Finite Group Databasebeta

← #11782044

Subgroups — #11782044

Order 1152.

236 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 43 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#10593835C211yesmaximal, characteristic
2#10593395C211yesmaximal, characteristic
3#10591631C212yesmaximal
4#10590041C211yesmaximal, characteristic
5#10590040C212yesmaximal
6Q8×C3⋊Dic3C2211yescharacteristic
7#63919C2212yes—
8#63779—21no—
9#63777—21no—
10C4⋊#622C2211yescharacteristic
11C4×#622C2211yescharacteristic
12#63743—21no—
13#63743—21no—
14C3×#835—22no—
15#63575—22no—
16#63572C2212yes—
17#4793—62no—
18C2×C32×Q8D411yescharacteristic
19C2×#627—22no—
20C2×#622—21no—
21C2×#622D411yescharacteristic
22C2×#622D411yescharacteristic
23C4⋊(C3⋊Dic3)—21no—
24C4⋊(C3⋊Dic3)D411yescharacteristic
25C4×C3⋊Dic3—21no—
26C4×C3⋊Dic3C2311yescharacteristic
27C3×C4⋊Dic3—22no—
28C2×C3×C3⋊C8—22no—
29#3724—22no—
30#1696—91nomaximal, Sylow
31Q8×Dic3—62no—
32#888—62no—
33C3×#103—62no—
34#835—22no—
35#818—62no—
36Dic3⋊C8—62no—
37#807—62no—
38C32×Q8—22no—
39C2×C32×C4—21no—
40C2×C32×C4C2×D411yescharacteristic
41C2×C3⋊Dic3—21no—
42C2×C3⋊Dic3C2×D411yescharacteristic
43C2×C3⋊Dic3#4111yescharacteristic
44C2×C3×Dic3—42no—
45#627—82no—
46#622—21no—
47#622—41no—
48#622Q1612yes—
49C3×C3⋊C8—42no—
50#500—91no—
51#477—92no—
52#446—91no—
53#334—91no—
54#333—92no—
55C2×C3×Q8—22no—
56C2×Dic6—122no—
57C2×C3×C8—62no—
58C3×C4⋊C4—62no—
59C4⋊Dic3—22no—
60C4⋊Dic3—62no—
61C4⋊Dic3—122no—
62Dic3⋊C4—122no—
63C4×Dic3—62no—
64C4×Dic3—122no—
65C2×C3⋊C8—22no—
66C22×C32#12111yescharacteristic
67C32×C4—41no—
68C32×C4#13712yes—
69C3⋊Dic3—21no—
70C3⋊Dic3—41no—
71C3⋊Dic3C2×Q1611yescharacteristic
72C3⋊Dic3#13711yescharacteristic
73C3×Dic3—82no—
74C4⋊Q8—92no—
75C4×Q8—91no—
76#107—182no—
77#107—181no—
78#107—181no—
79C4⋊C8—92no—
80C4⋊C8—91no—
81C4⋊C8—181no—
82#103—62no—
83#97—181no—
84C4×C8—91no—
85C3×Q8—24no—
86C3×Q8—42no—
87C2×C3×C4—22no—
88C2×C3×C4—42no—
89C2×C3×C4—122no—
90C2×Dic3—42no—
91C2×Dic3—62no—
92C2×Dic3—62no—
93C2×Dic3—122no—
94Dic6—244no—
95C3×C8—122no—
96C3⋊C8—42no—
97C2×C32#46211yescharacteristic
98C2×C32#47011yescharacteristic
99C2×C32#47211yescharacteristic
100C2×Q8—182no—
101C2×Q8GO+(4,𝔽2)11yescharacteristic
102C2×C8—62no—
103C2×C8—91no—
104C2×C8—91no—
105C2×C8—181no—
106C4⋊C4—62no—
107C4⋊C4—91no—
108C4⋊C4—181no—
109C4⋊C4—182no—
110C42—91no—
111C42—181no—
112C22×C3—22no—
113C3×C4—22no—
114C3×C4—22no—
115C3×C4—44no—
116C3×C4—242no—
117Dic3—62no—
118Dic3—62no—
119Dic3—82no—
120Dic3—122no—
121Dic3—242no—
122C32#169611yescharacteristic, complemented, Sylow
123Q8—22no—
124Q8—722no—
125C2×C4—21no—
126C2×C4—91no—
127C2×C4—91no—
128C2×C4—122no—
129C2×C4—181no—
130C2×C4C2×GO+(4,𝔽2)11yescharacteristic
131C8—92no—
132C8—122no—
133C8—181no—
134C8—361no—
135C2×C3—22no—
136C2×C3—22no—
137C2×C3—22no—
138C22#6424211yescharacteristic
139C4—41no—
140C4—91no—
141C4—91no—
142C4—181no—
143C4—242no—
144C4—361no—
145C4#6423912yes—
146C3—22no—
147C2#1059347711yescharacteristic
148C2#1059347911yescharacteristic
149C2#1059350811yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×Q8D4
socle, prime radicalC22×C32#121
hypercenterC2×Q8GO+(4,𝔽2)
hypocenterC32#1696
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
122. C32#1696semidirect

Maximal subgroups

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

subgroupindex
#105938352
#105933952
#105916312
#105900412
#105900402
#16969