Finite Group Databasebeta

← C2×#20260887 #27150919

Subgroups — C2×#20260887 #27150919

Order 12416.

996 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C22×D4×D97C211yesmaximal, characteristic
2C22×#13095500C211yesmaximal, characteristic, complemented
3C22×#13095499C211yesmaximal, characteristic, complemented
4C2×#15690790C211yesmaximal, characteristic, complemented
5#20260887C218yesmaximal, direct product factor
6C2×#15690730C211yesmaximal, characteristic, complemented
7C2×#15690722C211yesmaximal, characteristic, complemented
8C2×#102×C97C211yesmaximal, characteristic, complemented
9C24×D97—21no—
10C22×Dic194C2211yescharacteristic, complemented
11C22×D388C2211yescharacteristic
12C22×C22⋊D97—21no—
13C2×D4×D97—24no—
14C2×D4×D97—22no—
15C2×D4×D97—24no—
16C2×D4×D97C2214yes—
17C22×C4×D97C2211yescharacteristic
18C2×#13095500—24no—
19C2×#13095500C2214yescomplemented
20C2×#13095499—24no—
21C2×#13095499C2214yescomplemented
22C22×#11715895C2211yescharacteristic, complemented
23#15690790—22no—
24#15690790C2214yescomplemented
25C2×C4⋊Dic97—21no—
26C2×#13095488—21no—
27#15690730C2214yescomplemented
28#15690722C2214yescomplemented
29C22×D4×C97C2211yescharacteristic
30C22×C8×C97C2211yescharacteristic, complemented
31C2×C4⋊C4×C97C2211yescharacteristic, complemented
32#102×C97C2214yescomplemented
33C23×D97—28no—
34C23×D97—21no—
35C23×D97—24no—
36C23×D97—44no—
37C23×D97—44no—
38C23×D97D411yescharacteristic
39C2×Dic194—22no—
40C2×Dic194—22no—
41C2×Dic194—21no—
42C2×Dic194C2312yescomplemented
43C2×D388—21no—
44C2×D388—22no—
45C2×D388D414yes—
46C2×D388C2312yes—
47C2×C22⋊D97—28no—
48C2×C22⋊D97—24no—
49D4×D97—216no—
50D4×D97—28no—
51D4×D97—28no—
52C22×Dic97—21no—
53C22×Dic97D411yescharacteristic
54C2×C4×D97—22no—
55C2×C4×D97—22no—
56C2×C4×D97D412yes—
57C2×C4×D97C2312yes—
58#13095500—28no—
59#13095499—28no—
60C2×#11715895—22no—
61C2×#11715895C2312yescomplemented
62C4⋊Dic97—24no—
63#13095488—24no—
64C24×C97—21no—
65C2×D4×C97—21no—
66C2×D4×C97—22no—
67C2×D4×C97D414yes—
68C2×D4×C97C2312yes—
69C22×C4×C97—21no—
70C22×C4×C97C2311yescharacteristic
71C2×C8×C97—22no—
72C2×C8×C97C2312yescomplemented
73C4⋊C4×C97—21no—
74C4⋊C4×C97C2312yescomplemented
75C23×C97—24no—
76C23×C97—22no—
77C23×C97—42no—
78C23×C97—42no—
79C23×C97C2×D411yescharacteristic
80C22×D97—22no—
81C22×D97—22no—
82C22×D97—216no—
83C22×D97—24no—
84C22×D97—22no—
85C22×D97—48no—
86C22×D97—432no—
87C22×D97—42no—
88C22×D97—42no—
89C22×D97—48no—
90C22×D97SD1614yescomplemented
91C22×D97C2×D412yes—
92D4×C97—24no—
93D4×C97—22no—
94D4×C97C2×D414yes—
95C2×C4×C97—22no—
96C2×C4×C97—42no—
97C2×C4×C97C2×D411yescharacteristic
98C2×C4×C97C2×D412yes—
99C2×C4×C97C2×D412yes—
100C2×C4×C97C2411yescharacteristic
101C22⋊D97—216no—
102C2×Dic97—22no—
103C2×Dic97—22no—
104C2×Dic97—42no—
105C2×Dic97C2×D412yes—
106D388—24no—
107D388—22no—
108D388C2×D414yes—
109C4×D97—24no—
110C4×D97—22no—
111C4×D97—22no—
112Dic194—22no—
113Dic194—22no—
114Dic194—42no—
115C8×C97—22no—
116#11715895—22no—
117C22×C97—24no—
118C22×C97—42no—
119C22×C97—42no—
120C22×C97—48no—
121C22×C97#12012yes—
122C22×C97C2×SD1612yes—
123C22×C97AGL(1,ℤ/8)12yes—
124C22×C97C22×D411yescharacteristic
125C2×D97—22no—
126C2×D97—22no—
127C2×D97—28no—
128C2×D97—24no—
129C2×D97—432no—
130C2×D97—42no—
131C2×D97—42no—
132C2×D97—48no—
133C2×D97C2×SD1614yescomplemented
134C4×C97—42no—
135C4×C97#12012yes—
136C4×C97C22×D411yescharacteristic
137C4×C97C22×D411yescharacteristic
138Dic97—22no—
139Dic97—42no—
140C2×C97—44no—
141C2×C97#45014yescomplemented
142C2×C97C2×#12011yescharacteristic
143C2×C97C22×SD1611yescharacteristic
144C2×C97C2×AGL(1,ℤ/8)11yescharacteristic
145D97—24no—
146D97—44no—
147C2×#450—971nomaximal, Sylow
148C97C2×#45011yescharacteristic, complemented, Sylow
149C23×D4—971no—
150C22×SD16—971no—
151C22×SD16—971no—
152C2×C22⋊Q8—971no—
153#450—978no—
154C2×#102—971no—
155C2×#102D9711yescharacteristic, complemented
156C2×C22⋊C8—971no—
