Finite Group Databasebeta

← #37549246

Subgroups — #37549246

Order 23168.

198 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 58 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#26042302C211yesmaximal, characteristic
2#26042297C211yesmaximal, characteristic
3#26042139C212yesmaximal, complemented
4#26042138C212yesmaximal, complemented
5#26041833C211yesmaximal, characteristic
6#19153883C2212yes—
7#19153883C2212yes—
8#19153873—21no—
9#19153873—21no—
10#19153871—21no—
11C4×#13089685—21no—
12#19153815C2211yescharacteristic
13#19153814C2211yescharacteristic
14#19153806—21no—
15#19153796C411yescharacteristic
16#19153794—21no—
17#19153792C411yescharacteristic
18C4×Dic362—21no—
19C4×Dic362C411yescharacteristic
20#19153773—21no—
21C42×D181C2211yescharacteristic
22C4×Q8×C181C411yescharacteristic
23C2×#13089685—22no—
24C2×#13089685—22no—
25C2×Dic362—21no—
26C2×Dic362C2×C411yescharacteristic
27C2×C4×D181C2×C411yescharacteristic
28C2×C4×D181D411yescharacteristic
29C2×C4×D181D411yescharacteristic
30C4⋊Dic181—21no—
31C4⋊Dic181C2×C411yescharacteristic
32#15668428—21no—
33#15668428—21no—
34#15668428—21no—
35#15668428—21no—
36#15668428—21no—
37#15668426—21no—
38#15668426—21no—
39C4×Dic181—21no—
40C4×Dic181D411yescharacteristic
41C4×Dic181D411yescharacteristic
42C4×Dic181C2311yescharacteristic
43C2×Q8×C181C2×C411yescharacteristic
44C4⋊C4×C181—21no—
45C4⋊C4×C181C2×C411yescharacteristic
46C42×C181—21no—
47C42×C181C2×C411yescharacteristic
48#13089685—42no—
49#13089685—42no—
50C22×D181C22⋊C411yescharacteristic
51Dic362—42no—
52Dic362—41no—
53C2×Dic181—21no—
54C2×Dic181—21no—
55C2×Dic181C22⋊C411yescharacteristic
56C2×Dic181C2×D411yescharacteristic
57C2×Dic181C2×D411yescharacteristic
58C4×D181—22no—
59C4×D181—22no—
60C4×D181—41no—
61Q8×C181—41no—
62C2×C4×C181—21no—
63C2×C4×C181—21no—
64C2×C4×C181C22⋊C411yescharacteristic
65C2×C4×C181C22⋊C411yescharacteristic
66C2×C4×C181C22×C411yescharacteristic
67C22×C181C2×C22⋊C411yescharacteristic
68C2×D181—21no—
69C2×D181—21no—
70C2×D181—21no—
71C4×C181—21no—
72C4×C181—21no—
73C4×C181—21no—
74C4×C181—41no—
75C4×C181—41no—
76Dic181—21no—
77Dic181—41no—
78Dic181—41no—
79Dic181#13512yes—
80Dic181#13712yes—
81C2×C181#41311yescharacteristic
82C2×C181#41611yescharacteristic
83C2×C181#41911yescharacteristic
84D181—41no—
85C181#155411yescharacteristic, complemented, Sylow
86#1554—1811nomaximal, Sylow
87#533—1811no—
88#432—1811no—
89#431—1811no—
90#333—1812no—
91#332—1812no—
92C4⋊Q8—1811no—
93C4⋊Q8—1811no—
94#125—3621no—
95C22⋊Q8—3621no—
96C22⋊Q8—1811no—
97C22⋊Q8—1811no—
98C4×Q8—3621no—
99C4×Q8—1811no—
100C4×Q8#1062438211yescharacteristic
101#117—3621no—
102C2×C42—1811no—
103C4⋊C8—1812no—
104C4⋊C8—1812no—
105C22⋊C8—3621no—
106C22⋊C8—3621no—
107#97—3621no—
108C4×C8—3621no—
109C2×Q8—3621no—
110C2×Q8—1811no—
111C2×Q8C2×#1062438211yescharacteristic
112C22×C4—1811no—
113C22×C4—1811no—
114C22×C4—1811no—
115C2×C8—3622no—
116C2×C8—3622no—
117C4⋊C4—21no—
118C4⋊C4—3621no—
119C4⋊C4—3621no—
120C4⋊C4—3621no—
121C4⋊C4—3621no—
122C4⋊C4—3621no—
123C4⋊C4—3621no—
124C4⋊C4—1811no—
125C4⋊C4C2×#1062438211yescharacteristic
126C22⋊C4—3621no—
127C22⋊C4—3621no—
128C42—21no—
129C42—3621no—
130C42—1811no—
131C42—1811no—
132C42—1811no—
133C42C2×#1062438211yescharacteristic
134C23—1811no—
135Q8—41no—
136Q8—7241no—
137Q8—7242no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—3622no—
141C2×C4—3622no—
142C2×C4—3621no—
143C2×C4—3621no—
144C2×C4—1811no—
145C2×C4—1811no—
146C2×C4—1811no—
147C2×C4—7241no—
148C2×C4C22⋊#1062438211yescharacteristic
149C2×C4C22⋊#1062438211yescharacteristic
150C2×C4C22×#1062438211yescharacteristic
151C8—7242no—
152C8—7242no—
153C22—3621no—
154C22—3621no—
155C22—3621no—
156C22C2×C22⋊#1062438211yescharacteristic
157C4—21no—
158C4—21no—
159C4—21no—
160C4—41no—
161C4—41no—
162C4—3621no—
163C4—1812no—
164C4—1812no—
165C4—7241no—
166C4—7241no—
167C2—7241no—
168C2#2604226511yescharacteristic
169C2#2604226911yescharacteristic
170C2#2604227211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC4×Q8×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC22×D181C22⋊C4
cosocleC4×Dic181C23
hypercenterC4×Q8#10624382
hypocenterC181#1554
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #26042139C2semidirect
4. #26042138C2semidirect
85. C181#1554semidirect

Maximal subgroups

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

subgroupindex
#260423022
#260422972
#260421392
#260421382
#260418332
#1554181