Finite Group Databasebeta

← C2×#13081254 #15633333

Subgroups — C2×#13081254 #15633333

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×Q8×D44C211yesmaximal, characteristic
2#13081254C2116yesmaximal, direct product factor
3C2×#10622694C213yesmaximal, complemented
4C2×#10622633C213yesmaximal, complemented
5C2×#10622696C213yesmaximal
6C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
7C2×C4×#4325C213yesmaximal
8C2×C11×#557C211yesmaximal, characteristic, complemented
9C22×Q8×D11—21no—
10C11×#557—24no—
11C11×#557C2218yescomplemented
12C2×C11×C4⋊Q8C2213yes—
13C2×C11×#125—23no—
14C2×C4×Q8×C11—21no—
15C2×C4×Q8×C11C2213yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C22×#4325C2213yes—
18Q8×D44—24no—
19Q8×D44C2218yes—
20C2×#66950—23no—
21C2×C4×D44C2213yes—
22C2×#66922C2213yes—
23C2×#66899C2216yes—
24C2×#66899C2213yes—
25#10622696C22124yes—
26#10622694C22124yescomplemented
27C4×#4325C22124yes—
28Q8×C11⋊C8C2218yescomplemented
29#10622633C22124yescomplemented
30C2×#66873C2211yescharacteristic
31C2×#66872C2213yes—
32C2×C4⋊(C11⋊C8)C2213yes—
33C2×C4×C11⋊C8C2213yes—
34C22×Q8×C11D411yescharacteristic
35C22×Q8×C11C2313yes—
36C2×Q8×D11—28no—
37C2×Q8×D11—48no—
38C22×D44C2311yescharacteristic
39C22×C4×D11—23no—
40C22×Dic22—23no—
41C11×C4⋊Q8—26no—
42C11×C4⋊Q8C23112yes—
43C11×#125—224no—
44C4×Q8×C11—28no—
45C4×Q8×C11—26no—
46C4×Q8×C11D414yes—
47C4×Q8×C11C23112yes—
48C4×Q8×C11C2314yes—
49C2×C11×C4⋊C4—23no—
50C2×C11×C4⋊C4—23no—
51C2×C11×C4⋊C4—23no—
52C2×C11×C4⋊C4D413yes—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C42×C11—23no—
55C2×C42×C11C2313yes—
56C2×#4325—212no—
57C2×#4325C23112yes—
58C2×(C2×D11)⋊C4—23no—
59C2×C4⋊Dic11—23no—
60C2×C4⋊Dic11C2313yes—
61C22×C11⋊C8C2311yescharacteristic
62C22×C11⋊C8C2313yes—
63#66950—224no—
64C4×D44—26no—
65C4×D44C23112yes—
66#66922—26no—
67#66922C23112yes—
68#66899C23124yes—
69#66899C23112yes—
70#66873C2314yes—
71#66872C23112yes—
72C4⋊(C11⋊C8)C23112yes—
73C4×C11⋊C8C23112yes—
74C2×#3359—111nomaximal, Sylow
75C23×D11—21no—
76C2×Q8×C11—23no—
77C2×Q8×C11—26no—
78C2×Q8×C11—26no—
79C2×Q8×C11SD1618yescomplemented
80C2×Q8×C11C2×D414yes—
81C2×Q8×C11C2416yes—
82C22×C4×C11—21no—
83C22×C4×C11—23no—
84C22×C4×C11C2×D413yes—
85C22×C4×C11C2×D413yes—
86C22×C4×C11C2411yescharacteristic
87C22×Dic11—23no—
88Q8×D11—432no—
89C2×D44—21no—
90C2×D44—22no—
91C2×D44#4114yes—
92C2×D44C2412yes—
93C2×C4×D11—212no—
94C2×C4×D11—412no—
95C2×Dic22—212no—
96C2×Dic22—412no—
97C11×C4⋊C4—212no—
98C11×C4⋊C4—212no—
99C11×C4⋊C4—212no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4C2×D4112yes—
102C11×C4⋊C4C2412yes—
103C42×C11—212no—
104C42×C11C2×D416yes—
105C42×C11C2416yes—
106#4325—224no—
107(C2×D11)⋊C4—212no—
108C4⋊Dic11—23no—
109C4⋊Dic11—212no—
110C4⋊Dic11C2416yes—
111C2×C11⋊C8—26no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8C2412yes—
114C2×C11⋊C8C2416yes—
115C2×#557D1111yescharacteristic, complemented
116C2×D4×Q8—111no—
117#3359—1116no—
118C2×#487—113no—
119C2×#475—113no—
120C2×#461—113no—
121C2×C8×Q8—111no—
122C2×C4×SD16—113no—
123C23×C11C22×D411yescharacteristic
124C22×D11—24no—
125C22×D11—22no—
126C22×D11—42no—
127C22×D11—42no—
128Q8×C11—26no—
129Q8×C11—26no—
130Q8×C11—46no—
131Q8×C11C2×SD16116yescomplemented
132C2×C4×C11—26no—
133C2×C4×C11—22no—
134C2×C4×C11—26no—
135C2×C4×C11—46no—
136C2×C4×C11—42no—
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—26no—
145C2×Dic11—46no—
146D44—24no—
147D44—22no—
148D44C2×#4114yes—
149C4×D11—424no—
150Dic22—424no—
151C11⋊C8—26no—
152C11⋊C8—22no—
153C23×Q8—221no—
154C22×SD16—113no—
155#557—24no—
156#557C2×D1118yescomplemented
157D4×Q8—118no—
158D4×Q8—224no—
159C2×C4⋊Q8—113no—
160C2×C4⋊Q8C2×D1113yes—
161C2×#125—23no—
162C2×C22⋊Q8—223no—
163C2×C4×Q8—21no—
164C2×C4×Q8C2×D1113yes—
165C2×C4×Q8C2×D1111yescharacteristic
