Finite Group Databasebeta

← C2×#13078277 #15620975

Subgroups — C2×#13078277 #15620975

Order 2816.

2806 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67003C211yesmaximal, characteristic, complemented
2C22×#66960C211yesmaximal, characteristic, complemented
3C2×#10623041C211yesmaximal, characteristic, complemented
4C2×#10623364C211yesmaximal, characteristic, complemented
5#13078277C2116yesmaximal, direct product factor
6C2×#10622429C212yesmaximal, complemented
7C2×#10622395C212yesmaximal, complemented
8C2×#10622420C212yesmaximal, complemented
9C2×#10622391C212yesmaximal, complemented
10C22×#66872C211yesmaximal, characteristic, complemented
11C2×#10622746C211yesmaximal, characteristic, complemented
12C2×C11×#417C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C22×#4339C2211yescharacteristic
16C22×C11×M16C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18#10623364—24no—
19#10623364C2218yescomplemented
20C2×#67003—28no—
21C2×#67003C2218yescomplemented
22C2×#66999C2212yes—
23C22×#4326C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C2×#66992—22no—
26C2×#66991C2212yes—
27C22×#4324C2211yescharacteristic
28C22×#4323C2211yescharacteristic
29C2×#66983—22no—
30C2×#66983—21no—
31C22×C4⋊Dic11C2211yescharacteristic
32C2×#66977—21no—
33C23×C11⋊C8C2211yescharacteristic
34C2×#66960—28no—
35C2×#66960C2218yescomplemented
36C22×#4313C2212yes—
37C22×C8×D11C2212yes—
38#10623041—24no—
39#10623041C2218yescomplemented
40C2×#66950—21no—
41C2×#66950C2212yes—
42C2×#66948—21no—
43C2×#66948C2212yes—
44C11×#417C2218yescomplemented
45C2×C11×#103C2212yes—
46C2×C11×#102C2212yes—
47#10622746C2218yescomplemented
48C2×#66885C2212yes—
49C2×#66880C2212yes—
50C2×#66872C2212yes—
51C2×#66872C2212yes—
52C2×#66872C2218yescomplemented
53#10622429C22116yescomplemented
54#10622420C22116yescomplemented
55#10622395C22116yescomplemented
56#10622391C22116yescomplemented
57C2×C11×#41—22no—
58C2×C11×#41—24no—
59C2×C11×#41—24no—
60C2×C11×#41C2314yes—
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×C22⋊D11—22no—
69C22×C22⋊D11D412yes—
70C23×Dic11—21no—
71C2×#4339—24no—
72C2×#4339—24no—
73C2×#4339—22no—
74C2×#4339—24no—
75C2×#4339—24no—
76C2×#4339D414yes—
77C2×#4339C2314yes—
78C2×#4339C2314yes—
79C22×D44—22no—
80C22×D44D411yescharacteristic
81C22×D44C2311yescharacteristic
82C22×C4×D11—21no—
83C22×C4×D11C2312yes—
84C22×Dic22D411yescharacteristic
85C22×Dic22C2311yescharacteristic
86C2×C11×M16—24no—
87C2×C11×M16C2314yes—
88C22×C8×C11C2312yes—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2314yes—
93C2×C22⋊Dic11—22no—
94#67003—232no—
95#66999—24no—
96#66999C2318yes—
97C2×#4326—24no—
98C2×#4326C2314yes—
99C2×#4325—24no—
100C2×#4325C2314yes—
101#66992—216no—
102#66991—24no—
103#66991C2318yes—
104C2×#4324—24no—
105C2×#4324C2314yes—
106C2×#4323—24no—
107C2×#4323C2314yes—
108#66983—216no—
109#66983—28no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11—22no—
