Finite Group Databasebeta

← C2×#13069051 #14755458

Subgroups — C2×#13069051 #14755458

Order 2816.

2310 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4313C211yesmaximal, characteristic, complemented
2C22×#66991C211yesmaximal, characteristic
3C22×#66896C211yesmaximal, characteristic, complemented
4C2×#10622600C211yesmaximal, characteristic, complemented
5#13069051C218yesmaximal, direct product factor
6C2×#10622189C211yesmaximal, characteristic, complemented
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—22no—
16C2×#66991—24no—
17C2×#66991C418yescomplemented
18C2×#66991C2214yes—
19C22×(C2×D11)⋊C4—21no—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C22×#4313—24no—
24C22×#4313—24no—
25C22×#4313—24no—
26C22×#4313C2214yescomplemented
27C2×C11×#102—24no—
28C2×C11×#102C2214yescomplemented
29C2×#66896—24no—
30C2×#66896C2214yescomplemented
31C2×C11⋊#95—21no—
32#10622600—22no—
33#10622600C2214yescomplemented
34#10622189C2214yescomplemented
35#10622167C2214yescomplemented
36C25×C11—21no—
37C24×D11D411yescharacteristic
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—21no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11C2×C414yes—
45C22×D4×C11C2312yes—
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—28no—
49C22×C22⋊D11—24no—
50C22×C22⋊D11—44no—
51C22×C22⋊D11—44no—
52C23×Dic11—21no—
53C23×Dic11—21no—
54C23×Dic11D411yescharacteristic
55C22×C4×D11—22no—
56C22×C4×D11—22no—
57C22×C4×D11—22no—
58C22×C4×D11—22no—
59C22×C4×D11C2×C414yes—
60C22×C4×D11D412yes—
61C22×C4×D11D414yes—
62C22×C4×D11C2312yes—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11D414yescomplemented
66C22×C8×C11C2312yes—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2312yes—
71C2×C22⋊Dic11—28no—
72C2×C22⋊Dic11—24no—
73#66991—216no—
74#66991—28no—
75#66991C2×C4116yescomplemented
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—44no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2×C414yes—
84C2×C4⋊Dic11C2312yes—
85C2×C4⋊Dic11C2312yes—
86C22×C11⋊C8—22no—
87C22×C11⋊C8—22no—
88C22×C11⋊C8D414yescomplemented
89C22×C11⋊C8C2312yes—
90C2×#4313—232no—
91C2×#4313—28no—
92C2×#4313—28no—
93C2×#4313—28no—
94C11×#102—28no—
95#66896—28no—
96C11⋊#95—24no—
97C2×#1895—111nomaximal, Sylow
98C24×C11—24no—
99C24×C11—22no—
100C24×C11—42no—
101C24×C11—42no—
102C24×C11—42no—
103C24×C11—42no—
104C24×C11—42no—
105C24×C11—42no—
106C24×C11C2×D411yescharacteristic
107C23×D11—22no—
108C23×D11—22no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11C22⋊C414yes—
114C23×D11C2×D412yes—
115C2×D4×C11—24no—
116C2×D4×C11—28no—
117C2×D4×C11—28no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—44no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11—44no—
127C2×D4×C11C22×C414yes—
128C22×C4×C11—22no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11#4112yes—
138C22×C4×C11#4112yes—
139C22×C4×C11C2411yescharacteristic
140C2×C22⋊D11—216no—
141C2×C22⋊D11—48no—
142C2×C22⋊D11—48no—
143C2×C22⋊D11—432no—
144C22×Dic11—24no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—42no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11C22⋊C414yes—
155C22×Dic11C2×D412yes—
156C2×C4×D11—28no—
157C2×C4×D11—28no—
158C2×C4×D11—28no—
159C2×C4×D11—24no—
160C2×C4×D11—24no—
161C2×C4×D11—28no—
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×C4×D11—22no—
166C2×C4×D11C22⋊C418yes—
167C2×C4×D11C22×C414yes—
