Finite Group Databasebeta

← C2×#13077860 #15620139

Subgroups — C2×#13077860 #15620139

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×#4341C211yesmaximal, characteristic, complemented
2C22×#66962C211yesmaximal, characteristic, complemented
3C22×#66985C211yesmaximal, characteristic, complemented
4C2×#10623055C211yesmaximal, characteristic, complemented
5#13077860C2116yesmaximal, direct product factor
6C2×#10622396C214yesmaximal, complemented
7C2×#10622394C214yesmaximal, complemented
8C2×#10622617C211yesmaximal, characteristic, complemented
9C2×#10622739C211yesmaximal, characteristic, complemented
10C2×C11×#418C211yesmaximal, characteristic, complemented
11C23×D4×C11C2211yescharacteristic
12C23×C22⋊D11—21no—
13C24×Dic11—21no—
14C22×#4341—28no—
15C22×#4341—22no—
16C22×#4341—24no—
17C22×#4341—28no—
18C22×#4341C2214yes—
19C22×#4341C2218yescomplemented
20C22×#4339C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×Dic22C2211yescharacteristic
23C22×C11×M16C2211yescharacteristic
24C2×C11×#117C2211yescharacteristic
25C22×#4324C2212yescomplemented
26C2×#66985—28no—
27C2×#66985C2218yescomplemented
28C22×#4323C2212yescomplemented
29C22×#4318C2211yescharacteristic
30C2×#66962—28no—
31C2×#66962C2218yescomplemented
32C22×Dic44C2212yescomplemented
33C22×#4314C2212yescomplemented
34#10623055—24no—
35#10623055C2218yescomplemented
36C2×#66950C2212yescomplemented
37C2×#66948C2212yescomplemented
38C2×#66939—21no—
39C2×#66935—21no—
40C2×C4×D44—22no—
41C11×#418C2218yescomplemented
42C2×C11×#102C2214yescomplemented
43#10622739C2218yescomplemented
44C2×(C2×D11)⋊C8C2214yescomplemented
45#10622617C2218yescomplemented
46C2×#66874C2214yescomplemented
47#10622396C22132yescomplemented
48#10622394C22132yescomplemented
49C25×C11—21no—
50C24×D11D411yescharacteristic
51C22×D4×C11—21no—
52C22×D4×C11—22no—
53C22×D4×C11—24no—
54C22×D4×C11D418yescomplemented
55C22×D4×C11C2312yes—
56C22×D4×C11C2314yes—
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—216no—
59C22×C22⋊D11—24no—
60C22×C22⋊D11—28no—
61C22×C22⋊D11—21no—
62C23×Dic11—216no—
63C23×Dic11—21no—
64C23×Dic11—24no—
65C23×Dic11—28no—
66C23×Dic11D411yescharacteristic
67C2×#4341—232no—
68C2×#4341—264no—
69C2×#4341—216no—
70C2×#4341—232no—
71C2×#4341—28no—
72C2×#4341—216no—
73C2×#4341—216no—
74C2×#4341—232no—
75C2×#4341C23116yes—
76C2×#4339—22no—
77C2×#4339—24no—
78C2×#4339—24no—
79C2×#4339C2314yes—
80C22×D44—22no—
81C22×D44C2311yescharacteristic
82C22×C4×D11—24no—
83C22×C4×D11—24no—
84C22×C4×D11—21no—
85C22×C4×D11D412yes—
86C22×C4×D11D414yes—
87C22×C4×D11C2312yes—
88C22×C4×D11C2314yes—
89C22×Dic22—24no—
90C22×Dic22—21no—
91C22×Dic22—22no—
92C22×Dic22D418yescomplemented
93C22×Dic22C2311yescharacteristic
94C22×Dic22C2312yes—
95C22×Dic22C2314yes—
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×#4324—28no—
105C2×#4324C2318yescomplemented
106#66985—232no—
107C2×#4323—28no—
108C2×#4323C2318yescomplemented
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×C4⋊Dic11—22no—
112C2×#4318—24no—