115C2×C4⋊Dic11—22no—
116C2×C4⋊Dic11C2312yes—
117C2×C4⋊Dic11C2314yes—
118#66977—28no—
119C2×Dic11⋊C4—22no—
120C22×C11⋊C8D418yescomplemented
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2314yes—
124#66960—232no—
125C2×#4313—28no—
126C2×#4313C2318yes—
127C2×C8×D11—28no—
128C2×C8×D11C2318yes—
129#66950—24no—
130#66950—28no—
131#66950C2318yes—
132#66948—28no—
133#66948—24no—
134#66948C2318yes—
135C11×#103C2318yes—
136C11×#102C2318yes—
137#66885C2318yes—
138#66880C2318yes—
139#66872C2318yes—
140#66872C2318yes—
141C2×#3060—111nomaximal, Sylow
142C24×C11—21no—
143C24×C11C2×D411yescharacteristic
144C23×D11—21no—
145C23×D11C2×D412yes—
146C11×#41—28no—
147C11×#41—28no—
148C11×#41—48no—
149C2×Q8×C11—21no—
150C2×Q8×C11—22no—
151C2×Q8×C11—22no—
152C2×Q8×C11C2412yes—
153C2×D4×C11—24no—
154C2×D4×C11—22no—
155C2×D4×C11—21no—
156C2×D4×C11—22no—
157C2×D4×C11—44no—
158C2×D4×C11C2412yes—
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11—24no—
162C22×C4×C11—24no—
163C22×C4×C11—44no—
164C22×C4×C11—82no—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D414yes—
168C22×C4×C11#4114yes—
169C22×C4×C11C2411yescharacteristic
170C22×C4×C11C2412yes—
171C2×C22⋊D11—28no—
172C2×C22⋊D11—24no—
173C2×C22⋊D11—28no—
174C2×C22⋊D11—44no—
175C2×C22⋊D11—84no—
176C2×C22⋊D11C2×D418yes—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—24no—
180C22×Dic11—82no—
181C22×Dic11C2×D412yes—
182#4339—216no—
183#4339—28no—
184#4339—28no—
185#4339—28no—
186#4339—28no—
187#4339—48no—
188C2×D44—28no—
189C2×D44—24no—
190C2×D44—21no—
191C2×D44—22no—
192C2×D44—22no—
193C2×D44—84no—
194C2×D44C2×D414yes—
195C2×D44C2412yes—
196C2×C4×D11—24no—
197C2×C4×D11—24no—
198C2×C4×D11—24no—
199C2×C4×D11—44no—
200C2×C4×D11C2×D414yes—
201C2×C4×D11C2414yes—
202C2×Dic22—24no—
203C2×Dic22—22no—
204C2×Dic22—21no—
205C2×Dic22—22no—
206C2×Dic22C2×D414yes—
207C2×Dic22C2412yes—
208C11×M16—28no—
209C2×C8×C11—24no—
210C2×C8×C11C2414yes—
211C11×C4⋊C4—22no—
212C11×C4⋊C4—24no—
213C11×C4⋊C4C2414yes—
214C22⋊Dic11—28no—
215#4326—28no—
216#4325—28no—
217#4324—28no—
218#4323—28no—
219(C2×D11)⋊C4—28no—
220(C2×D11)⋊C4—28no—
221(C2×D11)⋊C4—28no—
222C4⋊Dic11—28no—
223C4⋊Dic11—24no—
224C4⋊Dic11—22no—
225C4⋊Dic11C2414yes—
226Dic11⋊C4—28no—
227C2×C11⋊C8C2×D414yes—
228C2×C11⋊C8C2×D414yes—
229C2×C11⋊C8C2×D4116yescomplemented
230C2×C11⋊C8C2412yes—
231C2×C11⋊C8C2412yes—
232#4313—216no—
233C8×D11—216no—
234C22×#135—111no—
235C22×#131—111no—
236C2×#537—111no—
237C2×#537—111no—
238#3060—1116no—
239C2×#470—112no—
240C2×#469—112no—
241C2×#465—112no—
242C2×#465—112no—
243C22×#106—111no—
244C2×#417—111no—
245C2×#417D1111yescharacteristic, complemented
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—42no—
250C23×C11—42no—
251C23×C11—42no—
252C23×C11#12114yes—
253C23×C11C22×D412yes—
254C23×C11C22×D411yescharacteristic
255C22×D11—24no—
256C22×D11—24no—
257C22×D11—24no—
258C22×D11—22no—