168C2×C4×D11C2×D414yes—
169C2×C8×C11—28no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11C2×D414yescomplemented
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—42no—
176C22⋊Dic11—216no—
177(C2×D11)⋊C4—48no—
178C4⋊Dic11—24no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11—42no—
183C4⋊Dic11C22×C414yes—
184C2×C11⋊C8—28no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8C2×D414yescomplemented
188#4313—232no—
189C23×M16—111no—
190C22×#121—111no—
191C22×#102—111no—
192C22×#102D1111yescharacteristic, complemented
193C2×#380—111no—
194#1895—118no—
195C2×#340—111no—
196C2×#340—111no—
197C23×C11—24no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—48no—
205C23×C11—48no—
206C23×C11—48no—
207C23×C11—84no—
208C23×C11—84no—
209C23×C11—84no—
210C23×C11—84no—
211C23×C11C2×C22⋊C412yes—
212C23×C11#12112yes—
213C23×C11#12112yes—
214C23×C11AGL(1,ℤ/8)12yes—
215C23×C11AGL(1,ℤ/8)12yes—
216C23×C11AGL(1,ℤ/8)12yes—
217C23×C11#13712yes—
218C23×C11C22×D411yescharacteristic
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—22no—
224C22×D11—22no—
225C22×D11—28no—
226C22×D11—28no—
227C22×D11—28no—
228C22×D11—44no—
229C22×D11—44no—
230C22×D11—44no—
231C22×D11—44no—
232C22×D11C2×C22⋊C414yes—
233D4×C11—24no—
234D4×C11—24no—
235D4×C11—42no—
236D4×C11—42no—
237D4×C11—48no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—84no—
242C2×C4×C11C2×C22⋊C412yes—
243C2×C4×C11C4×D414yes—
244C2×C4×C11C4×D414yes—
245C2×C4×C11#12014yes—
246C2×C4×C11#12112yes—
247C2×C4×C11#12112yes—
248C2×C4×C11#12314yes—
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C22⋊D11—432no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—28no—
259C2×Dic11—24no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—48no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—84no—
267C2×Dic11C2×C22⋊C414yes—
268C4×D11—24no—
269C4×D11—24no—
270C4×D11—24no—
271C4×D11—24no—
272C4×D11—216no—
273C8×C11—24no—
274C11⋊C8—24no—
275C23×D4—221no—
276C23×D4C2×D1111yescharacteristic
277C24×C4—111no—
278C22×M16—114no—
279C22×M16—224no—
280C22×M16—224no—
281C22×M16—224no—
282C23×C8—111no—
283C23×C8C2×D1111yescharacteristic
284C2×#121—114no—
285C2×#121—118no—
286C2×#121—224no—
287C2×#121—222no—
288C22×C4⋊C4—111no—
289C22×C4⋊C4—111no—
290C22×C4⋊C4C2×D1111yescharacteristic
291C22×C22⋊C4—221no—
292C22×C22⋊C4—221no—
293C2×#102—24no—
294C2×#102—114no—
295C2×#102—224no—
296C2×#102C2×D1114yescomplemented
297#380—114no—
298#380—222no—
299C2×#95—221no—
300#340—114no—
301#340—114no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—816no—
306C22×C11—82no—
307C22×C11—82no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11#38614yes—
311C22×C11#41714yes—
312C22×C11#41814yes—
313C22×C11#46814yes—
314C22×C11#46814yes—
315C22×C11#46914yes—
316C22×C11#46914yes—
317C22×C11C22×C22⋊C411yescharacteristic
318C22×C11C2×#12111yescharacteristic
319C22×C11C2×#12111yescharacteristic
320C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
322C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
323C22×C11C2×#13711yescharacteristic
324C2×D11—24no—
325C2×D11—24no—
326C2×D11—24no—
327C2×D11—416no—
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—42no—
331C2×D11—42no—
332C4×C11—82no—
333C4×C11#38614yes—
334C4×C11C2×C4×D411yescharacteristic
335C4×C11C2×C4×D411yescharacteristic
336C4×C11C2×#12011yescharacteristic
