Finite Group Databasebeta

← C2×#13070606 #14907781

Subgroups — C2×#13070606 #14907781

Order 2816.

1320 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622666C211yesmaximal, characteristic, complemented
2C2×#10622645C211yesmaximal, characteristic
3C2×#10622674C211yesmaximal, characteristic, complemented
4#13070606C218yesmaximal, direct product factor
5C2×#10622179C211yesmaximal, characteristic, complemented
6C2×#10622177C211yesmaximal, characteristic, complemented
7C2×#10622174C211yesmaximal, characteristic, complemented
8C2×C11×#551C211yesmaximal, characteristic, complemented
9C2×#67037C2211yescharacteristic
10C11×#551—22no—
11C11×#551—22no—
12C11×#551—22no—
13C11×#551C2214yescomplemented
14C2×C11×#126—21no—
15C2×C11×#124C2211yescharacteristic
16C2×C11×#123—21no—
17C2×C11×#123C2211yescharacteristic
18C2×C11×C22⋊Q8—21no—
19C2×C11×#120C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C11×#117—21no—
22C22×C11×C22⋊C4—21no—
23C2×#67006—21no—
24C2×#66995—21no—
25C2×#66982—21no—
26C2×#66898C2211yescharacteristic
27C2×#66898C2211yescharacteristic
28C2×#66897C2211yescharacteristic
29#10622674—22no—
30#10622674C2214yescomplemented
31#10622666—22no—
32#10622666C2214yescomplemented
33#10622645—22no—
34#10622645C2214yes—
35C2×#66870—21no—
36C2×#66870—21no—
37C2×#66869—21no—
38#10622179C2214yescomplemented
39#10622177C2214yescomplemented
40#10622174C2214yescomplemented
41C25×C11D411yescharacteristic
42C22×Q8×C11D411yescharacteristic, complemented
43C22×D4×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×C4×C11—21no—
47C23×C4×C11D411yescharacteristic, complemented
48C22×C22⋊D11—21no—
49C22×C22⋊D11—21no—
50C22×C22⋊D11—41no—
51#67037—21no—
52#67037—21no—
53#67037—21no—
54#67037—42no—
55#67037C2312yes—
56C2×#4341—41no—
57C2×D4×D11—41no—
58C2×#4339—21no—
59C11×#126—24no—
60C11×#126—24no—
61C11×#124—21no—
62C11×#124—21no—
63C11×#124D412yescomplemented
64C11×#124C2312yes—
65C11×#123—24no—
66C11×#123—21no—
67C11×#123—21no—
68C11×#123—24no—
69C11×#123D412yescomplemented
70C11×#123C2312yes—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8—24no—
73C11×#120—21no—
74C11×#120—21no—
75C11×#120D412yes—
76C11×#120C2312yes—
77C4×D4×C11—24no—
78C4×D4×C11—24no—
79C11×#117—24no—
80C11×#117—24no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—24no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—24no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C11×C22⋊C4D411yescharacteristic, complemented
95C2×C42×C11—21no—
96C2×C42×C11D411yescharacteristic, complemented
97#67006—24no—
98#67006—42no—
99C2×C22⋊Dic11—21no—
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11—41no—
102C2×#4326—41no—
103#66995—24no—
104#66995—42no—
105C2×#4325—41no—
106#66982—24no—
107#66982—42no—
108C2×(C2×D11)⋊C4—41no—
109C2×Dic11⋊C4—41no—
110C2×#4318—21no—
111#66898—21no—
112#66898—21no—
113#66898C2312yes—
114#66898C2312yes—
115#66897—21no—
116#66897C2312yes—
117#66870—24no—
118#66870—24no—
119#66869—24no—
120C2×#2197—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11—21no—
123C24×C11—41no—
124C24×C11—44no—
125C24×C11—41no—
126C24×C11C2×D411yescharacteristic
127C24×C11C2×D411yescharacteristic
128C24×C11C2×D412yes—
129C23×D11—21no—
130C23×D11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—41no—
133C2×Q8×C11—41no—
134C2×Q8×C11C2×D412yescomplemented
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—41no—
138C2×D4×C11—41no—
139C2×D4×C11—44no—
140C2×D4×C11C2×D411yescharacteristic
141C2×D4×C11C2×D411yescharacteristic
142C2×D4×C11C2×D411yescharacteristic
143C2×D4×C11C2411yescharacteristic
144C22×C4×C11—24no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—24no—
151C22×C4×C11—21no—
152C22×C4×C11—44no—
153C22×C4×C11—41no—
154C22×C4×C11—41no—
155C22×C4×C11—81no—
156C22×C4×C11—81no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yescomplemented
159C2×C22⋊D11—22no—
160C2×C22⋊D11—22no—
161C2×C22⋊D11—22no—
162C2×C22⋊D11—22no—
163C2×C22⋊D11—44no—
164C2×C22⋊D11—41no—
165C2×C22⋊D11—41no—
166C2×C22⋊D11—41no—
167C2×C22⋊D11—41no—
168C2×C22⋊D11—41no—
169C2×C22⋊D11—41no—
170C2×C22⋊D11—41no—
171C2×C22⋊D11—84no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—41no—
175C22×Dic11—41no—
176#4341—42no—
177#4341—42no—
178#4341—42no—
179#4341—42no—
180D4×D11—42no—
181D4×D11—42no—
182D4×D11—42no—
183D4×D11—42no—
184#4339—22no—
185#4339—22no—
186#4339—41no—
