Finite Group Databasebeta

← C2×#13080849 #15630604

Subgroups — C2×#13080849 #15630604

Order 2816.

2566 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic, complemented
2C2×D4×D44C211yesmaximal, characteristic
3#13080849C2116yesmaximal, direct product factor
4C2×#10622307C211yesmaximal, characteristic, complemented
5C2×#10622479C212yesmaximal, complemented
6C2×#10622620C211yesmaximal, characteristic, complemented
7C2×#10622425C212yesmaximal, complemented
8C2×#10622640C211yesmaximal, characteristic, complemented
9C2×#10622782C212yesmaximal, complemented
10C2×#10622301C211yesmaximal, characteristic, complemented
11C2×#10622383C212yesmaximal, complemented
12C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
13C22×D4×D11C2212yes—
14C23×D44—21no—
15C22×C11×SD16C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic, complemented
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66999C2212yescomplemented
19C22×#4325C2212yescomplemented
20C2×#66983—21no—
21C22×#4313C2212yescomplemented
22#10623115—24no—
23#10623115C2218yescomplemented
24D4×D44—24no—
25D4×D44C2218yes—
26C2×#66951—22no—
27C2×#66948C2212yes—
28C2×#66945C2212yescomplemented
29C2×#66935—22no—
30C2×#66928—21no—
31C2×#66927C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×#66922C2211yescharacteristic, complemented
34C2×C4×Dic22—21no—
35C4×C11×SD16C2218yescomplemented
36C2×C11×#106C2211yescharacteristic, complemented
37C2×C11×#103C2211yescharacteristic, complemented
38C2×C11×#102C2211yescharacteristic
39C2×C4×C8×C11C2211yescharacteristic, complemented
40C2×#66896C2212yes—
41#10622782C22116yescomplemented
42C2×#66885C2212yescomplemented
43C2×#66885C2212yescomplemented
44C2×(C2×D11)⋊C8C2212yescomplemented
45#10622640C2218yescomplemented
46#10622620C2218yescomplemented
47C2×#66873C2212yescomplemented
48C2×#66871C2212yescomplemented
49C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
50#10622479C22116yescomplemented
51#10622425C22116yescomplemented
52#10622383C22116yescomplemented
53#10622307C2218yescomplemented
54#10622301C2218yescomplemented
55C24×D11—22no—
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C22×C22⋊D11—22no—
60C2×D4×D11—28no—
61C2×D4×D11—24no—
62C2×D4×D11—44no—
63C2×D4×D11C2318yes—
64C22×D44—22no—
65C22×D44—21no—
66C22×D44—21no—
67C22×D44—28no—
68C22×D44—48no—
69C22×D44D411yescharacteristic
70C22×D44C2312yes—
71C22×C4×D11C2312yes—
72C22×Dic22—21no—
73C2×C11×SD16—24no—
74C2×C11×SD16C2314yes—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C4×Q8×C11—22no—
78C4×Q8×C11C2314yescomplemented
79C4×D4×C11—22no—
80C4×D4×C11C2314yes—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87#66999—24no—
88#66999C2318yescomplemented
89C2×#4325—44no—
90C2×#4325C2318yescomplemented
91#66983—28no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4D412yes—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11D411yescharacteristic
