Finite Group Databasebeta

← C2×#13069624 #14780569

Subgroups — C2×#13069624 #14780569

Order 2816.

2182 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×#4326C211yesmaximal, characteristic, complemented
2C22×#66977C211yesmaximal, characteristic
3C22×#66899C211yesmaximal, characteristic, complemented
4C22×#66874C211yesmaximal, characteristic, complemented
5C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic
6#13069624C218yesmaximal, direct product factor
7C2×#10622167C211yesmaximal, characteristic, complemented
8C22×C11×C22⋊Q8C211yesmaximal, characteristic
9C23×Q8×C11C2211yescharacteristic
10C24×C4×C11C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C2×C11×C22⋊Q8—24no—
13C2×C11×C22⋊Q8—22no—
14C2×C11×C22⋊Q8—24no—
15C2×C11×C22⋊Q8C2214yes—
16C22×C11×C4⋊C4—21no—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4—21no—
19C22×C22⋊Dic11—21no—
20C22×#4326—24no—
21C22×#4326—24no—
22C22×#4326—24no—
23C22×#4326C2214yescomplemented
24C22×C4⋊Dic11C2211yescharacteristic
25C2×#66977—22no—
26C2×#66977—24no—
27C2×#66977—24no—
28C2×#66977C2214yes—
29C22×Dic11⋊C4—21no—
30C23×C11⋊C8C2211yescharacteristic
31C23×C11⋊C8C2211yescharacteristic
32C2×#66899—24no—
33C2×#66899C2214yescomplemented
34C2×C22⋊(C11⋊C8)—24no—
35C2×C22⋊(C11⋊C8)C2214yes—
36C2×#66874—24no—
37C2×#66874C2214yescomplemented
38#10622167C2214yescomplemented
39C25×C11D411yescharacteristic
40C22×Q8×C11—22no—
41C22×Q8×C11—21no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11—22no—
45C22×Q8×C11—22no—
46C22×Q8×C11D414yes—
47C22×Q8×C11C2312yes—
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11—22no—
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11—22no—
56C23×C4×C11D411yescharacteristic
57C23×C4×C11D412yes—
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C23×Dic11—21no—
61C23×Dic11—21no—
62C22×Dic22—22no—
63C22×Dic22—22no—
64C22×Dic22—22no—
65C22×Dic22—22no—
66C22×Dic22—22no—
67C22×Dic22—21no—
68C22×Dic22D414yes—
69C22×Dic22C2312yes—
70C11×C22⋊Q8—216no—
71C11×C22⋊Q8—28no—
72C11×C22⋊Q8—28no—
73C2×C11×C4⋊C4—28no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4D414yes—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C22⋊C4—28no—
80C2×C11×C22⋊C4—24no—
81C2×C22⋊Dic11—28no—
82C2×C22⋊Dic11—24no—
83C2×#4326—232no—
84C2×#4326—28no—
85C2×#4326—28no—
86C2×#4326—28no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11D414yes—
90C2×C4⋊Dic11C2312yes—
91#66977—216no—
92#66977—28no—
93#66977—28no—
94C2×Dic11⋊C4—28no—
95C2×Dic11⋊C4—24no—
96C22×C11⋊C8—22no—
97C22×C11⋊C8—22no—
98C22×C11⋊C8—22no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8—22no—
101C22×C11⋊C8D414yes—
102C22×C11⋊C8C2312yes—
103C22×C11⋊C8C2312yes—
104#66899—28no—
105C22⋊(C11⋊C8)—28no—
106#66874—28no—
107C2×#2001—111nomaximal, Sylow
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11Q1614yescomplemented
115C24×C11C2×D412yes—
116C24×C11C2×D411yescharacteristic
117C2×Q8×C11—24no—
118C2×Q8×C11—22no—
119C2×Q8×C11—28no—
120C2×Q8×C11—28no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—42no—
126C2×Q8×C11—42no—
127C2×Q8×C11—44no—
128C2×Q8×C11—44no—
129C2×Q8×C11C2×D414yes—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—44no—
