Finite Group Databasebeta

← #11797358

Subgroups — #11797358

Order 1152.

268 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 64 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#10592821C211yesmaximal, characteristic
2C22⋊#3708C212yesmaximal
3#10590177C212yesmaximal, complemented
4#10590175C211yesmaximal, characteristic, complemented
5#10590174C211yesmaximal, characteristic, complemented
6C2×C32×M16C411yescharacteristic
7#64135C411yescharacteristic
8C22×C3⋊(C3⋊C8)C2211yescharacteristic
9C2×#3708C2212yes—
10C2×#3708C2212yes—
11#63642C411yescharacteristic
12#63642C411yescharacteristic
13C8×C3⋊Dic3C2211yescharacteristic
14C8×C3⋊Dic3C2211yescharacteristic
15#5122—62no—
16C22×C32×C4C2×C411yescharacteristic
17C32×M16—22no—
18C2×C32×C8C2×C411yescharacteristic
19C2×C32×C8C2×C411yescharacteristic
20#3757C812yes—
21C4⋊(C3⋊Dic3)C812yes—
22C4×C3⋊Dic3C2×C411yescharacteristic
23C4×C3⋊Dic3C2×C411yescharacteristic
24C2×C3⋊(C3⋊C8)—22no—
25C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
26C2×C3⋊(C3⋊C8)C2311yescharacteristic
27#3708—22no—
28#3708—22no—
29#2164—91nomaximal, Sylow
30C2×C3×M16—22no—
31#926—62no—
32C22×C3⋊C8—62no—
33#815—62no—
34#815—62no—
35C8×Dic3—62no—
36C8×Dic3—62no—
37C23×C32C2×C811yescharacteristic
38C2×C32×C4—21no—
39C2×C32×C4—21no—
40C2×C32×C4C2×C811yescharacteristic
41C2×C32×C4C22×C411yescharacteristic
42C2×C3⋊Dic3C2×C812yes—
43C2×C3⋊Dic3C2×C812yes—
44C32×C8—21no—
45C32×C8M1612yes—
46C3⋊(C3⋊C8)—21no—
47C3⋊(C3⋊C8)#4112yes—
48#405—91no—
49C4⋊C16—92no—
50C22⋊C16—92no—
51#346—91no—
52C4×C16—91no—
53C22×C3×C4—22no—
54C3×M16—28no—
55C2×C3×C8—22no—
56C2×C3×C8—22no—
57#217—64no—
58C4⋊Dic3—64no—
59C4×Dic3—62no—
60C4×Dic3—62no—
61C2×C3⋊C8—62no—
62C2×C3⋊C8—62no—
63C2×C3⋊C8—68no—
64C22×C32—21no—
65C22×C32—22no—
66C22×C32C22×C811yescharacteristic
67C32×C4—21no—
68C32×C4#11711yescharacteristic
69C32×C4C2×M1611yescharacteristic
70C3⋊Dic3—22no—
71C3⋊Dic3—22no—
72C2×M16#15711yescharacteristic
73C22×C8—91no—
74#117—91no—
75C2×C16—92no—
76C2×C16—92no—
77#97—91no—
78#97—91no—
79C4×C8—91no—
80C4×C8—91no—
81C23×C3—22no—
82C2×C3×C4—24no—
83C2×C3×C4—24no—
84C2×C3×C4—22no—
85C2×C3×C4—22no—
86C2×Dic3—64no—
87C2×Dic3—64no—
88C3×C8—24no—
89C3×C8—24no—
90C3⋊C8—64no—
91C3⋊C8—64no—
92C2×C32—41no—
93C2×C32#43111yescharacteristic
94C2×C32#50412yes—
95C22×C4C2×#15711yescharacteristic
96M16—22no—
97C2×C8—91no—
98C2×C8—91no—
99C2×C8—182no—
100C2×C8C2×#15711yescharacteristic
101C2×C8C2×#15711yescharacteristic
102C4⋊C4—92no—
103C22⋊C4—92no—
104C42—91no—
105C42—91no—
106C16—182no—
107C16—182no—
108C22×C3—24no—
109C22×C3—22no—
110C22×C3—44no—
111C3×C4—24no—
112C3×C4—22no—
113C3×C4—22no—
114Dic3—124no—
115Dic3—124no—
116C32#216411yescharacteristic, complemented, Sylow
117C23#378711yescharacteristic
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—92no—
121C2×C4—92no—
122C2×C4#378711yescharacteristic
123C2×C4C22×#15711yescharacteristic
124C8—21no—
125C8—92no—
126C8—181no—
127C8#379212yes—
128C2×C3—22no—
129C2×C3—24no—
130C2×C3—44no—
131C22—21no—
132C22—22no—
133C22C2×#378711yescharacteristic
134C4—21no—
135C4—182no—
136C4—182no—
137C4#6428611yescharacteristic
138C4C2×#379211yescharacteristic
139C3—22no—
140C2—41no—
141C2#1059377212yes—
142C2#1059380111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#157
commutator, socleC22×C32C22×C8
FittingC2×C32×M16C4
prime radicalC23×C32C2×C8
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC2×M16#157
hypocenterC32#2164
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. #10590177C2semidirect
4. #10590175C2semidirect
5. #10590174C2semidirect
116. C32#2164semidirect

Maximal subgroups

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

subgroupindex
#105928212
C22⋊#37082
#105901772
#105901752
#105901742
#21649