Finite Group Databasebeta

← #11777929

Subgroups — #11777929

Order 1152.

258 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 56 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#10593756C212yesmaximal
2#10592572C211yesmaximal, characteristic
3#10590170C211yesmaximal, characteristic
4#10590168C211yesmaximal, characteristic
5#10590161C212yesmaximal
6C2×#3746C411yescharacteristic
7#64096C2212yes—
8#63777—22no—
9C4⋊#622—22no—
10C4⋊#622C2212yes—
11C4×#622C2211yescharacteristic
12C4×#622C2211yescharacteristic
13C32×#107C411yescharacteristic
14C8×C3⋊Dic3C2211yescharacteristic
15#63637C412yes—
16#4873—62no—
17C2×#634C2×C412yes—
18C2×#622—22no—
19C2×#622—21no—
20C2×#622D412yes—
21C2×C32×C8C2×C411yescharacteristic
22C32×C4⋊C4C2×C412yes—
23#3750—22no—
24C4×C3⋊Dic3—22no—
25C4×C3⋊Dic3C2311yescharacteristic
26C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
27#3746—22no—
28#1593—91nomaximal, Sylow
29C2×Dic12—62no—
30#887—64no—
31C3×#107—22no—
32C8×Dic3—62no—
33#810—64no—
34C2×C32×C4—22no—
35C2×C32×C4C22×C411yescharacteristic
36C2×C3⋊Dic3—22no—
37C2×C3⋊Dic3C2×D411yescharacteristic
38C2×C3⋊Dic3#4111yescharacteristic
39#634—22no—
40#634—22no—
41#622—22no—
42#622—41no—
43#622—42no—
44C32×C8M1612yes—
45C3⋊(C3⋊C8)—21no—
46#446—92no—
47C4×Q16—91no—
48#334—91no—
49Q8⋊C8—92no—
50#322—91no—
51C2×Dic6—64no—
52C2×C3×C8—22no—
53C3×C4⋊C4—24no—
54Dic3⋊C4—124no—
55C4×Dic3—62no—
56C4×Dic3—124no—
57C2×C3⋊C8—62no—
58Dic12—68no—
59C22×C32C4×D411yescharacteristic
60C32×C4—42no—
61C32×C4C2×M1611yescharacteristic
62C32×C4#13111yescharacteristic
63C3⋊Dic3—21no—
64C3⋊Dic3—42no—
65C3⋊Dic3#13712yes—
66C2×Q16—91no—
67C4×Q8—92no—
68#107#15711yescharacteristic
69C4⋊C8—92no—
70C4⋊C8—182no—
71#103—92no—
72#97—182no—
73C4×C8—91no—
74C4×C8—91no—
75C4×C8—91no—
76C2×C3×C4—22no—
77C2×C3×C4—44no—
78C2×Dic3—62no—
79C2×Dic3—62no—
80C2×Dic3—124no—
81Dic6—68no—
82Dic6—124no—
83C3×C8—24no—
84C3⋊C8—122no—
85C2×C32#43611yescharacteristic
86C2×C32#44111yescharacteristic
87C2×C32#44411yescharacteristic
88C2×Q8—92no—
89Q16—182no—
90C2×C8—92no—
91C2×C8—91no—
92C2×C8—181no—
93C2×C8—182no—
94C2×C8C2×#15711yescharacteristic
95C4⋊C4—182no—
96C4⋊C4C2×#15712yes—
97C42—91no—
98C42—182no—
99C22×C3—22no—
100C3×C4—22no—
101C3×C4—22no—
102C3×C4—84no—
103Dic3—64no—
104Dic3—122no—
105Dic3—128no—
106C32#159311yescharacteristic, complemented, Sylow
107Q8—182no—
108Q8—182no—
109C2×C4—22no—
110C2×C4—91no—
111C2×C4—91no—
112C2×C4—182no—
113C2×C4C22×#15711yescharacteristic
114C8—182no—
115C8—181no—
116C8—362no—
117C8—361no—
118C8#378812yes—
119C2×C3—22no—
120C2×C3—22no—
121C2×C3—22no—
122C22D4×#15711yescharacteristic
123C4—42no—
124C4—92no—
125C4—181no—
126C4—362no—
127C4C2×#378811yescharacteristic
128C4#6428911yescharacteristic
129C3—22no—
130C2#1059375211yescharacteristic
131C2#1059378011yescharacteristic
132C2#1059378611yescharacteristic
subgroupG/H
centerC22D4×#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#107C4
socle, prime radicalC22×C32C4×D4
cosocleC4×C3⋊Dic3C23
hypercenter#107#157
hypocenterC32#1593
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
106. C32#1593semidirect

Maximal subgroups

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

subgroupindex
#105937562
#105925722
#105901702
#105901682
#105901612
#15939