Finite Group Databasebeta

← C2×#13078294 #15621006

Subgroups — C2×#13078294 #15621006

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×#66985C211yesmaximal, characteristic, complemented
2C22×#66954C211yesmaximal, characteristic, complemented
3C2×#10623041C211yesmaximal, characteristic, complemented
4C2×#10623336C211yesmaximal, characteristic, complemented
5#13078294C2116yesmaximal, direct product factor
6C2×#10622395C212yesmaximal, complemented
7C2×#10622393C212yesmaximal, complemented
8C2×#10622388C212yesmaximal, complemented
9C2×#10622391C212yesmaximal, complemented
10C2×#10622577C211yesmaximal, characteristic, complemented
11C2×#10622726C211yesmaximal, characteristic, complemented
12C22×C11×#102C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C22×#4339C2211yescharacteristic
16C23×C8×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#67006—22no—
19#10623336—24no—
20#10623336C2218yescomplemented
21C2×#66993—21no—
22C2×#66991C2212yes—
23C2×#66991C2212yes—
24C2×#66989—21no—
25C22×#4324C2212yes—
26C2×#66985—28no—
27C2×#66985C2218yescomplemented
28C22×#4323C2212yes—
29C2×#66983—22no—
30C2×#66979C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32C2×#66954—28no—
33C2×#66954C2218yescomplemented
34C22×#4313C2212yescomplemented
35C22×C8×D11C2212yescomplemented
36#10623041—24no—
37#10623041C2218yescomplemented
38C2×#66950—21no—
39C2×#66950C2212yescomplemented
40C2×#66948—21no—
41C2×#66948C2212yescomplemented
42C2×C11×#102C2212yes—
43C2×C11×#102C2212yes—
44C2×C11×#102C2218yescomplemented
45#10622726C2218yescomplemented
46C2×#66885C2211yescharacteristic, complemented
47C2×#66885C2211yescharacteristic, complemented
48C2×#66880C2211yescharacteristic, complemented
49C2×#66880C2211yescharacteristic, complemented
50#10622577C2218yescomplemented
51C2×#66872C2212yescomplemented
52C2×#66871C2212yescomplemented
53#10622395C22116yescomplemented
54#10622393C22116yescomplemented
55#10622391C22116yescomplemented
56#10622388C22116yescomplemented
57C25×C11—21no—
58C22×D4×C11—24no—
59C22×D4×C11—21no—
60C22×D4×C11—22no—
61C22×D4×C11—24no—
62C22×D4×C11C2312yes—
63C22×D4×C11C2314yes—
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C22×C22⋊D11—22no—
68C22×C22⋊D11—22no—
69C22×C22⋊D11D412yes—
70C2×#4339—24no—
71C2×#4339—24no—
72C2×#4339—22no—
73C2×#4339—24no—
74C2×#4339—24no—
75C2×#4339D414yes—
76C2×#4339C2314yes—
77C2×#4339C2314yes—
78C22×D44—22no—
79C22×D44D411yescharacteristic
80C22×D44C2311yescharacteristic
81C22×C4×D11—21no—
82C22×C4×D11C2312yes—
83C22×Dic22D411yescharacteristic
84C22×Dic22C2311yescharacteristic
85C22×C8×C11—24no—
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2314yes—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2314yes—
93#67006—216no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97#66993—28no—
98#66991—24no—
99#66991—24no—
100#66991C2318yes—
101#66991C2318yes—
102#66989—28no—
103C2×#4324—28no—
104C2×#4324C2318yes—
105#66985—232no—
106C2×#4323—28no—
107C2×#4323C2318yes—
108#66983—216no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111#66979—22no—
112#66979C2314yes—
113C2×C4⋊Dic11—22no—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4×Dic11—21no—
117C2×#4318D418yescomplemented
118C2×#4318C2314yes—
119C22×C11⋊C8C2312yes—
120#66954—232no—
121C2×#4313—28no—
122C2×#4313C2318yescomplemented
123C2×C8×D11—28no—
124C2×C8×D11C2318yescomplemented
125#66950—24no—
126#66950—28no—
127#66950C2318yescomplemented
128#66948—28no—
129#66948—24no—
130#66948C2318yescomplemented
