Finite Group Databasebeta

← C2×#13066863 #14675439

Subgroups — C2×#13066863 #14675439

Order 2816.

4622 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Dic11C211yesmaximal, characteristic
2C23×C22⋊Dic11C211yesmaximal, characteristic
3C22×C11⋊#95C212yesmaximal, complemented
4C22×C11⋊#95C212yesmaximal, complemented
5#13066863C218yesmaximal, direct product factor
6C23×C11×C22⋊C4C211yesmaximal, characteristic
7C26×C11C2211yescharacteristic
8C24×C4×C11C2212yes—
9C24×Dic11C2211yescharacteristic
10C24×Dic11C2211yescharacteristic
11C24×Dic11C2212yes—
12C22×C11×C22⋊C4—24no—
13C22×C11×C22⋊C4—28no—
14C22×C11×C22⋊C4C2214yes—
15C22×C22⋊Dic11—24no—
16C22×C22⋊Dic11—24no—
17C22×C22⋊Dic11—24no—
18C22×C22⋊Dic11—28no—
19C22×C22⋊Dic11C418yescomplemented
20C22×C22⋊Dic11C2214yes—
21C22×C22⋊Dic11C2214yes—
22C2×C11⋊#95—28no—
23C2×C11⋊#95—28no—
24C2×C11⋊#95C2218yescomplemented
25C2×C11⋊#95C2218yescomplemented
26C25×C11—24no—
27C25×C11—24no—
28C25×C11—24no—
29C25×C11—24no—
30C25×C11—24no—
31C25×C11—24no—
32C25×C11C2×C414yes—
33C25×C11D414yes—
34C25×C11D414yes—
35C25×C11C2312yes—
36C25×C11C2311yescharacteristic
37C23×C4×C11—24no—
38C23×C4×C11—24no—
39C23×C4×C11—24no—
40C23×C4×C11—24no—
41C23×C4×C11—24no—
42C23×C4×C11—24no—
43C23×C4×C11D418yes—
44C23×C4×C11C2314yes—
45C23×Dic11—24no—
46C23×Dic11—24no—
47C23×Dic11—24no—
48C23×Dic11—22no—
49C23×Dic11—22no—
50C23×Dic11—24no—
51C23×Dic11—24no—
52C23×Dic11—22no—
53C23×Dic11—22no—
54C23×Dic11—24no—
55C23×Dic11—24no—
56C23×Dic11—24no—
57C23×Dic11—24no—
58C23×Dic11—24no—
59C23×Dic11C2×C414yes—
60C23×Dic11C2×C414yes—
61C23×Dic11D418yes—
62C23×Dic11C2312yes—
63C23×Dic11C2312yes—
64C23×Dic11C2314yes—
65C2×C11×C22⋊C4—232no—
66C2×C11×C22⋊C4—28no—
67C2×C11×C22⋊C4—216no—
68C2×C22⋊Dic11—232no—
69C2×C22⋊Dic11—232no—
70C2×C22⋊Dic11—28no—
71C2×C22⋊Dic11—28no—
72C2×C22⋊Dic11—28no—
73C2×C22⋊Dic11—216no—
74C2×C22⋊Dic11C2×C4116yescomplemented
75C11⋊#95—216no—
76C11⋊#95—216no—
77C2×#1440—111nomaximal, Sylow
78C24×C11—28no—
79C24×C11—28no—
80C24×C11—216no—
81C24×C11—216no—
82C24×C11—28no—
83C24×C11—28no—
84C24×C11—216no—
85C24×C11—216no—
86C24×C11—216no—
87C24×C11—216no—
88C24×C11—28no—
89C24×C11—28no—
90C24×C11—24no—
91C24×C11—24no—
92C24×C11—24no—
93C24×C11—24no—
94C24×C11—24no—
95C24×C11—24no—
96C24×C11—48no—
97C24×C11—48no—
98C24×C11—48no—
99C24×C11—48no—
100C24×C11—48no—
101C24×C11—48no—
102C24×C11—48no—
103C24×C11—48no—
104C24×C11C22⋊C4116yes—
105C24×C11C22×C414yes—
106C24×C11C22×C412yes—
107C24×C11C2×D414yes—
108C24×C11C2×D414yes—
109C24×C11C2×D412yes—
110C24×C11C2×D412yes—
111C24×C11C2×D414yes—
112C24×C11C2×D414yes—
