Finite Group Databasebeta

← C2×#13074573 #14920223

Subgroups — C2×#13074573 #14920223

Order 2816.

2546 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074573C2116yesmaximal, direct product factor
2C2×C11⋊#401C211yesmaximal, characteristic, complemented
3C2×#10622595C213yesmaximal, complemented
4C2×#10622565C213yesmaximal, complemented
5C2×#10622569C213yesmaximal
6C2×#10622602C213yesmaximal, complemented
7C2×D11×#95C211yesmaximal, characteristic, complemented
8C2×C11×#396C211yesmaximal, characteristic, complemented
9C23×C22⋊D11C2211yescharacteristic
10C23×C4×D11C2213yes—
11C22×C11×C4⋊C4C2213yes—
12C22×C11×C22⋊C4C2213yes—
13C22×C22⋊Dic11C2213yes—
14C22×(C2×D11)⋊C4C2213yes—
15C22×Dic11⋊C4C2213yes—
16C11×#396C2218yescomplemented
17C2×C11×#95C2211yescharacteristic
18C2×C11⋊#95C2213yes—
19C2×C11⋊#95C2213yes—
20C2×C11⋊#95C2213yes—
21C2×C11⋊#95C2213yes—
22C2×C11⋊#95C2213yes—
23#10622602C22124yescomplemented
24#10622595C22124yescomplemented
25#10622569C22124yes—
26#10622565C22124yescomplemented
27D11×#95C2218yescomplemented
28C11⋊#401C2218yescomplemented
29C25×C11C2311yescharacteristic
30C24×D11C2311yescharacteristic
31C23×C4×C11C2313yes—
32C23×C4×C11C2313yes—
33C22×C22⋊D11—212no—
34C22×C22⋊D11C2314yes—
35C23×Dic11C2313yes—
36C23×Dic11C2313yes—
37C23×Dic11C2311yescharacteristic
38C22×C4×D11—212no—
39C22×C4×D11—46no—
40C22×C4×D11—46no—
41C22×C4×D11C23112yes—
42C2×C11×C4⋊C4—46no—
43C2×C11×C4⋊C4C23112yes—
44C2×C11×C22⋊C4—46no—
45C2×C11×C22⋊C4C23112yes—
46C2×C22⋊Dic11—46no—
47C2×C22⋊Dic11C23112yes—
48C2×(C2×D11)⋊C4—212no—
49C2×(C2×D11)⋊C4C23112yes—
50C2×Dic11⋊C4—46no—
51C2×Dic11⋊C4C23112yes—
52C11×#95C2314yes—
53C11⋊#95C23112yes—
54C11⋊#95C23112yes—
55C11⋊#95C23112yes—
56C11⋊#95C23112yes—
57C11⋊#95C23112yes—
58C2×#2643—111nomaximal, Sylow
59C24×C11—26no—
60C24×C11—26no—
61C24×C11—22no—
62C24×C11C2412yes—
63C24×C11C2411yescharacteristic
64C23×D11—26no—
65C23×D11—22no—
66C23×D11#41112yes—
67C23×D11C2412yes—
68C22×C4×C11—26no—
69C22×C4×C11—26no—
70C22×C4×C11—26no—
71C22×C4×C11—26no—
72C22×C4×C11—26no—
73C22×C4×C11—26no—
74C22×C4×C11C2416yes—
75C22×C4×C11C2416yes—
76C2×C22⋊D11—224no—
77C2×C22⋊D11—416no—
78C22×Dic11—26no—
79C22×Dic11—26no—
80C22×Dic11—26no—
81C22×Dic11—26no—
82C22×Dic11—26no—
83C22×Dic11—26no—
84C22×Dic11—26no—
85C22×Dic11C2412yes—
86C22×Dic11C2416yes—
87C22×Dic11C2416yes—
88C2×C4×D11—224no—
89C2×C4×D11—412no—
90C2×C4×D11—412no—
91C2×C4×D11—448no—
92C11×C4⋊C4—412no—
93C11×C22⋊C4—412no—
94C22⋊Dic11—412no—
95(C2×D11)⋊C4—224no—
96Dic11⋊C4—412no—
