Finite Group Databasebeta

← C2×#13078547 #15621560

Subgroups — C2×#13078547 #15621560

Order 2816.

2346 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2#13078547C2116yesmaximal, direct product factor
3C2×#10622609C214yesmaximal, complemented
4C2×#10622616C214yesmaximal, complemented
5C2×#10622577C212yesmaximal, complemented
6C2×#10622579C212yesmaximal, complemented
7C2×#10622820C211yesmaximal, characteristic, complemented
8C22×C11×#117C211yesmaximal, characteristic, complemented
9C24×C4×C11C2211yescharacteristic
10C22×#4339C2211yescharacteristic
11C2×C11×#117—22no—
12C2×C11×#117—24no—
13C2×C11×#117C2214yes—
14C2×C11×#117C2218yescomplemented
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C22⋊C4—21no—
17C22×C42×C11—21no—
18C2×#67006—21no—
19#10623322—24no—
20#10623322C2218yes—
21C2×#66983C2212yes—
22C2×#66982—21no—
23C2×C4×C22⋊D11—22no—
24C2×#66979C2211yescharacteristic
25C2×#66977C2212yes—
26C22×#4318C2212yes—
27#10622820C2218yescomplemented
28C2×C22⋊(C11⋊C8)C2214yes—
29#10622616C22132yescomplemented
30#10622609C22132yescomplemented
31C2×#66874C2214yescomplemented
32#10622579C22116yescomplemented
33C2×#66873C2214yescomplemented
34#10622577C22116yescomplemented
35C2×#66872C2214yescomplemented
36C2×#66871C2214yescomplemented
37C25×C11D411yescharacteristic
38C23×C4×C11—28no—
39C23×C4×C11—22no—
40C23×C4×C11D412yes—
41C23×C4×C11D411yescharacteristic
42C23×C4×C11D414yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2314yes—
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11—22no—
47C22×C22⋊D11—21no—
48C2×#4339—22no—
49C2×#4339—28no—
50C2×#4339C2314yes—
51C22×D44C2311yescharacteristic
52C22×C4×D11—21no—
53C22×Dic22C2311yescharacteristic
54C11×#117—28no—
55C11×#117—216no—
56C11×#117C23116yes—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—24no—
59C2×C11×C4⋊C4C2314yes—
60C2×C11×C4⋊C4C2318yes—
61C2×C11×C22⋊C4—24no—
62C2×C11×C22⋊C4—28no—
63C2×C42×C11—24no—
64C2×C42×C11—28no—
65#67006—28no—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—21no—
68#66983—24no—
69#66983C2318yes—
70#66982—28no—
71C4×C22⋊D11—216no—
72C2×(C2×D11)⋊C4—22no—
73#66979—22no—
74#66979C2314yes—
75C2×C4⋊Dic11C2312yes—
76#66977—24no—
77#66977C2318yes—
78C2×Dic11⋊C4—22no—
79C2×C4×Dic11—21no—
80C2×#4318—28no—
81C2×#4318C2318yes—
82C22×C11⋊C8C2314yes—
83C22⋊(C11⋊C8)C23116yes—
84#66874C23116yescomplemented
85#66873C23116yescomplemented
86#66872C23116yescomplemented
87#66871C23116yescomplemented
88C2×#3093—111nomaximal, Sylow
89C24×C11—24no—
90C24×C11—44no—
91C24×C11C2×D412yes—
92C24×C11C2×D411yescharacteristic
93C24×C11C2×D414yes—
94C23×D11—21no—
95C22×C4×C11—24no—
96C22×C4×C11—28no—
97C22×C4×C11—216no—
98C22×C4×C11—28no—
99C22×C4×C11—216no—
100C22×C4×C11—28no—
101C22×C4×C11—24no—
102C22×C4×C11—48no—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D414yes—
105C22×C4×C11C2×D418yes—
106C22×C4×C11C2×D414yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11#4118yes—
110C22×C4×C11C2414yes—
111C22×C4×C11C2411yescharacteristic
112C22×C4×C11C2412yes—
113C2×C22⋊D11—28no—
114C2×C22⋊D11—24no—
115C2×C22⋊D11—48no—
116C2×C22⋊D11—44no—
117C22×Dic11—22no—
118C22×Dic11—21no—
119#4339—216no—
120#4339—48no—
121C2×D44—21no—
122C2×D44—24no—
123C2×D44C2412yes—
124C2×C4×D11—24no—
125C2×C4×D11—44no—
126C2×Dic22—21no—
127C2×Dic22—24no—
128C2×Dic22C2412yes—
129C11×C4⋊C4—28no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4C2418yes—
