Finite Group Databasebeta

← C2×#13078297 #15621009

Subgroups — C2×#13078297 #15621009

Order 2816.

2934 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66961C211yesmaximal, characteristic, complemented
2C22×#66960C211yesmaximal, characteristic, complemented
3C2×#10623041C211yesmaximal, characteristic, complemented
4C2×#10623056C211yesmaximal, characteristic, complemented
5#13078297C2116yesmaximal, direct product factor
6C2×#10622478C212yesmaximal, complemented
7C2×#10622499C212yesmaximal, complemented
8C2×#10622496C212yesmaximal, complemented
9C2×#10622477C212yesmaximal, complemented
10C2×#10622615C211yesmaximal, characteristic, complemented
11C22×#66873C211yesmaximal, characteristic, complemented
12C2×C11×#428C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C23×D44C2211yescharacteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66983—22no—
20C23×C11⋊C8C2211yescharacteristic
21C2×#66961—28no—
22C2×#66961C2218yescomplemented
23C2×#66960—28no—
24C2×#66960C2218yescomplemented
25C22×D88C2212yes—
26C22×#4314C2212yes—
27C22×#4313C2212yescomplemented
28C22×C8×D11C2212yescomplemented
29#10623056—24no—
30#10623056C2218yescomplemented
31#10623041—24no—
32#10623041C2218yescomplemented
33C2×#66950—21no—
34C2×#66950C2212yescomplemented
35C2×#66948—21no—
36C2×#66948C2212yes—
37C2×#66948C2212yes—
38C2×#66948C2212yescomplemented
39C2×#66935—22no—
40C2×#66928—21no—
41C2×#66927—21no—
42C11×#428C2218yescomplemented
43C2×C11×#107C2212yescomplemented
44C2×C11×#106C2212yescomplemented
45#10622615C2218yescomplemented
46C2×#66874C2211yescharacteristic, complemented
47C2×#66874C2211yescharacteristic, complemented
48C2×#66873C2212yes—
49C2×#66873C2212yes—
50C2×#66873C2218yescomplemented
51C2×#66873C2211yescharacteristic, complemented
52C2×#66873C2211yescharacteristic, complemented
53#10622499C22116yescomplemented
54#10622496C22116yescomplemented
55#10622478C22116yescomplemented
56#10622477C22116yescomplemented
57C24×D11—21no—
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×C22⋊D11D412yes—
62C2×#4339—24no—
63C2×#4339—24no—
64C2×#4339—22no—
65C2×#4339—24no—
66C2×#4339—24no—
67C2×#4339D414yes—
68C2×#4339C2314yes—
69C2×#4339C2314yes—
70C22×D44—24no—
71C22×D44—24no—
72C22×D44—21no—
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44—22no—
77C22×D44D411yescharacteristic
78C22×D44C2312yes—
79C22×D44C2311yescharacteristic
80C22×D44C2314yes—
81C22×C4×D11—21no—
82C22×C4×D11C2312yes—
83C22×Dic22D411yescharacteristic
84C22×Dic22C2311yescharacteristic
85C2×C11×M16D418yescomplemented
86C2×C11×M16C2314yes—
87C22×C8×C11C2312yes—
88C11×#117—22no—
89C11×#117C2314yes—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2314yes—
96C2×C11×C22⋊C4—21no—
97C2×C42×C11—21no—
98#66983—216no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×C4⋊Dic11—22no—
104C22×C11⋊C8—24no—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2314yes—
108#66961—232no—
109#66960—232no—
110C2×D88—28no—
111C2×D88C2318yes—
112C2×#4314—28no—
113C2×#4314C2318yes—
114C2×#4313—28no—
115C2×#4313C2318yescomplemented
