Finite Group Databasebeta

← C2×#13076707 #14960085

Subgroups — C2×#13076707 #14960085

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#13076707C2116yesmaximal, direct product factor
2C2×C11⋊#401C211yesmaximal, characteristic, complemented
3C2×#10622606C213yesmaximal, complemented
4C2×#10622604C213yesmaximal, complemented
5C2×#10622284C211yesmaximal, characteristic, complemented
6C2×#10622573C213yesmaximal, complemented
7C2×#10622571C213yesmaximal, complemented
8C2×C11×#396C211yesmaximal, characteristic, complemented
9C23×C22⋊D11C2213yes—
10C24×Dic11C2211yescharacteristic
11C23×D44C2213yes—
12C22×C11×C4⋊C4C2213yes—
13C22×C11×C22⋊C4C2213yes—
14C22×(C2×D11)⋊C4C2213yes—
15C22×(C2×D11)⋊C4C2213yes—
16C22×(C2×D11)⋊C4C2213yes—
17C22×(C2×D11)⋊C4C2213yes—
18C11×#396C2218yescomplemented
19C2×C11×#95C2211yescharacteristic
20C2×C11⋊#95C2213yes—
21C2×C11⋊#95C2213yes—
22C2×C11⋊#95C2213yes—
23#10622606C22124yescomplemented
24#10622604C22124yescomplemented
25#10622573C22124yescomplemented
26#10622571C22124yescomplemented
27#10622284C2218yescomplemented
28C11⋊#401C2218yescomplemented
29C25×C11C2311yescharacteristic
30C24×D11C2313yes—
31C23×C4×C11C2313yes—
32C23×C4×C11C2313yes—
33C22×C22⋊D11—212no—
34C22×C22⋊D11—46no—
35C22×C22⋊D11—46no—
36C22×C22⋊D11C23112yes—
37C23×Dic11—46no—
38C23×Dic11C2311yescharacteristic
39C23×Dic11C2311yescharacteristic
40C23×Dic11C2313yes—
41C23×Dic11C2314yes—
42C22×D44—46no—
43C22×D44—46no—
44C22×D44—46no—
45C22×D44C23112yes—
46C2×C11×C4⋊C4—46no—
47C2×C11×C4⋊C4C23112yes—
48C2×C11×C22⋊C4—46no—
49C2×C11×C22⋊C4C23112yes—
50C2×(C2×D11)⋊C4—46no—
51C2×(C2×D11)⋊C4—46no—
52C2×(C2×D11)⋊C4—46no—
53C2×(C2×D11)⋊C4—46no—
54C2×(C2×D11)⋊C4C23112yes—
55C2×(C2×D11)⋊C4C23112yes—
56C2×(C2×D11)⋊C4C23112yes—
57C2×(C2×D11)⋊C4C23112yes—
58C11×#95C2314yes—
59C11⋊#95C23112yes—
60C11⋊#95C23112yes—
61C11⋊#95C23112yes—
62C2×#2825—111nomaximal, Sylow
63C24×C11—26no—
64C24×C11—26no—
65C24×C11#4114yes—
66C24×C11C2412yes—
67C24×C11C2411yescharacteristic
68C23×D11—26no—
69C23×D11—26no—
70C23×D11—26no—
71C23×D11—26no—
72C23×D11—26no—
73C23×D11—26no—
74C23×D11—26no—
75C23×D11C2416yes—
76C22×C4×C11—26no—
77C22×C4×C11—26no—
78C22×C4×C11—26no—
79C22×C4×C11—26no—
80C22×C4×C11—26no—
81C22×C4×C11—26no—
82C22×C4×C11C2416yes—
83C22×C4×C11C2416yes—
84C2×C22⋊D11—224no—
85C2×C22⋊D11—412no—
86C2×C22⋊D11—412no—
87C2×C22⋊D11—448no—
88C22×Dic11—26no—
89C22×Dic11—26no—
90C22×Dic11—26no—
91C22×Dic11—26no—
92C22×Dic11—26no—
93C22×Dic11—412no—
94C22×Dic11—416no—
95C22×Dic11C2416yes—
96C22×Dic11C2412yes—
97C22×Dic11C2412yes—
98C2×D44—412no—
99C2×D44—412no—
100C2×D44—412no—
101C2×D44—448no—
102C11×C4⋊C4—412no—
103C11×C22⋊C4—412no—
