Finite Group Databasebeta

← #11797038

Subgroups — #11797038

Order 1152.

198 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 69 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#10593765C211yesmaximal, characteristic
2#10593762C211yesmaximal, characteristic
3C2×#63764C211yesmaximal, characteristic
4#10590082C214yesmaximal, complemented
5#64286C411yescharacteristic
6#64283C411yescharacteristic
7C2×C8×C3⋊D3C2211yescharacteristic
8#63773—21no—
9C2×#3708—21no—
10#63767C412yes—
11C8×#157C2212yes—
12#63765—21no—
13#63764—21no—
14#63764C2212yes—
15#63764C2212yes—
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C22⋊#157C812yes—
18#3792—21no—
19C4⋊#157C812yes—
20C4×#157C2×C412yes—
21#3788—21no—
22#3787C2×C412yes—
23C2×C32×C8Q811yescharacteristic
24C2×C3⋊(C3⋊C8)D411yescharacteristic
25C8×C3⋊D3C2×C411yescharacteristic
26C8×C3⋊D3D411yescharacteristic
27C8×C3⋊D3Q811yescharacteristic
28C8×C3⋊D3C2311yescharacteristic
29#3708—22no—
30#3708—22no—
31#2151—91nomaximal, Sylow
32C2×D3×C8—121no—
33C22×C3⋊D3C2×C811yescharacteristic
34C2×#157C2×C814yes—
35C2×C32×C4C4⋊C411yescharacteristic
36C2×C3⋊Dic3M1611yescharacteristic
37C4×C3⋊D3C4⋊C411yescharacteristic
38C4×C3⋊D3C2×C811yescharacteristic
39C4×C3⋊D3M1611yescharacteristic
40C4×C3⋊D3C22×C411yescharacteristic
41#622—22no—
42C32×C8C4⋊C411yescharacteristic
43C32×C8C2×Q811yescharacteristic
44C3⋊(C3⋊C8)C4⋊C411yescharacteristic
45C3⋊(C3⋊C8)C2×D411yescharacteristic
46C2×M32—91no—
47C22×C16—91no—
48#405—91no—
49C4⋊C16—94no—
50C2×C4×D3—121no—
51C2×C3×C8—41no—
52C2×C3⋊C8—121no—
53D3×C8—121no—
54D3×C8—121no—
55D3×C8—121no—
56D3×C8—121no—
57C22×C32C4⋊C811yescharacteristic
58C2×C3⋊D3—22no—
59C2×C3⋊D3C4⋊C811yescharacteristic
60C2×C3⋊D3C22×C811yescharacteristic
61#157—24no—
62C32×C4C4⋊C811yescharacteristic
63C32×C4C2×C4⋊C411yescharacteristic
64C3⋊Dic3C4⋊C811yescharacteristic
65C3⋊Dic3C2×M1611yescharacteristic
66C2×M16—91no—
67C22×C8—91no—
68#117—91no—
69M32—181no—
70M32—181no—
71C2×C16—92no—
72C2×C16—92no—
73C2×C16—181no—
74C2×C16—181no—
75#97—92no—
76C4×C8—92no—
77C22×D3—121no—
78C2×C3×C4—41no—
79C2×Dic3—121no—
80C4×D3—121no—
81C4×D3—121no—
82C4×D3—121no—
83C4×D3—121no—
84C3×C8—41no—
85C3×C8—41no—
86C3⋊C8—121no—
87C3⋊C8—121no—
88C2×C32—21no—
89C2×C32C2×C4⋊C811yescharacteristic
90C3⋊D3—21no—
91C3⋊D3#50412yes—
92C22×C4—91no—
93M16—181no—
94M16—181no—
95C2×C8—91no—
96C2×C8—91no—
97C2×C8—91no—
98C2×C8—91no—
99C2×C8—91no—
100C2×C8—92no—
101C2×C8PSU(3,𝔽2)11yescharacteristic
102C4⋊C4—92no—
103C22⋊C4—92no—
104C42—92no—
105C16—182no—
106C16—182no—
107C22×C3—41no—
108C2×D3—121no—
109C2×D3—121no—
110C2×D3—124no—
111C3×C4—41no—
112C3×C4—41no—
113Dic3—121no—
114Dic3—121no—
115C32#215111yescharacteristic, complemented, Sylow
116C23—91no—
117C2×C4—91no—
118C2×C4—91no—
119C2×C4—91no—
120C2×C4—91no—
121C2×C4—91no—
122C2×C4—94no—
123C2×C4#377711yescharacteristic
124C8—91no—
125C8—91no—
126C8—182no—
127C8#377711yescharacteristic
128C8C2×PSU(3,𝔽2)11yescharacteristic
129C2×C3—42no—
130C2×C3—41no—
131D3—122no—
132D3—122no—
133C22—91no—
134C22—91no—
135C22—182no—
136C22#6374411yescharacteristic
137C4—91no—
138C4—91no—
139C4—184no—
140C4#6374411yescharacteristic
141C4C2×#377711yescharacteristic
142C3—41no—
143C2—21no—
144C2—92no—
145C2—181no—
146C2C2×#6374411yescharacteristic
subgroupG/H
center, FrattiniC8C2×PSU(3,𝔽2)
commutatorC2×C3⋊D3C22×C8
FittingC2×C32×C8Q8
socleC2×C32C2×C4⋊C8
prime radicalC22×C3⋊D3C2×C8
cosocleC8×C3⋊D3C23
hypercenterC2×C8PSU(3,𝔽2)
hypocenterC32#2151
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C8 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
4. #10590082C2semidirect
115. C32#2151semidirect

Maximal subgroups

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

subgroupindex
#105937652
#105937622
C2×#637642
#105900822
#21519