Finite Group Databasebeta

← #11772589

Subgroups — #11772589

Order 1152.

316 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 40 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#10593808C212yesmaximal
2#10592828C211yesmaximal, characteristic
3C2×#3828C2211yescharacteristic
4#64283—22no—
5C2×C32×M16C411yescharacteristic
6C22×C3⋊(C3⋊C8)C411yescharacteristic
7#63788C414yes—
8#63780—22no—
9#63647—22no—
10#5129—62no—
11C22×C32×C4C2×C411yescharacteristic
12C2×#638C2×C412yes—
13#3828—41no—
14#3828—41no—
15C2×C4⋊(C3⋊D3)Q811yescharacteristic
16C2×C4×C3⋊D3D412yes—
17C2×#634D411yescharacteristic
18#3792—24no—
19#3788—42no—
20#3787—42no—
21C32×M16—41no—
22C2×C32×C8—21no—
23C2×C3⋊(C3⋊C8)—21no—
24C2×C3⋊(C3⋊C8)—41no—
25#1392—91nomaximal, Sylow
26C2×#235—62no—
27C2×C3×M16—22no—
28C22×C3⋊C8—62no—
29(C2×D3)⋊C8—68no—
30C23×C32C4211yescharacteristic
31C22×C3⋊D3C4⋊C412yes—
32C2×C32×C4—21no—
33C2×C32×C4—21no—
34C2×C32×C4C22⋊C411yescharacteristic
35C2×C32×C4C4⋊C411yescharacteristic
36#638—42no—
37C2×C3⋊Dic3C22⋊C412yes—
38C4⋊(C3⋊D3)—41no—
39C4×C3⋊D3—22no—
40C4×C3⋊D3—22no—
41#634—41no—
42#622—44no—
43C32×C8—41no—
44C3⋊(C3⋊C8)—41no—
45#413—92no—
46#408—91no—
47C22×C3×C4—22no—
48C2×#67—64no—
49#235—124no—
50#235—124no—
51C2×D12—62no—
52C2×C4×D3—64no—
53C2×Dic6—62no—
54C3×M16—44no—
55C2×C3×C8—24no—
56C2×C3⋊C8—64no—
57C2×C3⋊C8—124no—
58C22×C32—21no—
59C22×C32—41no—
60C22×C32#9511yescharacteristic
61C2×C3⋊D3—22no—
62C2×C3⋊D3—42no—
63C32×C4—21no—
64C32×C4#9911yescharacteristic
65C32×C4#9911yescharacteristic
66C3⋊Dic3—22no—
67C2×#41—91no—
68C2×M16—182no—
69C2×M16#15711yescharacteristic
70C22×C8—91no—
71#101—182no—
72#100—94no—
73C22⋊C8—182no—
74C23×C3—22no—
75C22×D3—64no—
76C2×C3×C4—24no—
77C2×C3×C4—24no—
78C2×C3×C4—22no—
79C2×C3×C4—22no—
80#67—128no—
81C2×Dic3—64no—
82D12—124no—
83C4×D3—124no—
84C4×D3—124no—
85Dic6—124no—
86C3×C8—44no—
87C3⋊C8—124no—
88C2×C32—21no—
89C2×C32—41no—
90C2×C32#34211yescharacteristic
91C3⋊D3—42no—
92#41—361no—
93#41—361no—
94C2×Q8—91no—
95C2×D4—92no—
96C2×D4—91no—
97C22×C4—92no—
98C22×C4C2×#15711yescharacteristic
99M16—41no—
100M16—184no—
101M16—362no—
102C2×C8—21no—
103C2×C8—181no—
104C2×C8—362no—
105C2×C8—361no—
106C22×C3—24no—
107C22×C3—22no—
108C22×C3—44no—
109C2×D3—124no—
110C2×D3—128no—
111C3×C4—24no—
112C3×C4—22no—
113C3×C4—22no—
114Dic3—124no—
115C32#139211yescharacteristic, complemented, Sylow
116C23—92no—
117C23C4×#15711yescharacteristic
118Q8—361no—
119D4—361no—
120D4—362no—
121C2×C4—21no—
122C2×C4—21no—
123C2×C4—92no—
124C2×C4—182no—
125C2×C4—182no—
126C2×C4C4⋊#15711yescharacteristic
127C2×C4C22⋊#15711yescharacteristic
128C8—41no—
129C8—364no—
130C8—361no—
131C2×C3—24no—
132C2×C3—22no—
133C2×C3—44no—
134D3—244no—
135C22—21no—
136C22—41no—
137C22—182no—
138C22—362no—
139C22#6378111yescharacteristic
140C4—21no—
141C4—182no—
142C4#6377411yescharacteristic
143C4#6378611yescharacteristic
144C3—22no—
145C2—21no—
146C2—41no—
147C2—362no—
148C2#1059020611yescharacteristic
subgroupG/H
centerC4#63774
commutatorC23×C32C42
FrattiniC22×C4C2×#157
FittingC2×C32×M16C4
socleC2×C32#342
prime radical, cosocleC2×#3828C22
hypercenterC2×M16#157
hypocenterC32#1392
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
115. C32#1392semidirect

Maximal subgroups

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

subgroupindex
#105938082
#105928282
#13929