Finite Group Databasebeta

← #11786113

Subgroups — #11786113

Order 1152.

326 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 66 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#10593729C211yesmaximal, characteristic
2#10593728C211yesmaximal, characteristic
3C3⋊D3×#97C211yesmaximal, characteristic
4#10590185C214yesmaximal
5C2×#3788C2212yes—
6C2×#3788C2212yes—
7C2×C8×C3⋊D3C2212yes—
8C42×C3⋊D3C2211yescharacteristic
9#63779—22no—
10C4⋊#622—22no—
11C32×#97C411yescharacteristic
12#63642C412yes—
13#63630C411yescharacteristic
14D3×#97—62no—
15C2×C4×C3⋊D3Q812yes—
16C2×C4×C3⋊D3C2311yescharacteristic
17C2×#622—22no—
18C2×#622—22no—
19#3788—24no—
20#3788—24no—
21C2×C32×C8C2×C412yes—
22C32×C42C2×C411yescharacteristic
23C4×C3⋊Dic3C2×C411yescharacteristic
24C4×C3⋊Dic3D412yes—
25C2×C3⋊(C3⋊C8)C2×C412yes—
26C8×C3⋊D3—22no—
27C8×C3⋊D3—22no—
28#1838—91nomaximal, Sylow
29C2×D3×C8—64no—
30C42×D3—62no—
31C3×#97—22no—
32#815—64no—
33#803—62no—
34C22×C3⋊D3C2×Q811yescharacteristic
35C2×C32×C4C4⋊C412yes—
36C2×C32×C4C22×C411yescharacteristic
37C2×C3⋊Dic3C4⋊C412yes—
38C2×C3⋊Dic3C2×D411yescharacteristic
39C4×C3⋊D3—42no—
40C4×C3⋊D3#4112yes—
41C4×C3⋊D3#4112yes—
42#622—42no—
43#622—42no—
44C32×C8—22no—
45C3⋊(C3⋊C8)—22no—
46#423—91no—
47#423—91no—
48C2×#97—91no—
49#341—94no—
50C2×C4×D3—62no—
51C2×C4×D3—64no—
52C2×C3×C8—24no—
53C3×C42—22no—
54C4×Dic3—62no—
55C4×Dic3—64no—
56C2×C3⋊C8—64no—
57D3×C8—68no—
58D3×C8—68no—
59C22×C32C2×C4⋊C411yescharacteristic
60C2×C3⋊D3—22no—
61C2×C3⋊D3#12512yes—
62C32×C4—22no—
63C32×C4#11712yes—
64C3⋊Dic3—22no—
65C3⋊Dic3#12411yescharacteristic
66C3⋊Dic3#12411yescharacteristic
67C2×M16—92no—
68C2×M16—92no—
69C22×C8—92no—
70C2×C42—91no—
71C4⋊C8—182no—
72C4⋊C8—182no—
73#97—92no—
74#97—91no—
75#97#15711yescharacteristic
76C22×D3—62no—
77C2×C3×C4—22no—
78C2×C3×C4—24no—
79C2×Dic3—62no—
80C2×Dic3—64no—
81C4×D3—64no—
82C4×D3—64no—
83C4×D3—128no—
84C3×C8—28no—
85C3⋊C8—68no—
86C2×C32#38211yescharacteristic
87C2×C32#43012yes—
88C3⋊D3—22no—
89C22×C4—91no—
90C22×C4—92no—
91M16—184no—
92M16—184no—
93C2×C8—92no—
94C2×C8—182no—
95C2×C8—182no—
96C2×C8—182no—
97C2×C8—182no—
98C2×C8C2×#15712yes—
99C42—91no—
100C42—92no—
101C42C2×#15711yescharacteristic
102C22×C3—22no—
103C2×D3—64no—
104C2×D3—68no—
105C3×C4—24no—
106C3×C4—44no—
107Dic3—62no—
108Dic3—62no—
109Dic3—124no—
110C32#183811yescharacteristic, complemented, Sylow
111C23—91no—
112C2×C4—91no—
113C2×C4—92no—
114C2×C4—92no—
115C2×C4—92no—
116C2×C4—362no—
117C2×C4C4⋊#15712yes—
118C2×C4C22×#15711yescharacteristic
119C8—22no—
120C8—182no—
121C8—362no—
122C8—362no—
123C2×C3—22no—
124C2×C3—24no—
125D3—68no—
126C22—92no—
127C22—182no—
128C22C2×C4⋊#15711yescharacteristic
129C4—22no—
130C4—91no—
131C4—91no—
132C4—182no—
133C4#6428612yes—
134C3—22no—
135C2—182no—
136C2#1059373611yescharacteristic
137C2#1059377612yes—
subgroupG/H
centerC22C2×C4⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#97C4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C2×Q8
cosocleC2×C4×C3⋊D3C23
hypercenter#97#157
hypocenterC32#1838
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
110. C32#1838semidirect

Maximal subgroups

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

subgroupindex
#105937292
#105937282
C3⋊D3×#972
#105901852
#18389