Finite Group Databasebeta

← #11772818

Subgroups — #11772818

Order 1152.

222 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 20 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#10592785C211yesmaximal, characteristic
2#10590145C211yesmaximal, characteristic
3#10590143C211yesmaximal, characteristic
4C32×C4⋊Q8C411yescharacteristic, complemented
5C2×#3756—21no—
6C2×#3755—21no—
7#64084C2211yescharacteristic
8#63780—21no—
9#63774—21no—
10#63630C411yescharacteristic, complemented
11#5086—62no—
12C2×C32×Q8—21no—
13C2×C4⋊(C3⋊D3)D411yescharacteristic
14C2×#634D411yescharacteristic
15C22⋊#157—41no—
16#3792—41no—
17C32×C4⋊C4—41no—
18C32×C42C2×C411yescharacteristic
19#3756—42no—
20#3755—42no—
21#3752—41no—
22C2×C3⋊(C3⋊C8)—21no—
23#1407—91nomaximal, Sylow
24C3×C4⋊Q8—22no—
25C2×#216—64no—
26C2×#215—64no—
27#875—62no—
28#803—62no—
29C22×C3⋊D3—21no—
30C2×#157—81no—
31C32×Q8—41no—
32C32×Q8—41no—
33C2×C32×C4—21no—
34C2×C32×C4—41no—
35C2×C32×C4C22⋊C411yescharacteristic
36C2×C3⋊Dic3—21no—
37C4⋊(C3⋊D3)—41no—
38#634—41no—
39#622—81no—
40C3⋊(C3⋊C8)—22no—
41#497—91no—
42#355—91no—
43#354—91no—
44C2×C3×Q8—24no—
45C2×D12—62no—
46C2×Dic6—62no—
47C3×C4⋊C4—44no—
48C3×C42—22no—
49#216—128no—
50#215—128no—
51(C2×D3)⋊C4—124no—
52C2×C3⋊C8—64no—
53C22×C32#9911yescharacteristic
54C2×C3⋊D3—41no—
55C2×C3⋊D3—81no—
56#157—161no—
57C32×C4—21no—
58C32×C4—41no—
59C32×C4—81no—
60C3⋊Dic3—41no—
61C2×Q16—181no—
62C2×SD16—181no—
63C4⋊Q8#15711yescharacteristic, complemented
64#124—91no—
65#101—181no—
66#99—181no—
67#97—91no—
68C22×D3—122no—
69C3×Q8—44no—
70C3×Q8—44no—
71C2×C3×C4—24no—
72C2×C3×C4—22no—
73C2×C3×C4—44no—
74C2×Dic3—122no—
75D12—124no—
76Dic6—124no—
77C3⋊C8—68no—
78C2×C32—21no—
79C2×C32#35311yescharacteristic
80C3⋊D3—81no—
81C2×Q8—21no—
82C2×Q8—91no—
83C2×D4—91no—
84Q16—362no—
85SD16—362no—
86M16—361no—
87C2×C8—181no—
88C4⋊C4—41no—
89C22⋊C4—361no—
90C22⋊C4—361no—
91C42C2×#15711yescharacteristic
92C22×C3—22no—
93C2×D3—242no—
94C2×D3—244no—
95C3×C4—24no—
96C3×C4—44no—
97C3×C4—84no—
98Dic3—242no—
99C32#140711yescharacteristic, complemented, Sylow
100C23—181no—
101Q8—41no—
102Q8—41no—
103Q8—361no—
104D4—361no—
105C2×C4—21no—
106C2×C4—41no—
107C2×C4—181no—
108C2×C4—721no—
109C2×C4C22⋊#15711yescharacteristic
110C8—182no—
111C8—721no—
112C2×C3—24no—
113C2×C3—22no—
114D3—482no—
115C22—361no—
116C22—721no—
117C22#6378611yescharacteristic
118C4—21no—
119C4—41no—
120C4—81no—
121C4—361no—
122C4—1441no—
123C3—22no—
124C2—21no—
125C2—721no—
126C2#1059021111yescharacteristic
subgroupG/H
centerC2#10590211
commutatorC32×C42C2×C4
FrattiniC42C2×#157
FittingC32×C4⋊Q8C4
socleC2×C32#353
prime radicalC2×C4⋊(C3⋊D3)D4
cosocle#64084C22
hypercenterC4⋊Q8#157
hypocenterC32#1407
LCSG ▷ C32×C42 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. C32×C4⋊Q8C4semidirect
10. #63630C4semidirect
63. C4⋊Q8#157semidirect
99. C32#1407semidirect

Maximal subgroups

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

subgroupindex
#105927852
#105901452
#105901432
#14079