Finite Group Databasebeta

← C2×#13077862 #15620141

Subgroups — C2×#13077862 #15620141

Order 2816.

5098 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4343C211yesmaximal, characteristic, complemented
2C22×#66995C211yesmaximal, characteristic, complemented
3C22×#66961C211yesmaximal, characteristic, complemented
4C2×#10623055C211yesmaximal, characteristic, complemented
5#13077862C2116yesmaximal, direct product factor
6C2×#10622423C214yesmaximal, complemented
7C2×#10622424C214yesmaximal, complemented
8C2×#10622614C211yesmaximal, characteristic, complemented
9C2×#10622739C211yesmaximal, characteristic, complemented
10C2×C11×#419C211yesmaximal, characteristic, complemented
11C23×Q8×C11C2211yescharacteristic
12C22×#4343—28no—
13C22×#4343—28no—
14C22×#4343—22no—
15C22×#4343—24no—
16C22×#4343C2214yes—
17C22×#4343C2218yescomplemented
18C22×#4339C2211yescharacteristic
19C23×D44—21no—
20C23×D44C2211yescharacteristic
21C23×C4×D11—21no—
22C23×C4×D11C2211yescharacteristic
23C22×C11×M16C2211yescharacteristic
24C2×C11×#117C2211yescharacteristic
25C22×#4326C2212yescomplemented
26C2×#66995—28no—
27C2×#66995C2218yescomplemented
28C22×#4325C2212yescomplemented
29C22×#4318C2211yescharacteristic
30C2×#66961—28no—
31C2×#66961C2218yescomplemented
32C22×D88C2212yescomplemented
33C22×#4314C2212yescomplemented
34#10623055—24no—
35#10623055C2218yescomplemented
36C2×#66950C2212yescomplemented
37C2×#66948C2212yescomplemented
38C2×#66939—21no—
39C2×#66935—21no—
40C2×C4×D44—22no—
41C11×#419C2218yescomplemented
42C2×C11×#103C2214yescomplemented
43#10622739C2218yescomplemented
44C2×(C2×D11)⋊C8C2214yescomplemented
45#10622614C2218yescomplemented
46C2×#66873C2214yescomplemented
47#10622424C22132yescomplemented
48#10622423C22132yescomplemented
49C24×D11—21no—
50C24×D11D411yescharacteristic
51C22×Q8×C11—24no—
52C22×Q8×C11—21no—
53C22×Q8×C11—22no—
54C22×Q8×C11D418yescomplemented
55C22×Q8×C11C2312yes—
56C22×Q8×C11C2314yes—
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—21no—
60C23×Dic11D411yescharacteristic
61C2×#4343—232no—
62C2×#4343—264no—
63C2×#4343—216no—
64C2×#4343—232no—
65C2×#4343—216no—
66C2×#4343—232no—
67C2×#4343—28no—
68C2×#4343—216no—
69C2×#4343C23116yes—
70C2×#4339—22no—
71C2×#4339—24no—
72C2×#4339—24no—
73C2×#4339C2314yes—
74C22×D44—216no—
75C22×D44—24no—
76C22×D44—28no—
77C22×D44—24no—
78C22×D44—21no—
79C22×D44—22no—
80C22×D44—22no—
81C22×D44D418yescomplemented
82C22×D44C2311yescharacteristic
83C22×D44C2312yes—
84C22×D44C2314yes—
85C22×C4×D11—216no—
86C22×C4×D11—24no—
87C22×C4×D11—24no—
88C22×C4×D11—24no—
89C22×C4×D11—28no—
90C22×C4×D11—21no—
91C22×C4×D11D412yes—
92C22×C4×D11D414yes—
93C22×C4×D11C2312yes—
94C22×C4×D11C2314yes—
95C22×Dic22C2311yescharacteristic
96C2×C11×M16—24no—
97C2×C11×M16C2314yes—
98C22×C8×C11C2312yes—
99C11×#117—22no—
100C11×#117C2314yes—
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C22⋊C4—21no—
103C2×C42×C11—21no—
104C2×#4326—28no—
105C2×#4326C2318yescomplemented
