Finite Group Databasebeta

← C2×#19152035 #26033376

Subgroups — C2×#19152035 #26033376

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×#15668035C211yesmaximal, characteristic, complemented
2C2×D8×D89C211yesmaximal, characteristic, complemented
3#19152035C218yesmaximal, direct product factor
4C2×#15667955C211yesmaximal, characteristic, complemented
5C2×D1424C211yesmaximal, characteristic, complemented
6C2×#15667953C211yesmaximal, characteristic, complemented
7C2×#15667951C211yesmaximal, characteristic, complemented
8C2×SD32×C89C211yesmaximal, characteristic, complemented
9C2×#13083575—21no—
10C2×D4×D89—21no—
11#15668035—22no—
12#15668035C2214yescomplemented
13C2×#13083561—21no—
14C2×D712C2211yescharacteristic
15C2×D712C2211yescharacteristic, complemented
16C2×#13083559—21no—
17D8×D89—22no—
18D8×D89C2214yescomplemented
19C2×C8×D89C2211yescharacteristic
20#15667955C2214yescomplemented
21D1424C2214yescomplemented
22#15667953C2214yescomplemented
23#15667951C2214yescomplemented
24C2×#13083549C2211yescharacteristic, complemented
25C2×Q16×C89C2211yescharacteristic, complemented
26C2×D8×C89C2211yescharacteristic
27SD32×C89C2214yescomplemented
28C2×C16×C89C2211yescharacteristic, complemented
29C23×D89—41no—
30#13083575—24no—
31#13083575—42no—
32C2×D356—21no—
33C2×D356—21no—
34C2×D356—41no—
35C2×C22⋊D89—41no—
36D4×D89—24no—
37D4×D89—42no—
38C2×C4×D89—41no—
39C2×C4×D89D411yescharacteristic
40#13083561—24no—
41D712—21no—
42D712—21no—
43D712C2312yes—
44D712C2312yescomplemented
45#13083559—24no—
46C2×#10623494D411yescharacteristic
47C8×D89D412yes—
48C8×D89C2312yes—
49#13083549C2312yescomplemented
50C2×Q8×C89—21no—
51C2×D4×C89—21no—
52Q16×C89—21no—
53Q16×C89C2312yescomplemented
54D8×C89—21no—
55D8×C89C2312yes—
56C2×C8×C89C2311yescharacteristic
57C16×C89C2312yescomplemented
58C23×C89—41no—
59C22×D89—41no—
60C22×D89—41no—
61C22×D89—44no—
62C22×D89—84no—
63C22×D89D811yescharacteristic
64Q8×C89—22no—
65Q8×C89—41no—
66D4×C89—22no—
67D4×C89—41no—
68C2×C4×C89—41no—
69C2×C4×C89C2×D411yescharacteristic
70C22⋊D89—44no—
71C2×Dic89D811yescharacteristic
72D356—22no—
73D356—22no—
74D356—44no—
75D356—41no—
76D356—41no—
77C4×D89—44no—
78C4×D89D812yes—
79C4×D89C2×D412yes—
80C8×C89C2×D411yescharacteristic
81C8×C89C2411yescharacteristic
82#10623494C2×D412yes—
83C22×C89—42no—
84C22×C89—82no—
85C22×C89C2×D811yescharacteristic
86C2×D89—22no—
87C2×D89—42no—
88C2×D89—42no—
89C2×D89—88no—
90C2×D89—82no—
91C2×D89—82no—
92C2×D89C2×D812yes—
93C4×C89—42no—
94C4×C89C2×D811yescharacteristic
95C4×C89C22×D411yescharacteristic
96Dic89C2×D812yes—
97C2×C89—82no—
98C2×C89#50912yescomplemented
99C2×C89C22×D811yescharacteristic
100D89—22no—
101D89—82no—
102D89—82no—
103C2×#509—891nomaximal, Sylow
104C89C2×#50911yescharacteristic, complemented, Sylow
105C2×#135—891no—
106C22×D8—891no—
107#509—898no—
108C2×SD32—891no—
109C2×SD32D8911yescharacteristic, complemented
110C2×D16—891no—
111C2×D16—891no—
112C2×M32—891no—
