #10590170C2semidirect
52. C32×C8M16semidirect
54. C3⋊(C3⋊C8)M16semidirect
138. C32#1566semidirect
154. C8#3792semidirect

Maximal subgroups

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

subgroupindex
#105938052
C2×C8×C3⋊Dic32
#105901722
#105901702
#15669