Finite Group Databasebeta

← #37550017

Subgroups — #37550017

Order 23168.

230 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 52 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
1D181⋊#101C212yesmaximal, complemented
2#26042190C212yesmaximal, complemented
3#26042187C212yesmaximal, complemented
4#26041849C211yesmaximal, characteristic
5D181⋊M16—22no—
6#19153877—22no—
7#19153877C2214yes—
8C2×#15668448C411yescharacteristic
9C2×Q8×D181C2211yescharacteristic
10#19153816C2211yescharacteristic
11#19153814C411yescharacteristic
12#19153803C2211yescharacteristic
13#19153798—22no—
14#19153793—22no—
15#19153773C411yescharacteristic
16#124×C181C411yescharacteristic
17#15668459—42no—
18#15668458—24no—
19D181⋊C8—42no—
20#15668448—42no—
21C2×Dic362C2×C411yescharacteristic
22C2×Dic362D412yes—
23C2×Dic362C2311yescharacteristic
24Q8×D181—42no—
25C2×C22⋊D181—21no—
26C22×Dic181—21no—
27C2×C4×D181C2×C411yescharacteristic
28C2×C4×D181D412yes—
29C4⋊Dic181—22no—
30#15668428—21no—
31#15668428—22no—
32C22⋊Dic181—22no—
33#15668426—21no—
34C4×Dic181C2×C411yescharacteristic
35C2×Q8×C181C2×C411yescharacteristic
36C2×D4×C181C2×C411yescharacteristic
37C22⋊C4×C181—22no—
38C42×C181C2×C411yescharacteristic
39#13089685—44no—
40C22×D181C22⋊C411yescharacteristic
41Dic362—42no—
42Dic362—41no—
43Dic362—41no—
44C22⋊D181—42no—
45C2×Dic181—21no—
46C2×Dic181—21no—
47C2×Dic181—42no—
48C2×Dic181C22⋊C411yescharacteristic
49C2×Dic181C2×D412yes—
50C4×D181—22no—
51C4×D181—22no—
52C4×D181—22no—
53C23×C181—21no—
54Q8×C181—41no—
55D4×C181—41no—
56C2×C4×C181—21no—
57C2×C4×C181C22⋊C412yes—
58C2×C4×C181C22×C411yescharacteristic
59C22×C181—42no—
60C22×C181—41no—
61C22×C181C2×C22⋊C411yescharacteristic
62C2×D181—41no—
63C2×D181#9912yes—
64C4×C181—22no—
65C4×C181—21no—
66C4×C181—41no—
67Dic181—21no—
68Dic181—22no—
69Dic181—41no—
70Dic181—41no—
71C2×C181—21no—
72C2×C181—81no—
73C2×C181C2×#9911yescharacteristic
74D181—22no—
75C181#213311yescharacteristic, complemented, Sylow
76#2133—1811nomaximal, Sylow
77#536—1811no—
78C2×#101—1812no—
79#356—1812no—
80#355—1812no—
81C2×#41—1811no—
82C22×Q8—1811no—
83C2×M16—3622no—
84C4⋊Q8—1811no—
85C4⋊Q8—1811no—
86#124—1811no—
87#124#1062438211yescharacteristic
88#123—3622no—
89C22⋊Q8—3622no—
90#117—1811no—
91#101—3622no—
92#101—1814no—
93#41—7242no—
94C2×Q8—1811no—
95C2×Q8—1812no—
96C2×Q8—1811no—
97C2×Q8—7242no—
98C2×Q8C2×#1062438211yescharacteristic
99C2×D4—3621no—
100C2×D4C2×#1062438211yescharacteristic
101C22×C4—3621no—
102C22×C4—1812no—
103C22×C4—1811no—
104M16—3624no—
105M16—7242no—
106C2×C8—7242no—
107C4⋊C4—3621no—
108C4⋊C4—3622no—
109C4⋊C4—3622no—
110C22⋊C4—22no—
111C22⋊C4—3621no—
112C22⋊C4—3622no—
113C42—1811no—
114C42C2×#1062438211yescharacteristic
115C23—21no—
116C23—1811no—
117Q8—41no—
118Q8—7242no—
119Q8—7241no—
120Q8—7241no—
121D4—41no—
122D4—7242no—
123C2×C4—21no—
124C2×C4—3622no—
125C2×C4—3622no—
126C2×C4—3622no—
127C2×C4—3621no—
128C2×C4—3621no—
129C2×C4—1812no—
130C2×C4—1811no—
131C2×C4—7242no—
132C2×C4C22⋊#1062438212yes—
133C2×C4C22×#1062438211yescharacteristic
134C8—7244no—
135C22—42no—
136C22—41no—
137C22—1812no—
138C22—7241no—
139C22C2×C22⋊#1062438211yescharacteristic
140C4—22no—
141C4—21no—
142C4—41no—
143C4—3622no—
144C4—3621no—
145C4—7241no—
146C4—7241no—
147C2—21no—
148C2—81no—
149C2—3622no—
150C2D181⋊#9911yescharacteristic
subgroupG/H
centerC2D181⋊#99
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
Fitting#124×C181C4
socleC2×C181C2×#99
prime radicalC2×#15668448C4
cosocleC2×Dic362C23
hypercenter#124#10624382
hypocenterC181#2133
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

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

NH ≅ G/Ntype
1. D181⋊#101C2semidirect
2. #26042190C2semidirect
3. #26042187C2semidirect
75. C181#2133semidirect

Maximal subgroups

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

subgroupindex
D181⋊#1012
#260421902
#260421872
#260418492
#2133181