131C11×#102C2318yes—
132C11×#102C2318yes—
133#66885C2314yescomplemented
134#66885C2314yescomplemented
135#66880C2314yescomplemented
136#66880C2314yescomplemented
137#66872C2318yescomplemented
138#66871C2318yescomplemented
139C2×#3062—111nomaximal, Sylow
140C24×C11—22no—
141C24×C11—24no—
142C24×C11—44no—
143C24×C11—82no—
144C24×C11—82no—
145C24×C11C2×D411yescharacteristic
146C23×D11—21no—
147C23×D11C2×D412yes—
148C2×D4×C11—24no—
149C2×D4×C11—28no—
150C2×D4×C11—24no—
151C2×D4×C11—22no—
152C2×D4×C11—24no—
153C2×D4×C11—28no—
154C2×D4×C11—44no—
155C2×D4×C11—48no—
156C2×D4×C11C2414yes—
157C22×C4×C11—22no—
158C22×C4×C11—24no—
159C22×C4×C11—82no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D414yes—
163C22×C4×C11#4114yes—
164C22×C4×C11C2411yescharacteristic
165C22×C4×C11C2412yes—
166C2×C22⋊D11—28no—
167C2×C22⋊D11—24no—
168C2×C22⋊D11—28no—
169C2×C22⋊D11—28no—
170C2×C22⋊D11—44no—
171C2×C22⋊D11—84no—
172C2×C22⋊D11—84no—
173C2×C22⋊D11C2×D418yes—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11C2×D412yes—
178#4339—216no—
179#4339—28no—
180#4339—28no—
181#4339—28no—
182#4339—28no—
183#4339—48no—
184C2×D44—28no—
185C2×D44—24no—
186C2×D44—21no—
187C2×D44—22no—
188C2×D44—22no—
189C2×D44—84no—
190C2×D44C2×D414yes—
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—
204C2×C8×C11—22no—
205C2×C8×C11—22no—
206C2×C8×C11—28no—
207C2×C8×C11C2412yes—
208C2×C8×C11C2412yes—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—22no—
211C11×C4⋊C4C2414yes—
212C22⋊Dic11—28no—
213C22⋊Dic11—28no—
214C22⋊Dic11—24no—
215#4324—216no—
216#4323—216no—
217(C2×D11)⋊C4—28no—
218(C2×D11)⋊C4—28no—
219C4⋊Dic11—28no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11C2412yes—
223C4⋊Dic11C2412yes—
224C4×Dic11—24no—
225#4318C2×D4116yescomplemented
226C2×C11⋊C8C2×D418yes—
227C2×C11⋊C8C2414yes—
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×#428—111no—
240C2×#416—111no—
241C22×#102D1111yescharacteristic, complemented
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—24no—
245C23×C11—48no—
246C23×C11—44no—
247C23×C11—44no—
248C23×C11—44no—
249C23×C11—84no—
250C23×C11—84no—
251C23×C11—816no—
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—
263D4×C11—24no—
264D4×C11—24no—
265D4×C11—48no—
266D4×C11—44no—
267C2×C4×C11—24no—
268C2×C4×C11—44no—
269C2×C4×C11—84no—
270C2×C4×C11#12114yes—
271C2×C4×C11#12118yes—
272C2×C4×C11C22×D412yes—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D412yes—
275C2×C4×C11C22×D414yes—
276C2×C4×C11C2×#4112yes—
277C2×C4×C11C2×#4114yes—
278C2×C4×C11C2511yescharacteristic
279C22⋊D11—216no—
280C22⋊D11—48no—
281C22⋊D11—88no—
282C22⋊D11—88no—
283C2×Dic11—24no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11C22×D414yes—
291D44—28no—
292D44—22no—
293D44—22no—
294D44—42no—
295D44—88no—
296C4×D11—28no—
297C4×D11—24no—
298C4×D11—24no—
299C4×D11—48no—
300Dic22—28no—
301Dic22—22no—
302Dic22—22no—
303Dic22—42no—
304C8×C11—22no—
305C8×C11—22no—
306C11⋊C8C22×D418yes—
307C22×#41—111no—
308C22×#41—111no—
309C23×D4C2×D1111yescharacteristic
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—111no—
317C22×M16—112no—
318C23×C8—112no—
319C23×C8C2×D1111yescharacteristic
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×#117—111no—
335C22×C4⋊C4C2×D1111yescharacteristic
336#469—1116no—
337#468—1116no—
338#466—1116no—
339#465—1116no—
340#428—118no—
341C2×#107—112no—
342C2×#106—112no—
343#416—118no—
344C2×#103—111no—
345C2×#103—111no—
346C2×#102—111no—
347C2×#102—111no—
348C2×#102C2×D1112yes—
349C2×#102C2×D1112yes—