97#2643—1116no—
98C2×#401—111no—
99C2×#400—113no—
100C2×#397—113no—
101C2×#396D1111yescharacteristic, complemented
102C2×#386—113no—
103C2×#385—113no—
104C22×#95—111no—
105C23×C11—26no—
106C23×C11—26no—
107C23×C11—22no—
108C23×C11—44no—
109C23×C11—412no—
110C23×C11—412no—
111C23×C11C2×#4116yes—
112C23×C11H(5,𝔽2)16yes—
113C23×C112−1+412yes—
114C23×C11C2511yescharacteristic
115C22×D11—224no—
116C22×D11—224no—
117C22×D11—26no—
118C22×D11—22no—
119C22×D11#126116yes—
120C22×D11C2×#41112yes—
121C2×C4×C11—26no—
122C2×C4×C11—26no—
123C2×C4×C11—26no—
124C2×C4×C11—26no—
125C2×C4×C11—26no—
126C2×C4×C11—26no—
127C2×C4×C11—412no—
128C2×C4×C11—412no—
129C22⋊D11—416no—
130C2×Dic11—26no—
131C2×Dic11—26no—
132C2×Dic11—26no—
133C2×Dic11—26no—
134C2×Dic11—26no—
135C2×Dic11—26no—
136C2×Dic11—26no—
137C2×Dic11—44no—
138C2×Dic11—412no—
139C2×Dic11—412no—
140C4×D11—448no—
141C23×D4—111no—
142C24×C4—113no—
143C22×C4⋊C4—113no—
144C22×C4⋊C4C2×D1113yes—
145C22×C22⋊C4—113no—
146C22×C22⋊C4—113no—
147C22×C22⋊C4C2×D1113yes—
148#401—118no—
149#400—1124no—
150#397—1124no—
151#396C2×D1118yescomplemented
152#386—1124no—
153#385—1124no—
154C2×#95—113no—
155C2×#95—113no—
156C2×#95—113no—
157C2×#95—113no—
158C2×#95—113no—
159C2×#95—118no—
160C2×#95C2×D1111yescharacteristic
161C22×C11—42no—
162C22×C11—46no—
163C22×C11—46no—
164C22×C11—88no—
165C22×C11C2×#12614yes—
166C22×C11#538112yes—
167C22×C11#539112yes—
168C22×C11C22×#4113yes—
169C22×C11C2×H(5,𝔽2)13yes—
170C22×C11C2×2−1+411yescharacteristic
171C2×D11—232no—
172C2×D11—212no—
173C2×D11—212no—
174C2×D11C2×#12618yes—
175C4×C11—46no—
176C4×C11—46no—
177Dic11—42no—
178Dic11—46no—
179Dic11—46no—
180C25—111no—
181C25C22×D1111yescharacteristic
182C22×D4—114no—
183C22×D4—2212no—
184C23×C4—113no—
185C23×C4—113no—
186C23×C4—111no—
187C23×C4—1112no—
188C23×C4—2212no—
189C23×C4—446no—
190C23×C4—446no—
191C23×C4C22×D1113yes—
192C23×C4C22×D1113yes—
193C2×C4⋊C4—46no—
194C2×C4⋊C4—1112no—
195C2×C4⋊C4—446no—
196C2×C4⋊C4C22×D11112yes—
197C2×C22⋊C4—46no—
198C2×C22⋊C4—1112no—
199C2×C22⋊C4—1112no—
200C2×C22⋊C4—2212no—
201C2×C22⋊C4—446no—
202C2×C22⋊C4C22×D11112yes—
203#95—1112no—
204#95—1112no—
205#95—1112no—
206#95—1112no—
207#95—1112no—
208#95C22×D1114yes—
209C2×C11—82no—
210C2×C11#264318yescomplemented
211C2×C11C22×#12611yescharacteristic
212C2×C11C2×#53813yes—
213C2×C11C2×#53913yes—
214D11—28no—
215C24—26no—
216C24—22no—
217C24—26no—
218C24—1112no—
219C24—112no—
220C24—226no—
221C24—222no—
222C24C23×D1112yes—
223C24C23×D1111yescharacteristic
