Finite Group Databasebeta

← #11786343

Subgroups — #11786343

Order 1152.

250 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 77 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#10593771C212yesmaximal
2C2×#63767C211yesmaximal, characteristic
3#10593546C212yesmaximal
4#10593539C212yesmaximal
5C2×C4×#157C2211yescharacteristic
6#64283C2214yes—
7C2×#3787C2211yescharacteristic
8C2×C8×C3⋊D3C2211yescharacteristic
9#63771—22no—
10#63770—22no—
11#63767C414yes—
12#63748—24no—
13#63744—24no—
14C22×#157Q812yes—
15C2×C4×C3⋊D3C2311yescharacteristic
16#3792—24no—
17C2×#622D412yes—
18C4×#157C2×C412yes—
19C4×#157D412yes—
20#3788—24no—
21#3787—24no—
22#3787C2×C412yes—
23#3787Q812yes—
24C2×C32×C8Q811yescharacteristic
25C2×C3⋊(C3⋊C8)Q811yescharacteristic
26C8×C3⋊D3C2×C412yes—
27C8×C3⋊D3D412yes—
28#1849—91nomaximal, Sylow
29C2×D3×C8—121no—
30C22×C3⋊D3C2×Q811yescharacteristic
31C2×#157—42no—
32C2×#157C4⋊C414yes—
33C2×C32×C4C2×Q811yescharacteristic
34C2×C3⋊Dic3C2×D411yescharacteristic
35C4×C3⋊D3C22×C411yescharacteristic
36C4×C3⋊D3C2×D411yescharacteristic
37C4×C3⋊D3C2×D411yescharacteristic
38C4×C3⋊D3C2×Q811yescharacteristic
39#622—44no—
40#622C4⋊C414yes—
41C32×C8C4⋊C412yes—
42C3⋊(C3⋊C8)C4⋊C412yes—
43C2×#108—92no—
44C2×#108—92no—
45#423—92no—
46C2×#97—91no—
47C2×C4×D3—121no—
48C2×C3×C8—41no—
49C2×C3⋊C8—121no—
50D3×C8—122no—
51D3×C8—122no—
52C22×C32C4⋊Q811yescharacteristic
53C2×C3⋊D3—22no—
54C2×C3⋊D3C2×C4⋊C411yescharacteristic
55C2×C3⋊D3C4⋊Q811yescharacteristic
56#157—24no—
57C32×C4C2×C4⋊C411yescharacteristic
58C32×C4C4⋊Q811yescharacteristic
59C3⋊Dic3C2×C4⋊C411yescharacteristic
60C3⋊Dic3#12711yescharacteristic
61C2×M16—94no—
62C22×C8—91no—
63C22×C8—91no—
64C2×C42—91no—
65#108—184no—
66#108—182no—
67#108—182no—
68C4⋊C8—184no—
69#97—94no—
70C22×D3—121no—
71C2×C3×C4—41no—
72C2×Dic3—121no—
73C4×D3—121no—
74C4×D3—121no—
75C4×D3—121no—
76C4×D3—121no—
77C3×C8—42no—
78C3⋊C8—122no—
79C2×C32—21no—
80C2×C32#38411yescharacteristic
81C3⋊D3—21no—
82C3⋊D3#43012yes—
83C22×C4—91no—
84C22×C4—92no—
85M16—184no—
86M16—184no—
87C2×C8—92no—
88C2×C8—92no—
89C2×C8—92no—
90C2×C8—91no—
91C2×C8—92no—
92C2×C8—92no—
93C2×C8—184no—
94C2×C8PSU(3,𝔽2)11yescharacteristic
95C42—92no—
96C42—92no—
97C22×C3—41no—
98C2×D3—121no—
99C2×D3—121no—
100C2×D3—124no—
101C3×C4—41no—
102C3×C4—41no—
103Dic3—121no—
104Dic3—121no—
105C32#184911yescharacteristic, complemented, Sylow
106C23—91no—
107C2×C4—91no—
108C2×C4—91no—
109C2×C4—91no—
110C2×C4—91no—
111C2×C4—91no—
112C2×C4—94no—
113C2×C4—362no—
114C2×C4C2×PSU(3,𝔽2)11yescharacteristic
115C8—94no—
116C8—92no—
117C8—364no—
118C8#377712yes—
119C2×C3—42no—
120C2×C3—41no—
121D3—122no—
122D3—122no—
123C22—91no—
124C22—91no—
125C22—182no—
126C22C4⋊PSU(3,𝔽2)11yescharacteristic
127C4—91no—
128C4—91no—
129C4—184no—
130C4C4⋊PSU(3,𝔽2)11yescharacteristic
131C4C2×#377711yescharacteristic
132C3—41no—
133C2—21no—
134C2—92no—
135C2—181no—
136C2#1059355311yescharacteristic
subgroupG/H
centerC4C4⋊PSU(3,𝔽2)
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×PSU(3,𝔽2)
FittingC2×C32×C8Q8
socleC2×C32#384
prime radicalC22×C3⋊D3C2×Q8
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8PSU(3,𝔽2)
hypocenterC32#1849
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
105. C32#1849semidirect

Maximal subgroups

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

subgroupindex
#105937712
C2×#637672
#105935462
#105935392
#18499