Finite Group Databasebeta

← C2×#13066858 #14675433

Subgroups — C2×#13066858 #14675433

Order 2816.

4926 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D11)⋊C4C212yesmaximal
2C23×(C2×D11)⋊C4C211yesmaximal, characteristic
3C22×C11⋊#95C211yesmaximal, characteristic, complemented
4C22×C11⋊#95C212yesmaximal, complemented
5#13066858C218yesmaximal, direct product factor
6C23×C11×C4⋊C4C211yesmaximal, characteristic, complemented
7C25×D11C2211yescharacteristic
8C24×C4×C11C2212yes—
9C24×C4×C11C2211yescharacteristic
10C24×Dic11C2211yescharacteristic
11C24×Dic11C2212yes—
12C22×C11×C4⋊C4—28no—
13C22×C11×C4⋊C4—24no—
14C22×C11×C4⋊C4C2214yescomplemented
15C22×(C2×D11)⋊C4—28no—
16C22×(C2×D11)⋊C4—24no—
17C22×(C2×D11)⋊C4—28no—
18C22×(C2×D11)⋊C4—24no—
19C22×(C2×D11)⋊C4—28no—
20C22×(C2×D11)⋊C4C418yescomplemented
21C22×(C2×D11)⋊C4C2218yes—
22C22×(C2×D11)⋊C4C2214yes—
23C2×C11⋊#95—24no—
24C2×C11⋊#95—28no—
25C2×C11⋊#95C2214yescomplemented
26C2×C11⋊#95C2218yescomplemented
27C25×C11C2311yescharacteristic
28C24×D11—22no—
29C24×D11—24no—
30C24×D11—22no—
31C24×D11—24no—
32C24×D11—24no—
33C24×D11—22no—
34C24×D11—22no—
35C24×D11—24no—
36C24×D11C2×C414yes—
37C24×D11D414yes—
38C24×D11Q814yes—
39C24×D11C2312yes—
40C23×C4×C11—24no—
41C23×C4×C11—24no—
42C23×C4×C11—24no—
43C23×C4×C11—24no—
44C23×C4×C11—24no—
45C23×C4×C11—24no—
46C23×C4×C11—24no—
47C23×C4×C11—24no—
48C23×C4×C11C2×C414yes—
49C23×C4×C11D414yes—
50C23×C4×C11D418yes—
51C23×C4×C11D414yes—
52C23×C4×C11C2314yes—
53C23×C4×C11C2312yes—
54C23×Dic11—22no—
55C23×Dic11—24no—
56C23×Dic11—22no—
57C23×Dic11—24no—
58C23×Dic11—24no—
59C23×Dic11—24no—
60C23×Dic11—24no—
61C23×Dic11—24no—
62C23×Dic11—24no—
63C23×Dic11—24no—
64C23×Dic11C2×C414yes—
65C23×Dic11D418yes—
66C23×Dic11C2312yes—
67C23×Dic11C2314yes—
68C2×C11×C4⋊C4—232no—
69C2×C11×C4⋊C4—216no—
70C2×C11×C4⋊C4—28no—
71C2×(C2×D11)⋊C4—264no—
72C2×(C2×D11)⋊C4—216no—
73C2×(C2×D11)⋊C4—232no—
74C2×(C2×D11)⋊C4—28no—
75C2×(C2×D11)⋊C4—216no—
76C2×(C2×D11)⋊C4—28no—
77C2×(C2×D11)⋊C4—216no—
78C2×(C2×D11)⋊C4C2×C4116yescomplemented
79C11⋊#95—28no—
80C11⋊#95—216no—
81C2×#1439—111nomaximal, Sylow
82C24×C11C22×C412yes—
83C24×C11C2×D412yes—
84C24×C11C2×D412yes—
85C24×C11C2×D412yes—
86C24×C11C2×D414yes—
87C24×C11C2×D414yes—
88C24×C11C2×Q812yes—
89C24×C11#4112yes—
90C24×C11#4112yes—
91C24×C11#4114yes—
92C24×C11#4114yes—
93C24×C11C2411yescharacteristic
94C23×D11—28no—
95C23×D11—28no—
96C23×D11—216no—
97C23×D11—216no—
98C23×D11—216no—
99C23×D11—28no—
100C23×D11—28no—
101C23×D11—28no—
102C23×D11—28no—
103C23×D11—216no—
104C23×D11—216no—
105C23×D11—216no—
106C23×D11—22no—
107C23×D11—22no—
108C23×D11—24no—
109C23×D11—24no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—24no—
113C23×D11—24no—
114C23×D11—44no—
115C23×D11—48no—
116C23×D11—48no—
117C23×D11—48no—
118C23×D11—44no—
119C23×D11—48no—
120C23×D11—48no—
121C23×D11—44no—
122C23×D11—48no—
123C23×D11—44no—
124C23×D11C4⋊C4116yescomplemented
125C23×D11C22×C414yes—
126C23×D11C2×D414yes—
127C23×D11C2×Q814yes—
128C22×C4×C11—216no—