224C2×D4—2224no—
225C2×D4—4416no—
226C22×C4—26no—
227C22×C4—26no—
228C22×C4—26no—
229C22×C4—26no—
230C22×C4—26no—
231C22×C4—26no—
232C22×C4—112no—
233C22×C4—116no—
234C22×C4—116no—
235C22×C4—2224no—
236C22×C4—226no—
237C22×C4—226no—
238C22×C4—226no—
239C22×C4—226no—
240C22×C4—226no—
241C22×C4—226no—
242C22×C4—226no—
243C22×C4—4412no—
244C22×C4—4412no—
245C22×C4—4448no—
246C22×C4C23×D1116yes—
247C22×C4C23×D1116yes—
248C4⋊C4—412no—
249C4⋊C4—4412no—
250C22⋊C4—412no—
251C22⋊C4—2224no—
252C22⋊C4—4412no—
253C11C2×#264311yescharacteristic, complemented, Sylow
254C23—26no—
255C23—22no—
256C23—26no—
257C23—44no—
258C23—412no—
259C23—412no—
260C23—1116no—
261C23—1112no—
262C23—2224no—
263C23—2224no—
264C23—226no—
265C23—222no—
266C23#6703716yes—
267C23#6704012yes—
268C23#41×D1116yes—
269C23C24×D1111yescharacteristic
270D4—4416no—
271C2×C4—26no—
272C2×C4—26no—
273C2×C4—26no—
274C2×C4—26no—
275C2×C4—26no—
276C2×C4—26no—
277C2×C4—412no—
278C2×C4—412no—
279C2×C4—226no—
280C2×C4—226no—
281C2×C4—226no—
282C2×C4—226no—
283C2×C4—226no—
284C2×C4—226no—
285C2×C4—226no—
286C2×C4—4448no—
287C2×C4—444no—
288C2×C4—4412no—
289C2×C4—4412no—
290C22—42no—
291C22—46no—
292C22—46no—
293C22—88no—
294C22—118no—
295C22—2212no—
296C22—2212no—
297C22—2232no—
298C22#10623144112yes—
299C22#10623169112yes—
300C22D11×#12614yes—
301C22C2×#6703713yes—
302C22C2×#6704011yescharacteristic
303C22C2×#41×D1113yes—
304C4—46no—
305C4—46no—
306C4—442no—
307C4—446no—
308C4—446no—
309C2—82no—
310C2—228no—
311C2#1307457318yesdirect product factor
312C2C2×D11×#12611yescharacteristic
313C2C2×#1062314413yes—
314C2C2×#1062316913yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#396C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#396D11
hypocenterC11C2×#2643
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. #13074573C2direct (N × H)
2. C2×C11⋊#401C2semidirect
3. C2×#10622595C2semidirect
4. C2×#10622565C2semidirect
6. C2×#10622602C2semidirect
7. C2×D11×#95C2semidirect
8. C2×C11×#396C2semidirect
16. C11×#396C22semidirect
23. #10622602C22semidirect
24. #10622595C22semidirect
26. #10622565C22semidirect
27. D11×#95C22semidirect
28. C11⋊#401C22semidirect
101. C2×#396D11semidirect
151. #396C2×D11semidirect
210. C2×C11#2643semidirect
253. C11C2×#2643semidirect
311. C2#13074573direct (N × H)

Maximal subgroups

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

subgroupindex
#130745732
C2×C11⋊#4012
C2×#106225952
C2×#106225652
C2×#106225692
C2×#106226022
C2×D11×#952
C2×C11×#3962
C2×#264311