Finite Group Databasebeta

← #11799734

Subgroups — #11799734

Order 1152.

360 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 105 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#10592895C211yesmaximal, characteristic
2#10592557C211yesmaximal, characteristic, complemented
3C32×#360C211yesmaximal, characteristic
4#10589432C211yesmaximal, characteristic
5#10589379C211yesmaximal, characteristic, complemented
6#10589377C211yesmaximal, characteristic, complemented
7#10589353C211yesmaximal, characteristic, complemented
8#69247—34nomaximal
9C32×#135C2211yescharacteristic
10#64157—21no—
11#64099—21no—
12C32×M32C2211yescharacteristic
13C32×#106C2211yescharacteristic
14#63664—21no—
15#63646C2211yescharacteristic
16#63644C2211yescharacteristic
17C8×C3⋊Dic3C2211yescharacteristic
18#63639C2211yescharacteristic
19#63634—21no—
20#5196—34no—
21#4858—34no—
22C3×#360D314yes—
23#4566—34no—
24#4513—34no—
25#4511—34no—
26#4487—34no—
27C32×#41—21no—
28C32×Q16Q811yescharacteristic
29C32×SD16—21no—
30C32×D8Q811yescharacteristic
31C2×C32×C8C2311yescharacteristic
32C32×C4⋊C4—21no—
33C4⋊(C3⋊Dic3)—21no—
34C4⋊(C3⋊Dic3)—41no—
35#3750—41no—
36C4×C3⋊Dic3D411yescharacteristic
37#3748—21no—
38#3748—41no—
39C2×C3⋊(C3⋊C8)—41no—
40C2×C3⋊(C3⋊C8)D411yescharacteristic
41C32×C16—21no—
42C3⋊(C3⋊C16)—21no—
43#2231—91noSylow
44C3×#135C2×D314yes—
45#948—64no—
46#890—64no—
47C3×M32C2×D314yes—
48C3×#106C2×D314yes—
49#837—64no—
50#819—34no—
51#817—34no—
52C8×Dic3—34no—
53#812—34no—
54#807—64no—
55C32×Q8—21no—
56C32×D4—21no—
57C32×D4—41no—
58C2×C32×C4—41no—
59C2×C32×C4—41no—
60C2×C32×C4C2×D411yescharacteristic
61C2×C3⋊Dic3—21no—
62C2×C3⋊Dic3—41no—
63C32×C8C2×Q811yescharacteristic
64C32×C8#4111yescharacteristic
65C3⋊(C3⋊C8)—41no—
66C3⋊(C3⋊C8)SD1611yescharacteristic
67C3⋊(C3⋊C8)SD1611yescharacteristic
68#499—91no—
69#443—91no—
70#365—91no—
71#365—91no—
72#364—91no—
73#360—91no—
74#360C3⋊D311yescharacteristic
75C3×#41—24no—
76C3×Q16Dic614yes—
77C3×SD16—24no—
78C3×D8Dic614yes—
79C2×C3×C8C22×D314yes—
80C3×C4⋊C4—24no—
81C4⋊Dic3—64no—
82C4⋊Dic3—124no—
83Dic3⋊C4—124no—
84C4×Dic3—34no—
85#208—64no—
86#208—124no—
87C2×C3⋊C8—34no—
88C2×C3⋊C8—124no—
89C3×C16—24no—
90C3⋊C16—64no—
91C22×C32—41no—
92C22×C32AGL(1,ℤ/8)11yescharacteristic
93C32×C4—41no—
94C32×C4—81no—
95C32×C4C22⋊Q811yescharacteristic
96C32×C4C2×SD1611yescharacteristic
97C3⋊Dic3—41no—
98C3⋊Dic3—81no—
99#135C2×C3⋊D311yescharacteristic
100#131—181no—
101#125—181no—
102M32—91no—
103M32C2×C3⋊D311yescharacteristic
104#108—91no—
105#107—181no—
106#106—91no—
107#106C2×C3⋊D311yescharacteristic
108#104—181no—
109C4×C8—91no—
110C3×Q8—24no—
111C3×D4—24no—
112C3×D4—44no—
113C2×C3×C4—44no—
114C2×C3×C4—44no—
115C2×C3×C4D3×D414yes—
116C2×Dic3—64no—
117C2×Dic3—124no—
118C3×C8C2×Dic614yes—
119C3×C8#23714yes—
120C3⋊C8—34no—
121C3⋊C8—34no—
122C3⋊C8—124no—
123C2×C32—21no—
124C2×C32—81no—
125C2×C32#47611yescharacteristic
126#41—21no—
127Q16#63411yescharacteristic
128SD16—21no—
129D8#63411yescharacteristic
130M16—181no—
131M16—361no—
132C2×C8—91no—
133C2×C8—361no—
134C2×C8C22×C3⋊D311yescharacteristic
135C4⋊C4—21no—
136C4⋊C4—181no—
137C4⋊C4—361no—
138C4⋊C4—361no—
139C42—91no—
140C16—21no—
141C16—181no—
142C22×C3—44no—
143C22×C3#91114yes—
144C3×C4—44no—
145C3×C4—84no—
146C3×C4#87814yes—
147C3×C4D3×SD1614yes—
148Dic3—124no—
149Dic3—244no—
150C32#223111yescharacteristic, complemented, Sylow
151Q8—21no—
152D4—21no—
153D4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—181no—
157C2×C4—361no—
158C2×C4D4×C3⋊D311yescharacteristic
159C8—91no—
160C8—91no—
161C8—361no—
162C8C2×#63411yescharacteristic
163C8#383011yescharacteristic
164C2×C3—24no—
165C2×C3—84no—
166C2×C3#476114yes—
167C22—41no—
168C22#6412011yescharacteristic
169C4—41no—
170C4—81no—
171C4—361no—
172C4—721no—
173C4#6408711yescharacteristic
174C4SD16×C3⋊D311yescharacteristic
175C3#6924714yescomplemented
176C2—21no—
177C2—81no—
178C2#1059246011yescharacteristic
subgroupG/H
centerC2#10592460
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#360C2
socleC2×C32#476
prime radicalC32×#135C22
hypercenter#360C3⋊D3
hypocenterC32#2231
LCSG ▷ C2×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
2. #10592557C2semidirect
5. #10589379C2semidirect
6. #10589377C2semidirect
7. #10589353C2semidirect
150. C32#2231semidirect
175. C3#69247semidirect

Maximal subgroups

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

subgroupindex
#105928952
#105925572
C32×#3602
#105894322
#105893792
#105893772
#105893532
#692473