Finite Group Databasebeta

← C2×#13069730 #14780965

Subgroups — C2×#13069730 #14780965

Order 2816.

2030 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic, complemented
2C23×#4324C211yesmaximal, characteristic, complemented
3C22×#66888C211yesmaximal, characteristic, complemented
4C22×#66897C211yesmaximal, characteristic, complemented
5C2×#10622847C211yesmaximal, characteristic, complemented
6#13069730C218yesmaximal, direct product factor
7C2×#10622196C211yesmaximal, characteristic, complemented
8C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C2×C11×AGL(1,ℤ/8)—22no—
13C2×C11×AGL(1,ℤ/8)—24no—
14C2×C11×AGL(1,ℤ/8)—24no—
15C2×C11×AGL(1,ℤ/8)C2214yes—
16C22×C11×SD16—21no—
17C22×C11×D8—21no—
18C22×C11×M16C2211yescharacteristic
19C2×#67004—22no—
20C2×#67004—24no—
21C2×#67004—24no—
22C2×#67004C2214yescomplemented
23C22×#4326—21no—
24C22×#4324—24no—
25C22×#4324—21no—
26C22×#4324—24no—
27C22×#4324—22no—
28C22×#4324—22no—
29C22×#4324C2214yescomplemented
30C22×#4318C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32C23×C11⋊C8C2211yescharacteristic
33#10622847—22no—
34#10622847C2214yescomplemented
35C2×#66897—24no—
36C2×#66897C2214yescomplemented
37C2×C22⋊(C11⋊C8)—22no—
38C2×#66888—24no—
39C2×#66888C2214yescomplemented
40#10622196C2214yescomplemented
41C25×C11—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41D412yes—
49C2×C11×#41C2312yes—
50C22×Q8×C11D411yescharacteristic
51C22×D4×C11—21no—
52C22×D4×C11—22no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—22no—
58C22×D4×C11—22no—
59C22×D4×C11—21no—
60C22×D4×C11D411yescharacteristic
61C22×D4×C11D414yes—
62C22×D4×C11C2312yes—
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C22×Dic22—21no—
67C22×Dic22—21no—
68C22×Dic22—22no—
69C22×Dic22—21no—
70C22×Dic22—22no—
71C22×Dic22—21no—
72C22×Dic22—22no—
73C22×Dic22—21no—
74C22×Dic22D414yes—
75C22×Dic22C2312yes—
76C11×AGL(1,ℤ/8)—216no—
77C11×AGL(1,ℤ/8)—28no—
78C11×AGL(1,ℤ/8)—28no—
79C2×C11×SD16—28no—
80C2×C11×SD16—24no—
81C2×C11×D8—28no—
82C2×C11×D8—24no—
83C2×C11×M16—22no—
84C2×C11×M16—21no—
85C2×C11×M16D414yes—
86C2×C11×M16C2312yes—
87C22×C8×C11—21no—
88#67004—216no—
89#67004—28no—
90#67004—28no—
91C2×#4326—28no—
92C2×#4326—24no—
93C2×#4324—216no—
94C2×#4324—216no—
95C2×#4324—28no—
96C2×#4324—28no—
97C2×#4324—24no—
98C2×#4324—28no—
99C2×#4324—28no—
100C2×#4318—22no—
101C2×#4318—21no—
102C2×#4318—21no—
103C2×#4318—22no—
104C2×#4318—22no—
105C2×#4318D414yes—
106C2×#4318C2312yes—
107C2×#4318C2312yes—
108C22×C11⋊C8—22no—
109C22×C11⋊C8—22no—
110C22×C11⋊C8—21no—
111C22×C11⋊C8—21no—
112C22×C11⋊C8D412yes—
113C22×C11⋊C8D412yes—
114C22×C11⋊C8C2312yes—
115#66897—28no—
116C22⋊(C11⋊C8)—28no—
117#66888—28no—
118C2×#2019—111nomaximal, Sylow
119C24×C11—21no—