106#66995—232no—
107C2×#4325—28no—
108C2×#4325C2318yescomplemented
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×C4⋊Dic11—22no—
112C2×#4318—24no—
113C2×#4318C2314yes—
114C22×C11⋊C8C2312yes—
115#66961—232no—
116C2×D88—28no—
117C2×D88C2318yescomplemented
118C2×#4314—28no—
119C2×#4314C2318yescomplemented
120#66950—24no—
121#66950C2318yescomplemented
122#66948—24no—
123#66948C2318yescomplemented
124#66939—28no—
125#66935—28no—
126C4×D44—216no—
127C11×#103C23116yescomplemented
128(C2×D11)⋊C8C23116yescomplemented
129#66873C23116yescomplemented
130C2×#3005—111nomaximal, Sylow
131C24×C11C2×D411yescharacteristic
132C23×D11—24no—
133C23×D11—28no—
134C23×D11—22no—
135C23×D11—24no—
136C23×D11—21no—
137C23×D11—44no—
138C23×D11—48no—
139C23×D11C2×D412yes—
140C23×D11C2×D414yes—
141C2×Q8×C11—28no—
142C2×Q8×C11—216no—
143C2×Q8×C11—24no—
144C2×Q8×C11—28no—
145C2×Q8×C11—24no—
146C2×Q8×C11—22no—
147C2×Q8×C11C2×D418yes—
148C2×Q8×C11C2×D4116yescomplemented
149C2×Q8×C11C2414yes—
150C22×C4×C11—28no—
151C22×C4×C11—22no—
152C22×C4×C11—24no—
153C22×C4×C11—22no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2411yescharacteristic
159C22×C4×C11C2412yes—
160C2×C22⋊D11—24no—
161C2×C22⋊D11—44no—
162C22×Dic11—24no—
163C22×Dic11—21no—
164C22×Dic11C2×D414yes—
165C22×Dic11C2×D412yes—
166#4343—264no—
167#4343—2128no—
168#4343—232no—
169#4343—232no—
170#4339—28no—
171#4339—28no—
172#4339—48no—
173C2×D44—232no—
174C2×D44—264no—
175C2×D44—216no—
176C2×D44—28no—
177C2×D44—28no—
178C2×D44—216no—
179C2×D44—24no—
180C2×D44—28no—
181C2×D44—24no—
182C2×D44—22no—
183C2×D44—21no—
184C2×D44—22no—
185C2×D44—22no—
186C2×D44—48no—
187C2×D44C2×D418yes—
188C2×D44C2×D4116yescomplemented
189C2×D44C2412yes—
190C2×D44C2414yes—
191C2×C4×D11—232no—
192C2×C4×D11—264no—
193C2×C4×D11—216no—
194C2×C4×D11—28no—
195C2×C4×D11—216no—
196C2×C4×D11—24no—
197C2×C4×D11—28no—
198C2×C4×D11—24no—
199C2×C4×D11—28no—
200C2×C4×D11—24no—
201C2×C4×D11—44no—
202C2×C4×D11C2×D418yes—
203C2×C4×D11C2×D414yes—
204C2×C4×D11C2414yes—
205C2×Dic22—22no—
206C2×Dic22—22no—
207C2×Dic22—21no—
208C2×Dic22C2412yes—
209C11×M16—28no—
210C2×C8×C11—24no—
211C2×C8×C11C2414yes—
212C11×C4⋊C4—22no—
213C11×C4⋊C4C2414yes—
214C11×C22⋊C4—24no—
215C42×C11—24no—
216#4326—216no—
217#4325—216no—
218(C2×D11)⋊C4—28no—
219(C2×D11)⋊C4—28no—
220C4⋊Dic11—28no—
221#4318—28no—
222C2×C11⋊C8—24no—
223C2×C11⋊C8C2414yes—
224D88—216no—
225#4314—216no—
226C23×#41—111no—
227C22×#137—111no—
228C22×AGL(1,ℤ/8)—111no—
229C2×#525—111no—
230#3005—1116no—
231C2×#452—114no—
232C2×#449—114no—
233C2×#419D1111yescharacteristic, complemented
234C2×#418—111no—
235C2×#407—111no—
236C23×C11—24no—
237C23×C11#12014yes—
238C23×C11C22×D412yes—
239C23×C11C22×D411yescharacteristic
240C22×D11—28no—
241C22×D11—24no—
242C22×D11—28no—
243C22×D11—216no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—24no—
247C22×D11—22no—
248C22×D11—48no—
249C22×D11—416no—
250C22×D11—432no—
251C22×D11—416no—
252C22×D11—48no—
253C22×D11—42no—