259C22×D11—42no—
260C22×D11—42no—
261C22×D11—42no—
262C22×D11C22×D414yes—
263Q8×C11—22no—
264Q8×C11—22no—
265Q8×C11—42no—
266D4×C11—22no—
267D4×C11—22no—
268D4×C11—48no—
269D4×C11—42no—
270C2×C4×C11—22no—
271C2×C4×C11—24no—
272C2×C4×C11—42no—
273C2×C4×C11—44no—
274C2×C4×C11—48no—
275C2×C4×C11—84no—
276C2×C4×C11#12114yes—
277C2×C4×C11#12118yes—
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×D412yes—
280C2×C4×C11C22×D412yes—
281C2×C4×C11C22×D414yes—
282C2×C4×C11C2×#4112yes—
283C2×C4×C11C2×#4114yes—
284C2×C4×C11C2511yescharacteristic
285C22⋊D11—216no—
286C22⋊D11—48no—
287C22⋊D11—88no—
288C2×Dic11—24no—
289C2×Dic11—24no—
290C2×Dic11—22no—
291C2×Dic11—42no—
292C2×Dic11—44no—
293C2×Dic11—84no—
294C2×Dic11C22×D414yes—
295D44—28no—
296D44—22no—
297D44—22no—
298D44—42no—
299D44—88no—
300C4×D11—28no—
301C4×D11—24no—
302C4×D11—24no—
303C4×D11—48no—
304Dic22—28no—
305Dic22—22no—
306Dic22—22no—
307Dic22—42no—
308C8×C11—24no—
309C11⋊C8C22×D414yes—
310C11⋊C8C22×D414yes—
311C22×#41—111no—
312C22×#41—111no—
313C22×#41C2×D1111yescharacteristic
314C2×#135—118no—
315C2×#135—228no—
316C22×Q16—111no—
317C22×SD16—111no—
318C22×SD16—111no—
319C22×D8—111no—
320C2×#131—118no—
321C2×#131—228no—
322C22×M16—112no—
323C22×M16C2×D1111yescharacteristic
324C23×C8—111no—
325C23×C8—112no—
326#537—118no—
327#537—118no—
328#537—224no—
329#537—224no—
330C2×C22⋊Q8—112no—
331C2×C22⋊Q8—112no—
332C2×C22⋊Q8—221no—
333C2×C22⋊Q8—221no—
334C2×#121—112no—
335C2×#121—112no—
336C2×#121—221no—
337C2×#121—222no—
338C2×#121—221no—
339C2×#121—222no—
340C22×C4⋊C4—111no—
341C22×C4⋊C4C2×D1111yescharacteristic
342#470—1116no—
343#469—1116no—
344#465—1116no—
345#465—1116no—
346C2×#106—112no—
347C2×#106—112no—
348C2×#106—118no—
349#417—118no—
350#417C2×D1118yescomplemented
351C2×#103—112no—
352C2×#103C2×D1112yes—
353C2×#102—112no—
354C2×#102C2×D1112yes—
355C22×C11—28no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—84no—
362C22×C11C2×#12114yes—
363C22×C11C2×#12112yes—
364C22×C11#57712yes—
365C22×C11#57712yes—
366C22×C11C23×D411yescharacteristic
367C2×D11—24no—
368C2×D11—24no—
369C2×D11—24no—
370C2×D11—48no—
371C2×D11—42no—
372C2×D11—42no—
373C2×D11—42no—
374C2×D11—84no—
375C4×C11—42no—
376C4×C11—44no—
377C4×C11C2×#12114yes—
378C4×C11C2×#12112yes—
379C4×C11C23×D411yescharacteristic
380C4×C11C22×#4111yescharacteristic
381Dic11—24no—
382Dic11—42no—
383Dic11—44no—
384C2×#41—22no—
385C2×#41—24no—
386C2×#41—24no—
387C2×#41—114no—
388C2×#41—114no—
389C2×#41—114no—
390C2×#41—224no—
391C2×#41—224no—
392C2×#41—222no—
393C2×#41—224no—
394C2×#41—224no—
395C2×#41C22×D1114yes—
396C22×Q8—111no—
397C22×Q8—111no—
398C22×Q8C22×D1111yescharacteristic
399C22×D4—21no—
400C22×D4—112no—
401C22×D4—111no—
402C22×D4—111no—
403C22×D4—222no—
404C22×D4—221no—
405C22×D4—222no—
406C22×D4C22×D1111yescharacteristic
407C23×C4—21no—
408C23×C4—21no—
409C23×C4—112no—
410C23×C4—221no—
411C23×C4—221no—
