Finite Group Databasebeta

← #11797901

Subgroups — #11797901

Order 1152.

426 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C32×#441C211yesmaximal, characteristic, complemented
2#10592878C211yesmaximal, characteristic
3#10592416C211yesmaximal, characteristic
4#10589431C211yesmaximal, characteristic, complemented
5#10589354C211yesmaximal, characteristic
6#10589353C211yesmaximal, characteristic, complemented
7#10589332C211yesmaximal, characteristic, complemented
8#70917—34nomaximal
9C2×C32×Q16C2211yescharacteristic
10C32×C4×Q8—21no—
11#64113C2211yescharacteristic
12#64110—21no—
13C32×#106C2211yescharacteristic
14C32×#103—21no—
15C32×#97C2211yescharacteristic
16#63656C412yescomplemented
17#63655C412yescomplemented
18#63646C2211yescharacteristic
19#63639C2211yescharacteristic
20#63639C2211yescharacteristic
21#63632—21no—
22C3×#441D314yescomplemented
23#5179—34no—
24#4717—34no—
25#4565—34no—
26#4488—34no—
27#4487—34no—
28#4466—34no—
29C2×C32×Q8—21no—
30#3828—21no—
31C32×Q16—21no—
32C32×Q16C2×C412yes—
33C2×C32×C8D411yescharacteristic
34C2×C32×C8C2311yescharacteristic
35C32×C4⋊C4—21no—
36C32×C4⋊C4—41no—
37C32×C42—41no—
38C32×C42D411yescharacteristic
39#3748—21no—
40#3746C2×C411yescharacteristic
41#3745C2×C411yescharacteristic
42#3744—21no—
43#3743—41no—
44C8×C3⋊D3—41no—
45C3⋊(C3⋊C16)—21no—
46C3⋊(C3⋊C16)C2×C412yes—
47#2180—91noSylow
48C2×C3×Q16C2×D314yes—
49C3×C4×Q8—24no—
50#904—34no—
51#901—64no—
52C3×#106C2×D314yes—
53C3×#103—24no—
54C3×#97C2×D314yes—
55#829—38no—
56#828—38no—
57#819—34no—
58#812—34no—
59#812—34no—
60#805—64no—
61C32×Q8—22no—
62C32×Q8—41no—
63C2×C32×C4—21no—
64C2×C32×C4—41no—
65C2×C32×C4—41no—
66C2×C32×C4C2×D411yescharacteristic
67#638—41no—
68C4⋊(C3⋊D3)—21no—
69C4×C3⋊D3—41no—
70#634—21no—
71C32×C8—21no—
72C32×C8C22×C411yescharacteristic
73C32×C8#4111yescharacteristic
74C3⋊(C3⋊C8)—41no—
75#510—91no—
76#444—91no—
77#441C3⋊D311yescharacteristic, complemented
78#365—91no—
79#362—91no—
80#360—91no—
81#347—91no—
82C2×C3×Q8—24no—
83#235—64no—
84C3×Q16—24no—
85C3×Q16C4×D318yes—
86C2×C3×C8#6714yes—
87C2×C3×C8C22×D314yes—
88C3×C4⋊C4—24no—
89C3×C4⋊C4—44no—
90C3×C42—44no—
91C3×C42#6714yes—
92#208—64no—
93Dic12—34no—
94D24—34no—
95#204—64no—
96ΓL(1,𝔽25)—124no—
97D3×C8—124no—
98C3⋊C16—38no—
99C3⋊C16—64no—
100C22×C32AGL(1,ℤ/8)11yescharacteristic
101C2×C3⋊D3—41no—
102C32×C4—41no—
103C32×C4—42no—
104C32×C4—81no—
105C32×C4C4×D411yescharacteristic
106C32×C4AGL(1,ℤ/8)11yescharacteristic
107C3⋊Dic3—41no—
108#135—91no—
109C2×Q16C2×C3⋊D311yescharacteristic
110#131—181no—
111C4×Q8—21no—
112Q32—92no—
113SD32—92no—
114M32—91no—
115M32—91no—
116#108—91no—
117#106C2×C3⋊D311yescharacteristic
118#104—181no—
119#103—21no—
120#97C2×C3⋊D311yescharacteristic
121C3×Q8—28no—
122C3×Q8—44no—
123C2×C3×C4—24no—
124C2×C3×C4—44no—
125C2×C3×C4—44no—
126C2×C3×C4C2×#6714yes—
127#67—124no—
128D12—64no—
129C4×D3—124no—
130Dic6—64no—
131C3×C8—24no—
132C3×C8C2×C4×D314yes—
133C3×C8#23514yes—
134C3⋊C8—124no—
135C2×C32—21no—
136C2×C32#44211yescharacteristic
137C3⋊D3—81no—
138#41—181no—
139C2×Q8—21no—
140Q16—21no—
141Q16—91no—
142Q16C4×C3⋊D312yes—
143SD16—181no—
144D8—91no—
145M16—181no—
146M16—361no—
147C2×C8—361no—
148C2×C8#63811yescharacteristic
149C2×C8C22×C3⋊D311yescharacteristic
150C4⋊C4—21no—
151C4⋊C4—41no—
152C42—41no—
153C42#63811yescharacteristic
154C16—92no—
155C16—181no—
156C22×C3#93214yes—
157C2×D3—124no—
158C3×C4—44no—
159C3×C4—48no—
160C3×C4—84no—
161C3×C4C4×#6714yes—
162C3×C4#94914yes—
163Dic3—124no—
164C32#218011yescharacteristic, complemented, Sylow
165Q8—22no—
166Q8—41no—
167Q8—181no—
168D4—181no—
169D4—361no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—361no—
174C2×C4C2×#63811yescharacteristic
175C8—21no—
176C8—361no—
177C8C2×C4×C3⋊D311yescharacteristic
178C8#382811yescharacteristic
179C2×C3—24no—
180C2×C3#501414yes—
181D3—244no—
182C22—361no—
183C22#6414111yescharacteristic
184C4—41no—
185C4—42no—
186C4—81no—
187C4—361no—
188C4C4×#63811yescharacteristic
189C4#6415811yescharacteristic
190C3#7091714yescomplemented
191C2—21no—
192C2—721no—
193C2#1059271311yescharacteristic
subgroupG/H
centerC2#10592713
commutatorC32×C8C22×C4
FrattiniC2×C8C22×C3⋊D3
FittingC32×#441C2
socleC2×C32#442
prime radical#64113C22
cosocleC2×C32×C8C23
hypercenter#441C3⋊D3
hypocenterC32#2180
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #441

Complements

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

NH ≅ G/Ntype
1. C32×#441C2semidirect
4. #10589431C2semidirect
6. #10589353C2semidirect
7. #10589332C2semidirect
16. #63656C4semidirect
17. #63655C4semidirect
22. C3×#441D3semidirect
77. #441C3⋊D3semidirect
164. C32#2180semidirect
190. C3#70917semidirect

Maximal subgroups

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

subgroupindex
C32×#4412
#105928782
#105924162
#105894312
#105893542
#105893532
#105893322
#709173