Finite Group Databasebeta

← #11799622

Subgroups — #11799622

Order 1152.

408 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 117 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
1D8×C3⋊Dic3C211yesmaximal, characteristic
2#10592577C211yesmaximal, characteristic, complemented
3C32×#357C211yesmaximal, characteristic
4#10589428C211yesmaximal, characteristic
5#10589371C211yesmaximal, characteristic, complemented
6#10589367C211yesmaximal, characteristic, complemented
7#10589355C211yesmaximal, characteristic, complemented
8#69181—34nomaximal
9C2×C32×D8C2211yescharacteristic
10D4×C3⋊Dic3—21no—
11#64099—21no—
12C2×C32×C16C2211yescharacteristic
13C32×#107C2211yescharacteristic
14#63659—21no—
15#63645C2211yescharacteristic
16#63645C2211yescharacteristic
17C8×C3⋊Dic3C2211yescharacteristic
18C2×C3⋊(C3⋊C16)C2211yescharacteristic
19#63635—21no—
20Dic3×D8—34no—
21#4878—34no—
22C3×#357D314yes—
23#4562—34no—
24#4505—34no—
25Dic3⋊C16—34no—
26#4489—34no—
27C2×C32×D4—21no—
28C22×C3⋊Dic3—41no—
29C32×D8—21no—
30C32×D8Q812yes—
31C2×C32×C8C2311yescharacteristic
32C32×C4⋊C4—21no—
33#3757—41no—
34C4⋊(C3⋊Dic3)—21no—
35C4⋊(C3⋊Dic3)—21no—
36C4⋊(C3⋊Dic3)—41no—
37#3750—41no—
38C4×C3⋊Dic3D411yescharacteristic
39C2×C3⋊(C3⋊C8)D411yescharacteristic
40C32×C16—21no—
41C3⋊(C3⋊C16)—21no—
42#2228—91noSylow
43C2×C3×D8C2×D314yes—
44D4×Dic3—64no—
45#890—64no—
46C2×C3×C16C2×D314yes—
47C3×#107C2×D314yes—
48#832—64no—
49#818—34no—
50#818—34no—
51C8×Dic3—34no—
52C2×C3⋊C16—34no—
53#808—64no—
54C23×C32—41no—
55C32×D4—22no—
56C32×D4—41no—
57C2×C32×C4—41no—
58C2×C32×C4C2×D411yescharacteristic
59C2×C3⋊Dic3—41no—
60C2×C3⋊Dic3—41no—
61C2×C3⋊Dic3—82no—
62C2×C3⋊Dic3D811yescharacteristic
63C2×C3⋊Dic3D811yescharacteristic
64C32×C8C2×Q811yescharacteristic
65C32×C8#4111yescharacteristic
66C3⋊(C3⋊C8)—21no—
67#499—91no—
68C4×D8—91no—
69#367—91no—
70#366—91no—
71C4⋊C16—91no—
72#357—91no—
73#357C3⋊D311yescharacteristic
74C2×C3×D4—24no—
75C22×Dic3—124no—
76C3×D8—24no—
77C3×D8Dic618yes—
78C2×C3×C8C22×D314yes—
79C3×C4⋊C4—24no—
80#217—124no—
81C4⋊Dic3—64no—
82C4⋊Dic3—64no—
83C4⋊Dic3—124no—
84Dic3⋊C4—124no—
85C4×Dic3—34no—
86C2×C3⋊C8—34no—
87C3×C16—24no—
88C3⋊C16—64no—
89C22×C32—42no—
90C22×C32—81no—
91C22×C32—81no—
92C22×C32C2×D811yescharacteristic
93C32×C4—81no—
94C32×C4C22⋊Q811yescharacteristic
95C32×C4#13711yescharacteristic
96C3⋊Dic3—21no—
97C3⋊Dic3—21no—
98C3⋊Dic3—81no—
99C3⋊Dic3—81no—
100C2×D8C2×C3⋊D311yescharacteristic
101#125—181no—
102C4×D4—181no—
103C2×C16—91no—
104C2×C16C2×C3⋊D311yescharacteristic
105#107—91no—
106#107—91no—
107#107C2×C3⋊D311yescharacteristic
108#106—181no—
109#102—181no—
110C4×C8—91no—
111C23×C3—44no—
112C3×D4—28no—
113C3×D4—44no—
114C2×C3×C4—44no—
115C2×C3×C4D3×D414yes—
116C2×Dic3—34no—
117C2×Dic3—34no—
118C2×Dic3—124no—
119C2×Dic3—124no—
120C2×Dic3—248no—
121C3×C8C2×Dic614yes—
122C3×C8#23714yes—
123C3⋊C8—64no—
124C2×C32—82no—
125C2×C32#47411yescharacteristic
126C2×C32#50811yescharacteristic
127C2×C32#50911yescharacteristic
128C2×D4—21no—
129C22×C4—361no—
130D8—21no—
131D8#63412yes—
132C2×C8—91no—
133C2×C8C22×C3⋊D311yescharacteristic
134C4⋊C4—21no—
135C4⋊C4—181no—
136C4⋊C4—181no—
137C4⋊C4—361no—
138C4⋊C4—361no—
139C22⋊C4—361no—
140C42—91no—
141C16—21no—
142C16—181no—
143C22×C3—48no—
144C22×C3—84no—
145C22×C3—84no—
146C22×C3D3×D814yes—
147C3×C4—84no—
148C3×C4#87814yes—
149C3×C4#91514yes—
150Dic3—64no—
151Dic3—64no—
152Dic3—244no—
153Dic3—244no—
154C32#222811yescharacteristic, complemented, Sylow
155C23—41no—
156D4—22no—
157D4—41no—
158C2×C4—41no—
159C2×C4—91no—
160C2×C4—91no—
161C2×C4—361no—
162C2×C4—361no—
163C2×C4—722no—
164C2×C4D4×C3⋊D311yescharacteristic
165C8—181no—
166C8C2×#63411yescharacteristic
167C8#383011yescharacteristic
168C2×C3—88no—
169C2×C3#475914yes—
170C2×C3#491114yes—
171C2×C3#491614yes—
172C22—42no—
173C22—81no—
174C22—81no—
175C22D8×C3⋊D311yescharacteristic
176C4—81no—
177C4—181no—
178C4—181no—
179C4—721no—
180C4—721no—
181C4#6408711yescharacteristic
182C4#6412411yescharacteristic
183C3#6918114yescomplemented
184C2—82no—
185C2#1059245811yescharacteristic
186C2#1059261011yescharacteristic
187C2#1059261511yescharacteristic
subgroupG/H
centerC22D8×C3⋊D3
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#357C2
socleC22×C32C2×D8
prime radicalC2×C32×D8C22
hypercenter#357C3⋊D3
hypocenterC32#2228
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
2. #10592577C2semidirect
5. #10589371C2semidirect
6. #10589367C2semidirect
7. #10589355C2semidirect
154. C32#2228semidirect
183. C3#69181semidirect

Maximal subgroups

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

subgroupindex
D8×C3⋊Dic32
#105925772
C32×#3572
#105894282
#105893712
#105893672
#105893552
#691813