337C4×C11C2×#12311yescharacteristic
338Dic11—24no—
339Dic11—44no—
340Dic11—82no—
341C25—21no—
342C25—111no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—21no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—228no—
350C22×D4—224no—
351C22×D4—444no—
352C22×D4—444no—
353C22×D4C4×D1114yes—
354C22×D4C22×D1112yes—
355C23×C4—21no—
356C23×C4—111no—
357C23×C4—114no—
358C23×C4—114no—
359C23×C4—112no—
360C23×C4—112no—
361C23×C4—222no—
362C23×C4—222no—
363C23×C4—222no—
364C23×C4—222no—
365C23×C4—221no—
366C23×C4—221no—
367C23×C4C22×D1111yescharacteristic
368C2×M16—228no—
369C2×M16—228no—
370C2×M16—2232no—
371C2×M16—228no—
372C22×C8—22no—
373C22×C8—22no—
374C22×C8—114no—
375C22×C8—112no—
376C22×C8—222no—
377C22×C8—222no—
378C22×C8C22⋊D1114yescomplemented
379C22×C8C22×D1112yes—
380#121—1116no—
381#121—2216no—
382#121—228no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—114no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—112no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4C22×D1112yes—
395C2×C22⋊C4—228no—
396C2×C22⋊C4—224no—
397C2×C22⋊C4—224no—
398C2×C22⋊C4—444no—
399#102—28no—
400#102—228no—
401#95—224no—
402C2×C11—84no—
403C2×C11#189518yescomplemented
404C2×C11C2×#38611yescharacteristic
405C2×C11C2×#41811yescharacteristic
406C2×C11C2×#41711yescharacteristic
407C2×C11C2×#46811yescharacteristic
408C2×C11C2×#46811yescharacteristic
409C2×C11C2×#46911yescharacteristic
410C2×C11C2×#46911yescharacteristic
411D11—44no—
412C24—24no—
413C24—22no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—114no—
421C24—112no—
422C24—222no—
423C24—222no—
424C24—222no—
425C24—222no—
426C24—222no—
427C24—222no—
428C24D4×D1111yescharacteristic
429C2×D4—24no—
430C2×D4—28no—
431C2×D4—28no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—44no—
438C2×D4—42no—
439C2×D4—44no—
440C2×D4—42no—
441C2×D4—2216no—
442C2×D4—448no—
443C2×D4—448no—
444C2×D4—4432no—
445C2×D4C2×C4×D1114yes—
446C22×C4—22no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—114no—
451C22×C4—112no—
452C22×C4—118no—
453C22×C4—114no—
454C22×C4—114no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—228no—
458C22×C4—228no—
459C22×C4—224no—
460C22×C4—228no—
461C22×C4—228no—
462C22×C4—224no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—224no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—442no—
471C22×C4—442no—
472C22×C4—442no—
473C22×C4—442no—
474C22×C4—442no—
475C22×C4C2×C4×D1112yes—
476C22×C4#433912yes—
477C22×C4D4×D1111yescharacteristic
478C22×C4D4×D1112yes—
479C22×C4D4×D1112yes—
480C22×C4#434112yes—
481C22×C4C2×C22⋊D1112yes—
482C22×C4C23×D1111yescharacteristic
483M16—2232no—
484C2×C8—28no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—114no—
488C2×C8—228no—
489C2×C8—222no—
490C2×C8—222no—
491C2×C8C2×C22⋊D1114yescomplemented
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—42no—
495C4⋊C4—114no—
496C4⋊C4—224no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—442no—
501C22⋊C4—2216no—
502C22⋊C4—448no—
503C11C2×#189511yescharacteristic, complemented, Sylow
504C23—24no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—48no—
512C23—48no—
513C23—48no—
514C23—84no—
515C23—84no—
516C23—84no—
517C23—84no—
518C23—114no—
519C23—222no—
520C23—222no—
521C23—222no—
522C23—222no—
523C23—222no—
524C23—222no—
525C23—228no—
526C23—228no—
527C23—228no—
528C23—444no—
529C23—444no—
