Finite Group Databasebeta

← #11771663

Subgroups — #11771663

Order 1152.

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

normal subgroups only

This group has 202 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#10592895C211yesmaximal, characteristic
2#10590178C211yesmaximal, characteristic, complemented
3#10590168C211yesmaximal, characteristic, complemented
4C32×#135C411yescharacteristic
5#64157—21no—
6C4×#622—21no—
7#63773—21no—
8#63664—21no—
9#63646C411yescharacteristic
10C8×C3⋊Dic3C2211yescharacteristic
11#5196—62no—
12C32×#41—21no—
13C2×#622—22no—
14C32×Q16C811yescharacteristic, complemented
15C32×SD16—21no—
16C32×D8C811yescharacteristic, complemented
17C2×C32×C8C2×C411yescharacteristic
18C4×C3⋊Dic3D411yescharacteristic
19#3748—21no—
20#3748—41no—
21C2×C3⋊(C3⋊C8)—41no—
22C2×C3⋊(C3⋊C8)D411yescharacteristic
23#3708—41no—
24#1336—91nomaximal, Sylow
25C3×#135—22no—
26#948—64no—
27#837—64no—
28#819—62no—
29C8×Dic3—62no—
30C32×Q8—21no—
31C32×D4—21no—
32C32×D4—41no—
33C2×C32×C4—41no—
34C2×C32×C4C22⋊C411yescharacteristic
35C2×C3⋊Dic3—21no—
36#622—42no—
37C32×C8C2×C811yescharacteristic
38C32×C8M1611yescharacteristic
39C3⋊(C3⋊C8)—41no—
40C3⋊(C3⋊C8)D811yescharacteristic
41C3⋊(C3⋊C8)SD1611yescharacteristic
42#443—91no—
43#364—91no—
44#322—91no—
45C3×#41—24no—
46C3×Q16—22no—
47C3×SD16—24no—
48C3×D8—22no—
49C2×C3×C8—22no—
50C4×Dic3—62no—
51#208—64no—
52#208—124no—
53C2×C3⋊C8—62no—
54C2×C3⋊C8—124no—
55C22×C32—41no—
56C22×C32#10411yescharacteristic
57C32×C4—41no—
58C32×C4C22⋊C811yescharacteristic
59C32×C4#10211yescharacteristic
60C3⋊Dic3—22no—
61#135#15711yescharacteristic
62#131—181no—
63M32—181no—
64#108—91no—
65#104—181no—
66C4×C8—91no—
67C4×C8—181no—
68C3×Q8—24no—
69C3×D4—24no—
70C3×D4—44no—
71C2×C3×C4—22no—
72C2×C3×C4—44no—
73C2×Dic3—122no—
74C3×C8—22no—
75C3×C8—22no—
76C3⋊C8—62no—
77C3⋊C8—62no—
78C3⋊C8—124no—
79C2×C32—21no—
80C2×C32—81no—
81C2×C32D4⋊C811yescharacteristic
82#41—21no—
83Q16#62211yescharacteristic, complemented
84SD16—21no—
85D8#62211yescharacteristic, complemented
86M16—181no—
87M16—361no—
88C2×C8—91no—
89C2×C8—182no—
90C2×C8—361no—
91C2×C8C2×#15711yescharacteristic
92C42—91no—
93C16—361no—
94C22×C3—22no—
95C22×C3—44no—
96C3×C4—22no—
97C3×C4—22no—
98C3×C4—44no—
99Dic3—124no—
100C32#133611yescharacteristic, complemented, Sylow
101Q8—21no—
102D4—21no—
103D4—41no—
104C2×C4—41no—
105C2×C4—181no—
106C2×C4C22⋊#15711yescharacteristic
107C8—91no—
108C8—91no—
109C8—362no—
110C8—361no—
111C8C2×#62211yescharacteristic
112C8#379211yescharacteristic
113C2×C3—22no—
114C2×C3—42no—
115C2×C3—84no—
116C22—41no—
117C22#6378311yescharacteristic
118C4—41no—
119C4—182no—
120C4#6378211yescharacteristic
121C4C22⋊#62211yescharacteristic
122C3—22no—
123C2—21no—
124C2—81no—
125C2D4⋊#62211yescharacteristic
subgroupG/H
centerC4#63782
commutatorC32×C8C2×C8
FrattiniC2×C8C2×#157
Fitting, prime radicalC32×#135C4
socleC2×C32D4⋊C8
cosocleC8×C3⋊Dic3C22
hypercenter#135#157
hypocenterC32#1336
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
2. #10590178C2semidirect
3. #10590168C2semidirect
14. C32×Q16C8semidirect
16. C32×D8C8semidirect
83. Q16#622semidirect
85. D8#622semidirect
100. C32#1336semidirect

Maximal subgroups

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

subgroupindex
#105928952
#105901782
#105901682
#13369