132C11×C22⋊C4—216no—
133C42×C11—216no—
134C22⋊Dic11—28no—
135C22⋊Dic11—24no—
136(C2×D11)⋊C4—28no—
137C4⋊Dic11—22no—
138C4⋊Dic11C2414yes—
139Dic11⋊C4—28no—
140C4×Dic11—24no—
141#4318—216no—
142C2×C11⋊C8—28no—
143C2×C11⋊C8C2418yes—
144C2×#525—111no—
145C22×#117D1111yescharacteristic, complemented
146#3093—1116no—
147C2×#485—114no—
148C2×#482—114no—
149C2×#428—112no—
150C2×#417—112no—
151C2×#407—111no—
152C23×C11—24no—
153C23×C11—28no—
154C23×C11—24no—
155C23×C11—24no—
156C23×C11—24no—
157C23×C11—48no—
158C23×C11—416no—
159C23×C11#12314yes—
160C23×C11C22×D414yes—
161C23×C11C22×D412yes—
162C23×C11C22×D411yescharacteristic
163C22×D11—22no—
164C22×D11—42no—
165C22×D11—44no—
166C2×C4×C11—28no—
167C2×C4×C11—24no—
168C2×C4×C11—28no—
169C2×C4×C11—216no—
170C2×C4×C11—28no—
171C2×C4×C11—28no—
172C2×C4×C11—416no—
173C2×C4×C11—48no—
174C2×C4×C11#12314yes—
175C2×C4×C11#12318yes—
176C2×C4×C11C22×D414yes—
177C2×C4×C11C22×D412yes—
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11C2×#4114yes—
180C2×C4×C11C2×#4118yes—
181C2×C4×C11C2511yescharacteristic
182C22⋊D11—416no—
183C22⋊D11—48no—
184C2×Dic11—24no—
185C2×Dic11—22no—
186C2×Dic11—42no—
187C2×Dic11—44no—
188D44—24no—
189D44—42no—
190C4×D11—48no—
191Dic22—24no—
192Dic22—42no—
193C11⋊C8—28no—
194C22×#41—111no—
195C24×C4C2×D1111yescharacteristic
196C22×M16—112no—
197#525—118no—
198#525—224no—
199C2×#123—221no—
200C2×C22⋊Q8—112no—
201C2×#121—112no—
202C2×#120—221no—
203C2×C4×D4—222no—
204C2×#117—22no—
205C2×#117—24no—
206C2×#117—111no—
207C2×#117C2×D1114yes—
208C2×#117C2×D1118yescomplemented
209C22×C4⋊C4C2×D1112yes—
210C22×C22⋊C4—21no—
211C22×C42—21no—
212#485—1132no—
213#482—1132no—
214#428—1116no—
215C2×#107—114no—
216C2×#106—114no—
217#417—1116no—
218C2×#103—114no—
219C2×#102—114no—
220#407—118no—
221C2×C22⋊C8—114no—
222C22×C11—28no—
223C22×C11—24no—
224C22×C11—24no—
225C22×C11—24no—
226C22×C11—24no—
227C22×C11—416no—
228C22×C11—48no—
229C22×C11C2×#12314yes—
230C22×C11C2×#12312yes—
231C22×C11#57514yes—
232C22×C11C23×D411yescharacteristic
233C2×D11—42no—
234C2×D11—44no—
235C2×D11—84no—
236C4×C11—24no—
237C4×C11—48no—
238C4×C11C2×#12312yes—
239C4×C11C2×#12314yes—
240C4×C11C22×#4112yes—
241Dic11—42no—
242Dic11—44no—
243C25C22⋊D1111yescharacteristic
244C2×#41—114no—
245C2×#41—222no—
246C2×#41—228no—
247C22×Q8—111no—
248C22×D4—111no—
249C22×D4—222no—
250C22×D4—221no—
251C23×C4—28no—
252C23×C4—22no—
253C23×C4—221no—
254C23×C4C22⋊D1112yes—
255C23×C4C22⋊D1114yes—
256C23×C4C22⋊D1111yescharacteristic
257C23×C4C22×D1112yes—
258C23×C4C22×D1114yes—
259C23×C4C22×D1111yescharacteristic
260C2×M16—118no—
261C2×M16—228no—
262C22×C8—114no—
263#123—228no—
264C22⋊Q8—118no—
265C22⋊Q8—224no—
266#121—118no—
267#121—224no—
268#120—228no—
269C4×D4—2216no—
270#117—28no—
271#117—216no—
272#117—114no—
273#117—222no—
274#117C22×D11116yes—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—112no—
278C2×C4⋊C4—222no—
279C2×C4⋊C4C22×D1114yes—
280C2×C4⋊C4C22×D1118yes—
281C2×C22⋊C4—24no—
282C2×C22⋊C4—28no—
283C2×C22⋊C4—221no—
284C2×C22⋊C4—222no—
285C2×C22⋊C4—222no—
286C2×C42—24no—
287C2×C42—28no—
288C2×C42—221no—
289#107—1116no—
290#106—1116no—
291#103—1116no—
292#102—1116no—
293C22⋊C8—1116no—
294C2×C11—24no—
295C2×C11—44no—
296C2×C11#309314yescomplemented
297C2×C11C22×#12311yescharacteristic
298C2×C11C2×#57512yes—
299D11—82no—
300C24—24no—
301C24—44no—