254C22×D11—44no—
255C22×D11C22×D414yes—
256Q8×C11—28no—
257Q8×C11—216no—
258Q8×C11—24no—
259Q8×C11C22×D418yes—
260C2×C4×C11—28no—
261C2×C4×C11—216no—
262C2×C4×C11—24no—
263C2×C4×C11—24no—
264C2×C4×C11—44no—
265C2×C4×C11#12014yes—
266C2×C4×C11#12018yes—
267C2×C4×C11C22×D412yes—
268C2×C4×C11C22×D414yes—
269C2×C4×C11C22×D412yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D412yes—
272C2×C4×C11C22×D414yes—
273C2×C4×C11C2511yescharacteristic
274C22⋊D11—48no—
275C2×Dic11—28no—
276C2×Dic11—24no—
277C2×Dic11—22no—
278C2×Dic11—42no—
279C2×Dic11C22×D414yes—
280D44—264no—
281D44—28no—
282D44—216no—
283D44—24no—
284D44—22no—
285D44—22no—
286D44—416no—
287D44—42no—
288D44C22×D418yes—
289C4×D11—264no—
290C4×D11—28no—
291C4×D11—216no—
292C4×D11—24no—
293C4×D11—24no—
294C4×D11—48no—
295Dic22—22no—
296Dic22—22no—
297Dic22—42no—
298C8×C11—24no—
299C11⋊C8—24no—
300C22×#41—114no—
301C22×#41—118no—
302C22×#41—111no—
303C22×#41—222no—
304C22×#41—224no—
305C22×#41—228no—
306C22×#41—228no—
307C23×Q8C2×D1111yescharacteristic
308C23×D4—111no—
309C23×D4—221no—
310C24×C4—111no—
311C24×C4—221no—
312C2×#137—118no—
313C2×#137—228no—
314C2×AGL(1,ℤ/8)—118no—
315C2×AGL(1,ℤ/8)—228no—
316C22×Q16—112no—
317C22×SD16—112no—
318C22×SD16—112no—
319C22×D8—112no—
320C22×M16—111no—
321C22×M16C2×D1111yescharacteristic
322#525—118no—
323#525—224no—
324C2×#123—221no—
325C2×C22⋊Q8—112no—
326C2×#121—112no—
327C2×#120—221no—
328C2×C4×D4—222no—
329C2×#117C2×D1111yescharacteristic
330#452—1132no—
331#449—1132no—
332#419C2×D1118yescomplemented
333#418—118no—
334C2×#103C2×D1114yescomplemented
335C2×#102—114no—
336#407—118no—
337C2×C22⋊C8—114no—
338C22×C11—28no—
339C22×C11—24no—
340C22×C11C2×#12014yes—
341C22×C11C2×#12012yes—
342C22×C11#57514yes—
343C22×C11C23×D411yescharacteristic
344C2×D11—28no—
345C2×D11—24no—
346C2×D11—24no—
347C2×D11—24no—
348C2×D11—416no—
349C2×D11—432no—
350C2×D11—48no—
351C2×D11—416no—
352C2×D11—48no—
353C2×D11—42no—
354C2×D11—44no—
355C2×D11—84no—
356C4×C11—28no—
357C4×C11—44no—
358C4×C11C2×#12012yes—
359C4×C11C2×#12014yes—
360C4×C11C23×D411yescharacteristic
361C4×C11C23×D411yescharacteristic
362Dic11—24no—
363Dic11—42no—
364C25—111no—
365C25—221no—
366C2×#41—1116no—
367C2×#41—114no—
368C2×#41—2216no—
369C2×#41—228no—
370C2×#41—2216no—
371C2×#41—2232no—
372C2×#41—2232no—
373C2×#41—2264no—
374C2×#41—2216no—
375C2×#41—2232no—
376C2×#41—222no—
377C2×#41—224no—
378C2×#41—224no—
379C22×Q8—24no—
380C22×Q8—22no—
381C22×Q8—21no—
382C22×Q8—111no—
383C22×Q8D4418yescomplemented
384C22×Q8C22×D1112yes—
385C22×Q8C22×D1114yes—
386C22×D4—118no—
387C22×D4—112no—
388C22×D4—114no—
389C22×D4—111no—
390C22×D4—228no—
391C22×D4—224no—
392C22×D4—2216no—
393C22×D4—222no—
394C22×D4—221no—
395C22×D4—224no—
396C22×D4—222no—
397C22×D4—221no—
398C23×C4—21no—
399C23×C4—111no—
400C23×C4—112no—
401C23×C4—114no—
402C23×C4—112no—
403C23×C4—114no—
404C23×C4—228no—
405C23×C4—224no—
406C23×C4—2216no—
407C23×C4—224no—
408C23×C4—224no—
409C23×C4—221no—
