Finite Group Databasebeta

← C2×#21446847 #29706896

Subgroups — C2×#21446847 #29706896

Order 15616.

2190 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519807C211yesmaximal, characteristic, complemented
2C2×#16840326C211yesmaximal, characteristic
3C22×#14519765C211yesmaximal, characteristic, complemented
4C2×#16839772C211yesmaximal, characteristic, complemented
5C22×#14519693C211yesmaximal, characteristic, complemented
6#21446847C218yesmaximal, direct product factor
7C2×#16839522C211yesmaximal, characteristic, complemented
8C22×#104×C61C211yesmaximal, characteristic, complemented
9C23×Dic122C2211yescharacteristic
10C23×D244C2211yescharacteristic
11C2×#14519807—24no—
12C2×#14519807—22no—
13C2×#14519807—24no—
14C2×#14519807C2214yescomplemented
15C22×#11758202—21no—
16C22×#11758200—21no—
17C22×#11758194C2211yescharacteristic
18#16840326—22no—
19#16840326—22no—
20#16840326—22no—
21#16840326C2214yes—
22C2×#14519773—21no—
23C2×#14519766—21no—
24C2×#14519765—24no—
25C2×#14519765—24no—
26C2×#14519765—22no—
27C2×#14519765C2214yescomplemented
28C2×#14519751—22no—
29C2×#14519745—22no—
30C2×#14519736C2211yescharacteristic
31C22×#11758198—22no—
32#16839772—22no—
33#16839772C2214yescomplemented
34C2×#14519702—22no—
35C2×#14519693—24no—
36C2×#14519693C2214yescomplemented
37#16839522C2214yescomplemented
38C22×#41×C61C2211yescharacteristic
39C22×M16×C61C2211yescharacteristic
40C22×C42×C61C2211yescharacteristic
41C2×#104×C61—24no—
42C2×#104×C61C2214yescomplemented
43C24×D61D412yes—
44C22×Dic122—21no—
45C22×Dic122—21no—
46C22×Dic122—21no—
47C22×Dic122—22no—
48C22×Dic122—21no—
49C22×Dic122—22no—
50C22×Dic122—21no—
51C22×Dic122—22no—
52C22×Dic122D414yescomplemented
53C22×Dic122C2312yes—
54C22×D244—22no—
55C22×D244—21no—
56C22×D244—22no—
57C22×D244—22no—
58C22×D244—21no—
59C22×D244—21no—
60C22×D244—21no—
61C22×D244—22no—
62C22×D244D412yes—
63C22×D244C2312yes—
64C22×C22⋊D61—24no—
65C23×Dic61—21no—
66#14519807—216no—
67#14519807—28no—
68#14519807—28no—
69C2×#11758202—28no—
70C2×#11758202—24no—
71C2×#11758200—28no—
72C2×#11758200—24no—
73C2×#11758194—22no—
74C2×#11758194—21no—
75C2×#11758194D414yescomplemented
76C2×#11758194C2312yes—
77C22×#92418—21no—
78#14519773—24no—
79#14519773—24no—
80#14519766—24no—
81#14519766—24no—
82#14519765—216no—
83#14519765—28no—
84#14519765—28no—
85#14519751—28no—
86#14519751—28no—
87#14519745—28no—
88#14519745—28no—
89#14519736—21no—
90#14519736—21no—
91#14519736D412yes—
92#14519736C2312yes—
93C2×C4⋊Dic61D412yes—
94C2×C22⋊Dic61—21no—
95C2×#11758198—216no—
96C2×#11758198—24no—
97C2×#11758198—28no—
98C2×C4×Dic61—21no—
99#14519702—28no—
100#14519693—28no—
101C2×#41×C61—21no—
102C2×#41×C61—21no—
103C2×#41×C61—22no—
104C2×#41×C61—22no—
105C2×#41×C61—22no—
106C2×#41×C61—22no—
107C2×#41×C61D412yes—
108C2×#41×C61C2312yes—
109C22×Q8×C61D411yescharacteristic
110C22×D4×C61—21no—
111C22×D4×C61D411yescharacteristic
112C23×C4×C61—21no—
113C23×C4×C61—21no—
114C23×C4×C61C2311yescharacteristic
115C2×M16×C61—21no—
116C2×M16×C61—22no—
117C2×M16×C61—22no—
118C2×M16×C61C2312yes—
119C22×C8×C61—21no—
120C2×C42×C61—21no—
121C2×C42×C61—22no—
