Finite Group Databasebeta

← C2×#13069797 #14781220

Subgroups — C2×#13069797 #14781220

Order 2816.

2006 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
1C22×#66991C211yesmaximal, characteristic
2C22×#66882C211yesmaximal, characteristic, complemented
3C22×#66896C211yesmaximal, characteristic, complemented
4C22×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
5C2×#10622600C211yesmaximal, characteristic, complemented
6#13069797C218yesmaximal, direct product factor
7C2×#10622167C211yesmaximal, characteristic, complemented
8C22×C11×#102C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C23×C22⋊D11—21no—
11C23×C4×D11C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C22⋊Dic11—21no—
15C2×#66991—24no—
16C2×#66991—22no—
17C2×#66991—24no—
18C2×#66991C2214yes—
19C22×(C2×D11)⋊C4—21no—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×C11×#102—24no—
24C2×C11×#102C2214yescomplemented
25C2×#66896—24no—
26C2×#66896C2214yescomplemented
27C2×C11⋊#95—21no—
28C2×(C2×D11)⋊C8—24no—
29C2×(C2×D11)⋊C8C2214yescomplemented
30C2×#66882—24no—
31C2×#66882C2214yescomplemented
32#10622600—22no—
33#10622600C2214yescomplemented
34#10622167C2214yescomplemented
35C25×C11—21no—
36C24×D11D411yescharacteristic
37C22×D4×C11—22no—
38C22×D4×C11—21no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11D414yes—
44C22×D4×C11C2312yes—
45C23×C4×C11—21no—
46C23×C4×C11C2311yescharacteristic
47C22×C22⋊D11—28no—
48C22×C22⋊D11—24no—
49C22×C22⋊D11—44no—
50C22×C22⋊D11—44no—
51C23×Dic11—21no—
52C23×Dic11—21no—
53C23×Dic11D411yescharacteristic
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11—22no—
57C22×C4×D11—22no—
58C22×C4×D11—22no—
59C22×C4×D11—22no—
60C22×C4×D11D412yes—
61C22×C4×D11C2312yes—
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11D414yescomplemented
65C22×C8×C11C2312yes—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2312yes—
70C2×C22⋊Dic11—28no—
71C2×C22⋊Dic11—24no—
72#66991—216no—
73#66991—28no—
74#66991—28no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—44no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11D414yes—
83C2×C4⋊Dic11C2312yes—
84C2×C4⋊Dic11C2312yes—
85C22×C11⋊C8—22no—
86C22×C11⋊C8—22no—
87C22×C11⋊C8—22no—
88C22×C11⋊C8C2312yes—
89C11×#102—28no—
90#66896—28no—
91C11⋊#95—24no—
92(C2×D11)⋊C8—28no—
93#66882—28no—
94C2×#2033—111nomaximal, Sylow
95C24×C11—24no—
96C24×C11—22no—
97C24×C11—42no—
98C24×C11—42no—
99C24×C11—42no—
100C24×C11—42no—
101C24×C11—42no—
102C24×C11—42no—
103C24×C11C2×D411yescharacteristic
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—22no—
107C23×D11—22no—
108C23×D11—22no—
109C23×D11—22no—
110C23×D11D814yes—
111C23×D11C2×D412yes—
112C2×D4×C11—24no—
113C2×D4×C11—28no—
114C2×D4×C11—28no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—42no—
121C2×D4×C11—44no—
122C2×D4×C11—42no—
123C2×D4×C11—44no—
124C2×D4×C11C2×D414yes—
125C22×C4×C11—22no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11#4112yes—
134C22×C4×C11#4112yes—
135C22×C4×C11#4112yes—
136C22×C4×C11C2411yescharacteristic
137C2×C22⋊D11—216no—
138C2×C22⋊D11—48no—
139C2×C22⋊D11—432no—
140C2×C22⋊D11—48no—
141C22×Dic11—24no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11C2×D412yes—