151C22×C4×C11—44no—
152C22×C4×C11—44no—
153C22×C4×C11—44no—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11#4112yes—
162C22×C4×C11C2411yescharacteristic
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—42no—
168C22×Dic11—42no—
169C22×Dic11—42no—
170C22×Dic11—42no—
171C2×Dic22—28no—
172C2×Dic22—24no—
173C2×Dic22—28no—
174C2×Dic22—22no—
175C2×Dic22—22no—
176C2×Dic22—22no—
177C2×Dic22—22no—
178C2×Dic22—22no—
179C2×Dic22—42no—
180C2×Dic22—44no—
181C2×Dic22—42no—
182C2×Dic22—44no—
183C2×Dic22C2×D414yes—
184C11×C4⋊C4—216no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4C2×D414yes—
188C11×C22⋊C4—216no—
189C22⋊Dic11—216no—
190#4326—232no—
191C4⋊Dic11—24no—
192C4⋊Dic11—22no—
193C4⋊Dic11C2×D414yes—
194Dic11⋊C4—216no—
195C2×C11⋊C8—28no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—44no—
202C2×C11⋊C8C2×D414yes—
203C23×Q16—111no—
204C22×C22⋊Q8—111no—
205C22×C22⋊Q8D1111yescharacteristic
206C22×#103—111no—
207C22×#103—111no—
208C22×C22⋊C8—111no—
209#2001—118no—
210C2×#340—111no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—28no—
218C23×C11—28no—
219C23×C11—28no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11—44no—
224C23×C11#12012yes—
225C23×C11#12012yes—
226C23×C11#12112yes—
227C23×C11C2×Q1612yes—
228C23×C11C2×Q1614yescomplemented
229C23×C11#13512yes—
230C23×C11#13712yes—
231C23×C11#13712yes—
232C23×C11C22×D411yescharacteristic
233Q8×C11—24no—
234Q8×C11—24no—
235Q8×C11—42no—
236Q8×C11—42no—
237Q8×C11—48no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—44no—
248C2×C4×C11—48no—
249C2×C4×C11—48no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—48no—
255C2×C4×C11#12014yes—
256C2×C4×C11#12012yes—
257C2×C4×C11#12012yes—
258C2×C4×C11#12114yes—
259C2×C4×C11#12114yes—
260C2×C4×C11#12112yes—
261C2×C4×C11#12714yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—48no—
275C2×Dic11—48no—
276Dic22—24no—
277Dic22—24no—
278Dic22—42no—
279Dic22—42no—
280Dic22—48no—
281C11⋊C8—24no—
282C11⋊C8—42no—
283C23×Q8—111no—
284C23×Q8C2×D1111yescharacteristic
285C24×C4C2×D1111yescharacteristic
286C22×Q16—114no—
287C22×Q16—224no—
288C22×Q16—224no—
289C22×Q16—224no—
290C23×C8—111no—
291C23×C8—111no—
292C2×C22⋊Q8—24no—
293C2×C22⋊Q8—22no—
294C2×C22⋊Q8—24no—
295C2×C22⋊Q8—114no—
296C2×C22⋊Q8—224no—
297C2×C22⋊Q8—224no—
298C2×C22⋊Q8—222no—
299C2×C22⋊Q8C2×D1114yes—
300C22×C4⋊C4—21no—
301C22×C4⋊C4—111no—
302C22×C4⋊C4—221no—
303C22×C4⋊C4C2×D1111yescharacteristic
304C22×C22⋊C4—21no—
305C22×C22⋊C4—221no—
306C2×#103—114no—
307C2×#103—114no—
308C2×#103—224no—
309C2×#103—224no—
310C2×C22⋊C8—114no—
311C2×C22⋊C8—224no—
312#340—114no—
313C22×C11—24no—
314C22×C11—24no—
315C22×C11—24no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—416no—
320C22×C11—42no—
321C22×C11#39214yes—
322C22×C11#45114yes—
323C22×C11#45114yes—
324C22×C11#45214yes—
325C22×C11#45214yes—
326C22×C11#46714yes—
327C22×C11#47014yes—
328C22×C11C2×#12011yescharacteristic
329C22×C11C2×#12011yescharacteristic
330C22×C11C2×#12111yescharacteristic
331C22×C11C22×Q1611yescharacteristic
332C22×C11C2×#13511yescharacteristic
333C22×C11C2×#13711yescharacteristic
334C22×C11C2×#13711yescharacteristic
