Finite Group Databasebeta

← #37549114

Subgroups — #37549114

Order 23168.

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

normal subgroups only

This group has 228 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#26042215C211yesmaximal, characteristic
3#26042133C212yesmaximal
4#26042132C212yesmaximal
5#26041833C211yesmaximal, characteristic
6C2×C4×#10624382—21no—
7#19153883—21no—
8#19153873C2212yes—
9#19153871—21no—
10(C2×#10624382)⋊C4—21no—
11(C2×#10624382)⋊C4C2212yes—
12#19153815C411yescharacteristic, complemented
13#19153814C411yescharacteristic, complemented
14#19153806—21no—
15#19153796C2211yescharacteristic
16#19153794—21no—
17#19153792C2211yescharacteristic
18C4×Dic362—21no—
19C4×Dic362C411yescharacteristic, complemented
20#19153773—21no—
21C42×D181C2211yescharacteristic
22C4×Q8×C181C411yescharacteristic, complemented
23C22×#10624382—22no—
24C2×#13089685—22no—
25C4×#10624382—24no—
26C2×Dic362—21no—
27C2×Dic362C2×C411yescharacteristic
28C2×C4×D181D411yescharacteristic
29C2×C4×D181D411yescharacteristic
30C2×C4×D181C2311yescharacteristic
31C4⋊Dic181—21no—
32C4⋊Dic181C2×C411yescharacteristic
33#15668428—21no—
34#15668428—21no—
35#15668428—21no—
36#15668428—21no—
37#15668428—21no—
38#15668426—21no—
39#15668426—21no—
40C4×Dic181—21no—
41C4×Dic181C2×C411yescharacteristic
42C4×Dic181D411yescharacteristic
43C4×Dic181D411yescharacteristic
44C2×Q8×C181C2×C411yescharacteristic
45C4⋊C4×C181—21no—
46C4⋊C4×C181C2×C411yescharacteristic
47C42×C181—21no—
48C42×C181C2×C411yescharacteristic
49C2×#10624382—24no—
50C2×#10624382—42no—
51C2×#10624382—42no—
52#13089685—42no—
53C22×D181C2×D411yescharacteristic
54Dic362—42no—
55Dic362—41no—
56C2×Dic181—21no—
57C2×Dic181—21no—
58C2×Dic181C22⋊C411yescharacteristic
59C2×Dic181C22⋊C411yescharacteristic
60C2×Dic181C2×D411yescharacteristic
61C4×D181—22no—
62C4×D181—22no—
63C4×D181—41no—
64Q8×C181—41no—
65C2×C4×C181—21no—
66C2×C4×C181—21no—
67C2×C4×C181C22⋊C411yescharacteristic
68C2×C4×C181C22⋊C411yescharacteristic
69C2×C4×C181C22×C411yescharacteristic
70C22×C181C2×C22⋊C411yescharacteristic
71C2×D181—21no—
72C2×D181—21no—
73C2×D181#13712yes—
74#10624382—44no—
75C4×C181—21no—
76C4×C181—21no—
77C4×C181—21no—
78C4×C181—41no—
79C4×C181—41no—
80Dic181—21no—
81Dic181—21no—
82Dic181—41no—
83Dic181—41no—
84Dic181#10412yes—
85C2×C181#41011yescharacteristic
86C2×C181#41911yescharacteristic
87C2×C181C2×#10411yescharacteristic
88D181—22no—
89C181#150611yescharacteristic, complemented, Sylow
90#1506—1811nomaximal, Sylow
91#533—1811no—
92#432—1811no—
93#376—1811no—
94#328—1812no—
95#328—1812no—
96C4⋊Q8—1811no—
97C4⋊Q8—1811no—
98#125—3621no—
99C22⋊Q8—3621no—
100C22⋊Q8—1811no—
101C22⋊Q8—1811no—
102C4×Q8—3621no—
103C4×Q8—1811no—
104C4×Q8#1062438211yescharacteristic, complemented
105#117—3621no—
106C2×C42—3621no—
107C2×C42—1811no—
108C4⋊C8—3621no—
109C22⋊C8—1812no—
110#97—3621no—
111#95—3621no—
112#95—1812no—
113C2×Q8—3621no—
114C2×Q8—1811no—
115C2×Q8C2×#1062438211yescharacteristic
116C22×C4—3622no—
117C22×C4—1811no—
118C22×C4—1811no—
119C22×C4—1811no—
120C2×C8—3622no—
121C4⋊C4—21no—
122C4⋊C4—3621no—
123C4⋊C4—3621no—
124C4⋊C4—3621no—
125C4⋊C4—3621no—
126C4⋊C4—3621no—
127C4⋊C4—3621no—
128C4⋊C4—1811no—
129C4⋊C4C2×#1062438211yescharacteristic
130C22⋊C4—3621no—
131C22⋊C4—3621no—
132C42—21no—
133C42—3624no—
134C42—3621no—
135C42—1811no—
136C42—1811no—
137C42—1811no—
138C42C2×#1062438211yescharacteristic
139C23—1811no—
140Q8—41no—
141Q8—7241no—
142Q8—7242no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—3622no—
146C2×C4—3622no—
147C2×C4—3624no—
148C2×C4—3621no—
149C2×C4—3621no—
150C2×C4—1811no—
151C2×C4—1811no—
152C2×C4—1811no—
153C2×C4—7241no—
154C2×C4—7242no—
155C2×C4—7242no—
156C2×C4C22⋊#1062438211yescharacteristic
157C2×C4C22⋊#1062438211yescharacteristic
158C2×C4C22×#1062438211yescharacteristic
159C8—7242no—
160C22—3621no—
161C22—3621no—
162C22—1812no—
163C22C2×C22⋊#1062438211yescharacteristic
164C4—21no—
165C4—21no—
166C4—21no—
167C4—41no—
168C4—41no—
169C4—3621no—
170C4—3621no—
171C4—1812no—
172C4—7244no—
173C4—7241no—
174C4—7241no—
175C2—3622no—
176C2#2604225811yescharacteristic
177C2#2604227211yescharacteristic
178C2D181⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC4×Q8×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC22×D181C2×D4
cosocleC2×C4×D181C23
hypercenterC4×Q8#10624382
hypocenterC181#1506
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
12. #19153815C4semidirect
13. #19153814C4semidirect
19. C4×Dic362C4semidirect
22. C4×Q8×C181C4semidirect
89. C181#1506semidirect
104. C4×Q8#10624382semidirect

Maximal subgroups

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

subgroupindex
#260423022
#260422152
#260421332
#260421322
#260418332
#1506181