Finite Group Databasebeta

← #11797770

Subgroups — #11797770

Order 1152.

444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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
1Q16×C3⋊Dic3C211yesmaximal, characteristic
2C2×#63656C211yesmaximal, characteristic
3#10592572C211yesmaximal, characteristic
4C32×#358C211yesmaximal, characteristic
5#10589369C211yesmaximal, characteristic
6#10589368C211yesmaximal, characteristic
7#10589356C211yesmaximal, characteristic
8#69209—34nomaximal
9C2×C32×Q16C2211yescharacteristic
10Q8×C3⋊Dic3—21no—
11C2×#3746C2211yescharacteristic
12#64096—21no—
13C2×C32×C16C2211yescharacteristic
14C32×#107C2211yescharacteristic
15#63662—21no—
16#63656C414yescomplemented
17#63645C2211yescharacteristic
18C8×C3⋊Dic3C2211yescharacteristic
19C2×C3⋊(C3⋊C16)C2211yescharacteristic
20#63637—21no—
21Dic3×Q16—34no—
22C2×#829—34no—
23#4873—34no—
24C3×#358D314yes—
25#4503—34no—
26#4502—34no—
27#4490—34no—
28C2×C32×Q8—21no—
29C2×#634—21no—
30C32×Q16—21no—
31C32×Q16C2×C412yes—
32C2×C32×C8C2311yescharacteristic
33C32×C4⋊C4—21no—
34C4⋊(C3⋊Dic3)—21no—
35C4⋊(C3⋊Dic3)—41no—
36#3750—41no—
37C4×C3⋊Dic3—41no—
38C4×C3⋊Dic3—41no—
39C4×C3⋊Dic3D411yescharacteristic
40C2×C3⋊(C3⋊C8)D411yescharacteristic
41#3746—21no—
42#3746C2×C412yes—
43C32×C16—21no—
44C3⋊(C3⋊C16)C2×C412yes—
45#2176—91noSylow
46C2×C3×Q16C2×D314yes—
47Q8×Dic3—64no—
48C2×Dic12—34no—
49#887—64no—
50C2×C3×C16C2×D314yes—
51C3×#107C2×D314yes—
52#835—64no—
53#829—316no—
54#818—34no—
55C8×Dic3—34no—
56C2×C3⋊C16—34no—
57#810—64no—
58C32×Q8—22no—
59C32×Q8—41no—
60C2×C32×C4—41no—
61C2×C32×C4—41no—
62C2×C32×C4C2×D411yescharacteristic
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3D811yescharacteristic
66C2×C3⋊Dic3D811yescharacteristic
67#634—22no—
68#634—41no—
69C32×C8C22×C411yescharacteristic
70C32×C8#4111yescharacteristic
71C3⋊(C3⋊C8)—21no—
72C2×Q32—91no—
73C4×Q16—91no—
74C4×Q16—91no—
75#367—91no—
76#358—91no—
77#358C3⋊D311yescharacteristic
78#346—91no—
79C2×C3×Q8—24no—
80C2×Dic6—64no—
81C3×Q16—24no—
82C3×Q16C4×D318yes—
83C2×C3×C8C22×D314yes—
84C3×C4⋊C4—24no—
85C4⋊Dic3—64no—
86C4⋊Dic3—124no—
87Dic3⋊C4—124no—
88C4×Dic3—34no—
89C4×Dic3—124no—
90C4×Dic3—124no—
91C2×C3⋊C8—34no—
92Dic12—38no—
93Dic12—64no—
94C3×C16—24no—
95C3⋊C16—38no—
96C22×C32C2×D811yescharacteristic
97C32×C4—42no—
98C32×C4—81no—
99C32×C4C4×D411yescharacteristic
100C32×C4#13511yescharacteristic
101C3⋊Dic3—21no—
102C3⋊Dic3—21no—
103C3⋊Dic3—42no—
104C3⋊Dic3—81no—
105C2×Q16—91no—
106C2×Q16C2×C3⋊D311yescharacteristic
107C4×Q8—181no—
108C4×Q8—181no—
109Q32—94no—
110C2×C16—91no—
111C2×C16C2×C3⋊D311yescharacteristic
112#107—91no—
113#107C2×C3⋊D311yescharacteristic
114#103—181no—
115#103—181no—
116C4×C8—91no—
117C3×Q8—28no—
118C3×Q8—44no—
119C2×C3×C4—44no—
120C2×C3×C4—44no—
121C2×C3×C4D3×D414yes—
122C2×Dic3—34no—
123C2×Dic3—34no—
124C2×Dic3—124no—
125C2×Dic3—124no—
126Dic6—68no—
127Dic6—124no—
128C3×C8C2×C4×D314yes—
129C3×C8#23714yes—
130C3⋊C8—64no—
131C2×C32C4×D811yescharacteristic
132C2×C32#51011yescharacteristic
133C2×C32#51011yescharacteristic
134C2×Q8—21no—
135C2×Q8—181no—
136Q16—21no—
137Q16—92no—
138Q16—181no—
139Q16C4×C3⋊D312yes—
140C2×C8—91no—
141C2×C8C22×C3⋊D311yescharacteristic
142C4⋊C4—21no—
143C4⋊C4—181no—
144C4⋊C4—361no—
145C4⋊C4—361no—
146C42—91no—
147C42—361no—
148C42—361no—
149C16—21no—
150C16—92no—
151C22×C3D3×D814yes—
152C3×C4—48no—
153C3×C4—84no—
154C3×C4#67⋊C414yes—
155C3×C4#91614yes—
156Dic3—64no—
157Dic3—64no—
158Dic3—128no—
159Dic3—244no—
160C32#217611yescharacteristic, complemented, Sylow
161Q8—22no—
162Q8—41no—
163Q8—182no—
164Q8—361no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—91no—
168C2×C4—91no—
169C2×C4—361no—
170C2×C4—361no—
171C2×C4D4×C3⋊D311yescharacteristic
172C8—181no—
173C8C2×C4×C3⋊D311yescharacteristic
174C8#383011yescharacteristic
175C2×C3#475614yes—
176C2×C3#491514yes—
177C2×C3#491814yes—
178C22D8×C3⋊D311yescharacteristic
179C4—42no—
180C4—81no—
181C4—181no—
182C4—181no—
183C4—362no—
184C4—721no—
185C4#6409011yescharacteristic
186C4#6412511yescharacteristic
187C3#6920914yescomplemented
188C2#1059245511yescharacteristic
189C2#1059261411yescharacteristic
190C2#1059261711yescharacteristic
subgroupG/H
centerC22D8×C3⋊D3
commutatorC32×C8C22×C4
FrattiniC2×C8C22×C3⋊D3
FittingC32×#358C2
socle, prime radicalC22×C32C2×D8
cosocleC2×C32×C8C23
hypercenter#358C3⋊D3
hypocenterC32#2176
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
16. #63656C4semidirect
160. C32#2176semidirect
187. C3#69209semidirect

Maximal subgroups

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

subgroupindex
Q16×C3⋊Dic32
C2×#636562
#105925722
C32×#3582
#105893692
#105893682
#105893562
#692093