Finite Group Databasebeta

← C2×#13076705 #14960087

Subgroups — C2×#13076705 #14960087

Order 2816.

2930 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076705C2116yesmaximal, direct product factor
2C2×C11⋊#401C211yesmaximal, characteristic, complemented
3C2×#10622565C213yesmaximal, complemented
4C2×#10622289C211yesmaximal, characteristic, complemented
5C2×#10622835C213yesmaximal, complemented
6C2×#10622836C213yesmaximal, complemented
7C2×#10622569C213yesmaximal, complemented
8C2×C11×#392C211yesmaximal, characteristic, complemented
9C23×D4×C11C2213yes—
10C23×C22⋊D11C2213yes—
11C23×C4×D11C2211yescharacteristic
12C22×C11×C22⋊C4C2213yes—
13C22×C22⋊Dic11C2213yes—
14C22×C22⋊Dic11C2213yes—
15C22×C22⋊Dic11C2213yes—
16C22×(C2×D11)⋊C4C2213yes—
17C22×Dic11⋊C4C2213yes—
18C11×#392C2218yescomplemented
19C2×C11×#95C2211yescharacteristic
20#10622836C22124yescomplemented
21#10622835C22124yescomplemented
22C2×C11⋊#95C2213yes—
23C2×C11⋊#95C2213yes—
24C2×C11⋊#95C2213yes—
25#10622569C22124yescomplemented
26#10622565C22124yescomplemented
27#10622289C2218yescomplemented
28C11⋊#401C2218yescomplemented
29C25×C11C2313yes—
30C24×D11C2311yescharacteristic
31C22×D4×C11—46no—
32C22×D4×C11—46no—
33C22×D4×C11—46no—
34C22×D4×C11C23112yes—
35C23×C4×C11C2313yes—
36C23×C4×C11C2311yescharacteristic
37C22×C22⋊D11—212no—
38C22×C22⋊D11—46no—
39C22×C22⋊D11—46no—
40C22×C22⋊D11C23112yes—
41C23×Dic11C2313yes—
42C23×Dic11C2313yes—
43C23×Dic11C2311yescharacteristic
44C22×C4×D11—46no—
45C22×C4×D11C2314yes—
46C2×C11×C22⋊C4—46no—
47C2×C11×C22⋊C4C23112yes—
48C2×C22⋊Dic11—46no—
49C2×C22⋊Dic11—46no—
50C2×C22⋊Dic11—46no—
51C2×C22⋊Dic11C23112yes—
52C2×C22⋊Dic11C23112yes—
53C2×C22⋊Dic11C23112yes—
54C2×(C2×D11)⋊C4—46no—
55C2×(C2×D11)⋊C4C23112yes—
56C2×Dic11⋊C4—46no—
57C2×Dic11⋊C4C23112yes—
58C11×#95C2314yes—
59C11⋊#95C23112yes—
60C11⋊#95C23112yes—
61C11⋊#95C23112yes—
62C2×#2825—111nomaximal, Sylow
63C24×C11—26no—
64C24×C11—26no—
65C24×C11—26no—
66C24×C11—26no—
67C24×C11—26no—
68C24×C11—26no—
69C24×C11—26no—
70C24×C11C2416yes—
71C24×C11C2411yescharacteristic
72C23×D11—26no—
73C23×D11—26no—
74C23×D11#4114yes—
75C23×D11C2412yes—
76C2×D4×C11—412no—
77C2×D4×C11—412no—
78C2×D4×C11—412no—
79C2×D4×C11—448no—
80C22×C4×C11—26no—
81C22×C4×C11—26no—
82C22×C4×C11—26no—
83C22×C4×C11—26no—
84C22×C4×C11C2412yes—
85C22×C4×C11C2416yes—
86C2×C22⋊D11—224no—
87C2×C22⋊D11—412no—
88C2×C22⋊D11—412no—
89C2×C22⋊D11—448no—
90C22×Dic11—26no—
91C22×Dic11—26no—
92C22×Dic11—26no—
93C22×Dic11—26no—
94C22×Dic11—26no—
95C22×Dic11—26no—
96C22×Dic11—26no—
97C22×Dic11C2416yes—
98C22×Dic11C2412yes—
99C22×Dic11C2416yes—
100C2×C4×D11—412no—
101C2×C4×D11—416no—
102C11×C22⋊C4—412no—
103C22⋊Dic11—412no—
104C22⋊Dic11—412no—
105C22⋊Dic11—412no—
106(C2×D11)⋊C4—412no—
107Dic11⋊C4—412no—