98C2×C4⋊Dic11C2312yes—
99C2×Dic11⋊C4—22no—
100C2×C4×Dic11—22no—
101C22×C11⋊C8C2312yes—
102C2×#4313—44no—
103C2×#4313C2318yescomplemented
104#66951—216no—
105#66948—24no—
106#66948C2318yes—
107#66945—24no—
108#66945C2318yescomplemented
109#66935—216no—
110#66928—28no—
111#66927—22no—
112#66927C2314yes—
113C4×D44D414yes—
114C4×D44C2314yes—
115#66922—22no—
116#66922C2314yescomplemented
117C4×Dic22—28no—
118C11×#106C2314yescomplemented
119C11×#103C2314yescomplemented
120C11×#102C2314yes—
121C4×C8×C11C2314yescomplemented
122#66896C2318yes—
123#66885C2318yescomplemented
124#66885C2318yescomplemented
125(C2×D11)⋊C8C2318yescomplemented
126#66873C2318yescomplemented
127#66871C2318yescomplemented
128C4⋊(C11⋊C8)C2314yescomplemented
129C2×#3324—111nomaximal, Sylow
130C24×C11—21no—
131C23×D11—22no—
132C23×D11—28no—
133C23×D11—48no—
134C23×D11—48no—
135C23×D11—84no—
136C23×D11C2×D412yes—
137C2×Q8×C11—21no—
138C2×Q8×C11—22no—
139C2×Q8×C11—22no—
140C2×Q8×C11C2412yes—
141C2×D4×C11—21no—
142C2×D4×C11—22no—
143C2×D4×C11#4114yes—
144C2×D4×C11C2412yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—24no—
149C22×C4×C11—44no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—28no—
154C2×C22⋊D11—48no—
155C22×Dic11—22no—
156C22×Dic11C2×D412yes—
157D4×D11—216no—
158D4×D11—48no—
159D4×D11—416no—
160C2×D44—28no—
161C2×D44—24no—
162C2×D44—22no—
163C2×D44—24no—
164C2×D44—24no—
165C2×D44—24no—
166C2×D44—24no—
167C2×D44—48no—
168C2×D44—432no—
169C2×D44—44no—
170C2×D44—82no—
171C2×D44C2×D414yes—
172C2×D44C2414yes—
173C2×C4×D11—24no—
174C2×C4×D11—24no—
175C2×C4×D11C2×D414yes—
176C2×C4×D11C2414yes—
177C2×Dic22—24no—
178C2×Dic22—44no—
179C11×SD16—28no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11C2412yes—
183C2×C8×C11C2412yes—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—24no—
187C11×C4⋊C4C2412yes—
188C11×C4⋊C4C2412yes—
189C11×C22⋊C4—24no—
190C42×C11—24no—
191C42×C11C2×D412yes—
192C42×C11C2412yes—
193#4325—48no—
194(C2×D11)⋊C4—28no—
195(C2×D11)⋊C4—28no—
196(C2×D11)⋊C4—28no—
197(C2×D11)⋊C4C2×D418yes—
198C4⋊Dic11—22no—
199C4⋊Dic11—24no—
200C4⋊Dic11C2×D414yes—
201C4⋊Dic11C2414yes—
202Dic11⋊C4—28no—
203C4×Dic11—28no—
204C2×C11⋊C8—24no—
205C2×C11⋊C8C2414yes—
206#4313—48no—
207C2×#556—111no—
208C2×D42—111no—
209#3324—1116no—
210C2×#486—111no—
211C2×#482—112no—
212C2×#474—111no—
213C2×#468—112no—
214C2×#460—111no—
215C2×#450—112no—
216C2×C4×SD16D1111yescharacteristic, complemented
217C2×#436—111no—
218C2×#418—112no—
219C23×C11—24no—
220C23×C11—22no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11C22×D411yescharacteristic
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—416no—
229C22×D11—416no—
230C22×D11—44no—
231C22×D11—44no—
232C22×D11—44no—
233C22×D11—88no—
234C22×D11—832no—
235C22×D11C22×D414yes—
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—42no—
239D4×C11—24no—
240D4×C11—22no—
