Finite Group Databasebeta

← C2×#13067679 #14729626

Subgroups — C2×#13067679 #14729626

Order 2816.

1438 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623108C211yesmaximal, characteristic, complemented
2C2×#10622686C211yesmaximal, characteristic, complemented
3C2×#10622685C211yesmaximal, characteristic, complemented
4#13067679C218yesmaximal, direct product factor
5C2×#10622123C211yesmaximal, characteristic, complemented
6C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×#10622121C211yesmaximal, characteristic, complemented
8C2×C11×#460C211yesmaximal, characteristic, complemented
9C22×#4343—21no—
10C22×C11×SD16—21no—
11C2×C11×#127C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C22×#4323—21no—
14C22×#4323—22no—
15#10623108—22no—
16#10623108—22no—
17#10623108—22no—
18#10623108C2214yescomplemented
19C2×#66948—22no—
20C2×#66948—21no—
21C2×#66927—21no—
22C2×#66927C2211yescharacteristic
23C2×C4×D44—21no—
24C2×C4×D44C2211yescharacteristic
25C11×#460—22no—
26C11×#460C2214yescomplemented
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#102—21no—
29C2×#66896—21no—
30#10622686—22no—
31#10622686C2214yescomplemented
32#10622685—22no—
33#10622685C2214yescomplemented
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36Q8⋊(C11⋊C8)C2214yescomplemented
37#10622123C2214yescomplemented
38#10622121C2214yescomplemented
39C22×Q8×C11D411yescharacteristic
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C2×#4343—24no—
44C2×#4343—24no—
45C2×#4343—44no—
46C2×#4343—44no—
47C22×D44—22no—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44—22no—
51C22×D44D411yescharacteristic
52C22×D44D412yes—
53C22×C4×D11—22no—
54C22×C4×D11—21no—
55C2×C11×SD16—24no—
56C2×C11×SD16—44no—
57C22×C8×C11—21no—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127—21no—
61C11×#127C2312yes—
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11D412yes—
65C4×Q8×C11C2312yes—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×#4323—24no—
71C2×#4323—28no—
72C2×#4323—48no—
73C2×#4323—44no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—21no—
76C2×C4⋊Dic11D411yescharacteristic
77C22×C11⋊C8—21no—
78C22×C11⋊C8—21no—
79#66948—24no—
80#66948—28no—
81#66948—28no—
82#66948—24no—
83#66927—24no—
84#66927—24no—
85#66927—21no—
86#66927—21no—
87#66927D412yes—
88#66927C2312yes—
89C4×D44—24no—
90C4×D44—21no—
91C4×D44—21no—
92C4×D44—24no—
93C4×D44D412yes—
94C4×D44C2312yes—
95C11×C4⋊C8—21no—
96C11×C4⋊C8C2312yes—
97C11×#102—24no—
98#66896—24no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)C2312yes—
101C4×C11⋊C8—21no—
102C4×C11⋊C8C2312yes—
103C2×#1621—111nomaximal, Sylow
104C24×C11—41no—
105C23×D11—21no—
106C23×D11—22no—
107C2×Q8×C11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11D814yescomplemented
110C2×Q8×C11C2×D412yes—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—44no—
115C2×D4×C11—41no—
116C2×D4×C11—41no—
117C2×D4×C11—41no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×Dic11—21no—
128#4343—48no—
129#4343—416no—
130#4343—48no—
131C2×D44—28no—
132C2×D44—28no—
133C2×D44—21no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—22no—
141C2×D44—48no—
142C2×D44—44no—
143C2×D44—42no—
144C2×D44—42no—
145C2×D44—42no—
146C2×D44—42no—
147C2×D44—84no—
148C2×D44C2×D412yes—
149C2×D44C2×D414yes—
150C2×C4×D11—28no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—48no—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C11×SD16—48no—
157C2×C8×C11—22no—
158C2×C8×C11—42no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4C2×D412yes—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11C2×D411yescharacteristic
166C42×C11C2×D411yescharacteristic
167C42×C11C2×D411yescharacteristic
168C42×C11C2411yescharacteristic
169#4323—416no—
170#4323—48no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—22no—
173(C2×D11)⋊C4—22no—
174C4⋊Dic11—21no—
175C4⋊Dic11C2×D412yes—
176C2×C11⋊C8—24no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—42no—
