Finite Group Databasebeta

← C2×#13069053 #14755460

Subgroups — C2×#13069053 #14755460

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×#66948C211yesmaximal, characteristic
3C22×#66885C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic, complemented
5C2×#10622600C211yesmaximal, characteristic, complemented
6#13069053C218yesmaximal, direct product factor
7C2×#10622167C211yesmaximal, characteristic, complemented
8C2×C11×#340C211yesmaximal, characteristic, complemented
9C23×D44—21no—
10C23×D44C2211yescharacteristic
11C23×C4×D11C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×(C2×D11)⋊C4—21no—
16C22×(C2×D11)⋊C4—21no—
17C22×C4⋊Dic11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C22×#4313—24no—
20C22×#4313—24no—
21C22×#4313—24no—
22C22×#4313C2214yescomplemented
23C2×#66948—22no—
24C2×#66948—24no—
25C2×#66948C418yescomplemented
26C2×#66948C2214yes—
27C2×C11⋊#95—21no—
28C2×#66885—24no—
29C2×#66885C2214yescomplemented
30#10622600—22no—
31#10622600C2214yescomplemented
32C2×#66873—24no—
33C2×#66873C2214yescomplemented
34C11×#340C2214yescomplemented
35#10622167C2214yescomplemented
36C24×D11—21no—
37C24×D11D411yescharacteristic
38C23×C4×C11—21no—
39C23×C4×C11—21no—
40C23×C4×C11C2311yescharacteristic
41C23×Dic11—21no—
42C23×Dic11D411yescharacteristic
43C22×D44—22no—
44C22×D44—22no—
45C22×D44—22no—
46C22×D44—22no—
47C22×D44—28no—
48C22×D44—24no—
49C22×D44—21no—
50C22×D44—22no—
51C22×D44—44no—
52C22×D44—44no—
53C22×D44C2×C414yes—
54C22×D44C2312yes—
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—21no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2×C414yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2312yes—
75C2×(C2×D11)⋊C4—28no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—44no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11C2312yes—
83C22×C11⋊C8—22no—
84C22×C11⋊C8—22no—
85C22×C11⋊C8D414yescomplemented
86C22×C11⋊C8C2312yes—
87C2×#4313—232no—
88C2×#4313—28no—
89C2×#4313—28no—
90C2×#4313—28no—
91#66948—216no—
92#66948—28no—
93#66948C2×C4116yescomplemented
94C11⋊#95—24no—
95#66885—28no—
96#66873—28no—
97C2×#1895—111nomaximal, Sylow
98C24×C11C2×D411yescharacteristic
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11—22no—
105C23×D11—24no—
106C23×D11—22no—
107C23×D11—42no—
108C23×D11—42no—
109C23×D11—42no—
110C23×D11—42no—
111C23×D11—42no—
112C23×D11—42no—
113C23×D11C22⋊C414yes—
114C23×D11C2×D412yes—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11#4112yes—
129C22×C4×C11#4112yes—
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—42no—
135C22×Dic11—42no—
136C22×Dic11—42no—
137C22×Dic11C22⋊C414yes—
138C22×Dic11C2×D412yes—
139C2×D44—216no—
140C2×D44—24no—
141C2×D44—28no—
142C2×D44—28no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—48no—
149C2×D44—48no—
150C2×D44—432no—
151C2×D44—44no—
152C2×D44—42no—
153C2×D44—42no—
154C2×D44—44no—
155C2×D44C22×C414yes—
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—24no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4C22×C414yes—
179(C2×D11)⋊C4—216no—
180(C2×D11)⋊C4—48no—
181C4⋊Dic11—22no—
182C4⋊Dic11—22no—
183C4⋊Dic11—42no—
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×#102—111no—
193C2×#380—111no—
194#1895—118no—
195C2×#340—111no—
196C2×#340D1111yescharacteristic, complemented
197C23×C11C2×C22⋊C412yes—
198C23×C11#12112yes—
199C23×C11#12112yes—
200C23×C11AGL(1,ℤ/8)12yes—
201C23×C11AGL(1,ℤ/8)12yes—
202C23×C11AGL(1,ℤ/8)12yes—
203C23×C11#13712yes—
204C23×C11C22×D411yescharacteristic
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—28no—
212C22×D11—28no—
213C22×D11—28no—
214C22×D11—24no—
215C22×D11—44no—
216C22×D11—44no—
217C22×D11—44no—
218C22×D11—44no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—48no—
226C22×D11—48no—
227C22×D11—48no—
228C22×D11—84no—
229C22×D11—84no—
230C22×D11—84no—
231C22×D11—84no—
232C22×D11C2×C22⋊C414yes—
233C2×C4×C11—24no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—48no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—84no—
