Finite Group Databasebeta

← C2×#13069849 #14781440

Subgroups — C2×#13069849 #14781440

Order 2816.

2230 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66993C211yesmaximal, characteristic
2C22×#66885C211yesmaximal, characteristic, complemented
3C22×#66896C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic, complemented
5C2×#10622598C211yesmaximal, characteristic, complemented
6#13069849C218yesmaximal, direct product factor
7C2×#10622188C211yesmaximal, characteristic, complemented
8C22×C11×#102C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C23×C22⋊D11—21no—
11C23×C22⋊D11—21no—
12C23×D44C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66993—24no—
16C2×#66993—24no—
17C2×#66993—22no—
18C2×#66993C2214yes—
19C22×C4⋊Dic11—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×#66885—24no—
29C2×#66885C2214yescomplemented
30#10622598—22no—
31#10622598C2214yescomplemented
32C2×#66873—24no—
33C2×#66873C2214yescomplemented
34#10622188C2214yescomplemented
35C25×C11—21no—
36C24×D11—21no—
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—28no—
49C22×C22⋊D11—24no—
50C22×C22⋊D11—24no—
51C22×C22⋊D11—44no—
52C22×C22⋊D11—44no—
53C22×C22⋊D11—44no—
54C22×C22⋊D11—44no—
55C23×Dic11—21no—
56C23×Dic11D411yescharacteristic
57C23×Dic11D411yescharacteristic
58C22×D44—22no—
59C22×D44—22no—
60C22×D44—22no—
61C22×D44—22no—
62C22×D44—22no—
63C22×D44—21no—
64C22×D44D414yes—
65C22×D44C2312yes—
66C22×C8×C11—22no—
67C22×C8×C11—22no—
68C22×C8×C11—22no—
69C22×C8×C11C2312yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4D414yescomplemented
73C2×C11×C4⋊C4C2312yes—
74#66993—216no—
75#66993—28no—
76#66993—28no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—24no—
81C2×C4⋊Dic11—44no—
82C2×C4⋊Dic11C2312yes—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11D412yes—
86C2×C4×Dic11C2312yes—
87C22×C11⋊C8—22no—
88C22×C11⋊C8—22no—
89C22×C11⋊C8—22no—
90C22×C11⋊C8C2312yes—
91C11×#102—28no—
92#66896—28no—
93C11⋊#95—24no—
94#66885—28no—
95#66873—28no—
96C2×#2041—111nomaximal, Sylow
97C24×C11—24no—
98C24×C11—22no—
99C24×C11—42no—
100C24×C11—42no—
101C24×C11—42no—
102C24×C11—42no—
103C24×C11—42no—
104C24×C11—42no—
105C24×C11C2×D411yescharacteristic
106C23×D11—24no—
107C23×D11—22no—
108C23×D11—42no—
109C23×D11—42no—
110C23×D11—42no—
111C23×D11—42no—
112C23×D11—42no—
113C23×D11—42no—
114C2×D4×C11—24no—
115C2×D4×C11—28no—
116C2×D4×C11—28no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—44no—
123C2×D4×C11—42no—
124C2×D4×C11—44no—
125C2×D4×C11—42no—
126C2×D4×C11C2×D414yes—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11#4112yes—
136C22×C4×C11#4112yes—
137C22×C4×C11#4112yes—
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—216no—
140C2×C22⋊D11—216no—
141C2×C22⋊D11—48no—
142C2×C22⋊D11—48no—
143C2×C22⋊D11—432no—
144C2×C22⋊D11—432no—
145C2×C22⋊D11—48no—
146C2×C22⋊D11—48no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—42no—
155C22×Dic11D814yes—
156C22×Dic11SD1614yes—
157C22×Dic11C2×D412yes—
158C22×Dic11C2×D412yes—
159C2×D44—24no—
160C2×D44—28no—
161C2×D44—28no—
162C2×D44—22no—
163C2×D44—22no—
164C2×D44—22no—
165C2×D44—22no—
166C2×D44—22no—
167C2×D44—44no—
168C2×D44—42no—
169C2×D44—44no—
170C2×D44—42no—
