Finite Group Databasebeta

← C2×#13074578 #14920887

Subgroups — C2×#13074578 #14920887

Order 2816.

2222 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074578C2116yesmaximal, direct product factor
2C2×#10622565C213yesmaximal, complemented
3C2×#10622606C213yesmaximal, complemented
4C2×#10622289C211yesmaximal, characteristic, complemented
5C2×#10622570C213yesmaximal
6C2×#10622585C213yesmaximal, complemented
7C2×#10622261C211yesmaximal, characteristic, complemented
8C2×C11×#396C211yesmaximal, characteristic, complemented
9C23×C22⋊D11C2211yescharacteristic
10C22×C11×C4⋊C4C2213yes—
11C22×C11×C22⋊C4C2213yes—
12C22×C22⋊Dic11C2213yes—
13C22×(C2×D11)⋊C4C2213yes—
14C22×(C2×D11)⋊C4C2213yes—
15C22×Dic11⋊C4C2213yes—
16C22×Dic11⋊C4C2213yes—
17C22×C4×Dic11C2213yes—
18C11×#396C2218yescomplemented
19C2×C11×#95C2211yescharacteristic
20C2×C11⋊#95C2213yes—
21C2×C11⋊#95C2216yes—
22#10622606C22124yescomplemented
23#10622585C22124yescomplemented
24#10622570C22124yes—
25#10622565C22124yescomplemented
26#10622289C2218yescomplemented
27#10622261C2218yescomplemented
28C25×C11C2311yescharacteristic
29C24×D11C2311yescharacteristic
30C23×C4×C11C2313yes—
31C23×C4×C11C2313yes—
32C22×C22⋊D11—212no—
33C22×C22⋊D11C2314yes—
34C23×Dic11C2313yes—
35C23×Dic11C2313yes—
36C23×Dic11C2311yescharacteristic
37C2×C11×C4⋊C4—46no—
38C2×C11×C4⋊C4C23112yes—
39C2×C11×C22⋊C4—46no—
40C2×C11×C22⋊C4C23112yes—
41C2×C22⋊Dic11—46no—
42C2×C22⋊Dic11C23112yes—
43C2×(C2×D11)⋊C4—46no—
44C2×(C2×D11)⋊C4—46no—
45C2×(C2×D11)⋊C4C23112yes—
46C2×(C2×D11)⋊C4C23112yes—
47C2×Dic11⋊C4—212no—
48C2×Dic11⋊C4—46no—
49C2×Dic11⋊C4C23112yes—
50C2×Dic11⋊C4C23112yes—
51C2×C4×Dic11—212no—
52C2×C4×Dic11C23112yes—
53C11×#95C2314yes—
54C11⋊#95C23112yes—
55C11⋊#95C23124yes—
56C2×#2644—111nomaximal, Sylow
57C24×C11—26no—
58C24×C11—26no—
59C24×C11—22no—
60C24×C11C2412yes—
61C24×C11C2411yescharacteristic
62C23×D11—26no—
63C23×D11—26no—
64C23×D11—22no—
65C23×D11C2412yes—
66C22×C4×C11—26no—
67C22×C4×C11—26no—
68C22×C4×C11—26no—
69C22×C4×C11—26no—
70C22×C4×C11—26no—
71C22×C4×C11—26no—
72C22×C4×C11C2416yes—
73C22×C4×C11C2416yes—
74C2×C22⋊D11—224no—
75C2×C22⋊D11—416no—
76C22×Dic11—26no—
77C22×Dic11—26no—
78C22×Dic11—26no—
79C22×Dic11—26no—
80C22×Dic11—26no—
81C22×Dic11—26no—
82C22×Dic11#41112yes—
83C22×Dic11C2416yes—
84C22×Dic11C2416yes—
85C22×Dic11C2412yes—
86C11×C4⋊C4—412no—
87C11×C22⋊C4—412no—
88C22⋊Dic11—412no—
89(C2×D11)⋊C4—412no—
90(C2×D11)⋊C4—412no—
91Dic11⋊C4—224no—
92Dic11⋊C4—412no—