116C2×C8×D11—28no—
117C2×C8×D11C2318yescomplemented
118#66950—24no—
119#66950—28no—
120#66950C2318yescomplemented
121#66948—28no—
122#66948—24no—
123#66948—24no—
124#66948—24no—
125#66948C2318yes—
126#66948C2318yes—
127#66948C2318yescomplemented
128#66935—216no—
129#66928—28no—
130#66927—28no—
131C11×#107C2318yescomplemented
132C11×#106C2318yescomplemented
133#66874C2314yescomplemented
134#66874C2314yescomplemented
135#66873C2318yes—
136#66873C2318yes—
137#66873C2314yescomplemented
138#66873C2314yescomplemented
139C2×#3062—111nomaximal, Sylow
140C24×C11C2×D411yescharacteristic
141C23×D11—21no—
142C23×D11—22no—
143C23×D11—24no—
144C23×D11—44no—
145C23×D11—82no—
146C23×D11—82no—
147C23×D11C2×D412yes—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—24no—
152C22×C4×C11—82no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D414yes—
156C22×C4×C11#4114yes—
157C22×C4×C11C2411yescharacteristic
158C22×C4×C11C2412yes—
159C2×C22⋊D11—28no—
160C2×C22⋊D11—24no—
161C2×C22⋊D11—44no—
162C2×C22⋊D11C2×D418yes—
163C22×Dic11—21no—
164C22×Dic11C2×D412yes—
165#4339—216no—
166#4339—28no—
167#4339—28no—
168#4339—28no—
169#4339—28no—
170#4339—48no—
171C2×D44—28no—
172C2×D44—28no—
173C2×D44—28no—
174C2×D44—24no—
175C2×D44—24no—
176C2×D44—22no—
177C2×D44—21no—
178C2×D44—24no—
179C2×D44—22no—
180C2×D44—28no—
181C2×D44—24no—
182C2×D44—28no—
183C2×D44—22no—
184C2×D44—44no—
185C2×D44—48no—
186C2×D44—84no—
187C2×D44—84no—
188C2×D44—84no—
189C2×D44C2×D414yes—
190C2×D44C2414yes—
191C2×D44C2412yes—
192C2×C4×D11—24no—
193C2×C4×D11—24no—
194C2×C4×D11—24no—
195C2×C4×D11—44no—
196C2×C4×D11C2×D414yes—
197C2×C4×D11C2414yes—
198C2×Dic22—24no—
199C2×Dic22—22no—
200C2×Dic22—21no—
201C2×Dic22—22no—
202C2×Dic22C2×D414yes—
203C2×Dic22C2412yes—
204C11×M16C2×D4116yescomplemented
205C2×C8×C11C2×D418yes—
206C2×C8×C11C2414yes—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—22no—
211C11×C4⋊C4C2414yes—
212C11×C4⋊C4C2412yes—
213C11×C4⋊C4C2412yes—
214C11×C22⋊C4—24no—
215C42×C11—24no—
216(C2×D11)⋊C4—28no—
217(C2×D11)⋊C4—28no—
218(C2×D11)⋊C4—28no—
219(C2×D11)⋊C4—28no—
220C4⋊Dic11—28no—
221C2×C11⋊C8—22no—
222C2×C11⋊C8—22no—
223C2×C11⋊C8—28no—
224C2×C11⋊C8C2412yes—
225C2×C11⋊C8C2412yes—
226D88—216no—
227#4314—216no—
228#4313—216no—
229C8×D11—216no—
230C22×AGL(1,ℤ/8)—111no—
231C22×#131—111no—
232C2×#537—111no—
233C2×#535—111no—
234#3062—1116no—
235C2×#469—112no—
236C2×#468—112no—
237C2×#466—112no—
238C2×#465—112no—
239C2×#428D1111yescharacteristic, complemented
240C2×#416—111no—
241C22×#102—111no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11#12114yes—
245C23×C11C22×D412yes—
246C23×C11C22×D411yescharacteristic
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—22no—
251C22×D11—24no—
252C22×D11—42no—
253C22×D11—48no—
254C22×D11—44no—
255C22×D11—42no—
256C22×D11—44no—
257C22×D11—44no—
258C22×D11—42no—
259C22×D11—84no—
260C22×D11—84no—
261C22×D11—816no—
262C22×D11C22×D414yes—
263C2×C4×C11—24no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—42no—
267C2×C4×C11—44no—
268C2×C4×C11—42no—
269C2×C4×C11—84no—