113C2×#4318C2314yes—
114C22×C11⋊C8C2312yes—
115#66962—232no—
116C2×Dic44—28no—
117C2×Dic44C2318yescomplemented
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×#102C23116yescomplemented
128(C2×D11)⋊C8C23116yescomplemented
129#66874C23116yescomplemented
130C2×#3005—111nomaximal, Sylow
131C24×C11—28no—
132C24×C11—22no—
133C24×C11—24no—
134C24×C11—48no—
135C24×C11C2×D411yescharacteristic
136C23×D11—24no—
137C23×D11—21no—
138C23×D11—44no—
139C23×D11C2×D412yes—
140C23×D11C2×D414yes—
141C2×D4×C11—28no—
142C2×D4×C11—216no—
143C2×D4×C11—24no—
144C2×D4×C11—22no—
145C2×D4×C11—24no—
146C2×D4×C11—28no—
147C2×D4×C11C2×D418yes—
148C2×D4×C11C2×D4116yescomplemented
149C2×D4×C11C2414yes—
150C22×C4×C11—22no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2×D414yes—
155C22×C4×C11C2411yescharacteristic
156C22×C4×C11C2412yes—
157C2×C22⋊D11—232no—
158C2×C22⋊D11—264no—
159C2×C22⋊D11—24no—
160C2×C22⋊D11—216no—
161C2×C22⋊D11—44no—
162C22×Dic11—232no—
163C22×Dic11—264no—
164C22×Dic11—216no—
165C22×Dic11—28no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11C2×D414yes—
171C22×Dic11C2×D412yes—
172#4341—264no—
173#4341—2128no—
174#4341—232no—
175#4341—232no—
176#4339—28no—
177#4339—28no—
178#4339—48no—
179C2×D44—28no—
180C2×D44—21no—
181C2×D44—22no—
182C2×D44—22no—
183C2×D44—48no—
184C2×D44C2412yes—
185C2×C4×D11—28no—
186C2×C4×D11—216no—
187C2×C4×D11—24no—
188C2×C4×D11—28no—
189C2×C4×D11—24no—
190C2×C4×D11—28no—
191C2×C4×D11—24no—
192C2×C4×D11—44no—
193C2×C4×D11C2×D418yes—
194C2×C4×D11C2×D414yes—
195C2×C4×D11C2414yes—
196C2×Dic22—28no—
197C2×Dic22—216no—
198C2×Dic22—24no—
199C2×Dic22—28no—
200C2×Dic22—24no—
201C2×Dic22—22no—
202C2×Dic22—22no—
203C2×Dic22—22no—
204C2×Dic22—21no—
205C2×Dic22C2×D418yes—
206C2×Dic22C2×D4116yescomplemented
207C2×Dic22C2412yes—
208C2×Dic22C2414yes—
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#4324—216no—
217#4323—216no—
218(C2×D11)⋊C4—28no—
219(C2×D11)⋊C4—28no—
220C4⋊Dic11—28no—
221#4318—28no—
222C2×C11⋊C8—24no—
223C2×C11⋊C8C2414yes—
224Dic44—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×#419—111no—
234C2×#418D1111yescharacteristic, complemented
235C2×#407—111no—
236C23×C11—24no—
237C23×C11—28no—
238C23×C11—216no—
239C23×C11—24no—
240C23×C11—432no—
241C23×C11—416no—
242C23×C11—48no—
243C23×C11#12014yes—
244C23×C11C22×D412yes—
245C23×C11C22×D411yescharacteristic
246C22×D11—28no—
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—22no—
251C22×D11—48no—
252C22×D11—416no—
253C22×D11—42no—
254C22×D11—44no—
255C22×D11C22×D414yes—
256D4×C11—28no—
257D4×C11—216no—
258D4×C11—24no—
259D4×C11C22×D418yes—
260C2×C4×C11—24no—
261C2×C4×C11—44no—
262C2×C4×C11#12014yes—
263C2×C4×C11#12018yes—
264C2×C4×C11C22×D412yes—
265C2×C4×C11C22×D414yes—
266C2×C4×C11C22×D412yes—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D412yes—
269C2×C4×C11C22×D414yes—
270C2×C4×C11C2511yescharacteristic
271C22⋊D11—264no—
272C22⋊D11—48no—
273C2×Dic11—264no—
274C2×Dic11—28no—
275C2×Dic11—216no—