171C2×D44C2×D414yes—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—44no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4C2×D414yescomplemented
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—48no—
182C4⋊Dic11—42no—
183C4×Dic11—24no—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—44no—
190C22×#127—111no—
191C22×#102—111no—
192C22×#102—111no—
193C22×#102—111no—
194C22×#102D1111yescharacteristic, complemented
195C2×#389—111no—
196#2041—118no—
197C2×#336—111no—
198C23×C11—24no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—48no—
206C23×C11—48no—
207C23×C11—48no—
208C23×C11—84no—
209C23×C11—84no—
210C23×C11—84no—
211C23×C11—84no—
212C23×C11#12012yes—
213C23×C11#12112yes—
214C23×C11#12412yes—
215C23×C11C2×D812yes—
216C23×C11C2×SD1612yes—
217C23×C11AGL(1,ℤ/8)12yes—
218C23×C11AGL(1,ℤ/8)12yes—
219C23×C11C22×D411yescharacteristic
220C22×D11—24no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—48no—
228C22×D11—48no—
229C22×D11—48no—
230C22×D11—84no—
231C22×D11—84no—
232C22×D11—84no—
233C22×D11—84no—
234D4×C11—24no—
235D4×C11—24no—
236D4×C11—42no—
237D4×C11—42no—
238D4×C11—48no—
239C2×C4×C11—24no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—48no—
243C2×C4×C11#12012yes—
244C2×C4×C11#12114yes—
245C2×C4×C11#12114yes—
246C2×C4×C11#12112yes—
247C2×C4×C11#12314yes—
248C2×C4×C11#12314yes—
249C2×C4×C11#12412yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C22⋊D11—432no—
257C22⋊D11—432no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—28no—
263C2×Dic11—28no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—84no—
268C2×Dic11C2×D814yes—
269C2×Dic11C2×SD1614yes—
270D44—24no—
271D44—24no—
272D44—42no—
273D44—42no—
274D44—48no—
275C8×C11—42no—
276C11⋊C8—42no—
277C23×D4—111no—
278C23×D4—221no—
279C23×D4—221no—
280C23×D4C2×D1111yescharacteristic
281C23×C8—111no—
282C23×C8C2×D1111yescharacteristic
283C2×#127—114no—
284C2×#127—222no—
285C2×#127—224no—
286C2×#127—224no—
287C22×C4⋊C4—111no—
288C22×C4⋊C4—221no—
289C22×C4⋊C4C2×D1111yescharacteristic
290C22×C42—111no—
291C2×#102—24no—
292C2×#102—114no—
293C2×#102—114no—
294C2×#102—114no—
295C2×#102—224no—
296C2×#102—224no—
297C2×#102—224no—
298C2×#102C2×D1114yescomplemented
299#389—114no—
300#389—222no—
301C2×#95—221no—
302#336—114no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—82no—
307C22×C11—82no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11—816no—
311C22×C11#39414yes—
312C22×C11#44714yes—
313C22×C11#45014yes—
314C22×C11#45914yes—
315C22×C11#46014yes—
316C22×C11#48614yes—
317C22×C11#49014yes—
318C22×C11C2×#12011yescharacteristic
319C22×C11C2×#12111yescharacteristic
320C22×C11C2×#12411yescharacteristic
321C22×C11C22×D811yescharacteristic
322C22×C11C22×SD1611yescharacteristic
323C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
324C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
325C2×D11—44no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—82no—
329C2×D11—82no—
330C2×D11—82no—
331C2×D11—82no—
332C2×D11—816no—
333C4×C11—44no—
334C4×C11#39414yes—
335C4×C11C2×#12111yescharacteristic
336C4×C11C2×#12111yescharacteristic
337C4×C11C2×#12311yescharacteristic
338C4×C11C2×#12311yescharacteristic
