Finite Group Databasebeta

← #37549250

Subgroups — #37549250

Order 23168.

228 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 62 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#26042299C211yesmaximal, characteristic
2#26042299C211yesmaximal, characteristic
3#26042138C214yesmaximal, complemented
4C2×#19153815C211yesmaximal, characteristic
5#19153883C2212yes—
6#19153883C2212yes—
7C22⋊#13089685—21no—
8C22⋊#13089685—21no—
9#19153871—21no—
10#19153871—21no—
11C22×Dic362—21no—
12#19153815—21no—
13#19153815—21no—
14#19153815C412yes—
15#19153815C2212yes—
16C2×C4⋊Dic181C411yescharacteristic
17C2×#15668428—21no—
18C2×C4×Dic181C2211yescharacteristic
19C2×C4⋊C4×C181C411yescharacteristic
20C2×#13089685—22no—
21C2×#13089685—22no—
22C2×Dic362—22no—
23C2×Dic362—22no—
24C2×Dic362—44no—
25C22×Dic181—21no—
26C22×Dic181D411yescharacteristic
27C22×Dic181D411yescharacteristic
28C4⋊Dic181—21no—
29C4⋊Dic181C2×C412yes—
30#15668428—22no—
31#15668428—22no—
32C4×Dic181C2×C411yescharacteristic
33C4×Dic181D411yescharacteristic
34C4×Dic181D411yescharacteristic
35C4×Dic181C2311yescharacteristic
36C22×C4×C181—21no—
37C22×C4×C181C2×C411yescharacteristic
38C4⋊C4×C181—21no—
39C4⋊C4×C181C2×C412yes—
40#13089685—42no—
41#13089685—42no—
42Dic362—44no—
43Dic362—44no—
44C2×Dic181—22no—
45C2×Dic181—22no—
46C2×Dic181—22no—
47C2×Dic181—42no—
48C2×Dic181C22⋊C411yescharacteristic
49C2×Dic181C22⋊C411yescharacteristic
50C2×Dic181C2×D411yescharacteristic
51C2×Dic181C2×D411yescharacteristic
52C23×C181C22⋊C411yescharacteristic
53C2×C4×C181—22no—
54C2×C4×C181—22no—
55C2×C4×C181—42no—
56C2×C4×C181C22⋊C411yescharacteristic
57C2×C4×C181C22×C411yescharacteristic
58C22×C181—21no—
59C22×C181—21no—
60C22×C181#10112yes—
61C22×C181C2×C22⋊C411yescharacteristic
62C4×C181—21no—
63C4×C181—21no—
64C4×C181—42no—
65Dic181—21no—
66Dic181—21no—
67Dic181—42no—
68Dic181AGL(1,ℤ/8)12yes—
69Dic181#13712yes—
70C2×C181—22no—
71C2×C181C2×#10111yescharacteristic
72C2×C181#41811yescharacteristic
73C2×C181#41911yescharacteristic
74C181#155611yescharacteristic, complemented, Sylow
75#1556—1811nomaximal, Sylow
76C2×C4⋊Q8—1811no—
77#432—1811no—
78#432—1811no—
79#332—1814no—
80C22×Q8—3621no—
81C4⋊Q8—3621no—
82C4⋊Q8—3621no—
83C4⋊Q8—1812no—
84C4⋊Q8—1812no—
85C2×C4⋊C4—3621no—
86C2×C4⋊C4—1811no—
87C2×C4⋊C4#1062438211yescharacteristic
88C2×C42—1811no—
89C4⋊C8—1812no—
90C4⋊C8—1812no—
91C22⋊C8—3621no—
92C22⋊C8—3621no—
93#97—3621no—
94#97—3621no—
95C2×Q8—3622no—
96C2×Q8—3622no—
97C2×Q8—7244no—
98C22×C4—21no—
99C22×C4—3621no—
100C22×C4—1811no—
101C22×C4—1811no—
102C22×C4C2×#1062438211yescharacteristic
103C2×C8—3622no—
104C2×C8—3622no—
105C4⋊C4—21no—
106C4⋊C4—3622no—
107C4⋊C4—3622no—
108C4⋊C4—3621no—
109C4⋊C4—1812no—
110C4⋊C4C2×#1062438212yes—
111C42—1811no—
112C42—1811no—
113C42—1811no—
114C42—1811no—
115C23C22⋊#1062438211yescharacteristic
116Q8—7244no—
117Q8—7244no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—42no—
121C2×C4—3622no—
122C2×C4—3622no—
123C2×C4—3622no—
124C2×C4—1811no—
125C2×C4—1811no—
126C2×C4—1811no—
127C2×C4—1811no—
128C2×C4—7242no—
129C2×C4C22⋊#1062438211yescharacteristic
130C2×C4C22×#1062438211yescharacteristic
131C8—7242no—
132C8—7242no—
133C22—21no—
134C22—21no—
135C22#1915387712yes—
136C22C2×C22⋊#1062438211yescharacteristic
137C4—21no—
138C4—21no—
139C4—42no—
140C4—3621no—
141C4—3621no—
142C4—1812no—
143C4—1812no—
144C4—7242no—
145C2—22no—
146C2C2×#1915387711yescharacteristic
147C2#2604227111yescharacteristic
148C2#2604227211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC2×C4⋊C4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC23×C181C22⋊C4
cosocleC4×Dic181C23
hypercenterC2×C4⋊C4#10624382
hypocenterC181#1556
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #26042138C2semidirect
74. C181#1556semidirect

Maximal subgroups

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

subgroupindex
#260422992
#260421382
C2×#191538152
#1556181