335C4×C11—42no—
336C4×C11—44no—
337C4×C11—44no—
338C4×C11#39214yes—
339C4×C11C2×#12011yescharacteristic
340C4×C11C2×#12111yescharacteristic
341C4×C11C2×#12111yescharacteristic
342C4×C11C2×#12711yescharacteristic
343Dic11—44no—
344Dic11—44no—
345C25C22⋊D1111yescharacteristic
346C22×Q8—22no—
347C22×Q8—21no—
348C22×Q8—22no—
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—22no—
352C22×Q8—114no—
353C22×Q8—112no—
354C22×Q8—222no—
355C22×Q8—221no—
356C22×Q8—222no—
357C22×Q8—222no—
358C22×Q8—222no—
359C22×Q8—222no—
360C22×Q8C22⋊D1114yes—
361C22×Q8C22×D1112yes—
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—221no—
371C23×C4—221no—
372C23×C4C22⋊D1112yes—
373C23×C4C22⋊D1111yescharacteristic
374C23×C4C22×D1112yes—
375C23×C4C22×D1111yescharacteristic
376C2×Q16—228no—
377C2×Q16—228no—
378C2×Q16—2232no—
379C2×Q16—228no—
380C22×C8—114no—
381C22×C8—112no—
382C22×C8—112no—
383C22×C8—222no—
384C22×C8—222no—
385C22×C8—222no—
386C22×C8—222no—
387C22×C8—222no—
388C22⋊Q8—216no—
389C22⋊Q8—28no—
390C22⋊Q8—28no—
391C22⋊Q8—228no—
392C22⋊Q8—228no—
393C22⋊Q8—2216no—
394C2×C4⋊C4—28no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—114no—
399C2×C4⋊C4—112no—
400C2×C4⋊C4—228no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—224no—
404C2×C4⋊C4C22⋊D1114yes—
405C2×C4⋊C4C22×D1112yes—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—228no—
409C2×C22⋊C4—224no—
410#103—228no—
411#103—228no—
412C22⋊C8—228no—
413C2×C11—44no—
414C2×C11#200118yescomplemented
415C2×C11C2×#39211yescharacteristic
416C2×C11C2×#45111yescharacteristic
417C2×C11C2×#45111yescharacteristic
418C2×C11C2×#45211yescharacteristic
419C2×C11C2×#45211yescharacteristic
420C2×C11C2×#46711yescharacteristic
421C2×C11C2×#47011yescharacteristic
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24#432614yescomplemented
429C24C2×C22⋊D1112yes—
430C24C2×C22⋊D1111yescharacteristic
431C2×Q8—24no—
432C2×Q8—22no—
433C2×Q8—28no—
434C2×Q8—28no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—42no—
440C2×Q8—44no—
441C2×Q8—42no—
442C2×Q8—44no—
443C2×Q8—114no—
444C2×Q8—224no—
445C2×Q8—222no—
446C2×Q8—228no—
447C2×Q8—228no—
448C2×Q8—222no—
449C2×Q8—222no—
450C2×Q8—222no—
451C2×Q8—222no—
452C2×Q8—442no—
453C2×Q8—444no—
454C2×Q8—444no—
455C2×Q8—442no—
456C2×Q8C2×C22⋊D1114yes—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—44no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4—44no—
481C22×C4—224no—
482C22×C4—224no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—442no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4D4×D1112yes—
490C22×C4D4×D1112yes—
491C22×C4D4×D1112yes—
492C22×C4#434112yes—
493C22×C4C2×C22⋊D1112yes—
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1112yes—
496C22×C4C2×C22⋊D1112yes—
497C22×C4C23×D1111yescharacteristic
498Q16—2232no—
499C2×C8—114no—
500C2×C8—228no—
501C2×C8—222no—
502C2×C8—222no—
503C2×C8—222no—
504C2×C8—222no—
505C2×C8—222no—
506C2×C8—444no—
507C4⋊C4—216no—
508C4⋊C4—24no—
509C4⋊C4—22no—
510C4⋊C4—114no—
511C4⋊C4—2216no—
512C4⋊C4—224no—
513C4⋊C4—222no—
514C4⋊C4C2×C22⋊D1114yes—
515C22⋊C4—216no—
516C22⋊C4—2216no—
517C11C2×#200111yescharacteristic, complemented, Sylow