180C2×#550—111no—
181C2×#493—111no—
182C2×#460D1111yescharacteristic, complemented
183C2×#459—111no—
184#1621—118no—
185C2×#331—111no—
186C2×Q8⋊C8—111no—
187C2×D4⋊C8—111no—
188C23×C11—42no—
189C23×C11—82no—
190C23×C11—82no—
191C23×C11—82no—
192C23×C11#12011yescharacteristic
193C22×D11—22no—
194C22×D11—24no—
195C22×D11—44no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—44no—
199C22×D11—44no—
200C22×D11—42no—
201Q8×C11—22no—
202Q8×C11—24no—
203Q8×C11C2×D814yescomplemented
204D4×C11—44no—
205D4×C11—42no—
206D4×C11—42no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—82no—
210D4×C11—82no—
211D4×C11—82no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—42no—
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11#12011yescharacteristic
219C2×C4×C11#12011yescharacteristic
220C2×C4×C11C2×D812yes—
221C2×C4×C11#13512yes—
222C2×C4×C11AGL(1,ℤ/8)12yes—
223C2×C4×C11AGL(1,ℤ/8)12yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×Dic11—22no—
228C2×Dic11—42no—
229D44—22no—
230D44—22no—
231D44—44no—
232D44—416no—
233D44—42no—
234D44—42no—
235D44—42no—
236D44—42no—
237D44—44no—
238D44—42no—
239D44—44no—
240D44—82no—
241D44—88no—
242C4×D11—416no—
243C4×D11—42no—
244C4×D11—42no—
245C4×D11—44no—
246C8×C11—42no—
247C11⋊C8—24no—
248C11⋊C8—42no—
249C22×#41—221no—
250C22×SD16—21no—
251C22×D8—222no—
252C22×D8—221no—
253#550—114no—
254#550—222no—
255#550—222no—
256#550—222no—
257C2×#127—111no—
258C2×#127—221no—
259C2×#127C2×D1111yescharacteristic
260C2×#121—222no—
261C2×#121—221no—
262C2×C4×Q8C2×D1111yescharacteristic
263C2×C4×D4—111no—
264C2×C4×D4—221no—
265#493—114no—
266#493—222no—
267#460—22no—
268#460C2×D1114yescomplemented
269#459—114no—
270#459—222no—
271C2×C4⋊C8—111no—
272C2×C4⋊C8C2×D1111yescharacteristic
273C2×#102—21no—
274C2×#102—221no—
275C2×C4×C8—111no—
276#331—114no—
277Q8⋊C8—114no—
278D4⋊C8—114no—
279C22×C11—82no—
280C22×C11—82no—
281C22×C11—82no—
282C22×C11—164no—
283C22×C11#44712yes—
284C22×C11#44912yes—
285C22×C11#45312yes—
286C22×C11C2×#12011yescharacteristic
287C2×D11—44no—
288C2×D11—42no—
289C2×D11—42no—
290C2×D11—44no—
291C2×D11—44no—
292C2×D11—42no—
293C2×D11—84no—
294C2×D11—88no—
295C4×C11—24no—
296C4×C11—21no—
297C4×C11—21no—
298C4×C11—42no—
299C4×C11#44712yes—
300C4×C11#44912yes—
301C4×C11C22×D811yescharacteristic
302C4×C11C2×#13511yescharacteristic
303C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
304C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
305Dic11—42no—
306C2×#41—224no—
307C2×#41—224no—
308C2×#41—444no—
309C2×#41—444no—
310C22×Q8C22⋊D1111yescharacteristic
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—111no—
315C22×D4—112no—
316C22×D4—222no—
317C22×D4—222no—
318C22×D4—221no—
319C22×D4—221no—
320C23×C4—222no—
321C23×C4—221no—
322C2×SD16—24no—
323C2×SD16—44no—
324C2×D8—224no—
325C2×D8—228no—
326C2×D8—448no—
327C2×D8—444no—
328C22×C8—21no—
329C22×C8—221no—
330C22×C8—221no—
331#127—21no—
332#127—21no—
333#127—21no—
334#127—112no—
335#127—112no—
336#127—224no—
337#127—224no—
338#127—221no—
339#127—221no—
340#127C22×D1112yes—
341#121—228no—
342#121—224no—
343#121—228no—
344#121—224no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8C22⋊D1112yes—
348C4×Q8C22×D1112yes—
349C4×D4—112no—
350C4×D4—112no—
351C4×D4—224no—
352C4×D4—224no—
353C4×D4—221no—
354C4×D4—221no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4C22⋊D1111yescharacteristic
358C2×C22⋊C4—222no—
359C2×C22⋊C4—221no—
360C2×C42—21no—
361C2×C42C22×D1111yescharacteristic
362C4⋊C8—21no—
363C4⋊C8—112no—
364C4⋊C8—221no—
365C4⋊C8C22×D1112yes—
366#102—24no—
367#102—224no—
368C4×C8—112no—
369C4×C8—221no—
370C2×C11—162no—
371C2×C11#162114yescomplemented
372C2×C11C2×#44711yescharacteristic
373C2×C11C2×#44911yescharacteristic
374C2×C11C2×#45311yescharacteristic
375D11—82no—
376D11—84no—
377C24—41no—
378C24—221no—
379C24—222no—
380#41—448no—
381#41—4416no—
382#41—448no—
383C2×Q8—21no—
384C2×Q8—22no—
385C2×Q8#432314yescomplemented
