Finite Group Databasebeta

← #11797898

Subgroups — #11797898

Order 1152.

426 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 111 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#10592896C211yesmaximal, characteristic
2#10592894C211yesmaximal, characteristic
3#10592552C211yesmaximal, characteristic, complemented
4C32×#360C211yesmaximal, characteristic
5#10589383C211yesmaximal, characteristic, complemented
6#10589378C211yesmaximal, characteristic, complemented
7#10589353C211yesmaximal, characteristic, complemented
8#69248—34nomaximal
9C32×#135C2211yescharacteristic
10#64157—21no—
11C2×#3746C2211yescharacteristic
12#64096—21no—
13C32×M32C2211yescharacteristic
14C32×#106C2211yescharacteristic
15#63664—21no—
16#63656C412yescomplemented
17#63654C412yescomplemented
18#63646C2211yescharacteristic
19#63642C2211yescharacteristic
20#63639C2211yescharacteristic
21#63637—21no—
22#5197—34no—
23#5195—34no—
24#4853—34no—
25C3×#360D314yes—
26#4517—34no—
27#4512—34no—
28#4487—34no—
29C32×#41—21no—
30C2×#634—21no—
31C32×Q16C2×C411yescharacteristic
32C32×SD16—21no—
33C32×D8C2×C411yescharacteristic
34C2×C32×C8C2311yescharacteristic
35C32×C4⋊C4—21no—
36#3750—41no—
37C4×C3⋊Dic3—41no—
38C4×C3⋊Dic3D411yescharacteristic
39#3748—21no—
40#3748—41no—
41C2×C3⋊(C3⋊C8)—41no—
42C2×C3⋊(C3⋊C8)D411yescharacteristic
43#3746—21no—
44#3746C2×C412yes—
45C32×C16—21no—
46C3⋊(C3⋊C16)C2×C412yes—
47#2180—91noSylow
48C3×#135C2×D314yes—
49#948—64no—
50C2×Dic12—34no—
51#887—64no—
52C3×M32C2×D314yes—
53C3×#106C2×D314yes—
54#837—64no—
55#829—38no—
56#827—38no—
57#819—34no—
58#815—34no—
59#812—34no—
60#810—64no—
61C32×Q8—21no—
62C32×D4—21no—
63C32×D4—41no—
64C2×C32×C4—41no—
65C2×C32×C4—41no—
66C2×C32×C4C2×D411yescharacteristic
67C2×C3⋊Dic3—21no—
68C2×C3⋊Dic3—41no—
69#634—22no—
70#634—41no—
71C32×C8C22×C411yescharacteristic
72C32×C8#4111yescharacteristic
73C3⋊(C3⋊C8)—21no—
74C3⋊(C3⋊C8)—41no—
75#510—91no—
76#444—91no—
77#441—91no—
78#365—91no—
79#362—91no—
80#360C3⋊D311yescharacteristic
81#347—91no—
82C3×#41—24no—
83C2×Dic6—64no—
84C3×Q16C4×D314yes—
85C3×SD16—24no—
86C3×D8C4×D314yes—
87C2×C3×C8C22×D314yes—
88C3×C4⋊C4—24no—
89Dic3⋊C4—124no—
90C4×Dic3—34no—
91C4×Dic3—124no—
92#208—64no—
93#208—124no—
94C2×C3⋊C8—34no—
95C2×C3⋊C8—124no—
96Dic12—38no—
97Dic12—64no—
98C3×C16—24no—
99C3⋊C16—38no—
100C22×C32—41no—
101C22×C32AGL(1,ℤ/8)11yescharacteristic
102C32×C4—41no—
103C32×C4—81no—
104C32×C4C4×D411yescharacteristic
105C32×C4AGL(1,ℤ/8)11yescharacteristic
106C3⋊Dic3—41no—
107C3⋊Dic3—42no—
108#135C2×C3⋊D311yescharacteristic
109C2×Q16—91no—
110#131—181no—
111C4×Q8—181no—
112Q32—92no—
113SD32—92no—
114M32—91no—
115M32C2×C3⋊D311yescharacteristic
116#108—91no—
117#106C2×C3⋊D311yescharacteristic
118#104—181no—
119#103—181no—
120#97—91no—
121C3×Q8—24no—
122C3×D4—24no—
123C3×D4—44no—
124C2×C3×C4—44no—
125C2×C3×C4—44no—
126C2×C3×C4D3×D414yes—
127C2×Dic3—64no—
128C2×Dic3—124no—
129Dic6—68no—
130Dic6—124no—
131C3×C8C2×C4×D314yes—
132C3×C8#23714yes—
133C3⋊C8—64no—
134C3⋊C8—124no—
135C2×C32—21no—
136C2×C32—81no—
137C2×C32#44211yescharacteristic
138#41—21no—
139C2×Q8—181no—
140Q16—92no—
141Q16—181no—
142Q16C4×C3⋊D311yescharacteristic
143SD16—21no—
144D8C4×C3⋊D311yescharacteristic
145M16—181no—
146M16—361no—
147C2×C8—91no—
148C2×C8—361no—
149C2×C8C22×C3⋊D311yescharacteristic
150C4⋊C4—21no—
151C4⋊C4—361no—
152C42—91no—
153C42—361no—
154C16—21no—
155C16—92no—
156C22×C3—44no—
157C22×C3#91114yes—
158C3×C4—44no—
159C3×C4—84no—
160C3×C4#67⋊C414yes—
161C3×C4#91414yes—
162Dic3—124no—
163Dic3—128no—
164C32#218011yescharacteristic, complemented, Sylow
165Q8—21no—
166Q8—182no—
167Q8—361no—
168D4—21no—
169D4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—181no—
173C2×C4—361no—
174C2×C4D4×C3⋊D311yescharacteristic
175C8—181no—
176C8—361no—
177C8C2×C4×C3⋊D311yescharacteristic
178C8#383011yescharacteristic
179C2×C3—24no—
180C2×C3—84no—
181C2×C3#478514yes—
182C22—41no—
183C22#6412011yescharacteristic
184C4—41no—
185C4—81no—
186C4—361no—
187C4—362no—
188C4#6409011yescharacteristic
189C4#6412311yescharacteristic
190C3#6924814yescomplemented
191C2—21no—
192C2—81no—
193C2#1059248411yescharacteristic
subgroupG/H
centerC2#10592484
commutatorC32×C8C22×C4
FrattiniC2×C8C22×C3⋊D3
FittingC32×#360C2
socleC2×C32#442
prime radicalC32×#135C22
cosocleC2×C32×C8C23
hypercenter#360C3⋊D3
hypocenterC32#2180
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
3. #10592552C2semidirect
5. #10589383C2semidirect
6. #10589378C2semidirect
7. #10589353C2semidirect
16. #63656C4semidirect
17. #63654C4semidirect
164. C32#2180semidirect
190. C3#69248semidirect

Maximal subgroups

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

subgroupindex
#105928962
#105928942
#105925522
C32×#3602
#105893832
#105893782
#105893532
#692483