Finite Group Databasebeta

← C2×#13066861 #14675436

Subgroups — C2×#13066861 #14675436

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×C4⋊Dic11C211yesmaximal, characteristic, complemented
2C23×C22⋊Dic11C212yesmaximal
3C22×C11⋊#95C211yesmaximal, characteristic, complemented
4C22×C11⋊#95C212yesmaximal, complemented
5#13066861C218yesmaximal, direct product factor
6C23×C11×C22⋊C4C211yesmaximal, characteristic
7C26×C11C2211yescharacteristic
8C24×C4×C11C2211yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C24×Dic11C2212yes—
11C24×Dic11C2212yes—
12C22×C11×C22⋊C4—24no—
13C22×C11×C22⋊C4—24no—
14C22×C11×C22⋊C4C418yescomplemented
15C22×C11×C22⋊C4C2214yes—
16C22×C22⋊Dic11—28no—
17C22×C22⋊Dic11—28no—
18C22×C22⋊Dic11—28no—
19C22×C22⋊Dic11C2218yes—
20C22×C4⋊Dic11—24no—
21C22×C4⋊Dic11—28no—
22C22×C4⋊Dic11C2214yescomplemented
23C2×C11⋊#95—24no—
24C2×C11⋊#95—28no—
25C2×C11⋊#95C2214yescomplemented
26C2×C11⋊#95C2218yescomplemented
27C25×C11—24no—
28C25×C11—24no—
29C25×C11—22no—
30C25×C11—22no—
31C25×C11—22no—
32C25×C11—22no—
33C25×C11—24no—
34C25×C11—24no—
35C25×C11C2×C414yes—
36C25×C11D414yes—
37C25×C11Q814yes—
38C25×C11C2312yes—
39C25×C11C2311yescharacteristic
40C23×C4×C11—24no—
41C23×C4×C11—24no—
42C23×C4×C11—24no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—24no—
46C23×C4×C11C2×C414yes—
47C23×C4×C11C2×C414yes—
48C23×C4×C11D414yes—
49C23×C4×C11D414yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2312yes—
52C23×Dic11—24no—
53C23×Dic11—24no—
54C23×Dic11—24no—
55C23×Dic11—24no—
56C23×Dic11—24no—
57C23×Dic11—24no—
58C23×Dic11—24no—
59C23×Dic11—24no—
60C23×Dic11—24no—
61C23×Dic11—24no—
62C23×Dic11—24no—
63C23×Dic11—24no—
64C23×Dic11D418yes—
65C23×Dic11D418yes—
66C23×Dic11C2314yes—
67C23×Dic11C2314yes—
68C2×C11×C22⋊C4—232no—
69C2×C11×C22⋊C4—28no—
70C2×C11×C22⋊C4—28no—
71C2×C11×C22⋊C4C2×C4116yescomplemented
72C2×C22⋊Dic11—264no—
73C2×C22⋊Dic11—216no—
74C2×C22⋊Dic11—216no—
75C2×C22⋊Dic11—216no—
76C2×C4⋊Dic11—232no—
77C2×C4⋊Dic11—28no—
78C2×C4⋊Dic11—216no—
79C11⋊#95—28no—
80C11⋊#95—216no—
81C2×#1439—111nomaximal, Sylow
82C24×C11—28no—
83C24×C11—28no—
84C24×C11—216no—
85C24×C11—216no—
86C24×C11—216no—
87C24×C11—28no—
88C24×C11—28no—
89C24×C11—28no—
90C24×C11—28no—
91C24×C11—216no—
92C24×C11—216no—
93C24×C11—216no—
94C24×C11—24no—
95C24×C11—24no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—24no—
101C24×C11—24no—
102C24×C11—44no—
103C24×C11—48no—
104C24×C11—48no—
105C24×C11—48no—
106C24×C11—44no—
107C24×C11—48no—
108C24×C11—48no—
109C24×C11—44no—
110C24×C11—48no—
111C24×C11—44no—
112C24×C11C4⋊C4116yescomplemented
113C24×C11C22×C414yes—
114C24×C11C22×C412yes—
115C24×C11C2×D414yes—
116C24×C11C2×D412yes—
117C24×C11C2×D412yes—
118C24×C11C2×D412yes—
119C24×C11C2×D414yes—
120C24×C11C2×D414yes—
121C24×C11C2×Q814yes—
122C24×C11C2×Q812yes—
123C24×C11#4112yes—
124C24×C11#4112yes—
125C24×C11#4114yes—
126C24×C11#4114yes—
127C24×C11C2411yescharacteristic
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—28no—