166C2×C4×D4—113no—
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#54812yes—
179C22×C11C22×SD1612yes—
180C22×C11#57812yes—
181C22×C11C23×D411yescharacteristic
182C2×D11—24no—
183C2×D11—48no—
184C2×D11—42no—
185C2×D11—42no—
186C4×C11—26no—
187C4×C11—46no—
188C4×C11—42no—
189C4×C11#54812yes—
190C4×C11C22×SD16112yes—
191C4×C11C22×#4111yescharacteristic
192C4×C11C2×2−1+411yescharacteristic
193Dic11—46no—
194C22×Q8—228no—
195C22×Q8—223no—
196C22×Q8—448no—
197C22×Q8C22⋊D1111yescharacteristic
198C22×Q8C22×D1113yes—
199C22×D4—111no—
200C23×C4—223no—
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—224no—
210C22⋊Q8—2224no—
211C4×Q8—28no—
212C4×Q8—26no—
213C4×Q8C22⋊D1114yes—
214C4×Q8C22×D11112yes—
215C4×Q8C22×D1114yes—
216C4×D4—1112no—
217C4×D4—226no—
218C2×C4⋊C4—23no—
219C2×C4⋊C4—23no—
220C2×C4⋊C4—23no—
221C2×C4⋊C4—113no—
222C2×C4⋊C4—223no—
223C2×C4⋊C4C22⋊D1113yes—
224C2×C4⋊C4C22×D1111yescharacteristic
225C2×C22⋊C4—223no—
226C2×C42—23no—
227C2×C42C22×D1113yes—
228#106—1112no—
229C4⋊C8—1112no—
230#103—1112no—
231#103—1124no—
232#102—114no—
233C4×C8—1112no—
234C2×C11#335914yescomplemented
235C2×C11C2×#54811yescharacteristic
236C2×C11C23×SD1611yescharacteristic
237C2×C11C2×#57811yescharacteristic
238D11—44no—
239C24—221no—
240C2×Q8—23no—
241C2×Q8—26no—
242C2×Q8—26no—
243C2×Q8—2212no—
244C2×Q8—4432no—
245C2×Q8—4412no—
246C2×Q8#432518yescomplemented
247C2×Q8C2×C22⋊D1114yes—
248C2×Q8C23×D1116yes—
249C2×D4—114no—
250C2×D4—112no—
251C2×D4—222no—
252C2×D4—221no—
253C22×C4—21no—
254C22×C4—23no—
255C22×C4—223no—
256C22×C4—2212no—
257C22×C4—4412no—
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—212no—
268C4⋊C4—212no—
269C4⋊C4—21no—
270C4⋊C4—116no—
271C4⋊C4—223no—
272C4⋊C4—2212no—
273C4⋊C4C2×C22⋊D11112yes—
274C4⋊C4C23×D1112yes—
275C22⋊C4—2212no—
276C42—212no—
277C42C2×C22⋊D1116yes—
278C42C23×D1116yes—
279C11C2×#335911yescharacteristic, complemented, Sylow
280C23—224no—
281C23—222no—
282C23—442no—
283C23—442no—
284C23C22×C22⋊D1111yescharacteristic
285Q8—26no—
286Q8—26no—
287Q8—46no—
288Q8—4424no—
289Q8C2×#4325116yescomplemented
290D4—114no—
291D4—224no—
292D4—222no—
293C2×C4—26no—
294C2×C4—22no—
295C2×C4—26no—
296C2×C4—46no—
297C2×C4—42no—
298C2×C4—226no—
299C2×C4—446no—
300C2×C4—4424no—
301C2×C4C2×#4325112yes—
302C2×C4#41×D1112yes—
303C2×C4#6704312yes—
304C2×C4C22×C22⋊D1116yes—
305C2×C4C22×C22⋊D1116yes—
306C2×C4C22×C22⋊D1111yescharacteristic
307C2×C4C24×D1111yescharacteristic
308C8—226no—
309C8—222no—
310C22—224no—
311C22—448no—
312C22—442no—
313C22—442no—
314C22C22×#432512yes—
315C22#1062336212yes—
316C22#1062336912yes—
317C22C23×C22⋊D1111yescharacteristic
318C4—26no—
319C4—46no—
320C4—42no—
321C4—446no—
322C4C22×#4325112yes—
323C4#1062336212yes—
324C4C2×#41×D1111yescharacteristic
325C4C2×#6704311yescharacteristic
326C2—444no—
327C2#1308125414yesdirect product factor
328C2C2×#1062336211yescharacteristic
329C2C23×#432511yescharacteristic
330C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#557C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#557D11
hypocenterC11C2×#3359
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #13081254C2direct (N × H)
3. C2×#10622694C2semidirect
4. C2×#10622633C2semidirect
6. C2×Q8×C11⋊C8C2semidirect
8. C2×C11×#557C2semidirect
11. C11×#557C22semidirect
26. #10622694C22semidirect
28. Q8×C11⋊C8C22semidirect
29. #10622633C22semidirect
79. C2×Q8×C11SD16semidirect
115. C2×#557D11semidirect
131. Q8×C11C2×SD16semidirect
156. #557C2×D11semidirect
234. C2×C11#3359semidirect
246. C2×Q8#4325semidirect
279. C11C2×#3359semidirect
289. Q8C2×#4325semidirect
327. C2#13081254direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×D442
#130812542
C2×#106226942
C2×#106226332
C2×#106226962
C2×Q8×C11⋊C82
C2×C4×#43252
C2×C11×#5572
C2×#335911