Finite Group Databasebeta

← C2×#13079011 #15623064

Subgroups — C2×#13079011 #15623064

Order 2816.

2398 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic
2C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
3#13079011C2116yesmaximal, direct product factor
4C2×#10622408C214yesmaximal, complemented
5C2×#10622694C211yesmaximal, characteristic, complemented
6C2×#10622701C211yesmaximal, characteristic, complemented
7C2×#10622307C211yesmaximal, characteristic, complemented
8C2×#10622416C214yesmaximal, complemented
9C2×C4×#4313C211yesmaximal, characteristic, complemented
10C2×C11×#487C211yesmaximal, characteristic, complemented
11C22×#4343C2212yes—
12C22×Q8×D11—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×#67000C2212yes—
16C2×#66997—21no—
17C22×#4313C2212yes—
18#10623256—24no—
19#10623256C2218yes—
20D11×C4⋊Q8—24no—
21D11×C4⋊Q8C2218yescomplemented
22C2×#66948—21no—
23C2×#66948—21no—
24C2×#66946—21no—
25C2×#66946—21no—
26C2×C4⋊C4×D11—21no—
27C2×C4⋊C4×D11C2212yes—
28C2×#66941—21no—
29C2×#66941C2212yes—
30C2×#66927C2211yescharacteristic
31C2×C42×D11C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C11×#487C2218yescomplemented
34C2×C11×#103C2214yes—
35C2×C4×C8×C11C2211yescharacteristic
36C2×#66899C2214yes—
37C2×#66885C2214yes—
38C2×#66879C2212yes—
39#10622701C2218yescomplemented
40#10622694C2218yescomplemented
41C2×#66873C2214yes—
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622416C22132yescomplemented
44#10622408C22132yescomplemented
45#10622307C2218yescomplemented
46C4×#4313C2218yescomplemented
47C22×Q8×C11—21no—
48C22×Q8×C11C2312yes—
49C2×#4343—24no—
50C2×#4343—216no—
51C2×#4343C2318yes—
52C2×Q8×D11—28no—
53C2×Q8×D11—48no—
54C22×D44—22no—
55C22×D44—21no—
56C22×D44—21no—
57C22×D44C2312yes—
58C22×C4×D11—22no—
59C22×C4×D11—22no—
60C22×C4×D11D411yescharacteristic
61C22×C4×D11D411yescharacteristic
62C22×C4×D11C2311yescharacteristic
63C22×Dic22—21no—
64C22×Dic22—22no—
65C22×C8×C11C2312yes—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2314yes—
69C11×C4⋊Q8C2314yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2312yes—
74C2×C42×C11C2311yescharacteristic
75#67000—24no—
76#67000C2318yes—
77#66997—28no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—22no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2312yes—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4—22no—
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11D411yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88C2×#4313—28no—
89C2×#4313C2318yes—
90#66948—28no—
91#66948—28no—
92#66946—28no—
93#66946—28no—
94C4⋊C4×D11—24no—
95C4⋊C4×D11—28no—
96C4⋊C4×D11C2318yes—
97#66941—24no—
98#66941—28no—
99#66941C2318yes—
100#66927—22no—
101#66927C2314yes—
102C42×D11D414yes—
103C42×D11C2314yes—
104#66922—22no—
105#66922C2314yes—
106C11×#103C23116yes—
107C4×C8×C11C2314yes—
108#66899C23116yes—
109#66885C23116yes—