113C24×C11#4114yes—
114C24×C11#4114yes—
115C24×C11#4114yes—
116C24×C11#4114yes—
117C24×C11C2411yescharacteristic
118C22×C4×C11—216no—
119C22×C4×C11—216no—
120C22×C4×C11—216no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—48no—
128C22×C4×C11—48no—
129C22×C4×C11—48no—
130C22×C4×C11—48no—
131C22×C4×C11C2×D418yes—
132C22×Dic11—28no—
133C22×Dic11—28no—
134C22×Dic11—216no—
135C22×Dic11—216no—
136C22×Dic11—216no—
137C22×Dic11—216no—
138C22×Dic11—216no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—44no—
154C22×Dic11—44no—
155C22×Dic11—48no—
156C22×Dic11—48no—
157C22×Dic11—48no—
158C22×Dic11—48no—
159C22×Dic11—48no—
160C22×Dic11—44no—
161C22×Dic11—44no—
162C22×Dic11—48no—
163C22×Dic11C22×C414yes—
164C22×Dic11C22×C414yes—
165C22×Dic11C2×D418yes—
166C11×C22⋊C4—232no—
167C22⋊Dic11—232no—
168C22⋊Dic11—232no—
169C23×C22⋊C4—111no—
170C23×C22⋊C4—111no—
171C23×C22⋊C4D1111yescharacteristic
172C22×#95—112no—
173C22×#95—112no—
174#1440—118no—
175C23×C11—24no—
176C23×C11—24no—
177C23×C11—28no—
178C23×C11—28no—
179C23×C11—24no—
180C23×C11—24no—
181C23×C11—28no—
182C23×C11—28no—
183C23×C11—28no—
184C23×C11—24no—
185C23×C11—24no—
186C23×C11—28no—
187C23×C11—232no—
188C23×C11—232no—
189C23×C11—232no—
190C23×C11—44no—
191C23×C11—44no—
192C23×C11—44no—
193C23×C11—44no—
194C23×C11—44no—
195C23×C11—44no—
196C23×C11—44no—
197C23×C11—44no—
198C23×C11—432no—
199C23×C11—432no—
200C23×C11—432no—
201C23×C11—432no—
202C23×C11—432no—
203C23×C11—432no—
204C23×C11C2×C22⋊C418yes—
205C23×C11C2×C22⋊C414yes—
206C23×C11#11714yes—
207C23×C11#11714yes—
208C23×C11C4×D418yes—
209C23×C11C4×D418yes—
210C23×C11#12014yes—
211C23×C11#12014yes—
212C23×C11#12118yes—
213C23×C11#12118yes—
214C23×C11#12118yes—
215C23×C11#12118yes—
216C23×C11#12318yes—
217C23×C11#12318yes—
218C23×C11#12314yes—
219C23×C11#12314yes—
220C23×C11#12318yes—
221C23×C11#12318yes—
222C23×C11#12418yes—
223C23×C11#12418yes—
224C23×C11#12618yes—
225C23×C11#12618yes—
226C23×C11C23×C411yescharacteristic
227C23×C11C22×D411yescharacteristic
228C23×C11C22×D412yes—
229C23×C11C22×D411yescharacteristic
230C23×C11C22×D412yes—
231C23×C11C2×#4112yes—
232C23×C11C2×#4112yes—
233C23×C11C2×#4112yes—
234C23×C11C2×#4112yes—
235C2×C4×C11—28no—
236C2×C4×C11—28no—
237C2×C4×C11—28no—
238C2×C4×C11—44no—
239C2×C4×C11—44no—
240C2×C4×C11—44no—
241C2×C4×C11—44no—
242C2×C4×C11—432no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—28no—
246C2×Dic11—28no—
247C2×Dic11—28no—
248C2×Dic11—28no—
249C2×Dic11—28no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—44no—
253C2×Dic11—44no—
254C2×Dic11—44no—
255C2×Dic11—44no—
