Finite Group Databasebeta

← C2×#20260888 #27150920

Subgroups — C2×#20260888 #27150920

Order 12416.

996 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C23×D388C211yesmaximal, characteristic
2C22×#13095500C212yesmaximal, complemented
3C2×#15690789C211yesmaximal, characteristic, complemented
4#20260888C218yesmaximal, direct product factor
5C2×#15690732C212yesmaximal, complemented
6C2×C22⋊C8×C97C211yesmaximal, characteristic, complemented
7C24×D97—21no—
8C22×Dic194C2211yescharacteristic, complemented
9C22×D388—28no—
10C22×D388—21no—
11C22×D388—22no—
12C22×D388C2214yes—
13C22×D388C2212yes—
14C2×#13095500—28no—
15C2×#13095500C2218yescomplemented
16#15690789—22no—
17#15690789C2214yescomplemented
18C2×C4⋊Dic97C2211yescharacteristic, complemented
19C2×#13095490—21no—
20C2×C22⋊Dic97—21no—
21#15690732C2218yescomplemented
22C23×C4×C97C2211yescharacteristic
23C22×C8×C97C2212yescomplemented
24C22⋊C8×C97C2214yescomplemented
25C23×D97—28no—
26C23×D97—24no—
27C23×D97—22no—
28C23×D97—44no—
29C23×D97—44no—
30C2×Dic194—24no—
31C2×Dic194—21no—
32C2×Dic194C2312yescomplemented
33C2×D388—28no—
34C2×D388—216no—
35C2×D388—24no—
36C2×D388—24no—
37C2×D388—22no—
38C2×D388—216no—
39C2×D388D418yes—
40C2×D388C2314yes—
41C22×Dic97—21no—
42C22×Dic97—21no—
43#13095500—216no—
44C4⋊Dic97—21no—
45C4⋊Dic97C2312yescomplemented
46#13095490—24no—
47C22⋊Dic97—24no—
48C24×C97D411yescharacteristic
49C22×C4×C97—24no—
50C22×C4×C97D411yescharacteristic
51C22×C4×C97D412yes—
52C22×C4×C97C2312yes—
53C22×C4×C97C2311yescharacteristic
54C2×C8×C97—24no—
55C2×C8×C97C2314yescomplemented
56C23×C97—22no—
57C23×C97—22no—
58C23×C97SD1614yescomplemented
59C23×C97C2×D412yes—
60C23×C97C2×D411yescharacteristic
61C22×D97—216no—
62C22×D97—28no—
63C22×D97—24no—
64C22×D97—48no—
65C22×D97—432no—
66C22×D97—44no—
67C22×D97—48no—
68C22×D97—44no—
69C2×C4×C97—22no—
70C2×C4×C97—24no—
71C2×C4×C97—24no—
72C2×C4×C97C2×D414yes—
73C2×C4×C97C2×D412yes—
74C2×C4×C97C2×D411yescharacteristic
75C2×C4×C97C2411yescharacteristic
76C2×Dic97—22no—
77C2×Dic97—22no—
78C2×Dic97—42no—
79C2×Dic97—42no—
80D388—216no—
81D388—28no—
82D388—24no—
83D388C2×D418yes—
84Dic194—24no—
85Dic194—42no—
86C8×C97—24no—
87C22×C97—22no—
88C22×C97—22no—
89C22×C97—28no—
90C22×C97#12012yes—
91C22×C97C2×SD1612yes—
92C22×C97C2×SD1614yescomplemented
93C22×C97AGL(1,ℤ/8)12yes—
94C22×C97C22×D411yescharacteristic
95C2×D97—28no—
96C2×D97—432no—
97C2×D97—44no—
98C2×D97—44no—
99C2×D97—416no—
100C4×C97—22no—
101C4×C97#12012yes—
102C4×C97C22×D412yes—
103Dic97—42no—
104Dic97—42no—
105C2×C97—24no—
106C2×C97#45014yescomplemented
107C2×C97C2×#12011yescharacteristic
108C2×C97C22×SD1611yescharacteristic
109C2×C97C2×AGL(1,ℤ/8)11yescharacteristic
110D97—48no—
111C2×#450—971nomaximal, Sylow
112C97C2×#45011yescharacteristic, complemented, Sylow
113C23×D4—971no—
114C22×SD16—972no—
115C2×C22⋊Q8—971no—
116#450—978no—
117C2×#102—972no—
118C2×C22⋊C8D9711yescharacteristic, complemented
119C25—1941no—
120C22×Q8—971no—
121C22×D4—972no—
122C22×D4—974no—
123C22×D4—1948no—
124C22×D4—1942no—
