Finite Group Databasebeta

← C2×D8×#10621924 #36370310

Subgroups — C2×D8×#10621924 #36370310

Order 22144.

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×#10621924C212yesmaximal, complemented
2D8×#10621924C218yesmaximal, direct product factor
3C2×#19149748C211yesmaximal, characteristic, complemented
4C2×#19149741C212yesmaximal, complemented
5C2×C8×#10621924C211yesmaximal, characteristic, complemented
6C2×D8×D173C211yesmaximal, characteristic
7C23×#10621924—22no—
8C2×D173⋊C8C2211yescharacteristic
9D4×#10621924—24no—
10D4×#10621924C2218yescomplemented
11C2×C4⋊#10621924C2212yes—
12C2×C22⋊#10621924—22no—
13C2×C4×#10621924C2211yescharacteristic
14#19149748C2214yescomplemented
15#19149741C2218yescomplemented
16C8×#10621924C2214yescomplemented
17C2×D4×D173C2212yes—
18C2×D1384C411yescharacteristic, complemented
19C2×#14583811C412yescomplemented
20D8×D173C414yescomplemented
21D8×D173C2214yes—
22C2×C8×D173C2211yescharacteristic
23C2×D8×C173C411yescharacteristic, complemented
24C22×#10621924—28no—
25C22×#10621924—22no—
26C22×#10621924—48no—
27C22×#10621924D411yescharacteristic
28C22×#10621924D411yescharacteristic
29D173⋊C8—21no—
30D173⋊C8C2312yes—
31C2×#13063443—21no—
32C4⋊#10621924—22no—
33C4⋊#10621924C2314yes—
34C22⋊#10621924—28no—
35C4×#10621924D412yes—
36C4×#10621924C2312yes—
37C23×D173—22no—
38C2×D692C2×C412yescomplemented
39C2×C22⋊D173—22no—
40D4×D173—22no—
41D4×D173—22no—
42D4×D173C2×C414yescomplemented
43D4×D173C2314yes—
44C2×C4×D173C2311yescharacteristic
45D1384C2×C414yescomplemented
46#14583811C2×C418yescomplemented
47C2×#13063436C2×C411yescharacteristic, complemented
48C8×D173C2×C412yescomplemented
49C8×D173C2312yes—
50C2×D4×C173C2×C412yescomplemented
51D8×C173C2×C414yescomplemented
52C2×C8×C173C2×C411yescharacteristic, complemented
53C2×#10621924—22no—
54C2×#10621924—24no—
55C2×#10621924—44no—
56C2×#10621924—416no—
57C2×#10621924D814yesdirect product factor
58C2×#10621924C2×D412yes—
59C2×#10621924C2×D412yes—
60#13063443—22no—
61C22×D173—22no—
62C22×D173—24no—
63C22×D173—24no—
64C22×D173—44no—
65C22×D173—44no—
66C22×D173C2×D411yescharacteristic
67D692—22no—
68D692C22×C414yescomplemented
69C22⋊D173—24no—
70C22⋊D173—24no—
71C2×Dic173#4111yescharacteristic
72C4×D173C22×C411yescharacteristic
73C4×D173C2×D411yescharacteristic
74C4×D173#4111yescharacteristic
75C4×D173C2411yescharacteristic
76#13063436C22×C412yescomplemented
77C23×C173—22no—
78D4×C173—22no—
79D4×C173C22×C414yescomplemented
80C2×C4×C173C22×C411yescharacteristic
81C8×C173C22×C412yescomplemented
82C22×C173—24no—
83C22×C173—44no—
84C22×C173C4×D411yescharacteristic
85C2×D173—24no—
86C2×D173—44no—
87C2×D173—44no—
88C2×D173—44no—
89C2×D173—48no—
90C2×D173C4×D411yescharacteristic
91C2×D173C2×D812yes—
92C2×D173#13512yes—
93C2×D173C22×D411yescharacteristic
94#10621924—22no—
95#10621924—44no—
96#10621924C2×D814yesdirect product factor
97C4×C173C4×D411yescharacteristic
98C4×C173C23×C411yescharacteristic
99Dic173C4×D411yescharacteristic
100Dic173C2×#4111yescharacteristic
101C2×C173—44no—
102C2×C173C4×D812yescomplemented
103C2×C173C2×C4×D411yescharacteristic
104D173—44no—
105D173C4×D812yescomplemented
106D173C22×D811yescharacteristic
107D173C2×#13511yescharacteristic
108C173C2×C4×D811yescharacteristic, complemented, Sylow
109C2×C4×D8—1731nomaximal, Sylow
110C22×D8—1731no—
111C2×C4×D4—1732no—
112C4×D8—1738no—
113C2×#107—1731no—
114C2×#102—1732no—
115C2×C4×C8—1731no—
116C22×D4—1732no—
117C23×C4—3462no—