256C2×Dic11—44no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—44no—
260C2×Dic11—416no—
261C2×Dic11—416no—
262C2×Dic11—432no—
263C26C2×D1111yescharacteristic
264C24×C4—111no—
265C24×C4—111no—
266C24×C4—112no—
267C24×C4C2×D1112yes—
268C22×C22⋊C4—24no—
269C22×C22⋊C4—28no—
270C22×C22⋊C4—114no—
271C22×C22⋊C4—118no—
272C22×C22⋊C4—114no—
273C22×C22⋊C4—228no—
274C22×C22⋊C4—224no—
275C22×C22⋊C4—224no—
276C22×C22⋊C4—224no—
277C22×C22⋊C4C2×D1114yes—
278C2×#95—118no—
279C2×#95—118no—
280C2×#95—228no—
281C2×#95—228no—
282C22×C11—28no—
283C22×C11—28no—
284C22×C11—28no—
285C22×C11—48no—
286C22×C11—48no—
287C22×C11—48no—
288C22×C11—48no—
289C22×C11—464no—
290C22×C11—48no—
291C22×C11—48no—
292C22×C11#38118yes—
293C22×C11#38618yes—
294C22×C11#38618yes—
295C22×C11#388116yes—
296C22×C11#388116yes—
297C22×C11#394116yes—
298C22×C11#394116yes—
299C22×C11#397116yes—
300C22×C11#397116yes—
301C22×C11C22×C22⋊C411yescharacteristic
302C22×C11C2×#11711yescharacteristic
303C22×C11C2×#11711yescharacteristic
304C22×C11C2×C4×D412yes—
305C22×C11C2×C4×D412yes—
306C22×C11C2×#12011yescharacteristic
307C22×C11C2×#12011yescharacteristic
308C22×C11C2×#12112yes—
309C22×C11C2×#12112yes—
310C22×C11C2×#12112yes—
311C22×C11C2×#12112yes—
312C22×C11C2×#12312yes—
313C22×C11C2×#12312yes—
314C22×C11C2×#12311yescharacteristic
315C22×C11C2×#12311yescharacteristic
316C22×C11C2×#12312yes—
317C22×C11C2×#12312yes—
318C22×C11C2×#12412yes—
319C22×C11C2×#12412yes—
320C22×C11C2×#12612yes—
321C22×C11C2×#12612yes—
322C4×C11—48no—
323Dic11—48no—
324Dic11—44no—
325Dic11—44no—
326C25—24no—
327C25—24no—
328C25—24no—
329C25—24no—
330C25—24no—
331C25—24no—
332C25C4×D1114yes—
333C25D4414yes—
334C25C22⋊D1114yes—
335C25C22×D1112yes—
336C25C22×D1111yescharacteristic
337C23×C4—24no—
338C23×C4—24no—
339C23×C4—24no—
340C23×C4—24no—
341C23×C4—24no—
342C23×C4—24no—
343C23×C4—114no—
344C23×C4—114no—
345C23×C4—118no—
346C23×C4—112no—
347C23×C4—112no—
348C23×C4—114no—
349C23×C4—224no—
350C23×C4—222no—
351C23×C4—222no—
352C23×C4—224no—
353C23×C4—224no—
354C23×C4—224no—
355C23×C4—224no—
356C23×C4—224no—
357C23×C4—224no—
358C23×C4—224no—
359C23×C4—222no—
360C23×C4—222no—
361C23×C4—224no—
362C23×C4—224no—
363C23×C4C22⋊D1118yes—
364C23×C4C22×D1114yes—
365C2×C22⋊C4—232no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—216no—
368C2×C22⋊C4—1116no—
369C2×C22⋊C4—2216no—
370C2×C22⋊C4—2232no—
371C2×C22⋊C4—2232no—
372C2×C22⋊C4—228no—
373C2×C22⋊C4—228no—
374C2×C22⋊C4—228no—
375#95—2216no—
376#95—2216no—
377C2×C11—48no—
378C2×C11#1440116yescomplemented
379C2×C11C2×#38111yescharacteristic
380C2×C11C2×#38611yescharacteristic
381C2×C11C2×#38611yescharacteristic