113C2×#41—1781no—
114C22×D4—1781no—
115#135—894no—
116#135—1782no—
117C2×Q16C2×D8911yescharacteristic, complemented
118C2×SD16—1781no—
119C2×D8—894no—
120C2×D8—891no—
121C2×D8—891no—
122C2×D8—1782no—
123C2×D8—1781no—
124C2×D8C2×D8911yescharacteristic
125C22×C8—891no—
126SD32—894no—
127SD32C2×D8914yescomplemented
128D16—894no—
129D16—894no—
130M32—894no—
131C2×C16—891no—
132C2×C16C2×D8911yescharacteristic, complemented
133C24—3561no—
134#41—3562no—
135#41—1784no—
136C2×Q8—21no—
137C2×D4—21no—
138C2×D4—3561no—
139C2×D4—3562no—
140C2×D4—3561no—
141C2×D4—1784no—
142C2×D4—1781no—
143C2×D4—1781no—
144C22×C4—891no—
145C22×C4—3561no—
146Q16—21no—
147Q16C22×D8912yescomplemented
148SD16—1784no—
149D8—21no—
150D8—892no—
151D8—892no—
152D8—1784no—
153D8—1781no—
154D8—1781no—
155D8C22×D8912yes—
156C2×C8—891no—
157C2×C8—892no—
158C2×C8—892no—
159C2×C8C22×D8911yescharacteristic
160C16—892no—
161C16C22×D8912yescomplemented
162C23—41no—
163C23—891no—
164C23—3564no—
165C23—3561no—
166C23—3561no—
167C23—7124no—
168Q8—22no—
169Q8—41no—
170D4—22no—
171D4—41no—
172D4—3564no—
173D4—3564no—
174D4—3561no—
175D4—3561no—
176D4—1782no—
177D4—1782no—
178C2×C4—41no—
179C2×C4—891no—
180C2×C4—892no—
181C2×C4—892no—
182C2×C4—3564no—
183C2×C4D4×D8911yescharacteristic
184C8—892no—
185C8D4×D8911yescharacteristic
186C8C23×D8911yescharacteristic
187C22—42no—
188C22—82no—
189C22—892no—
190C22—3562no—
191C22—3562no—
192C22—1782no—
193C22—7128no—
194C22—7122no—
195C22—7122no—
196C22D8×D8911yescharacteristic
197C4—42no—
198C4—892no—
199C4D8×D8911yescharacteristic
200C4C2×D4×D8911yescharacteristic
201C2—82no—
202C2—1782no—
203C2—7122no—
204C2—7122no—
205C2#1915203512yesdirect product factor
206C2C2×D8×D8911yescharacteristic
subgroupG/H
centerC22D8×D89
commutator, cosocleC8×C89C24
FrattiniC8C23×D89
FittingC2×SD32×C89C2
socleC22×C89C2×D8
hypercenterC2×SD32D89
hypocenterC89C2×#509
LCSG ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#15668035C2semidirect
2. C2×D8×D89C2semidirect
3. #19152035C2direct (N × H)
4. C2×#15667955C2semidirect
5. C2×D1424C2semidirect
6. C2×#15667953C2semidirect
7. C2×#15667951C2semidirect
8. C2×SD32×C89C2semidirect
12. #15668035C22semidirect
15. C2×D712C22semidirect
18. D8×D89C22semidirect
20. #15667955C22semidirect
21. D1424C22semidirect
22. #15667953C22semidirect
23. #15667951C22semidirect
24. C2×#13083549C22semidirect
25. C2×Q16×C89C22semidirect
27. SD32×C89C22semidirect
28. C2×C16×C89C22semidirect
44. D712C23semidirect
49. #13083549C23semidirect
53. Q16×C89C23semidirect
57. C16×C89C23semidirect
98. C2×C89#509semidirect
104. C89C2×#509semidirect
109. C2×SD32D89semidirect
117. C2×Q16C2×D89semidirect
127. SD32C2×D89semidirect
132. C2×C16C2×D89semidirect
147. Q16C22×D89semidirect
161. C16C22×D89semidirect
205. C2#19152035direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156680352
C2×D8×D892
#191520352
C2×#156679552
C2×D14242
C2×#156679532
C2×#156679512
C2×SD32×C892
C2×#50989