412C23×C4C22×D1111yescharacteristic
413#135—2232no—
414C2×Q16—114no—
415C2×Q16—224no—
416C2×SD16—114no—
417C2×SD16—114no—
418C2×SD16—224no—
419C2×SD16—224no—
420C2×D8—114no—
421C2×D8—224no—
422#131—2232no—
423C2×M16—24no—
424C2×M16—118no—
425C2×M16—228no—
426C2×M16C22×D1114yes—
427C22×C8—118no—
428C22×C8—111no—
429C22×C8—111no—
430C22×C8—114no—
431C22×C8—118no—
432C22×C8—228no—
433C22×C8C22×D1112yes—
434C22⋊Q8—118no—
435C22⋊Q8—118no—
436C22⋊Q8—224no—
437C22⋊Q8—228no—
438C22⋊Q8—228no—
439C22⋊Q8—224no—
440#121—118no—
441#121—118no—
442#121—224no—
443#121—228no—
444#121—2216no—
445#121—228no—
446#121—224no—
447#121—2216no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—112no—
451C2×C4⋊C4—114no—
452C2×C4⋊C4—222no—
453C2×C4⋊C4—222no—
454C2×C4⋊C4—221no—
455C2×C4⋊C4—222no—
456C2×C4⋊C4C22×D1112yes—
457C2×C4⋊C4C22×D1114yes—
458C2×C22⋊C4—222no—
459C2×C22⋊C4—222no—
460C2×C22⋊C4—222no—
461C2×C22⋊C4—222no—
462#106—118no—
463#106—118no—
464#103—118no—
465#103C22×D1118yes—
466#102—118no—
467#102C22×D1118yes—
468C2×C11—24no—
469C2×C11—82no—
470C2×C11#306014yescomplemented
471C2×C11C22×#12111yescharacteristic
472C2×C11C2×#57711yescharacteristic
473C2×C11C2×#57711yescharacteristic
474D11—44no—
475D11—82no—
476C24—21no—
477C24—112no—
478C24—221no—
479C24D4×D1111yescharacteristic
480#41—28no—
481#41—28no—
482#41—48no—
483#41—2216no—
484#41—228no—
485#41—228no—
486#41—228no—
487#41—228no—
488#41—448no—
489C2×Q8—21no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—114no—
493C2×Q8—112no—
494C2×Q8—224no—
495C2×Q8—221no—
496C2×Q8—222no—
497C2×Q8—222no—
498C2×Q8C23×D1112yes—
499C2×D4—24no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—21no—
503C2×D4—44no—
504C2×D4—118no—
505C2×D4—114no—
506C2×D4—112no—
507C2×D4—228no—
508C2×D4—228no—
509C2×D4—224no—
510C2×D4—228no—
511C2×D4—224no—
512C2×D4—222no—
513C2×D4—222no—
514C2×D4—221no—
515C2×D4—444no—
516C2×D4—884no—
517C2×D4—884no—
518C2×D4C23×D1112yes—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—44no—
524C22×C4—82no—
525C22×C4—112no—
526C22×C4—114no—
527C22×C4—114no—
528C22×C4—224no—
529C22×C4—224no—
530C22×C4—222no—
531C22×C4—221no—
532C22×C4—224no—
533C22×C4—224no—
534C22×C4—444no—
535C22×C4—882no—
536C22×C4#433914yes—
537C22×C4D4×D1112yes—
538C22×C4D4×D1111yescharacteristic
539C22×C4D4×D1114yes—
540C22×C4C23×D1112yes—
541C22×C4C23×D1111yescharacteristic
542Q16—228no—
543SD16—228no—
544SD16—228no—
545D8—228no—
546M16—28no—
547M16—2216no—
548C2×C8—24no—
549C2×C8—114no—
550C2×C8—114no—
551C2×C8—1116no—
552C2×C8—112no—
553C2×C8—112no—
554C2×C8—2216no—
555C2×C8C23×D1114yes—
556C4⋊C4—24no—
557C4⋊C4—22no—
558C4⋊C4—114no—
559C4⋊C4—228no—
560C4⋊C4—228no—
561C4⋊C4—224no—
562C4⋊C4—222no—
563C4⋊C4C23×D1114yes—
564C22⋊C4—228no—
565C22⋊C4—228no—
566C22⋊C4—228no—
567C22⋊C4—228no—
568C11C2×#306011yescharacteristic, complemented, Sylow
569C23—22no—
570C23—22no—