153C2×C4×D11—24no—
154C2×C4×D11—24no—
155C2×C4×D11—24no—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—44no—
163C2×C4×D11—44no—
164C2×C4×D11—44no—
165C2×C4×D11—44no—
166C2×C8×C11—28no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11C2×D414yescomplemented
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—42no—
173C22⋊Dic11—216no—
174(C2×D11)⋊C4—48no—
175C4⋊Dic11—24no—
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—42no—
180C4⋊Dic11C2×D414yes—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—44no—
185C22×#121—111no—
186C22×#107—111no—
187C22×#102—111no—
188C22×#102D1111yescharacteristic, complemented
189C22×C22⋊C8—111no—
190C2×#380—111no—
191#2033—118no—
192C2×#340—111no—
193C23×C11—24no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—48no—
201C23×C11—48no—
202C23×C11—48no—
203C23×C11—84no—
204C23×C11—84no—
205C23×C11—84no—
206C23×C11—84no—
207C23×C11#12012yes—
208C23×C11#12112yes—
209C23×C11#12312yes—
210C23×C11C2×D812yes—
211C23×C11#13512yes—
212C23×C11AGL(1,ℤ/8)12yes—
213C23×C11#13712yes—
214C23×C11C22×D411yescharacteristic
215C22×D11—22no—
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—28no—
222C22×D11—28no—
223C22×D11—28no—
224C22×D11—44no—
225C22×D11—44no—
226C22×D11—44no—
227C22×D11—44no—
228C22×D11C2×D814yes—
229D4×C11—24no—
230D4×C11—24no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—48no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—84no—
238C2×C4×C11#12012yes—
239C2×C4×C11#12114yes—
240C2×C4×C11#12112yes—
241C2×C4×C11#12114yes—
242C2×C4×C11#12312yes—
243C2×C4×C11#12314yes—
244C2×C4×C11#12414yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C22⋊D11—432no—
252C2×Dic11—24no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—44no—
259C2×Dic11—48no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—84no—
264C4×D11—42no—
265C4×D11—42no—
266C4×D11—42no—
267C4×D11—42no—
268C4×D11—48no—
269C8×C11—24no—
270C11⋊C8—42no—
271C23×D4—221no—
272C23×D4C2×D1111yescharacteristic
273C24×C4—111no—
274C23×C8—111no—
275C23×C8C2×D1111yescharacteristic
276C2×#121—114no—
277C2×#121—224no—
278C2×#121—222no—
279C2×#121—224no—
280C22×C4⋊C4—111no—
281C22×C4⋊C4—111no—
282C22×C4⋊C4C2×D1111yescharacteristic
283C22×C22⋊C4—221no—
284C22×C22⋊C4—221no—
285C2×#107—114no—
286C2×#107—224no—
287C2×#102—24no—
288C2×#102—114no—
289C2×#102—224no—
290C2×#102C2×D1114yescomplemented
291C2×C22⋊C8—114no—
292C2×C22⋊C8—224no—
293#380—114no—
294#380—222no—
295C2×#95—221no—
296#340—114no—
297C22×C11—44no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—816no—
305C22×C11#39414yes—
306C22×C11#44714yes—
307C22×C11#45214yes—
308C22×C11#46614yes—
309C22×C11#46814yes—
310C22×C11#48014yes—
311C22×C11#48214yes—
312C22×C11C2×#12011yescharacteristic
313C22×C11C2×#12111yescharacteristic
314C22×C11C2×#12311yescharacteristic
315C22×C11C22×D811yescharacteristic
316C22×C11C2×#13511yescharacteristic
317C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C11C2×#13711yescharacteristic
319C2×D11—24no—
320C2×D11—24no—
321C2×D11—24no—
322C2×D11—42no—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—416no—
327C4×C11—82no—
328C4×C11#39414yes—
