Finite Group Databasebeta

← #11771874

Subgroups — #11771874

Order 1152.

230 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 32 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#10592586C211yesmaximal, characteristic
2#10590182C211yesmaximal, characteristic
3#10590176C211yesmaximal, characteristic
4C2×C4⋊#157—21no—
5C2×#3746C411yescharacteristic, complemented
6C2×C8×C3⋊D3C2211yescharacteristic
7#64106—21no—
8C2×#3708—21no—
9C32×#107C411yescharacteristic, complemented
10#63637—21no—
11#4887—62no—
12C22×#157—41no—
13C2×C4×C3⋊D3D411yescharacteristic
14C2×#634—21no—
15C4⋊#157—22no—
16C4⋊#157—41no—
17C2×C32×C8C2×C411yescharacteristic
18C32×C4⋊C4—21no—
19#3752—41no—
20C4⋊(C3⋊Dic3)—41no—
21C2×C3⋊(C3⋊C8)D411yescharacteristic
22#3746—41no—
23C8×C3⋊D3—41no—
24#3708—41no—
25#1348—91nomaximal, Sylow
26C2×Dic12—62no—
27C2×D3×C8—62no—
28#897—64no—
29C3×#107—22no—
30#810—64no—
31C22×C3⋊D3D811yescharacteristic
32C2×#157—42no—
33C2×#157—81no—
34C2×#157—81no—
35C2×C32×C4—41no—
36C2×C32×C4C22⋊C411yescharacteristic
37C2×C3⋊Dic3—41no—
38C2×C3⋊Dic3SD1611yescharacteristic
39C4×C3⋊D3—21no—
40C4×C3⋊D3—21no—
41#634—41no—
42#634—41no—
43C32×C8—21no—
44C3⋊(C3⋊C8)—21no—
45#467—91no—
46C22⋊C16—91no—
47#340—91no—
48C2×C4×D3—62no—
49C2×Dic6—64no—
50C2×C3×C8—22no—
51C3×C4⋊C4—24no—
52(C2×D3)⋊C4—124no—
53C4⋊Dic3—124no—
54C2×C3⋊C8—62no—
55Dic12—124no—
56D3×C8—124no—
57C22×C32#10211yescharacteristic
58C2×C3⋊D3—21no—
59C2×C3⋊D3—21no—
60C2×C3⋊D3SD3211yescharacteristic
61C2×C3⋊D3Q3211yescharacteristic
62#157—82no—
63C32×C4—81no—
64C32×C4#9911yescharacteristic
65C32×C4#10411yescharacteristic
66C3⋊Dic3—21no—
67C3⋊Dic3—81no—
68C2×Q16—91no—
69C22×C8—91no—
70C22⋊Q8—181no—
71C2×C4⋊C4—181no—
72C2×C16—181no—
73#107#15711yescharacteristic, complemented
74#103—181no—
75C22×D3—62no—
76C2×C3×C4—22no—
77C2×C3×C4—44no—
78C2×Dic3—62no—
79C2×Dic3—124no—
80C4×D3—122no—
81C4×D3—122no—
82Dic6—124no—
83Dic6—124no—
84C3×C8—24no—
85C3⋊C8—122no—
86C2×C32#32711yescharacteristic
87C2×C32#35811yescharacteristic
88C2×C32#36011yescharacteristic
89C3⋊D3—21no—
90C3⋊D3—21no—
91C2×Q8—181no—
92C22×C4—91no—
93C22×C4—361no—
94Q16—361no—
95C2×C8—91no—
96C2×C8—361no—
97C2×C8C2×#15711yescharacteristic
98C4⋊C4—21no—
99C4⋊C4—182no—
100C4⋊C4—361no—
101C4⋊C4—361no—
102C22⋊C4—361no—
103C16—361no—
104C22×C3—22no—
105C2×D3—62no—
106C2×D3—62no—
107C2×D3—122no—
108C2×D3—122no—
109C3×C4—22no—
110C3×C4—22no—
111C3×C4—84no—
112Dic3—122no—
113Dic3—244no—
114C32#134811yescharacteristic, complemented, Sylow
115C23—91no—
116Q8—361no—
117Q8—361no—
118C2×C4—41no—
119C2×C4—91no—
120C2×C4—181no—
121C2×C4—181no—
122C2×C4—362no—
123C2×C4—361no—
124C2×C4—721no—
125C2×C4—721no—
126C2×C4C22⋊#15711yescharacteristic
127C8—21no—
128C8—181no—
129C2×C3—22no—
130C2×C3—22no—
131C2×C3—22no—
132D3—122no—
133D3—122no—
134C22—91no—
135C22—91no—
136C22—181no—
137C22—181no—
138C22#6378211yescharacteristic
139C4—81no—
140C4—181no—
141C4—722no—
142C4—721no—
143C4#6377411yescharacteristic
144C4#6378511yescharacteristic
145C3—22no—
146C2—181no—
147C2—181no—
148C2#1059015711yescharacteristic
149C2#1059019211yescharacteristic
150C2#1059019711yescharacteristic
subgroupG/H
centerC22#63782
commutatorC2×C32×C8C2×C4
FrattiniC2×C8C2×#157
FittingC32×#107C4
socleC22×C32#102
prime radicalC22×C3⋊D3D8
cosocleC2×C8×C3⋊D3C22
hypercenter#107#157
hypocenterC32#1348
LCSG ▷ C2×C32×C8 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
5. C2×#3746C4semidirect
9. C32×#107C4semidirect
73. #107#157semidirect
114. C32#1348semidirect

Maximal subgroups

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

subgroupindex
#105925862
#105901822
#105901762
#13489