241D4×C11C2×#4114yes—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—48no—
250C2×C4×C11AGL(1,ℤ/8)14yes—
251C2×C4×C11C22×D412yes—
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D412yes—
254C2×C4×C11C2×#4112yes—
255C2×C4×C11H(5,𝔽2)12yes—
256C2×C4×C11C2511yescharacteristic
257C22⋊D11—416no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—44no—
261C2×Dic11C22×D414yes—
262D44—28no—
263D44—24no—
264D44—24no—
265D44—416no—
266D44—44no—
267D44—48no—
268D44—84no—
269C4×D11—28no—
270C4×D11—24no—
271C4×D11—24no—
272Dic22—48no—
273C8×C11—22no—
274C8×C11—22no—
275C11⋊C8—24no—
276C23×D4—112no—
277C23×D4—221no—
278C22×SD16—112no—
279C22×SD16C2×D1111yescharacteristic
280C22×M16—112no—
281#556—118no—
282#556—224no—
283D42—118no—
284D42—224no—
285C2×C4⋊Q8—111no—
286C2×#127—111no—
287C2×#126—222no—
288C2×#124—221no—
289C2×C22⋊Q8—112no—
290C2×#121—112no—
291C2×#121—221no—
292C2×#120—222no—
293C2×C4×Q8—221no—
294C2×C4×Q8C2×D1111yescharacteristic, complemented
295C2×C4×D4—111no—
296C2×C4×D4C2×D1111yescharacteristic
297C2×#117—112no—
298#486—118no—
299#482—1116no—
300#474—118no—
301#468—1116no—
302#460—118no—
303#450—1116no—
304C4×SD16C2×D1118yescomplemented
305#436—118no—
306C2×#107—112no—
307C2×#106C2×D1111yescharacteristic, complemented
308C2×C4⋊C8—111no—
309#418—1116no—
310C2×#103C2×D1111yescharacteristic, complemented
311C2×#102—112no—
312C2×#102—112no—
313C2×#102—112no—
314C2×#102—112no—
315C2×#102C2×D1111yescharacteristic
316C2×C22⋊C8—112no—
317C2×C4×C8C2×D1111yescharacteristic, complemented
318C22×C11—24no—
319C22×C11—42no—
320C22×C11—48no—
321C22×C11—42no—
322C22×C11#54612yes—
323C22×C11C2×AGL(1,ℤ/8)12yes—
324C22×C11#57712yes—
325C22×C11C23×D411yescharacteristic
326C2×D11—24no—
327C2×D11—24no—
328C2×D11—24no—
329C2×D11—48no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—832no—
334C2×D11—88no—
335C4×C11—22no—
336C4×C11—42no—
337C4×C11—42no—
338C4×C11—42no—
339C4×C11#54612yes—
340C4×C11C2×AGL(1,ℤ/8)14yes—
341C4×C11C22×#4111yescharacteristic
342C4×C11C2×H(5,𝔽2)11yescharacteristic
343Dic11—24no—
344Dic11—44no—
345C25—222no—
346C22×Q8—221no—
347C22×Q8C22×D1111yescharacteristic
348C22×D4—118no—
349C22×D4—111no—
350C22×D4—112no—
351C22×D4—228no—
352C22×D4—222no—
353C22×D4—224no—
354C22×D4—222no—
355C22×D4—228no—
356C22×D4—221no—
357C22×D4—221no—
358C22×D4—448no—
359C22×D4—444no—
360C22×D4C22×D1111yescharacteristic
361C23×C4—21no—
362C23×C4—112no—
363C2×SD16—24no—
364C2×SD16—118no—
365C2×SD16—444no—
366C2×SD16C22×D1114yes—
367C2×M16—118no—
368C2×M16—444no—
369C22×C8—112no—
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372C4⋊Q8—114no—
373C4⋊Q8—222no—
374#127—114no—
375#127—222no—
376#126—2216no—
377#124—228no—
378C22⋊Q8—118no—
379C22⋊Q8—224no—
380#121—118no—
381#121—224no—
382#121—228no—
383#120—2216no—
384C4×Q8—22no—
385C4×Q8—228no—
386C4×Q8C22×D1114yescomplemented
387C4×D4—22no—
388C4×D4—114no—
389C4×D4—114no—
390C4×D4C22×D1114yes—