241C2×C4×C11C2×C22⋊C412yes—
242C2×C4×C11C4×D414yes—
243C2×C4×C11C4×D414yes—
244C2×C4×C11#12014yes—
245C2×C4×C11#12112yes—
246C2×C4×C11#12112yes—
247C2×C4×C11#12314yes—
248C2×C4×C11C23×C411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—28no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—84no—
261C2×Dic11C2×C22⋊C414yes—
262D44—24no—
263D44—24no—
264D44—432no—
265D44—42no—
266D44—42no—
267D44—48no—
268C4×D11—24no—
269C4×D11—24no—
270C4×D11—24no—
271C4×D11—24no—
272C4×D11—216no—
273C8×C11—24no—
274C11⋊C8—24no—
275C23×D4—111no—
276C23×D4—221no—
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⋊C4C2×D1111yescharacteristic
290C22×C4⋊C4C2×D1111yescharacteristic
291C22×C22⋊C4—221no—
292C22×C22⋊C4—221no—
293C2×#102—114no—
294C2×#102—114no—
295C2×#102—224no—
296C2×#102—224no—
297#380—114no—
298#380—222no—
299C2×#95—221no—
300#340—114no—
301#340C2×D1114yescomplemented
302C22×C11#38614yes—
303C22×C11#41714yes—
304C22×C11#41814yes—
305C22×C11#46814yes—
306C22×C11#46814yes—
307C22×C11#46914yes—
308C22×C11#46914yes—
309C22×C11C22×C22⋊C411yescharacteristic
310C22×C11C2×#12111yescharacteristic
311C22×C11C2×#12111yescharacteristic
312C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C11C2×#13711yescharacteristic
316C2×D11—24no—
317C2×D11—24no—
318C2×D11—24no—
319C2×D11—416no—
320C2×D11—42no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—42no—
324C2×D11—44no—
325C2×D11—44no—
326C2×D11—44no—
327C2×D11—816no—
328C2×D11—82no—
329C2×D11—82no—
330C2×D11—82no—
331C2×D11—82no—
332C4×C11—44no—
333C4×C11—82no—
334C4×C11#38614yes—
335C4×C11C2×C4×D411yescharacteristic
336C4×C11C2×C4×D411yescharacteristic
337C4×C11C2×#12011yescharacteristic
338C4×C11C2×#12311yescharacteristic
339Dic11—24no—
340Dic11—82no—
341C25—111no—
342C25—221no—
343C22×D4—114no—
344C22×D4—112no—
345C22×D4—228no—
346C22×D4—224no—
347C22×D4—222no—
348C22×D4—222no—
349C22×D4—222no—
350C22×D4—221no—
351C22×D4—222no—
352C22×D4—222no—
353C22×D4—444no—
354C22×D4—444no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—111no—
358C23×C4—114no—
359C23×C4—114no—
360C23×C4—112no—
361C23×C4—112no—
362C23×C4—222no—
363C23×C4—222no—
364C23×C4—222no—
365C23×C4—222no—
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×C8D4414yescomplemented
379C22×C8C22×D1112yes—
380#121—1116no—
381#121—2216no—
382#121—228no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—112no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4C4×D1114yes—
393C2×C4⋊C4C22×D1112yes—
394C2×C4⋊C4C22×D1112yes—
395C2×C22⋊C4—228no—
396C2×C22⋊C4—224no—
397C2×C22⋊C4—224no—
398C2×C22⋊C4—444no—
399#102—228no—
400#102—228no—
401#95—224no—
402C2×C11#189518yescomplemented
403C2×C11C2×#38611yescharacteristic
404C2×C11C2×#41811yescharacteristic
405C2×C11C2×#41711yescharacteristic
406C2×C11C2×#46811yescharacteristic
407C2×C11C2×#46811yescharacteristic
408C2×C11C2×#46911yescharacteristic
409C2×C11C2×#46911yescharacteristic
410D11—44no—
411D11—84no—
412C24—114no—
413C24—112no—
414C24—222no—
415C24—222no—
416C24—222no—
417C24—222no—
418C24—222no—
419C24—222no—
420C24—224no—
421C24—222no—
422C24—442no—
423C24—442no—
424C24—442no—
425C24—442no—
426C24—442no—
427C24—442no—
428C24D4×D1111yescharacteristic
429C2×D4—114no—
430C2×D4—2216no—
431C2×D4—228no—
432C2×D4—224no—
433C2×D4—228no—
434C2×D4—222no—
435C2×D4—222no—
436C2×D4—222no—
437C2×D4—222no—
438C2×D4—222no—
439C2×D4—448no—
440C2×D4—448no—
441C2×D4—4432no—
442C2×D4—444no—
443C2×D4—442no—
444C2×D4—444no—
445C2×D4—442no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—114no—
455C22×C4—112no—
456C22×C4—118no—
457C22×C4—114no—
458C22×C4—114no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—228no—
462C22×C4—228no—
463C22×C4—224no—
464C22×C4—228no—
465C22×C4—228no—
466C22×C4—224no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—442no—
473C22×C4—442no—
474C22×C4—442no—
475C22×C4C2×C4×D1112yes—
476C22×C4C2×D4412yes—
477C22×C4#433912yes—
478C22×C4D4×D1111yescharacteristic
479C22×C4D4×D1112yes—
480C22×C4D4×D1112yes—