135C22×C4×C11—216no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—24no—
140C22×C4×C11—48no—
141C22×C4×C11—44no—
142C22×C4×C11—44no—
143C22×C4×C11C22⋊C4116yescomplemented
144C22×C4×C11C22×C414yes—
145C22×C4×C11C22×C414yes—
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2×D414yes—
148C22×Dic11—216no—
149C22×Dic11—216no—
150C22×Dic11—216no—
151C22×Dic11—216no—
152C22×Dic11—216no—
153C22×Dic11—216no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—48no—
167C22×Dic11—48no—
168C22×Dic11—48no—
169C22×Dic11—48no—
170C22×Dic11—48no—
171C22×Dic11—48no—
172C22×Dic11—48no—
173C22×Dic11—48no—
174C22×Dic11C2×D418yes—
175C22×Dic11C2×D418yes—
176C11×C22⋊C4—232no—
177C22⋊Dic11—264no—
178C4⋊Dic11—232no—
179C23×C4⋊C4—111no—
180C23×C22⋊C4—112no—
181C23×C22⋊C4D1111yescharacteristic
182C22×#95—112no—
183C22×#95—111no—
184#1439—118no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—28no—
188C23×C11—28no—
189C23×C11—28no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—28no—
193C23×C11—28no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—28no—
197C23×C11—232no—
198C23×C11—264no—
199C23×C11—42no—
200C23×C11—44no—
201C23×C11—44no—
202C23×C11—44no—
203C23×C11—44no—
204C23×C11—42no—
205C23×C11—44no—
206C23×C11—42no—
207C23×C11—44no—
208C23×C11—42no—
209C23×C11—416no—
210C23×C11—432no—
211C23×C11—416no—
212C23×C11—416no—
213C23×C11—416no—
214C23×C11—432no—
215C23×C11—432no—
216C23×C11—416no—
217C23×C11—416no—
218C23×C11C2×C22⋊C414yes—
219C23×C11C2×C4⋊C414yes—
220C23×C11C2×C4⋊C418yescomplemented
221C23×C11#11714yes—
222C23×C11C4×D418yes—
223C23×C11C4×D418yes—
224C23×C11#12018yes—
225C23×C11#12014yes—
226C23×C11#12118yes—
227C23×C11#12114yes—
228C23×C11#12114yes—
229C23×C11#12118yes—
230C23×C11#12118yes—
231C23×C11C22⋊Q818yes—
232C23×C11C22⋊Q818yes—
233C23×C11C22⋊Q814yes—
234C23×C11C22⋊Q814yes—
235C23×C11#12318yes—
236C23×C11#12318yes—
237C23×C11#12314yes—
238C23×C11#12418yes—
239C23×C11#12414yes—
240C23×C11#12618yes—
241C23×C11#12714yes—
242C23×C11C23×C411yescharacteristic
243C23×C11C22×D411yescharacteristic
244C23×C11C22×D412yes—
245C23×C11C22×D412yes—
246C23×C11C22×D411yescharacteristic
247C23×C11C22×D411yescharacteristic
248C23×C11C22×Q811yescharacteristic
249C23×C11C2×#4111yescharacteristic
250C23×C11C2×#4111yescharacteristic
251C23×C11C2×#4112yes—
252C23×C11C2×#4112yes—
253C2×C4×C11—28no—
254C2×C4×C11—24no—
255C2×C4×C11—28no—
256C2×C4×C11—24no—
257C2×C4×C11—232no—
258C2×C4×C11—24no—
259C2×C4×C11—28no—
260C2×C4×C11—44no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—416no—
264C2×C4×C11C2×C22⋊C418yescomplemented
265C2×Dic11—28no—
266C2×Dic11—28no—
267C2×Dic11—28no—
268C2×Dic11—28no—
269C2×Dic11—28no—
270C2×Dic11—28no—
271C2×Dic11—44no—
272C2×Dic11—44no—
273C2×Dic11—44no—
274C2×Dic11—44no—
275C2×Dic11—44no—
276C2×Dic11—44no—
277C2×Dic11—44no—
278C2×Dic11—44no—
279C2×Dic11—432no—
280C2×Dic11—432no—
281C26C2×D1111yescharacteristic
282C24×C4—112no—
283C24×C4—112no—
284C24×C4C2×D1111yescharacteristic
285C24×C4C2×D1111yescharacteristic
