Finite Group Databasebeta

← C2×#13069125 #14755697

Subgroups — C2×#13069125 #14755697

Order 2816.

1826 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66961C211yesmaximal, characteristic
2C22×#66960C211yesmaximal, characteristic, complemented
3C2×#10622579C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic, complemented
5C22×#66887C211yesmaximal, characteristic, complemented
6#13069125C218yesmaximal, direct product factor
7C2×#10622196C211yesmaximal, characteristic, complemented
8C2×C11×#343C211yesmaximal, characteristic, complemented
9C22×#4339C2211yescharacteristic
10C23×D44C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C2×#66961—24no—
17C2×#66961—22no—
18C2×#66961C418yescomplemented
19C2×#66961C2214yes—
20C2×#66960—24no—
21C2×#66960—24no—
22C2×#66960—22no—
23C2×#66960C2214yescomplemented
24C22×D88—21no—
25C22×#4314—21no—
26C22×#4313—21no—
27C22×C8×D11—21no—
28C2×#66887—24no—
29C2×#66887C2214yescomplemented
30C2×#66874—21no—
31#10622579—22no—
32#10622579C2214yescomplemented
33C2×#66873—21no—
34C2×#66873—21no—
35C2×#66873—21no—
36C2×#66873—22no—
37C2×#66873C2214yescomplemented
38C11×#343C2214yescomplemented
39#10622196C2214yescomplemented
40C24×D11—21no—
41C23×C4×C11—21no—
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11—21no—
44C2×#4339—22no—
45C2×#4339—21no—
46C2×#4339—21no—
47C2×#4339—22no—
48C2×#4339C2×C414yes—
49C2×#4339D414yes—
50C2×#4339D412yes—
51C2×#4339C2312yes—
52C22×D44—21no—
53C22×D44—22no—
54C22×D44—21no—
55C22×D44—21no—
56C22×D44—21no—
57C22×D44—22no—
58C22×D44—22no—
59C22×D44—21no—
60C22×D44C2×C414yes—
61C22×D44D411yescharacteristic
62C22×D44C2312yes—
63C22×C4×D11—21no—
64C22×Dic22D411yescharacteristic
65C2×C11×M16—22no—
66C2×C11×M16—21no—
67C2×C11×M16—22no—
68C2×C11×M16—21no—
69C2×C11×M16C2×C414yes—
70C2×C11×M16D414yes—
71C2×C11×M16C2312yes—
72C2×C11×M16C2312yes—
73C22×C8×C11—21no—
74C22×C8×C11—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2312yes—
81C2×#4318—21no—
82C2×#4318—22no—
83C2×#4318—22no—
84C2×#4318C2312yes—
85C22×C11⋊C8—22no—
86C22×C11⋊C8—22no—
87C22×C11⋊C8—21no—
88C22×C11⋊C8D411yescharacteristic
89C22×C11⋊C8D411yescharacteristic
90C22×C11⋊C8D412yes—
91C22×C11⋊C8C2312yes—
92#66961—216no—
93#66961—28no—
94#66961C2×C4116yescomplemented
95#66960—216no—
96#66960—28no—
97#66960—28no—
98C2×D88—28no—
99C2×D88—24no—
100C2×#4314—28no—
101C2×#4314—24no—
102C2×#4313—28no—
103C2×#4313—24no—
104C2×C8×D11—28no—
105C2×C8×D11—24no—
106#66887—28no—
107#66874—24no—
108#66873—24no—
109#66873—24no—
110#66873—24no—
111C2×#1907—111nomaximal, Sylow
112C24×C11#4111yescharacteristic
113C23×D11—21no—
114C23×D11—24no—
115C23×D11—22no—
116C23×D11—41no—
117C23×D11—41no—
118C23×D11—42no—
119C23×D11—82no—
120C23×D11—82no—
121C22×C4×C11—22no—
122C22×C4×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11—82no—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11#4111yescharacteristic
133C22×C4×C11#4112yes—
134C22×C4×C11C2411yescharacteristic
135C2×C22⋊D11—24no—
136C2×C22⋊D11—22no—
137C2×C22⋊D11—24no—
138C2×C22⋊D11—22no—
139C22×Dic11—21no—
140#4339—24no—
141#4339—24no—
142#4339—24no—
143#4339—24no—
144#4339—24no—
145#4339—22no—
146#4339—22no—
147#4339C22⋊C418yes—
148#4339C22×C414yes—
149#4339C2×D414yes—
150C2×D44—24no—
151C2×D44—24no—
152C2×D44—24no—
153C2×D44—24no—
154C2×D44—24no—
155C2×D44—21no—
156C2×D44—22no—