120C24×C11—24no—
121C24×C11—22no—
122C24×C11—42no—
123C24×C11—41no—
124C24×C11—41no—
125C24×C11—84no—
126C24×C11#4111yescharacteristic
127C11×#41—24no—
128C11×#41—24no—
129C11×#41—22no—
130C11×#41—22no—
131C11×#41—22no—
132C11×#41—22no—
133C11×#41—42no—
134C11×#41—42no—
135C11×#41—42no—
136C11×#41—42no—
137C2×Q8×C11—21no—
138C2×Q8×C11—22no—
139C2×Q8×C11—22no—
140C2×Q8×C11C2×D412yes—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—24no—
144C2×D4×C11—24no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—24no—
148C2×D4×C11—24no—
149C2×D4×C11—24no—
150C2×D4×C11—21no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—42no—
157C2×D4×C11—42no—
158C2×D4×C11—42no—
159C2×D4×C11—42no—
160C2×D4×C11—42no—
161C2×D4×C11—41no—
162C2×D4×C11—41no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11C2×D412yes—
166C2×D4×C11C2×D414yes—
167C22×C4×C11—21no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D412yes—
180C22×C4×C11#4111yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C22×Dic11—24no—
183C22×Dic11—22no—
184C22×Dic11—41no—
185C22×Dic11—42no—
186C22×Dic11—41no—
187C2×Dic22—24no—
188C2×Dic22—24no—
189C2×Dic22—24no—
190C2×Dic22—24no—
191C2×Dic22—24no—
192C2×Dic22—22no—
193C2×Dic22—22no—
194C2×Dic22—22no—
195C2×Dic22—22no—
196C2×Dic22—22no—
197C2×Dic22—42no—
198C2×Dic22—42no—
199C2×Dic22—41no—
200C2×Dic22—42no—
201C2×Dic22—41no—
202C2×Dic22—42no—
203C2×Dic22—42no—
204C2×Dic22C2×D414yes—
205C11×SD16—216no—
206C11×D8—216no—
207C11×M16—24no—
208C11×M16—22no—
209C11×M16C2×D414yes—
210C2×C8×C11—24no—
211C2×C8×C11—22no—
212#4326—216no—
213#4324—232no—
214#4324—216no—
215#4318—24no—
216#4318—22no—
217#4318—22no—
218#4318—22no—
219#4318—42no—
220#4318C2×D414yes—
221C2×C11⋊C8—24no—
222C2×C11⋊C8—24no—
223C2×C11⋊C8—24no—
224C2×C11⋊C8—22no—
225C2×C11⋊C8—22no—
226C2×C11⋊C8—22no—
227C2×C11⋊C8—22no—
228C2×C11⋊C8—42no—
229C2×C11⋊C8C2×D414yes—
230C22×#137—111no—
231C22×AGL(1,ℤ/8)D1111yescharacteristic
232C23×SD16—111no—
233C22×#101—111no—
234C22×#100—111no—
235C2×#408—111no—
236#2019—118no—
237C2×#341—111no—
238C23×C11—24no—
239C23×C11—22no—
240C23×C11—24no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—44no—
245C23×C11—44no—
246C23×C11—44no—
247C23×C11—88no—
248C23×C11—84no—
249C23×C11—88no—
250C23×C11—84no—
251C23×C11—84no—
252C23×C11#12112yes—
253C23×C11#12111yescharacteristic
254C23×C11#12112yes—
255C23×C11#12111yescharacteristic
256C23×C11C2×#4111yescharacteristic
257Q8×C11—22no—
258Q8×C11—22no—
259Q8×C11—42no—
260D4×C11—24no—
261D4×C11—22no—
262D4×C11—22no—
263D4×C11—24no—
264D4×C11—42no—
265D4×C11—42no—
266D4×C11—44no—
267D4×C11—42no—
268D4×C11—42no—
269D4×C11—44no—
270D4×C11—44no—
271D4×C11—42no—
272C2×C4×C11—22no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—44no—