286C22×C4⋊C4—114no—
287C22×C4⋊C4—228no—
288C22×C4⋊C4—224no—
289C22×C22⋊C4—24no—
290C22×C22⋊C4—24no—
291C22×C22⋊C4—118no—
292C22×C22⋊C4—228no—
293C22×C22⋊C4—228no—
294C22×C22⋊C4—228no—
295C22×C22⋊C4Dic1118yescomplemented
296C22×C22⋊C4C2×D1114yes—
297C2×#95—118no—
298C2×#95—114no—
299C2×#95—228no—
300C2×#95—224no—
301C22×C11—28no—
302C22×C11—216no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—48no—
306C22×C11—48no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11—464no—
310C22×C11—44no—
311C22×C11—48no—
312C22×C11—44no—
313C22×C11#38018yes—
314C22×C11#385116yes—
315C22×C11#38618yes—
316C22×C11#388116yes—
317C22×C11#39018yes—
318C22×C11#39218yes—
319C22×C11#39318yes—
320C22×C11#394116yes—
321C22×C11#396116yes—
322C22×C11#39718yes—
323C22×C11#39918yes—
324C22×C11C22×C22⋊C411yescharacteristic
325C22×C11C22×C4⋊C411yescharacteristic
326C22×C11C2×#11711yescharacteristic
327C22×C11C2×C4×D412yes—
328C22×C11C2×C4×D412yes—
329C22×C11C2×#12012yes—
330C22×C11C2×#12011yescharacteristic
331C22×C11C2×#12112yes—
332C22×C11C2×#12111yescharacteristic
333C22×C11C2×#12111yescharacteristic
334C22×C11C2×#12112yes—
335C22×C11C2×#12112yes—
336C22×C11C2×C22⋊Q812yes—
337C22×C11C2×C22⋊Q812yes—
338C22×C11C2×C22⋊Q811yescharacteristic
339C22×C11C2×C22⋊Q811yescharacteristic
340C22×C11C2×#12312yes—
341C22×C11C2×#12312yes—
342C22×C11C2×#12311yescharacteristic
343C22×C11C2×#12412yes—
344C22×C11C2×#12411yescharacteristic
345C22×C11C2×#12612yes—
346C22×C11C2×#12711yescharacteristic
347C4×C11—28no—
348C4×C11—44no—
349Dic11—48no—
350Dic11—48no—
351C25—22no—
352C25—22no—
353C25—24no—
354C25—24no—
355C25—24no—
356C25—24no—
357C25—22no—
358C25—22no—
359C25Dic2214yes—
360C25D4414yes—
361C25C2×Dic1114yes—
362C25C22×D1112yes—
363C25C22×D1111yescharacteristic
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—118no—
371C23×C4—118no—
372C23×C4—114no—
373C23×C4—114no—
374C23×C4—224no—
375C23×C4—224no—
376C23×C4—224no—
377C23×C4—224no—
378C23×C4—224no—
379C23×C4—224no—
380C23×C4—224no—
381C23×C4—224no—
382C23×C4—224no—
383C23×C4—224no—
384C23×C4—224no—
385C23×C4—224no—
386C23×C4C2×Dic1114yes—
387C23×C4C2×Dic1114yes—
388C23×C4C22⋊D1114yes—
389C23×C4C22⋊D1114yes—
390C23×C4C22×D1112yes—
391C23×C4C22×D1112yes—
392C2×C4⋊C4—2216no—
393C2×C4⋊C4—2232no—
394C2×C4⋊C4—228no—
395C2×C22⋊C4—232no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—2216no—
399C2×C22⋊C4—2216no—
400C2×C22⋊C4—2264no—
401C2×C22⋊C4—2216no—
402C2×C22⋊C4C2×Dic11116yescomplemented
403#95—2216no—
404#95—228no—
405C2×C11—48no—
406C2×C11#1439116yescomplemented
407C2×C11C2×#38011yescharacteristic
408C2×C11C2×#38512yes—
409C2×C11C2×#38611yescharacteristic
410C2×C11C2×#38812yes—
411C2×C11C2×#39011yescharacteristic
412C2×C11C2×#39211yescharacteristic
413C2×C11C2×#39311yescharacteristic
414C2×C11C2×#39412yes—
415C2×C11C2×#39612yes—
416C2×C11C2×#39711yescharacteristic
417C2×C11C2×#39911yescharacteristic
418C24—216no—
419C24—216no—
420C24—216no—
421C24—216no—
422C24—28no—
423C24—28no—
424C24—28no—