157C25—1941no—
158C22×Q8—971no—
159C22×D4—974no—
160C22×D4—971no—
161C22×D4—1942no—
162C22×D4—1941no—
163C22×D4—1944no—
164C22×D4—1944no—
165C22×D4C2×D9711yescharacteristic
166C23×C4—971no—
167C2×SD16—974no—
168C2×SD16—974no—
169C2×SD16—1944no—
170C2×SD16—1944no—
171C22×C8—971no—
172C22×C8C2×D9711yescharacteristic, complemented
173C22⋊Q8—974no—
174C22⋊Q8—1942no—
175C2×C4⋊C4—1941no—
176C2×C4⋊C4C2×D9711yescharacteristic, complemented
177C2×C22⋊C4—1941no—
178#102—974no—
179#102C2×D9714yescomplemented
180C22⋊C8—974no—
181C24—21no—
182C24—971no—
183C24—3884no—
184C24—3884no—
185C24—1944no—
186C24—1948no—
187C24—1941no—
188C2×Q8—972no—
189C2×Q8—1942no—
190C2×Q8—1942no—
191C2×Q8—1941no—
192C2×D4—21no—
193C2×D4—22no—
194C2×D4—974no—
195C2×D4—972no—
196C2×D4—1944no—
197C2×D4—1948no—
198C2×D4—19416no—
199C2×D4—1948no—
200C2×D4—1948no—
201C2×D4—1941no—
202C2×D4—1942no—
203C2×D4D38814yes—
204C2×D4C22×D9712yes—
205C22×C4—21no—
206C22×C4—971no—
207C22×C4—972no—
208C22×C4—972no—
209C22×C4—1941no—
210C22×C4—1942no—
211C22×C4—1942no—
212C22×C4C22×D9711yescharacteristic
213SD16—1948no—
214SD16—1948no—
215C2×C8—22no—
216C2×C8—972no—
217C2×C8—1942no—
218C2×C8C22×D9712yescomplemented
219C4⋊C4—21no—
220C4⋊C4—1944no—
221C4⋊C4C22×D9712yescomplemented
222C22⋊C4—1944no—
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—974no—
228C23—972no—
229C23—3888no—
230C23—38832no—
231C23—3888no—
232C23—3882no—
233C23—3882no—
234C23—19416no—
235C23—1944no—
236C23—1942no—
237C23—1942no—
238C23—1942no—
239C23D4×D9711yescharacteristic
240Q8—3882no—
241Q8—1942no—
242Q8—1942no—
243D4—24no—
244D4—22no—
245D4—974no—
246D4—19416no—
247D4—1944no—
248D4—1942no—
249D4C2×D38814yes—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—972no—
253C2×C4—3882no—
254C2×C4—1942no—
255C2×C4—1942no—
256C2×C4—1944no—
257C2×C4—1942no—
258C2×C4—1942no—
259C2×C4D4×D9711yescharacteristic
260C2×C4D4×D9712yes—
261C2×C4C2×D38812yes—
262C2×C4C23×D9711yescharacteristic
263C8—22no—
264C8—1942no—
265C22—24no—
266C22—48no—
267C22—42no—
268C22—42no—
269C22—974no—
270C22—38832no—
271C22—3888no—
272C22—3882no—
273C22—3882no—
274C22—1944no—
275C22—1948no—
276C22—1942no—
277C22—1942no—
278C22#1569078012yes—
279C22SD16×D9712yes—
280C22#1569083412yes—
281C22C2×D4×D9711yescharacteristic
282C4—42no—
283C4—3882no—
284C4—1942no—
285C4#1569078012yes—
286C4C2×D4×D9711yescharacteristic
287C4C22×D38811yescharacteristic
288C2—44no—
289C2—3884no—
290C2—1944no—
291C2#2026088714yesdirect product factor
292C2C2×#1569078011yescharacteristic
293C2C2×SD16×D9711yescharacteristic
294C2C2×#1569083411yescharacteristic
subgroupG/H
centerC23D4×D97
commutator, cosocleC2×C4×C97C24
FrattiniC2×C4C23×D97
FittingC2×#102×C97C2
socleC23×C97C2×D4
prime radicalC22×D4×D97C2
hypercenterC2×#102D97
hypocenterC97C2×#450
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C22×#13095500C2semidirect
3. C22×#13095499C2semidirect
4. C2×#15690790C2semidirect
5. #20260887C2direct (N × H)
6. C2×#15690730C2semidirect
7. C2×#15690722C2semidirect
8. C2×#102×C97C2semidirect
10. C22×Dic194C22semidirect
19. C2×#13095500C22semidirect
21. C2×#13095499C22semidirect
22. C22×#11715895C22semidirect
24. #15690790C22semidirect
27. #15690730C22semidirect
28. #15690722C22semidirect
30. C22×C8×C97C22semidirect
31. C2×C4⋊C4×C97C22semidirect
32. #102×C97C22semidirect
42. C2×Dic194C23semidirect
61. C2×#11715895C23semidirect
72. C2×C8×C97C23semidirect
74. C4⋊C4×C97C23semidirect
90. C22×D97SD16semidirect
133. C2×D97C2×SD16semidirect
141. C2×C97#450semidirect
148. C97C2×#450semidirect
155. C2×#102D97semidirect
172. C22×C8C2×D97semidirect
176. C2×C4⋊C4C2×D97semidirect
179. #102C2×D97semidirect
218. C2×C8C22×D97semidirect
221. C4⋊C4C22×D97semidirect
291. C2#20260887direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D972
C22×#130955002
C22×#130954992
C2×#156907902
#202608872
C2×#156907302
C2×#156907222
C2×#102×C972
C2×#45097