329C4×C11C2×#12111yescharacteristic
330C4×C11C2×#12111yescharacteristic
331C4×C11C2×#12311yescharacteristic
332C4×C11C2×#12411yescharacteristic
333Dic11—42no—
334Dic11—44no—
335Dic11—82no—
336C25—21no—
337C25—111no—
338C22×D4—22no—
339C22×D4—21no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—224no—
345C22×D4—228no—
346C22×D4—444no—
347C22×D4—444no—
348C22×D4D4414yes—
349C22×D4C22×D1112yes—
350C23×C4—21no—
351C23×C4—111no—
352C23×C4—112no—
353C23×C4—112no—
354C23×C4—221no—
355C23×C4—222no—
356C23×C4—222no—
357C23×C4—222no—
358C23×C4—222no—
359C23×C4—222no—
360C23×C4—222no—
361C23×C4—221no—
362C23×C4C22×D1111yescharacteristic
363C22×C8—22no—
364C22×C8—22no—
365C22×C8—112no—
366C22×C8—222no—
367C22×C8—222no—
368C22×C8—222no—
369C22×C8C22⋊D1114yescomplemented
370C22×C8C22×D1112yes—
371#121—228no—
372#121—2216no—
373#121—228no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—112no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4C22×D1112yes—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—228no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—444no—
390#107—228no—
391#102—28no—
392#102—228no—
393C22⋊C8—228no—
394#95—224no—
395C2×C11—84no—
396C2×C11#203318yescomplemented
397C2×C11C2×#39411yescharacteristic
398C2×C11C2×#44711yescharacteristic
399C2×C11C2×#45211yescharacteristic
400C2×C11C2×#46611yescharacteristic
401C2×C11C2×#46811yescharacteristic
402C2×C11C2×#48011yescharacteristic
403C2×C11C2×#48211yescharacteristic
404D11—44no—
405C24—24no—
406C24—22no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—114no—
414C24—112no—
415C24—222no—
416C24—222no—
417C24—222no—
418C24—222no—
419C24—222no—
420C24—222no—
421C24D4×D1111yescharacteristic
422C2×D4—24no—
423C2×D4—28no—
424C2×D4—28no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—42no—
431C2×D4—44no—
432C2×D4—42no—
433C2×D4—44no—
434C2×D4—2216no—
435C2×D4—448no—
436C2×D4—448no—
437C2×D4—4432no—
438C2×D4C2×D4414yes—
439C22×C4—22no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—112no—
444C22×C4—222no—
445C22×C4—224no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—442no—
460C22×C4—442no—
461C22×C4—444no—
462C22×C4—444no—
463C22×C4—444no—
464C22×C4—444no—
465C22×C4—442no—
466C22×C4—442no—
467C22×C4—442no—
468C22×C4C2×D4412yes—
469C22×C4#433912yes—
470C22×C4D4×D1111yescharacteristic
471C22×C4D4×D1112yes—
472C22×C4#434112yes—
473C22×C4#434112yes—
474C22×C4C2×C22⋊D1112yes—
475C22×C4C23×D1111yescharacteristic
476C2×C8—28no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—222no—
480C2×C8—222no—
481C2×C8—222no—
482C2×C8—444no—
483C2×C8C2×C22⋊D1114yescomplemented
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—42no—
487C4⋊C4—114no—
488C4⋊C4—224no—
489C4⋊C4—222no—
490C4⋊C4—222no—
491C4⋊C4—222no—
492C4⋊C4—442no—
493C22⋊C4—2216no—
494C22⋊C4—448no—
495C11C2×#203311yescharacteristic, complemented, Sylow
496C23—24no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—48no—
504C23—48no—
505C23—48no—
506C23—84no—
507C23—84no—
508C23—84no—
509C23—84no—
510C23—114no—
511C23—222no—
512C23—222no—
513C23—228no—
514C23—222no—
515C23—222no—
516C23—222no—
517C23—222no—
518C23—228no—
519C23—228no—