339Dic11—24no—
340Dic11—24no—
341Dic11—82no—
342C25—21no—
343C25—221no—
344C22×D4—22no—
345C22×D4—21no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—114no—
351C22×D4—112no—
352C22×D4—224no—
353C22×D4—224no—
354C22×D4—228no—
355C22×D4—228no—
356C22×D4—222no—
357C22×D4—222no—
358C22×D4—221no—
359C22×D4—222no—
360C22×D4—222no—
361C22×D4—222no—
362C22×D4—444no—
363C22×D4—444no—
364C22×D4—444no—
365C22×D4—444no—
366C22×D4D4414yes—
367C22×D4C22×D1112yes—
368C23×C4—21no—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4—221no—
372C23×C4C22×D1111yescharacteristic
373C22×C8—22no—
374C22×C8—22no—
375C22×C8—22no—
376C22×C8—112no—
377C22×C8—222no—
378C22×C8—222no—
379C22×C8—222no—
380C22×C8C22×D1112yes—
381#127—228no—
382#127—2216no—
383#127—228no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—112no—
387C2×C4⋊C4—222no—
388C2×C4⋊C4—222no—
389C2×C4⋊C4—224no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—444no—
392C2×C4⋊C4C22⋊D1114yescomplemented
393C2×C4⋊C4C22×D1112yes—
394C2×C42—112no—
395C2×C42—112no—
396C2×C42—222no—
397C2×C42—222no—
398#102—28no—
399#102—228no—
400#102—228no—
401#102—228no—
402#95—224no—
403C2×C11—84no—
404C2×C11#204118yescomplemented
405C2×C11C2×#39411yescharacteristic
406C2×C11C2×#44711yescharacteristic
407C2×C11C2×#45011yescharacteristic
408C2×C11C2×#45911yescharacteristic
409C2×C11C2×#46011yescharacteristic
410C2×C11C2×#48611yescharacteristic
411C2×C11C2×#49011yescharacteristic
412D11—84no—
413C24—24no—
414C24—22no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—224no—
422C24—222no—
423C24—442no—
424C24—442no—
425C24—442no—
426C24—442no—
427C24—442no—
428C24—442no—
429C24D4×D1111yescharacteristic
430C2×D4—24no—
431C2×D4—28no—
432C2×D4—28no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—44no—
439C2×D4—42no—
440C2×D4—44no—
441C2×D4—42no—
442C2×D4—114no—
443C2×D4—2216no—
444C2×D4—2216no—
445C2×D4—224no—
446C2×D4—228no—
447C2×D4—228no—
448C2×D4—222no—
449C2×D4—222no—
450C2×D4—222no—
451C2×D4—222no—
452C2×D4—222no—
453C2×D4—448no—
454C2×D4—448no—
455C2×D4—448no—
456C2×D4—448no—
457C2×D4—4432no—
458C2×D4—4432no—
459C2×D4—442no—
460C2×D4—444no—
461C2×D4—444no—
462C2×D4—442no—
463C2×D4C2×D4414yes—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—114no—
469C22×C4—114no—
470C22×C4—112no—
471C22×C4—112no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—442no—
478C22×C4—442no—
479C22×C4—442no—
480C22×C4C2×D4412yes—
481C22×C4#433912yes—
482C22×C4D4×D1111yescharacteristic
483C22×C4D4×D1112yes—
484C22×C4#434112yes—
485C22×C4#434112yes—
486C22×C4C2×C22⋊D1112yes—
487C22×C4C23×D1111yescharacteristic
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—44no—
492C2×C8—222no—
493C2×C8—222no—
494C2×C8—222no—
495C2×C8—444no—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—448no—
501C4⋊C4—442no—
502C4⋊C4C2×C22⋊D1114yescomplemented
503C42—224no—
504C42—222no—
505C42—222no—
506C11C2×#204111yescharacteristic, complemented, Sylow
507C23—24no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—48no—
515C23—48no—
516C23—48no—
517C23—84no—
518C23—84no—
519C23—84no—
520C23—84no—
521C23—224no—
522C23—442no—
523C23—442no—
524C23—442no—
525C23—442no—
526C23—442no—
