Finite Group Databasebeta

← C2×#20260963 #27151295

Subgroups — C2×#20260963 #27151295

Order 12416.

564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13095499C211yesmaximal, characteristic, complemented
2C22×C8×D97C211yesmaximal, characteristic, complemented
3C2×#15690790C211yesmaximal, characteristic, complemented
4C2×#15690781C211yesmaximal, characteristic
5#20260963C218yesmaximal, direct product factor
6C2×#15690741C211yesmaximal, characteristic, complemented
7C2×#15690735C211yesmaximal, characteristic, complemented
8C2×#102×C97C211yesmaximal, characteristic, complemented
9C22×Dic194C2211yescharacteristic
10C22×C22⋊D97—21no—
11C22×C4×D97C2211yescharacteristic
12C2×#13095499—24no—
13C2×#13095499C2214yescomplemented
14C22×#11715895C2211yescharacteristic
15C2×C8×D97—24no—
16C2×C8×D97C2214yescomplemented
17#15690790—22no—
18#15690790C2214yescomplemented
19#15690781—22no—
20#15690781C2214yes—
21C2×C4⋊Dic97—21no—
22C2×C4⋊Dic97C2211yescharacteristic
23C2×C22⋊Dic97—21no—
24C2×#13095488—21no—
25#15690741C2214yescomplemented
26#15690735C2214yescomplemented
27C22×D4×C97C2211yescharacteristic
28C22×C8×C97C2211yescharacteristic
29C2×C4⋊C4×C97C2211yescharacteristic
30#102×C97C2214yescomplemented
31C23×D97D411yescharacteristic
32C2×Dic194—22no—
33C2×Dic194—22no—
34C2×Dic194—21no—
35C2×Dic194C2312yes—
36C2×C22⋊D97—24no—
37C2×C22⋊D97—44no—
38C22×Dic97—21no—
39C22×Dic97—21no—
40C22×Dic97D411yescharacteristic
41C2×C4×D97—22no—
42C2×C4×D97—22no—
43C2×C4×D97D412yes—
44C2×C4×D97C2312yes—
45#13095499—28no—
46C2×#11715895D414yescomplemented
47C2×#11715895C2312yes—
48C8×D97—28no—
49C4⋊Dic97—21no—
50C4⋊Dic97—24no—
51C4⋊Dic97C2312yes—
52C22⋊Dic97—24no—
53#13095488—24no—
54C24×C97—21no—
55C2×D4×C97—22no—
56C2×D4×C97—21no—
57C2×D4×C97—22no—
58C2×D4×C97C2312yes—
59C22×C4×C97—21no—
60C22×C4×C97C2311yescharacteristic
61C2×C8×C97—22no—
62C2×C8×C97C2312yes—
63C4⋊C4×C97—21no—
64C4⋊C4×C97C2312yes—
65C23×C97—22no—
66C23×C97—42no—
67C23×C97—42no—
68C23×C97—42no—
69C23×C97C2×D411yescharacteristic
70C22×D97—22no—
71C22×D97—22no—
72C22×D97SD1614yescomplemented
73C22×D97C2×D412yes—
74D4×C97—22no—
75D4×C97—22no—
76D4×C97—42no—
77C2×C4×C97—22no—
78C2×C4×C97—42no—
79C2×C4×C97C2×D411yescharacteristic
80C2×C4×C97C2×D412yes—
81C2×C4×C97#4112yes—
82C2×C4×C97C2411yescharacteristic
83C22⋊D97—48no—
84C2×Dic97—22no—
85C2×Dic97—22no—
86C2×Dic97—22no—
87C2×Dic97—42no—
88C2×Dic97—42no—
89C2×Dic97C2×D412yes—
90C4×D97—24no—
91C4×D97—22no—
92C4×D97—22no—
93Dic194—22no—
94Dic194—22no—
95Dic194—42no—
96C8×C97—22no—
97#11715895C2×D414yescomplemented
98C22×C97—42no—
99C22×C97—42no—
100C22×C97—42no—
101C22×C97—84no—
102C22×C97#12112yes—
103C22×C97C2×SD1612yes—
104C22×C97#13512yes—
105C22×C97C22×D411yescharacteristic
106C2×D97—22no—
107C2×D97—22no—
108C2×D97—28no—
109C2×D97C2×SD1614yescomplemented
110C4×C97—42no—
111C4×C97#12112yes—
112C4×C97C22×D411yescharacteristic
113C4×C97C2×#4111yescharacteristic
114Dic97—22no—
115Dic97—42no—
116Dic97—42no—
117C2×C97—82no—
118C2×C97#46514yescomplemented
119C2×C97C2×#12111yescharacteristic
120C2×C97C22×SD1611yescharacteristic
121C2×C97C2×#13511yescharacteristic
122D97—24no—
123C2×#465—971nomaximal, Sylow
124C97C2×#46511yescharacteristic, complemented, Sylow
125C22×SD16—971no—
126C23×C8—971no—
127C2×C22⋊Q8—971no—
128C2×#121—971no—
