Finite Group Databasebeta

← C2×#13079775 #15625841

Subgroups — C2×#13079775 #15625841

Order 2816.

1778 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic
2#13079775C2116yesmaximal, direct product factor
3C2×#10622691C211yesmaximal, characteristic, complemented
4C2×#10622692C211yesmaximal, characteristic, complemented
5C2×#10622706C211yesmaximal, characteristic, complemented
6C2×#10622706C211yesmaximal, characteristic, complemented
7C2×#10622609C214yesmaximal
8C2×#10622676C214yesmaximal, complemented
9C2×#10622538C211yesmaximal, characteristic
10C2×C11×#533C211yesmaximal, characteristic
11C11×#533—24no—
12C11×#533C2218yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125C2212yes—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11—21no—
20C2×C11×#117C2212yes—
21C22×C42×C11C2211yescharacteristic
22C2×#66979—21no—
23C2×#66977—21no—
24C2×#66977C2212yes—
25#10623001—24no—
26#10623001C2218yes—
27C2×#66923—21no—
28C2×#66922C2211yescharacteristic
29C2×#66922C2211yescharacteristic
30C2×C4×Dic22—21no—
31C2×C4×Dic22C2212yes—
32C2×C22⋊(C11⋊C8)C2212yes—
33#10622706C2218yescomplemented
34#10622706C2218yescomplemented
35#10622692C2218yescomplemented
36#10622691C2218yescomplemented
37#10622676C22132yescomplemented
38#10622609C22132yes—
39C2×#66874C2214yes—
40C2×#66874C2214yes—
41C2×#66872C2214yes—
42C2×#66871C2214yes—
43#10622538C2218yes—
44C2×C4⋊(C11⋊C8)C2212yes—
45C2×C4×C11⋊C8C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47C22×Q8×C11—21no—
48C22×Q8×C11—21no—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×Dic22—21no—
53C22×Dic22C2312yes—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8C2314yes—
57C11×C4⋊Q8C2314yes—
58C11×#125—24no—
59C11×#125C2318yes—
60C11×C22⋊Q8—28no—
61C11×C22⋊Q8—28no—
62C4×Q8×C11—28no—
63C4×Q8×C11—28no—
64C11×#117—24no—
65C11×#117C2318yes—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C22⋊C4—22no—
73C2×C42×C11—22no—
74C2×C42×C11D411yescharacteristic
75C2×C42×C11D411yescharacteristic
76C2×C42×C11D414yes—
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2314yes—
80C2×C22⋊Dic11—22no—
81#66979—28no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2312yes—
86#66977—24no—
87#66977—28no—
88#66977C2318yes—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×C4×Dic11—22no—
92C22×C11⋊C8C2312yes—
93C22×C11⋊C8C2312yes—
94#66923—28no—
95#66922—22no—
96#66922—22no—
97#66922C2314yes—
98#66922C2314yes—
99C4×Dic22—28no—
100C4×Dic22—24no—
101C4×Dic22C2318yes—
102C22⋊(C11⋊C8)C2318yes—
103#66874C23116yes—
104#66874C23116yes—
105#66872C23116yes—
106#66871C23116yes—
107C4⋊(C11⋊C8)C2318yes—
108C4×C11⋊C8C2314yes—
109C4×C11⋊C8C2314yes—
110C2×#3231—111nomaximal, Sylow
111C24×C11C2×D411yescharacteristic
112C2×Q8×C11—24no—
113C2×Q8×C11—24no—
114C2×Q8×C11—44no—
115C2×Q8×C11—44no—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D414yes—
126C22×C4×C11C2×D414yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2412yes—
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—22no—
132C22×Dic11—22no—
133C2×Dic22—22no—
134C2×Dic22—24no—
135C2×Dic22—28no—
136C2×Dic22—44no—
137C2×Dic22C2414yes—
138C11×C4⋊C4—28no—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4C2414yes—
145C11×C4⋊C4C2414yes—
146C11×C22⋊C4—28no—
147C42×C11—28no—
148C42×C11C2×D414yes—
149C42×C11C2×D412yes—
150C42×C11C2×D412yes—
151C42×C11C2×D414yes—