110#66879C2318yes—
111#66873C23116yes—
112C4×C11⋊C8C2314yes—
113C2×#3141—111nomaximal, Sylow
114C23×D11—22no—
115C23×D11C2×D411yescharacteristic
116C2×Q8×C11—24no—
117C2×Q8×C11—22no—
118C2×Q8×C11—28no—
119C2×Q8×C11—44no—
120C2×Q8×C11C2414yes—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C22×Dic11—22no—
127C22×Dic11C2×D411yescharacteristic
128C22×Dic11C2×D411yescharacteristic
129C22×Dic11C2×D411yescharacteristic
130#4343—232no—
131#4343—416no—
132Q8×D11—432no—
133C2×D44—28no—
134C2×D44—22no—
135C2×D44—24no—
136C2×D44—24no—
137C2×D44—28no—
138C2×D44—48no—
139C2×D44—44no—
140C2×D44—44no—
141C2×D44C2414yes—
142C2×C4×D11—28no—
143C2×C4×D11—28no—
144C2×C4×D11—24no—
145C2×C4×D11—24no—
146C2×C4×D11—48no—
147C2×C4×D11—48no—
148C2×C4×D11C2×D414yes—
149C2×C4×D11C2×D414yes—
150C2×C4×D11C2×D412yes—
151C2×C4×D11#4118yes—
152C2×C4×D11C2412yes—
153C2×Dic22—28no—
154C2×Dic22—24no—
155C2×Dic22—48no—
156C2×Dic22—44no—
157C2×C8×C11—24no—
158C2×C8×C11C2414yes—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4C2414yes—
164C42×C11C2×D412yes—
165C42×C11C2412yes—
166(C2×D11)⋊C4—28no—
167(C2×D11)⋊C4—28no—
168C4⋊Dic11—22no—
169C4⋊Dic11—24no—
170C4⋊Dic11C2414yes—
171Dic11⋊C4—28no—
172Dic11⋊C4—28no—
173C4×Dic11C2×D412yes—
174C4×Dic11C2×D414yes—
175C4×Dic11C2×D414yes—
176C4×Dic11C2412yes—
177C2×C11⋊C8—24no—
178C2×C11⋊C8C2414yes—
179#4313—216no—
180C2×#532—111no—
181C22×C4⋊Q8—111no—
182#3141—1116no—
183C2×#489—114no—
184C2×#487—111no—
185C2×#487D1111yescharacteristic, complemented
186C2×#486—111no—
187C2×#486—111no—
188C2×#417—114no—
189C2×C4×M16—111no—
190C23×C11C22×D411yescharacteristic
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—24no—
194C22×D11—44no—
195C22×D11—44no—
196C22×D11—44no—
197C22×D11#12414yes—
198C22×D11C22×D412yes—
199Q8×C11—28no—
200Q8×C11—44no—
201Q8×C11—48no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—44no—
205C2×C4×C11—44no—
206C2×C4×C11AGL(1,ℤ/8)14yes—
207C2×C4×C11#13714yes—
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D412yes—
210C2×C4×C11C22×D412yes—
211C2×C4×C11C2×#4114yes—
212C2×C4×C11C2511yescharacteristic
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—24no—
216C2×Dic11—44no—
217C2×Dic11#12414yes—
218C2×Dic11C22×D412yes—
219C2×Dic11C22×D412yes—
220C2×Dic11C22×D412yes—
221D44—28no—
222D44—416no—
223D44—44no—
224D44—48no—
225D44—48no—
226C4×D11—28no—
227C4×D11—28no—
228C4×D11—416no—
229C4×D11—416no—
230C4×D11#12418yes—
231C4×D11C2×#4118yes—
232Dic22—416no—
233Dic22—48no—
234C8×C11—24no—
235C11⋊C8—24no—
236C22×#41—112no—
237C23×Q8—221no—
238C22×M16—112no—
239#532—118no—
240#532—224no—
241C2×C4⋊Q8—118no—
242C2×C4⋊Q8—112no—
243C2×C4⋊Q8—111no—
244C2×C4⋊Q8—221no—
245C2×C4⋊Q8—224no—
246C2×C4⋊Q8—221no—
247C2×C4⋊Q8C2×D1111yescharacteristic
248C2×C4⋊Q8C2×D1111yescharacteristic
249C2×#127—111no—
250C2×#124—112no—
251C2×#121—221no—
252C2×#121—221no—
253C2×C4×D4—221no—
