Finite Group Databasebeta

← #11795322

Subgroups — #11795322

Order 1152.

294 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 51 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#10593755C211yesmaximal, characteristic
2#10593396C211yesmaximal, characteristic
3#10590584C212yesmaximal
4#10590052C212yesmaximal
5#10590051C211yesmaximal, characteristic
6C2×#3788C2211yescharacteristic
7C2×#3787C2211yescharacteristic
8#64101C2211yescharacteristic
9#63900C2212yes—
10C2×#3712C2212yes—
11#63779—21no—
12C4⋊#622—21no—
13#63743—21no—
14#63743—21no—
15C3×#808—22no—
16#63575—22no—
17#4861—62no—
18C2×C4×C3⋊D3C2311yescharacteristic
19C2×#624—22no—
20C2×#622—21no—
21C2×#622D411yescharacteristic
22C2×#622D411yescharacteristic
23#3788—22no—
24#3787—22no—
25C32×C4⋊C4D411yescharacteristic
26#3752—21no—
27C4⋊(C3⋊Dic3)D411yescharacteristic
28C4×C3⋊Dic3—21no—
29C3×C4⋊Dic3—22no—
30C2×C3×C3⋊C8—22no—
31#3724—22no—
32#3712—22no—
33#3712Q814yes—
34#2089—91nomaximal, Sylow
35C2×ΓL(1,𝔽25)—62no—
36#892—62no—
37D3×C4⋊C4—62no—
38C3×#106—62no—
39#818—62no—
40#808—22no—
41#807—62no—
42C22×C3⋊D3#4111yescharacteristic
43C2×C32×C4—21no—
44C2×C32×C4C2×D411yescharacteristic
45C2×C3⋊Dic3—21no—
46C2×C3⋊Dic3C2×D411yescharacteristic
47C4×C3⋊D3C2×Q812yes—
48C4×C3⋊D3#4112yes—
49C2×C3×Dic3—42no—
50#624—82no—
51#622—21no—
52#622—21no—
53#622—41no—
54C3×C3⋊C8—24no—
55#428—92no—
56C2×#107—91no—
57#424—91no—
58#343—92no—
59#341—91no—
60C2×C4×D3—62no—
61C2×C4×D3—122no—
62C2×C3×C8—62no—
63C3×C4⋊C4—22no—
64C3×C4⋊C4—62no—
65(C2×D3)⋊C4—122no—
66C4⋊Dic3—22no—
67C4⋊Dic3—62no—
68Dic3⋊C4—122no—
69C4×Dic3—122no—
70C2×C3⋊C8—22no—
71ΓL(1,𝔽25)—64no—
72ΓL(1,𝔽25)—64no—
73C22×C32#12111yescharacteristic
74C2×C3⋊D3—21no—
75C2×C3⋊D3—21no—
76C2×C3⋊D3#12512yes—
77C32×C4—41no—
78C32×C4C22⋊Q812yes—
79C3⋊Dic3—41no—
80C3⋊Dic3#12311yescharacteristic
81C3⋊Dic3C4⋊Q811yescharacteristic
82C3×Dic3—82no—
83C2×M16—92no—
84C2×M16—91no—
85C22×C8—91no—
86#117—91no—
87C2×C4⋊C4—92no—
88#107—182no—
89#107—181no—
90#107—181no—
91#106—62no—
92C4⋊C8—181no—
93C4⋊C8—181no—
94C22×D3—62no—
95C2×C3×C4—22no—
96C2×C3×C4—42no—
97C2×C3×C4—122no—
98C2×Dic3—42no—
99C2×Dic3—62no—
100C2×Dic3—122no—
101C4×D3—62no—
102C4×D3—62no—
103C4×D3—62no—
104C4×D3—62no—
105C4×D3—244no—
106C3×C8—64no—
107C3⋊C8—24no—
108C2×C32#39811yescharacteristic
109C2×C32#47211yescharacteristic
110C2×C32#47311yescharacteristic
111C3⋊D3—22no—
112C22×C4—91no—
113C22×C4—182no—
114M16—94no—
115M16—182no—
116M16—182no—
117C2×C8—62no—
118C2×C8—91no—
119C2×C8—91no—
120C2×C8—182no—
121C2×C8—181no—
122C4⋊C4—62no—
123C4⋊C4—91no—
124C4⋊C4—182no—
125C4⋊C4GO+(4,𝔽2)11yescharacteristic
126C22⋊C4—181no—
127C42—181no—
128C22×C3—22no—
129C2×D3—62no—
130C2×D3—62no—
131C2×D3—122no—
132C2×D3—122no—
133C3×C4—22no—
134C3×C4—22no—
135C3×C4—82no—
136C3×C4—242no—
137Dic3—62no—
138Dic3—62no—
139Dic3—82no—
140Dic3—242no—
141C32#208911yescharacteristic, complemented, Sylow
142C23—91no—
143C2×C4—21no—
144C2×C4—91no—
145C2×C4—92no—
146C2×C4—92no—
147C2×C4—122no—
148C2×C4—181no—
149C2×C4—722no—
150C2×C4C2×GO+(4,𝔽2)11yescharacteristic
151C8—64no—
152C8—181no—
153C8—181no—
154C8—361no—
155C2×C3—22no—
156C2×C3—22no—
157C2×C3—22no—
158D3—122no—
159D3—122no—
160C22—92no—
161C22—181no—
162C22—181no—
163C22#6424211yescharacteristic
164C4—41no—
165C4—91no—
166C4—91no—
167C4—242no—
168C4—361no—
169C4D32⋊Q812yes—
170C3—22no—
171C2—182no—
172C2#1059334011yescharacteristic
173C2#1059346811yescharacteristic
174C2#1059347911yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC2×C4×C3⋊D3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#121
prime radicalC22×C3⋊D3#41
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#2089
LCSG ▷ C2×C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
141. C32#2089semidirect

Maximal subgroups

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

subgroupindex
#105937552
#105933962
#105905842
#105900522
#105900512
#20899