425C24—28no—
426C24—28no—
427C24—216no—
428C24—216no—
429C24—28no—
430C24—22no—
431C24—22no—
432C24—24no—
433C24—24no—
434C24—24no—
435C24—24no—
436C24—22no—
437C24—22no—
438C24—48no—
439C24—48no—
440C24—48no—
441C24—48no—
442C24—44no—
443C24—44no—
444C24—44no—
445C24—48no—
446C24—48no—
447C24—44no—
448C24C4⋊Dic11116yescomplemented
449C24C2×Dic2214yes—
450C24C2×Dic2212yes—
451C24C2×D4414yes—
452C24C2×D4412yes—
453C24#433912yes—
454C24#433912yes—
455C24D4×D1114yes—
456C24D4×D1114yes—
457C24#434114yes—
458C24#434114yes—
459C24C22×Dic1114yes—
460C24C22×Dic1112yes—
461C24C2×C22⋊D1112yes—
462C24C2×C22⋊D1112yes—
463C24C23×D1111yescharacteristic
464C22×C4—216no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—216no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—216no—
471C22×C4—28no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—44no—
477C22×C4—48no—
478C22×C4—44no—
479C22×C4—118no—
480C22×C4—118no—
481C22×C4—2216no—
482C22×C4—2216no—
483C22×C4—2216no—
484C22×C4—2216no—
485C22×C4—2216no—
486C22×C4—2216no—
487C22×C4—224no—
488C22×C4—224no—
489C22×C4—224no—
490C22×C4—224no—
491C22×C4—224no—
492C22×C4—224no—
493C22×C4—224no—
494C22×C4—224no—
495C22×C4—224no—
496C22×C4—224no—
497C22×C4—224no—
498C22×C4—224no—
499C22×C4—448no—
500C22×C4—448no—
501C22×C4—448no—
502C22×C4—448no—
503C22×C4—448no—
504C22×C4—448no—
505C22×C4—448no—
506C22×C4—448no—
507C22×C4C22⋊Dic11116yescomplemented
508C22×C4C22×Dic1114yes—
509C22×C4C22×Dic1114yes—
510C22×C4C2×C22⋊D1114yes—
511C22×C4C2×C22⋊D1114yes—
512C4⋊C4—2232no—
513C22⋊C4—232no—
514C22⋊C4—2264no—
515C11C2×#143911yescharacteristic, complemented, Sylow
516C23—28no—
517C23—28no—
518C23—28no—
519C23—28no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—24no—
525C23—28no—
526C23—28no—
527C23—264no—
528C23—232no—
529C23—24no—
530C23—44no—
531C23—44no—
532C23—44no—
533C23—44no—
534C23—42no—
535C23—416no—
536C23—42no—
537C23—432no—
538C23—416no—
539C23—42no—
540C23—44no—
541C23—432no—
542C23—44no—
543C23—416no—
544C23—42no—
545C23—416no—
546C23—432no—
547C23—416no—
548C23—416no—
549C23#6693118yes—
550C23#6693118yes—
551C23#6693218yes—
552C23#6693518yes—
553C23#6693618yes—
554C23#6693718yes—
555C23#6693818yes—
556C23#6693918yes—
557C23#6697714yes—
558C23#6697714yes—
559C23C2×C4⋊Dic1114yes—
560C23C2×C4⋊Dic1118yescomplemented
561C23#6697914yes—
562C23#6698314yes—
563C23#6698314yes—
564C23D4×Dic1118yes—
565C23D4×Dic1118yes—
566C23#6698814yes—
567C23#6698914yes—
568C23#6699014yes—
569C23#6699118yes—
570C23#6699218yes—
571C23#6699314yes—
572C23C2×C22⋊Dic1114yes—
573C23C22×Dic2211yescharacteristic
574C23C22×D4411yescharacteristic
575C23C2×#433911yescharacteristic
576C23C2×#433911yescharacteristic
577C23C2×D4×D1112yes—
578C23C2×D4×D1112yes—
579C23C2×#434112yes—
580C23C2×#434112yes—
581C23C23×Dic1111yescharacteristic
582C23C22×C22⋊D1111yescharacteristic
583C23C22×C22⋊D1111yescharacteristic
584C2×C4—28no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—28no—
588C2×C4—232no—
589C2×C4—28no—
