Finite Group Databasebeta

← C2×#20261169 #27154857

Subgroups — C2×#20261169 #27154857

Order 12416.

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×#15690829C211yesmaximal, characteristic, complemented
2C2×D8×D97C211yesmaximal, characteristic, complemented
3#20261169C218yesmaximal, direct product factor
4C2×#15690755C211yesmaximal, characteristic, complemented
5C2×#15690754C211yesmaximal, characteristic, complemented
6C2×#15690751C211yesmaximal, characteristic, complemented
7C2×#15690749C211yesmaximal, characteristic, complemented
8C2×D16×C97C211yesmaximal, characteristic, complemented
9C2×#13095510—21no—
10C2×D4×D97—21no—
11#15690829—22no—
12#15690829C2214yescomplemented
13C2×Dic388C2211yescharacteristic, complemented
14C2×#13095499—21no—
15C2×D776C2211yescharacteristic
16C2×#13095496—21no—
17D8×D97—22no—
18D8×D97C2214yescomplemented
19C2×C8×D97C2211yescharacteristic
20#15690755C2214yescomplemented
21#15690754C2214yescomplemented
22#15690751C2214yescomplemented
23#15690749C2214yescomplemented
24C2×#13095486C2211yescharacteristic, complemented
25C2×D8×C97C2211yescharacteristic
26C2×D8×C97C2211yescharacteristic, complemented
27D16×C97C2214yescomplemented
28C2×C16×C97C2211yescharacteristic, complemented
29C23×D97—41no—
30#13095510—24no—
31#13095510—42no—
32C2×Dic194—21no—
33C2×D388—21no—
34C2×C22⋊D97—41no—
35C2×C22⋊D97—41no—
36D4×D97—24no—
37D4×D97—42no—
38C22×Dic97—41no—
39C2×C4×D97D411yescharacteristic
40Dic388—21no—
41Dic388C2312yescomplemented
42#13095499—24no—
43D776—21no—
44D776C2312yes—
45#13095496—24no—
46C2×#11715895D411yescharacteristic
47C8×D97D412yes—
48C8×D97C2312yes—
49#13095486C2312yescomplemented
50C2×D4×C97—21no—
51C2×D4×C97—21no—
52D8×C97—21no—
53D8×C97—21no—
54D8×C97C2312yes—
55D8×C97C2312yescomplemented
56C2×C8×C97C2311yescharacteristic
57C16×C97C2312yescomplemented
58C23×C97—41no—
59C23×C97—41no—
60C22×D97—41no—
61C22×D97—44no—
62C22×D97—84no—
63C22×D97D811yescharacteristic
64D4×C97—22no—
65D4×C97—22no—
66D4×C97—41no—
67D4×C97—41no—
68C2×C4×C97C2×D411yescharacteristic
69C22⋊D97—44no—
70C22⋊D97—44no—
71C2×Dic97—41no—
72C2×Dic97—44no—
73C2×Dic97D811yescharacteristic
74D388—22no—
75D388—41no—
76C4×D97D812yes—
77C4×D97C2×D412yes—
78Dic194—22no—
79Dic194—41no—
80C8×C97C2×D411yescharacteristic
81C8×C97C2411yescharacteristic
82#11715895C2×D412yes—
83C22×C97—42no—
84C22×C97—42no—
85C22×C97—82no—
86C22×C97—82no—
87C22×C97C2×D811yescharacteristic
88C2×D97—22no—
89C2×D97—42no—
90C2×D97—88no—
91C2×D97—82no—
92C2×D97C2×D812yes—
93C4×C97C2×D811yescharacteristic
94C4×C97C22×D411yescharacteristic
95Dic97—42no—
96Dic97C2×D812yes—
97C2×C97—82no—
98C2×C97—82no—
99C2×C97#50912yescomplemented
100C2×C97C22×D811yescharacteristic
101D97—22no—
102D97—82no—
103C2×#509—971nomaximal, Sylow
104C97C2×#50911yescharacteristic, complemented, Sylow
105C2×#135—971no—
106C22×D8—971no—
107#509—978no—
108C2×SD32—971no—
109C2×SD32—971no—
110C2×D16—971no—
111C2×D16D9711yescharacteristic, complemented
112C2×M32—971no—