187#4339—41no—
188C2×D44—21no—
189C2×C4×D11—41no—
190C2×Dic22—21no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—24no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4—21no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4C2×D412yes—
209C11×C22⋊C4C2×D412yescomplemented
210C42×C11—24no—
211C42×C11—21no—
212C42×C11C2×D412yescomplemented
213C22⋊Dic11—22no—
214C22⋊Dic11—22no—
215C22⋊Dic11—41no—
216C22⋊Dic11—41no—
217C22⋊Dic11—44no—
218#4326—44no—
219#4325—44no—
220(C2×D11)⋊C4—44no—
221Dic11⋊C4—44no—
222#4318—22no—
223#4318—41no—
224C2×C11⋊C8—41no—
225C2×#551D1111yescharacteristic, complemented
226C2×#458—111no—
227C2×B(4,𝔽2)—111no—
228C2×#455—111no—
229#2197—118no—
230C2×#354—111no—
231C2×#352—111no—
232C2×AΣL(1,𝔽16)—111no—
233C23×C11—24no—
234C23×C11—22no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—44no—
244C23×C11—44no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—44no—
248C23×C11—81no—
249C23×C11—84no—
250C23×C11—82no—
251C23×C11#12011yescharacteristic
252C23×C11#12011yescharacteristic
253C23×C11#12011yescharacteristic
254C23×C11C22×D411yescharacteristic
255C23×C11C22×D411yescharacteristic
256C22×D11—22no—
257C22×D11—22no—
258C22×D11—41no—
259C22×D11—41no—
260C22×D11—41no—
261C22×D11—82no—
262C22×D11—82no—
263Q8×C11—42no—
264Q8×C11—81no—
265D4×C11—41no—
266D4×C11—41no—
267D4×C11—41no—
268D4×C11—41no—
269D4×C11—44no—
270D4×C11—44no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—48no—
281C2×C4×C11—42no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—42no—
287C2×C4×C11—81no—
288C2×C4×C11—84no—
289C2×C4×C11#12011yescharacteristic
290C2×C4×C11C22×D411yescharacteristic
291C22⋊D11—42no—
292C22⋊D11—42no—
293C22⋊D11—42no—
294C22⋊D11—42no—
295C22⋊D11—42no—
296C22⋊D11—42no—
297C22⋊D11—88no—
298C2×Dic11—22no—
299C2×Dic11—22no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—42no—
304C2×Dic11—42no—
305C2×Dic11—82no—
306C2×Dic11—82no—
307D44—22no—
308D44—41no—
309C4×D11—42no—
310C4×D11—42no—
311Dic22—22no—
312Dic22—41no—
313C11⋊C8—42no—
314C2×H(5,𝔽2)—111no—
315C2×#137—221no—
316#551—22no—
317#551—22no—
318#551—22no—
319#551C2×D1114yescomplemented
320C2×#126—21no—
321C2×#124C2×D1111yescharacteristic
322C2×#123—21no—
323C2×#123—221no—
324C2×#123C2×D1111yescharacteristic
325C2×C22⋊Q8—21no—
326C2×#120—221no—
327C2×#120C2×D1111yescharacteristic
328C2×C4×D4—21no—
329C2×#117—21no—
330C22×C22⋊C4—21no—
331#458—114no—
332#458—222no—
333B(4,𝔽2)—114no—
334B(4,𝔽2)—222no—
335#455—114no—
336#455—222no—
337C2×#104—221no—
338C2×#100—111no—
339C2×#99—111no—
340C2×#99—111no—
341C2×#99—221no—
342C2×#99—221no—
343#354—114no—
344#352—114no—
345AΣL(1,𝔽16)—114no—
346C22×C11—22no—
347C22×C11—24no—
348C22×C11—21no—
349C22×C11—21no—
350C22×C11—21no—
351C22×C11—21no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—42no—
357C22×C11—44no—
358C22×C11—44no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—44no—
362C22×C11—42no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—82no—
366C22×C11—84no—
367C22×C11B(4,𝔽2)11yescharacteristic
368C22×C11B(4,𝔽2)11yescharacteristic
369C22×C11C2×#12011yescharacteristic
370C2×D11—42no—
371C2×D11—82no—
372C2×D11—82no—
373C2×D11—82no—
374C2×D11—161no—
375C2×D11—161no—
376C4×C11—21no—
377C4×C11—21no—
378C4×C11—42no—
379C4×C11—42no—
380C4×C11—42no—
381C4×C11—42no—
382C4×C11—42no—
383Dic11—42no—
384Dic11—82no—
385Dic11—82no—
386C25C22⋊D1111yescharacteristic
387H(5,𝔽2)—112no—
388H(5,𝔽2)—221no—
389H(5,𝔽2)—221no—
390H(5,𝔽2)—221no—
391H(5,𝔽2)—442no—
392C2×#41—221no—
393C2×#41—441no—
394C22×Q8C22⋊D1111yescharacteristic, complemented
395C22×D4—21no—
396C22×D4—221no—
397C22×D4—221no—
398C22×D4—441no—
399C22×D4—441no—
400C22×D4C22×D1111yescharacteristic
401C23×C4—21no—
402C23×C4—21no—
403C23×C4C22⋊D1111yescharacteristic, complemented
404#137—224no—
405#137—442no—
406C2×Q16—441no—
407C2×SD16—441no—
408C2×M16—221no—
409#126—24no—
410#126—24no—
411#124—21no—
412#124—21no—
413#124C22⋊D1112yescomplemented
414#124C22×D1112yes—
415#123—24no—
416#123—21no—
417#123—21no—
418#123—24no—
419#123—224no—
420#123—442no—
421#123C22⋊D1112yescomplemented
422#123C22×D1112yes—
423C22⋊Q8—24no—
424C22⋊Q8—24no—
425#120—21no—
426#120—21no—
427#120—224no—
428#120—442no—
429#120C22⋊D1112yes—
430#120C22×D1112yes—
431C4×D4—24no—
432C4×D4—24no—
433#117—24no—
434#117—24no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—441no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C22⋊C4—441no—