302C24—221no—
303C24C2×C22⋊D1112yes—
304C24C2×C22⋊D1111yescharacteristic
305C24C2×C22⋊D1114yes—
306#41—2216no—
307#41—448no—
308C2×Q8—112no—
309C2×Q8—221no—
310C2×Q8—224no—
311C2×D4—112no—
312C2×D4—228no—
313C2×D4—224no—
314C2×D4—224no—
315C2×D4—221no—
316C2×D4—448no—
317C2×D4—444no—
318C22×C4—24no—
319C22×C4—28no—
320C22×C4—216no—
321C22×C4—28no—
322C22×C4—216no—
323C22×C4—28no—
324C22×C4—24no—
325C22×C4—48no—
326C22×C4—222no—
327C22×C4—221no—
328C22×C4—224no—
329C22×C4—444no—
330C22×C4#433918yes—
331C22×C4C2×C22⋊D1114yes—
332C22×C4C2×C22⋊D1118yes—
333C22×C4C2×C22⋊D1114yes—
334C22×C4C2×C22⋊D1112yes—
335C22×C4C2×C22⋊D1112yes—
336C22×C4C2×C22⋊D1111yescharacteristic
337C22×C4C23×D1114yes—
338C22×C4C23×D1112yes—
339C22×C4C23×D1111yescharacteristic
340M16—2216no—
341C2×C8—118no—
342C2×C8—228no—
343C4⋊C4—28no—
344C4⋊C4—24no—
345C4⋊C4—114no—
346C4⋊C4—222no—
347C4⋊C4—228no—
348C4⋊C4C23×D1118yes—
349C22⋊C4—216no—
350C22⋊C4—224no—
351C22⋊C4—228no—
352C22⋊C4—228no—
353C42—216no—
354C42—224no—
355C11C2×#309311yescharacteristic, complemented, Sylow
356C23—24no—
357C23—28no—
358C23—24no—
359C23—24no—
360C23—24no—
361C23—48no—
362C23—416no—
363C23—222no—
364C23—442no—
365C23—444no—
366C23#6698214yes—
367C23C22×C22⋊D1114yes—
368C23C22×C22⋊D1112yes—
369C23C22×C22⋊D1111yescharacteristic
370Q8—224no—
371Q8—442no—
372D4—224no—
373D4—4416no—
374D4—448no—
375D4—442no—
376C2×C4—28no—
377C2×C4—24no—
378C2×C4—216no—
379C2×C4—28no—
380C2×C4—28no—
381C2×C4—28no—
382C2×C4—416no—
383C2×C4—48no—
384C2×C4—224no—
385C2×C4—222no—
386C2×C4—442no—
387C2×C4—444no—
388C2×C4—448no—
389C2×C4#6698214yes—
390C2×C4#6698218yes—
391C2×C4C2×#433914yes—
392C2×C4C2×#433918yes—
393C2×C4C22×C22⋊D1114yes—
394C2×C4C22×C22⋊D1112yes—
395C2×C4C22×C22⋊D1111yescharacteristic
396C2×C4C24×D1111yescharacteristic
397C8—228no—
398C22—28no—
399C22—24no—
400C22—24no—
401C22—24no—
402C22—24no—
403C22—416no—
404C22—48no—
405C22—444no—
406C22—442no—
407C22—884no—
408C22C2×#6698214yes—
409C22C2×#6698212yes—
410C22#1062335314yes—
411C22C23×C22⋊D1111yescharacteristic
412C4—24no—
413C4—48no—
414C4—444no—
415C4—442no—
416C4C2×#6698214yes—
417C4C2×#6698212yes—
418C4C22×#433912yes—
419C2—24no—
420C2—44no—
421C2—882no—
422C2#1307854714yesdirect product factor
423C2C22×#6698211yescharacteristic
424C2C2×#1062335312yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#117C2
socleC23×C11C22×D4
prime radicalC2×#10623322C2
hypercenterC22×#117D11
hypocenterC11C2×#3093
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. #13078547C2direct (N × H)
3. C2×#10622609C2semidirect
4. C2×#10622616C2semidirect
5. C2×#10622577C2semidirect
6. C2×#10622579C2semidirect
7. C2×#10622820C2semidirect
8. C22×C11×#117C2semidirect
14. C2×C11×#117C22semidirect
27. #10622820C22semidirect
29. #10622616C22semidirect
30. #10622609C22semidirect
31. C2×#66874C22semidirect
32. #10622579C22semidirect
33. C2×#66873C22semidirect
34. #10622577C22semidirect
35. C2×#66872C22semidirect
36. C2×#66871C22semidirect
84. #66874C23semidirect
85. #66873C23semidirect
86. #66872C23semidirect
87. #66871C23semidirect
145. C22×#117D11semidirect
208. C2×#117C2×D11semidirect
296. C2×C11#3093semidirect
355. C11C2×#3093semidirect
422. C2#13078547direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233222
#130785472
C2×#106226092
C2×#106226162
C2×#106225772
C2×#106225792
C2×#106228202
C22×C11×#1172
C2×#309311