350C2×#102C2×D1118yescomplemented
351C22×C11—28no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—44no—
355C22×C11—44no—
356C22×C11—44no—
357C22×C11—816no—
358C22×C11—88no—
359C22×C11C2×#12114yes—
360C22×C11C2×#12112yes—
361C22×C11#57612yes—
362C22×C11#57712yes—
363C22×C11C23×D411yescharacteristic
364C2×D11—24no—
365C2×D11—24no—
366C2×D11—24no—
367C2×D11—48no—
368C2×D11—42no—
369C2×D11—42no—
370C2×D11—42no—
371C2×D11—84no—
372C4×C11—44no—
373C4×C11C2×#12114yes—
374C4×C11C2×#12112yes—
375C4×C11C23×D411yescharacteristic
376C4×C11C22×#4111yescharacteristic
377Dic11—24no—
378Dic11—42no—
379Dic11—42no—
380Dic11—42no—
381C25—21no—
382C2×#41—114no—
383C2×#41—114no—
384C2×#41—114no—
385C2×#41—224no—
386C2×#41—224no—
387C2×#41—222no—
388C2×#41—224no—
389C2×#41—224no—
390C22×Q8—111no—
391C22×Q8—111no—
392C22×D4—24no—
393C22×D4—24no—
394C22×D4—21no—
395C22×D4—22no—
396C22×D4—112no—
397C22×D4—111no—
398C22×D4—111no—
399C22×D4—222no—
400C22×D4—221no—
401C22×D4—222no—
402C22×D4—222no—
403C22×D4C22×D1112yes—
404C22×D4C22×D1114yes—
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—114no—
417C2×M16—118no—
418C2×M16—228no—
419C22×C8—24no—
420C22×C8—112no—
421C22×C8—118no—
422C22×C8—228no—
423C22×C8C22×D1111yescharacteristic
424C22×C8C22×D1111yescharacteristic
425C22×C8C22×D1114yes—
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—228no—
436#121—2216no—
437#121—224no—
438#121—224no—
439#120—2216no—
440#117—114no—
441#117—222no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—111no—
445C2×C4⋊C4—111no—
446C2×C4⋊C4—222no—
447C2×C4⋊C4C22×D1112yes—
448C2×C4⋊C4C22×D1114yes—
449C2×C22⋊C4—222no—
450C2×C22⋊C4—222no—
451C2×C22⋊C4—222no—
452C2×C22⋊C4—222no—
453C2×C22⋊C4—221no—
454C2×C42—221no—
455#107—118no—
456#106—118no—
457#103—114no—
458#103—114no—
459#102—114no—
460#102—114no—
461#102C22×D1118yes—
462#102C22×D1118yes—
463C2×C11—24no—
464C2×C11—84no—
465C2×C11#306214yescomplemented
466C2×C11C22×#12111yescharacteristic
467C2×C11C2×#57611yescharacteristic
468C2×C11C2×#57711yescharacteristic
469D11—44no—
470D11—82no—
471C24—22no—
472C24—24no—
473C24—44no—
474C24—82no—
475C24—82no—
476C24—112no—
477C24—221no—
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—24no—
492C2×D4—28no—
493C2×D4—24no—
494C2×D4—28no—
495C2×D4—22no—
496C2×D4—24no—
497C2×D4—44no—
498C2×D4—48no—
499C2×D4—118no—
500C2×D4—114no—
501C2×D4—112no—
502C2×D4—228no—
503C2×D4—228no—
504C2×D4—224no—
505C2×D4—228no—
506C2×D4—228no—
507C2×D4—224no—
508C2×D4—222no—
509C2×D4—222no—
510C2×D4—221no—
511C2×D4—444no—
512C2×D4—884no—
513C2×D4—884no—
514C2×D4—884no—
515C2×D4C23×D1114yes—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—82no—
519C22×C4—112no—
520C22×C4—114no—
521C22×C4—114no—
522C22×C4—224no—
523C22×C4—224no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4—224no—
528C22×C4—444no—
529C22×C4#433914yes—
530C22×C4D4×D1112yes—
531C22×C4D4×D1111yescharacteristic
532C22×C4D4×D1114yes—
533C22×C4C23×D1112yes—
534C22×C4C23×D1111yescharacteristic
535SD16—2216no—
536D8—2216no—
537M16—1116no—
538M16—2216no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—28no—
542C2×C8—118no—
543C2×C8—114no—
544C2×C8—2216no—
545C2×C8C23×D1112yes—
546C2×C8C23×D1112yes—
547C4⋊C4—24no—
548C4⋊C4—22no—
549C4⋊C4—112no—
550C4⋊C4—112no—
551C4⋊C4—228no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4C23×D1114yes—
555C22⋊C4—228no—
556C22⋊C4—228no—
557C22⋊C4—228no—
558C22⋊C4—228no—
559C22⋊C4—224no—
560C42—224no—
561C11C2×#306211yescharacteristic, complemented, Sylow
