Finite Group Databasebeta

← C2×#13081258 #15633337

Subgroups — C2×#13081258 #15633337

Order 2816.

2058 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623101C211yesmaximal, characteristic, complemented
2#13081258C2116yesmaximal, direct product factor
3C2×#10622706C213yesmaximal, complemented
4C2×#10622707C213yesmaximal, complemented
5C2×#10622632C213yesmaximal
6C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
7C2×C4×#4324C213yesmaximal
8C2×D4×Q8×C11C211yesmaximal, characteristic
9C23×Q8×C11—21no—
10D4×Q8×C11—24no—
11D4×Q8×C11C2218yes—
12C2×C11×C4⋊Q8C2213yes—
13C2×C11×C22⋊Q8—23no—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2213yes—
16C2×Q8×Dic11—21no—
17C22×#4324C2213yes—
18#10623101—24no—
19#10623101C2218yescomplemented
20C2×#66943—23no—
21C2×#66922C2213yes—
22C2×C4×Dic22C2213yes—
23C2×#66896C2211yescharacteristic
24#10622707C22124yescomplemented
25#10622706C22124yescomplemented
26Q8×C11⋊C8C2218yescomplemented
27#10622632C22124yes—
28C4×#4324C22124yes—
29C2×#66874C2216yes—
30C2×#66874C2213yes—
31C2×#66872C2213yes—
32C2×C4⋊(C11⋊C8)C2213yes—
33C2×C4×C11⋊C8C2213yes—
34C22×Q8×C11—28no—
35C22×Q8×C11—23no—
36C22×Q8×C11—48no—
37C22×Q8×C11D411yescharacteristic
38C22×D4×C11C2311yescharacteristic
39C23×C4×C11—23no—
40C22×Dic22C2313yes—
41C11×C4⋊Q8—26no—
42C11×C4⋊Q8C23112yes—
43C11×C22⋊Q8—224no—
44C4×Q8×C11D414yes—
45C4×Q8×C11C2314yes—
46C4×D4×C11—26no—
47C4×D4×C11C23112yes—
48C2×C11×C4⋊C4—23no—
49C2×C11×C4⋊C4D413yes—
50C2×C11×C4⋊C4C2313yes—
51C2×C11×C22⋊C4—23no—
52C2×C42×C11C2313yes—
53Q8×Dic11—28no—
54C2×#4324—212no—
55C2×#4324C23112yes—
56C2×C4⋊Dic11—23no—
57C2×C4⋊Dic11—23no—
58C2×C4⋊Dic11C2311yescharacteristic
59C2×Dic11⋊C4—23no—
60C2×C4×Dic11—23no—
61C22×C11⋊C8C2311yescharacteristic
62C22×C11⋊C8C2313yes—
63#66943—224no—
64#66922—26no—
65#66922C23112yes—
66C4×Dic22—26no—
67C4×Dic22C23112yes—
68#66896C2314yes—
69#66874C23112yes—
70#66874C23124yes—
71#66872C23112yes—
72C4⋊(C11⋊C8)C23112yes—
73C4×C11⋊C8C23112yes—
74C2×#3359—111nomaximal, Sylow
75C24×C11—21no—
76C2×Q8×C11—212no—
77C2×Q8×C11—432no—
78C2×Q8×C11—412no—
79C2×Q8×C11SD1618yescomplemented
80C2×Q8×C11C2×D414yes—
81C2×D4×C11—21no—
82C2×D4×C11—22no—
83C2×D4×C11#4114yes—
84C2×D4×C11C2412yes—
85C22×C4×C11—23no—
86C22×C4×C11—212no—
87C22×C4×C11—412no—
88C22×C4×C11C2×D413yes—
89C22×C4×C11C2×D413yes—
90C22×C4×C11C2411yescharacteristic
91C22×Dic11—21no—
92C22×Dic11—23no—
93C2×Dic22—23no—
94C2×Dic22—26no—
95C2×Dic22—26no—
96C2×Dic22C2416yes—
97C11×C4⋊C4—212no—
98C11×C4⋊C4—23no—
99C11×C4⋊C4C2×D4112yes—
100C11×C4⋊C4C2416yes—
101C11×C22⋊C4—212no—
102C42×C11C2×D416yes—
103C42×C11C2416yes—
104#4324—224no—
105C4⋊Dic11—21no—
106C4⋊Dic11—212no—
107C4⋊Dic11—212no—