276C2×Dic11—28no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—22no—
280C2×Dic11—42no—
281C2×Dic11C22×D414yes—
282D44—22no—
283D44—22no—
284D44—416no—
285D44—42no—
286C4×D11—28no—
287C4×D11—216no—
288C4×D11—24no—
289C4×D11—24no—
290C4×D11—48no—
291Dic22—28no—
292Dic22—216no—
293Dic22—24no—
294Dic22—22no—
295Dic22—22no—
296Dic22—42no—
297Dic22C22×D418yes—
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×Q8—111no—
308C23×D4—221no—
309C23×D4C2×D1111yescharacteristic
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#419—118no—
333#418C2×D1118yescomplemented
334C2×#103—114no—
335C2×#102C2×D1114yescomplemented
336#407—118no—
337C2×C22⋊C8—114no—
338C22×C11—28no—
339C22×C11—24no—
340C22×C11—28no—
341C22×C11—432no—
342C22×C11—416no—
343C22×C11—48no—
344C22×C11C2×#12014yes—
345C22×C11C2×#12012yes—
346C22×C11#57514yes—
347C22×C11C23×D411yescharacteristic
348C2×D11—24no—
349C2×D11—24no—
350C2×D11—24no—
351C2×D11—416no—
352C2×D11—48no—
353C2×D11—42no—
354C2×D11—44no—
355C2×D11—84no—
356C4×C11—44no—
357C4×C11C2×#12012yes—
358C4×C11C2×#12014yes—
359C4×C11C23×D411yescharacteristic
360C4×C11C23×D411yescharacteristic
361Dic11—28no—
362Dic11—24no—
363Dic11—42no—
364C25—21no—
365C25—111no—
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—118no—
380C22×Q8—112no—
381C22×Q8—114no—
382C22×Q8—111no—
383C22×Q8—224no—
384C22×Q8—222no—
385C22×Q8—221no—
386C22×D4—22no—
387C22×D4—21no—
388C22×D4—24no—
389C22×D4—111no—
390C22×D4—222no—
391C22×D4—228no—
392C22×D4—224no—
393C22×D4—2216no—
394C22×D4—221no—
395C22×D4D4418yescomplemented
396C22×D4C22×D1112yes—
397C22×D4C22×D1114yes—
398C23×C4—111no—
399C23×C4—112no—
400C23×C4—114no—
401C23×C4—112no—
402C23×C4—114no—
403C23×C4—228no—
404C23×C4—224no—
405C23×C4—2216no—
406C23×C4—221no—
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#103—1116no—
443#102C22×D11116yescomplemented
444C22⋊C8—1116no—
445C2×C11—24no—
446C2×C11—48no—
447C2×C11#300514yescomplemented
448C2×C11C22×#12011yescharacteristic
449C2×C11C2×#57512yes—
450D11—44no—
451D11—82no—
452C24—28no—
453C24—24no—
454C24—22no—
455C24—48no—
456C24—112no—
457C24—114no—
458C24—224no—
459C24—221no—
460C24—444no—
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—118no—
470C2×Q8—1116no—
471C2×Q8—114no—
472C2×Q8—112no—
473C2×Q8—228no—
474C2×Q8—2216no—
475C2×Q8—224no—
476C2×Q8—228no—
477C2×Q8—224no—
478C2×Q8—222no—
479C2×Q8—221no—
480C2×Q8—222no—
481C2×Q8—222no—
482C2×D4—28no—
483C2×D4—216no—
484C2×D4—24no—
485C2×D4—22no—
486C2×D4—24no—
487C2×D4—28no—
488C2×D4—112no—
489C2×D4—228no—
490C2×D4—2216no—
491C2×D4—2232no—
492C2×D4—2264no—
493C2×D4—224no—
494C2×D4—222no—
495C2×D4—222no—
496C2×D4—221no—
497C2×D4—448no—
498C2×D4—444no—
499C2×D4C2×D4418yes—
500C2×D4C2×D44116yescomplemented
501C2×D4C23×D1114yes—
502C22×C4—22no—
503C22×C4—114no—
504C22×C4—112no—
505C22×C4—118no—
506C22×C4—114no—
507C22×C4—114no—
508C22×C4—2216no—
509C22×C4—2232no—
510C22×C4—2264no—
511C22×C4—224no—
512C22×C4—228no—
513C22×C4—224no—
514C22×C4—222no—
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—28no—