451C2×C22⋊C4—441no—
452C2×C22⋊C4C22⋊D1111yescharacteristic
453C2×C22⋊C4C22⋊D1111yescharacteristic, complemented
454C2×C42—21no—
455C2×C42C22⋊D1111yescharacteristic, complemented
456#104—224no—
457#100—112no—
458#100—221no—
459#99—112no—
460#99—112no—
461#99—221no—
462#99—221no—
463#99—224no—
464#99—224no—
465C2×C11—21no—
466C2×C11—21no—
467C2×C11—41no—
468C2×C11—41no—
469C2×C11—41no—
470C2×C11—41no—
471C2×C11—44no—
472C2×C11#219712yescomplemented
473C2×C11C2×B(4,𝔽2)11yescharacteristic
474D11—82no—
475C24—21no—
476C24—21no—
477C24—41no—
478C24—44no—
479C24—41no—
480C24—221no—
481C24—221no—
482C24C2×C22⋊D1111yescharacteristic
483C24C2×C22⋊D1111yescharacteristic
484C24C2×C22⋊D1112yes—
485#41—222no—
486#41—222no—
487#41—441no—
488#41—442no—
489#41—442no—
490#41—442no—
491#41—442no—
492#41—441no—
493C2×Q8—21no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8—221no—
497C2×Q8C2×C22⋊D1112yescomplemented
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—41no—
501C2×D4—41no—
502C2×D4—44no—
503C2×D4—221no—
504C2×D4—222no—
505C2×D4—222no—
506C2×D4—222no—
507C2×D4—222no—
508C2×D4—442no—
509C2×D4—442no—
510C2×D4—442no—
511C2×D4—442no—
512C2×D4—441no—
513C2×D4—441no—
514C2×D4—441no—
515C2×D4—441no—
516C2×D4—441no—
517C2×D4—441no—
518C2×D4—441no—
519C2×D4—444no—
520C2×D4—884no—
521C2×D4C2×C22⋊D1111yescharacteristic
522C2×D4C2×C22⋊D1111yescharacteristic
523C2×D4C2×C22⋊D1111yescharacteristic
524C2×D4C23×D1111yescharacteristic
525C22×C4—24no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—44no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4—221no—
539C22×C4—221no—
540C22×C4—441no—
541C22×C4—441no—
542C22×C4—441no—
543C22×C4C2×C22⋊D1111yescharacteristic
544C22×C4C2×C22⋊D1112yescomplemented
545Q16—444no—
546SD16—444no—
547M16—222no—
548M16—441no—
549C2×C8—441no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—444no—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—222no—
569C22⋊C4—222no—
570C22⋊C4—444no—
571C22⋊C4—444no—
572C22⋊C4—441no—
573C22⋊C4—441no—
574C22⋊C4C2×C22⋊D1112yes—
575C22⋊C4C2×C22⋊D1112yescomplemented
576C42—24no—
577C42—21no—
578C42C2×C22⋊D1112yescomplemented
579C11C2×#219711yescharacteristic, complemented, Sylow
580C23—24no—
581C23—21no—
582C23—21no—
583C23—22no—
584C23—21no—
585C23—21no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—44no—
591C23—44no—
592C23—41no—
593C23—41no—
594C23—44no—
595C23—81no—
596C23—84no—
597C23—82no—
598C23—222no—
599C23—222no—
600C23—441no—
601C23—441no—
602C23—441no—
603C23—882no—
604C23—882no—
605C23#6700611yescharacteristic
606C23#6700611yescharacteristic
607C23#6700611yescharacteristic
608C23C22×C22⋊D1111yescharacteristic
609C23C22×C22⋊D1111yescharacteristic
610Q8—42no—
611Q8—81no—
612Q8—222no—
613Q8—441no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—44no—
619D4—44no—
620D4—222no—
621D4—441no—
622D4—442no—
623D4—442no—
624D4—442no—
625D4—442no—
626D4—442no—
627D4—442no—
628D4—888no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—48no—
639C2×C4—42no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—81no—
646C2×C4—84no—
647C2×C4—222no—
648C2×C4—222no—
649C2×C4—442no—
650C2×C4—442no—
651C2×C4—441no—
652C2×C4—441no—
653C2×C4—441no—
654C2×C4—442no—
655C2×C4—442no—
656C2×C4—882no—
657C2×C4—882no—
658C2×C4#6700611yescharacteristic
659C2×C4C22×C22⋊D1111yescharacteristic
660C8—442no—
661C22—22no—
662C22—24no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—42no—
672C22—44no—
673C22—44no—
674C22—42no—
675C22—42no—
676C22—44no—
677C22—42no—
678C22—81no—
679C22—81no—
680C22—82no—
681C22—84no—
682C22—442no—
683C22—882no—
684C22—882no—
685C22—882no—
686C22—1761no—
687C22—1761no—
688C22#1062285711yescharacteristic
689C22#1062285711yescharacteristic
690C22C2×#6700611yescharacteristic
691C4—21no—
692C4—21no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—442no—
699C4—882no—
700C4—882no—
701C2—21no—
702C2—21no—
703C2—41no—
704C2—41no—
705C2—44no—
706C2—41no—
707C2—41no—
708C2—882no—
709C2#1307060612yesdirect product factor
710C2C2×#1062285711yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×D4×C11C24
FrattiniC2×D4C23×D11
FittingC2×C11×#551C2
socleC22×C11B(4,𝔽2)
prime radicalC2×#10622645C2
hypercenterC2×#551D11
hypocenterC11C2×#2197
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#551