157C2×D44—22no—
158C2×D44—22no—
159C2×D44—22no—
160C2×D44—22no—
161C2×D44—22no—
162C2×D44—42no—
163C2×D44—42no—
164C2×D44—41no—
165C2×D44—41no—
166C2×D44—42no—
167C2×D44—42no—
168C2×D44—42no—
169C2×D44C22⋊C414yes—
170C2×D44C22×C414yes—
171C2×D44C2×D412yes—
172C2×C4×D11—24no—
173C2×C4×D11—24no—
174C2×C4×D11—22no—
175C2×C4×D11—22no—
176C2×Dic22—21no—
177C2×Dic22—22no—
178C2×Dic22C22⋊C414yes—
179C2×Dic22C2×D412yes—
180C11×M16—24no—
181C11×M16—24no—
182C11×M16—22no—
183C11×M16—22no—
184C11×M16C22×C414yes—
185C11×M16C2×D414yes—
186C2×C8×C11—24no—
187C2×C8×C11—24no—
188C2×C8×C11—22no—
189C2×C8×C11—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—41no—
193C11×C4⋊C4—41no—
194#4318—22no—
195#4318—22no—
196#4318—42no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—24no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—42no—
204C2×C11⋊C8C2×D412yes—
205C2×C11⋊C8C2×D412yes—
206D88—216no—
207#4314—216no—
208#4313—216no—
209C8×D11—216no—
210C22×AGL(1,ℤ/8)—111no—
211C22×#131—111no—
212C2×#417—111no—
213C22×#102—111no—
214C22×#100—111no—
215#1907—118no—
216C2×#343D1111yescharacteristic, complemented
217C2×#341—111no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11C4×D412yes—
221C23×C11#12111yescharacteristic
222C23×C11#12111yescharacteristic
223C23×C11#12312yes—
224C23×C11C2×#4111yescharacteristic
225C22×D11—22no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11—44no—
233C22×D11—44no—
234C22×D11—88no—
235C22×D11—82no—
236C22×D11—82no—
237C22×D11—82no—
238C22×D11—82no—
239C22×D11—88no—
240C22×D11—82no—
241C22×D11—82no—
242C2×C4×C11—42no—
243C2×C4×C11—82no—
244C2×C4×C11—82no—
245C2×C4×C11—82no—
246C2×C4×C11C2×C22⋊C412yes—
247C2×C4×C11C2×C22⋊C412yes—
248C2×C4×C11C4×D412yes—
249C2×C4×C11C4×D412yes—
250C2×C4×C11C4×D412yes—
251C2×C4×C11#12012yes—
252C2×C4×C11#12012yes—
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11#12112yes—
256C2×C4×C11#12112yes—
257C2×C4×C11#12312yes—
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C22⋊D11—24no—
265C22⋊D11—24no—
266C22⋊D11—28no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269D44—24no—
270D44—24no—
271D44—22no—
272D44—24no—
273D44—42no—
274D44—42no—
275D44—44no—
276D44—44no—
277D44C2×C22⋊C414yes—
278C4×D11—24no—
279C4×D11—24no—
280C4×D11—28no—
281Dic22—22no—
282Dic22—24no—
283Dic22C2×C22⋊C414yes—
284C8×C11—24no—
285C8×C11—24no—
286C11⋊C8—22no—
287C11⋊C8—22no—
288C11⋊C8—42no—
289C22×#41—111no—
290C23×D4—111no—
291C2×AGL(1,ℤ/8)—114no—
292C2×AGL(1,ℤ/8)—118no—
293C2×AGL(1,ℤ/8)—224no—
294C2×AGL(1,ℤ/8)—222no—
295C22×SD16—221no—
296C22×D8—221no—
297C2×#131—114no—
298C2×#131—222no—
299C2×#131—224no—
300C2×#131—224no—
301C22×M16—111no—
302C22×M16—221no—
303C22×M16C2×D1111yescharacteristic
304C22×M16C2×D1111yescharacteristic
305C23×C8—111no—
306C23×C8—221no—
307C22×C4⋊C4C2×D1111yescharacteristic
308#417—114no—
309#417—222no—
310C2×#103—221no—
311C2×#102—114no—
312C2×#102—221no—
313C2×#102—221no—
314C2×#102—222no—
315C2×#102—221no—
316C2×#100—114no—
317C2×#100—224no—
318#343C2×D1114yescomplemented
319#341—114no—
320C22×C11—24no—
321C22×C11—24no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11#38612yes—
327C22×C11#38612yes—
328C22×C11#47112yes—
329C22×C11#47212yes—
330C22×C11C2×C4×D411yescharacteristic
331C22×C11C2×#12111yescharacteristic
332C22×C11C2×#12311yescharacteristic
333C2×D11—24no—