129C22×C4×C11—28no—
130C22×C4×C11—216no—
131C22×C4×C11—28no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—216no—
135C22×C4×C11—216no—
136C22×C4×C11—216no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—48no—
144C22×C4×C11—48no—
145C22×C4×C11—48no—
146C22×C4×C11—48no—
147C22×C4×C11C22⋊C4116yescomplemented
148C22×C4×C11C22×C414yes—
149C22×C4×C11C2×D418yes—
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2×D414yes—
152C22×Dic11—28no—
153C22×Dic11—216no—
154C22×Dic11—216no—
155C22×Dic11—216no—
156C22×Dic11—216no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—22no—
160C22×Dic11—24no—
161C22×Dic11—22no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—48no—
168C22×Dic11—48no—
169C22×Dic11—48no—
170C22×Dic11—48no—
171C22×Dic11—48no—
172C22×Dic11—44no—
173C22×Dic11—44no—
174C22×Dic11C22×C414yes—
175C22×Dic11C2×D418yes—
176C11×C4⋊C4—232no—
177(C2×D11)⋊C4—264no—
178(C2×D11)⋊C4—232no—
179C23×C4⋊C4D1111yescharacteristic, complemented
180C23×C22⋊C4—111no—
181C23×C22⋊C4—112no—
182C22×#95—112no—
183C22×#95—111no—
184#1439—118no—
185C23×C11C2×C22⋊C414yes—
186C23×C11C2×C4⋊C414yes—
187C23×C11#11714yes—
188C23×C11C4×D418yes—
189C23×C11C4×D418yes—
190C23×C11#12018yes—
191C23×C11#12014yes—
192C23×C11#12114yes—
193C23×C11#12118yes—
194C23×C11#12118yes—
195C23×C11#12114yes—
196C23×C11#12118yes—
197C23×C11C22⋊Q818yes—
198C23×C11C22⋊Q814yes—
199C23×C11C22⋊Q814yes—
200C23×C11C22⋊Q818yes—
201C23×C11#12318yes—
202C23×C11#12318yes—
203C23×C11#12314yes—
204C23×C11#12418yes—
205C23×C11#12414yes—
206C23×C11#12618yes—
207C23×C11#12714yes—
208C23×C11C23×C411yescharacteristic
209C23×C11C22×D411yescharacteristic
210C23×C11C22×D411yescharacteristic
211C23×C11C22×D412yes—
212C23×C11C22×D411yescharacteristic
213C23×C11C22×D412yes—
214C23×C11C22×Q811yescharacteristic
215C23×C11C2×#4112yes—
216C23×C11C2×#4111yescharacteristic
217C23×C11C2×#4111yescharacteristic
218C23×C11C2×#4112yes—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—28no—
222C22×D11—28no—
223C22×D11—28no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—28no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—28no—
230C22×D11—28no—
231C22×D11—232no—
232C22×D11—264no—
233C22×D11—42no—
234C22×D11—44no—
235C22×D11—44no—
236C22×D11—44no—
237C22×D11—44no—
238C22×D11—42no—
239C22×D11—44no—
240C22×D11—42no—
241C22×D11—44no—
242C22×D11—42no—
243C22×D11—416no—
244C22×D11—432no—
245C22×D11—416no—
246C22×D11—416no—
247C22×D11—416no—
248C22×D11—432no—
249C22×D11—432no—
250C22×D11—416no—
251C22×D11—416no—
252C22×D11C2×C4⋊C418yescomplemented
253C2×C4×C11—28no—
254C2×C4×C11—24no—
255C2×C4×C11—28no—
256C2×C4×C11—24no—
257C2×C4×C11—232no—
258C2×C4×C11—28no—
259C2×C4×C11—28no—
260C2×C4×C11—28no—
261C2×C4×C11—44no—
262C2×C4×C11—44no—
263C2×C4×C11—44no—
264C2×C4×C11—44no—
265C2×C4×C11—432no—
266C2×C4×C11C2×C22⋊C418yescomplemented
267C2×Dic11—24no—
268C2×Dic11—28no—
269C2×Dic11—28no—
270C2×Dic11—28no—
271C2×Dic11—28no—
272C2×Dic11—44no—
273C2×Dic11—44no—
274C2×Dic11—44no—
275C2×Dic11—44no—
