Finite Group Databasebeta

← #37549143

Subgroups — #37549143

Order 23168.

208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 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#26042301C211yesmaximal, characteristic
2#26042224C211yesmaximal, characteristic
3#26042133C212yesmaximal
4#26042132C212yesmaximal
5#26041833C211yesmaximal, characteristic
6C4⋊#13089685—21no—
7#19153873C2212yes—
8#19153871—21no—
9(C2×#10624382)⋊C4—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—
25C2×Dic362—21no—
26C2×Dic362C2×C411yescharacteristic
27C2×C4×D181D411yescharacteristic
28C2×C4×D181D411yescharacteristic
29C2×C4×D181C2311yescharacteristic
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×Dic181C2×C411yescharacteristic
41C4×Dic181D411yescharacteristic
42C4×Dic181D411yescharacteristic
43C2×Q8×C181C2×C411yescharacteristic
44C4⋊C4×C181—21no—
45C4⋊C4×C181C2×C411yescharacteristic
46C42×C181—21no—
47C42×C181C2×C411yescharacteristic
48C2×#10624382—42no—
49C2×#10624382—42no—
50C2×#10624382—42no—
51#13089685—42no—
52C22×D181C2×D411yescharacteristic
53Dic362—42no—
54Dic362—41no—
55C2×Dic181—21no—
56C2×Dic181—21no—
57C2×Dic181C22⋊C411yescharacteristic
58C2×Dic181C22⋊C411yescharacteristic
59C2×Dic181C2×D411yescharacteristic
60C4×D181—22no—
61C4×D181—41no—
62C4×D181—41no—
63Q8×C181—41no—
64C2×C4×C181—21no—
65C2×C4×C181—21no—
66C2×C4×C181C22⋊C411yescharacteristic
67C2×C4×C181C22⋊C411yescharacteristic
68C2×C4×C181C22×C411yescharacteristic
69C22×C181C2×C22⋊C411yescharacteristic
70C2×D181—21no—
71C2×D181—21no—
72C2×D181#13712yes—
73#10624382—82no—
74C4×C181—21no—
75C4×C181—21no—
76C4×C181—21no—
77C4×C181—41no—
78C4×C181—41no—
79Dic181—21no—
80Dic181—21no—
81Dic181—21no—
82Dic181—41no—
83Dic181—41no—
84C2×C181#41011yescharacteristic
85C2×C181#41911yescharacteristic
86C2×C181#42111yescharacteristic
87D181—22no—
88C181#151511yescharacteristic, complemented, Sylow
89#1515—1811nomaximal, Sylow
90#533—1811no—
91#432—1811no—
92#383—1811no—
93#328—1812no—
94#328—1812no—
95C4⋊Q8—1811no—
96C4⋊Q8—1811no—
97#125—3621no—
98C22⋊Q8—3621no—
99C22⋊Q8—1811no—
100C22⋊Q8—1811no—
101C4×Q8—3621no—
102C4×Q8—1811no—
103C4×Q8#1062438211yescharacteristic, complemented
104#117—3621no—
105C2×C42—1811no—
106C4⋊C8—3621no—
107C22⋊C8—1812no—
108#97—3621no—
109#95—3621no—
110#95—3621no—
111#95—1812no—
112C2×Q8—3621no—
113C2×Q8—1811no—
114C2×Q8C2×#1062438211yescharacteristic
115C22×C4—3622no—
116C22×C4—1811no—
117C22×C4—1811no—
118C22×C4—1811no—
119C2×C8—3622no—
120C4⋊C4—21no—
121C4⋊C4—3621no—
122C4⋊C4—3621no—
123C4⋊C4—3621no—
124C4⋊C4—3621no—
125C4⋊C4—3621no—
126C4⋊C4—3621no—
127C4⋊C4—1811no—
128C4⋊C4C2×#1062438211yescharacteristic
129C22⋊C4—3621no—
130C22⋊C4—3621no—
131C42—21no—
132C42—3621no—
133C42—1811no—
134C42—1811no—
135C42—1811no—
136C42C2×#1062438211yescharacteristic
137C23—1811no—
138Q8—41no—
139Q8—7241no—
140Q8—7242no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—3622no—
144C2×C4—3621no—
145C2×C4—3621no—
146C2×C4—1811no—
147C2×C4—1811no—
148C2×C4—1811no—
149C2×C4—7241no—
150C2×C4—7241no—
151C2×C4—7242no—
152C2×C4—7242no—
153C2×C4—7242no—
154C2×C4C22⋊#1062438211yescharacteristic
155C2×C4C22⋊#1062438211yescharacteristic
156C2×C4C22×#1062438211yescharacteristic
157C8—7242no—
158C22—3621no—
159C22—3621no—
160C22—1812no—
161C22C2×C22⋊#1062438211yescharacteristic
162C4—21no—
163C4—21no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—3621no—
168C4—3621no—
169C4—3621no—
170C4—14482no—
171C4—7241no—
172C4—7241no—
173C2—3622no—
174C2#2604225811yescharacteristic
175C2#2604227211yescharacteristic
176C2#2604227611yescharacteristic
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#1515
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
88. C181#1515semidirect
103. C4×Q8#10624382semidirect

Maximal subgroups

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

subgroupindex
#260423012
#260422242
#260421332
#260421322
#260418332
#1515181