122C2×C42×C61D414yescomplemented
123C2×C42×C61C2312yes—
124#104×C61—28no—
125C24×C61—21no—
126C24×C61C2×D411yescharacteristic
127C23×D61—22no—
128C23×D61—24no—
129C23×D61—22no—
130C23×D61—24no—
131C23×D61—48no—
132C23×D61C2×D414yes—
133#41×C61—24no—
134#41×C61—24no—
135#41×C61—22no—
136#41×C61—22no—
137#41×C61—22no—
138#41×C61—22no—
139#41×C61—42no—
140#41×C61—42no—
141#41×C61—42no—
142#41×C61—42no—
143C2×Q8×C61—21no—
144C2×Q8×C61—22no—
145C2×Q8×C61—22no—
146C2×Q8×C61C2×D412yes—
147C2×D4×C61—22no—
148C2×D4×C61—22no—
149C2×D4×C61—22no—
150C2×D4×C61—21no—
151C2×D4×C61—22no—
152C2×D4×C61—42no—
153C2×D4×C61—42no—
154C2×D4×C61C2×D412yes—
155C22×C4×C61—24no—
156C22×C4×C61—21no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—44no—
161C22×C4×C61—42no—
162C22×C4×C61—42no—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D412yes—
167C22×C4×C61C2×D412yes—
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D412yes—
171C22×C4×C61#4112yes—
172C22×C4×C61C2411yescharacteristic
173C2×C22⋊D61—216no—
174C2×C22⋊D61—88no—
175C22×Dic61—24no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—41no—
179C22×Dic61—41no—
180C22×Dic61—42no—
181C2×D244—22no—
182C2×D244—24no—
183C2×D244—22no—
184C2×D244—24no—
185C2×D244—22no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—22no—
190C2×D244—22no—
191C2×D244—42no—
192C2×D244—42no—
193C2×D244—42no—
194C2×D244—42no—
195C2×D244—42no—
196C2×D244—42no—
197C2×D244—42no—
198C2×D244—42no—
199C2×Dic122—24no—
200C2×Dic122—24no—
201C2×Dic122—24no—
202C2×Dic122—24no—
203C2×Dic122—22no—
204C2×Dic122—22no—
205C2×Dic122—22no—
206C2×Dic122—22no—
207C2×Dic122—24no—
208C2×Dic122—22no—
209C2×Dic122—41no—
210C2×Dic122—41no—
211C2×Dic122—42no—
212C2×Dic122—42no—
213C2×Dic122—42no—
214C2×Dic122—42no—
215C2×Dic122—42no—
216C2×Dic122C2×D414yescomplemented
217M16×C61—22no—
218M16×C61—22no—
219M16×C61—42no—
220C2×C8×C61—22no—
221C2×C8×C61—42no—
222C42×C61—24no—
223C42×C61—22no—
224C42×C61C2×D414yescomplemented
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227#11758202—216no—
228#11758200—216no—
229#11758198—232no—
230#11758198—216no—
231C4⋊Dic61—22no—
232C4⋊Dic61C2×D414yes—
233C4×Dic61—22no—
234C4×Dic61—22no—
235#11758194—24no—
236#11758194—22no—
237#11758194C2×D414yescomplemented
238C2×#92418—24no—
239C2×#92418—22no—
240C23×C61—24no—
241C23×C61—22no—
242C23×C61—42no—
243C23×C61—44no—
244C23×C61#12012yes—
245C23×C61#12011yescharacteristic
246C23×C61#12011yescharacteristic
247C23×C61#12112yes—
248C23×C61C22×D411yescharacteristic
249C22×D61—24no—
250C22×D61—24no—
251C22×D61—24no—
252C22×D61—48no—
253C22×D61—416no—
254C22×D61—44no—
255C22×D61—44no—
256C22×D61—48no—
257C22×D61—84no—
258C22×D61—88no—
259Q8×C61—22no—
260Q8×C61—22no—
261Q8×C61—42no—
262D4×C61—22no—
263D4×C61—22no—
264D4×C61—42no—
265D4×C61—42no—
266D4×C61—44no—
267D4×C61—42no—
268C2×C4×C61—24no—
269C2×C4×C61—22no—
270C2×C4×C61—44no—
271C2×C4×C61—48no—
272C2×C4×C61—42no—
273C2×C4×C61—42no—
274C2×C4×C61—42no—
275C2×C4×C61—44no—
276C2×C4×C61#12012yes—
277C2×C4×C61#12012yes—
278C2×C4×C61#12012yes—
279C2×C4×C61#12011yescharacteristic
