Finite Group Databasebeta

← #11874897

Subgroups — #11874897

Order 1152.

714 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 714 conjugacy classes of subgroups — too many to draw. Only its 147 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#10593909C212yesmaximal
2C4×#3787C211yesmaximal, characteristic
3#10593387C214yesmaximal
4#10593384C218yesmaximal, complemented
5C2×#3797—22no—
6C2×#3787C2212yes—
7C42×C3⋊D3C2211yescharacteristic
8C3×#869—22no—
9#63919—22no—
10#63919C2214yes—
11#63900—22no—
12#63900C2214yes—
13#63873C2214yes—
14C4×#622C2214yes—
15#63742C22116yes—
16D3×C4⋊Q8—62no—
17C2×C4×C3⋊D3D412yes—
18C2×C4×C3⋊D3C2311yescharacteristic
19C2×C3×Dic6—24no—
20C2×#627—24no—
21C2×#624—24no—
22#3797—48no—
23C2×#622C2314yes—
24#3787Q818yescomplemented
25C32×C42D411yescharacteristic
26C4×C3⋊Dic3D411yescharacteristic
27C4×C3⋊Dic3C2312yes—
28C3×C4⋊Dic3—24no—
29C3×C4⋊Dic3—24no—
30#3724—24no—
31#3724C2318yes—
32C2×#498—91nomaximal, Sylow
33C2×D3×Q8—64no—
34C3×C4⋊Q8—62no—
35#944—64no—
36D3×C4⋊C4—64no—
37D3×C4⋊C4—64no—
38#888—64no—
39#888—64no—
40C42×D3—62no—
41#869—22no—
42C22×C3⋊D3C2×D411yescharacteristic
43C2×C32×C4C2×D411yescharacteristic
44C2×C32×C4C2×D412yes—
45C2×C3⋊Dic3C2×D412yes—
46C2×C3⋊Dic3C2411yescharacteristic
47C4×C3⋊D3SD1618yes—
48C4×C3⋊D3C2×Q814yes—
49C2×C3×Dic3—28no—
50C3×Dic6—48no—
51#627—48no—
52#624—48no—
53#622C2×Q818yescomplemented
54C2×C4⋊Q8—92no—
55#498—98no—
56C2×#106—94no—
57C2×C4×C8—91no—
58C2×C3×Q8—64no—
59D3×Q8—1216no—
60C2×C4×D3—62no—
61C2×C4×D3—62no—
62C2×C4×D3—62no—
63C2×C4×D3—68no—
64C2×Dic6—24no—
65C2×Dic6—68no—
66C3×C4⋊C4—64no—
67C3×C4⋊C4—64no—
68C3×C42—22no—
69C4⋊Dic3—24no—
70C4⋊Dic3—24no—
71Dic3⋊C4—68no—
72Dic3⋊C4—68no—
73C4×Dic3—62no—
74C4×Dic3—62no—
75C4×Dic3—62no—
76C22×C32C22×D411yescharacteristic
77C2×C3⋊D3C4⋊Q812yes—
78C2×C3⋊D3C2×SD1614yes—
79C32×C4C4⋊Q812yes—
80C32×C4C2×SD1614yes—
81C3⋊Dic3C2×SD1614yes—
82C3⋊Dic3C22×Q812yes—
83C3×Dic3—48no—
84C22×Q8—182no—
85C22×C8—92no—
86C4⋊Q8—62no—
87C4⋊Q8—94no—
88C4⋊Q8—94no—
89C4⋊Q8—182no—
90C2×C4⋊C4—94no—
91C2×C4⋊C4—182no—
92C2×C42—91no—
93#106—916no—
94C4×C8—94no—
95C22×D3—62no—
96C3×Q8—128no—
97C2×C3×C4—22no—
98C2×C3×C4—22no—
99C2×C3×C4—22no—
100C2×C3×C4—68no—
101C2×Dic3—28no—
102C2×Dic3—62no—
103C2×Dic3—62no—
104C2×Dic3—62no—
105C4×D3—68no—
106C4×D3—68no—
107C4×D3—68no—
108C4×D3—1216no—
109Dic6—48no—
110Dic6—1216no—
111C2×C32C2×C4⋊Q811yescharacteristic
112C2×C32C22×SD1612yes—
113C3⋊D3#49814yescomplemented
114C2×Q8—64no—
115C2×Q8—184no—
116C2×Q8—368no—
117C22×C4—91no—
118C22×C4—92no—
119C22×C4—184no—
120C2×C8—94no—
121C2×C8—98no—
122C4⋊C4—64no—
123C4⋊C4—64no—
124C4⋊C4—98no—
125C4⋊C4—184no—
126C42—92no—
127C42—91no—
128C42GO+(4,𝔽2)11yescharacteristic
129C22×C3—22no—
130C2×D3—64no—
131C2×D3—64no—
132C2×D3—64no—
133C3×C4—24no—
134C3×C4—24no—
135C3×C4—24no—
136C3×C4—128no—
137Dic3—48no—
138Dic3—64no—
139Dic3—64no—
140Dic3—64no—
141C32C2×#49811yescharacteristic, complemented, Sylow
142C23—91no—
143Q8—128no—
144Q8—368no—
145C2×C4—68no—
146C2×C4—91no—
147C2×C4—92no—
148C2×C4—94no—
149C2×C4—98no—
150C2×C4—368no—
151C2×C4C2×GO+(4,𝔽2)11yescharacteristic
152C2×C4C2×GO+(4,𝔽2)12yes—
153C8—98no—
154C2×C3—22no—
155C2×C3—22no—
156C2×C3—22no—
157D3—68no—
158C22—92no—
159C22—94no—
160C22C22×GO+(4,𝔽2)11yescharacteristic
161C4—92no—
162C4—94no—
163C4—128no—
164C4#6422212yes—
165C4#6422714yes—
166C3—22no—
167C2—94no—
168C2C2×#6422211yescharacteristic
169C2C2×#6422712yes—
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×#498
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10593384C2semidirect
24. #3787Q8semidirect
53. #622C2×Q8semidirect
113. C3⋊D3#498semidirect
141. C32C2×#498semidirect

Maximal subgroups

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

subgroupindex
#105939092
C4×#37872
#105933872
#105933842
C2×#4989