Finite Group Databasebeta

← #11786217

Subgroups — #11786217

Order 1152.

466 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C2×C4×#622C211yesmaximal, characteristic
2C2×#63742C214yesmaximal
3#10591359C212yesmaximal
4C22×#622C2212yes—
5C2×C4×C3⋊Dic3C2211yescharacteristic
6C2×C3×C4⋊Dic3—22no—
7C2×#3724—22no—
8C2×#3724C2214yes—
9C4×#622C414yescomplemented
10#63742—28no—
11#4975—62no—
12C22×C32×C4D411yescharacteristic
13C22×C3⋊Dic3D411yescharacteristic
14C22×C3⋊Dic3C2311yescharacteristic
15C22×C3×Dic3—24no—
16C2×#622C2×C414yes—
17C2×#622D414yes—
18C2×#622Q814yes—
19C4×C3⋊Dic3C2×C412yes—
20C4×C3⋊Dic3Q812yes—
21C3×C4⋊Dic3—44no—
22#3724—28no—
23#3724—44no—
24#1844—91nomaximal, Sylow
25C2×C3×C4⋊C4—62no—
26C2×C4⋊Dic3—22no—
27C2×Dic3⋊C4—64no—
28C2×Dic3⋊C4—64no—
29C2×C4×Dic3—62no—
30C23×C32C2×D411yescharacteristic
31C2×C32×C4C4⋊C412yes—
32C2×C32×C4SD1614yes—
33C2×C3⋊Dic3C4⋊C412yes—
34C2×C3⋊Dic3SD1614yes—
35C2×C3⋊Dic3C22×C411yescharacteristic
36C2×C3⋊Dic3C2×D412yes—
37C2×C3⋊Dic3C2×Q812yes—
38C2×C3⋊Dic3C2×Q811yescharacteristic
39C2×C3×Dic3—44no—
40C2×C3×Dic3—44no—
41C2×C3×Dic3—44no—
42#622C4⋊C418yescomplemented
43C2×#106—94no—
44C2×C4×C8—91no—
45#384—92no—
46C22×C3×C4—22no—
47C22×C3×C4—64no—
48C22×Dic3—24no—
49C22×Dic3—62no—
50C22×Dic3—62no—
51C3×C4⋊C4—124no—
52C4⋊Dic3—44no—
53Dic3⋊C4—128no—
54Dic3⋊C4—128no—
55C4×Dic3—64no—
56C4×Dic3—64no—
57C22×C32C2×C4⋊C411yescharacteristic
58C22×C32#12711yescharacteristic
59C22×C32C4⋊Q811yescharacteristic
60C22×C32C2×SD1612yes—
61C22×C32C2×SD1612yes—
62C32×C4#10614yescomplemented
63C3⋊Dic3#10614yescomplemented
64C3⋊Dic3C2×C4⋊C412yes—
65C3⋊Dic3C4⋊Q812yes—
66C3×Dic3—84no—
67C22×C8—92no—
68C2×C4⋊C4—62no—
69C2×C4⋊C4—94no—
70C2×C4⋊C4—182no—
71C2×C42—91no—
72#106—188no—
73C4×C8—94no—
74C23×C3—22no—
75C2×C3×C4—24no—
76C2×C3×C4—24no—
77C2×C3×C4—24no—
78C2×C3×C4—124no—
79C2×C3×C4—124no—
80C2×C3×C4—124no—
81C2×Dic3—44no—
82C2×Dic3—44no—
83C2×Dic3—44no—
84C2×Dic3—64no—
85C2×Dic3—64no—
86C2×Dic3—64no—
87C2×Dic3—62no—
88C2×Dic3—64no—
89C2×Dic3—62no—
90C2×Dic3—64no—
91C2×C32#38411yescharacteristic
92C2×C32C2×#10611yescharacteristic
93C2×C32C2×#10611yescharacteristic
94C2×C32#49212yes—
95C2×C32#49812yes—
96C22×C4—64no—
97C22×C4—91no—
98C22×C4—91no—
99C22×C4GO+(4,𝔽2)11yescharacteristic
100C2×C8—94no—
101C2×C8—94no—
102C2×C8—94no—
103C4⋊C4—124no—
104C4⋊C4—188no—
105C4⋊C4—364no—
106C42—92no—
107C42—92no—
108C22×C3—22no—
109C22×C3—22no—
110C22×C3—22no—
111C22×C3—22no—
112C22×C3—22no—
113C22×C3—22no—
114C22×C3—22no—
115C3×C4—28no—
116C3×C4—244no—
117Dic3—68no—
118Dic3—64no—
119Dic3—64no—
120Dic3—84no—
121C32#184411yescharacteristic, complemented, Sylow
122C23C2×GO+(4,𝔽2)11yescharacteristic
123C2×C4—92no—
124C2×C4—94no—
125C2×C4—92no—
126C2×C4—91no—
127C2×C4—92no—
128C2×C4—91no—
129C2×C4—124no—
130C2×C4—124no—
131C2×C4—124no—
132C2×C4#377312yes—
133C2×C4#377514yes—
134C8—98no—
135C2×C3—22no—
136C2×C3—22no—
137C2×C3—22no—
138C2×C3—22no—
139C2×C3—22no—
140C2×C3—22no—
141C2×C3—22no—
142C22#6422211yescharacteristic
143C22#6422712yes—
144C22#6423111yescharacteristic
145C22C2×#377311yescharacteristic
146C22C2×#377512yes—
147C4—94no—
148C4—92no—
149C4—92no—
150C4—244no—
151C4#6374214yescomplemented
152C3—22no—
153C2#1059338412yes—
154C2#1059338711yescharacteristic
155C2#1059341311yescharacteristic
156C2#1059344212yes—
157C2C2×#6374211yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1844
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
9. C4×#622C4semidirect
42. #622C4⋊C4semidirect
62. C32×C4#106semidirect
63. C3⋊Dic3#106semidirect
121. C32#1844semidirect
151. C4#63742semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6222
C2×#637422
#105913592
#18449