104(C2×D11)⋊C4—412no—
105(C2×D11)⋊C4—412no—
106(C2×D11)⋊C4—412no—
107(C2×D11)⋊C4—412no—
108#2825—1116no—
109C2×#401—111no—
110C2×#397—113no—
111C2×#396D1111yescharacteristic, complemented
112C2×#394—113no—
113C2×#392—111no—
114C2×#392—113no—
115C2×#386—113no—
116C23×C11—224no—
117C23×C11—26no—
118C23×C11—26no—
119C23×C11—44no—
120C23×C11—412no—
121C23×C11C2×#4114yes—
122C23×C11C2×#4112yes—
123C23×C11H(5,𝔽2)16yes—
124C23×C11H(5,𝔽2)16yes—
125C23×C11C2511yescharacteristic
126C22×D11—26no—
127C22×D11—26no—
128C22×D11—26no—
129C22×D11—26no—
130C22×D11—26no—
131C22×D11—26no—
132C22×D11—26no—
133C22×D11—412no—
134C22×D11—412no—
135C22×D11—412no—
136C22×D11—412no—
137C22×D11—412no—
138C22×D11—412no—
139C22×D11—412no—
140C2×C4×C11—26no—
141C2×C4×C11—26no—
142C2×C4×C11—26no—
143C2×C4×C11—26no—
144C2×C4×C11—26no—
145C2×C4×C11—26no—
146C2×C4×C11—412no—
147C2×C4×C11—412no—
148C22⋊D11—448no—
149C2×Dic11—26no—
150C2×Dic11—26no—
151C2×Dic11—26no—
152C2×Dic11—26no—
153C2×Dic11—26no—
154C2×Dic11—416no—
155C2×Dic11—412no—
156C2×Dic11—44no—
157C2×Dic11—44no—
158D44—448no—
159C23×D4—113no—
160C23×D4—113no—
161C24×C4—111no—
162C22×C4⋊C4C2×D1113yes—
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#396C2×D1118yescomplemented
171#394—1124no—
172#392—1124no—
173#392—118no—
174#386—1124no—
175C2×#95—113no—
176C2×#95—113no—
177C2×#95—113no—
178C2×#95C2×D1111yescharacteristic
179C22×C11—212no—
180C22×C11—416no—
181C22×C11—46no—
182C22×C11—42no—
183C22×C11#538112yes—
184C22×C11#56014yes—
185C22×C11#560112yes—
186C22×C11C22×#4111yescharacteristic
187C22×C11C2×H(5,𝔽2)13yes—
188C22×C11C2×H(5,𝔽2)13yes—
189C2×D11—46no—
190C2×D11—46no—
191C2×D11—46no—
192C2×D11—46no—
193C2×D11—46no—
194C2×D11—46no—
195C2×D11—46no—
196C2×D11—824no—
197C4×C11—46no—
198C4×C11—46no—
199Dic11—46no—
200Dic11—42no—
201Dic11—42no—
202C25—113no—
203C25C22×D1111yescharacteristic
204C22×D4—1112no—
205C22×D4—1112no—
206C22×D4—2212no—
207C22×D4—446no—
208C22×D4—446no—
209C22×D4—446no—
210C22×D4—446no—
211C22×D4—446no—
212C23×C4—111no—
213C23×C4—111no—
214C23×C4—113no—
215C23×C4—114no—
216C23×C4—446no—
217C23×C4C22×D1113yes—
218C23×C4C22×D1113yes—
219C2×C4⋊C4—46no—
220C2×C4⋊C4C22×D11112yes—
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—44no—
236C2×C11#282518yescomplemented
237C2×C11C2×#53813yes—
238C2×C11C2×#56013yes—
239C2×C11C2×#56011yescharacteristic
240D11—86no—
241C24—26no—
242C24—26no—
243C24—116no—
244C24—226no—
245C24—226no—
246C24—226no—
247C24—226no—
248C24—226no—
249C24—226no—
250C24—226no—
251C24#434314yes—
252C24C23×D1112yes—
253C24C23×D1111yescharacteristic
254C2×D4—2224no—
255C2×D4—4412no—
256C2×D4—4412no—
257C2×D4—4412no—
258C2×D4—4448no—
