Finite Group Databasebeta

← #11797357

Subgroups — #11797357

Order 1152.

268 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 62 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#10592407C211yesmaximal, characteristic
2#10590177C212yesmaximal, complemented
3#10590176C212yesmaximal
4#10590148C211yesmaximal, characteristic, complemented
5C4×#3708C211yesmaximal, characteristic, complemented
6C2×#3743C411yescharacteristic
7C2×C8×C3⋊D3C2211yescharacteristic
8#64081C411yescharacteristic
9C2×#3708C2212yes—
10C2×#3708C2212yes—
11C32×#97C411yescharacteristic
12#63642C411yescharacteristic
13C8×C3⋊Dic3C2211yescharacteristic
14C4×C3⋊(C3⋊C8)C2211yescharacteristic
15#4708—62no—
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C2×C32×C8C2×C411yescharacteristic
18C2×C32×C8C2×C411yescharacteristic
19C32×C42C2×C411yescharacteristic
20#3752C812yes—
21#3750C812yes—
22C4×C3⋊Dic3C2×C411yescharacteristic
23C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
24C2×C3⋊(C3⋊C8)C2311yescharacteristic
25#3743—22no—
26C8×C3⋊D3—22no—
27#3708—22no—
28#3708—22no—
29#2164—91nomaximal, Sylow
30C2×ΓL(1,𝔽25)—62no—
31C2×D3×C8—62no—
32#872—62no—
33C3×#97—22no—
34#815—62no—
35C8×Dic3—62no—
36C4×C3⋊C8—62no—
37C22×C3⋊D3C2×C811yescharacteristic
38C2×C32×C4C2×C812yes—
39C2×C32×C4C22×C411yescharacteristic
40C2×C3⋊Dic3C2×C812yes—
41C2×C3⋊Dic3C2×C811yescharacteristic
42C4×C3⋊D3—21no—
43C4×C3⋊D3—21no—
44C32×C8—21no—
45C32×C8—21no—
46C3⋊(C3⋊C8)M1612yes—
47C3⋊(C3⋊C8)#4112yes—
48#405—91no—
49C4⋊C16—92no—
50C22⋊C16—92no—
51#346—91no—
52C4×C16—91no—
53C2×C4×D3—62no—
54C2×C3×C8—22no—
55C2×C3×C8—22no—
56C3×C42—22no—
57(C2×D3)⋊C4—64no—
58Dic3⋊C4—64no—
59C4×Dic3—62no—
60C2×C3⋊C8—62no—
61C2×C3⋊C8—62no—
62ΓL(1,𝔽25)—68no—
63D3×C8—68no—
64C22×C32C22×C811yescharacteristic
65C2×C3⋊D3—21no—
66C2×C3⋊D3—22no—
67C32×C4—22no—
68C32×C4#11711yescharacteristic
69C32×C4C2×M1611yescharacteristic
70C3⋊Dic3—21no—
71C3⋊Dic3—22no—
72C2×M16—91no—
73C22×C8—91no—
74#117—91no—
75C2×C16—92no—
76C2×C16—92no—
77#97—91no—
78#97#15711yescharacteristic
79C4×C8—91no—
80C4×C8—91no—
81C22×D3—62no—
82C2×C3×C4—22no—
83C2×C3×C4—24no—
84C2×Dic3—62no—
85C2×Dic3—64no—
86C4×D3—64no—
87C4×D3—64no—
88C3×C8—24no—
89C3×C8—24no—
90C3⋊C8—64no—
91C3⋊C8—64no—
92C2×C32#43111yescharacteristic
93C2×C32#50412yes—
94C3⋊D3—41no—
95C22×C4—91no—
96M16—182no—
97C2×C8—91no—
98C2×C8—91no—
99C2×C8—182no—
100C2×C8C2×#15711yescharacteristic
101C2×C8C2×#15711yescharacteristic
102C4⋊C4—92no—
103C22⋊C4—92no—
104C42—91no—
105C42C2×#15711yescharacteristic
106C16—182no—
107C16—182no—
108C22×C3—22no—
109C2×D3—64no—
110C2×D3—124no—
111C3×C4—22no—
112C3×C4—22no—
113C3×C4—44no—
114Dic3—64no—
115Dic3—124no—
116C32#216411yescharacteristic, complemented, Sylow
117C23—91no—
118C2×C4—92no—
119C2×C4—91no—
120C2×C4—181no—
121C2×C4—181no—
122C2×C4#378712yes—
123C2×C4C22×#15711yescharacteristic
124C8—21no—
125C8—21no—
126C8—92no—
127C8—92no—
128C2×C3—22no—
129C2×C3—24no—
130D3—124no—
131C22—181no—
132C22—182no—
133C22C2×#378711yescharacteristic
134C4—22no—
135C4—181no—
136C4—182no—
137C4#6428311yescharacteristic
138C4#6428611yescharacteristic
139C3—22no—
140C2—361no—
141C2#1059372511yescharacteristic
142C2#1059377212yes—
subgroupG/H
center, FrattiniC2×C4C22×#157
commutator, socleC22×C32C22×C8
FittingC32×#97C4
prime radicalC22×C3⋊D3C2×C8
cosocleC2×C3⋊(C3⋊C8)C23
hypercenter#97#157
hypocenterC32#2164
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #10590177C2semidirect
4. #10590148C2semidirect
5. C4×#3708C2semidirect
116. C32#2164semidirect

Maximal subgroups

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

subgroupindex
#105924072
#105901772
#105901762
#105901482
C4×#37082
#21649