410C23×C4C22×D1111yescharacteristic
411#137—2232no—
412AGL(1,ℤ/8)—2232no—
413C2×Q16—118no—
414C2×Q16—228no—
415C2×SD16—118no—
416C2×SD16—118no—
417C2×SD16—228no—
418C2×SD16—228no—
419C2×D8—118no—
420C2×D8—228no—
421C2×M16—24no—
422C2×M16—114no—
423C2×M16—224no—
424C2×M16C22×D1114yes—
425C22×C8—112no—
426C22×C8C22×D1112yes—
427#123—228no—
428C22⋊Q8—118no—
429C22⋊Q8—224no—
430#121—118no—
431#121—224no—
432#120—228no—
433C4×D4—2216no—
434#117—22no—
435#117C22×D1114yes—
436C2×C4⋊C4—222no—
437C2×C4⋊C4C22×D1112yes—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—222no—
440C2×C22⋊C4—222no—
441C2×C42—21no—
442#103C22×D11116yescomplemented
443#102—1116no—
444C22⋊C8—1116no—
445C2×C11—24no—
446C2×C11#300514yescomplemented
447C2×C11C22×#12011yescharacteristic
448C2×C11C2×#57512yes—
449D11—44no—
450D11—48no—
451D11—82no—
452C24—112no—
453C24—114no—
454C24—228no—
455C24—224no—
456C24—224no—
457C24—222no—
458C24—221no—
459C24—444no—
460C24—448no—
461C24D4×D1111yescharacteristic
462#41—2232no—
463#41—2264no—
464#41—22128no—
465#41—2232no—
466#41—228no—
467#41—228no—
468#41—448no—
469C2×Q8—28no—
470C2×Q8—216no—
471C2×Q8—24no—
472C2×Q8—28no—
473C2×Q8—24no—
474C2×Q8—22no—
475C2×Q8—112no—
476C2×Q8—221no—
477C2×Q8—222no—
478C2×Q8—222no—
479C2×Q8C2×D4418yes—
480C2×Q8C2×D44116yescomplemented
481C2×Q8C23×D1114yes—
482C2×D4—118no—
483C2×D4—1116no—
484C2×D4—114no—
485C2×D4—112no—
486C2×D4—2216no—
487C2×D4—2232no—
488C2×D4—2264no—
489C2×D4—228no—
490C2×D4—224no—
491C2×D4—228no—
492C2×D4—2216no—
493C2×D4—224no—
494C2×D4—228no—
495C2×D4—222no—
496C2×D4—224no—
497C2×D4—222no—
498C2×D4—222no—
499C2×D4—221no—
500C2×D4—448no—
501C2×D4—444no—
502C22×C4—28no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—114no—
507C22×C4—112no—
508C22×C4—118no—
509C22×C4—114no—
510C22×C4—114no—
511C22×C4—2216no—
512C22×C4—2232no—
513C22×C4—2264no—
514C22×C4—224no—
515C22×C4—228no—
516C22×C4—2216no—
517C22×C4—224no—
518C22×C4—228no—
519C22×C4—224no—
520C22×C4—228no—
521C22×C4—221no—
522C22×C4—224no—
523C22×C4—444no—
524C22×C4C2×D4414yes—
525C22×C4D4×D1112yes—
526C22×C4D4×D1111yescharacteristic
527C22×C4D4×D1114yes—
528C22×C4C23×D1112yes—
529C22×C4C23×D1111yescharacteristic
530Q16—2216no—
531SD16—2216no—
532SD16—2216no—
533D8—2216no—
534M16—28no—
535M16—228no—
536C2×C8—24no—
537C2×C8—114no—
538C2×C8—224no—
539C2×C8C23×D1114yes—
540C4⋊C4—22no—
541C4⋊C4—228no—
542C4⋊C4C23×D1114yes—
543C22⋊C4—24no—
544C22⋊C4—228no—
545C22⋊C4—228no—
546C42—24no—
547C11C2×#300511yescharacteristic, complemented, Sylow
548C23—24no—
549C23—114no—
550C23—2216no—
551C23—228no—
552C23—228no—
553C23—224no—
554C23—224no—
555C23—224no—
556C23—224no—
557C23—222no—
558C23—448no—
559C23—4416no—
560C23—4432no—
561C23—4416no—
562C23—448no—
563C23—442no—
564C23—444no—
565C23#6693514yes—
566C23C2×D4×D1112yes—
567C23C2×D4×D1111yescharacteristic
568Q8—28no—
569Q8—216no—
570Q8—24no—
571Q8—222no—
572Q8—222no—
573Q8—442no—
574Q8C22×D4418yes—
575D4—118no—
576D4—2264no—