334C2×D11—48no—
335C2×D11—42no—
336C2×D11—42no—
337C2×D11—44no—
338C2×D11—84no—
339C2×D11—88no—
340C2×D11—88no—
341C2×D11—82no—
342C2×D11—82no—
343C2×D11—84no—
344C4×C11—82no—
345C4×C11#38612yes—
346C4×C11#38612yes—
347C4×C11C22×C22⋊C411yescharacteristic
348C4×C11C2×C4×D411yescharacteristic
349C4×C11C2×#12011yescharacteristic
350C4×C11C2×#12111yescharacteristic
351Dic11—24no—
352C25—221no—
353C2×#41—114no—
354C2×#41—114no—
355C2×#41—112no—
356C2×#41—112no—
357C2×#41—222no—
358C2×#41—221no—
359C2×#41—221no—
360C2×#41—222no—
361C22×Q8—111no—
362C22×D4—114no—
363C22×D4—111no—
364C22×D4—112no—
365C22×D4—221no—
366C22×D4—222no—
367C22×D4—221no—
368C22×D4—221no—
369C22×D4—222no—
370C22×D4—221no—
371C22×D4—221no—
372C22×D4—221no—
373C22×D4—222no—
374C23×C4—21no—
375C23×C4—221no—
376C23×C4C22×D1111yescharacteristic
377AGL(1,ℤ/8)—1116no—
378AGL(1,ℤ/8)—2216no—
379AGL(1,ℤ/8)—228no—
380C2×SD16—228no—
381C2×SD16—224no—
382C2×D8—228no—
383C2×D8—224no—
384#131—228no—
385#131—2216no—
386#131—228no—
387C2×M16—22no—
388C2×M16—21no—
389C2×M16—22no—
390C2×M16—21no—
391C2×M16—112no—
392C2×M16—224no—
393C2×M16—228no—
394C2×M16—221no—
395C2×M16—222no—
396C2×M16—222no—
397C2×M16C4×D1114yes—
398C2×M16D4414yes—
399C2×M16C22×D1112yes—
400C2×M16C22×D1112yes—
401C22×C8—21no—
402C22×C8—21no—
403C22×C8—111no—
404C22×C8—111no—
405C22×C8—112no—
406C22×C8—112no—
407C22×C8—224no—
408C22×C8—228no—
409C22×C8—222no—
410C22×C8—222no—
411C22×C8—221no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4C22×D1112yes—
418#103—224no—
419#102—224no—
420#102—224no—
421#102—224no—
422#100—228no—
423C2×C11—21no—
424C2×C11—21no—
425C2×C11—22no—
426C2×C11#190714yescomplemented
427C2×C11C2×#38611yescharacteristic
428C2×C11C2×#47111yescharacteristic
429C2×C11C2×#47211yescharacteristic
430D11—44no—
431D11—84no—
432C24—221no—
433C24—224no—
434C24—222no—
435C24—441no—
436C24—441no—
437C24—442no—
438C24—882no—
439C24—882no—
440C24#433911yescharacteristic
441#41—118no—
442#41—114no—
443#41—114no—
444#41—224no—
445#41—224no—
446#41—224no—
447#41—224no—
448#41—224no—
449#41—222no—
450#41—222no—
451C2×Q8—114no—
452C2×Q8—112no—
453C2×Q8—221no—
454C2×Q8—222no—
455C2×D4—114no—
456C2×D4—114no—
457C2×D4—112no—
458C2×D4—224no—
459C2×D4—222no—
460C2×D4—224no—
461C2×D4—222no—
462C2×D4—224no—
463C2×D4—224no—
464C2×D4—224no—
465C2×D4—221no—
466C2×D4—224no—
467C2×D4—224no—
468C2×D4—222no—
469C2×D4—222no—
470C2×D4—222no—
471C2×D4—222no—
472C2×D4—222no—
473C2×D4—222no—
474C2×D4—442no—
475C2×D4—442no—
476C2×D4—441no—
477C2×D4—441no—
478C2×D4—442no—
479C2×D4—442no—
480C2×D4—442no—
481C22×C4—22no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—82no—
485C22×C4—221no—
486C22×C4—224no—
487C22×C4—222no—
488C22×C4—224no—
489C22×C4—222no—
490C22×C4C2×C4×D1112yes—
491C22×C4C2×D4412yes—
492C22×C4#433911yescharacteristic
493C22×C4D4×D1112yes—
494C22×C4D4×D1111yescharacteristic
495C22×C4D4×D1111yescharacteristic
496C22×C4D4×D1111yescharacteristic
497C22×C4D4×D1111yescharacteristic
498C22×C4#434312yes—
499C22×C4C23×D1111yescharacteristic
500SD16—2216no—
501D8—2216no—
502M16—24no—
503M16—24no—
504M16—22no—
505M16—22no—
506M16—2216no—
507M16—222no—
508M16—222no—
509M16—442no—
510M16C2×C4×D1114yes—
511M16C2×D4414yes—
512C2×C8—24no—
513C2×C8—24no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—112no—
517C2×C8—112no—