276C2×Dic11—44no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—416no—
280C2×Dic11—432no—
281C26—111no—
282C24×C4—111no—
283C24×C4—112no—
284C24×C4C2×D1112yes—
285C24×C4C2×D1111yescharacteristic
286C22×C4⋊C4—28no—
287C22×C4⋊C4—24no—
288C22×C4⋊C4C2×D1114yescomplemented
289C22×C22⋊C4—114no—
290C22×C22⋊C4—118no—
291C22×C22⋊C4—118no—
292C22×C22⋊C4—228no—
293C22×C22⋊C4—228no—
294C22×C22⋊C4—224no—
295C22×C22⋊C4—228no—
296C22×C22⋊C4—224no—
297C2×#95—118no—
298C2×#95—114no—
299C2×#95—228no—
300C2×#95—224no—
301C22×C11#38018yes—
302C22×C11#385116yes—
303C22×C11#38618yes—
304C22×C11#388116yes—
305C22×C11#39018yes—
306C22×C11#39218yes—
307C22×C11#39318yes—
308C22×C11#394116yes—
309C22×C11#396116yes—
310C22×C11#39718yes—
311C22×C11#39918yes—
312C22×C11C22×C22⋊C411yescharacteristic
313C22×C11C22×C4⋊C411yescharacteristic
314C22×C11C2×#11711yescharacteristic
315C22×C11C2×C4×D412yes—
316C22×C11C2×C4×D412yes—
317C22×C11C2×#12012yes—
318C22×C11C2×#12011yescharacteristic
319C22×C11C2×#12111yescharacteristic
320C22×C11C2×#12112yes—
321C22×C11C2×#12112yes—
322C22×C11C2×#12111yescharacteristic
323C22×C11C2×#12112yes—
324C22×C11C2×C22⋊Q812yes—
325C22×C11C2×C22⋊Q811yescharacteristic
326C22×C11C2×C22⋊Q812yes—
327C22×C11C2×C22⋊Q811yescharacteristic
328C22×C11C2×#12312yes—
329C22×C11C2×#12312yes—
330C22×C11C2×#12311yescharacteristic
331C22×C11C2×#12412yes—
332C22×C11C2×#12411yescharacteristic
333C22×C11C2×#12612yes—
334C22×C11C2×#12711yescharacteristic
335C2×D11—28no—
336C2×D11—216no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—48no—
340C2×D11—48no—
341C2×D11—44no—
342C2×D11—44no—
343C2×D11—464no—
344C2×D11—44no—
345C2×D11—48no—
346C2×D11—44no—
347C4×C11—28no—
348C4×C11—48no—
349Dic11—48no—
350Dic11—44no—
351C25—114no—
352C25—114no—
353C25—114no—
354C25—112no—
355C25—222no—
356C25—224no—
357C25—224no—
358C25—222no—
359C25—222no—
360C25—224no—
361C25—222no—
362C25—224no—
363C25C22×D1111yescharacteristic
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—114no—
373C23×C4—118no—
374C23×C4—112no—
375C23×C4—114no—
376C23×C4—222no—
377C23×C4—224no—
378C23×C4—224no—
379C23×C4—224no—
380C23×C4—224no—
381C23×C4—224no—
382C23×C4—224no—
383C23×C4—224no—
384C23×C4—222no—
385C23×C4—224no—
386C23×C4C4×D1114yes—
387C23×C4D4414yes—
388C23×C4C22⋊D1118yes—
389C23×C4C22⋊D1114yes—
390C23×C4C22×D1114yes—
391C23×C4C22×D1112yes—
392C2×C4⋊C4—232no—
393C2×C4⋊C4—216no—
394C2×C4⋊C4—28no—
395C2×C22⋊C4—1116no—
396C2×C22⋊C4—2216no—
397C2×C22⋊C4—2216no—
398C2×C22⋊C4—2264no—
399C2×C22⋊C4—2232no—
400C2×C22⋊C4—228no—
401C2×C22⋊C4—2216no—
402C2×C22⋊C4—228no—
403#95—2216no—
404#95—228no—
405C2×C11#1439116yescomplemented
406C2×C11C2×#38011yescharacteristic
407C2×C11C2×#38512yes—
408C2×C11C2×#38611yescharacteristic
409C2×C11C2×#38812yes—
410C2×C11C2×#39011yescharacteristic
411C2×C11C2×#39211yescharacteristic
412C2×C11C2×#39311yescharacteristic
413C2×C11C2×#39412yes—
414C2×C11C2×#39612yes—
415C2×C11C2×#39711yescharacteristic
416C2×C11C2×#39911yescharacteristic
417D11—48no—
418C24—1116no—