277C2×C4×C11#12012yes—
278C2×C4×C11#12012yes—
279C2×C4×C11#12012yes—
280C2×C4×C11#12012yes—
281C2×C4×C11#12012yes—
282C2×C4×C11#12012yes—
283C2×C4×C11#12112yes—
284C2×C4×C11#12111yescharacteristic
285C2×C4×C11#12112yes—
286C2×C4×C11#12111yescharacteristic
287C2×C4×C11#12712yes—
288C2×C4×C11#12712yes—
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C22×D411yescharacteristic
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C22×D411yescharacteristic
295C2×Dic11—24no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—44no—
299C2×Dic11—44no—
300Dic22—24no—
301Dic22—24no—
302Dic22—42no—
303Dic22—42no—
304Dic22—44no—
305Dic22—44no—
306C8×C11—24no—
307C11⋊C8—24no—
308C11⋊C8—24no—
309C11⋊C8—42no—
310C22×#41C2×D1111yescharacteristic
311C23×Q8—111no—
312C23×D4C2×D1111yescharacteristic
313C2×#137—114no—
314C2×#137—224no—
315C2×#137—224no—
316C2×#137—222no—
317C2×AGL(1,ℤ/8)—22no—
318C2×AGL(1,ℤ/8)—24no—
319C2×AGL(1,ℤ/8)—24no—
320C2×AGL(1,ℤ/8)C2×D1114yes—
321C22×Q16—221no—
322C22×SD16—21no—
323C22×SD16—114no—
324C22×SD16—222no—
325C22×SD16—222no—
326C22×SD16—224no—
327C22×SD16—224no—
328C22×SD16—221no—
329C22×D8—21no—
330C22×M16—111no—
331C22×M16—111no—
332C22×M16C2×D1111yescharacteristic
333C23×C8—111no—
334C2×#101—114no—
335C2×#101—224no—
336C2×#100—114no—
337C2×#100—224no—
338#408—114no—
339#408—222no—
340C2×C22⋊C8—222no—
341#341—114no—
342C22×C11—24no—
343C22×C11—24no—
344C22×C11—22no—
345C22×C11—22no—
346C22×C11—42no—
347C22×C11—44no—
348C22×C11—44no—
349C22×C11—84no—
350C22×C11—84no—
351C22×C11—88no—
352C22×C11—84no—
353C22×C11—88no—
354C22×C11—84no—
355C22×C11#39212yes—
356C22×C11#39212yes—
357C22×C11#47114yes—
358C22×C11C2×#12111yescharacteristic
359C22×C11C2×#12111yescharacteristic
360C22×C11C2×#12111yescharacteristic
361C4×C11—42no—
362C4×C11#39212yes—
363C4×C11#39212yes—
364C4×C11C2×#12011yescharacteristic
365C4×C11C2×#12011yescharacteristic
366C4×C11C2×#12011yescharacteristic
367C4×C11C2×#12711yescharacteristic
368Dic11—44no—
369C25—21no—
370C2×#41—21no—
371C2×#41—21no—
372C2×#41—22no—
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—22no—
376C2×#41C22⋊D1112yes—
377C2×#41C22×D1112yes—
378C22×Q8—114no—
379C22×Q8—112no—
380C22×Q8—221no—
381C22×Q8—222no—
382C22×Q8—221no—
383C22×Q8—221no—
384C22×Q8—222no—
385C22×Q8—222no—
386C22×Q8—221no—
387C22×Q8—221no—
388C22×Q8C22⋊D1111yescharacteristic
389C22×D4—21no—
390C22×D4—22no—
391C22×D4—21no—
392C22×D4—21no—
393C22×D4—22no—
394C22×D4—21no—
395C22×D4—21no—
396C22×D4—21no—
397C22×D4—22no—
398C22×D4C22⋊D1111yescharacteristic
399C22×D4C22⋊D1114yes—
400C22×D4C22×D1112yes—
401C23×C4—21no—
402C23×C4—221no—
403C23×C4C22×D1111yescharacteristic
404#137—228no—
405#137—228no—
406#137—2216no—
407AGL(1,ℤ/8)—216no—