577D4—2216no—
578D4—228no—
579D4—224no—
580D4—222no—
581D4—222no—
582D4—4416no—
583D4—448no—
584D4—442no—
585C2×C4—28no—
586C2×C4—216no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—44no—
590C2×C4—114no—
591C2×C4—2264no—
592C2×C4—228no—
593C2×C4—224no—
594C2×C4—2216no—
595C2×C4—228no—
596C2×C4—224no—
597C2×C4—224no—
598C2×C4—222no—
599C2×C4—442no—
600C2×C4—448no—
601C2×C4#6693514yes—
602C2×C4#6693518yes—
603C2×C4C22×D4412yes—
604C2×C4C22×D4414yes—
605C2×C4C2×D4×D1112yes—
606C2×C4C2×D4×D1111yescharacteristic
607C2×C4C2×D4×D1112yes—
608C2×C4C2×D4×D1114yes—
609C2×C4C24×D1111yescharacteristic
610C8—24no—
611C8—224no—
612C22—28no—
613C22—24no—
614C22—224no—
615C22—224no—
616C22—228no—
617C22—224no—
618C22—4416no—
619C22—4432no—
620C22—448no—
621C22—4416no—
622C22—448no—
623C22—444no—
624C22—442no—
625C22—884no—
626C22C2×#6693514yes—
627C22C2×#6693512yes—
628C22#1062330814yes—
629C22C22×D4×D1111yescharacteristic
630C4—28no—
631C4—44no—
632C4—224no—
633C4—442no—
634C4C2×#6693514yes—
635C4C2×#6693512yes—
636C4C23×D4411yescharacteristic
637C4C22×D4×D1111yescharacteristic
638C2—24no—
639C2—444no—
640C2—448no—
641C2—882no—
642C2#1307786214yesdirect product factor
643C2C22×#6693511yescharacteristic
644C2C2×#1062330812yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#419C2
socleC23×C11C22×D4
hypercenterC2×#419D11
hypocenterC11C2×#3005
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
1. C23×#4343C2semidirect
2. C22×#66995C2semidirect
3. C22×#66961C2semidirect
4. C2×#10623055C2semidirect
5. #13077862C2direct (N × H)
6. C2×#10622423C2semidirect
7. C2×#10622424C2semidirect
8. C2×#10622614C2semidirect
9. C2×#10622739C2semidirect
10. C2×C11×#419C2semidirect
17. C22×#4343C22semidirect
25. C22×#4326C22semidirect
27. C2×#66995C22semidirect
28. C22×#4325C22semidirect
31. C2×#66961C22semidirect
32. C22×D88C22semidirect
33. C22×#4314C22semidirect
35. #10623055C22semidirect
36. C2×#66950C22semidirect
37. C2×#66948C22semidirect
41. C11×#419C22semidirect
42. C2×C11×#103C22semidirect
43. #10622739C22semidirect
44. C2×(C2×D11)⋊C8C22semidirect
45. #10622614C22semidirect
46. C2×#66873C22semidirect
47. #10622424C22semidirect
48. #10622423C22semidirect
54. C22×Q8×C11D4semidirect
81. C22×D44D4semidirect
105. C2×#4326C23semidirect
108. C2×#4325C23semidirect
117. C2×D88C23semidirect
119. C2×#4314C23semidirect
121. #66950C23semidirect
123. #66948C23semidirect
127. C11×#103C23semidirect
128. (C2×D11)⋊C8C23semidirect
129. #66873C23semidirect
148. C2×Q8×C11C2×D4semidirect
188. C2×D44C2×D4semidirect
233. C2×#419D11semidirect
332. #419C2×D11semidirect
334. C2×#103C2×D11semidirect
383. C22×Q8D44semidirect
442. #103C22×D11semidirect
446. C2×C11#3005semidirect
480. C2×Q8C2×D44semidirect
547. C11C2×#3005semidirect
642. C2#13077862direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43432
C22×#669952
C22×#669612
C2×#106230552
#130778622
C2×#106224232
C2×#106224242
C2×#106226142
C2×#106227392
C2×C11×#4192
C2×#300511