129#465—978no—
130C2×#106—971no—
131C2×#103—971no—
132C2×#102D9711yescharacteristic, complemented
133C22×Q8—971no—
134C22×D4—1941no—
135C22×D4C2×D9711yescharacteristic
136C23×C4—971no—
137C2×SD16—974no—
138C2×SD16—1944no—
139C22×C8—971no—
140C22×C8—974no—
141C22×C8—1944no—
142C22×C8C2×D9711yescharacteristic
143C22⋊Q8—974no—
144C22⋊Q8—1942no—
145#121—974no—
146#121—1942no—
147C2×C4⋊C4—971no—
148C2×C4⋊C4—1941no—
149C2×C4⋊C4C2×D9711yescharacteristic
150C2×C22⋊C4—1941no—
151C2×C22⋊C4—1941no—
152#106—974no—
153#103—974no—
154#102C2×D9714yescomplemented
155C24—21no—
156C24—971no—
157C2×Q8—972no—
158C2×Q8—1942no—
159C2×Q8—1942no—
160C2×Q8—1941no—
161C2×D4—22no—
162C2×D4—21no—
163C2×D4—22no—
164C2×D4—3884no—
165C2×D4—1944no—
166C2×D4C22×D9712yes—
167C22×C4—21no—
168C22×C4—971no—
169C22×C4—972no—
170C22×C4—972no—
171C22×C4—1941no—
172C22×C4—1941no—
173C22×C4—1942no—
174C22×C4—1942no—
175C22×C4C22×D9711yescharacteristic
176SD16—1948no—
177C2×C8—22no—
178C2×C8—974no—
179C2×C8—972no—
180C2×C8—1948no—
181C2×C8C22×D9712yes—
182C4⋊C4—21no—
183C4⋊C4—972no—
184C4⋊C4—1944no—
185C4⋊C4—1941no—
186C4⋊C4C22×D9712yes—
187C22⋊C4—1944no—
188C22⋊C4—1944no—
189C23—22no—
190C23—42no—
191C23—42no—
192C23—42no—
193C23—974no—
194C23—972no—
195C23—1942no—
196C23—1942no—
197C23D4×D9711yescharacteristic
198Q8—3882no—
199Q8—1942no—
200Q8—1942no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—3888no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—972no—
208C2×C4—3882no—
209C2×C4—3882no—
210C2×C4—1942no—
211C2×C4—1942no—
212C2×C4—1942no—
213C2×C4—1944no—
214C2×C4—1942no—
215C2×C4—1942no—
216C2×C4D4×D9711yescharacteristic
217C2×C4D4×D9712yes—
218C2×C4#1309551112yes—
219C2×C4C23×D9711yescharacteristic
220C8—22no—
221C8—974no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—84no—
226C22—974no—
227C22—1948no—
228C22—1942no—
229C22—1942no—
230C22#1569078312yes—
231C22SD16×D9712yes—
232C22#1569082912yes—
233C22C2×D4×D9711yescharacteristic
234C4—42no—
235C4—3882no—
236C4—3882no—
237C4—1942no—
238C4#1569078312yes—
239C4C2×D4×D9711yescharacteristic
240C4C2×#1309551111yescharacteristic
241C2—82no—
242C2—1944no—
243C2#2026096314yesdirect product factor
244C2C2×#1569078311yescharacteristic
245C2C2×SD16×D9711yescharacteristic
246C2C2×#1569082911yescharacteristic
subgroupG/H
centerC23D4×D97
commutator, cosocleC2×C4×C97C24
FrattiniC2×C4C23×D97
FittingC2×#102×C97C2
socleC23×C97C2×D4
prime radicalC2×#15690781C2
hypercenterC2×#102D97
hypocenterC97C2×#465
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
1. C22×#13095499C2semidirect
2. C22×C8×D97C2semidirect
3. C2×#15690790C2semidirect
5. #20260963C2direct (N × H)
6. C2×#15690741C2semidirect
7. C2×#15690735C2semidirect
8. C2×#102×C97C2semidirect
13. C2×#13095499C22semidirect
16. C2×C8×D97C22semidirect
18. #15690790C22semidirect
25. #15690741C22semidirect
26. #15690735C22semidirect
30. #102×C97C22semidirect
46. C2×#11715895D4semidirect
72. C22×D97SD16semidirect
97. #11715895C2×D4semidirect
109. C2×D97C2×SD16semidirect
118. C2×C97#465semidirect
124. C97C2×#465semidirect
132. C2×#102D97semidirect
154. #102C2×D97semidirect
243. C2#20260963direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130954992
C22×C8×D972
C2×#156907902
C2×#156907812
#202609632
C2×#156907412
C2×#156907352
C2×#102×C972
C2×#46597