Finite Group Databasebeta

← #37550480

Subgroups — #37550480

Order 23168.

528 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 160 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#26042346C212yesmaximal, complemented
2#26042320C214yesmaximal, complemented
3D8×#10624382C214yesmaximal, complemented
4#26042289C211yesmaximal, characteristic, complemented
5#26042271C212yesmaximal, complemented
6#26042242C211yesmaximal, characteristic, complemented
7C2×D8×D181C211yesmaximal, characteristic
8D181⋊M16C2211yescharacteristic
9D4×#10624382—24no—
10D4×#10624382C2218yescomplemented
11#19153895C2212yes—
12#19153895C2211yescharacteristic
13C2×C22⋊#10624382—24no—
14#19153885C2212yescomplemented
15#19153884C2212yescomplemented
16#19153878C2218yescomplemented
17#19153870C2212yescomplemented
18C8×#10624382C2212yescomplemented
19C2×D4×D181C2212yes—
20C2×D1448C411yescharacteristic, complemented
21C2×#15668434C412yescomplemented
22D8×D181C412yescomplemented
23D8×D181C412yescomplemented
24D8×D181C2212yes—
25D8×D181C2212yes—
26C2×C8×D181C2211yescharacteristic
27C2×D8×C181C411yescharacteristic, complemented
28C22×#10624382—28no—
29#15668459—21no—
30#15668458—21no—
31D181⋊C8C2312yes—
32C4⋊#10624382D412yes—
33C4⋊#10624382C2314yes—
34C22⋊#10624382—28no—
35C22⋊#10624382—22no—
36C22⋊#10624382D412yes—
37C4×#10624382—22no—
38C4×#10624382C2312yes—
39C23×D181—22no—
40C2×D724C2×C412yescomplemented
41C2×C22⋊D181—22no—
42D4×D181—22no—
43D4×D181—22no—
44D4×D181C2×C414yescomplemented
45D4×D181C2314yes—
46C2×C4×D181C2311yescharacteristic
47D1448C2×C412yescomplemented
48D1448C2×C412yescomplemented
49#15668434C2×C414yescomplemented
50#15668434C2×C414yescomplemented
51C2×#13089678C2×C411yescharacteristic, complemented
52C8×D181C2×C411yescharacteristic, complemented
53C8×D181C2×C411yescharacteristic, complemented
54C8×D181C2311yescharacteristic
55C8×D181C2311yescharacteristic
56C2×D4×C181C2×C412yescomplemented
57D8×C181C2×C412yescomplemented
58D8×C181C2×C412yescomplemented
59C2×C8×C181C2×C411yescharacteristic, complemented
60C2×#10624382—24no—
61C2×#10624382—88no—
62C2×#10624382C2×D414yes—
63#13089685—22no—
64C22×D181—22no—
65C22×D181—24no—
66C22×D181—24no—
67C22×D181—84no—
68C22×D181C2×D411yescharacteristic
69D724—22no—
70D724C22×C414yes—
71C22⋊D181—24no—
72C22⋊D181—24no—
73C2×Dic181#4111yescharacteristic
74C4×D181C22×C411yescharacteristic
75C4×D181C2×D411yescharacteristic
76C4×D181#4111yescharacteristic
77C4×D181C2411yescharacteristic
78#13089678C22×C411yescharacteristic
79#13089678C22×C411yescharacteristic
80C23×C181—22no—
81D4×C181—22no—
82D4×C181C22×C414yes—
83C2×C4×C181C22×C411yescharacteristic
84C8×C181C22×C411yescharacteristic
85C8×C181C22×C411yescharacteristic
86C22×C181—24no—
87C22×C181—82no—
88C22×C181C4×D411yescharacteristic
89C2×D181—22no—
90C2×D181—24no—
91C2×D181—48no—
92C2×D181—84no—
93C2×D181—82no—
94C2×D181C4×D411yescharacteristic
95C2×D181C22×D411yescharacteristic
96#10624382—24no—
97#10624382—44no—
98C4×C181C4×D411yescharacteristic
99C4×C181C23×C411yescharacteristic
100Dic181C4×D411yescharacteristic
101Dic181C2×#4111yescharacteristic
102C2×C181—21no—
103C2×C181—44no—
104C2×C181C2×C4×D411yescharacteristic
105D181—21no—
106D181—44no—
107D181#57612yes—
108C181#294811yescharacteristic, complemented, Sylow
109#2948—1811nomaximal, Sylow
110C22×D8—1811no—
111#518—1812no—
112#442—1814no—
113C4×D8—1814no—
114#427—1811no—