382C2×C11C2×#38812yes—
383C2×C11C2×#38812yes—
384C2×C11C2×#39412yes—
385C2×C11C2×#39412yes—
386C2×C11C2×#39712yes—
387C2×C11C2×#39712yes—
388C24—28no—
389C24—28no—
390C24—216no—
391C24—28no—
392C24—216no—
393C24—28no—
394C24—216no—
395C24—28no—
396C24—216no—
397C24—216no—
398C24—216no—
399C24—28no—
400C24—24no—
401C24—24no—
402C24—24no—
403C24—24no—
404C24—24no—
405C24—24no—
406C24—48no—
407C24—48no—
408C24—48no—
409C24—48no—
410C24—48no—
411C24—48no—
412C24—48no—
413C24—48no—
414C24(C2×D11)⋊C4116yes—
415C24C2×C4×D1114yes—
416C24C2×C4×D1112yes—
417C24C2×D4414yes—
418C24C2×D4412yes—
419C24#433914yes—
420C24D4×D1114yes—
421C24#434114yes—
422C24#434114yes—
423C24#434114yes—
424C24C2×C22⋊D1114yes—
425C24C2×C22⋊D1112yes—
426C24C2×C22⋊D1114yes—
427C24C23×D1111yescharacteristic
428C22×C4—216no—
429C22×C4—216no—
430C22×C4—216no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—48no—
438C22×C4—48no—
439C22×C4—48no—
440C22×C4—48no—
441C22×C4—114no—
442C22×C4—114no—
443C22×C4—118no—
444C22×C4—2216no—
445C22×C4—2216no—
446C22×C4—2216no—
447C22×C4—228no—
448C22×C4—228no—
449C22×C4—2216no—
450C22×C4—2216no—
451C22×C4—224no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—224no—
455C22×C4—224no—
456C22×C4—224no—
457C22×C4—224no—
458C22×C4—224no—
459C22×C4—224no—
460C22×C4—224no—
461C22×C4—224no—
462C22×C4—224no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—444no—
466C22×C4—448no—
467C22×C4—444no—
468C22×C4—448no—
469C22×C4—444no—
470C22×C4—448no—
471C22×C4—448no—
472C22×C4—448no—
473C22×C4—448no—
474C22×C4—444no—
475C22×C4C2×C22⋊D1118yes—
476C22⋊C4—232no—
477C22⋊C4—2232no—
478C22⋊C4—2232no—
479C11C2×#144011yescharacteristic, complemented, Sylow
480C23—24no—
481C23—24no—
482C23—28no—
483C23—24no—
484C23—28no—
485C23—24no—
486C23—28no—
487C23—24no—
488C23—28no—
489C23—232no—
490C23—28no—
491C23—28no—
492C23—232no—
493C23—232no—
494C23—24no—
495C23—44no—
496C23—44no—
497C23—44no—
498C23—44no—
499C23—432no—
500C23—432no—
501C23—44no—
502C23—44no—
503C23—44no—
504C23—432no—
505C23—44no—
506C23—432no—
507C23—432no—
508C23—432no—
509C23#6693014yes—
510C23#6693014yes—
511C23#6693218yes—
512C23#6693218yes—
513C23(C22⋊D11)⋊C418yes—
514C23#6693514yes—
515C23#6693618yes—
516C23#6693818yes—
517C23#6693918yes—
518C23#6693914yes—
519C23C2×(C2×D11)⋊C418yes—
520C23C2×(C2×D11)⋊C414yes—
521C23C4×C22⋊D1118yes—
522C23#6698214yes—
523C23#6698318yes—
524C23#6698818yes—
525C23#6698818yes—
526C23#6698918yes—
527C23#6699118yes—
528C23#6699218yes—
529C23#6699218yes—
530C23#6700614yes—
531C23C22×C4×D1111yescharacteristic
532C23C22×D4411yescharacteristic