391#117—118no—
392#117—224no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—112no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—112no—
402C2×C22⋊C4—222no—
403C2×C22⋊C4—222no—
404C2×C22⋊C4—222no—
405C2×C42—21no—
406C2×C42—222no—
407C2×C42C22×D1111yescharacteristic
408#107—118no—
409#106C22×D1114yescomplemented
410C4⋊C8—114no—
411#103C22×D1114yescomplemented
412#102—118no—
413#102—118no—
414#102—118no—
415#102—118no—
416#102C22×D1114yes—
417C22⋊C8—118no—
418C4×C8C22×D1114yescomplemented
419C2×C11—44no—
420C2×C11#332414yescomplemented
421C2×C11C2×#54611yescharacteristic
422C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
423C2×C11C2×#57711yescharacteristic
424D11—44no—
425D11—84no—
426C24—21no—
427C24—112no—
428C24—228no—
429C24—222no—
430C24—448no—
431C24—448no—
432C24—884no—
433C2×Q8—21no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—224no—
437C2×Q8—444no—
438C2×Q8C23×D1112yes—
439C2×D4—21no—
440C2×D4—22no—
441C2×D4—114no—
442C2×D4—114no—
443C2×D4—228no—
444C2×D4—228no—
445C2×D4—2216no—
446C2×D4—224no—
447C2×D4—224no—
448C2×D4—224no—
449C2×D4—222no—
450C2×D4—224no—
451C2×D4—224no—
452C2×D4—4432no—
453C2×D4—448no—
454C2×D4—448no—
455C2×D4—4416no—
456C2×D4—448no—
457C2×D4—444no—
458C2×D4—882no—
459C2×D4#433914yes—
460C2×D4C23×D1112yes—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—24no—
465C22×C4—44no—
466C22×C4—112no—
467C22×C4—114no—
468C22×C4—114no—
469C22×C4—224no—
470C22×C4—224no—
471C22×C4—222no—
472C22×C4D4×D1111yescharacteristic
473C22×C4D4×D1111yescharacteristic
474C22×C4C23×D1111yescharacteristic
475SD16—28no—
476SD16—448no—
477M16—448no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—114no—
481C2×C8—224no—
482C2×C8C23×D1112yes—
483C2×C8C23×D1112yes—
484C4⋊C4—24no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—114no—
488C4⋊C4—114no—
489C4⋊C4—228no—
490C4⋊C4—222no—
491C4⋊C4—224no—
492C4⋊C4C23×D1112yes—
493C4⋊C4C23×D1112yes—
494C22⋊C4—24no—
495C22⋊C4—118no—
496C22⋊C4—228no—
497C22⋊C4—228no—
498C22⋊C4—228no—
499C42—24no—
500C42—228no—
501C42D4×D1112yes—
502C42C23×D1112yes—
503C11C2×#332411yescharacteristic, complemented, Sylow
504C23—24no—
505C23—22no—
506C23—42no—
507C23—42no—
508C23—114no—
509C23—224no—
510C23—224no—
511C23—224no—
512C23—224no—
513C23—4416no—
514C23—4416no—
515C23—444no—
516C23—444no—
517C23—444no—
518C23—888no—
519C23—8832no—
520C23C2×D4×D1111yescharacteristic
521Q8—22no—
522Q8—22no—
523Q8—42no—
524Q8—448no—
525D4—24no—
526D4—22no—
527D4—228no—
528D4—224no—
529D4—224no—
530D4—4416no—
531D4—4416no—
532D4—448no—
533D4—444no—
534D4—884no—
535D4C2×#433914yes—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—48no—
544C2×C4—114no—
545C2×C4—224no—
546C2×C4—228no—
547C2×C4—224no—
548C2×C4—224no—
549C2×C4—224no—
550C2×C4—444no—
551C2×C4#6696714yes—
552C2×C4C2×#433912yes—
553C2×C4C2×D4×D1112yes—
554C2×C4C2×D4×D1112yes—
555C2×C4C2×D4×D1111yescharacteristic