113C2×#41—1941no—
114C22×D4—1941no—
115#135—974no—
116#135—1942no—
117C2×Q16—971no—
118C2×SD16—1941no—
119C2×D8—974no—
120C2×D8—971no—
121C2×D8—1942no—
122C2×D8—1941no—
123C2×D8C2×D9711yescharacteristic
124C2×D8C2×D9711yescharacteristic, complemented
125C22×C8—971no—
126SD32—974no—
127SD32—974no—
128D16—974no—
129D16C2×D9714yescomplemented
130M32—974no—
131C2×C16—971no—
132C2×C16C2×D9711yescharacteristic, complemented
133C24—3881no—
134#41—3882no—
135#41—1944no—
136C2×Q8—1941no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—3882no—
140C2×D4—3881no—
141C2×D4—3881no—
142C2×D4—1944no—
143C2×D4—1941no—
144C22×C4—971no—
145C22×C4—3881no—
146Q16—972no—
147Q16—1941no—
148SD16—1944no—
149D8—21no—
150D8—21no—
151D8—972no—
152D8—1944no—
153D8—1941no—
154D8C22×D9712yes—
155D8C22×D9712yescomplemented
156C2×C8—971no—
157C2×C8—972no—
158C2×C8—972no—
159C2×C8C22×D9711yescharacteristic
160C16—972no—
161C16C22×D9712yescomplemented
162C23—41no—
163C23—41no—
164C23—7764no—
165C23—971no—
166C23—3884no—
167C23—3881no—
168Q8—3881no—
169Q8—1942no—
170D4—22no—
171D4—22no—
172D4—41no—
173D4—41no—
174D4—3884no—
175D4—3884no—
176D4—3881no—
177D4—1942no—
178C2×C4—971no—
179C2×C4—972no—
180C2×C4—972no—
181C2×C4—3884no—
182C2×C4—3881no—
183C2×C4D4×D9711yescharacteristic
184C8—972no—
185C8D4×D9711yescharacteristic
186C8C23×D9711yescharacteristic
187C22—42no—
188C22—42no—
189C22—82no—
190C22—82no—
191C22—7768no—
192C22—7762no—
193C22—972no—
194C22—3882no—
195C22—1942no—
196C22D8×D9711yescharacteristic
197C4—972no—
198C4—3882no—
199C4D8×D9711yescharacteristic
200C4C2×D4×D9711yescharacteristic
201C2—82no—
202C2—82no—
203C2—7762no—
204C2—1942no—
205C2#2026116912yesdirect product factor
206C2C2×D8×D9711yescharacteristic
subgroupG/H
centerC22D8×D97
commutator, cosocleC8×C97C24
FrattiniC8C23×D97
FittingC2×D16×C97C2
socleC22×C97C2×D8
hypercenterC2×D16D97
hypocenterC97C2×#509
LCSG ▷ C8×C97 ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. C2×#15690829C2semidirect
2. C2×D8×D97C2semidirect
3. #20261169C2direct (N × H)
4. C2×#15690755C2semidirect
5. C2×#15690754C2semidirect
6. C2×#15690751C2semidirect
7. C2×#15690749C2semidirect
8. C2×D16×C97C2semidirect
12. #15690829C22semidirect
13. C2×Dic388C22semidirect
18. D8×D97C22semidirect
20. #15690755C22semidirect
21. #15690754C22semidirect
22. #15690751C22semidirect
23. #15690749C22semidirect
24. C2×#13095486C22semidirect
26. C2×D8×C97C22semidirect
27. D16×C97C22semidirect
28. C2×C16×C97C22semidirect
41. Dic388C23semidirect
49. #13095486C23semidirect
55. D8×C97C23semidirect
57. C16×C97C23semidirect
99. C2×C97#509semidirect
104. C97C2×#509semidirect
111. C2×D16D97semidirect
124. C2×D8C2×D97semidirect
129. D16C2×D97semidirect
132. C2×C16C2×D97semidirect
155. D8C22×D97semidirect
161. C16C22×D97semidirect
205. C2#20261169direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156908292
C2×D8×D972
#202611692
C2×#156907552
C2×#156907542
C2×#156907512
C2×#156907492
C2×D16×C972
C2×#50997