254C2×C4×D4—221no—
255C22×C4⋊C4—112no—
256C22×C4⋊C4—221no—
257C22×C42—111no—
258#489—1132no—
259#487—118no—
260#487C2×D1118yescomplemented
261#486—118no—
262#486—118no—
263#417—1132no—
264C2×#103—114no—
265C2×#103C2×D1114yes—
266C2×#102—114no—
267C2×#102—114no—
268C4×M16—118no—
269C2×#97—112no—
270C2×C4×C8—111no—
271C2×C4×C8C2×D1111yescharacteristic
272C22×C11C2×#12412yes—
273C22×C11C2×AGL(1,ℤ/8)12yes—
274C22×C11C2×#13712yes—
275C22×C11C23×D411yescharacteristic
276C2×D11—28no—
277C2×D11—22no—
278C2×D11—22no—
279C2×D11—44no—
280C2×D11—44no—
281C2×D11—44no—
282C2×D11—88no—
283C2×D11C2×#12414yes—
284C4×C11—44no—
285C4×C11—44no—
286C4×C11C2×#12412yes—
287C4×C11C2×AGL(1,ℤ/8)14yes—
288C4×C11C2×#13714yes—
289C4×C11C22×#4112yes—
290Dic11—22no—
291Dic11—22no—
292Dic11—44no—
293Dic11C2×#12414yes—
294C2×#41—118no—
295C2×#41—224no—
296C2×#41—2216no—
297C22×Q8—21no—
298C22×Q8—222no—
299C22×Q8—228no—
300C22×Q8—221no—
301C22×Q8—448no—
302C22×Q8C22×D1112yes—
303C22×D4—112no—
304C22×D4—222no—
305C22×D4—221no—
306C22×D4—221no—
307C23×C4—111no—
308C23×C4—111no—
309C23×C4—111no—
310C23×C4—222no—
311C23×C4—222no—
312C2×M16—118no—
313C2×M16—228no—
314C22×C8—112no—
315C22×C8C22×D1112yes—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—118no—
319C4⋊Q8—114no—
320C4⋊Q8—228no—
321C4⋊Q8—224no—
322C4⋊Q8—228no—
323C4⋊Q8—222no—
324C4⋊Q8C22×D1114yes—
325C4⋊Q8C22×D1114yes—
326#127—114no—
327#127—222no—
328#124—118no—
329#124—224no—
330#121—228no—
331#121—228no—
332C4×D4—228no—
333C4×D4—228no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—112no—
338C2×C4⋊C4—118no—
339C2×C4⋊C4—224no—
340C2×C4⋊C4—228no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4—222no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4C22×D1112yes—
345C2×C22⋊C4—222no—
346C2×C22⋊C4—222no—
347C2×C42—111no—
348C2×C42—111no—
349C2×C42—111no—
350C2×C42—114no—
351C2×C42—114no—
352C2×C42C22×D1111yescharacteristic
353#103—1116no—
354#103C22×D11116yes—
355#102—1116no—
356#102—1116no—
357#97—118no—
358C4×C8—114no—
359C4×C8C22×D1114yes—
360C2×C11#314114yescomplemented
361C2×C11C22×#12411yescharacteristic
362C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
363C2×C11C22×#13711yescharacteristic
364D11—24no—
365D11—84no—
366C24—111no—
367C24—222no—
368#41—2232no—
369#41—4416no—
370C2×Q8—22no—
371C2×Q8—24no—
372C2×Q8—28no—
373C2×Q8—44no—
374C2×Q8—228no—
375C2×Q8—224no—
376C2×Q8—448no—
377C2×Q8—4432no—
378C2×Q8—444no—
379C2×Q8C23×D1114yes—
380C2×D4—114no—
381C2×D4—228no—
382C2×D4—224no—
383C2×D4—224no—
384C2×D4—222no—
385C2×D4—228no—
386C2×D4—448no—
387C2×D4—444no—
388C2×D4—444no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—111no—
392C22×C4—112no—
393C22×C4—118no—
394C22×C4—112no—
395C22×C4—111no—
396C22×C4—111no—
397C22×C4—114no—
398C22×C4—114no—
399C22×C4—228no—
400C22×C4—228no—
401C22×C4—224no—
402C22×C4—224no—
403C22×C4—222no—
404C22×C4—448no—
