Finite Group Databasebeta

← C2×#19152032 #26033373

Subgroups — C2×#19152032 #26033373

Order 11392.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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×#15668031C211yesmaximal, characteristic, complemented
2C2×D8×D89C211yesmaximal, characteristic, complemented
3#19152032C218yesmaximal, direct product factor
4C2×#15667957C211yesmaximal, characteristic, complemented
5C2×#15667956C211yesmaximal, characteristic, complemented
6C2×#15667953C211yesmaximal, characteristic, complemented
7C2×#15667951C211yesmaximal, characteristic, complemented
8C2×D16×C89C211yesmaximal, characteristic, complemented
9C2×#13083573—21no—
10C2×D4×D89—21no—
11#15668031—22no—
12#15668031C2214yescomplemented
13C2×Dic356C2211yescharacteristic, complemented
14C2×#13083562—21no—
15C2×D712C2211yescharacteristic
16C2×#13083559—21no—
17D8×D89—22no—
18D8×D89C2214yescomplemented
19C2×C8×D89C2211yescharacteristic
20#15667957C2214yescomplemented
21#15667956C2214yescomplemented
22#15667953C2214yescomplemented
23#15667951C2214yescomplemented
24C2×#13083549C2211yescharacteristic, complemented
25C2×D8×C89C2211yescharacteristic
26C2×D8×C89C2211yescharacteristic, complemented
27D16×C89C2214yescomplemented
28C2×C16×C89C2211yescharacteristic, complemented
29C23×D89—41no—
30#13083573—24no—
31#13083573—42no—
32C2×Dic178—21no—
33C2×D356—21no—
34C2×C22⋊D89—41no—
35C2×C22⋊D89—41no—
36D4×D89—24no—
37D4×D89—42no—
38C22×Dic89—41no—
39C2×C4×D89D411yescharacteristic
40Dic356—21no—
41Dic356C2312yescomplemented
42#13083562—24no—
43D712—21no—
44D712C2312yes—
45#13083559—24no—
46C2×#10623494D411yescharacteristic
47C8×D89D412yes—
48C8×D89C2312yes—
49#13083549C2312yescomplemented
50C2×D4×C89—21no—
51C2×D4×C89—21no—
52D8×C89—21no—
53D8×C89—21no—
54D8×C89C2312yes—
55D8×C89C2312yescomplemented
56C2×C8×C89C2311yescharacteristic
57C16×C89C2312yescomplemented
58C23×C89—41no—
59C23×C89—41no—
60C22×D89—41no—
61C22×D89—44no—
62C22×D89—84no—
63C22×D89D811yescharacteristic
64D4×C89—22no—
65D4×C89—22no—
66D4×C89—41no—
67D4×C89—41no—
68C2×C4×C89C2×D411yescharacteristic
69C22⋊D89—44no—
70C22⋊D89—44no—
71C2×Dic89—41no—
72C2×Dic89—44no—
73C2×Dic89D811yescharacteristic
74D356—22no—
75D356—41no—
76C4×D89D812yes—
77C4×D89C2×D412yes—
78Dic178—22no—
79Dic178—41no—
80C8×C89C2×D411yescharacteristic
81C8×C89C2411yescharacteristic
82#10623494C2×D412yes—
83C22×C89—42no—
84C22×C89—42no—
85C22×C89—82no—
86C22×C89—82no—
87C22×C89C2×D811yescharacteristic
88C2×D89—22no—
89C2×D89—42no—
90C2×D89—88no—
91C2×D89—82no—
92C2×D89C2×D812yes—
93C4×C89C2×D811yescharacteristic
94C4×C89C22×D411yescharacteristic
95Dic89—42no—
96Dic89C2×D812yes—
97C2×C89—82no—
98C2×C89—82no—
99C2×C89#50912yescomplemented
100C2×C89C22×D811yescharacteristic
101D89—22no—
102D89—82no—
103C2×#509—891nomaximal, Sylow
104C89C2×#50911yescharacteristic, complemented, Sylow
105C2×#135—891no—
106C22×D8—891no—
107#509—898no—
108C2×SD32—891no—
109C2×SD32—891no—
110C2×D16—891no—
111C2×D16D8911yescharacteristic, complemented