108C4⋊Dic11C2412yes—
109Dic11⋊C4—212no—
110C4×Dic11—212no—
111C2×C11⋊C8—26no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8C2412yes—
114C2×C11⋊C8C2416yes—
115C2×#557—111no—
116C2×D4×Q8D1111yescharacteristic
117#3359—1116no—
118C2×#487—113no—
119C2×#475—113no—
120C2×#461—113no—
121C2×C8×Q8—111no—
122C2×C4×SD16—113no—
123C23×C11—24no—
124C23×C11—22no—
125C23×C11—42no—
126C23×C11—42no—
127C23×C11C22×D411yescharacteristic
128Q8×C11—424no—
129Q8×C11C2×SD16116yescomplemented
130D4×C11—24no—
131D4×C11—22no—
132D4×C11C2×#4114yes—
133C2×C4×C11—26no—
134C2×C4×C11—26no—
135C2×C4×C11—46no—
136C2×C4×C11—424no—
137C2×C4×C11C2×SD16112yes—
138C2×C4×C11C22×D416yes—
139C2×C4×C11C22×D411yescharacteristic
140C2×C4×C11C22×D416yes—
141C2×C4×C11C2×#4112yes—
142C2×C4×C112−1+412yes—
143C2×C4×C11C2511yescharacteristic
144C2×Dic11—22no—
145C2×Dic11—26no—
146C2×Dic11—46no—
147C2×Dic11—42no—
148Dic22—26no—
149Dic22—26no—
150Dic22—46no—
151C11⋊C8—26no—
152C11⋊C8—22no—
153C23×Q8—21no—
154C22×SD16—113no—
155#557—118no—
156#557—224no—
157D4×Q8—24no—
158D4×Q8C2×D1118yes—
159C2×C4⋊Q8—113no—
160C2×C4⋊Q8C2×D1113yes—
161C2×#125—223no—
162C2×C22⋊Q8—23no—
163C2×C4×Q8—113no—
164C2×C4×Q8—221no—
165C2×C4×Q8C2×D1111yescharacteristic
166C2×C4×D4C2×D1113yes—
167#487—1124no—
168#475—1124no—
169#461—1124no—
170C8×Q8—118no—
171C4×SD16—1124no—
172C2×#106—113no—
173C2×C4⋊C8—113no—
174C2×#103—116no—
175C2×#103—113no—
176C2×#102—111no—
177C2×C4×C8—113no—
178C22×C11—24no—
179C22×C11—48no—
180C22×C11—42no—
181C22×C11—42no—
182C22×C11#54812yes—
183C22×C11C22×SD1612yes—
184C22×C11#57812yes—
185C22×C11C23×D411yescharacteristic
186C4×C11—26no—
187C4×C11—46no—
188C4×C11#54812yes—
189C4×C11C22×SD16112yes—
190C4×C11C22×#4111yescharacteristic
191C4×C11C2×2−1+411yescharacteristic
192Dic11—46no—
193Dic11—42no—
194C22×Q8—28no—
195C22×Q8—23no—
196C22×Q8—48no—
197C22×Q8—113no—
198C22×Q8C22⋊D1111yescharacteristic
199C22×D4C22×D1111yescharacteristic
200C23×C4—23no—
201C2×SD16—1112no—
202C2×SD16—2212no—
203C22×C8—113no—
204C22×C8—111no—
205C4⋊Q8—26no—
206C4⋊Q8—1112no—
207C4⋊Q8—226no—
208C4⋊Q8C22×D11112yes—
209#125—2224no—
210C22⋊Q8—224no—
211C4×Q8—1112no—
212C4×Q8—228no—
213C4×Q8—226no—
214C4×Q8C22⋊D1114yes—
215C4×Q8C22×D1114yes—
216C4×D4—26no—
217C4×D4C22×D11112yes—
218C2×C4⋊C4—23no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—223no—
221C2×C4⋊C4—223no—
222C2×C4⋊C4—223no—
223C2×C4⋊C4C22⋊D1113yes—
224C2×C4⋊C4C22×D1113yes—
225C2×C22⋊C4—23no—
226C2×C42—223no—
227C2×C42C22×D1113yes—
228#106—1112no—
229C4⋊C8—1112no—
230#103—1112no—
231#103—1124no—
232#102—114no—
233C4×C8—1112no—
234C2×C11—44no—
235C2×C11#335914yescomplemented
236C2×C11C2×#54811yescharacteristic