419C24—114no—
420C24—114no—
421C24—114no—
422C24—228no—
423C24—2216no—
424C24—2216no—
425C24—228no—
426C24—2216no—
427C24—228no—
428C24—228no—
429C24—2216no—
430C24—2216no—
431C24—228no—
432C24—228no—
433C24—2216no—
434C24—222no—
435C24—224no—
436C24—224no—
437C24—222no—
438C24—222no—
439C24—224no—
440C24—222no—
441C24—224no—
442C24—448no—
443C24—448no—
444C24—448no—
445C24—444no—
446C24—448no—
447C24—448no—
448C24—444no—
449C24—444no—
450C24—448no—
451C24—444no—
452C24C2×C4×D1112yes—
453C24C2×D4412yes—
454C24#433914yes—
455C24D4×D1112yes—
456C24D4×D1114yes—
457C24#434112yes—
458C24Q8×D1112yes—
459C24#434312yes—
460C24#434314yes—
461C24C2×C22⋊D1112yes—
462C24C2×C22⋊D1114yes—
463C24C23×D1111yescharacteristic
464C22×C4—216no—
465C22×C4—28no—
466C22×C4—216no—
467C22×C4—28no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—216no—
471C22×C4—216no—
472C22×C4—216no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—48no—
480C22×C4—48no—
481C22×C4—48no—
482C22×C4—48no—
483C22×C4—114no—
484C22×C4—118no—
485C22×C4—2216no—
486C22×C4—2216no—
487C22×C4—2216no—
488C22×C4—228no—
489C22×C4—2216no—
490C22×C4—224no—
491C22×C4—222no—
492C22×C4—224no—
493C22×C4—224no—
494C22×C4—224no—
495C22×C4—224no—
496C22×C4—224no—
497C22×C4—224no—
498C22×C4—222no—
499C22×C4—224no—
500C22×C4—448no—
501C22×C4—448no—
502C22×C4—448no—
503C22×C4—448no—
504C22×C4—444no—
505C22×C4—444no—
506C22×C4—448no—
507C22×C4(C2×D11)⋊C4116yescomplemented
508C22×C4C2×C4×D1114yes—
509C22×C4C2×D4414yes—
510C22×C4C2×C22⋊D1118yes—
511C22×C4C2×C22⋊D1114yes—
512C4⋊C4—232no—
513C22⋊C4—2264no—
514C22⋊C4—2232no—
515C11C2×#143911yescharacteristic, complemented, Sylow
516C23—118no—
517C23—224no—
518C23—228no—
519C23—228no—
520C23—224no—
521C23—228no—
522C23—224no—
523C23—224no—
524C23—228no—
525C23—228no—
526C23—224no—
527C23—224no—
528C23—228no—
529C23—2232no—
530C23—2264no—
531C23—444no—
532C23—444no—
533C23—444no—
534C23—442no—
535C23—444no—
536C23—444no—
537C23—442no—
538C23—4416no—
539C23—444no—
540C23—442no—
541C23—4416no—
542C23—4416no—
543C23—4416no—
544C23—4432no—
545C23—442no—
546C23—4432no—
547C23—4416no—
548C23—4416no—
549C23—4432no—
550C23C4⋊C4×D1114yes—
551C23#6694514yes—
552C23#6694618yes—
553C23#6694718yes—
554C23#6694718yes—
555C23#6694814yes—
556C23#6694818yes—
557C23#6694918yes—
558C23#6695014yes—
559C23#6695118yes—
560C23C2×(C2×D11)⋊C414yes—
561C23C4×C22⋊D1118yes—
562C23#6698214yes—
563C23#6698318yes—
564C23#6699018yes—
565C23#6699114yes—
566C23#6699218yes—
567C23#6699314yes—
568C23#6699914yes—
569C23#6699918yes—
570C23#6700014yes—
571C23#6700018yes—
572C23#6700614yes—
573C23C22×C4×D1111yescharacteristic
574C23C22×D4411yescharacteristic
575C23C2×#433912yes—
576C23C2×D4×D1111yescharacteristic
577C23C2×D4×D1112yes—
578C23C2×#434111yescharacteristic
579C23C2×Q8×D1111yescharacteristic
580C23C2×#434311yescharacteristic
581C23C2×#434312yes—
582C23C22×C22⋊D1111yescharacteristic
583C23C22×C22⋊D1112yes—
584C2×C4—28no—
585C2×C4—24no—
586C2×C4—28no—
587C2×C4—232no—
588C2×C4—24no—