Complements

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

NH ≅ G/Ntype
1. C2×#10622666C2semidirect
3. C2×#10622674C2semidirect
4. #13070606C2direct (N × H)
5. C2×#10622179C2semidirect
6. C2×#10622177C2semidirect
7. C2×#10622174C2semidirect
8. C2×C11×#551C2semidirect
13. C11×#551C22semidirect
30. #10622674C22semidirect
32. #10622666C22semidirect
38. #10622179C22semidirect
39. #10622177C22semidirect
40. #10622174C22semidirect
42. C22×Q8×C11D4semidirect
47. C23×C4×C11D4semidirect
63. C11×#124D4semidirect
69. C11×#123D4semidirect
94. C2×C11×C22⋊C4D4semidirect
96. C2×C42×C11D4semidirect
134. C2×Q8×C11C2×D4semidirect
158. C22×C4×C11C2×D4semidirect
209. C11×C22⋊C4C2×D4semidirect
212. C42×C11C2×D4semidirect
225. C2×#551D11semidirect
319. #551C2×D11semidirect
394. C22×Q8C22⋊D11semidirect
403. C23×C4C22⋊D11semidirect
413. #124C22⋊D11semidirect
421. #123C22⋊D11semidirect
453. C2×C22⋊C4C22⋊D11semidirect
455. C2×C42C22⋊D11semidirect
472. C2×C11#2197semidirect
497. C2×Q8C2×C22⋊D11semidirect
544. C22×C4C2×C22⋊D11semidirect
575. C22⋊C4C2×C22⋊D11semidirect
578. C42C2×C22⋊D11semidirect
579. C11C2×#2197semidirect
709. C2#13070606direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226662
C2×#106226452
C2×#106226742
#130706062
C2×#106221792
C2×#106221772
C2×#106221742
C2×C11×#5512
C2×#219711