Finite Group Databasebeta

← C2×D8×#10624382 #37550468

Subgroups — C2×D8×#10624382 #37550468

Order 23168.

616 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 178 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×D4×#10624382C212yesmaximal, complemented
2D8×#10624382C218yesmaximal, direct product factor
3C2×#19153885C211yesmaximal, characteristic, complemented
4C2×#19153878C212yesmaximal, complemented
5C2×C8×#10624382C211yesmaximal, characteristic, complemented
6C2×D8×D181C211yesmaximal, characteristic
7C23×#10624382—22no—
8C2×D181⋊C8C2211yescharacteristic
9D4×#10624382—24no—
10D4×#10624382C2218yescomplemented
11C2×C4⋊#10624382C2212yes—
12C2×C22⋊#10624382—22no—
13C2×C4×#10624382C2211yescharacteristic
14#19153885C2214yescomplemented
15#19153878C2218yescomplemented
16C8×#10624382C2214yescomplemented
17C2×D4×D181C2212yes—
18C2×D1448C411yescharacteristic, complemented
19C2×#15668434C412yescomplemented
20D8×D181C414yescomplemented
21D8×D181C2214yes—
22C2×C8×D181C2211yescharacteristic
23C2×D8×C181C411yescharacteristic, complemented
24C22×#10624382—28no—
25C22×#10624382—22no—
26C22×#10624382—48no—
27C22×#10624382D411yescharacteristic
28C22×#10624382D411yescharacteristic
29D181⋊C8—21no—
30D181⋊C8C2312yes—
31C2×#13089685—21no—
32C4⋊#10624382—22no—
33C4⋊#10624382C2314yes—
34C22⋊#10624382—28no—
35C4×#10624382D412yes—
36C4×#10624382C2312yes—
37C23×D181—22no—
38C2×D724C2×C412yescomplemented
39C2×C22⋊D181—22no—
40D4×D181—22no—
41D4×D181—22no—
42D4×D181C2×C414yescomplemented
43D4×D181C2314yes—
44C2×C4×D181C2311yescharacteristic
45D1448C2×C414yescomplemented
46#15668434C2×C418yescomplemented
47C2×#13089678C2×C411yescharacteristic, complemented
48C8×D181C2×C412yescomplemented
49C8×D181C2312yes—
50C2×D4×C181C2×C412yescomplemented
51D8×C181C2×C414yescomplemented
52C2×C8×C181C2×C411yescharacteristic, complemented
53C2×#10624382—22no—
54C2×#10624382—24no—
55C2×#10624382—44no—
56C2×#10624382—416no—
57C2×#10624382D814yesdirect product factor
58C2×#10624382C2×D412yes—
59C2×#10624382C2×D412yes—
60#13089685—22no—
61C22×D181—22no—
62C22×D181—24no—
63C22×D181—24no—
64C22×D181—44no—
65C22×D181—44no—
66C22×D181C2×D411yescharacteristic
67D724—22no—
68D724C22×C414yescomplemented
69C22⋊D181—24no—
70C22⋊D181—24no—
71C2×Dic181#4111yescharacteristic
72C4×D181C22×C411yescharacteristic
73C4×D181C2×D411yescharacteristic
74C4×D181#4111yescharacteristic
75C4×D181C2411yescharacteristic
76#13089678C22×C412yescomplemented
77C23×C181—22no—
78D4×C181—22no—
79D4×C181C22×C414yescomplemented
80C2×C4×C181C22×C411yescharacteristic
81C8×C181C22×C412yescomplemented
82C22×C181—24no—
83C22×C181—44no—
84C22×C181C4×D411yescharacteristic
85C2×D181—24no—
86C2×D181—44no—
87C2×D181—44no—
88C2×D181—44no—
89C2×D181—48no—
90C2×D181C4×D411yescharacteristic
91C2×D181C2×D812yes—
92C2×D181#13512yes—
93C2×D181C22×D411yescharacteristic
94#10624382—22no—
95#10624382—44no—
96#10624382C2×D814yesdirect product factor
97C4×C181C4×D411yescharacteristic
98C4×C181C23×C411yescharacteristic
99Dic181C4×D411yescharacteristic
100Dic181C2×#4111yescharacteristic
101C2×C181—44no—
102C2×C181C4×D812yescomplemented
103C2×C181C2×C4×D411yescharacteristic
104D181—44no—
105D181C4×D812yescomplemented
106D181C22×D811yescharacteristic
107D181C2×#13511yescharacteristic
108C181C2×C4×D811yescharacteristic, complemented, Sylow
109C2×C4×D8—1811nomaximal, Sylow
110C22×D8—1811no—
111C2×C4×D4—1812no—
112C4×D8—1818no—
113C2×#107—1811no—
114C2×#102—1812no—
115C2×C4×C8—1811no—