259C2×D4—4412no—
260C2×D4—4412no—
261C2×D4—4448no—
262C22×C4—26no—
263C22×C4—26no—
264C22×C4—26no—
265C22×C4—26no—
266C22×C4—26no—
267C22×C4—26no—
268C22×C4—116no—
269C22×C4—112no—
270C22×C4—112no—
271C22×C4—226no—
272C22×C4—226no—
273C22×C4—226no—
274C22×C4—226no—
275C22×C4—226no—
276C22×C4—4412no—
277C22×C4—4416no—
278C22×C4C23×D1116yes—
279C22×C4C23×D1116yes—
280C4⋊C4—412no—
281C22⋊C4—412no—
282C22⋊C4—4412no—
283C22⋊C4—4412no—
284C22⋊C4—4412no—
285C22⋊C4—4412no—
286C11C2×#282511yescharacteristic, complemented, Sylow
287C23—224no—
288C23—26no—
289C23—26no—
290C23—44no—
291C23—412no—
292C23—226no—
293C23—226no—
294C23—226no—
295C23—226no—
296C23—226no—
297C23—226no—
298C23—226no—
299C23—4412no—
300C23—4412no—
301C23—4412no—
302C23—4412no—
303C23—4412no—
304C23—4412no—
305C23—4412no—
306C23#6703716yes—
307C23C2×#434314yes—
308C23C2×#434312yes—
309C23#6704216yes—
310C23C24×D1111yescharacteristic
311D4—4448no—
312D4—4448no—
313C2×C4—26no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—26no—
317C2×C4—26no—
318C2×C4—26no—
319C2×C4—412no—
320C2×C4—412no—
321C2×C4—226no—
322C2×C4—226no—
323C2×C4—226no—
324C2×C4—226no—
325C2×C4—226no—
326C2×C4—4416no—
327C2×C4—444no—
328C2×C4—444no—
329C2×C4—4412no—
330C22—212no—
331C22—46no—
332C22—42no—
333C22—416no—
334C22—446no—
335C22—446no—
336C22—446no—
337C22—446no—
338C22—446no—
339C22—446no—
340C22—446no—
341C22—8824no—
342C22#10623151112yes—
343C22#10623175112yes—
344C22#1062324214yes—
345C22C2×#6703713yes—
346C22C22×#434311yescharacteristic
347C22C2×#6704213yes—
348C4—46no—
349C4—46no—
350C4—446no—
351C4—442no—
352C4—442no—
353C2—44no—
354C2—886no—
355C2#1307670718yesdirect product factor
356C2C2×#1062317513yes—
357C2C2×#1062315113yes—
358C2C2×#1062324211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#396C2
socleC24×C11C24
hypercenterC2×#396D11
hypocenterC11C2×#2825
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. #13076707C2direct (N × H)
2. C2×C11⋊#401C2semidirect
3. C2×#10622606C2semidirect
4. C2×#10622604C2semidirect
5. C2×#10622284C2semidirect
6. C2×#10622573C2semidirect
7. C2×#10622571C2semidirect
8. C2×C11×#396C2semidirect
18. C11×#396C22semidirect
23. #10622606C22semidirect
24. #10622604C22semidirect
25. #10622573C22semidirect
26. #10622571C22semidirect
27. #10622284C22semidirect
28. C11⋊#401C22semidirect
111. C2×#396D11semidirect
170. #396C2×D11semidirect
236. C2×C11#2825semidirect
286. C11C2×#2825semidirect
355. C2#13076707direct (N × H)

Maximal subgroups

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

subgroupindex
#130767072
C2×C11⋊#4012
C2×#106226062
C2×#106226042
C2×#106222842
C2×#106225732
C2×#106225712
C2×C11×#3962
C2×#282511