237C2×C11C23×SD1611yescharacteristic
238C2×C11C2×#57811yescharacteristic
239C24—21no—
240C2×Q8—212no—
241C2×Q8—432no—
242C2×Q8—412no—
243C2×Q8—116no—
244C2×Q8—223no—
245C2×Q8—226no—
246C2×Q8—226no—
247C2×Q8#432418yescomplemented
248C2×Q8C2×C22⋊D1114yes—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4#434314yes—
252C2×D4C23×D1112yes—
253C22×C4—23no—
254C22×C4—212no—
255C22×C4—412no—
256C22×C4—221no—
257C22×C4—223no—
258C22×C4C2×C22⋊D1113yes—
259C22×C4C2×C22⋊D1113yes—
260C22×C4C23×D1111yescharacteristic
261SD16—2224no—
262C2×C8—112no—
263C2×C8—116no—
264C2×C8—226no—
265C2×C8—222no—
266C4⋊C4—212no—
267C4⋊C4—23no—
268C4⋊C4—112no—
269C4⋊C4—221no—
270C4⋊C4—2212no—
271C4⋊C4—2212no—
272C4⋊C4—2212no—
273C4⋊C4C2×C22⋊D11112yes—
274C4⋊C4C23×D1116yes—
275C22⋊C4—212no—
276C42—2212no—
277C42C2×C22⋊D1116yes—
278C42C23×D1116yes—
279C11C2×#335911yescharacteristic, complemented, Sylow
280C23—24no—
281C23—22no—
282C23—42no—
283C23—42no—
284C23C22×C22⋊D1111yescharacteristic
285Q8—424no—
286Q8—226no—
287Q8—226no—
288Q8—446no—
289Q8C2×#4324116yescomplemented
290D4—24no—
291D4—22no—
292D4C2×#434314yes—
293C2×C4—26no—
294C2×C4—26no—
295C2×C4—46no—
296C2×C4—424no—
297C2×C4—222no—
298C2×C4—226no—
299C2×C4—446no—
300C2×C4—442no—
301C2×C4C2×#4324112yes—
302C2×C4C2×#434312yes—
303C2×C4#6704012yes—
304C2×C4C22×C22⋊D1116yes—
305C2×C4C22×C22⋊D1116yes—
306C2×C4C22×C22⋊D1111yescharacteristic
307C2×C4C24×D1111yescharacteristic
308C8—226no—
309C8—222no—
310C22—24no—
311C22—48no—
312C22—42no—
313C22—42no—
314C22C22×#432412yes—
315C22#1062334812yes—
316C22#1062336912yes—
317C22C23×C22⋊D1111yescharacteristic
318C4—26no—
319C4—46no—
320C4—446no—
321C4—442no—
322C4C22×#4324112yes—
323C4#1062334812yes—
324C4C22×#434311yescharacteristic
325C4C2×#6704011yescharacteristic
326C2—44no—
327C2#1308125814yesdirect product factor
328C2C2×#1062334811yescharacteristic
329C2C23×#432411yescharacteristic
330C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×D4×Q8×C11C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×D4×Q8D11
hypocenterC11C2×#3359
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10623101C2semidirect
2. #13081258C2direct (N × H)
3. C2×#10622706C2semidirect
4. C2×#10622707C2semidirect
6. C2×Q8×C11⋊C8C2semidirect
19. #10623101C22semidirect
24. #10622707C22semidirect
25. #10622706C22semidirect
26. Q8×C11⋊C8C22semidirect
79. C2×Q8×C11SD16semidirect
129. Q8×C11C2×SD16semidirect
235. C2×C11#3359semidirect
247. C2×Q8#4324semidirect
279. C11C2×#3359semidirect
289. Q8C2×#4324semidirect
327. C2#13081258direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231012
#130812582
C2×#106227062
C2×#106227072
C2×#106226322
C2×Q8×C11⋊C82
C2×C4×#43242
C2×D4×Q8×C112
C2×#335911