Finite Group Databasebeta

← C2×#13081256 #15633335

Subgroups — C2×#13081256 #15633335

Order 2816.

2058 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623098C211yesmaximal, characteristic, complemented
2C2×D4×Dic22C211yesmaximal, characteristic
3#13081256C2116yesmaximal, direct product factor
4C2×#10622294C211yesmaximal, characteristic, complemented
5C2×#10622405C212yesmaximal, complemented
6C2×#10622633C211yesmaximal, characteristic, complemented
7C2×#10622467C212yesmaximal, complemented
8C2×#10622632C211yesmaximal, characteristic
9C2×#10622775C212yesmaximal
10C2×C8×Dic22C211yesmaximal, characteristic, complemented
11C2×#10622371C212yesmaximal
12C2×C4×C11×SD16C211yesmaximal, characteristic
13C23×Dic22—21no—
14C22×C11×SD16C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66997C2212yes—
18C2×D4×Dic11C2212yes—
19C22×#4324C2212yes—
20C2×#66977—21no—
21#10623098—24no—
22#10623098C2218yescomplemented
23D4×Dic22—24no—
24D4×Dic22C2218yes—
25C2×#66942—22no—
26C2×#66941C2212yes—
27C2×#66940C2212yes—
28C2×#66931—22no—
29C2×#66923—21no—
30C2×#66922C2211yescharacteristic
31C2×#66922C2211yescharacteristic
32C2×C4×Dic22—21no—
33C2×C4×Dic22C2211yescharacteristic
34C4×C11×SD16C2218yes—
35C2×C11×#106C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66899C2212yes—
40#10622775C22116yes—
41C2×#66880C2212yes—
42C2×#66880C2212yes—
43C2×Dic11⋊C8C2212yes—
44C2×C8×Dic11C2212yes—
45#10622633C2218yescomplemented
46#10622632C2218yes—
47C2×#66874C2212yes—
48C2×#66872C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622467C22116yescomplemented
51#10622405C22116yescomplemented
52#10622371C22116yes—
53#10622294C2218yescomplemented
54C8×Dic22C2218yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×Dic11—22no—
59C22×Dic22—21no—
60C22×Dic22—22no—
61C22×Dic22—28no—
62C22×Dic22—48no—
63C22×Dic22D411yescharacteristic
64C22×Dic22C2312yes—
65C2×C11×SD16—24no—
66C2×C11×SD16C2314yes—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11C2314yes—
71C4×D4×C11—22no—
72C4×D4×C11C2314yes—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—22no—
80#66997—24no—
81#66997C2318yes—
82D4×Dic11—24no—
83D4×Dic11C2318yes—
84C2×#4324—28no—
85C2×#4324C2318yes—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11D411yescharacteristic
90C2×C4⋊Dic11C2312yes—
91#66977—28no—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4D412yes—
97C2×C4×Dic11—22no—
98C2×C4×Dic11C2312yes—
99C22×C11⋊C8C2312yes—
100#66942—216no—
101#66941—24no—
102#66941C2318yes—
103#66940—24no—
104#66940C2318yes—
105#66931—216no—
106#66923—28no—
107#66922—22no—
108#66922—22no—
109#66922C2314yes—
110#66922C2314yes—
111C4×Dic22—28no—
112C4×Dic22D414yes—
113C4×Dic22C2314yes—
114C11×#106C2314yes—
115C11×#103C2314yes—
116C11×#102C2314yes—
117C4×C8×C11C2314yes—
118#66899C2318yes—
119#66880C2318yes—
120#66880C2318yes—
121Dic11⋊C8C2318yes—
122C8×Dic11C2318yes—
123#66874C2318yes—
124#66872C2318yes—
125C4⋊(C11⋊C8)C2314yes—
126C2×#3359—111nomaximal, Sylow
127C24×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11C2412yes—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11#4114yes—
135C2×D4×C11C2412yes—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—24no—
140C22×C4×C11—44no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—28no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—48no—
148C22×Dic11C2×D412yes—
149C22×Dic11C2×D412yes—
150C2×Dic22—28no—
151C2×Dic22—22no—
152C2×Dic22—24no—
153C2×Dic22—24no—
154C2×Dic22—24no—
155C2×Dic22—48no—
156C2×Dic22—432no—
157C2×Dic22—44no—
158C2×Dic22SD1618yescomplemented
159C2×Dic22C2×D414yes—
160C2×Dic22C2414yes—
161C11×SD16—28no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11C2412yes—
165C2×C8×C11C2412yes—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4C2412yes—
170C11×C4⋊C4C2412yes—
