Finite Group Databasebeta

← #11776982

Subgroups — #11776982

Order 1152.

286 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 70 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#10593805C211yesmaximal, characteristic
2C2×C4⋊#622C211yesmaximal, characteristic
3#10592417C211yesmaximal, characteristic
4#10590172C212yesmaximal, complemented
5#10590170C212yesmaximal, complemented
6C2×#3792—21no—
7C22×#622—21no—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9#63779—21no—
10C4⋊#622—21no—
11C4⋊#622C2212yes—
12C4⋊#622C2211yescharacteristic
13C4⋊#622C2211yescharacteristic
14C32×C22⋊C8C411yescharacteristic
15#63657C411yescharacteristic
16#63641C412yes—
17C8×C3⋊Dic3C2212yes—
18#4718—62no—
19C22×C32×C4C2×C411yescharacteristic
20C22×C3⋊Dic3D411yescharacteristic
21C22×C3⋊Dic3Q811yescharacteristic
22#3792—42no—
23C2×#622—22no—
24C2×#622—21no—
25C2×#622—21no—
26C2×#622—42no—
27C2×C32×C8C2×C412yes—
28C4×C3⋊Dic3C2×C411yescharacteristic
29C4×C3⋊Dic3D411yescharacteristic
30C4×C3⋊Dic3Q811yescharacteristic
31C4×C3⋊Dic3C2311yescharacteristic
32C2×C3⋊(C3⋊C8)C2×C412yes—
33#1570—91nomaximal, Sylow
34C2×C4×Dic3—62no—
35C3×C22⋊C8—22no—
36#830—62no—
37Dic3⋊C8—64no—
38C8×Dic3—64no—
39C23×C32C4⋊C411yescharacteristic
40C2×C32×C4—22no—
41C2×C32×C4C4⋊C411yescharacteristic
42C2×C32×C4C22×C411yescharacteristic
43C2×C3⋊Dic3—41no—
44C2×C3⋊Dic3C4⋊C411yescharacteristic
45C2×C3⋊Dic3C4⋊C411yescharacteristic
46C2×C3⋊Dic3SD1612yes—
47C2×C3⋊Dic3SD1612yes—
48C2×C3⋊Dic3C2×D411yescharacteristic
49C2×C3⋊Dic3C2×Q811yescharacteristic
50#622—42no—
51#622—41no—
52#622—41no—
53C32×C8—22no—
54C3⋊(C3⋊C8)—22no—
55#431—91no—
56#423—91no—
57C2×C4⋊C8—91no—
58#334—92no—
59#334—92no—
60C22×C3×C4—22no—
61C22×Dic3—62no—
62C22×Dic3—62no—
63C2×C3×C8—24no—
64C4×Dic3—62no—
65C4×Dic3—62no—
66C4×Dic3—62no—
67C4×Dic3—62no—
68C2×C3⋊C8—64no—
69C22×C32—21no—
70C22×C32—21no—
71C22×C32#10612yes—
72C22×C32C2×C4⋊C411yescharacteristic
73C32×C4—21no—
74C32×C4#13112yes—
75C3⋊Dic3—21no—
76C3⋊Dic3—21no—
77C3⋊Dic3#10612yes—
78C3⋊Dic3C2×SD1611yescharacteristic
79C3⋊Dic3C2×SD1611yescharacteristic
80C2×M16—181no—
81C22×C8—181no—
82C2×C42—91no—
83C4⋊C8—92no—
84C4⋊C8—92no—
85C4⋊C8—91no—
86C4⋊C8—91no—
87C4⋊C8—181no—
88C4⋊C8—181no—
89C22⋊C8—91no—
90C22⋊C8#15711yescharacteristic
91C4×C8—92no—
92C23×C3—22no—
93C2×C3×C4—22no—
94C2×C3×C4—22no—
95C2×C3×C4—44no—
96C2×Dic3—62no—
97C2×Dic3—64no—
98C2×Dic3—64no—
99C2×Dic3—62no—
100C2×Dic3—62no—
101C2×Dic3—62no—
102C2×Dic3—124no—
103C3×C8—44no—
104C3⋊C8—124no—
105C2×C32—22no—
106C2×C32#42411yescharacteristic
107C2×C32C2×#10611yescharacteristic
108C2×C32#43011yescharacteristic
109C22×C4—91no—
110C22×C4—91no—
111C22×C4C2×#15711yescharacteristic
112M16—362no—
113C2×C8—92no—
114C2×C8—182no—
115C2×C8—181no—
116C2×C8—181no—
117C2×C8—362no—
118C2×C8C2×#15712yes—
119C42—91no—
120C42—91no—
121C42—91no—
122C42—91no—
123C22×C3—24no—
124C22×C3—22no—
125C22×C3—42no—
126C22×C3—42no—
127C3×C4—24no—
128C3×C4—42no—
129Dic3—64no—
130Dic3—62no—
131Dic3—62no—
132Dic3—64no—
133Dic3—122no—
134C32#157011yescharacteristic, complemented, Sylow
135C23C4⋊#15711yescharacteristic
136C2×C4—22no—
137C2×C4—92no—
138C2×C4—92no—
139C2×C4—91no—
140C2×C4—91no—
141C2×C4—91no—
142C2×C4—91no—
143C2×C4—361no—
144C2×C4C4⋊#15711yescharacteristic
145C2×C4C22×#15711yescharacteristic
146C8—22no—
147C8—182no—
148C8—362no—
149C8—361no—
150C8—361no—
151C2×C3—22no—
152C2×C3—22no—
153C2×C3—22no—
154C2×C3—44no—
155C22—21no—
156C22—21no—
157C22#6376812yes—
158C22C2×C4⋊#15711yescharacteristic
159C4—21no—
160C4—91no—
161C4—91no—
162C4—92no—
163C4—181no—
164C4—181no—
165C4#6428712yes—
166C3—22no—
167C2—22no—
168C2#1059374311yescharacteristic
169C2C2×#6376811yescharacteristic
170C2#1059377611yescharacteristic
subgroupG/H
centerC22C2×C4⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C22⋊C8C4
socleC22×C32C2×C4⋊C4
prime radicalC23×C32C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22⋊C8#157
hypocenterC32#1570
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
4. #10590172C2semidirect
5. #10590170C2semidirect
134. C32#1570semidirect

Maximal subgroups

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

subgroupindex
#105938052
C2×C4⋊#6222
#105924172
#105901722
#105901702
#15709