556C2×C4#6704212yes—
557C2×C4C24×D1111yescharacteristic
558C8—22no—
559C8—22no—
560C8—224no—
561C22—24no—
562C22—48no—
563C22—42no—
564C22—42no—
565C22—224no—
566C22—224no—
567C22—224no—
568C22—448no—
569C22—444no—
570C22—444no—
571C22—444no—
572C22—8832no—
573C22—888no—
574C22#1062308112yes—
575C22C2×#6696712yes—
576C22#1062330112yes—
577C22C22×D4×D1111yescharacteristic
578C4—22no—
579C4—42no—
580C4—42no—
581C4—42no—
582C4—224no—
583C4—444no—
584C4#1062308112yes—
585C4C2×#6696714yes—
586C4C22×#433911yescharacteristic
587C4C2×#6704211yescharacteristic
588C2—44no—
589C2—444no—
590C2—884no—
591C2#1308084914yesdirect product factor
592C2C2×#1062308111yescharacteristic
593C2C22×#6696711yescharacteristic
594C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×D4×D44C2
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3324
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×#10623115C2semidirect
3. #13080849C2direct (N × H)
4. C2×#10622307C2semidirect
5. C2×#10622479C2semidirect
6. C2×#10622620C2semidirect
7. C2×#10622425C2semidirect
8. C2×#10622640C2semidirect
9. C2×#10622782C2semidirect
10. C2×#10622301C2semidirect
11. C2×#10622383C2semidirect
12. C2×C4×C11×SD16C2semidirect
16. C2×C4×Q8×C11C22semidirect
18. C2×#66999C22semidirect
19. C22×#4325C22semidirect
21. C22×#4313C22semidirect
23. #10623115C22semidirect
28. C2×#66945C22semidirect
33. C2×#66922C22semidirect
35. C4×C11×SD16C22semidirect
36. C2×C11×#106C22semidirect
37. C2×C11×#103C22semidirect
39. C2×C4×C8×C11C22semidirect
41. #10622782C22semidirect
42. C2×#66885C22semidirect
43. C2×#66885C22semidirect
44. C2×(C2×D11)⋊C8C22semidirect
45. #10622640C22semidirect
46. #10622620C22semidirect
47. C2×#66873C22semidirect
48. C2×#66871C22semidirect
49. C2×C4⋊(C11⋊C8)C22semidirect
50. #10622479C22semidirect
51. #10622425C22semidirect
52. #10622383C22semidirect
53. #10622307C22semidirect
54. #10622301C22semidirect
78. C4×Q8×C11C23semidirect
88. #66999C23semidirect
90. C2×#4325C23semidirect
103. C2×#4313C23semidirect
108. #66945C23semidirect
116. #66922C23semidirect
118. C11×#106C23semidirect
119. C11×#103C23semidirect
121. C4×C8×C11C23semidirect
123. #66885C23semidirect
124. #66885C23semidirect
125. (C2×D11)⋊C8C23semidirect
126. #66873C23semidirect
127. #66871C23semidirect
128. C4⋊(C11⋊C8)C23semidirect
216. C2×C4×SD16D11semidirect
294. C2×C4×Q8C2×D11semidirect
304. C4×SD16C2×D11semidirect
307. C2×#106C2×D11semidirect
310. C2×#103C2×D11semidirect
317. C2×C4×C8C2×D11semidirect
386. C4×Q8C22×D11semidirect
409. #106C22×D11semidirect
411. #103C22×D11semidirect
418. C4×C8C22×D11semidirect
420. C2×C11#3324semidirect
503. C11C2×#3324semidirect
591. C2#13080849direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231152
C2×D4×D442
#130808492
C2×#106223072
C2×#106224792
C2×#106226202
C2×#106224252
C2×#106226402
C2×#106227822
C2×#106223012
C2×#106223832
C2×C4×C11×SD162
C2×#332411