Finite Group Databasebeta

← C2×SD32×D181 #37546828

Subgroups — C2×SD32×D181 #37546828

Order 23168.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×Q16×D181C211yesmaximal, characteristic, complemented
2C2×D8×D181C211yesmaximal, characteristic
3C2×#19153761C211yesmaximal, characteristic, complemented
4C2×#19153760C211yesmaximal, characteristic, complemented
5C2×#19153759C211yesmaximal, characteristic, complemented
6SD32×D181C218yesmaximal, direct product factor
7C2×C16×D181C211yesmaximal, characteristic, complemented
8C2×SD32×C181C211yesmaximal, characteristic, complemented
9C2×Q8×D181—21no—
10C2×D4×D181—21no—
11C2×Dic724C2211yescharacteristic, complemented
12C2×#15668439—21no—
13Q16×D181—22no—
14Q16×D181C2214yescomplemented
15C2×D1448C2211yescharacteristic
16C2×#15668434—21no—
17D8×D181—22no—
18D8×D181C2214yes—
19C2×C8×D181C2211yescharacteristic
20#19153761C2214yescomplemented
21#19153760C2214yescomplemented
22#19153759C2214yescomplemented
23C2×#15668424C2211yescharacteristic, complemented
24C16×D181C2214yescomplemented
25C2×Q16×C181C2211yescharacteristic, complemented
26C2×D8×C181C2211yescharacteristic
27SD32×C181C2214yescomplemented
28C2×C16×C181C2211yescharacteristic, complemented
29C23×D181—41no—
30C2×Dic362—21no—
31C2×Dic362—41no—
32Q8×D181—24no—
33Q8×D181—42no—
34C2×D724—21no—
35C2×C22⋊D181—41no—
36D4×D181—24no—
37D4×D181—42no—
38C2×C4×D181—41no—
39C2×C4×D181D411yescharacteristic
40Dic724—21no—
41Dic724C2312yescomplemented
42#15668439—24no—
43D1448—21no—
44D1448C2312yes—
45#15668434—24no—
46C2×#13089678D411yescharacteristic
47C8×D181D412yes—
48C8×D181C2312yes—
49#15668424C2312yescomplemented
50C2×Q8×C181—21no—
51C2×D4×C181—21no—
52Q16×C181—21no—
53Q16×C181C2312yescomplemented
54D8×C181—21no—
55D8×C181C2312yes—
56C2×C8×C181C2311yescharacteristic
57C16×C181C2312yescomplemented
58C22×D181—41no—
59C22×D181—44no—
60C22×D181—84no—
61C22×D181D811yescharacteristic
62Dic362—22no—
63Dic362—41no—
64Dic362—44no—
65D724—22no—
66D724—41no—
67C22⋊D181—44no—
68C2×Dic181—41no—
69C2×Dic181D811yescharacteristic
70C4×D181—44no—
71C4×D181D812yes—
72C4×D181C2×D412yes—
73#13089678C2×D412yes—
74C23×C181—41no—
75Q8×C181—22no—
76Q8×C181—41no—
77D4×C181—22no—
78D4×C181—41no—
79C2×C4×C181—41no—
80C2×C4×C181C2×D411yescharacteristic
81C8×C181C2×D411yescharacteristic
82C8×C181C2411yescharacteristic
83C22×C181—42no—
84C22×C181—82no—
85C22×C181C2×D811yescharacteristic
86C2×D181—42no—
87C2×D181—82no—
88C2×D181—88no—
89C2×D181SD3214yesdirect product factor
90C2×D181C2×D812yes—
91C4×C181—42no—
92C4×C181C2×D811yescharacteristic
93C4×C181C22×D411yescharacteristic
94Dic181—42no—
95Dic181C2×D812yes—
96C2×C181—82no—
97C2×C181C2×SD3212yescomplemented
98C2×C181C22×D811yescharacteristic
99D181—82no—
100D181C2×SD3214yesdirect product factor
101C181C22×SD3211yescharacteristic, complemented, Sylow
102C22×SD32—1811nomaximal, Sylow
103C22×Q16—1811no—
104C22×D8—1811no—
105C2×SD32—1811no—
106C2×SD32—1811no—
107C2×SD32—1818no—
108C2×SD32—1811no—
109C2×SD32D18111yescharacteristic, direct product factor
110C22×C16—1811no—