115#418—1812no—
116#405—1811no—
117C22×D4—1812no—
118C2×D8—1812no—
119C2×D8—1812no—
120C2×D8—1812no—
121C2×D8—1812no—
122C2×D8—1812no—
123C2×D8—1811no—
124C2×D8#1062438211yescharacteristic, complemented
125C2×M16—1811no—
126C22×C8—1811no—
127C4×D4—3624no—
128C4×D4—1818no—
129#117—1812no—
130#117—1811no—
131C2×C22⋊C4—3624no—
132#107—1812no—
133#106—1812no—
134#102—1818no—
135#97—1812no—
136C4×C8—1812no—
137C24—3622no—
138C2×D4—3622no—
139C2×D4—3622no—
140C2×D4—3622no—
141C2×D4—1814no—
142C2×D4—1814no—
143C2×D4—1812no—
144C2×D4C2×#1062438212yescomplemented
145C22×C4—3628no—
146C22×C4—1811no—
147D8—1814no—
148D8—1814no—
149D8—1812no—
150D8—1812no—
151D8C2×#1062438212yescomplemented
152D8C2×#1062438212yescomplemented
153M16—3621no—
154M16—3621no—
155C2×C8—1812no—
156C2×C8—1811no—
157C2×C8—1811no—
158C2×C8—1811no—
159C2×C8—1811no—
160C2×C8—1811no—
161C2×C8C2×#1062438211yescharacteristic, complemented
162C4⋊C4—1814no—
163C4⋊C4—1812no—
164C22⋊C4—3622no—
165C22⋊C4—3628no—
166C22⋊C4—1812no—
167C42—3622no—
168C42—1812no—
169C23—22no—
170C23—3624no—
171C23—3624no—
172C23—3622no—
173C23—14484no—
174C23—1811no—
175D4—22no—
176D4—3624no—
177D4—3624no—
178D4—3622no—
179D4—1814no—
180D4C22×#1062438214yes—
181C2×C4—3624no—
182C2×C4—14488no—
183C2×C4—1814no—
184C2×C4—1811no—
185C2×C4—1811no—
186C2×C4—1811no—
187C2×C4—1811no—
188C2×C4—1811no—
189C2×C4C22×#1062438211yescharacteristic
190C8—3622no—
191C8—1811no—
192C8—1811no—
193C8C22×#1062438211yescharacteristic
194C8C22×#1062438211yescharacteristic
195C22—24no—
196C22—82no—
197C22—3622no—
198C22—3624no—
199C22—14482no—
200C22—14484no—
201C22—1811no—
202C22—1811no—
203C22—7248no—
204C22D4×#1062438211yescharacteristic
205C4—3624no—
206C4—1811no—
207C4—1811no—
208C4—7244no—
209C4D4×#1062438211yescharacteristic
210C4C23×#1062438211yescharacteristic
211C2—21no—
212C2—44no—
213C2—3621no—
214C2—1812no—
215C2—7244no—
216C2C2×D4×#1062438211yescharacteristic
subgroupG/H
centerC2C2×D4×#10624382
commutatorC4×C181C23×C4
FrattiniC4C23×#10624382
FittingC2×D8×C181C4
socleC2×C181C2×C4×D4
prime radicalC2×D8×D181C2
cosocleC4×D181C24
hypercenterC2×D8#10624382
hypocenterC181#2948
LCSG ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #26042346C2semidirect
2. #26042320C2semidirect
3. D8×#10624382C2semidirect
4. #26042289C2semidirect
5. #26042271C2semidirect
6. #26042242C2semidirect
10. D4×#10624382C22semidirect
14. #19153885C22semidirect
15. #19153884C22semidirect
16. #19153878C22semidirect
17. #19153870C22semidirect
18. C8×#10624382C22semidirect
20. C2×D1448C4semidirect
21. C2×#15668434C4semidirect
22. D8×D181C4semidirect
23. D8×D181C4semidirect
27. C2×D8×C181C4semidirect
40. C2×D724C2×C4semidirect
44. D4×D181C2×C4semidirect
47. D1448C2×C4semidirect
48. D1448C2×C4semidirect
49. #15668434C2×C4semidirect
50. #15668434C2×C4semidirect
51. C2×#13089678C2×C4semidirect
52. C8×D181C2×C4semidirect
53. C8×D181C2×C4semidirect
56. C2×D4×C181C2×C4semidirect
57. D8×C181C2×C4semidirect
58. D8×C181C2×C4semidirect
59. C2×C8×C181C2×C4semidirect
108. C181#2948semidirect
124. C2×D8#10624382semidirect
144. C2×D4C2×#10624382semidirect
151. D8C2×#10624382semidirect
152. D8C2×#10624382semidirect
161. C2×C8C2×#10624382semidirect

Maximal subgroups

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

subgroupindex
#260423462
#260423202
D8×#106243822
#260422892
#260422712
#260422422
C2×D8×D1812
#2948181