386C2×Q8C2×C22⋊D1112yes—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—44no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—42no—
398C2×D4—112no—
399C2×D4—114no—
400C2×D4—228no—
401C2×D4—228no—
402C2×D4—222no—
403C2×D4—222no—
404C2×D4—222no—
405C2×D4—221no—
406C2×D4—222no—
407C2×D4—222no—
408C2×D4—222no—
409C2×D4—222no—
410C2×D4—448no—
411C2×D4—444no—
412C2×D4—442no—
413C2×D4—442no—
414C2×D4—442no—
415C2×D4—442no—
416C2×D4—884no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—228no—
420C22×C4—221no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—448no—
424C22×C4—442no—
425C22×C4—442no—
426C22×C4D4×D1111yescharacteristic
427C22×C4D4×D1111yescharacteristic
428C22×C4C2×C22⋊D1111yescharacteristic
429SD16—48no—
430D8—4416no—
431D8—448no—
432C2×C8—22no—
433C2×C8—42no—
434C2×C8—224no—
435C2×C8—222no—
436C2×C8—222no—
437C2×C8—442no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—112no—
442C4⋊C4—221no—
443C4⋊C4C2×C22⋊D1112yes—
444C22⋊C4—228no—
445C22⋊C4—222no—
446C22⋊C4—222no—
447C42—22no—
448C42—22no—
449C42D4×D1111yescharacteristic
450C42D4×D1111yescharacteristic
451C42C2×C22⋊D1111yescharacteristic
452C42C23×D1111yescharacteristic
453C11C2×#162111yescharacteristic, complemented, Sylow
454C23—42no—
455C23—82no—
456C23—82no—
457C23—82no—
458C23—222no—
459C23—224no—
460C23—442no—
461C23—444no—
462C23—444no—
463C23—442no—
464C23—444no—
465C23—442no—
466C23#6699011yescharacteristic
467Q8—22no—
468Q8—24no—
469Q8C2×#432314yescomplemented
470D4—44no—
471D4—42no—
472D4—42no—
473D4—42no—
474D4—42no—
475D4—82no—
476D4—82no—
477D4—82no—
478D4—222no—
479D4—222no—
480D4—444no—
481D4—4416no—
482D4—442no—
483D4—442no—
484D4—442no—
485D4—444no—
486D4—442no—
487D4—442no—
488D4—444no—
489D4—882no—
490D4—888no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—42no—
496C2×C4—222no—
497C2×C4—4416no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—444no—
502C2×C4#6696712yes—
503C2×C4#6696912yes—
504C2×C4C2×#432312yes—
505C2×C4#6699011yescharacteristic
506C2×C4#6699011yescharacteristic
507C2×C4#6699011yescharacteristic
508C2×C4#6700212yes—
509C2×C4C2×D4×D1111yescharacteristic
510C2×C4C2×D4×D1111yescharacteristic
511C2×C4C22×C22⋊D1111yescharacteristic
512C8—42no—
513C8—224no—
514C8—442no—
515C22—82no—
516C22—82no—
517C22—82no—
518C22—164no—
519C22—444no—
520C22—442no—
521C22—442no—
522C22—444no—
523C22—444no—
524C22—442no—
525C22—884no—
526C22—888no—
527C22#1062264912yes—
528C22#1062278512yes—
529C22#1062281112yes—
530C22C2×#6699011yescharacteristic
531C4—24no—
532C4—21no—
533C4—21no—
534C4—42no—
535C4—442no—
536C4#1062264912yes—
537C4#1062278512yes—
538C4C2×#6696711yescharacteristic
539C4C2×#6696911yescharacteristic
540C4C22×#432311yescharacteristic
541C4C2×#6700211yescharacteristic
542C2—162no—
543C2—882no—
544C2—884no—
545C2#1306767914yesdirect product factor
546C2C2×#1062264911yescharacteristic
547C2C2×#1062278511yescharacteristic
548C2C2×#1062281111yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#460C2
socleC23×C11#120
hypercenterC2×#460D11
hypocenterC11C2×#1621
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#10623108C2semidirect
2. C2×#10622686C2semidirect
3. C2×#10622685C2semidirect
4. #13067679C2direct (N × H)
5. C2×#10622123C2semidirect
6. C2×Q8⋊(C11⋊C8)C2semidirect
7. C2×#10622121C2semidirect
8. C2×C11×#460C2semidirect
18. #10623108C22semidirect
26. C11×#460C22semidirect
31. #10622686C22semidirect
33. #10622685C22semidirect
36. Q8⋊(C11⋊C8)C22semidirect
37. #10622123C22semidirect
38. #10622121C22semidirect
109. C2×Q8×C11D8semidirect
182. C2×#460D11semidirect
203. Q8×C11C2×D8semidirect
268. #460C2×D11semidirect
371. C2×C11#1621semidirect
385. C2×Q8#4323semidirect
453. C11C2×#1621semidirect
469. Q8C2×#4323semidirect
545. C2#13067679direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231082
C2×#106226862
C2×#106226852
#130676792
C2×#106221232
C2×Q8⋊(C11⋊C8)2
C2×#106221212
C2×C11×#4602
C2×#162111