152C42×C11C2412yes—
153C42×C11C2412yes—
154C22⋊Dic11—28no—
155C4⋊Dic11—22no—
156C4⋊Dic11—24no—
157C4⋊Dic11—24no—
158C4⋊Dic11—24no—
159C4⋊Dic11C2414yes—
160Dic11⋊C4—28no—
161Dic11⋊C4—28no—
162C4×Dic11—28no—
163C2×C11⋊C8—24no—
164C2×C11⋊C8—24no—
165C2×C11⋊C8C2414yes—
166C2×C11⋊C8C2414yes—
167C2×#533—111no—
168C2×#533D1111yescharacteristic
169#3231—1116no—
170C2×#500—111no—
171C2×#498—111no—
172C2×#487—111no—
173C2×#487—111no—
174C2×#485—114no—
175C2×#479—114no—
176C2×#431—111no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11C22×D412yes—
181C23×C11C22×D411yescharacteristic
182Q8×C11—48no—
183Q8×C11—48no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—28no—
189C2×C4×C11—28no—
190C2×C4×C11—24no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—44no—
194C2×C4×C11—44no—
195C2×C4×C11#13514yes—
196C2×C4×C11#13714yes—
197C2×C4×C11C22×D412yes—
198C2×C4×C11C22×D412yes—
199C2×C4×C11C22×D412yes—
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D412yes—
202C2×C4×C11C22×D412yes—
203C2×C4×C112−1+414yes—
204C2×C4×C11C2511yescharacteristic
205C2×Dic11—24no—
206C2×Dic11—24no—
207C2×Dic11—44no—
208C2×Dic11—44no—
209Dic22—28no—
210Dic22—44no—
211Dic22—48no—
212C11⋊C8—24no—
213C11⋊C8—24no—
214#533—24no—
215#533—118no—
216#533—224no—
217#533C2×D1118yes—
218C2×C4⋊Q8—111no—
219C2×C4⋊Q8—111no—
220C2×C4⋊Q8C2×D1111yescharacteristic
221C2×C4⋊Q8C2×D1111yescharacteristic
222C2×#125—221no—
223C2×#125C2×D1112yes—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—112no—
227C2×C22⋊Q8—221no—
228C2×C4×Q8—21no—
229C2×C4×Q8—21no—
230C2×C4×Q8—112no—
231C2×C4×Q8—221no—
232C2×#117—221no—
233C2×#117C2×D1112yes—
234C22×C42C2×D1111yescharacteristic
235#500—118no—
236#498—118no—
237#487—118no—
238#487—118no—
239#485—1132no—
240#479—1132no—
241#431—118no—
242C2×#107—114no—
243C2×#106—114no—
244C2×C4⋊C8—112no—
245C2×#103—114no—
246C2×#103—114no—
247C2×C22⋊C8—112no—
248C2×C4×C8—111no—
249C2×C4×C8—111no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—44no—
254C22×C11#53612yes—
255C22×C11C2×#13512yes—
256C22×C11C2×#13712yes—
257C22×C11C23×D411yescharacteristic
258C4×C11—22no—
259C4×C11—22no—
260C4×C11—22no—
261C4×C11—44no—
262C4×C11—44no—
263C4×C11#53612yes—
264C4×C11C2×#13514yes—
265C4×C11C2×#13714yes—
266C4×C11C2×2−1+412yes—
267Dic11—44no—
268Dic11—44no—
269C22×Q8—21no—
270C22×Q8—21no—
271C22×Q8—112no—
272C22×Q8—221no—
273C23×C4C22⋊D1111yescharacteristic
274C23×C4C22⋊D1111yescharacteristic
275C23×C4C22×D1111yescharacteristic
276C22×C8—112no—
277C22×C8—112no—
278C4⋊Q8—22no—
279C4⋊Q8—22no—
280C4⋊Q8—114no—
281C4⋊Q8—114no—
282C4⋊Q8—222no—
283C4⋊Q8—222no—
284C4⋊Q8C22×D1114yes—
285C4⋊Q8C22×D1114yes—
286#125—24no—
287#125—228no—
288#125C22×D1118yes—
289C22⋊Q8—28no—
290C22⋊Q8—28no—
291C22⋊Q8—118no—
292C22⋊Q8—224no—
293C22⋊Q8—228no—
294C4×Q8—28no—
295C4×Q8—28no—
296C4×Q8—118no—
297C4×Q8—224no—
298C4×Q8—228no—
299#117—24no—
300#117—228no—
301#117C22×D1118yes—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—112no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4C22×D1112yes—
313C2×C4⋊C4C22×D1112yes—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—222no—
316C2×C42—22no—
317C2×C42—222no—
318C2×C42C22⋊D1111yescharacteristic
319C2×C42C22⋊D1111yescharacteristic
320C2×C42C22⋊D1114yes—
321C2×C42C22×D1111yescharacteristic
322C2×C42C22×D1111yescharacteristic