108#2825—1116no—
109C2×#401—111no—
110C2×#397—113no—
111C2×#396—111no—
112C2×#394—113no—
113C2×#392—113no—
114C2×#392D1111yescharacteristic, complemented
115C2×#386—113no—
116C23×C11—26no—
117C23×C11—26no—
118C23×C11—26no—
119C23×C11—26no—
120C23×C11—26no—
121C23×C11—26no—
122C23×C11—26no—
123C23×C11—412no—
124C23×C11—412no—
125C23×C11—412no—
126C23×C11—412no—
127C23×C11—412no—
128C23×C11—412no—
129C23×C11—412no—
130C23×C11C2×#4112yes—
131C23×C11H(5,𝔽2)16yes—
132C23×C11H(5,𝔽2)16yes—
133C23×C11C2511yescharacteristic
134C22×D11—224no—
135C22×D11—26no—
136C22×D11—26no—
137C22×D11—44no—
138C22×D11—412no—
139C22×D11C2×#4114yes—
140D4×C11—448no—
141C2×C4×C11—26no—
142C2×C4×C11—26no—
143C2×C4×C11—26no—
144C2×C4×C11—26no—
145C2×C4×C11—44no—
146C2×C4×C11—412no—
147C22⋊D11—448no—
148C2×Dic11—26no—
149C2×Dic11—26no—
150C2×Dic11—26no—
151C2×Dic11—26no—
152C2×Dic11—26no—
153C2×Dic11—26no—
154C2×Dic11—26no—
155C2×Dic11—412no—
156C2×Dic11—44no—
157C2×Dic11—412no—
158C4×D11—416no—
159C23×D4—113no—
160C23×D4C2×D1113yes—
161C24×C4—111no—
162C22×C4⋊C4—113no—
163C22×C22⋊C4—113no—
164C22×C22⋊C4—113no—
165C22×C22⋊C4—113no—
166C22×C22⋊C4—113no—
167C22×C22⋊C4C2×D1113yes—
168#401—118no—
169#397—1124no—
170#396—118no—
171#394—1124no—
172#392—1124no—
173#392C2×D1118yescomplemented
174#386—1124no—
175C2×#95—113no—
176C2×#95—113no—
177C2×#95—113no—
178C2×#95C2×D1111yescharacteristic
179C22×C11—46no—
180C22×C11—46no—
181C22×C11—46no—
182C22×C11—46no—
183C22×C11—46no—
184C22×C11—46no—
185C22×C11—46no—
186C22×C11—824no—
187C22×C11#538112yes—
188C22×C11#56014yes—
189C22×C11#560112yes—
190C22×C11C22×#4111yescharacteristic
191C22×C11C2×H(5,𝔽2)13yes—
192C22×C11C2×H(5,𝔽2)13yes—
193C2×D11—212no—
194C2×D11—416no—
195C2×D11—46no—
196C2×D11—42no—
197C4×C11—46no—
198C4×C11—42no—
199Dic11—46no—
200Dic11—42no—
201Dic11—46no—
202C25—111no—
203C25C22×D1113yes—
204C22×D4—46no—
205C22×D4—46no—
206C22×D4—46no—
207C22×D4—1112no—
208C22×D4—2212no—
209C22×D4—446no—
210C22×D4—446no—
211C22×D4C22×D11112yes—
212C23×C4—113no—
213C23×C4—111no—
214C23×C4—113no—
215C23×C4—114no—
216C23×C4—446no—
217C23×C4C22×D1113yes—
218C23×C4C22×D1111yescharacteristic
219C2×C4⋊C4—1112no—
220C2×C4⋊C4—446no—
221C2×C22⋊C4—46no—
222C2×C22⋊C4—1112no—
223C2×C22⋊C4—1112no—
224C2×C22⋊C4—1112no—
225C2×C22⋊C4—1112no—
226C2×C22⋊C4—446no—
227C2×C22⋊C4—446no—
228C2×C22⋊C4—446no—
229C2×C22⋊C4—446no—
230C2×C22⋊C4C22×D11112yes—
231#95—1112no—
232#95—1112no—
233#95—1112no—
234#95C22×D1114yes—
235C2×C11—86no—
236C2×C11#282518yescomplemented
237C2×C11C2×#53813yes—
238C2×C11C2×#56011yescharacteristic
239C2×C11C2×#56013yes—
240D11—44no—
241C24—26no—
242C24—26no—
243C24—26no—
244C24—26no—
245C24—26no—
246C24—26no—
247C24—26no—
248C24—114no—
249C24—112no—
250C24—226no—
