Finite Group Databasebeta

← C2×#20261616 #27157443

Subgroups — C2×#20261616 #27157443

Order 12416.

388 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13095520C211yesmaximal, characteristic
2C22×#13095520C211yesmaximal, characteristic
3#20261616C214yesmaximal, direct product factor
4C2×#15690766C211yesmaximal, characteristic
5C2×#13095520—21no—
6C2×#13095520—21no—
7C2×#13095520—21no—
8C2×#13095520—21no—
9C2×#13095520—21no—
10C2×#13095520—21no—
11C2×#13095520—21no—
12C2×#13095520C412yescomplemented
13C2×#13095520C412yescomplemented
14C2×#13095520C412yescomplemented
15C2×#13095520C2212yes—
16C2×#13095520C2212yes—
17C22×#11715897—21no—
18C22×#11715897C412yescomplemented
19C23×Dic97C2211yescharacteristic
20#15690766—21no—
21#15690766—21no—
22#15690766C412yes—
23#15690766C2212yes—
24C2×#13095490—21no—
25C2×C22⋊Dic97C411yescharacteristic
26C2×C4×Dic97—21no—
27C2×C22⋊C4×C97C411yescharacteristic
28#13095520—22no—
29#13095520—22no—
30#13095520—22no—
31#13095520—22no—
32#13095520—22no—
33#13095520—22no—
34#13095520—22no—
35#13095520C2×C414yescomplemented
36C2×#11715897—22no—
37C2×#11715897—22no—
38C2×#11715897—22no—
39C2×#11715897—22no—
40C2×#11715897—22no—
41C2×#11715897C2×C414yescomplemented
42C22×Dic97—21no—
43C22×Dic97C2×C411yescharacteristic
44C22×Dic97C2×C411yescharacteristic
45C22×Dic97C2×C411yescharacteristic
46C22×Dic97C2×C411yescharacteristic
47C22×Dic97C2×C411yescharacteristic
48C22×Dic97D411yescharacteristic
49C22×Dic97D411yescharacteristic
50C22×Dic97D411yescharacteristic
51C22×Dic97D411yescharacteristic
52C22×Dic97D411yescharacteristic
53C22×Dic97D411yescharacteristic
54C22×Dic97Q811yescharacteristic
55C22×Dic97Q811yescharacteristic
56C22×Dic97C2311yescharacteristic
57#13095490—22no—
58#13095490—22no—
59C22⋊Dic97—21no—
60C22⋊Dic97C2×C412yes—
61C4×Dic97—22no—
62C4×Dic97—22no—
63C24×C97C2×C411yescharacteristic
64C22×C4×C97—21no—
65C22⋊C4×C97—21no—
66C22⋊C4×C97C2×C412yes—
67C23×C97—42no—
68C23×C97C4211yescharacteristic
69C23×C97C4211yescharacteristic
70C23×C97C22⋊C411yescharacteristic
71C23×C97C22⋊C411yescharacteristic
72C23×C97C4⋊C411yescharacteristic
73C23×C97C4⋊C411yescharacteristic
74C23×C97C22×C411yescharacteristic
75C2×C4×C97—22no—
76C2×C4×C97—42no—
77C2×Dic97—22no—
78C2×Dic97—42no—
79C2×Dic97C4211yescharacteristic
80C2×Dic97C4211yescharacteristic
81C2×Dic97C22⋊C411yescharacteristic
82C2×Dic97C22⋊C411yescharacteristic
83C2×Dic97C22⋊C411yescharacteristic
84C2×Dic97C22⋊C411yescharacteristic
85C2×Dic97C22⋊C411yescharacteristic
86C2×Dic97C22⋊C411yescharacteristic
87C2×Dic97C22⋊C411yescharacteristic
88C2×Dic97C22⋊C411yescharacteristic
89C2×Dic97C22⋊C411yescharacteristic
90C2×Dic97C22⋊C411yescharacteristic
91C2×Dic97C4⋊C411yescharacteristic
92C2×Dic97C4⋊C411yescharacteristic
93C2×Dic97C4⋊C411yescharacteristic
94C2×Dic97C4⋊C411yescharacteristic
95C2×Dic97C4⋊C411yescharacteristic
96C2×Dic97C4⋊C411yescharacteristic
97C2×Dic97C4⋊C411yescharacteristic
98C2×Dic97C4⋊C411yescharacteristic
99C2×Dic97C4⋊C411yescharacteristic
100C2×Dic97C4⋊C411yescharacteristic
101C2×Dic97C22×C411yescharacteristic
102C2×Dic97C22×C411yescharacteristic
103C2×Dic97C2×D411yescharacteristic
104C2×Dic97C2×D411yescharacteristic
105C2×Dic97C2×D411yescharacteristic
106C2×Dic97C2×Q811yescharacteristic
107#11715897—24no—
108#11715897—24no—
109C22×C97—22no—
110C22×C97—22no—
111C22×C97—22no—
112C22×C97—41no—
113C22×C97—41no—
114C22×C97—41no—
115C22×C97—41no—
116C22×C97#9511yescharacteristic
117C22×C97#9511yescharacteristic
118C22×C97#9511yescharacteristic
119C22×C97#9511yescharacteristic
120C22×C97C2×C4211yescharacteristic
121C22×C97C2×C22⋊C411yescharacteristic
122C22×C97C2×C4⋊C411yescharacteristic
123C4×C97—42no—
124Dic97—42no—
125Dic97#9511yescharacteristic
126Dic97#9511yescharacteristic