589C2×C4—28no—
590C2×C4—28no—
591C2×C4—28no—
592C2×C4—44no—
593C2×C4—44no—
594C2×C4—44no—
595C2×C4—44no—
596C2×C4—432no—
597C2×C4—228no—
598C2×C4—228no—
599C2×C4—228no—
600C2×C4—224no—
601C2×C4—228no—
602C2×C4—444no—
603C2×C4—444no—
604C2×C4—444no—
605C2×C4—444no—
606C2×C4—442no—
607C2×C4—444no—
608C2×C4—442no—
609C2×C4—4416no—
610C2×C4—4432no—
611C2×C4C2×(C2×D11)⋊C418yescomplemented
612C22—228no—
613C22—2216no—
614C22—4464no—
615C22—444no—
616C22—444no—
617C22—448no—
618C22—444no—
619C22—448no—
620C22—448no—
621C22—444no—
622C22—444no—
623C22—444no—
624C22#1062260018yes—
625C22#1062260118yes—
626C22#10622602116yes—
627C22#10622603116yes—
628C22#10622604116yes—
629C22#1062260518yes—
630C22#1062260618yes—
631C22#10622607116yes—
632C22#1062282618yes—
633C22#1062283618yes—
634C22#1062284418yes—
635C22C2×C4⋊C4×D1111yescharacteristic
636C22C2×#6694511yescharacteristic
637C22C2×#6694612yes—
638C22C2×#6694712yes—
639C22C2×#6694712yes—
640C22C2×#6694811yescharacteristic
641C22C2×#6694812yes—
642C22C2×#6694912yes—
643C22C2×#6695011yescharacteristic
644C22C2×#6695112yes—
645C22C22×(C2×D11)⋊C411yescharacteristic
646C22C2×C4×C22⋊D1112yes—
647C22C2×#6698211yescharacteristic
648C22C2×#6698312yes—
649C22C2×#6699012yes—
650C22C2×#6699111yescharacteristic
651C22C2×#6699212yes—
652C22C2×#6699311yescharacteristic
653C22C2×#6699911yescharacteristic
654C22C2×#6699912yes—
655C22C2×#6700012yes—
656C22C2×#6700011yescharacteristic
657C22C2×#6700611yescharacteristic
658C4—28no—
659C4—48no—
660C4—448no—
661C4—444no—
662C2—448no—
663C2#13066858116yesdirect product factor
664C2C2×#1062260011yescharacteristic
665C2C2×#1062260212yes—
666C2C2×#1062282611yescharacteristic
667C2C2×#1062260312yes—
668C2C2×#1062260111yescharacteristic
669C2C2×#1062283611yescharacteristic
670C2C2×#1062284411yescharacteristic
671C2C2×#1062260412yes—
672C2C2×#1062260712yes—
673C2C2×#1062260611yescharacteristic
674C2C2×#1062260511yescharacteristic
subgroupG/H
centerC25C22×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC23×C11×C4⋊C4C2
socleC25×C11C23
prime radicalC25×D11C22
cosocleC24×C11C24
hypercenterC23×C4⋊C4D11
hypocenterC11C2×#1439
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C25 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C11⋊#95C2semidirect
4. C22×C11⋊#95C2semidirect
5. #13066858C2direct (N × H)
6. C23×C11×C4⋊C4C2semidirect
14. C22×C11×C4⋊C4C22semidirect
20. C22×(C2×D11)⋊C4C4semidirect
25. C2×C11⋊#95C22semidirect
26. C2×C11⋊#95C22semidirect
78. C2×(C2×D11)⋊C4C2×C4semidirect
124. C23×D11C4⋊C4semidirect
147. C22×C4×C11C22⋊C4semidirect
179. C23×C4⋊C4D11semidirect
252. C22×D11C2×C4⋊C4semidirect
266. C2×C4×C11C2×C22⋊C4semidirect
288. C22×C4⋊C4C2×D11semidirect
405. C2×C11#1439semidirect
507. C22×C4(C2×D11)⋊C4semidirect
515. C11C2×#1439semidirect
611. C2×C4C2×(C2×D11)⋊C4semidirect
663. C2#13066858direct (N × H)

Maximal subgroups

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

subgroupindex
C23×(C2×D11)⋊C42
C22×C11⋊#952
#130668582
C23×C11×C4⋊C42
C2×#143911