251C24—226no—
252C24C23×D1116yes—
253C24C23×D1111yescharacteristic
254C2×D4—412no—
255C2×D4—412no—
256C2×D4—412no—
257C2×D4—448no—
258C2×D4—2224no—
259C2×D4—4412no—
260C2×D4—4412no—
261C2×D4—4448no—
262C22×C4—26no—
263C22×C4—26no—
264C22×C4—26no—
265C22×C4—26no—
266C22×C4—116no—
267C22×C4—112no—
268C22×C4—116no—
269C22×C4—226no—
270C22×C4—226no—
271C22×C4—226no—
272C22×C4—226no—
273C22×C4—226no—
274C22×C4—226no—
275C22×C4—226no—
276C22×C4—4412no—
277C22×C4—4416no—
278C22×C4C23×D1112yes—
279C22×C4C23×D1116yes—
280C4⋊C4—4412no—
281C22⋊C4—412no—
282C22⋊C4—4412no—
283C22⋊C4—4412no—
284C22⋊C4—4412no—
285C22⋊C4—4412no—
286C11C2×#282511yescharacteristic, complemented, Sylow
287C23—26no—
288C23—26no—
289C23—26no—
290C23—26no—
291C23—26no—
292C23—26no—
293C23—26no—
294C23—412no—
295C23—412no—
296C23—412no—
297C23—412no—
298C23—412no—
299C23—412no—
300C23—412no—
301C23—114no—
302C23—2224no—
303C23—226no—
304C23—226no—
305C23—444no—
306C23—4412no—
307C23#6703716yes—
308C23#6703716yes—
309C23#41×D1112yes—
310C23C24×D1111yescharacteristic
311D4—448no—
312D4—4448no—
313C2×C4—26no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—26no—
317C2×C4—44no—
318C2×C4—412no—
319C2×C4—226no—
320C2×C4—226no—
321C2×C4—226no—
322C2×C4—226no—
323C2×C4—226no—
324C2×C4—226no—
325C2×C4—226no—
326C2×C4—4416no—
327C2×C4—444no—
328C2×C4—4412no—
329C2×C4—4412no—
330C22—46no—
331C22—46no—
332C22—46no—
333C22—46no—
334C22—46no—
335C22—46no—
336C22—46no—
337C22—824no—
338C22—2212no—
339C22—442no—
340C22—446no—
341C22—4416no—
342C22#10623126112yes—
343C22#10623144112yes—
344C22#1062325114yes—
345C22C2×#6703713yes—
346C22C2×#6703713yes—
347C22C2×#41×D1111yescharacteristic
348C4—42no—
349C4—46no—
350C4—446no—
351C4—442no—
352C4—446no—
353C2—86no—
354C2—444no—
355C2#1307670518yesdirect product factor
356C2C2×#1062314413yes—
357C2C2×#1062325111yescharacteristic
358C2C2×#1062312613yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2825
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. #13076705C2direct (N × H)
2. C2×C11⋊#401C2semidirect
3. C2×#10622565C2semidirect
4. C2×#10622289C2semidirect
5. C2×#10622835C2semidirect
6. C2×#10622836C2semidirect
7. C2×#10622569C2semidirect
8. C2×C11×#392C2semidirect
18. C11×#392C22semidirect
20. #10622836C22semidirect
21. #10622835C22semidirect
25. #10622569C22semidirect
26. #10622565C22semidirect
27. #10622289C22semidirect
28. C11⋊#401C22semidirect
114. C2×#392D11semidirect
173. #392C2×D11semidirect
236. C2×C11#2825semidirect
286. C11C2×#2825semidirect
355. C2#13076705direct (N × H)

Maximal subgroups

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

subgroupindex
#130767052
C2×C11⋊#4012
C2×#106225652
C2×#106222892
C2×#106228352
C2×#106228362
C2×#106225692
C2×C11×#3922
C2×#282511