527C23—442no—
528C23—448no—
529C23—448no—
530C23—448no—
531C23—884no—
532C23—884no—
533C23—884no—
534C23—884no—
535C23#6693512yes—
536C23#6693812yes—
537C23D8×D1112yes—
538C23#6696412yes—
539C23SD16×D1112yes—
540C23#6696712yes—
541C23#6699212yes—
542C23C2×D4×D1111yescharacteristic
543D4—24no—
544D4—24no—
545D4—42no—
546D4—42no—
547D4—48no—
548D4—224no—
549D4—224no—
550D4—4432no—
551D4—4432no—
552D4—442no—
553D4—442no—
554D4—448no—
555C2×C4—24no—
556C2×C4—48no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—114no—
560C2×C4—114no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—228no—
566C2×C4—228no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—884no—
571C2×C4#6693512yes—
572C2×C4#6693614yes—
573C2×C4#6693812yes—
574C2×C4#6693914yes—
575C2×C4#6698314yes—
576C2×C4#6699114yes—
577C2×C4#6699212yes—
578C2×C4C22×D4411yescharacteristic
579C2×C4C2×#433911yescharacteristic
580C2×C4C2×D4×D1111yescharacteristic
581C2×C4C2×#434111yescharacteristic
582C2×C4C2×#434111yescharacteristic
583C2×C4C22×C22⋊D1111yescharacteristic
584C8—42no—
585C8—442no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—82no—
590C22—816no—
591C22—82no—
592C22—82no—
593C22—82no—
594C22—444no—
595C22—444no—
596C22—444no—
597C22—882no—
598C22—8816no—
599C22—882no—
600C22—882no—
601C22—882no—
602C22#1062237314yes—
603C22#1062237714yes—
604C22#1062238614yes—
605C22#1062238914yes—
606C22#1062257414yes—
607C22#1062276314yes—
608C22#1062277614yes—
609C22C2×#6693511yescharacteristic
610C22C2×#6693811yescharacteristic
611C22C2×D8×D1111yescharacteristic
612C22C2×#6696411yescharacteristic
613C22C2×SD16×D1111yescharacteristic
614C22C2×#6696711yescharacteristic
615C22C2×#6699211yescharacteristic
616C4—44no—
617C4—224no—
618C4—224no—
619C4—882no—
620C4#1062257414yes—
621C4C2×#6693611yescharacteristic
622C4C2×#6693911yescharacteristic
623C4C2×#6698311yescharacteristic
624C4C2×#6699111yescharacteristic
625C2—84no—
626C2—884no—
627C2#1306984918yesdirect product factor
628C2C2×#1062257411yescharacteristic
629C2C2×#1062238611yescharacteristic
630C2C2×#1062238911yescharacteristic
631C2C2×#1062276311yescharacteristic
632C2C2×#1062277611yescharacteristic
633C2C2×#1062237311yescharacteristic
634C2C2×#1062237711yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC24×C11C2×D4
prime radicalC22×#66993C2
hypercenterC22×#102D11
hypocenterC11C2×#2041
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×#66885C2semidirect
3. C22×#66896C2semidirect
4. C22×#66873C2semidirect
5. C2×#10622598C2semidirect
6. #13069849C2direct (N × H)
7. C2×#10622188C2semidirect
8. C22×C11×#102C2semidirect
24. C2×C11×#102C22semidirect
26. C2×#66896C22semidirect
29. C2×#66885C22semidirect
31. #10622598C22semidirect
33. C2×#66873C22semidirect
34. #10622188C22semidirect
72. C2×C11×C4⋊C4D4semidirect
178. C11×C4⋊C4C2×D4semidirect
194. C22×#102D11semidirect
298. C2×#102C2×D11semidirect
392. C2×C4⋊C4C22⋊D11semidirect
404. C2×C11#2041semidirect
502. C4⋊C4C2×C22⋊D11semidirect
506. C11C2×#2041semidirect
627. C2#13069849direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669932
C22×#668852
C22×#668962
C22×#668732
C2×#106225982
#130698492
C2×#106221882
C22×C11×#1022
C2×#204111