270C2×C4×C11#12114yes—
271C2×C4×C11#12118yes—
272C2×C4×C11C22×D412yes—
273C2×C4×C11C22×D414yes—
274C2×C4×C11C22×D412yes—
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C2×#4112yes—
277C2×C4×C11C2×#4114yes—
278C2×C4×C11C2511yescharacteristic
279C22⋊D11—216no—
280C22⋊D11—48no—
281C2×Dic11—24no—
282C2×Dic11—22no—
283C2×Dic11—42no—
284C2×Dic11C22×D414yes—
285D44—28no—
286D44—24no—
287D44—22no—
288D44—24no—
289D44—22no—
290D44—48no—
291D44—44no—
292D44—42no—
293D44—88no—
294D44—88no—
295D44—88no—
296C4×D11—28no—
297C4×D11—24no—
298C4×D11—24no—
299C4×D11—48no—
300Dic22—28no—
301Dic22—22no—
302Dic22—22no—
303Dic22—42no—
304C8×C11C22×D418yes—
305C11⋊C8—22no—
306C11⋊C8—22no—
307C22×#41—111no—
308C22×#41—111no—
309C23×D4—111no—
310C2×AGL(1,ℤ/8)—118no—
311C2×AGL(1,ℤ/8)—228no—
312C22×SD16—112no—
313C22×D8—112no—
314C2×#131—118no—
315C2×#131—228no—
316C22×M16—112no—
317C22×M16C2×D1111yescharacteristic
318C23×C8—111no—
319C23×C8—112no—
320#537—118no—
321#537—224no—
322#535—118no—
323#535—224no—
324C2×#127—221no—
325C2×#124—221no—
326C2×C22⋊Q8—112no—
327C2×C22⋊Q8—221no—
328C2×#121—112no—
329C2×#121—112no—
330C2×#121—112no—
331C2×#121—221no—
332C2×#121—222no—
333C2×#120—222no—
334C2×#117C2×D1111yescharacteristic
335C22×C4⋊C4C2×D1111yescharacteristic
336#469—1116no—
337#468—1116no—
338#466—1116no—
339#465—1116no—
340#428C2×D1118yescomplemented
341C2×#107C2×D1112yescomplemented
342C2×#106C2×D1112yescomplemented
343#416—118no—
344C2×#103—111no—
345C2×#103—111no—
346C2×#102—112no—
347C2×#102—112no—
348C2×#102—118no—
349C2×#102—111no—
350C2×#102—111no—
351C22×C11—28no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11C2×#12114yes—
355C22×C11C2×#12112yes—
356C22×C11#57612yes—
357C22×C11#57712yes—
358C22×C11C23×D411yescharacteristic
359C2×D11—24no—
360C2×D11—24no—
361C2×D11—24no—
362C2×D11—48no—
363C2×D11—44no—
364C2×D11—42no—
365C2×D11—44no—
366C2×D11—42no—
367C2×D11—42no—
368C2×D11—44no—
369C2×D11—816no—
370C2×D11—84no—
371C2×D11—88no—
372C4×C11—44no—
373C4×C11—42no—
374C4×C11—42no—
375C4×C11C2×#12114yes—
376C4×C11C2×#12112yes—
377C4×C11C23×D411yescharacteristic
378C4×C11C22×#4111yescharacteristic
379Dic11—24no—
380Dic11—42no—
381C25—221no—
382C2×#41—114no—
383C2×#41—114no—
384C2×#41—114no—
385C2×#41—224no—
386C2×#41—222no—
387C2×#41—224no—
388C2×#41—224no—
389C2×#41—224no—
390C22×Q8—111no—
391C22×Q8—111no—
392C22×D4—112no—
393C22×D4—111no—
394C22×D4—111no—
395C22×D4—112no—
396C22×D4—114no—
397C22×D4—222no—
398C22×D4—222no—
399C22×D4—222no—
400C22×D4—221no—
401C22×D4—224no—
402C22×D4—221no—
403C22×D4—222no—
404C22×D4—224no—
405C23×C4—21no—
406C23×C4—112no—
407C23×C4—221no—
408C23×C4C22×D1111yescharacteristic
409AGL(1,ℤ/8)—2232no—
410C2×SD16—118no—
411C2×SD16—228no—
412C2×D8—118no—
413C2×D8—228no—
414#131—2232no—
415C2×M16—118no—
416C2×M16—228no—
417C2×M16D4418yescomplemented
418C2×M16C22×D1114yes—
419C22×C8—111no—
420C22×C8—111no—
421C22×C8—114no—
422C22×C8—118no—
423C22×C8—224no—
424C22×C8—228no—
425C22×C8C22×D1112yes—
426#127—228no—
427#124—228no—
428C22⋊Q8—118no—
429C22⋊Q8—224no—
430C22⋊Q8—228no—
