Finite Group Databasebeta

← C2×#13069492 #14757609

Subgroups — C2×#13069492 #14757609

Order 2816.

2006 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D88C211yesmaximal, characteristic
2C22×#66881C211yesmaximal, characteristic, complemented
3C22×#66885C212yesmaximal, complemented
4C2×#10622552C212yesmaximal, complemented
5#13069492C218yesmaximal, direct product factor
6C22×C11×#97C211yesmaximal, characteristic, complemented
7C23×D44C2212yes—
8C23×C8×C11C2211yescharacteristic
9C23×C8×C11C2211yescharacteristic
10C22×C42×C11C2211yescharacteristic
11C22×(C2×D11)⋊C4—24no—
12C22×C4⋊Dic11C2212yes—
13C22×D88—24no—
14C22×D88—24no—
15C22×D88C418yescomplemented
16C22×D88C2214yes—
17C2×C11×#97—24no—
18C2×C11×#97C2214yescomplemented
19C2×#66885—28no—
20C2×#66885C2218yescomplemented
21C2×#66881—24no—
22C2×#66881C2214yescomplemented
23#10622552—24no—
24#10622552C2218yescomplemented
25C24×D11—22no—
26C23×C4×C11D412yes—
27C23×C4×C11C2311yescharacteristic
28C23×Dic11—22no—
29C22×D44—24no—
30C22×D44—24no—
31C22×D44—24no—
32C22×D44—24no—
33C22×D44—22no—
34C22×D44—24no—
35C22×D44C2×C418yes—
36C22×D44C2314yes—
37C22×C8×C11—22no—
38C22×C8×C11—22no—
39C22×C8×C11C2×C414yes—
40C22×C8×C11D414yes—
41C22×C8×C11D414yes—
42C22×C8×C11D414yes—
43C22×C8×C11C2312yes—
44C22×C8×C11C2312yes—
45C2×C42×C11—22no—
46C2×C42×C11—22no—
47C2×C42×C11D412yes—
48C2×C42×C11C2312yes—
49C2×(C2×D11)⋊C4—216no—
50C2×(C2×D11)⋊C4—416no—
51C2×C4⋊Dic11—24no—
52C2×C4⋊Dic11—24no—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11C2314yes—
55C2×D88—232no—
56C2×D88—28no—
57C2×D88—28no—
58C2×D88C2×C4116yescomplemented
59C11×#97—28no—
60#66885—216no—
61#66881—28no—
62C2×#1972—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C23×D11—28no—
65C23×D11—24no—
66C23×D11—44no—
67C23×D11—44no—
68C23×D11—48no—
69C23×D11—48no—
70C22×C4×C11—24no—
71C22×C4×C11—28no—
72C22×C4×C11C22×C412yes—
73C22×C4×C11C2×D414yes—
74C22×C4×C11C2×D412yes—
75C22×C4×C11C2×D412yes—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D412yes—
78C22×C4×C11#4112yes—
79C22×C4×C11#4112yes—
80C22×C4×C11C2411yescharacteristic
81C22×Dic11—24no—
82C22×Dic11—44no—
83C22×Dic11—48no—
84C2×D44—216no—
85C2×D44—28no—
86C2×D44—216no—
87C2×D44—24no—
88C2×D44—24no—
89C2×D44—24no—
90C2×D44—24no—
91C2×D44—24no—
92C2×D44—48no—
93C2×D44—44no—
94C2×D44—48no—
95C2×D44—44no—
96C2×D44C22×C418yes—
97C2×C8×C11—28no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11C22⋊C4116yescomplemented
101C2×C8×C11C22×C414yes—
102C2×C8×C11C2×D414yes—
103C2×C8×C11C2×D414yes—
104C2×C8×C11C2×D414yes—
105C42×C11—24no—
106C42×C11—22no—
107C42×C11—22no—
108(C2×D11)⋊C4—432no—
109C4⋊Dic11—24no—
110C4⋊Dic11—24no—
111C4⋊Dic11—44no—
112D88—232no—
113C23×D8—111no—
114C22×#106—111no—
115C22×#102—112no—
116C22×#97D1111yescharacteristic, complemented
117C2×#390—112no—
118#1972—118no—
119C23×C11C4×D412yes—
120C23×C11#12112yes—
121C23×C11#12712yes—
122C23×C11AGL(1,ℤ/8)18yes—
123C23×C11C22×D411yescharacteristic
124C22×D11—28no—
125C22×D11—44no—
126C22×D11—44no—
