Finite Group Databasebeta

← #37535071

Subgroups — #37535071

Order 23168.

230 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 73 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#26041910C211yesmaximal, characteristic
2#26041319C212yesmaximal
3#26041048C211yesmaximal, characteristic
4#26041039C212yesmaximal
5#382×C181C211yesmaximal, characteristic
6C2×#15668433C2212yes—
7#19153815—22no—
8#19153807—22no—
9#19153795—22no—
10#19153775C2212yes—
11#19153749—22no—
12#19153747—22no—
13C2×C4⋊C4×C181C2211yescharacteristic
14C2×C4⋊C4×C181C2211yescharacteristic
15C2×C42×C181C2211yescharacteristic
16#95×C181—22no—
17C2×Dic362—22no—
18#15668433—22no—
19#15668433Q814yescomplemented
20C2×#13089678—22no—
21C4⋊Dic181—22no—
22C4⋊Dic181D412yes—
23C4⋊Dic181D412yes—
24#15668428—24no—
25C22⋊Dic181—22no—
26C4×Dic181—22no—
27C22×C4×C181—21no—
28C22×C4×C181—21no—
29C22×C4×C181D412yes—
30C22×C4×C181C2311yescharacteristic
31C4⋊C4×C181—22no—
32C4⋊C4×C181—22no—
33C42×C181—21no—
34C42×C181Q812yescomplemented
35Dic362—82no—
36C2×Dic181—22no—
37C2×Dic181—22no—
38#13089678—24no—
39C23×C181C2×D411yescharacteristic
40C2×C4×C181—22no—
41C2×C4×C181—22no—
42C2×C4×C181—41no—
43C2×C4×C181—41no—
44C2×C4×C181—42no—
45C2×C4×C181—42no—
46C2×C4×C181—41no—
47C2×C4×C181C2×D412yes—
48C2×C4×C181C2×Q812yes—
49C2×C4×C181C2×Q811yescharacteristic
50C2×C4×C181#4111yescharacteristic
51C22×C181—21no—
52C22×C181—21no—
53C22×C181#12011yescharacteristic
54C22×C181C22⋊Q811yescharacteristic
55C22×C181C4⋊Q811yescharacteristic
56C4×C181—42no—
57C4×C181—42no—
58C4×C181—81no—
59C4×C181C22⋊Q812yes—
60C4×C181C4⋊Q812yes—
61Dic181—42no—
62Dic181—42no—
63C2×C181—21no—
64C2×C181—21no—
65C2×C181#39511yescharacteristic
66C2×C181#45411yescharacteristic
67C2×C181#45511yescharacteristic
68C181#206111yescharacteristic, complemented, Sylow
69#2061—1811nomaximal, Sylow
70#544—1811no—
71#428—1812no—
72#382D18111yescharacteristic
73#343—1811no—
74#339—1812no—
75C2×M16—1812no—
76C4⋊Q8—3622no—
77#125—3622no—
78C22⋊Q8—3622no—
79#117—1812no—
80C2×C4⋊C4C2×D18111yescharacteristic
81C2×C4⋊C4C2×D18111yescharacteristic
82C2×C42C2×D18111yescharacteristic
83#107—3622no—
84#106—3622no—
85#95—22no—
86C2×Q8—3622no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4C22⋊D18112yes—
90C22×C4C22×D18111yescharacteristic
91M16—3622no—
92M16—1814no—
93C2×C8—3622no—
94C4⋊C4—22no—
95C4⋊C4—22no—
96C4⋊C4—3622no—
97C4⋊C4—3624no—
98C4⋊C4—1812no—
99C4⋊C4—1812no—
100C22⋊C4—3622no—
101C42—21no—
102C42—3622no—
103C42Dic36212yescomplemented
104C23C2×C22⋊D18111yescharacteristic
105Q8—14482no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—42no—
111C2×C4—42no—
112C2×C4—41no—
113C2×C4—3622no—
114C2×C4—3622no—
115C2×C4D4×D18112yes—
116C2×C4Q8×D18112yes—
117C2×C4C2×Dic36211yescharacteristic
118C2×C4#1566844911yescharacteristic
119C8—3624no—
120C22—21no—
121C22—21no—
122C22#1915378411yescharacteristic
123C22#1915379511yescharacteristic
124C22#1915381411yescharacteristic
125C4—42no—
126C4—42no—
127C4—81no—
128C4—7242no—
129C4—7242no—
130C4#1915379412yes—
131C4#1915381512yes—
132C2—21no—
133C2—21no—
134C2#2604119911yescharacteristic
135C2#2604145111yescharacteristic
136C2#2604145611yescharacteristic
subgroupG/H
centerC22#19153784
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#382×C181C2
socleC22×C181#120
prime radicalC23×C181C2×D4
hypercenter#382D181
hypocenterC181#2061
LCSG ▷ C22×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #382

Complements

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

NH ≅ G/Ntype
19. #15668433Q8semidirect
34. C42×C181Q8semidirect
68. C181#2061semidirect
103. C42Dic362semidirect

Maximal subgroups

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

subgroupindex
#260419102
#260413192
#260410482
#260410392
#382×C1812
#2061181