Finite Group Databasebeta

← #11772889

Subgroups — #11772889

Order 1152.

201 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 201 conjugacy classes of subgroups — too many to draw. Only its 40 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#10592781C211yesmaximal, characteristic
2C3×#4548C212yesmaximal
3#67551—32nomaximal
4C32×C4⋊Q8C2211yescharacteristic
5#64079C411yescharacteristic
6#63662—22no—
7#63630C411yescharacteristic
8C3×#836—22no—
9#5082—32no—
10#5082—61no—
11C3×#356—32no—
12#4548D312yes—
13C2×C32×Q8D412yes—
14C32×C4⋊C4—41no—
15C32×C42C2×C411yescharacteristic
16C4⋊(C3⋊Dic3)—21no—
17#3750—41no—
18C2×C3⋊(C3⋊C8)—21no—
19C3×#208—42no—
20#1413—91noSylow
21C3×C4⋊Q8—21no—
22C3×C4⋊Q8C2×D312yes—
23#870—32no—
24#870—61no—
25C3×#101—62no—
26#836—22no—
27#835—64no—
28#835—62no—
29#835—62no—
30#803—32no—
31#803—61no—
32C32×Q8—42no—
33C2×C32×C4—21no—
34C2×C32×C4—22no—
35C2×C32×C4C22⋊C411yescharacteristic
36C2×C3⋊Dic3—41no—
37C3⋊(C3⋊C8)—41no—
38C3×C3⋊C8—82no—
39#491—91no—
40#356—32no—
41C2×C3×Q8—22no—
42C2×C3×Q8D1212yes—
43C2×C3×Q8#6712yes—
44C3×M16—122no—
45C3×C4⋊C4—42no—
46C3×C4⋊C4—42no—
47C3×C42—21no—
48C3×C42C4×D312yes—
49C4⋊Dic3—62no—
50C4⋊Dic3—62no—
51Dic3⋊C4—122no—
52Dic3⋊C4—122no—
53#208—42no—
54C2×C3⋊C8—62no—
55C2×C3⋊C8—62no—
56C22×C32#9911yescharacteristic
57C32×C4—21no—
58C32×C4—41no—
59C32×C4—42no—
60C3⋊Dic3—81no—
61C4⋊Q8D3211yescharacteristic
62#125—91no—
63#103—182no—
64#101—62no—
65#97—91no—
66C3×Q8—42no—
67C3×Q8—42no—
68C3×Q8—44no—
69C2×C3×C4—22no—
70C2×C3×C4—22no—
71C2×C3×C4—22no—
72C2×C3×C4—22no—
73C2×C3×C4—21no—
74C2×C3×C4—42no—
75C2×C3×C4(C2×D3)⋊C412yes—
76C2×Dic3—122no—
77C2×Dic3—122no—
78C3×C8—242no—
79C3⋊C8—82no—
80C3⋊C8—122no—
81C3⋊C8—122no—
82C2×C32—21no—
83C2×C32#35411yescharacteristic
84C2×Q8#62612yes—
85M16—122no—
86C2×C8—181no—
87C4⋊C4—41no—
88C4⋊C4—181no—
89C4⋊C4—361no—
90C42#62411yescharacteristic
91C22×C3—21no—
92C22×C3#80612yes—
93C3×C4—22no—
94C3×C4—22no—
95C3×C4—42no—
96C3×C4—42no—
97C3×C4—42no—
98C3×C4—42no—
99C3×C4—82no—
100Dic3—242no—
101Dic3—242no—
102C32#141311yescharacteristic, complemented, Sylow
103Q8—42no—
104C2×C4—21no—
105C2×C4—22no—
106C2×C4—361no—
107C2×C4#372211yescharacteristic
108C8—242no—
109C8—361no—
110C2×C3—22no—
111C2×C3—22no—
112C2×C3—21no—
113C2×C3#447312yes—
114C22#6358111yescharacteristic
115C4—21no—
116C4—41no—
117C4—42no—
118C4—721no—
119C3—21no—
120C3#6755112yescomplemented
121C2—21no—
122C2#1058918111yescharacteristic
subgroupG/H
centerC2#10589181
commutatorC32×C42C2×C4
Frattini, hypercenterC4⋊Q8D32
Fitting, cosocleC32×C4⋊Q8C22
socleC2×C32#354
prime radicalC22×C32#99
hypocenterC32#1413
LCSG ▷ C32×C42 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
102. C32#1413semidirect
120. C3#67551semidirect

Maximal subgroups

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

subgroupindex
#105927812
C3×#45482
#675513