280C2×C4×C61#12011yescharacteristic
281C2×C4×C61#12112yes—
282C2×C4×C61#12112yes—
283C2×C4×C61#12112yes—
284C2×C4×C61#12112yes—
285C2×C4×C61#12112yes—
286C2×C4×C61#12712yes—
287C2×C4×C61#12712yes—
288C2×C4×C61C22×D411yescharacteristic
289C2×C4×C61C22×D411yescharacteristic
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C22×D411yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C22⋊D61—816no—
295C2×Dic61—24no—
296C2×Dic61—24no—
297C2×Dic61—42no—
298C2×Dic61—42no—
299C2×Dic61—44no—
300C2×Dic61—44no—
301C2×Dic61—44no—
302D244—42no—
303D244—42no—
304D244—42no—
305D244—42no—
306D244—44no—
307D244—44no—
308Dic122—24no—
309Dic122—24no—
310Dic122—42no—
311Dic122—42no—
312Dic122—44no—
313Dic122—44no—
314C8×C61—42no—
315#92418—24no—
316C2×#2004—611nomaximal, Sylow
317C22×C61—22no—
318C22×C61—22no—
319C22×C61—24no—
320C22×C61—24no—
321C22×C61—42no—
322C22×C61—44no—
323C22×C61—84no—
324C22×C61#39212yes—
325C22×C61#39212yes—
326C22×C61#45514yes—
327C22×C61C2×#12011yescharacteristic
328C22×C61C2×#12011yescharacteristic
329C22×C61C2×#12111yescharacteristic
330C2×D61—48no—
331C2×D61—44no—
332C2×D61—48no—
333C2×D61—88no—
334C2×D61—88no—
335C2×D61—84no—
336C4×C61—44no—
337C4×C61—42no—
338C4×C61#39212yes—
339C4×C61#39212yes—
340C4×C61C2×#12011yescharacteristic
341C4×C61C2×#12111yescharacteristic
342C4×C61C2×#12111yescharacteristic
343C4×C61C2×#12711yescharacteristic
344Dic61—44no—
345Dic61—44no—
346C22×#137—611no—
347C2×#535—611no—
348C22×#124—611no—
349C22×#104D6111yescharacteristic, complemented
350C2×#419—611no—
351C22×#100—611no—
352#2004—618no—
353C2×#339—611no—
354C2×C61—21no—
355C2×C61—21no—
356C2×C61—22no—
357C2×C61—82no—
358C2×C61#200414yescomplemented
359C2×C61C2×#39211yescharacteristic
360C2×C61C2×#45512yes—
361D61—84no—
362C22×#41C2×D6111yescharacteristic
363C23×Q8—611no—
364C23×D4—611no—
365C2×#137—614no—
366C2×#137—1224no—
367C2×#137—1224no—
368C2×#137—1222no—
369C22×Q16—1221no—
370C22×SD16—1221no—
371C22×M16—611no—
372C22×M16C2×D6111yescharacteristic
373#535—614no—
374#535—1222no—
375#535—1222no—
376#535—1222no—
377C2×#127—1221no—
378C2×#124—614no—
379C2×#124—1222no—
380C2×#124—1224no—
381C2×#124—1221no—
382C2×#124—1224no—
383C2×#121—1222no—
384C2×#120—1222no—
385C2×#117—611no—
386C22×C22⋊C4—1222no—
387C22×C42C2×D6111yescharacteristic
388C2×#104—24no—
389C2×#104C2×D6114yescomplemented
390#419—614no—
391#419—1222no—
392C2×#103—1222no—
393C2×#100—614no—
394C2×#100—1224no—
395#339—614no—
396C61C2×#200411yescharacteristic, complemented, Sylow
397C25—612no—
398C2×#41—21no—
399C2×#41—21no—
400C2×#41—22no—
401C2×#41—22no—
402C2×#41—22no—
403C2×#41—22no—
404C2×#41D24412yes—
405C2×#41C22×D6112yes—
406C22×Q8—614no—
407C22×Q8—612no—
408C22×Q8—1221no—
409C22×Q8—1222no—
410C22×Q8—1221no—
411C22×Q8—1221no—
412C22×Q8—1222no—
413C22×Q8—1222no—
414C22×Q8—1221no—
415C22×Q8—1221no—
416C22×Q8D24411yescharacteristic
417C22×D4—21no—
418C22×D4—612no—
419C22×D4—612no—
420C22×D4—1224no—
421C22×D4—1221no—
422C22×D4—1221no—
423C22×D4—1222no—
424C22×D4—1221no—
425C22×D4—1222no—
426C22×D4—1221no—
427C22×D4—1222no—
428C22×D4—1222no—
429C22×D4D24411yescharacteristic