550C23—216no—
551C23—24no—
552C23—432no—
553C23—416no—
554C23—48no—
555C23—114no—
556C23—228no—
557C23—224no—
558C23—224no—
559C23—224no—
560C23—222no—
561C23—448no—
562C23—4416no—
563C23—442no—
564C23—444no—
565C23#6693514yes—
566C23C2×D4×D1112yes—
567C23C2×D4×D1111yescharacteristic
568Q8—118no—
569Q8—2216no—
570Q8—228no—
571Q8—224no—
572Q8—222no—
573Q8—222no—
574Q8—442no—
575D4—28no—
576D4—216no—
577D4—24no—
578D4—2264no—
579D4—222no—
580D4—222no—
581D4—4416no—
582D4—448no—
583D4—442no—
584D4C22×D4418yes—
585C2×C4—24no—
586C2×C4—44no—
587C2×C4—114no—
588C2×C4—2264no—
589C2×C4—228no—
590C2×C4—224no—
591C2×C4—2216no—
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—28no—
615C22—432no—
616C22—416no—
617C22—48no—
618C22—224no—
619C22—224no—
620C22—224no—
621C22—4416no—
622C22—448no—
623C22—444no—
624C22—442no—
625C22—884no—
626C22C2×#6693514yes—
627C22C2×#6693512yes—
628C22#1062330414yes—
629C22C22×D4×D1111yescharacteristic
630C4—44no—
631C4—224no—
632C4—228no—
633C4—442no—
634C4C2×#6693514yes—
635C4C2×#6693512yes—
636C4C23×D4411yescharacteristic
637C4C22×D4×D1111yescharacteristic
638C2—24no—
639C2—48no—
640C2—444no—
641C2—882no—
642C2#1307786014yesdirect product factor
643C2C22×#6693511yescharacteristic
644C2C2×#1062330412yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#418C2
socleC23×C11C22×D4
hypercenterC2×#418D11
hypocenterC11C2×#3005
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
1. C23×#4341C2semidirect
2. C22×#66962C2semidirect
3. C22×#66985C2semidirect
4. C2×#10623055C2semidirect
5. #13077860C2direct (N × H)
6. C2×#10622396C2semidirect
7. C2×#10622394C2semidirect
8. C2×#10622617C2semidirect
9. C2×#10622739C2semidirect
10. C2×C11×#418C2semidirect
19. C22×#4341C22semidirect
25. C22×#4324C22semidirect
27. C2×#66985C22semidirect
28. C22×#4323C22semidirect
31. C2×#66962C22semidirect
32. C22×Dic44C22semidirect
33. C22×#4314C22semidirect
35. #10623055C22semidirect
36. C2×#66950C22semidirect
37. C2×#66948C22semidirect
41. C11×#418C22semidirect
42. C2×C11×#102C22semidirect
43. #10622739C22semidirect
44. C2×(C2×D11)⋊C8C22semidirect
45. #10622617C22semidirect
46. C2×#66874C22semidirect
47. #10622396C22semidirect
48. #10622394C22semidirect
54. C22×D4×C11D4semidirect
92. C22×Dic22D4semidirect
105. C2×#4324C23semidirect
108. C2×#4323C23semidirect
117. C2×Dic44C23semidirect
119. C2×#4314C23semidirect
121. #66950C23semidirect
123. #66948C23semidirect
127. C11×#102C23semidirect
128. (C2×D11)⋊C8C23semidirect
129. #66874C23semidirect
148. C2×D4×C11C2×D4semidirect
206. C2×Dic22C2×D4semidirect
234. C2×#418D11semidirect
333. #418C2×D11semidirect
335. C2×#102C2×D11semidirect
395. C22×D4D44semidirect
443. #102C22×D11semidirect
447. C2×C11#3005semidirect
500. C2×D4C2×D44semidirect
547. C11C2×#3005semidirect
642. C2#13077860direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43412
C22×#669622
C22×#669852
C2×#106230552
#130778602
C2×#106223962
C2×#106223942
C2×#106226172
C2×#106227392
C2×C11×#4182
C2×#300511