408AGL(1,ℤ/8)—28no—
409AGL(1,ℤ/8)—28no—
410C2×Q16—228no—
411C2×Q16—224no—
412C2×SD16—28no—
413C2×SD16—24no—
414C2×SD16—228no—
415C2×SD16—228no—
416C2×SD16—2216no—
417C2×SD16—2216no—
418C2×SD16—228no—
419C2×SD16—228no—
420C2×SD16—224no—
421C2×D8—28no—
422C2×D8—24no—
423C2×M16—22no—
424C2×M16—21no—
425C2×M16—114no—
426C2×M16—112no—
427C2×M16—112no—
428C2×M16—222no—
429C2×M16—221no—
430C2×M16—221no—
431C2×M16—222no—
432C2×M16—222no—
433C2×M16C22⋊D1114yes—
434C2×M16C22×D1112yes—
435C22×C8—21no—
436C22×C8—112no—
437C22×C8—112no—
438C22×C8—112no—
439C22×C8—222no—
440C22×C8—222no—
441C22×C8—221no—
442C22×C8—221no—
443#101—228no—
444#100—228no—
445C22⋊C8—228no—
446C2×C11—21no—
447C2×C11—21no—
448C2×C11—22no—
449C2×C11—82no—
450C2×C11—84no—
451C2×C11#201914yescomplemented
452C2×C11C2×#39211yescharacteristic
453C2×C11C2×#47112yes—
454C24—21no—
455C24—24no—
456C24—22no—
457C24—42no—
458C24—41no—
459C24—41no—
460C24—84no—
461C24#434111yescharacteristic
462#41—24no—
463#41—24no—
464#41—22no—
465#41—22no—
466#41—22no—
467#41—22no—
468#41—42no—
469#41—42no—
470#41—42no—
471#41—42no—
472C2×Q8—21no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—114no—
476C2×Q8—224no—
477C2×Q8—222no—
478C2×Q8—224no—
479C2×Q8—224no—
480C2×Q8—224no—
481C2×Q8—224no—
482C2×Q8—222no—
483C2×Q8—222no—
484C2×Q8—222no—
485C2×Q8—222no—
486C2×Q8—441no—
487C2×Q8—442no—
488C2×Q8—441no—
489C2×Q8—442no—
490C2×Q8—442no—
491C2×Q8—442no—
492C2×Q8—442no—
493C2×Q8C2×C22⋊D1112yes—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—24no—
497C2×D4—24no—
498C2×D4—22no—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—22no—
502C2×D4—24no—
503C2×D4—24no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4C2×C22⋊D1112yes—
519C2×D4C2×C22⋊D1114yes—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—224no—
526C22×C4—222no—
527C22×C4—441no—
528C22×C4—442no—
529C22×C4—441no—
530C22×C4D4×D1112yes—
531C22×C4D4×D1111yescharacteristic
532C22×C4D4×D1112yes—
533C22×C4D4×D1111yescharacteristic
534C22×C4#434111yescharacteristic
535C22×C4C2×C22⋊D1112yes—
536C22×C4C2×C22⋊D1111yescharacteristic
537C22×C4C2×C22⋊D1111yescharacteristic
538C22×C4C2×C22⋊D1112yes—
539C22×C4C23×D1111yescharacteristic
540Q16—2216no—
541SD16—216no—
542SD16—2232no—
543SD16—2216no—
544D8—216no—
545M16—24no—
546M16—22no—
547M16—114no—
548M16—224no—
549M16—222no—
550M16—222no—
551M16—222no—
552M16—442no—
553M16C2×C22⋊D1114yes—
554C2×C8—24no—
555C2×C8—22no—
556C2×C8—114no—
557C2×C8—224no—
558C2×C8—224no—
559C2×C8—224no—
560C2×C8—222no—
561C2×C8—222no—
562C2×C8—222no—
563C2×C8—222no—
564C2×C8—442no—
565C11C2×#201911yescharacteristic, complemented, Sylow
566C23—24no—
567C23—22no—
568C23—24no—
569C23—44no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—44no—