571C23—22no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—114no—
576C23—224no—
577C23—224no—
578C23—224no—
579C23—222no—
580C23—442no—
581C23—442no—
582C23—442no—
583C23#6693714yes—
584C23C2×D4×D1112yes—
585C23C2×D4×D1111yescharacteristic
586Q8—22no—
587Q8—22no—
588Q8—42no—
589Q8—228no—
590Q8—222no—
591Q8—222no—
592Q8—442no—
593D4—22no—
594D4—22no—
595D4—48no—
596D4—42no—
597D4—2216no—
598D4—228no—
599D4—222no—
600D4—222no—
601D4—448no—
602D4—442no—
603D4—888no—
604D4—888no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—42no—
608C2×C4—44no—
609C2×C4—48no—
610C2×C4—84no—
611C2×C4—114no—
612C2×C4—224no—
613C2×C4—228no—
614C2×C4—224no—
615C2×C4—224no—
616C2×C4—224no—
617C2×C4—222no—
618C2×C4—442no—
619C2×C4—444no—
620C2×C4—448no—
621C2×C4—884no—
622C2×C4#6693714yes—
623C2×C4#6693718yes—
624C2×C4C2×#433912yes—
625C2×C4C2×#433914yes—
626C2×C4C2×D4×D1112yes—
627C2×C4C2×D4×D1111yescharacteristic
628C2×C4C2×D4×D1112yes—
629C2×C4C2×D4×D1114yes—
630C2×C4C24×D1111yescharacteristic
631C8—24no—
632C8—114no—
633C8—114no—
634C22—28no—
635C22—22no—
636C22—22no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—84no—
641C22—224no—
642C22—224no—
643C22—224no—
644C22—448no—
645C22—442no—
646C22—442no—
647C22—442no—
648C22—884no—
649C22C2×#6693714yes—
650C22C2×#6693712yes—
651C22#1062330612yes—
652C22#1062330912yes—
653C22C22×D4×D1111yescharacteristic
654C4—42no—
655C4—44no—
656C4—224no—
657C4—442no—
658C4—444no—
659C4C2×#6693714yes—
660C4C2×#6693712yes—
661C4C22×#433911yescharacteristic
662C4C22×D4×D1111yescharacteristic
663C2—24no—
664C2—82no—
665C2—444no—
666C2—882no—
667C2#1307827714yesdirect product factor
668C2C22×#6693711yescharacteristic
669C2C2×#1062330911yescharacteristic
670C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
hypercenterC2×#417D11
hypocenterC11C2×#3060
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C22×#67003C2semidirect
2. C22×#66960C2semidirect
3. C2×#10623041C2semidirect
4. C2×#10623364C2semidirect
5. #13078277C2direct (N × H)
6. C2×#10622429C2semidirect
7. C2×#10622395C2semidirect
8. C2×#10622420C2semidirect
9. C2×#10622391C2semidirect
10. C22×#66872C2semidirect
11. C2×#10622746C2semidirect
12. C2×C11×#417C2semidirect
19. #10623364C22semidirect
21. C2×#67003C22semidirect
35. C2×#66960C22semidirect
39. #10623041C22semidirect
44. C11×#417C22semidirect
47. #10622746C22semidirect
52. C2×#66872C22semidirect
53. #10622429C22semidirect
54. #10622420C22semidirect
55. #10622395C22semidirect
56. #10622391C22semidirect
120. C22×C11⋊C8D4semidirect
229. C2×C11⋊C8C2×D4semidirect
245. C2×#417D11semidirect
350. #417C2×D11semidirect
470. C2×C11#3060semidirect
568. C11C2×#3060semidirect
667. C2#13078277direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670032
C22×#669602
C2×#106230412
C2×#106233642
#130782772
C2×#106224292
C2×#106223952
C2×#106224202
C2×#106223912
C22×#668722
C2×#106227462
C2×C11×#4172
C2×#306011