125C22×D4—1941no—
126C23×C4C2×D9711yescharacteristic
127C2×SD16—978no—
128C2×SD16—1948no—
129C22×C8C2×D9712yescomplemented
130C22⋊Q8—974no—
131C22⋊Q8—1942no—
132C2×C4⋊C4—971no—
133C2×C4⋊C4—1941no—
134C2×C22⋊C4—1941no—
135#102—978no—
136C22⋊C8C2×D9714yescomplemented
137C24—3884no—
138C24—3884no—
139C24—1948no—
140C24—1944no—
141C24—1942no—
142C24D38811yescharacteristic
143C2×Q8—972no—
144C2×Q8—1944no—
145C2×Q8—1941no—
146C2×D4—978no—
147C2×D4—974no—
148C2×D4—19416no—
149C2×D4—1948no—
150C2×D4—19416no—
151C2×D4—1944no—
152C2×D4—1944no—
153C2×D4—1942no—
154C22×C4—24no—
155C22×C4—1941no—
156C22×C4—1941no—
157C22×C4D38812yes—
158C22×C4D38811yescharacteristic
159C22×C4C22×D9712yes—
160C22×C4C22×D9711yescharacteristic
161SD16—19416no—
162C2×C8—24no—
163C2×C8C22×D9714yescomplemented
164C4⋊C4—972no—
165C4⋊C4—1944no—
166C4⋊C4—1941no—
167C22⋊C4—1944no—
168C23—22no—
169C23—22no—
170C23—38832no—
171C23—3888no—
172C23—3884no—
173C23—3888no—
174C23—3884no—
175C23—19416no—
176C23—1948no—
177C23—1944no—
178C23#1309550014yescomplemented
179C23C2×D38812yes—
180C23C2×D38811yescharacteristic
181Q8—3882no—
182Q8—1944no—
183D4—978no—
184D4—19416no—
185D4—1948no—
186D4—1944no—
187C2×C4—22no—
188C2×C4—24no—
189C2×C4—24no—
190C2×C4—3882no—
191C2×C4—3882no—
192C2×C4—1942no—
193C2×C4—1942no—
194C2×C4D4×D9714yes—
195C2×C4C2×D38812yes—
196C2×C4C2×D38811yescharacteristic
197C2×C4C23×D9711yescharacteristic
198C8—24no—
199C22—28no—
200C22—22no—
201C22—22no—
202C22—38832no—
203C22—38816no—
204C22—3884no—
205C22—3884no—
206C22—1948no—
207C22#1569078012yes—
208C22C2×#1309550012yes—
209C22C2×#1309550014yescomplemented
210C22#1569083812yes—
211C22C22×D38811yescharacteristic
212C4—22no—
213C4—3882no—
214C4—3882no—
215C4#1569078012yes—
216C4C2×D4×D9712yes—
217C2—24no—
218C2—3888no—
219C2#2026088814yesdirect product factor
220C2C2×#1569078011yescharacteristic
221C2C22×#1309550011yescharacteristic
222C2C2×#1569083811yescharacteristic
subgroupG/H
centerC23C2×D388
commutator, cosocleC2×C4×C97C24
FrattiniC2×C4C23×D97
FittingC2×C22⋊C8×C97C2
socleC23×C97C2×D4
prime radicalC23×D388C2
hypercenterC2×C22⋊C8D97
hypocenterC97C2×#450
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×#13095500C2semidirect
3. C2×#15690789C2semidirect
4. #20260888C2direct (N × H)
5. C2×#15690732C2semidirect
6. C2×C22⋊C8×C97C2semidirect
8. C22×Dic194C22semidirect
15. C2×#13095500C22semidirect
17. #15690789C22semidirect
18. C2×C4⋊Dic97C22semidirect
21. #15690732C22semidirect
23. C22×C8×C97C22semidirect
24. C22⋊C8×C97C22semidirect
32. C2×Dic194C23semidirect
45. C4⋊Dic97C23semidirect
55. C2×C8×C97C23semidirect
58. C23×C97SD16semidirect
92. C22×C97C2×SD16semidirect
106. C2×C97#450semidirect
112. C97C2×#450semidirect
118. C2×C22⋊C8D97semidirect
129. C22×C8C2×D97semidirect
136. C22⋊C8C2×D97semidirect
163. C2×C8C22×D97semidirect
178. C23#13095500semidirect
209. C22C2×#13095500semidirect
219. C2#20260888direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3882
C22×#130955002
C2×#156907892
#202608882
C2×#156907322
C2×C22⋊C8×C972
C2×#45097