574C23—44no—
575C23—84no—
576C23—88no—
577C23—84no—
578C23—88no—
579C23—84no—
580C23#6699112yes—
581C23#6699211yescharacteristic
582C23#6699212yes—
583C23#6699211yescharacteristic
584C23C2×#434111yescharacteristic
585Q8—22no—
586Q8—22no—
587Q8—42no—
588Q8—224no—
589Q8—224no—
590Q8—442no—
591Q8—444no—
592Q8—444no—
593Q8—442no—
594D4—24no—
595D4—22no—
596D4—22no—
597D4—24no—
598D4—42no—
599D4—42no—
600D4—44no—
601D4—42no—
602D4—42no—
603D4—44no—
604D4—44no—
605D4—42no—
606C2×C4—22no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—44no—
611C2×C4—224no—
612C2×C4—442no—
613C2×C4—442no—
614C2×C4—444no—
615C2×C4—444no—
616C2×C4#6699012yes—
617C2×C4#6699012yes—
618C2×C4#6699012yes—
619C2×C4#6699012yes—
620C2×C4#6699112yes—
621C2×C4#6699211yescharacteristic
622C2×C4#6699212yes—
623C2×C4#6699211yescharacteristic
624C2×C4#6699312yes—
625C2×C4#6699312yes—
626C2×C4#6700612yes—
627C2×C4#6700612yes—
628C2×C4C2×D4×D1111yescharacteristic
629C2×C4C2×D4×D1111yescharacteristic
630C2×C4C2×D4×D1111yescharacteristic
631C2×C4C22×C22⋊D1111yescharacteristic
632C2×C4C22×C22⋊D1111yescharacteristic
633C2×C4C22×C22⋊D1111yescharacteristic
634C8—24no—
635C8—224no—
636C8—224no—
637C8—442no—
638C22—22no—
639C22—22no—
640C22—24no—
641C22—24no—
642C22—44no—
643C22—42no—
644C22—44no—
645C22—84no—
646C22—84no—
647C22—88no—
648C22—84no—
649C22—84no—
650C22—88no—
651C22#1062281314yes—
652C22#1062283612yes—
653C22#1062283612yes—
654C22C2×#6699111yescharacteristic
655C22C2×#6699211yescharacteristic
656C22C2×#6699211yescharacteristic
657C4—42no—
658C4—444no—
659C4#1062283612yes—
660C4#1062283612yes—
661C4C2×#6699011yescharacteristic
662C4C2×#6699011yescharacteristic
663C4C2×#6699311yescharacteristic
664C4C2×#6700611yescharacteristic
665C2—21no—
666C2—21no—
667C2—22no—
668C2—82no—
669C2—84no—
670C2#1306973014yesdirect product factor
671C2C2×#1062283611yescharacteristic
672C2C2×#1062281312yes—
subgroupG/H
centerC23#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC22×C11×AGL(1,ℤ/8)C2
socleC23×C11#121
hypercenterC22×AGL(1,ℤ/8)D11
hypocenterC11C2×#2019
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×#67004C2semidirect
2. C23×#4324C2semidirect
3. C22×#66888C2semidirect
4. C22×#66897C2semidirect
5. C2×#10622847C2semidirect
6. #13069730C2direct (N × H)
7. C2×#10622196C2semidirect
22. C2×#67004C22semidirect
29. C22×#4324C22semidirect
34. #10622847C22semidirect
36. C2×#66897C22semidirect
39. C2×#66888C22semidirect
40. #10622196C22semidirect
451. C2×C11#2019semidirect
565. C11C2×#2019semidirect
670. C2#13069730direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670042
C23×#43242
C22×#668882
C22×#668972
C2×#106228472
#130697302
C2×#106221962
C22×C11×AGL(1,ℤ/8)2
C2×#201911