481C22×C4#434312yes—
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×D4414yescomplemented
492C4⋊C4—24no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—42no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—442no—
500C4⋊C4C2×C4×D1114yes—
501C22⋊C4—2216no—
502C22⋊C4—448no—
503C11C2×#189511yescharacteristic, complemented, Sylow
504C23—114no—
505C23—222no—
506C23—222no—
507C23—222no—
508C23—222no—
509C23—222no—
510C23—222no—
511C23—228no—
512C23—228no—
513C23—228no—
514C23—224no—
515C23—444no—
516C23—444no—
517C23—444no—
518C23—444no—
519C23—442no—
520C23—442no—
521C23—442no—
522C23—442no—
523C23—442no—
524C23—442no—
525C23—448no—
526C23—448no—
527C23—448no—
528C23—884no—
529C23—884no—
530C23—884no—
531C23—884no—
532C23C22⋊C4×D1112yes—
533C23#6693712yes—
534C23#6694812yes—
535C23#6696412yes—
536C23#6696712yes—
537C23#6696712yes—
538C23#6697112yes—
539C23C2×D4×D1111yescharacteristic
540D4—224no—
541D4—224no—
542D4—4432no—
543D4—442no—
544D4—442no—
545D4—448no—
546C2×C4—24no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—48no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—84no—
554C2×C4—114no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—228no—
558C2×C4—224no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—2216no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4—884no—
567C2×C4C4×D4414yes—
568C2×C4C22⋊C4×D1112yes—
569C2×C4#6693514yes—
570C2×C4#6693712yes—
571C2×C4#6694614yes—
572C2×C4#6694714yes—
573C2×C4#6694812yes—
574C2×C4C22×C4×D1111yescharacteristic
575C2×C4C22×D4411yescharacteristic
576C2×C4C2×#433911yescharacteristic
577C2×C4C2×D4×D1111yescharacteristic
578C2×C4C2×D4×D1111yescharacteristic
579C2×C4C2×#434311yescharacteristic
580C8—24no—
581C8—224no—
582C22—224no—
583C22—224no—
584C22—224no—
585C22—442no—
586C22—442no—
587C22—442no—
588C22—442no—
589C22—4416no—
590C22—444no—
591C22—444no—
592C22—444no—
593C22—882no—
594C22—882no—
595C22—882no—
596C22—882no—
597C22—8816no—
598C22#1062227814yes—
599C22#1062238314yes—
600C22#1062239514yes—
601C22#1062241614yes—
602C22#1062242514yes—
603C22#1062247814yes—
604C22#1062249914yes—
605C22C2×C22⋊C4×D1111yescharacteristic
606C22C2×#6693711yescharacteristic
607C22C2×#6694811yescharacteristic
608C22C2×#6696411yescharacteristic
609C22C2×#6696711yescharacteristic
610C22C2×#6696711yescharacteristic
611C22C2×#6697111yescharacteristic
612C4—44no—
613C4—82no—
614C4—224no—
615C4—882no—
616C4#1062227814yes—
617C4C2×C4×D4411yescharacteristic
618C4C2×#6693511yescharacteristic
619C4C2×#6694611yescharacteristic
620C4C2×#6694711yescharacteristic
621C2—444no—
622C2—884no—
623C2#1306905318yesdirect product factor
624C2C2×#1062227811yescharacteristic
625C2C2×#1062238311yescharacteristic
626C2C2×#1062241611yescharacteristic
627C2C2×#1062249911yescharacteristic
628C2C2×#1062242511yescharacteristic
629C2C2×#1062239511yescharacteristic
630C2C2×#1062247811yescharacteristic
subgroupG/H
centerC24D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC24×C11C2×D4
prime radicalC22×#66948C2
cosocleC22×C4×C11C24
hypercenterC2×#340D11
hypocenterC11C2×#1895
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
1. C23×#4313C2semidirect
3. C22×#66885C2semidirect
4. C22×#66873C2semidirect
5. C2×#10622600C2semidirect
6. #13069053C2direct (N × H)
7. C2×#10622167C2semidirect
8. C2×C11×#340C2semidirect
22. C22×#4313C22semidirect
25. C2×#66948C4semidirect
29. C2×#66885C22semidirect
31. #10622600C22semidirect
33. C2×#66873C22semidirect
34. C11×#340C22semidirect
35. #10622167C22semidirect
65. C22×C8×C11D4semidirect
85. C22×C11⋊C8D4semidirect
93. #66948C2×C4semidirect
172. C2×C8×C11C2×D4semidirect
187. C2×C11⋊C8C2×D4semidirect
196. C2×#340D11semidirect
301. #340C2×D11semidirect
378. C22×C8D44semidirect
402. C2×C11#1895semidirect
491. C2×C8C2×D44semidirect
503. C11C2×#1895semidirect
623. C2#13069053direct (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×#669482
C22×#668852
C22×#668732
C2×#106226002
#130690532
C2×#106221672
C2×C11×#3402
C2×#189511