533C23C2×#433912yes—
534C23C2×D4×D1112yes—
535C23C2×#434112yes—
536C23C2×#434112yes—
537C23C2×#434112yes—
538C23C22×C22⋊D1111yescharacteristic
539C23C22×C22⋊D1112yes—
540C2×C4—28no—
541C2×C4—28no—
542C2×C4—28no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—44no—
546C2×C4—44no—
547C2×C4—432no—
548C2×C4—228no—
549C2×C4—228no—
550C2×C4—228no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—228no—
554C2×C4—228no—
555C2×C4—442no—
556C2×C4—444no—
557C2×C4—442no—
558C2×C4—444no—
559C2×C4—442no—
560C2×C4—444no—
561C2×C4—444no—
562C2×C4—444no—
563C2×C4—444no—
564C2×C4—4416no—
565C2×C4—4416no—
566C2×C4—4432no—
567C2×C4—442no—
568C22—28no—
569C22—28no—
570C22—28no—
571C22—464no—
572C22—48no—
573C22—48no—
574C22—48no—
575C22—48no—
576C22—48no—
577C22—48no—
578C22#1062255618yes—
579C22#10622557116yes—
580C22#10622558116yes—
581C22#10622565116yes—
582C22#10622566116yes—
583C22#1062257118yes—
584C22#10622574116yes—
585C22#1062282618yes—
586C22#10622835116yes—
587C22C2×#6693011yescharacteristic
588C22C2×#6693011yescharacteristic
589C22C2×#6693212yes—
590C22C2×#6693212yes—
591C22C2×(C22⋊D11)⋊C412yes—
592C22C2×#6693511yescharacteristic
593C22C2×#6693612yes—
594C22C2×#6693812yes—
595C22C2×#6693912yes—
596C22C2×#6693911yescharacteristic
597C22C22×(C2×D11)⋊C411yescharacteristic
598C22C2×C4×C22⋊D1112yes—
599C22C2×#6698211yescharacteristic
600C22C2×#6698312yes—
601C22C2×#6698812yes—
602C22C2×#6698812yes—
603C22C2×#6698912yes—
604C22C2×#6699112yes—
605C22C2×#6699212yes—
606C22C2×#6699212yes—
607C22C2×#6700611yescharacteristic
608C4—48no—
609C4—444no—
610C4—444no—
611C4—448no—
612C2—48no—
613C2#13066863116yesdirect product factor
614C2C2×#1062255611yescharacteristic
615C2C2×#1062257111yescharacteristic
616C2C2×#1062282611yescharacteristic
617C2C2×#1062255712yes—
618C2C2×#1062255812yes—
619C2C2×#1062283512yes—
620C2C2×#1062257412yes—
621C2C2×#1062256612yes—
622C2C2×#1062256512yes—
subgroupG/H
centerC25C22×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC23×C11×C22⋊C4C2
socleC25×C11C23
prime radicalC26×C11C22
cosocleC24×C11C24
hypercenterC23×C22⋊C4D11
hypocenterC11C2×#1440
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C25 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C11⋊#95C2semidirect
4. C22×C11⋊#95C2semidirect
5. #13066863C2direct (N × H)
19. C22×C22⋊Dic11C4semidirect
24. C2×C11⋊#95C22semidirect
25. C2×C11⋊#95C22semidirect
74. C2×C22⋊Dic11C2×C4semidirect
378. C2×C11#1440semidirect
479. C11C2×#1440semidirect
613. C2#13066863direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊Dic112
C22×C11⋊#952
#130668632
C23×C11×C22⋊C42
C2×#144011