171C11×C22⋊C4—24no—
172C42×C11—24no—
173C42×C11C2×D412yes—
174C42×C11C2412yes—
175C22⋊Dic11—28no—
176#4324—216no—
177C4⋊Dic11—24no—
178C4⋊Dic11—22no—
179C4⋊Dic11—24no—
180C4⋊Dic11—24no—
181C4⋊Dic11C2×D414yes—
182C4⋊Dic11C2414yes—
183Dic11⋊C4—28no—
184Dic11⋊C4—28no—
185Dic11⋊C4—28no—
186Dic11⋊C4—28no—
187Dic11⋊C4C2×D418yes—
188C4×Dic11—28no—
189C4×Dic11C2×D414yes—
190C4×Dic11C2414yes—
191C2×C11⋊C8—24no—
192C2×C11⋊C8C2414yes—
193C2×#557—111no—
194C2×D4×Q8—111no—
195#3359—1116no—
196C2×#487—112no—
197C2×#487—111no—
198C2×#475—112no—
199C2×#475—111no—
200C2×#461—112no—
201C2×#461—111no—
202C2×C8×Q8—111no—
203C2×C4×SD16—112no—
204C2×C4×SD16D1111yescharacteristic
205C23×C11—24no—
206C23×C11—22no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11C22×D411yescharacteristic
210Q8×C11—22no—
211Q8×C11—22no—
212Q8×C11—42no—
213D4×C11—24no—
214D4×C11—22no—
215D4×C11C2×#4114yes—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—48no—
224C2×C4×C11C2×SD1614yes—
225C2×C4×C11C22×D412yes—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D412yes—
228C2×C4×C11C2×#4112yes—
229C2×C4×C112−1+412yes—
230C2×C4×C11C2511yescharacteristic
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—44no—
235C2×Dic11—44no—
236C2×Dic11—416no—
237C2×Dic11C2×SD1618yes—
238C2×Dic11C22×D414yes—
239C2×Dic11C22×D414yes—
240Dic22—24no—
241Dic22—24no—
242Dic22—44no—
243Dic22—48no—
244Dic22—416no—
245Dic22C2×SD16116yescomplemented
246C8×C11—22no—
247C8×C11—22no—
248C11⋊C8—24no—
249C23×Q8—221no—
250C22×SD16—112no—
251C22×SD16C2×D1111yescharacteristic
252#557—118no—
253#557—224no—
254D4×Q8—118no—
255D4×Q8—224no—
256C2×C4⋊Q8—112no—
257C2×C4⋊Q8—112no—
258C2×C4⋊Q8—111no—
259C2×C4⋊Q8—111no—
260C2×#125—221no—
261C2×#125—222no—
262C2×C22⋊Q8—222no—
263C2×C22⋊Q8—221no—
264C2×C4×Q8—111no—
265C2×C4×Q8—112no—
266C2×C4×Q8—221no—
267C2×C4×Q8C2×D1111yescharacteristic
268C2×C4×D4—112no—
269C2×C4×D4C2×D1111yescharacteristic
270#487—1116no—
271#487—118no—
272#475—118no—
273#475—1116no—
274#461—1116no—
275#461—118no—
276C8×Q8—118no—
277C4×SD16—1116no—
278C4×SD16C2×D1118yes—
279C2×#106—112no—
280C2×#106C2×D1111yescharacteristic
281C2×C4⋊C8—112no—
282C2×C4⋊C8—111no—
283C2×#103—112no—
284C2×#103—112no—
285C2×#103—112no—
286C2×#103—112no—
287C2×#103C2×D1111yescharacteristic
288C2×#102C2×D1111yescharacteristic
289C2×C4×C8—112no—
290C2×C4×C8C2×D1111yescharacteristic
291C22×C11—24no—
292C22×C11—48no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11#54812yes—
296C22×C11C22×SD1612yes—
297C22×C11#57812yes—
298C22×C11C23×D411yescharacteristic
299C4×C11—22no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11#54812yes—
304C4×C11C22×SD1614yes—
305C4×C11C22×#4111yescharacteristic
306C4×C11C2×2−1+411yescharacteristic
307Dic11—24no—
308Dic11—44no—
309Dic11—44no—
310Dic11C22×SD1618yes—
311C22×Q8—111no—
312C22×Q8—112no—
313C22×Q8—222no—
314C22×Q8—228no—
315C22×Q8—221no—
316C22×Q8—448no—
317C22×Q8C22×D1111yescharacteristic
318C22×D4C22×D1111yescharacteristic
319C23×C4—21no—
320C23×C4—222no—
321C2×SD16—24no—
322C2×SD16—118no—
323C2×SD16—228no—
324C2×SD16C22×D1114yes—
325C22×C8—112no—
326C22×C8C22×D1111yescharacteristic
327C22×C8C22×D1111yescharacteristic
328C4⋊Q8—118no—
329C4⋊Q8—118no—
330C4⋊Q8—114no—
331C4⋊Q8—114no—
332C4⋊Q8—224no—
333C4⋊Q8—224no—
334C4⋊Q8—222no—
335C4⋊Q8—222no—
336#125—228no—
337#125—2216no—
338C22⋊Q8—2216no—
339C22⋊Q8—228no—
340C4×Q8—22no—
341C4×Q8—114no—
342C4×Q8—114no—
343C4×Q8—118no—
344C4×Q8—228no—
345C4×Q8—224no—
346C4×Q8C22×D1114yes—
347C4×D4—22no—
348C4×D4—118no—
349C4×D4—224no—
350C4×D4C22×D1114yes—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—112no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—112no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4C22×D1111yescharacteristic
