Finite Group Databasebeta

← #37549259

Subgroups — #37549259

Order 23168.

254 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 60 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#26042284C212yesmaximal, complemented
2#26042139C212yesmaximal, complemented
3#26042137C212yesmaximal, complemented
4#26041828C211yesmaximal, characteristic
5C2×#15668459—22no—
6#19153883—22no—
7#19153883C2214yes—
8C2×#15668450C411yescharacteristic
9C2×#15668448C411yescharacteristic
10#19153814C2211yescharacteristic
11#19153812C2211yescharacteristic
12#19153804C411yescharacteristic
13#19153789—22no—
14#19153776—22no—
15C42×D181C2211yescharacteristic
16#124×C181C411yescharacteristic
17#15668459—44no—
18C2×#13089685—24no—
19#15668450—42no—
20#15668448—42no—
21C2×Dic362C2×C411yescharacteristic
22C2×D724—21no—
23C2×D724C2×C411yescharacteristic
24C2×C22⋊D181—21no—
25C2×C22⋊D181—22no—
26C22×Dic181—21no—
27C2×C4×D181—21no—
28C2×C4×D181C2×C411yescharacteristic
29C2×C4×D181D412yes—
30#15668428—22no—
31#15668426—22no—
32C4×Dic181D412yes—
33C4×Dic181C2311yescharacteristic
34C2×Q8×C181C2×C411yescharacteristic
35C2×D4×C181C2×C411yescharacteristic
36C22⋊C4×C181—22no—
37C42×C181C2×C411yescharacteristic
38#13089685—44no—
39C22×D181—21no—
40C22×D181C22⋊C411yescharacteristic
41Dic362—41no—
42D724—41no—
43D724—42no—
44C22⋊D181—42no—
45C22⋊D181—42no—
46C22⋊D181—42no—
47C2×Dic181—21no—
48C2×Dic181—42no—
49C2×Dic181C22⋊C411yescharacteristic
50C2×Dic181C2×D412yes—
51C4×D181—22no—
52C4×D181—22no—
53C4×D181—22no—
54C4×D181—42no—
55C23×C181—21no—
56Q8×C181—41no—
57D4×C181—41no—
58C2×C4×C181—21no—
59C2×C4×C181C22⋊C412yes—
60C2×C4×C181C22×C411yescharacteristic
61C22×C181—41no—
62C22×C181—42no—
63C22×C181C2×C22⋊C411yescharacteristic
64C2×D181—21no—
65C2×D181—22no—
66C2×D181—41no—
67C2×D181—42no—
68C4×C181—21no—
69C4×C181—22no—
70C4×C181—41no—
71Dic181—41no—
72Dic181#10012yes—
73Dic181AGL(1,ℤ/8)12yes—
74Dic181#13712yes—
75C2×C181—81no—
76C2×C181C2×#10011yescharacteristic
77C2×C181#41712yes—
78D181—41no—
79D181—81no—
80C181#156011yescharacteristic, complemented, Sylow
81#1560—1811nomaximal, Sylow
82#532—1811no—
83#423—1812no—
84#333—1812no—
85#331—1812no—
86C2×#41—1811no—
87C2×#41—1811no—
88C2×M16—3622no—
89C4⋊Q8—1811no—
90#127—1811no—
91#124—1811no—
92#124#1062438211yescharacteristic
93#121—3622no—
94C4×D4—3622no—
95C2×C42—1811no—
96C4⋊C8—3622no—
97C4⋊C8—1814no—
98#41—7242no—
99#41—7242no—
100C2×Q8—1811no—
101C2×Q8C2×#1062438211yescharacteristic
102C2×D4—3621no—
103C2×D4—3621no—
104C2×D4—3622no—
105C2×D4—1811no—
106C2×D4C2×#1062438211yescharacteristic
107C22×C4—3621no—
108C22×C4—3621no—
109C22×C4—1812no—
110C22×C4—1811no—
111M16—7244no—
112C2×C8—3624no—
113C4⋊C4—3622no—
114C22⋊C4—22no—
115C22⋊C4—3622no—
116C42—1812no—
117C42—1811no—
118C42C2×#1062438211yescharacteristic
119C23—21no—
120C23—3621no—
121C23—1811no—
122Q8—41no—
123Q8—7241no—
124D4—41no—
125D4—7241no—
126D4—7242no—
127D4—7242no—
128D4—7242no—
129D4—7242no—
130C2×C4—21no—
131C2×C4—3622no—
132C2×C4—3622no—
133C2×C4—3622no—
134C2×C4—3621no—
135C2×C4—1812no—
136C2×C4—1811no—
137C2×C4—7242no—
138C2×C4—7242no—
139C2×C4C22⋊#1062438212yes—
140C2×C4C22×#1062438211yescharacteristic
141C8—7244no—
142C22—41no—
143C22—42no—
144C22—3621no—
145C22—3622no—
146C22—7241no—
147C22—7242no—
148C22C2×C22⋊#1062438211yescharacteristic
149C4—21no—
150C4—22no—
151C4—41no—
152C4—1812no—
153C4—1812no—
154C4—1812no—
155C4—7241no—
156C2—81no—
157C2—14481no—
158C2—7241no—
159C2D181⋊#10011yescharacteristic
160C2#2604227012yes—
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
Fitting#124×C181C4
socleC22×C181C2×C22⋊C4
prime radical#26041828C2
cosocleC4×Dic181C23
hypercenter#124#10624382
hypocenterC181#1560
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #26042284C2semidirect
2. #26042139C2semidirect
3. #26042137C2semidirect
80. C181#1560semidirect

Maximal subgroups

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

subgroupindex
#260422842
#260421392
#260421372
#260418282
#1560181