518C2×C8—2216no—
519C2×C8—222no—
520C2×C8—222no—
521C2×C8—224no—
522C2×C8—222no—
523C2×C8—222no—
524C2×C8—222no—
525C2×C8—442no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C11C2×#190711yescharacteristic, complemented, Sylow
531C23—22no—
532C23—22no—
533C23—222no—
534C23—224no—
535C23—224no—
536C23—442no—
537C23—442no—
538C23—442no—
539C23—442no—
540C23—444no—
541C23—444no—
542C23—882no—
543C23—882no—
544C23—888no—
545C23—882no—
546C23—882no—
547C23—888no—
548C23—882no—
549C23—882no—
550C23C4×D4412yes—
551C23#6693711yescharacteristic
552C23#6693711yescharacteristic
553C23#6694712yes—
554C23C2×#433911yescharacteristic
555Q8—114no—
556Q8—222no—
557Q8—224no—
558D4—114no—
559D4—224no—
560D4—224no—
561D4—228no—
562D4—224no—
563D4—224no—
564D4—222no—
565D4—224no—
566D4—442no—
567D4—442no—
568D4—444no—
569D4—444no—
570C2×C4—42no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4—222no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—228no—
579C2×C4C4×D4412yes—
580C2×C4C22⋊C4×D1112yes—
581C2×C4C22⋊C4×D1112yes—
582C2×C4#6693512yes—
583C2×C4#6693512yes—
584C2×C4#6693711yescharacteristic
585C2×C4#6693711yescharacteristic
586C2×C4#6694612yes—
587C2×C4#6694612yes—
588C2×C4#6694712yes—
589C2×C4#6694812yes—
590C2×C4#6694812yes—
591C2×C4C22×C4×D1111yescharacteristic
592C2×C4C22×D4411yescharacteristic
593C2×C4C2×D4×D1111yescharacteristic
594C2×C4C2×D4×D1111yescharacteristic
595C2×C4C2×D4×D1111yescharacteristic
596C2×C4C2×#434311yescharacteristic
597C8—24no—
598C8—24no—
599C8—222no—
600C8—222no—
601C8—442no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—24no—
607C22—24no—
608C22—224no—
609C22—442no—
610C22—442no—
611C22—448no—
612C22—444no—
613C22—884no—
614C22—884no—
615C22—888no—
616C22—882no—
617C22—882no—
618C22—888no—
619C22#1062227812yes—
620C22#1062227812yes—
621C22#1062236212yes—
622C22#1062236712yes—
623C22C2×C4×D4411yescharacteristic
624C22C2×#6693711yescharacteristic
625C22C2×#6694711yescharacteristic
626C4—82no—
627C4—224no—
628C4#1062227812yes—
629C4#1062227812yes—
630C4C2×C22⋊C4×D1111yescharacteristic
631C4C2×#6693511yescharacteristic
632C4C2×#6694611yescharacteristic
633C4C2×#6694811yescharacteristic
634C2—21no—
635C2—21no—
636C2—22no—
637C2—444no—
638C2—884no—
639C2#1306912514yesdirect product factor
640C2C2×#1062227811yescharacteristic
641C2C2×#1062236711yescharacteristic
642C2C2×#1062236211yescharacteristic
subgroupG/H
centerC23#66937
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#343C2
socleC23×C11#121
prime radicalC22×#66961C2
cosocleC22×C4×C11C24
hypercenterC2×#343D11
hypocenterC11C2×#1907
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
2. C22×#66960C2semidirect
3. C2×#10622579C2semidirect
4. C22×#66873C2semidirect
5. C22×#66887C2semidirect
6. #13069125C2direct (N × H)
7. C2×#10622196C2semidirect
8. C2×C11×#343C2semidirect
18. C2×#66961C4semidirect
23. C2×#66960C22semidirect
29. C2×#66887C22semidirect
32. #10622579C22semidirect
37. C2×#66873C22semidirect
38. C11×#343C22semidirect
39. #10622196C22semidirect
94. #66961C2×C4semidirect
216. C2×#343D11semidirect
318. #343C2×D11semidirect
426. C2×C11#1907semidirect
530. C11C2×#1907semidirect
639. C2#13069125direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669612
C22×#669602
C2×#106225792
C22×#668732
C22×#668872
#130691252
C2×#106221962
C2×C11×#3432
C2×#190711