562C23—22no—
563C23—22no—
564C23—24no—
565C23—48no—
566C23—44no—
567C23—44no—
568C23—44no—
569C23—84no—
570C23—84no—
571C23—816no—
572C23—114no—
573C23—224no—
574C23—224no—
575C23—224no—
576C23—222no—
577C23—442no—
578C23—442no—
579C23—442no—
580C23#6693714yes—
581C23C2×D4×D1112yes—
582C23C2×D4×D1111yescharacteristic
583Q8—228no—
584Q8—222no—
585Q8—222no—
586Q8—442no—
587D4—24no—
588D4—24no—
589D4—44no—
590D4—48no—
591D4—2216no—
592D4—228no—
593D4—222no—
594D4—222no—
595D4—448no—
596D4—442no—
597D4—888no—
598D4—888no—
599D4—888no—
600C2×C4—24no—
601C2×C4—44no—
602C2×C4—84no—
603C2×C4—114no—
604C2×C4—224no—
605C2×C4—228no—
606C2×C4—224no—
607C2×C4—224no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—442no—
612C2×C4—442no—
613C2×C4—442no—
614C2×C4—448no—
615C2×C4#6693714yes—
616C2×C4#6693718yes—
617C2×C4C2×#433912yes—
618C2×C4C2×#433914yes—
619C2×C4C2×D4×D1112yes—
620C2×C4C2×D4×D1111yescharacteristic
621C2×C4C2×D4×D1112yes—
622C2×C4C2×D4×D1114yes—
623C2×C4C24×D1111yescharacteristic
624C8—22no—
625C8—22no—
626C8—118no—
627C22—28no—
628C22—22no—
629C22—22no—
630C22—44no—
631C22—44no—
632C22—44no—
633C22—816no—
634C22—88no—
635C22—224no—
636C22—224no—
637C22—224no—
638C22—448no—
639C22—442no—
640C22—442no—
641C22—442no—
642C22—884no—
643C22C2×#6693714yes—
644C22C2×#6693712yes—
645C22#1062328812yes—
646C22#1062329312yes—
647C22C22×D4×D1111yescharacteristic
648C4—44no—
649C4—224no—
650C4—442no—
651C4—442no—
652C4—442no—
653C4C2×#6693712yes—
654C4C2×#6693714yes—
655C4C22×#433911yescharacteristic
656C4C22×D4×D1111yescharacteristic
657C2—24no—
658C2—84no—
659C2—444no—
660C2—882no—
661C2#1307829414yesdirect product factor
662C2C22×#6693711yescharacteristic
663C2C2×#1062328811yescharacteristic
664C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#102C2
socleC23×C11C22×D4
hypercenterC22×#102D11
hypocenterC11C2×#3062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C22×#66985C2semidirect
2. C22×#66954C2semidirect
3. C2×#10623041C2semidirect
4. C2×#10623336C2semidirect
5. #13078294C2direct (N × H)
6. C2×#10622395C2semidirect
7. C2×#10622393C2semidirect
8. C2×#10622388C2semidirect
9. C2×#10622391C2semidirect
10. C2×#10622577C2semidirect
11. C2×#10622726C2semidirect
12. C22×C11×#102C2semidirect
20. #10623336C22semidirect
27. C2×#66985C22semidirect
33. C2×#66954C22semidirect
34. C22×#4313C22semidirect
35. C22×C8×D11C22semidirect
37. #10623041C22semidirect
39. C2×#66950C22semidirect
41. C2×#66948C22semidirect
44. C2×C11×#102C22semidirect
45. #10622726C22semidirect
46. C2×#66885C22semidirect
47. C2×#66885C22semidirect
48. C2×#66880C22semidirect
49. C2×#66880C22semidirect
50. #10622577C22semidirect
51. C2×#66872C22semidirect
52. C2×#66871C22semidirect
53. #10622395C22semidirect
54. #10622393C22semidirect
55. #10622391C22semidirect
56. #10622388C22semidirect
117. C2×#4318D4semidirect
122. C2×#4313C23semidirect
124. C2×C8×D11C23semidirect
127. #66950C23semidirect
130. #66948C23semidirect
133. #66885C23semidirect
134. #66885C23semidirect
135. #66880C23semidirect
136. #66880C23semidirect
137. #66872C23semidirect
138. #66871C23semidirect
225. #4318C2×D4semidirect
241. C22×#102D11semidirect
350. C2×#102C2×D11semidirect
465. C2×C11#3062semidirect
561. C11C2×#3062semidirect
661. C2#13078294direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669852
C22×#669542
C2×#106230412
C2×#106233362
#130782942
C2×#106223952
C2×#106223932
C2×#106223882
C2×#106223912
C2×#106225772
C2×#106227262
C22×C11×#1022
C2×#306211