363C2×C4⋊C4C22×D1111yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—222no—
366C2×C42—21no—
367C2×C42—112no—
368C2×C42—222no—
369C2×C42C22×D1111yescharacteristic
370#106—118no—
371#106C22×D1114yes—
372C4⋊C8—118no—
373C4⋊C8—114no—
374#103—118no—
375#103—118no—
376#103—118no—
377#103—118no—
378#103C22×D1114yes—
379#102C22×D1114yes—
380C4×C8—118no—
381C4×C8C22×D1114yes—
382C2×C11—44no—
383C2×C11#335914yescomplemented
384C2×C11C2×#54811yescharacteristic
385C2×C11C23×SD1611yescharacteristic
386C2×C11C2×#57811yescharacteristic
387C24—21no—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—118no—
392C2×Q8—114no—
393C2×Q8—114no—
394C2×Q8—228no—
395C2×Q8—222no—
396C2×Q8—224no—
397C2×Q8—224no—
398C2×Q8—224no—
399C2×Q8—448no—
400C2×Q8—4432no—
401C2×Q8—444no—
402C2×Q8C23×D1112yes—
403C2×D4—21no—
404C2×D4—22no—
405C2×D4#433914yes—
406C2×D4C23×D1112yes—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—24no—
411C22×C4—44no—
412C22×C4—112no—
413C22×C4—112no—
414C22×C4—228no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—448no—
418C22×C4D4×D1111yescharacteristic
419C22×C4D4×D1111yescharacteristic
420C22×C4C23×D1111yescharacteristic
421SD16—28no—
422SD16—2216no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—114no—
426C2×C8—224no—
427C2×C8C23×D1112yes—
428C2×C8C23×D1112yes—
429C4⋊C4—24no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—118no—
433C4⋊C4—114no—
434C4⋊C4—114no—
435C4⋊C4—228no—
436C4⋊C4—228no—
437C4⋊C4—228no—
438C4⋊C4—228no—
439C4⋊C4—222no—
440C4⋊C4—224no—
441C4⋊C4—224no—
442C4⋊C4—224no—
443C4⋊C4C23×D1112yes—
444C4⋊C4C23×D1112yes—
445C22⋊C4—24no—
446C22⋊C4—228no—
447C42—24no—
448C42—114no—
449C42—114no—
450C42—228no—
451C42D4×D1112yes—
452C42C23×D1112yes—
453C11C2×#335911yescharacteristic, complemented, Sylow
454C23—24no—
455C23—22no—
456C23—42no—
457C23—42no—
458C23C2×D4×D1111yescharacteristic
459Q8—22no—
460Q8—22no—
461Q8—42no—
462Q8—1116no—
463Q8—224no—
464Q8—224no—
465Q8—4416no—
466Q8—448no—
467Q8—444no—
468D4—24no—
469D4—22no—
470D4C2×#433914yes—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—48no—
479C2×C4—118no—
480C2×C4—114no—
481C2×C4—114no—
482C2×C4—224no—
483C2×C4—224no—
484C2×C4—224no—
485C2×C4—4416no—
486C2×C4—444no—
487C2×C4—444no—
488C2×C4SD16×D1114yes—
489C2×C4C2×#433912yes—
490C2×C4C2×D4×D1112yes—
491C2×C4C2×D4×D1112yes—
492C2×C4C2×D4×D1111yescharacteristic
493C2×C4#6704312yes—
494C2×C4C24×D1111yescharacteristic
495C8—22no—
496C8—22no—
497C8—224no—
498C22—24no—
499C22—48no—
500C22—42no—
501C22—42no—
502C22#1062308312yes—
503C22C2×SD16×D1112yes—
504C22#1062330212yes—
505C22C22×D4×D1111yescharacteristic
506C4—22no—
507C4—42no—
508C4—42no—
509C4—42no—
510C4—118no—
511C4—224no—
512C4—444no—
513C4—444no—
514C4#1062308312yes—
515C4C2×SD16×D1114yes—
516C4C22×#433911yescharacteristic
517C4C2×#6704311yescharacteristic
518C2—44no—
519C2#1308125614yesdirect product factor
520C2C2×#1062308311yescharacteristic
521C2C22×SD16×D1111yescharacteristic
522C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3359
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10623098C2semidirect
3. #13081256C2direct (N × H)
4. C2×#10622294C2semidirect
5. C2×#10622405C2semidirect
6. C2×#10622633C2semidirect
7. C2×#10622467C2semidirect
10. C2×C8×Dic22C2semidirect
22. #10623098C22semidirect
45. #10622633C22semidirect
50. #10622467C22semidirect
51. #10622405C22semidirect
53. #10622294C22semidirect
54. C8×Dic22C22semidirect
158. C2×Dic22SD16semidirect
245. Dic22C2×SD16semidirect
383. C2×C11#3359semidirect
453. C11C2×#3359semidirect
519. C2#13081256direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230982
C2×D4×Dic222
#130812562
C2×#106222942
C2×#106224052
C2×#106226332
C2×#106224672
C2×#106226322
C2×#106227752
C2×C8×Dic222
C2×#106223712
C2×C4×C11×SD162
C2×#335911