590C2×C4—24no—
591C2×C4—42no—
592C2×C4—44no—
593C2×C4—42no—
594C2×C4—416no—
595C2×C4—228no—
596C2×C4—228no—
597C2×C4—228no—
598C2×C4—228no—
599C2×C4—228no—
600C2×C4—228no—
601C2×C4—444no—
602C2×C4—444no—
603C2×C4—444no—
604C2×C4—444no—
605C2×C4—444no—
606C2×C4—444no—
607C2×C4—444no—
608C2×C4—444no—
609C2×C4—4432no—
610C2×C4—4432no—
611C2×C4C2×C22⋊Dic1118yescomplemented
612C22—28no—
613C22—216no—
614C22—464no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—48no—
619C22—48no—
620C22—48no—
621C22—44no—
622C22—44no—
623C22—44no—
624C22#1062256018yes—
625C22#10622561116yes—
626C22#1062256218yes—
627C22#10622563116yes—
628C22#10622564116yes—
629C22#1062256618yes—
630C22#1062257318yes—
631C22#10622574116yes—
632C22#1062282518yes—
633C22#1062283318yes—
634C22#1062283418yes—
635C22C2×#6693112yes—
636C22C2×#6693112yes—
637C22C2×#6693212yes—
638C22C2×#6693512yes—
639C22C2×#6693612yes—
640C22C2×#6693712yes—
641C22C2×#6693812yes—
642C22C2×#6693912yes—
643C22C2×#6697711yescharacteristic
644C22C2×#6697711yescharacteristic
645C22C22×C4⋊Dic1111yescharacteristic
646C22C2×#6697911yescharacteristic
647C22C2×#6698311yescharacteristic
648C22C2×#6698311yescharacteristic
649C22C2×D4×Dic1112yes—
650C22C2×D4×Dic1112yes—
651C22C2×#6698811yescharacteristic
652C22C2×#6698911yescharacteristic
653C22C2×#6699011yescharacteristic
654C22C2×#6699112yes—
655C22C2×#6699212yes—
656C22C2×#6699311yescharacteristic
657C22C22×C22⋊Dic1111yescharacteristic
658C4—28no—
659C4—44no—
660C4—448no—
661C4—448no—
662C2—48no—
663C2#13066861116yesdirect product factor
664C2C2×#1062282511yescharacteristic
665C2C2×#1062256312yes—
666C2C2×#1062283311yescharacteristic
667C2C2×#1062256412yes—
668C2C2×#1062283411yescharacteristic
669C2C2×#1062257311yescharacteristic
670C2C2×#1062256011yescharacteristic
671C2C2×#1062257412yes—
672C2C2×#1062256112yes—
673C2C2×#1062256611yescharacteristic
674C2C2×#1062256211yescharacteristic
subgroupG/H
centerC25C22×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC23×C11×C22⋊C4C2
socleC25×C11C23
prime radicalC26×C11C22
cosocleC24×C11C24
hypercenterC23×C22⋊C4D11
hypocenterC11C2×#1439
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C25 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C4⋊Dic11C2semidirect
3. C22×C11⋊#95C2semidirect
4. C22×C11⋊#95C2semidirect
5. #13066861C2direct (N × H)
14. C22×C11×C22⋊C4C4semidirect
22. C22×C4⋊Dic11C22semidirect
25. C2×C11⋊#95C22semidirect
26. C2×C11⋊#95C22semidirect
71. C2×C11×C22⋊C4C2×C4semidirect
112. C24×C11C4⋊C4semidirect
143. C22×C4×C11C22⋊C4semidirect
220. C23×C11C2×C4⋊C4semidirect
264. C2×C4×C11C2×C22⋊C4semidirect
295. C22×C22⋊C4Dic11semidirect
402. C2×C22⋊C4C2×Dic11semidirect
406. C2×C11#1439semidirect
448. C24C4⋊Dic11semidirect
507. C22×C4C22⋊Dic11semidirect
515. C11C2×#1439semidirect
560. C23C2×C4⋊Dic11semidirect
611. C2×C4C2×C22⋊Dic11semidirect
663. C2#13066861direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊Dic112
C23×C22⋊Dic112
C22×C11⋊#952
#130668612
C23×C11×C22⋊C42
C2×#143911