93C4×Dic11—224no—
94#2644—1116no—
95C2×#397—113no—
96C2×#397—113no—
97C2×#396—111no—
98C2×#396D1111yescharacteristic, complemented
99C2×#390—113no—
100C2×#389—113no—
101C2×#376—111no—
102C23×C11—26no—
103C23×C11—26no—
104C23×C11—22no—
105C23×C11—44no—
106C23×C11—412no—
107C23×C11—412no—
108C23×C11C2×#4116yes—
109C23×C11H(5,𝔽2)16yes—
110C23×C112−1+412yes—
111C23×C11C2511yescharacteristic
112C22×D11—26no—
113C22×D11—26no—
114C22×D11—22no—
115C22×D11—44no—
116C22×D11—412no—
117C22×D11—412no—
118C2×C4×C11—26no—
119C2×C4×C11—26no—
120C2×C4×C11—26no—
121C2×C4×C11—26no—
122C2×C4×C11—26no—
123C2×C4×C11—26no—
124C2×C4×C11—412no—
125C2×C4×C11—412no—
126C22⋊D11—416no—
127C2×Dic11—26no—
128C2×Dic11—26no—
129C2×Dic11—26no—
130C2×Dic11—26no—
131C2×Dic11—26no—
132C2×Dic11—26no—
133C2×Dic11—412no—
134C2×Dic11—412no—
135C2×Dic11#126116yes—
136C2×Dic11C2×#41112yes—
137C23×D4—111no—
138C22×C4⋊C4—113no—
139C22×C4⋊C4—113no—
140C22×C4⋊C4C2×D1113yes—
141C22×C22⋊C4—113no—
142C22×C22⋊C4—113no—
143C22×C22⋊C4—113no—
144C22×C22⋊C4C2×D1113yes—
145C22×C42—113no—
146#397—1124no—
147#397—1124no—
148#396—118no—
149#396C2×D1118yescomplemented
150#390—1124no—
151#389—1124no—
152#376—118no—
153C2×#95—113no—
154C2×#95—116no—
155C2×#95C2×D1111yescharacteristic
156C22×C11—42no—
157C22×C11—46no—
158C22×C11—46no—
159C22×C11—88no—
160C22×C11C2×#12614yes—
161C22×C11#540112yes—
162C22×C11#542112yes—
163C22×C11C22×#4113yes—
164C22×C11C2×H(5,𝔽2)13yes—
165C22×C11C2×2−1+411yescharacteristic
166C2×D11—42no—
167C2×D11—46no—
168C2×D11—46no—
169C2×D11—88no—
170C4×C11—46no—
171C4×C11—46no—
172Dic11—46no—
173Dic11—46no—
174Dic11C2×#12618yes—
175C25—111no—
176C25C22×D1111yescharacteristic
177C22×D4—114no—
178C22×D4—2212no—
179C23×C4—111no—
180C23×C4—113no—
181C23×C4—113no—
182C23×C4C22×D1113yes—
183C23×C4C22×D1113yes—
184C2×C4⋊C4—46no—
185C2×C4⋊C4—1112no—
186C2×C4⋊C4—1112no—
187C2×C4⋊C4—2212no—
188C2×C4⋊C4—446no—
189C2×C4⋊C4C22×D11112yes—
190C2×C22⋊C4—46no—
191C2×C22⋊C4—1112no—
192C2×C22⋊C4—1112no—
193C2×C22⋊C4—1112no—
194C2×C22⋊C4—446no—
195C2×C22⋊C4—446no—
196C2×C22⋊C4—446no—
197C2×C22⋊C4C22×D11112yes—
198C2×C42—1112no—
199C2×C42—2212no—
200#95—1112no—
201#95—1124no—
202#95C22×D1114yes—
203C2×C11—82no—
204C2×C11#264418yescomplemented
205C2×C11C22×#12611yescharacteristic
206C2×C11C2×#54013yes—
207C2×C11C2×#54213yes—
208D11—82no—
209C24—26no—
210C24—22no—
211C24—26no—
212C24—112no—
213C24—226no—
214C24—222no—
215C24—226no—
216C24C23×D1112yes—
217C24C23×D1111yescharacteristic