127Dic97#9511yescharacteristic
128Dic97#9511yescharacteristic
129Dic97C2×C22⋊C411yescharacteristic
130Dic97C2×C22⋊C411yescharacteristic
131Dic97C2×C4⋊C411yescharacteristic
132Dic97C2×C4⋊C411yescharacteristic
133C2×C97—21no—
134C2×C97—21no—
135C2×C97—21no—
136C2×C97—21no—
137C2×C97—21no—
138C2×C97—21no—
139C2×C97#34412yescomplemented
140C2×C97C2×#9511yescharacteristic
141C2×#344—971nomaximal, Sylow
142C97C2×#34411yescharacteristic, complemented, Sylow
143C22×M16—971no—
144C22×M16—971no—
145C2×#117—971no—
146#344—974no—
147C23×C4—971no—
148C2×M16—972no—
149C2×M16—972no—
150C2×M16—972no—
151C2×M16—972no—
152C2×M16—972no—
153C2×M16—1941no—
154C2×M16—1941no—
155C2×M16—1941no—
156C2×M16—1941no—
157C2×M16—1941no—
158C2×M16—1941no—
159C2×M16—1941no—
160C22×C8—972no—
161C22×C8—1941no—
162#117—972no—
163#117—972no—
164#117—1941no—
165#117—1941no—
166C2×C4⋊C4—1941no—
167C2×C22⋊C4—971no—
168C2×C22⋊C4#8760411yescharacteristic
169C2×C42—1941no—
170C24C2×#8760411yescharacteristic
171C22×C4—21no—
172C22×C4—971no—
173C22×C4—971no—
174C22×C4—971no—
175C22×C4—971no—
176C22×C4—971no—
177C22×C4—971no—
178C22×C4—971no—
179C22×C4—971no—
180C22×C4—971no—
181C22×C4—971no—
182C22×C4—971no—
183C22×C4—971no—
184C22×C4—971no—
185C22×C4—971no—
186C22×C4—1941no—
187M16—974no—
188M16—1942no—
189M16—1942no—
190M16—1942no—
191M16—1942no—
192M16—1942no—
193M16—1942no—
194M16—1942no—
195C2×C8—974no—
196C2×C8—1942no—
197C2×C8—1942no—
198C2×C8—1942no—
199C2×C8—1942no—
200C2×C8—1942no—
201C4⋊C4—1942no—
202C4⋊C4—1942no—
203C22⋊C4—21no—
204C22⋊C4—972no—
205C22⋊C4—1941no—
206C22⋊C4C2×#8760412yes—
207C42—1942no—
208C42—1942no—
209C23—42no—
210C23C4×#8760411yescharacteristic
211C23C4×#8760411yescharacteristic
212C23C22⋊#8760411yescharacteristic
213C23C22⋊#8760411yescharacteristic
214C23C4⋊#8760411yescharacteristic
215C23C4⋊#8760411yescharacteristic
216C23C22×#8760411yescharacteristic
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—971no—
220C2×C4—971no—
221C2×C4—971no—
222C2×C4—971no—
223C2×C4—971no—
224C2×C4—971no—
225C2×C4—971no—
226C2×C4—971no—
227C2×C4—971no—
228C2×C4—971no—
229C2×C4—971no—
230C2×C4—971no—
231C2×C4—971no—
232C2×C4—971no—
233C2×C4—971no—
234C2×C4—971no—
235C2×C4—971no—
236C2×C4—971no—
237C2×C4—971no—
238C2×C4—971no—
239C2×C4—971no—
240C2×C4—971no—
241C2×C4—971no—
242C2×C4—971no—
243C2×C4—971no—
244C2×C4—971no—
245C2×C4—971no—
246C2×C4—971no—
247C2×C4—3882no—
248C2×C4—1942no—
249C8—1944no—
250C8—1944no—
251C22—22no—
252C22—22no—
253C22—22no—
254C22—41no—
255C22—41no—
256C22—41no—
257C22—41no—
258C22(C2×#87604)⋊C411yescharacteristic
259C22(C2×#87604)⋊C411yescharacteristic
260C22(C2×#87604)⋊C411yescharacteristic
261C22(C2×#87604)⋊C411yescharacteristic
262C22C2×C4×#8760411yescharacteristic
263C22C2×C22⋊#8760411yescharacteristic
264C22C2×C4⋊#8760411yescharacteristic
265C4—42no—
266C4—971no—
267C4—971no—
268C4—971no—
269C4—971no—
270C4—971no—
271C4—971no—
272C4—971no—
273C4—971no—
274C4—3882no—
275C2—21no—
276C2—21no—
277C2—21no—
278C2—21no—
279C2—21no—
280C2—21no—
281C2#2026161612yesdirect product factor
282C2C2×(C2×#87604)⋊C411yescharacteristic
subgroupG/H
centerC22(C2×#87604)⋊C4
commutatorC22×C97C2×C42
FrattiniC23C22×#87604
FittingC2×C22⋊C4×C97C4
socleC22×C97#95
prime radicalC24×C97C2×C4
cosocleC22×Dic97C23
hypercenterC2×C22⋊C4#87604
hypocenterC97C2×#344
LCSG ▷ C22×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #20261616C2direct (N × H)
12. C2×#13095520C4semidirect
13. C2×#13095520C4semidirect
14. C2×#13095520C4semidirect
18. C22×#11715897C4semidirect
35. #13095520C2×C4semidirect
41. C2×#11715897C2×C4semidirect
139. C2×C97#344semidirect
142. C97C2×#344semidirect
281. C2#20261616direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130955202
#202616162
C2×#156907662
C2×#34497