530C23—444no—
531C23—444no—
532C23C22⋊C4×D1112yes—
533C23#6693712yes—
534C23#6696412yes—
535C23#6696412yes—
536C23#6696712yes—
537C23#6696812yes—
538C23#6699112yes—
539C23C2×D4×D1111yescharacteristic
540D4—24no—
541D4—24no—
542D4—42no—
543D4—42no—
544D4—48no—
545D4—4432no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—84no—
550C2×C4—114no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—228no—
554C2×C4—224no—
555C2×C4—224no—
556C2×C4—224no—
557C2×C4—224no—
558C2×C4—2216no—
559C2×C4—224no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4—448no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4—884no—
567C2×C4C22⋊C4×D1112yes—
568C2×C4(C22⋊D11)⋊C414yes—
569C2×C4#6693614yes—
570C2×C4#6693712yes—
571C2×C4C4×C22⋊D1114yes—
572C2×C4#6699014yes—
573C2×C4#6699112yes—
574C2×C4C22×C4×D1111yescharacteristic
575C2×C4C2×#433911yescharacteristic
576C2×C4C2×D4×D1111yescharacteristic
577C2×C4C2×D4×D1111yescharacteristic
578C2×C4C2×#434111yescharacteristic
579C2×C4C22×C22⋊D1111yescharacteristic
580C8—24no—
581C8—224no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—82no—
586C22—82no—
587C22—82no—
588C22—82no—
589C22—816no—
590C22—224no—
591C22—224no—
592C22—224no—
593C22—442no—
594C22—442no—
595C22—442no—
596C22—442no—
597C22—4416no—
598C22#1062238314yes—
599C22#1062238414yes—
600C22#1062239314yes—
601C22#1062239514yes—
602C22#1062256914yes—
603C22#1062277214yes—
604C22#1062278714yes—
605C22C2×C22⋊C4×D1111yescharacteristic
606C22C2×#6693711yescharacteristic
607C22C2×#6696411yescharacteristic
608C22C2×#6696411yescharacteristic
609C22C2×#6696711yescharacteristic
610C22C2×#6696811yescharacteristic
611C22C2×#6699111yescharacteristic
612C4—82no—
613C4—224no—
614C4—444no—
615C4—882no—
616C4#1062256914yes—
617C4C2×(C22⋊D11)⋊C411yescharacteristic
618C4C2×#6693611yescharacteristic
619C4C2×C4×C22⋊D1111yescharacteristic
620C4C2×#6699011yescharacteristic
621C2—84no—
622C2—444no—
623C2#1306905118yesdirect product factor
624C2C2×#1062256911yescharacteristic
625C2C2×#1062238311yescharacteristic
626C2C2×#1062238411yescharacteristic
627C2C2×#1062278711yescharacteristic
628C2C2×#1062239311yescharacteristic
629C2C2×#1062277211yescharacteristic
630C2C2×#1062239511yescharacteristic
subgroupG/H
centerC24D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC24×C11C2×D4
prime radicalC22×#66991C2
cosocleC22×C4×C11C24
hypercenterC22×#102D11
hypocenterC11C2×#1895
LCSG ▷ C2×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
1. C23×#4313C2semidirect
3. C22×#66896C2semidirect
4. C2×#10622600C2semidirect
5. #13069051C2direct (N × H)
6. C2×#10622189C2semidirect
7. C2×#10622167C2semidirect
8. C22×C11×#102C2semidirect
17. C2×#66991C4semidirect
26. C22×#4313C22semidirect
28. C2×C11×#102C22semidirect
30. C2×#66896C22semidirect
33. #10622600C22semidirect
34. #10622189C22semidirect
35. #10622167C22semidirect
65. C22×C8×C11D4semidirect
75. #66991C2×C4semidirect
88. C22×C11⋊C8D4semidirect
172. C2×C8×C11C2×D4semidirect
187. C2×C11⋊C8C2×D4semidirect
192. C22×#102D11semidirect
296. C2×#102C2×D11semidirect
378. C22×C8C22⋊D11semidirect
403. C2×C11#1895semidirect
491. C2×C8C2×C22⋊D11semidirect
503. C11C2×#1895semidirect
623. C2#13069051direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43132
C22×#669912
C22×#668962
C2×#106226002
#130690512
C2×#106221892
C2×#106221672
C22×C11×#1022
C2×#189511