111C22×Q8—3621no—
112C22×D4—3621no—
113C2×Q16—3622no—
114C2×Q16—3621no—
115C2×Q16—1814no—
116C2×Q16—1811no—
117C2×Q16C2×D18111yescharacteristic, complemented
118C2×D8—3622no—
119C2×D8—3621no—
120C2×D8—1814no—
121C2×D8—1811no—
122C2×D8C2×D18111yescharacteristic
123C22×C8—1811no—
124SD32—1814no—
125SD32—1814no—
126SD32—1814no—
127SD32C2×D18114yesdirect product factor
128C2×C16—1811no—
129C2×C16—1814no—
130C2×C16C2×D18111yescharacteristic, complemented
131C24—7241no—
132C2×Q8—21no—
133C2×Q8—3624no—
134C2×Q8—3621no—
135C2×Q8—7241no—
136C2×Q8—7242no—
137C2×D4—21no—
138C2×D4—3624no—
139C2×D4—3621no—
140C2×D4—7242no—
141C2×D4—7241no—
142C22×C4—1811no—
143C22×C4—7241no—
144Q16—21no—
145Q16—3624no—
146Q16—3621no—
147Q16—1812no—
148Q16C22×D18112yescomplemented
149D8—21no—
150D8—3624no—
151D8—3621no—
152D8—1812no—
153D8C22×D18112yes—
154C2×C8—1811no—
155C2×C8—1812no—
156C2×C8—1812no—
157C2×C8C22×D18111yescharacteristic
158C16—1812no—
159C16C22×D18112yescomplemented
160C23—41no—
161C23—14484no—
162C23—1811no—
163C23—7244no—
164C23—7241no—
165Q8—22no—
166Q8—41no—
167Q8—3622no—
168Q8—7244no—
169Q8—7241no—
170D4—22no—
171D4—41no—
172D4—3622no—
173D4—7244no—
174D4—7241no—
175C2×C4—41no—
176C2×C4—1811no—
177C2×C4—1812no—
178C2×C4—1812no—
179C2×C4—7244no—
180C2×C4—7241no—
181C2×C4D4×D18111yescharacteristic
182C8—1812no—
183C8D4×D18111yescharacteristic
184C8C23×D18111yescharacteristic
185C22—42no—
186C22—82no—
187C22—14488no—
188C22—14482no—
189C22—1814no—
190C22—1812no—
191C22—7242no—
192C22D8×D18111yescharacteristic
193C4—42no—
194C4—1812no—
195C4—7242no—
196C4D8×D18111yescharacteristic
197C4C2×D4×D18111yescharacteristic
198C2—82no—
199C2—14482no—
200C2—1814no—
201C2SD32×D18112yesdirect product factor
202C2C2×D8×D18111yescharacteristic
subgroupG/H
centerC22D8×D181
commutator, cosocleC8×C181C24
FrattiniC8C23×D181
FittingC2×SD32×C181C2
socleC22×C181C2×D8
prime radicalC2×D8×D181C2
hypercenterC2×SD32D181
hypocenterC181C22×SD32
LCSG ▷ C8×C181 ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D181C2semidirect
3. C2×#19153761C2semidirect
4. C2×#19153760C2semidirect
5. C2×#19153759C2semidirect
6. SD32×D181C2direct (N × H)
7. C2×C16×D181C2semidirect
8. C2×SD32×C181C2semidirect
11. C2×Dic724C22semidirect
14. Q16×D181C22semidirect
20. #19153761C22semidirect
21. #19153760C22semidirect
22. #19153759C22semidirect
23. C2×#15668424C22semidirect
24. C16×D181C22semidirect
25. C2×Q16×C181C22semidirect
27. SD32×C181C22semidirect
28. C2×C16×C181C22semidirect
41. Dic724C23semidirect
49. #15668424C23semidirect
53. Q16×C181C23semidirect
57. C16×C181C23semidirect
89. C2×D181SD32direct (N × H)
97. C2×C181C2×SD32semidirect
100. D181C2×SD32direct (N × H)
101. C181C22×SD32semidirect
109. C2×SD32D181direct (N × H)
117. C2×Q16C2×D181semidirect
127. SD32C2×D181direct (N × H)
130. C2×C16C2×D181semidirect
148. Q16C22×D181semidirect
159. C16C22×D181semidirect
201. C2SD32×D181direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q16×D1812
C2×D8×D1812
C2×#191537612
C2×#191537602
C2×#191537592
SD32×D1812
C2×C16×D1812
C2×SD32×C1812
C22×SD32181