127C22×D11—48no—
128C22×D11—48no—
129C22×D11—416no—
130C22×D11—432no—
131C22×D11—816no—
132C22×D11—88no—
133C22×D11—88no—
134C2×C4×C11—24no—
135C2×C4×C11—28no—
136C2×C4×C11—48no—
137C2×C4×C11C2×C22⋊C414yes—
138C2×C4×C11C4×D414yes—
139C2×C4×C11C4×D412yes—
140C2×C4×C11#12114yes—
141C2×C4×C11#12112yes—
142C2×C4×C11#12414yes—
143C2×C4×C11#12712yes—
144C2×C4×C11C23×C411yescharacteristic
145C2×C4×C11C22×D411yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C22×D411yescharacteristic
148C2×C4×C11C2×#4111yescharacteristic
149C2×C4×C11C2×#4111yescharacteristic
150C2×Dic11—44no—
151C2×Dic11—48no—
152C2×Dic11—88no—
153D44—28no—
154D44—28no—
155D44—44no—
156D44—44no—
157D44—416no—
158C8×C11—24no—
159C8×C11C2×C22⋊C418yescomplemented
160C23×D4—112no—
161C22×D8—114no—
162C22×D8—118no—
163C22×D8—224no—
164C22×D8—224no—
165C23×C8C2×D1111yescharacteristic
166C23×C8C2×D1111yescharacteristic
167C22×C4⋊C4—112no—
168C22×C22⋊C4—224no—
169C22×C42C2×D1111yescharacteristic
170C2×#106—114no—
171C2×#106—224no—
172C2×#102—118no—
173C2×#102—228no—
174C2×#97—24no—
175C2×#97C2×D1114yescomplemented
176#390—118no—
177#390—224no—
178C22×C11#39014yes—
179C22×C11#44218yes—
180C22×C11#46918yes—
181C22×C11#49618yes—
182C22×C11C2×C4×D411yescharacteristic
183C22×C11C2×#12111yescharacteristic
184C22×C11C2×#12711yescharacteristic
185C22×C11C2×AGL(1,ℤ/8)14yes—
186C2×D11—416no—
187C2×D11—48no—
188C2×D11—84no—
189C2×D11—84no—
190C2×D11—832no—
191C2×D11—88no—
192C4×C11—44no—
193C4×C11#39014yes—
194C4×C11C22×C22⋊C411yescharacteristic
195C4×C11C2×C4×D411yescharacteristic
196C4×C11C2×#12111yescharacteristic
197C4×C11C2×#12411yescharacteristic
198Dic11—84no—
199C25—222no—
200C22×D4—118no—
201C22×D4—114no—
202C22×D4—224no—
203C22×D4—224no—
204C22×D4—222no—
205C22×D4—224no—
206C22×D4—224no—
207C22×D4—224no—
208C23×C4—222no—
209C23×C4D4412yes—
210C23×C4C22×D1111yescharacteristic
211C2×D8—1116no—
212C2×D8—2232no—
213C2×D8—228no—
214C2×D8—228no—
215C22×C8—22no—
216C22×C8—22no—
217C22×C8C4×D1114yes—
218C22×C8D4414yes—
219C22×C8D4414yes—
220C22×C8C22⋊D1114yes—
221C22×C8C22×D1112yes—
222C22×C8C22×D1112yes—
223C2×C4⋊C4—114no—
224C2×C4⋊C4—224no—
225C2×C4⋊C4—224no—
226C2×C4⋊C4—222no—
227C2×C22⋊C4—2216no—
228C2×C22⋊C4—4416no—
229C2×C42—22no—
230C2×C42—22no—
231C2×C42D4412yes—
232C2×C42C22×D1112yes—
233#106—228no—
234#102—2216no—
235#97—28no—
236C2×C11#197218yescomplemented
237C2×C11C2×#39011yescharacteristic
238C2×C11C2×#44212yes—
239C2×C11C2×#46912yes—
240C2×C11C2×#49612yes—
241D11—88no—
242C24—228no—
243C24—224no—
244C24—444no—
245C24—448no—
246C24—448no—
247C24—444no—
248C24C2×D4411yescharacteristic
249C2×D4—118no—
250C2×D4—2216no—
251C2×D4—228no—
252C2×D4—2216no—
253C2×D4—224no—
254C2×D4—224no—
255C2×D4—224no—
256C2×D4—224no—
257C2×D4—224no—
258C2×D4—444no—
259C2×D4—448no—
260C2×D4—444no—
261C2×D4—448no—
262C22×C4—28no—
263C22×C4—24no—
264C22×C4—224no—
265C22×C4—444no—
266C22×C4—448no—
267C22×C4C2×C4×D1112yes—
268C22×C4C2×D4414yes—
269C22×C4C2×D4411yescharacteristic
270C22×C4C2×D4412yes—
