Finite Group Databasebeta

← #37548820

Subgroups — #37548820

Order 23168.

162 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 38 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#26042266C211yesmaximal, characteristic
2#26042253C211yesmaximal, characteristic
3#26041251C211yesmaximal, characteristic
4C2×#15668459C411yescharacteristic, complemented
5C2×#15668458—21no—
6C2×D181⋊C8C411yescharacteristic, complemented
7#19153877C412yescomplemented
8#19153876—21no—
9C22⋊#13089685—21no—
10C22⋊#13089685—21no—
11C2×#15668448C2211yescharacteristic
12#19153772—21no—
13#19153731C411yescharacteristic
14#19153730—21no—
15#99×C181C411yescharacteristic
16#15668459—41no—
17#15668458—22no—
18#15668458—41no—
19D181⋊C8—41no—
20C2×#13089685—21no—
21C2×#13089685—21no—
22C2×#13089685—41no—
23#15668448—41no—
24#15668448—41no—
25C2×Dic362C2×C411yescharacteristic
26C2×C22⋊D181D411yescharacteristic
27C2×C22⋊D181Q811yescharacteristic
28C22×Dic181D411yescharacteristic
29C22×Dic181D411yescharacteristic
30C2×C4×D181C2×C411yescharacteristic
31#15668428—41no—
32C22⋊Dic181—21no—
33C4×Dic181—41no—
34C2×D4×C181C2×C411yescharacteristic
35C22⋊C4×C181—21no—
36#13089685—42no—
37#13089685—41no—
38#13089685—41no—
39C22×D181C4⋊C411yescharacteristic
40Dic362—41no—
41C22⋊D181—41no—
42C22⋊D181—41no—
43C2×Dic181—21no—
44C2×Dic181—21no—
45C2×Dic181—21no—
46C2×Dic181—21no—
47C2×Dic181—41no—
48C2×Dic181C22⋊C411yescharacteristic
49C2×Dic181C22⋊C411yescharacteristic
50C2×Dic181C4⋊C411yescharacteristic
51C4×D181—21no—
52C4×D181—21no—
53C23×C181C22⋊C411yescharacteristic
54C23×C181C4⋊C411yescharacteristic
55D4×C181—41no—
56C2×C4×C181—41no—
57C2×C4×C181C4211yescharacteristic
58C22×C181—21no—
59C22×C181—21no—
60C22×C181—41no—
61C22×C181—41no—
62C22×C181#9511yescharacteristic
63C2×D181—21no—
64C2×D181—41no—
65C4×C181—21no—
66C4×C181—81no—
67Dic181—21no—
68Dic181—21no—
69Dic181—81no—
70Dic181#9911yescharacteristic
71Dic181#9911yescharacteristic
72C2×C181—21no—
73C2×C181—41no—
74C2×C181—41no—
75C2×C181#34211yescharacteristic
76D181—41no—
77C181#139511yescharacteristic, complemented, Sylow
78#1395—1811nomaximal, Sylow
79#413—1811no—
80#410—1811no—
81#408—1811no—
82C2×#41—1811no—
83C2×M16—3621no—
84C2×M16—1811no—
85C22×C8—1811no—
86#117—3621no—
87#101—1812no—
88#100—3621no—
89#99—3621no—
90#99—1811no—
91#99#1062438211yescharacteristic
92C22⋊C8—3621no—
93C22⋊C8—3621no—
94#41—7241no—
95#41—7241no—
96C2×Q8—1811no—
97C2×D4—1811no—
98C2×D4—1811no—
99C2×D4C2×#1062438211yescharacteristic
100C22×C4—1811no—
101C22×C4—1811no—
102C22×C4—1811no—
103M16—3622no—
104M16—7241no—
105M16—7241no—
106C2×C8—3621no—
107C2×C8—3621no—
108C2×C8—7241no—
109C2×C8—7241no—
110C4⋊C4—7241no—
111C22⋊C4—21no—
112C22⋊C4—3621no—
113C42—7241no—
114C23—1811no—
115C23C22⋊#1062438211yescharacteristic
116C23C4⋊#1062438211yescharacteristic
117Q8—7241no—
118D4—41no—
119D4—7241no—
120D4—7241no—
121C2×C4—41no—
122C2×C4—3621no—
123C2×C4—3621no—
124C2×C4—3621no—
125C2×C4—3621no—
126C2×C4—3621no—
127C2×C4—3621no—
128C2×C4—1811no—
129C2×C4—1811no—
130C2×C4—1811no—
131C2×C4—7241no—
132C2×C4C4×#1062438211yescharacteristic
133C8—7242no—
134C8—7241no—
135C8—7241no—
136C22—21no—
137C22—21no—
138C22—41no—
139C22—41no—
140C22—3621no—
141C22—7241no—
142C22(C2×#10624382)⋊C411yescharacteristic
143C4—21no—
144C4—81no—
145C4—3621no—
146C4—3621no—
147C4—14481no—
148C4—1811no—
149C4—1811no—
150C2—21no—
151C2—41no—
152C2—41no—
153C2—7241no—
154C2#2604215611yescharacteristic
subgroupG/H
centerC2#26042156
commutatorC2×C4×C181C42
FrattiniC2×D4C2×#10624382
Fitting#99×C181C4
socleC2×C181#342
prime radical, cosocleC2×#15668448C22
hypercenter#99#10624382
hypocenterC181#1395
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
4. C2×#15668459C4semidirect
6. C2×D181⋊C8C4semidirect
7. #19153877C4semidirect
77. C181#1395semidirect

Maximal subgroups

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

subgroupindex
#260422662
#260422532
#260412512
#1395181