118C2×D8—1732no—
119C2×D8—1734no—
120C2×D8—1734no—
121C2×D8—1731no—
122C2×D8#1062192411yescharacteristic, direct product factor
123C22×C8—1731no—
124C22×C8—1731no—
125C4×D4—3464no—
126C4×D4—1738no—
127C2×C4⋊C4—1732no—
128C2×C22⋊C4—3462no—
129C2×C42—1731no—
130#107—1734no—
131#102—1738no—
132C4×C8—1734no—
133C24—3462no—
134C2×D4—3462no—
135C2×D4—3462no—
136C2×D4—3462no—
137C2×D4—1734no—
138C2×D4—1734no—
139C2×D4—1732no—
140C2×D4C2×#1062192412yescomplemented
141C22×C4—3462no—
142C22×C4—3468no—
143C22×C4—1731no—
144C22×C4—1731no—
145C22×C4—1731no—
146C22×C4—6928no—
147D8—1738no—
148D8—1734no—
149D8C2×#1062192414yesdirect product factor
150C2×C8—3461no—
151C2×C8—3461no—
152C2×C8—1732no—
153C2×C8—1731no—
154C2×C8—1732no—
155C2×C8—1732no—
156C2×C8C2×#1062192411yescharacteristic, complemented
157C4⋊C4—3462no—
158C4⋊C4—1734no—
159C22⋊C4—3468no—
160C42—1732no—
161C42—1732no—
162C23—22no—
163C23—3464no—
164C23—3464no—
165C23—3462no—
166C23—1731no—
167C23—6924no—
168C23—6924no—
169D4—22no—
170D4—3464no—
171D4—3464no—
172D4—3462no—
173D4—1734no—
174D4C22×#1062192414yescomplemented
175C2×C4—3462no—
176C2×C4—3464no—
177C2×C4—1732no—
178C2×C4—1734no—
179C2×C4—1732no—
180C2×C4—1731no—
181C2×C4—1731no—
182C2×C4—1731no—
183C2×C4—1731no—
184C2×C4—1731no—
185C2×C4—69216no—
186C2×C4—6924no—
187C2×C4C22×#1062192411yescharacteristic
188C8—3462no—
189C8—1732no—
190C8C22×#1062192412yescomplemented
191C22—24no—
192C22—44no—
193C22—3464no—
194C22—1732no—
195C22—1732no—
196C22—1731no—
197C22—1731no—
198C22—6924no—
199C22—6924no—
200C22—6928no—
201C22—6924no—
202C22D4×#1062192411yescharacteristic
203C4—3462no—
204C4—1734no—
205C4—1731no—
206C4—1731no—
207C4—6924no—
208C4D4×#1062192411yescharacteristic
209C4C23×#1062192411yescharacteristic
210C2—44no—
211C2—1731no—
212C2—1731no—
213C2—1732no—
214C2—6924no—
215C2D8×#1062192412yesdirect product factor
216C2C2×D4×#1062192411yescharacteristic
subgroupG/H
centerC22D4×#10621924
commutatorC4×C173C23×C4
FrattiniC4C23×#10621924
FittingC2×D8×C173C4
socleC22×C173C4×D4
prime radicalC2×D8×D173C2
cosocleC4×D173C24
hypercenterC2×D8#10621924
hypocenterC173C2×C4×D8
LCSG ▷ C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×#10621924C2semidirect
2. D8×#10621924C2direct (N × H)
3. C2×#19149748C2semidirect
4. C2×#19149741C2semidirect
5. C2×C8×#10621924C2semidirect
10. D4×#10621924C22semidirect
14. #19149748C22semidirect
15. #19149741C22semidirect
16. C8×#10621924C22semidirect
18. C2×D1384C4semidirect
19. C2×#14583811C4semidirect
20. D8×D173C4semidirect
23. C2×D8×C173C4semidirect
38. C2×D692C2×C4semidirect
42. D4×D173C2×C4semidirect
45. D1384C2×C4semidirect
46. #14583811C2×C4semidirect
47. C2×#13063436C2×C4semidirect
48. C8×D173C2×C4semidirect
50. C2×D4×C173C2×C4semidirect
51. D8×C173C2×C4semidirect
52. C2×C8×C173C2×C4semidirect
57. C2×#10621924D8direct (N × H)
68. D692C22×C4semidirect
76. #13063436C22×C4semidirect
79. D4×C173C22×C4semidirect
81. C8×C173C22×C4semidirect
96. #10621924C2×D8direct (N × H)
102. C2×C173C4×D8semidirect
105. D173C4×D8semidirect
108. C173C2×C4×D8semidirect
122. C2×D8#10621924direct (N × H)
140. C2×D4C2×#10621924semidirect
149. D8C2×#10621924direct (N × H)
156. C2×C8C2×#10621924semidirect
174. D4C22×#10621924semidirect
190. C8C22×#10621924semidirect
215. C2D8×#10621924direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×#106219242
D8×#106219242
C2×#191497482
C2×#191497412
C2×C8×#106219242
C2×D8×D1732
C2×C4×D8173