112C2×M32—891no—
113C2×#41—1781no—
114C22×D4—1781no—
115#135—894no—
116#135—1782no—
117C2×Q16—891no—
118C2×SD16—1781no—
119C2×D8—894no—
120C2×D8—891no—
121C2×D8—1782no—
122C2×D8—1781no—
123C2×D8C2×D8911yescharacteristic
124C2×D8C2×D8911yescharacteristic, complemented
125C22×C8—891no—
126SD32—894no—
127SD32—894no—
128D16—894no—
129D16C2×D8914yescomplemented
130M32—894no—
131C2×C16—891no—
132C2×C16C2×D8911yescharacteristic, complemented
133C24—3561no—
134#41—3562no—
135#41—1784no—
136C2×Q8—1781no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—3562no—
140C2×D4—3561no—
141C2×D4—3561no—
142C2×D4—1784no—
143C2×D4—1781no—
144C22×C4—891no—
145C22×C4—3561no—
146Q16—892no—
147Q16—1781no—
148SD16—1784no—
149D8—21no—
150D8—21no—
151D8—892no—
152D8—1784no—
153D8—1781no—
154D8C22×D8912yes—
155D8C22×D8912yescomplemented
156C2×C8—891no—
157C2×C8—892no—
158C2×C8—892no—
159C2×C8C22×D8911yescharacteristic
160C16—892no—
161C16C22×D8912yescomplemented
162C23—41no—
163C23—41no—
164C23—891no—
165C23—3564no—
166C23—3561no—
167C23—7124no—
168Q8—3561no—
169Q8—1782no—
170D4—22no—
171D4—22no—
172D4—41no—
173D4—41no—
174D4—3564no—
175D4—3564no—
176D4—3561no—
177D4—1782no—
178C2×C4—891no—
179C2×C4—892no—
180C2×C4—892no—
181C2×C4—3564no—
182C2×C4—3561no—
183C2×C4D4×D8911yescharacteristic
184C8—892no—
185C8D4×D8911yescharacteristic
186C8C23×D8911yescharacteristic
187C22—42no—
188C22—42no—
189C22—82no—
190C22—82no—
191C22—892no—
192C22—3562no—
193C22—1782no—
194C22—7128no—
195C22—7122no—
196C22D8×D8911yescharacteristic
197C4—892no—
198C4—3562no—
199C4D8×D8911yescharacteristic
200C4C2×D4×D8911yescharacteristic
201C2—82no—
202C2—82no—
203C2—1782no—
204C2—7122no—
205C2#1915203212yesdirect product factor
206C2C2×D8×D8911yescharacteristic
subgroupG/H
centerC22D8×D89
commutator, cosocleC8×C89C24
FrattiniC8C23×D89
FittingC2×D16×C89C2
socleC22×C89C2×D8
hypercenterC2×D16D89
hypocenterC89C2×#509
LCSG ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. C2×#15668031C2semidirect
2. C2×D8×D89C2semidirect
3. #19152032C2direct (N × H)
4. C2×#15667957C2semidirect
5. C2×#15667956C2semidirect
6. C2×#15667953C2semidirect
7. C2×#15667951C2semidirect
8. C2×D16×C89C2semidirect
12. #15668031C22semidirect
13. C2×Dic356C22semidirect
18. D8×D89C22semidirect
20. #15667957C22semidirect
21. #15667956C22semidirect
22. #15667953C22semidirect
23. #15667951C22semidirect
24. C2×#13083549C22semidirect
26. C2×D8×C89C22semidirect
27. D16×C89C22semidirect
28. C2×C16×C89C22semidirect
41. Dic356C23semidirect
49. #13083549C23semidirect
55. D8×C89C23semidirect
57. C16×C89C23semidirect
99. C2×C89#509semidirect
104. C89C2×#509semidirect
111. C2×D16D89semidirect
124. C2×D8C2×D89semidirect
129. D16C2×D89semidirect
132. C2×C16C2×D89semidirect
155. D8C22×D89semidirect
161. C16C22×D89semidirect
205. C2#19152032direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156680312
C2×D8×D892
#191520322
C2×#156679572
C2×#156679562
C2×#156679532
C2×#156679512
C2×D16×C892
C2×#50989