518C23—22no—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—28no—
523C23—22no—
524C23—22no—
525C23—28no—
526C23—28no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23—44no—
531C23#6699012yes—
532C23#6699212yes—
533C23#6699512yes—
534C23C2×#432612yes—
535C23C2×#432614yescomplemented
536C23#6700312yes—
537C23#6700412yes—
538C23#6700612yes—
539C23C22×C22⋊D1111yescharacteristic
540Q8—24no—
541Q8—24no—
542Q8—42no—
543Q8—42no—
544Q8—48no—
545Q8—224no—
546Q8—224no—
547Q8—442no—
548Q8—442no—
549Q8—448no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—44no—
558C2×C4—48no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—48no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—48no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—442no—
570C2×C4—442no—
571C2×C4—448no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—448no—
575C2×C4#6699014yes—
576C2×C4#6699012yes—
577C2×C4#6699114yes—
578C2×C4#6699214yes—
579C2×C4#6699212yes—
580C2×C4#6699314yes—
581C2×C4#6700612yes—
582C2×C4C2×D4×D1111yescharacteristic
583C2×C4C2×D4×D1111yescharacteristic
584C2×C4C2×D4×D1111yescharacteristic
585C2×C4C2×#434111yescharacteristic
586C2×C4C22×C22⋊D1111yescharacteristic
587C2×C4C22×C22⋊D1111yescharacteristic
588C8—224no—
589C8—442no—
590C22—24no—
591C22—24no—
592C22—24no—
593C22—416no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—42no—
598C22#1062266014yes—
599C22#1062266314yes—
600C22#1062266414yes—
601C22#1062266514yes—
602C22#1062283614yes—
603C22#1062284114yes—
604C22#1062285214yes—
605C22C2×#6699011yescharacteristic
606C22C2×#6699211yescharacteristic
607C22C2×#6699511yescharacteristic
608C22C22×#432611yescharacteristic
609C22C2×#6700311yescharacteristic
610C22C2×#6700411yescharacteristic
611C22C2×#6700611yescharacteristic
612C4—44no—
613C4—42no—
614C4—44no—
615C4—444no—
616C4—444no—
617C4#1062283614yes—
618C4C2×#6699011yescharacteristic
619C4C2×#6699111yescharacteristic
620C4C2×#6699211yescharacteristic
621C4C2×#6699311yescharacteristic
622C2—44no—
623C2#1306962418yesdirect product factor
624C2C2×#1062283611yescharacteristic
625C2C2×#1062266311yescharacteristic
626C2C2×#1062284111yescharacteristic
627C2C2×#1062266011yescharacteristic
628C2C2×#1062285211yescharacteristic
629C2C2×#1062266411yescharacteristic
630C2C2×#1062266511yescharacteristic
subgroupG/H
centerC24C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×C22⋊Q8C2
socleC24×C11C2×D4
prime radicalC25×C11D4
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#2001
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C23×#4326C2semidirect
3. C22×#66899C2semidirect
4. C22×#66874C2semidirect
6. #13069624C2direct (N × H)
7. C2×#10622167C2semidirect
23. C22×#4326C22semidirect
33. C2×#66899C22semidirect
37. C2×#66874C22semidirect
38. #10622167C22semidirect
114. C24×C11Q16semidirect
228. C23×C11C2×Q16semidirect
414. C2×C11#2001semidirect
428. C24#4326semidirect
517. C11C2×#2001semidirect
535. C23C2×#4326semidirect
623. C2#13069624direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43262
C22×#669772
C22×#668992
C22×#668742
C22×C22⋊(C11⋊C8)2
#130696242
C2×#106221672
C22×C11×C22⋊Q82
C2×#200111