431#121—118no—
432#121—118no—
433#121—118no—
434#121—224no—
435#121—224no—
436#121—224no—
437#121—228no—
438#121—2216no—
439#120—2216no—
440#117—22no—
441#117C22×D1114yes—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—222no—
445C2×C4⋊C4C22×D1112yes—
446C2×C4⋊C4C22×D1114yes—
447C2×C4⋊C4C22×D1111yescharacteristic
448C2×C4⋊C4C22×D1111yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—222no—
451C2×C22⋊C4—222no—
452C2×C22⋊C4—222no—
453C2×C22⋊C4—222no—
454C2×C42—21no—
455#107C22×D1118yescomplemented
456#106C22×D1118yescomplemented
457#103—114no—
458#103—114no—
459#102—118no—
460#102—118no—
461#102—114no—
462#102—114no—
463C2×C11—24no—
464C2×C11#306214yescomplemented
465C2×C11C22×#12111yescharacteristic
466C2×C11C2×#57611yescharacteristic
467C2×C11C2×#57711yescharacteristic
468D11—44no—
469D11—82no—
470D11—84no—
471C24—112no—
472C24—221no—
473C24—222no—
474C24—224no—
475C24—444no—
476C24—882no—
477C24—882no—
478C24D4×D1111yescharacteristic
479#41—2216no—
480#41—228no—
481#41—228no—
482#41—228no—
483#41—228no—
484#41—448no—
485C2×Q8—114no—
486C2×Q8—112no—
487C2×Q8—224no—
488C2×Q8—221no—
489C2×Q8—222no—
490C2×Q8—222no—
491C2×D4—118no—
492C2×D4—114no—
493C2×D4—112no—
494C2×D4—114no—
495C2×D4—228no—
496C2×D4—228no—
497C2×D4—228no—
498C2×D4—228no—
499C2×D4—224no—
500C2×D4—224no—
501C2×D4—222no—
502C2×D4—224no—
503C2×D4—228no—
504C2×D4—222no—
505C2×D4—221no—
506C2×D4—224no—
507C2×D4—224no—
508C2×D4—228no—
509C2×D4—222no—
510C2×D4—444no—
511C2×D4—444no—
512C2×D4—448no—
513C2×D4—884no—
514C2×D4—884no—
515C2×D4—884no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—82no—
521C22×C4—112no—
522C22×C4—114no—
523C22×C4—114no—
524C22×C4—224no—
525C22×C4—224no—
526C22×C4—221no—
527C22×C4—224no—
528C22×C4—444no—
529C22×C4C2×D4414yes—
530C22×C4D4×D1112yes—
531C22×C4D4×D1111yescharacteristic
532C22×C4#434314yes—
533C22×C4C23×D1112yes—
534C22×C4C23×D1111yescharacteristic
535SD16—2216no—
536D8—2216no—
537M16—2216no—
538M16C2×D44116yescomplemented
539C2×C8—112no—
540C2×C8—112no—
541C2×C8—222no—
542C2×C8—222no—
543C2×C8—228no—
544C2×C8—2216no—
545C2×C8C2×D4418yes—
546C2×C8C23×D1114yes—
547C4⋊C4—24no—
548C4⋊C4—22no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—228no—
552C4⋊C4C23×D1114yes—
553C4⋊C4C23×D1112yes—
554C4⋊C4C23×D1112yes—
555C22⋊C4—24no—
556C22⋊C4—228no—
557C22⋊C4—228no—
558C22⋊C4—228no—
559C22⋊C4—228no—
560C42—24no—
561C11C2×#306211yescharacteristic, complemented, Sylow
562C23—22no—
563C23—22no—
564C23—114no—
565C23—224no—
566C23—224no—
567C23—224no—
568C23—222no—
569C23—224no—
570C23—442no—
571C23—448no—
572C23—444no—
573C23—442no—
574C23—444no—
575C23—444no—
576C23—442no—
577C23—884no—
578C23—884no—
579C23—8816no—
580C23#6694814yes—
581C23C2×D4×D1112yes—
582C23C2×D4×D1111yescharacteristic
583Q8—228no—
584Q8—222no—
585Q8—222no—
586Q8—442no—
587D4—2216no—
588D4—228no—
589D4—222no—
590D4—224no—
591D4—224no—
592D4—222no—
593D4—448no—
594D4—444no—
595D4—448no—
596D4—442no—
597D4—888no—
598D4—888no—
599D4—888no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—24no—