218C2×D4—2224no—
219C2×D4—4416no—
220C22×C4—26no—
221C22×C4—26no—
222C22×C4—26no—
223C22×C4—26no—
224C22×C4—26no—
225C22×C4—26no—
226C22×C4—1112no—
227C22×C4—112no—
228C22×C4—116no—
229C22×C4—116no—
230C22×C4—226no—
231C22×C4—226no—
232C22×C4—226no—
233C22×C4—226no—
234C22×C4—226no—
235C22×C4—226no—
236C22×C4C23×D1116yes—
237C22×C4C23×D1116yes—
238C4⋊C4—412no—
239C4⋊C4—2224no—
240C4⋊C4—4412no—
241C22⋊C4—412no—
242C22⋊C4—4412no—
243C22⋊C4—4412no—
244C22⋊C4—4412no—
245C42—2224no—
246C11C2×#264411yescharacteristic, complemented, Sylow
247C23—26no—
248C23—22no—
249C23—26no—
250C23—44no—
251C23—412no—
252C23—412no—
253C23—226no—
254C23—222no—
255C23—226no—
256C23—444no—
257C23—4412no—
258C23—4412no—
259C23#6703716yes—
260C23#6704012yes—
261C23#41×D1116yes—
262C23C24×D1111yescharacteristic
263D4—4416no—
264C2×C4—26no—
265C2×C4—26no—
266C2×C4—26no—
267C2×C4—26no—
268C2×C4—26no—
269C2×C4—26no—
270C2×C4—412no—
271C2×C4—412no—
272C2×C4—1116no—
273C2×C4—1112no—
274C2×C4—226no—
275C2×C4—226no—
276C2×C4—226no—
277C2×C4—226no—
278C2×C4—226no—
279C2×C4—226no—
280C2×C4—4412no—
281C2×C4—4412no—
282C22—42no—
283C22—46no—
284C22—46no—
285C22—88no—
286C22—442no—
287C22—446no—
288C22—446no—
289C22—888no—
290C22#10623146112yes—
291C22#10623171112yes—
292C22D11×#12614yes—
293C22C2×#6703713yes—
294C22C2×#6704011yescharacteristic
295C22C2×#41×D1113yes—
296C4—46no—
297C4—46no—
298C4—118no—
299C4—446no—
300C4—446no—
301C2—82no—
302C2—882no—
303C2#1307457818yesdirect product factor
304C2C2×D11×#12611yescharacteristic
305C2C2×#1062314613yes—
306C2C2×#1062317113yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#396C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#396D11
hypocenterC11C2×#2644
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. #13074578C2direct (N × H)
2. C2×#10622565C2semidirect
3. C2×#10622606C2semidirect
4. C2×#10622289C2semidirect
6. C2×#10622585C2semidirect
7. C2×#10622261C2semidirect
8. C2×C11×#396C2semidirect
18. C11×#396C22semidirect
22. #10622606C22semidirect
23. #10622585C22semidirect
25. #10622565C22semidirect
26. #10622289C22semidirect
27. #10622261C22semidirect
98. C2×#396D11semidirect
149. #396C2×D11semidirect
204. C2×C11#2644semidirect
246. C11C2×#2644semidirect
303. C2#13074578direct (N × H)

Maximal subgroups

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

subgroupindex
#130745782
C2×#106225652
C2×#106226062
C2×#106222892
C2×#106225702
C2×#106225852
C2×#106222612
C2×C11×#3962
C2×#264411