520C23—444no—
521C23—444no—
522C23—444no—
523C23—444no—
524C23#6693512yes—
525C23#6693612yes—
526C23D8×D1112yes—
527C23#6696512yes—
528C23#6696712yes—
529C23#6696812yes—
530C23#6699112yes—
531C23C2×D4×D1111yescharacteristic
532D4—24no—
533D4—24no—
534D4—42no—
535D4—42no—
536D4—48no—
537D4—4432no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—84no—
542C2×C4—222no—
543C2×C4—224no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—442no—
547C2×C4—442no—
548C2×C4—444no—
549C2×C4—448no—
550C2×C4—442no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—448no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—884no—
559C2×C4#6693512yes—
560C2×C4#6693612yes—
561C2×C4#6693814yes—
562C2×C4#6693914yes—
563C2×C4#6698314yes—
564C2×C4#6699112yes—
565C2×C4#6699214yes—
566C2×C4C22×D4411yescharacteristic
567C2×C4C2×#433911yescharacteristic
568C2×C4C2×D4×D1111yescharacteristic
569C2×C4C2×#434111yescharacteristic
570C2×C4C2×#434111yescharacteristic
571C2×C4C22×C22⋊D1111yescharacteristic
572C8—24no—
573C8—442no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—82no—
578C22—82no—
579C22—82no—
580C22—82no—
581C22—816no—
582C22—224no—
583C22—224no—
584C22—224no—
585C22—442no—
586C22—442no—
587C22—442no—
588C22—442no—
589C22—4416no—
590C22#1062238614yes—
591C22#1062238714yes—
592C22#1062239614yes—
593C22#1062239714yes—
594C22#1062257414yes—
595C22#1062277014yes—
596C22#1062278714yes—
597C22C2×#6693511yescharacteristic
598C22C2×#6693611yescharacteristic
599C22C2×D8×D1111yescharacteristic
600C22C2×#6696511yescharacteristic
601C22C2×#6696711yescharacteristic
602C22C2×#6696811yescharacteristic
603C22C2×#6699111yescharacteristic
604C4—82no—
605C4—444no—
606C4—442no—
607C4—882no—
608C4#1062257414yes—
609C4C2×#6693811yescharacteristic
610C4C2×#6693911yescharacteristic
611C4C2×#6698311yescharacteristic
612C4C2×#6699211yescharacteristic
613C2—84no—
614C2—444no—
615C2#1306979718yesdirect product factor
616C2C2×#1062257411yescharacteristic
617C2C2×#1062238611yescharacteristic
618C2C2×#1062239611yescharacteristic
619C2C2×#1062277011yescharacteristic
620C2C2×#1062278711yescharacteristic
621C2C2×#1062238711yescharacteristic
622C2C2×#1062239711yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC24×C11C2×D4
prime radicalC22×#66991C2
hypercenterC22×#102D11
hypocenterC11C2×#2033
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#66882C2semidirect
3. C22×#66896C2semidirect
4. C22×(C2×D11)⋊C8C2semidirect
5. C2×#10622600C2semidirect
6. #13069797C2direct (N × H)
7. C2×#10622167C2semidirect
8. C22×C11×#102C2semidirect
24. C2×C11×#102C22semidirect
26. C2×#66896C22semidirect
29. C2×(C2×D11)⋊C8C22semidirect
31. C2×#66882C22semidirect
33. #10622600C22semidirect
34. #10622167C22semidirect
64. C22×C8×C11D4semidirect
169. C2×C8×C11C2×D4semidirect
188. C22×#102D11semidirect
290. C2×#102C2×D11semidirect
369. C22×C8C22⋊D11semidirect
396. C2×C11#2033semidirect
483. C2×C8C2×C22⋊D11semidirect
495. C11C2×#2033semidirect
615. C2#13069797direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669912
C22×#668822
C22×#668962
C22×(C2×D11)⋊C82
C2×#106226002
#130697972
C2×#106221672
C22×C11×#1022
C2×#203311