Finite Group Databasebeta

← #11786341

Subgroups — #11786341

Order 1152.

338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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#10593723C211yesmaximal, characteristic
2C2×#63733C214yesmaximal
3#10590340C212yesmaximal
4C2×#3787C2212yes—
5C42×C3⋊D3C2211yescharacteristic
6C2×#3712C2214yes—
7#63777C414yes—
8#63733—28no—
9C3×C4⋊(C3⋊C8)—22no—
10#63572—22no—
11#4837—62no—
12C2×C4×C3⋊D3Q812yes—
13C2×C4×C3⋊D3C2311yescharacteristic
14C2×#622C2×C414yes—
15#3787D414yes—
16#3787Q814yes—
17C32×C42D411yescharacteristic
18C4×C3⋊Dic3C2×C412yes—
19C4×C3⋊Dic3D411yescharacteristic
20C2×C3×C3⋊C8—24no—
21#3712—28no—
22#1849—91nomaximal, Sylow
23C2×ΓL(1,𝔽25)—64no—
24C42×D3—62no—
25C3×C4⋊C8—62no—
26Dic3⋊C8—64no—
27C4⋊(C3⋊C8)—22no—
28C22×C3⋊D3C2×Q811yescharacteristic
29C2×C32×C4C4⋊C412yes—
30C2×C32×C4C2×D411yescharacteristic
31C2×C3⋊Dic3C4⋊C412yes—
32C2×C3⋊Dic3C22×C411yescharacteristic
33C4×C3⋊D3—42no—
34C4×C3⋊D3C2×D412yes—
35C4×C3⋊D3C2×Q812yes—
36#622C4⋊C418yes—
37C3×C3⋊C8—44no—
38C2×#108—94no—
39#423—92no—
40C2×#97—91no—
41C2×C4×D3—62no—
42C2×C4×D3—62no—
43C2×C4×D3—62no—
44C2×C3×C8—64no—
45C3×C42—22no—
46C4×Dic3—62no—
47C4×Dic3—62no—
48C4×Dic3—62no—
49C2×C3⋊C8—24no—
50ΓL(1,𝔽25)—128no—
51C22×C32C2×C4⋊C411yescharacteristic
52C2×C3⋊D3—22no—
53C2×C3⋊D3C4⋊Q812yes—
54C32×C4—22no—
55C32×C4#12711yescharacteristic
56C32×C4C4⋊Q811yescharacteristic
57C3⋊Dic3—22no—
58C3⋊Dic3C2×C4⋊C412yes—
59C2×M16—94no—
60C22×C8—92no—
61C2×C42—91no—
62#108—188no—
63C4⋊C8—62no—
64C4⋊C8—182no—
65#97—94no—
66C22×D3—62no—
67C2×C3×C4—22no—
68C2×C3×C4—22no—
69C2×C3×C4—22no—
70C2×Dic3—62no—
71C2×Dic3—62no—
72C2×Dic3—62no—
73C4×D3—64no—
74C4×D3—64no—
75C4×D3—124no—
76C4×D3—124no—
77C3×C8—124no—
78C3⋊C8—44no—
79C2×C32#38411yescharacteristic
80C2×C32#43012yes—
81C3⋊D3—22no—
82C22×C4—91no—
83C22×C4—92no—
84M16—188no—
85C2×C8—64no—
86C2×C8—94no—
87C2×C8—94no—
88C2×C8—94no—
89C42—91no—
90C42—92no—
91C42GO+(4,𝔽2)11yescharacteristic
92C22×C3—22no—
93C2×D3—64no—
94C2×D3—122no—
95C2×D3—122no—
96C3×C4—24no—
97C3×C4—22no—
98C3×C4—22no—
99C3×C4—42no—
100Dic3—64no—
101Dic3—64no—
102Dic3—122no—
103C32#184911yescharacteristic, complemented, Sylow
104C23—91no—
105C2×C4—91no—
106C2×C4—92no—
107C2×C4—92no—
108C2×C4—92no—
109C2×C4—362no—
110C2×C4#377312yes—
111C2×C4C2×GO+(4,𝔽2)11yescharacteristic
112C8—98no—
113C8—124no—
114C2×C3—22no—
115C2×C3—22no—
116C2×C3—22no—
117D3—124no—
118C22—92no—
119C22—182no—
120C22C2×#377311yescharacteristic
121C4—22no—
122C4—92no—
123C4—182no—
124C4#6422211yescharacteristic
125C4#6423111yescharacteristic
126C3—22no—
127C2—182no—
128C2#1059333012yes—
129C2#1059341311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC32×C42D4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C2×Q8
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1849
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
103. C32#1849semidirect

Maximal subgroups

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

subgroupindex
#105937232
C2×#637332
#105903402
#18499