405C22×C4—448no—
406C22×C4D4×D1111yescharacteristic
407C22×C4D4×D1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409M16—2216no—
410C2×C8—24no—
411C2×C8—114no—
412C2×C8—224no—
413C2×C8C23×D1114yes—
414C4⋊C4—24no—
415C4⋊C4—24no—
416C4⋊C4—24no—
417C4⋊C4—22no—
418C4⋊C4—114no—
419C4⋊C4—228no—
420C4⋊C4—228no—
421C4⋊C4—222no—
422C4⋊C4—224no—
423C4⋊C4C23×D1114yes—
424C22⋊C4—228no—
425C22⋊C4—228no—
426C42—114no—
427C42—114no—
428C42—112no—
429C42—112no—
430C42D4×D1112yes—
431C42C23×D1112yes—
432C11C2×#314111yescharacteristic, complemented, Sylow
433C23—112no—
434C23—114no—
435C23—222no—
436C23—222no—
437C23—224no—
438C23—444no—
439C23—444no—
440C23—444no—
441C23C2×D4×D1111yescharacteristic
442Q8—28no—
443Q8—48no—
444Q8—44no—
445Q8—4416no—
446Q8—448no—
447D4—228no—
448D4—4416no—
449D4—448no—
450D4—448no—
451D4—444no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—44no—
455C2×C4—44no—
456C2×C4—112no—
457C2×C4—114no—
458C2×C4—118no—
459C2×C4—118no—
460C2×C4—112no—
461C2×C4—112no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—228no—
465C2×C4—228no—
466C2×C4—224no—
467C2×C4—4416no—
468C2×C4—4416no—
469C2×C4—444no—
470C2×C4#6696714yes—
471C2×C4#6697114yes—
472C2×C4C2×D4×D1112yes—
473C2×C4C2×D4×D1112yes—
474C2×C4C2×D4×D1111yescharacteristic
475C2×C4#41×D1114yes—
476C2×C4C24×D1111yescharacteristic
477C8—24no—
478C8—224no—
479C22—114no—
480C22—222no—
481C22—222no—
482C22—228no—
483C22—444no—
484C22—444no—
485C22—444no—
486C22—888no—
487C22D11×#12412yes—
488C22C2×#6696712yes—
489C22C2×#6697112yes—
490C22C22×D4×D1111yescharacteristic
491C4—44no—
492C4—44no—
493C4—114no—
494C4—222no—
495C4—222no—
496C4—444no—
497C4D11×#12412yes—
498C4C2×#6696714yes—
499C4C2×#6697114yes—
500C4C2×#41×D1112yes—
501C2—224no—
502C2—884no—
503C2#1307901114yesdirect product factor
504C2C2×D11×#12411yescharacteristic
505C2C22×#6696711yescharacteristic
506C2C22×#6697111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#487C2
socleC23×C11C22×D4
prime radicalC2×#10623256C2
hypercenterC2×#487D11
hypocenterC11C2×#3141
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
2. C2×D11×C4⋊Q8C2semidirect
3. #13079011C2direct (N × H)
4. C2×#10622408C2semidirect
5. C2×#10622694C2semidirect
6. C2×#10622701C2semidirect
7. C2×#10622307C2semidirect
8. C2×#10622416C2semidirect
9. C2×C4×#4313C2semidirect
10. C2×C11×#487C2semidirect
21. D11×C4⋊Q8C22semidirect
33. C11×#487C22semidirect
39. #10622701C22semidirect
40. #10622694C22semidirect
43. #10622416C22semidirect
44. #10622408C22semidirect
45. #10622307C22semidirect
46. C4×#4313C22semidirect
185. C2×#487D11semidirect
260. #487C2×D11semidirect
360. C2×C11#3141semidirect
432. C11C2×#3141semidirect
503. C2#13079011direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×D11×C4⋊Q82
#130790112
C2×#106224082
C2×#106226942
C2×#106227012
C2×#106223072
C2×#106224162
C2×C4×#43132
C2×C11×#4872
C2×#314111