271C22×C4C2×D4412yes—
272C22×C4#433912yes—
273C22×C4#433912yes—
274C22×C4C2×C22⋊D1112yes—
275C22×C4C23×D1111yescharacteristic
276D8—2232no—
277C2×C8—28no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8(C2×D11)⋊C4116yescomplemented
281C2×C8C2×C4×D1114yes—
282C2×C8C2×D4414yes—
283C2×C8C2×D4414yes—
284C2×C8C2×C22⋊D1114yes—
285C4⋊C4—224no—
286C4⋊C4—224no—
287C4⋊C4—444no—
288C22⋊C4—4432no—
289C42—24no—
290C42—22no—
291C42—22no—
292C11C2×#197211yescharacteristic, complemented, Sylow
293C23—228no—
294C23—444no—
295C23—448no—
296C23—448no—
297C23—4416no—
298C23—444no—
299C23—4432no—
300C23—8816no—
301C23—888no—
302C23—888no—
303C23C4×D4412yes—
304C23#6692712yes—
305C23#6696118yes—
306C23#6698312yes—
307C23C22×D4411yescharacteristic
308D4—228no—
309D4—228no—
310D4—444no—
311D4—4416no—
312D4—444no—
313C2×C4—28no—
314C2×C4—24no—
315C2×C4—48no—
316C2×C4—444no—
317C2×C4—448no—
318C2×C4—888no—
319C2×C4C4×D4414yes—
320C2×C4C4×D4412yes—
321C2×C4#6692712yes—
322C2×C4#6692814yes—
323C2×C4C2×(C2×D11)⋊C414yes—
324C2×C4#6698312yes—
325C2×C4#6698314yes—
326C2×C4C22×C4×D1111yescharacteristic
327C2×C4C22×D4411yescharacteristic
328C2×C4C22×D4411yescharacteristic
329C2×C4C2×#433911yescharacteristic
330C2×C4C2×#433911yescharacteristic
331C2×C4C22×C22⋊D1111yescharacteristic
332C8—24no—
333C8C2×(C2×D11)⋊C418yescomplemented
334C22—4416no—
335C22—448no—
336C22—884no—
337C22—884no—
338C22—8832no—
339C22—888no—
340C22#1062232418yes—
341C22#1062232518yes—
342C22#1062255214yes—
343C22#1062274818yes—
344C22C2×C4×D4411yescharacteristic
345C22C2×#6692711yescharacteristic
346C22C2×#6696114yes—
347C22C2×#6698311yescharacteristic
348C4—44no—
349C4—884no—
350C4#1062255214yes—
351C4C2×C4×D4411yescharacteristic
352C4C2×#6692811yescharacteristic
353C4C22×(C2×D11)⋊C411yescharacteristic
354C4C2×#6698311yescharacteristic
355C2—888no—
356C2#1306949218yesdirect product factor
357C2C2×#1062255211yescharacteristic
358C2C2×#1062232412yes—
359C2C2×#1062274812yes—
360C2C2×#1062232512yes—
subgroupG/H
centerC24C2×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#97C2
socleC24×C11C2×D4
prime radicalC23×D88C2
cosocleC22×C4×C11C24
hypercenterC22×#97D11
hypocenterC11C2×#1972
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#97

Complements

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

NH ≅ G/Ntype
2. C22×#66881C2semidirect
3. C22×#66885C2semidirect
4. C2×#10622552C2semidirect
5. #13069492C2direct (N × H)
6. C22×C11×#97C2semidirect
15. C22×D88C4semidirect
18. C2×C11×#97C22semidirect
20. C2×#66885C22semidirect
22. C2×#66881C22semidirect
24. #10622552C22semidirect
58. C2×D88C2×C4semidirect
100. C2×C8×C11C22⋊C4semidirect
116. C22×#97D11semidirect
159. C8×C11C2×C22⋊C4semidirect
175. C2×#97C2×D11semidirect
236. C2×C11#1972semidirect
280. C2×C8(C2×D11)⋊C4semidirect
292. C11C2×#1972semidirect
333. C8C2×(C2×D11)⋊C4semidirect
356. C2#13069492direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D882
C22×#668812
C22×#668852
C2×#106225522
#130694922
C22×C11×#972
C2×#197211