116C22×D4—1812no—
117C23×C4—3622no—
118C2×D8—1812no—
119C2×D8—1814no—
120C2×D8—1814no—
121C2×D8—1811no—
122C2×D8#1062438211yescharacteristic, direct product factor
123C22×C8—1811no—
124C22×C8—1811no—
125C4×D4—3624no—
126C4×D4—1818no—
127C2×C4⋊C4—1812no—
128C2×C22⋊C4—3622no—
129C2×C42—1811no—
130#107—1814no—
131#102—1818no—
132C4×C8—1814no—
133C24—3622no—
134C2×D4—3622no—
135C2×D4—3622no—
136C2×D4—3622no—
137C2×D4—1814no—
138C2×D4—1814no—
139C2×D4—1812no—
140C2×D4C2×#1062438212yescomplemented
141C22×C4—3622no—
142C22×C4—3628no—
143C22×C4—1811no—
144C22×C4—1811no—
145C22×C4—1811no—
146C22×C4—7248no—
147D8—1818no—
148D8—1814no—
149D8C2×#1062438214yesdirect product factor
150C2×C8—3621no—
151C2×C8—3621no—
152C2×C8—1812no—
153C2×C8—1811no—
154C2×C8—1812no—
155C2×C8—1812no—
156C2×C8C2×#1062438211yescharacteristic, complemented
157C4⋊C4—3622no—
158C4⋊C4—1814no—
159C22⋊C4—3628no—
160C42—1812no—
161C42—1812no—
162C23—22no—
163C23—3624no—
164C23—3624no—
165C23—3622no—
166C23—1811no—
167C23—7244no—
168C23—7244no—
169D4—22no—
170D4—3624no—
171D4—3624no—
172D4—3622no—
173D4—1814no—
174D4C22×#1062438214yescomplemented
175C2×C4—3622no—
176C2×C4—3624no—
177C2×C4—1812no—
178C2×C4—1812no—
179C2×C4—1814no—
180C2×C4—1811no—
181C2×C4—1811no—
182C2×C4—1811no—
183C2×C4—1811no—
184C2×C4—1811no—
185C2×C4—72416no—
186C2×C4—7244no—
187C2×C4C22×#1062438211yescharacteristic
188C8—3622no—
189C8—1812no—
190C8C22×#1062438212yescomplemented
191C22—24no—
192C22—44no—
193C22—3624no—
194C22—1812no—
195C22—1812no—
196C22—1811no—
197C22—1811no—
198C22—7244no—
199C22—7244no—
200C22—7248no—
201C22—7244no—
202C22D4×#1062438211yescharacteristic
203C4—3622no—
204C4—1814no—
205C4—1811no—
206C4—1811no—
207C4—7244no—
208C4D4×#1062438211yescharacteristic
209C4C23×#1062438211yescharacteristic
210C2—44no—
211C2—1811no—
212C2—1811no—
213C2—1812no—
214C2—7244no—
215C2D8×#1062438212yesdirect product factor
216C2C2×D4×#1062438211yescharacteristic
subgroupG/H
centerC22D4×#10624382
commutatorC4×C181C23×C4
FrattiniC4C23×#10624382
FittingC2×D8×C181C4
socleC22×C181C4×D4
prime radicalC2×D8×D181C2
cosocleC4×D181C24
hypercenterC2×D8#10624382
hypocenterC181C2×C4×D8
LCSG ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×#10624382C2semidirect
2. D8×#10624382C2direct (N × H)
3. C2×#19153885C2semidirect
4. C2×#19153878C2semidirect
5. C2×C8×#10624382C2semidirect
10. D4×#10624382C22semidirect
14. #19153885C22semidirect
15. #19153878C22semidirect
16. C8×#10624382C22semidirect
18. C2×D1448C4semidirect
19. C2×#15668434C4semidirect
20. D8×D181C4semidirect
23. C2×D8×C181C4semidirect
38. C2×D724C2×C4semidirect
42. D4×D181C2×C4semidirect
45. D1448C2×C4semidirect
46. #15668434C2×C4semidirect
47. C2×#13089678C2×C4semidirect
48. C8×D181C2×C4semidirect
50. C2×D4×C181C2×C4semidirect
51. D8×C181C2×C4semidirect
52. C2×C8×C181C2×C4semidirect
57. C2×#10624382D8direct (N × H)
68. D724C22×C4semidirect
76. #13089678C22×C4semidirect
79. D4×C181C22×C4semidirect
81. C8×C181C22×C4semidirect
96. #10624382C2×D8direct (N × H)
102. C2×C181C4×D8semidirect
105. D181C4×D8semidirect
108. C181C2×C4×D8semidirect
122. C2×D8#10624382direct (N × H)
140. C2×D4C2×#10624382semidirect
149. D8C2×#10624382direct (N × H)
156. C2×C8C2×#10624382semidirect
174. D4C22×#10624382semidirect
190. C8C22×#10624382semidirect
215. C2D8×#10624382direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×#106243822
D8×#106243822
C2×#191538852
C2×#191538782
C2×C8×#106243822
C2×D8×D1812
C2×C4×D8181