323C2×C42C22×D1114yes—
324#107—1116no—
325#106—1116no—
326C4⋊C8—118no—
327#103—1116no—
328#103—1116no—
329C22⋊C8—118no—
330C4×C8—114no—
331C4×C8—114no—
332C2×C11—42no—
333C2×C11#323114yescomplemented
334C2×C11C2×#53611yescharacteristic
335C2×C11C22×#13511yescharacteristic
336C2×C11C22×#13711yescharacteristic
337C24C2×C22⋊D1111yescharacteristic
338C2×Q8—24no—
339C2×Q8—24no—
340C2×Q8—44no—
341C2×Q8—44no—
342C2×Q8—114no—
343C2×Q8—224no—
344C2×Q8—222no—
345C2×Q8—228no—
346C2×Q8—444no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4C2×C22⋊D1114yes—
355C22×C4C2×C22⋊D1114yes—
356C22×C4C2×C22⋊D1112yes—
357C22×C4C2×C22⋊D1111yescharacteristic
358C22×C4C2×C22⋊D1111yescharacteristic
359C22×C4C2×C22⋊D1111yescharacteristic
360C22×C4C2×C22⋊D1111yescharacteristic
361C22×C4C2×C22⋊D1111yescharacteristic
362C22×C4C23×D1112yes—
363C22×C4C23×D1111yescharacteristic
364C2×C8—114no—
365C2×C8—114no—
366C2×C8—224no—
367C2×C8—224no—
368C4⋊C4—28no—
369C4⋊C4—28no—
370C4⋊C4—24no—
371C4⋊C4—24no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—114no—
375C4⋊C4—222no—
376C4⋊C4—224no—
377C4⋊C4—224no—
378C4⋊C4—228no—
379C4⋊C4—228no—
380C4⋊C4—224no—
381C4⋊C4C23×D1114yes—
382C4⋊C4C23×D1114yes—
383C22⋊C4—28no—
384C22⋊C4—228no—
385C42—28no—
386C42—228no—
387C42C2×C22⋊D1114yes—
388C42C2×C22⋊D1114yes—
389C42C2×C22⋊D1112yes—
390C42C2×C22⋊D1112yes—
391C42C23×D1112yes—
392C42C23×D1112yes—
393C11C2×#323111yescharacteristic, complemented, Sylow
394C23—22no—
395C23—22no—
396C23—22no—
397C23C22×C22⋊D1112yes—
398C23C22×C22⋊D1111yescharacteristic
399Q8—48no—
400Q8—48no—
401Q8—228no—
402Q8—444no—
403Q8—448no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—28no—
409C2×C4—28no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—224no—
416C2×C4—224no—
417C2×C4—444no—
418C2×C4—444no—
419C2×C4#6700314yes—
420C2×C4#6700414yes—
421C2×C4#6704014yes—
422C2×C4C22×C22⋊D1112yes—
423C2×C4C22×C22⋊D1112yes—
424C2×C4C22×C22⋊D1112yes—
425C2×C4C22×C22⋊D1111yescharacteristic
426C2×C4C22×C22⋊D1112yes—
427C2×C4C22×C22⋊D1112yes—
428C2×C4C24×D1111yescharacteristic
429C8—224no—
430C8—224no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—44no—
435C22#1062334712yes—
436C22C2×#6700312yes—
437C22C2×#6700412yes—
438C22C23×C22⋊D1111yescharacteristic
439C4—22no—
440C4—22no—
441C4—22no—
442C4—44no—
443C4—44no—
444C4—444no—
445C4—444no—
446C4#1062334712yes—
447C4C2×#6700314yes—
448C4C2×#6700414yes—
449C4C2×#6704012yes—
450C2—42no—
451C2#1307977514yesdirect product factor
452C2C2×#1062334711yescharacteristic
453C2C22×#6700311yescharacteristic
454C2C22×#6700411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#533C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#533D11
hypocenterC11C2×#3231
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #13079775C2direct (N × H)
3. C2×#10622691C2semidirect
4. C2×#10622692C2semidirect
5. C2×#10622706C2semidirect
6. C2×#10622706C2semidirect
8. C2×#10622676C2semidirect
33. #10622706C22semidirect
34. #10622706C22semidirect
35. #10622692C22semidirect
36. #10622691C22semidirect
37. #10622676C22semidirect
333. C2×C11#3231semidirect
393. C11C2×#3231semidirect
451. C2#13079775direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230012
#130797752
C2×#106226912
C2×#106226922
C2×#106227062
C2×#106226092
C2×#106226762
C2×#106225382
C2×C11×#5332
C2×#323111