Finite Group Databasebeta

← #37535024

Subgroups — #37535024

Order 23168.

264 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 67 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#26041307C211yesmaximal, characteristic, complemented
2#26041275C212yesmaximal, complemented
3#26041253C212yesmaximal, complemented
4#26041036C211yesmaximal, characteristic, complemented
5#575×C181C211yesmaximal, characteristic
6C22×#13089678C2211yescharacteristic
7#19153775C2212yes—
8#19153775C2211yescharacteristic
9#19153745—22no—
10#19153740—22no—
11#19153737—22no—
12#19153731—24no—
13C2×#41×C181C2212yes—
14#137×C181—22no—
15AGL(1,ℤ/8)×C181—22no—
16#135×C181—22no—
17C2×M16×C181C2211yescharacteristic
18C2×#13089678—22no—
19C2×#13089678—21no—
20C4⋊Dic181—22no—
21C4⋊Dic181—21no—
22C22⋊Dic181—22no—
23C22⋊Dic181D412yes—
24C4×Dic181—21no—
25C4×Dic181—22no—
26#41×C181—22no—
27#41×C181—22no—
28#41×C181—22no—
29#41×C181—22no—
30C2×Q8×C181D412yes—
31C2×D4×C181—22no—
32C2×D4×C181D412yes—
33C22×C4×C181—22no—
34C22×C4×C181C2311yescharacteristic
35Q16×C181—22no—
36SD16×C181—24no—
37D8×C181—22no—
38M16×C181—22no—
39C2×C8×C181D412yes—
40C2×Dic181—22no—
41C2×Dic181—42no—
42#13089678—41no—
43C23×C181—22no—
44C23×C181C2×D411yescharacteristic
45Q8×C181—22no—
46Q8×C181—22no—
47D4×C181—22no—
48D4×C181—22no—
49D4×C181—42no—
50D4×C181—42no—
51C2×C4×C181—22no—
52C2×C4×C181—42no—
53C2×C4×C181—42no—
54C2×C4×C181C2×D412yes—
55C2×C4×C181C2×D411yescharacteristic
56C2×C4×C181#4111yescharacteristic
57C2×C4×C181#4112yes—
58C8×C181—22no—
59C22×C181—41no—
60C22×C181—42no—
61C22×C181—82no—
62C22×C181#12111yescharacteristic
63C22×C181#12112yes—
64C4×C181—42no—
65C4×C181#12011yescharacteristic
66C4×C181#12312yes—
67C4×C181#12411yescharacteristic
68Dic181—42no—
69Dic181—82no—
70C2×C181—21no—
71C2×C181—22no—
72C2×C181—82no—
73C2×C181#39411yescharacteristic
74C181#205311yescharacteristic, complemented, Sylow
75#2053—1811nomaximal, Sylow
76#575D18111yescharacteristic
77#424—1811no—
78#416—1812no—
79#410—1812no—
80H(3,ℤ/4)—1811no—
81C2×#41C2×D18112yes—
82#137—22no—
83AGL(1,ℤ/8)—22no—
84#135—22no—
85C2×M16C2×D18111yescharacteristic
86C22×C8—1811no—
87#117—1812no—
88#117—1811no—
89C4⋊C8—3622no—
90#103—3622no—
91#102—3622no—
92#99—3624no—
93#41—22no—
94#41—22no—
95#41—22no—
96#41—22no—
97C2×Q8C22⋊D18112yes—
98C2×D4—22no—
99C2×D4C22⋊D18112yes—
100C22×C4—22no—
101C22×C4C22×D18111yescharacteristic
102Q16—22no—
103SD16—24no—
104D8—22no—
105M16—22no—
106C2×C8—3622no—
107C2×C8—3621no—
108C2×C8C22⋊D18112yes—
109C4⋊C4—3621no—
110C4⋊C4—3622no—
111C22⋊C4—3622no—
112C22⋊C4—1812no—
113C42—3621no—
114C42—3622no—
115C23—22no—
116C23D4×D18111yescharacteristic
117Q8—22no—
118Q8—22no—
119D4—22no—
120D4—22no—
121D4—42no—
122D4—42no—
123C2×C4—22no—
124C2×C4—42no—
125C2×C4—42no—
126C2×C4—3622no—
127C2×C4—7242no—
128C2×C4C2×C22⋊D18112yes—
129C2×C4C2×C22⋊D18111yescharacteristic
130C2×C4#1566844811yescharacteristic
131C2×C4#1566844812yes—
132C8—22no—
133C8—7241no—
134C22—41no—
135C22—42no—
136C22—82no—
137C22#1915378711yescharacteristic
138C22#1915378812yes—
139C4—42no—
140C4—14482no—
141C4—7242no—
142C4#1915378511yescharacteristic
143C4#1915379712yes—
144C4#1915380311yescharacteristic
145C2—22no—
146C2—21no—
147C2—82no—
148C2#2604119311yescharacteristic
subgroupG/H
centerC4#19153803
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting, prime radical#575×C181C2
socleC2×C181#394
hypercenter#575D181
hypocenterC181#2053
LCSG ▷ C22×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #26041307C2semidirect
2. #26041275C2semidirect
3. #26041253C2semidirect
4. #26041036C2semidirect
74. C181#2053semidirect

Maximal subgroups

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

subgroupindex
#260413072
#260412752
#260412532
#260410362
#575×C1812
#2053181