Finite Group Databasebeta

← #11772135

Subgroups — #11772135

Order 1152.

184 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 34 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#10592573C211yesmaximal, characteristic
2#10590177C211yesmaximal, characteristic
3#10590173C211yesmaximal, characteristic
4#64097—21no—
5C4⋊#622—21no—
6C2×#3708—21no—
7C32×#107C411yescharacteristic
8#63645C411yescharacteristic
9C8×C3⋊Dic3C2211yescharacteristic
10#63634—21no—
11#4874—62no—
12C2×#634—41no—
13C2×#622—41no—
14C2×C32×C8C2×C411yescharacteristic
15C32×C4⋊C4—21no—
16C4⋊(C3⋊Dic3)—21no—
17#3750—41no—
18C4×C3⋊Dic3D411yescharacteristic
19C2×C3⋊(C3⋊C8)D411yescharacteristic
20#3708—41no—
21#1365—91nomaximal, Sylow
22#888—64no—
23C3×#107—22no—
24#818—62no—
25C8×Dic3—62no—
26#807—64no—
27C2×C32×C4—41no—
28C2×C32×C4C22⋊C411yescharacteristic
29C2×C3⋊Dic3—41no—
30C2×C3⋊Dic3D811yescharacteristic
31C2×C3⋊Dic3SD1611yescharacteristic
32#634—82no—
33#622—81no—
34C32×C8—21no—
35C3⋊(C3⋊C8)SD1611yescharacteristic
36C3⋊(C3⋊C8)Q1611yescharacteristic
37#500—91no—
38C4⋊C16—91no—
39#335—91no—
40C2×Dic6—124no—
41C2×C3×C8—22no—
42C3×C4⋊C4—24no—
43C4⋊Dic3—64no—
44Dic3⋊C4—124no—
45C4×Dic3—62no—
46C2×C3⋊C8—62no—
47C22×C32#10211yescharacteristic
48C32×C4—81no—
49C32×C4#10111yescharacteristic
50C32×C4#10311yescharacteristic
51C3⋊Dic3—21no—
52C3⋊Dic3—81no—
53C3⋊Dic3SD3211yescharacteristic
54C3⋊Dic3Q3211yescharacteristic
55C4⋊Q8—181no—
56C2×C16—181no—
57#107—91no—
58#107—181no—
59#107#15711yescharacteristic
60C4⋊C8—181no—
61C4×C8—91no—
62C2×C3×C4—22no—
63C2×C3×C4—44no—
64C2×Dic3—62no—
65C2×Dic3—62no—
66C2×Dic3—124no—
67Dic6—248no—
68C3×C8—24no—
69C3⋊C8—62no—
70C3⋊C8—62no—
71C2×C32#33211yescharacteristic
72C2×C32#35811yescharacteristic
73C2×C32#36111yescharacteristic
74C2×Q8—361no—
75C2×C8—91no—
76C2×C8—361no—
77C2×C8C2×#15711yescharacteristic
78C4⋊C4—21no—
79C4⋊C4—181no—
80C4⋊C4—361no—
81C42—91no—
82C16—361no—
83C22×C3—22no—
84C3×C4—22no—
85C3×C4—22no—
86C3×C4—84no—
87Dic3—62no—
88Dic3—62no—
89Dic3—64no—
90Dic3—244no—
91C32#136511yescharacteristic, complemented, Sylow
92Q8—722no—
93C2×C4—41no—
94C2×C4—91no—
95C2×C4—91no—
96C2×C4—361no—
97C2×C4C22⋊#15711yescharacteristic
98C8—21no—
99C8—91no—
100C8—91no—
101C8—721no—
102C2×C3—22no—
103C2×C3—22no—
104C2×C3—22no—
105C22#6378211yescharacteristic
106C4—81no—
107C4—91no—
108C4—91no—
109C4—181no—
110C4—721no—
111C4#6378011yescharacteristic
112C4#6378411yescharacteristic
113C3—22no—
114C2#1059016211yescharacteristic
115C2#1059019511yescharacteristic
116C2#1059019711yescharacteristic
subgroupG/H
centerC22#63782
commutatorC2×C32×C8C2×C4
FrattiniC2×C8C2×#157
FittingC32×#107C4
socle, prime radicalC22×C32#102
cosocleC8×C3⋊Dic3C22
hypercenter#107#157
hypocenterC32#1365
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
91. C32#1365semidirect

Maximal subgroups

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

subgroupindex
#105925732
#105901772
#105901732
#13659