603C2×C4—44no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—84no—
607C2×C4—114no—
608C2×C4—224no—
609C2×C4—228no—
610C2×C4—224no—
611C2×C4—224no—
612C2×C4—222no—
613C2×C4—442no—
614C2×C4—448no—
615C2×C4#6694814yes—
616C2×C4#6694818yes—
617C2×C4C22×D4412yes—
618C2×C4C22×D4414yes—
619C2×C4C2×D4×D1112yes—
620C2×C4C2×D4×D1111yescharacteristic
621C2×C4C2×#434312yes—
622C2×C4C2×#434314yes—
623C2×C4C24×D1111yescharacteristic
624C8—222no—
625C8—222no—
626C8C22×D4418yes—
627C22—28no—
628C22—22no—
629C22—22no—
630C22—224no—
631C22—224no—
632C22—224no—
633C22—448no—
634C22—442no—
635C22—444no—
636C22—444no—
637C22—442no—
638C22—442no—
639C22—444no—
640C22—8816no—
641C22—888no—
642C22—884no—
643C22C2×#6694814yes—
644C22C2×#6694812yes—
645C22#1062330512yes—
646C22#1062330912yes—
647C22C22×D4×D1111yescharacteristic
648C4—44no—
649C4—42no—
650C4—42no—
651C4—224no—
652C4—442no—
653C4C2×#6694812yes—
654C4C2×#6694814yes—
655C4C23×D4411yescharacteristic
656C4C22×#434311yescharacteristic
657C2—24no—
658C2—444no—
659C2—884no—
660C2—882no—
661C2#1307829714yesdirect product factor
662C2C22×#6694811yescharacteristic
663C2C2×#1062330511yescharacteristic
664C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
hypercenterC2×#428D11
hypocenterC11C2×#3062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C22×#66961C2semidirect
2. C22×#66960C2semidirect
3. C2×#10623041C2semidirect
4. C2×#10623056C2semidirect
5. #13078297C2direct (N × H)
6. C2×#10622478C2semidirect
7. C2×#10622499C2semidirect
8. C2×#10622496C2semidirect
9. C2×#10622477C2semidirect
10. C2×#10622615C2semidirect
11. C22×#66873C2semidirect
12. C2×C11×#428C2semidirect
22. C2×#66961C22semidirect
24. C2×#66960C22semidirect
27. C22×#4313C22semidirect
28. C22×C8×D11C22semidirect
30. #10623056C22semidirect
32. #10623041C22semidirect
34. C2×#66950C22semidirect
38. C2×#66948C22semidirect
42. C11×#428C22semidirect
43. C2×C11×#107C22semidirect
44. C2×C11×#106C22semidirect
45. #10622615C22semidirect
46. C2×#66874C22semidirect
47. C2×#66874C22semidirect
50. C2×#66873C22semidirect
51. C2×#66873C22semidirect
52. C2×#66873C22semidirect
53. #10622499C22semidirect
54. #10622496C22semidirect
55. #10622478C22semidirect
56. #10622477C22semidirect
85. C2×C11×M16D4semidirect
115. C2×#4313C23semidirect
117. C2×C8×D11C23semidirect
120. #66950C23semidirect
127. #66948C23semidirect
131. C11×#107C23semidirect
132. C11×#106C23semidirect
133. #66874C23semidirect
134. #66874C23semidirect
137. #66873C23semidirect
138. #66873C23semidirect
204. C11×M16C2×D4semidirect
239. C2×#428D11semidirect
340. #428C2×D11semidirect
341. C2×#107C2×D11semidirect
342. C2×#106C2×D11semidirect
417. C2×M16D44semidirect
455. #107C22×D11semidirect
456. #106C22×D11semidirect
464. C2×C11#3062semidirect
538. M16C2×D44semidirect
561. C11C2×#3062semidirect
661. C2#13078297direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669612
C22×#669602
C2×#106230412
C2×#106230562
#130782972
C2×#106224782
C2×#106224992
C2×#106224962
C2×#106224772
C2×#106226152
C22×#668732
C2×C11×#4282
C2×#306211