430C23×C4—21no—
431C23×C4—21no—
432C23×C4—1221no—
433C23×C4C22×D6111yescharacteristic
434#137—1228no—
435#137—1228no—
436#137—12216no—
437C2×Q16—1228no—
438C2×Q16—1224no—
439C2×SD16—1228no—
440C2×SD16—1224no—
441C2×M16—21no—
442C2×M16—22no—
443C2×M16—22no—
444C2×M16—614no—
445C2×M16—612no—
446C2×M16—1221no—
447C2×M16—1222no—
448C2×M16C22×D6112yes—
449C22×C8—21no—
450C22×C8—1221no—
451#127—1224no—
452#127—1224no—
453#124—1228no—
454#124—12216no—
455#124—1224no—
456#124—1224no—
457#124—1228no—
458#121—1228no—
459#121—1228no—
460#120—1228no—
461#120—1228no—
462#117—612no—
463#117—612no—
464#117—1221no—
465#117—1221no—
466C2×C4⋊C4—612no—
467C2×C22⋊C4—1228no—
468C2×C22⋊C4—12216no—
469C2×C22⋊C4—1224no—
470C2×C22⋊C4—1221no—
471C2×C42—22no—
472C2×C42—21no—
473C2×C42—1221no—
474C2×C42C22⋊D6114yescomplemented
475C2×C42C22×D6112yes—
476#104—28no—
477#103—1228no—
478#100—1228no—
479C24—21no—
480C24—614no—
481C24—1222no—
482C24—1224no—
483C24—1224no—
484C24—1222no—
485C24—2448no—
486C24D4×D6111yescharacteristic
487#41—22no—
488#41—22no—
489#41—22no—
490#41—22no—
491#41—24no—
492#41—24no—
493#41—42no—
494#41—42no—
495#41—42no—
496#41—42no—
497C2×Q8—21no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—614no—
501C2×Q8—1222no—
502C2×Q8—1224no—
503C2×Q8—1222no—
504C2×Q8—1222no—
505C2×Q8—1222no—
506C2×Q8—1222no—
507C2×Q8—1224no—
508C2×Q8—1224no—
509C2×Q8—1224no—
510C2×Q8—1224no—
511C2×Q8—2441no—
512C2×Q8—2441no—
513C2×Q8—2442no—
514C2×Q8—2442no—
515C2×Q8—2442no—
516C2×Q8—2442no—
517C2×Q8—2442no—
518C2×Q8C2×D24412yes—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—21no—
523C2×D4—22no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—12216no—
527C2×D4—1222no—
528C2×D4—1222no—
529C2×D4—1222no—
530C2×D4—1222no—
531C2×D4—1222no—
532C2×D4—1222no—
533C2×D4—1224no—
534C2×D4—1222no—
535C2×D4—1222no—
536C2×D4—1224no—
537C2×D4—4888no—
538C2×D4—2442no—
539C2×D4—2442no—
540C2×D4—2442no—
541C2×D4—2442no—
542C2×D4—2442no—
543C2×D4—2442no—
544C2×D4—2442no—
545C2×D4—2442no—
546C2×D4C2×D24412yes—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—44no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—1222no—
556C22×C4—1224no—
557C22×C4—1222no—
558C22×C4—2441no—
559C22×C4—2441no—
560C22×C4—2442no—
561C22×C4C2×D24411yescharacteristic
562C22×C4C2×D24411yescharacteristic
563C22×C4#1175822212yes—
564C22×C4D4×D6112yes—
565C22×C4D4×D6112yes—
566C22×C4D4×D6111yescharacteristic
567C22×C4D4×D6111yescharacteristic
568C22×C4D4×D6111yescharacteristic
569C22×C4C2×C22⋊D6112yes—
570C22×C4C23×D6111yescharacteristic
571Q16—12216no—
572SD16—12216no—
573M16—22no—
574M16—22no—
575M16—42no—
576M16—614no—
577M16—1222no—
578M16—1224no—
579C2×C8—22no—
580C2×C8—42no—
581C2×C8—1222no—
582C2×C8—1224no—
583C4⋊C4—614no—
584C4⋊C4—1222no—
585C22⋊C4—12232no—
586C22⋊C4—12216no—
587C22⋊C4—1222no—
588C22⋊C4—1222no—
589C42—22no—
590C42—24no—
591C42—1222no—
592C42—1222no—
593C42C2×C22⋊D6114yescomplemented
594C23—24no—
595C23—22no—
596C23—44no—
597C23—42no—
598C23—1224no—
599C23—1224no—
600C23—1224no—
601C23—4888no—
602C23—4884no—
603C23—24416no—
604C23—2448no—
605C23—2448no—
606C23—2444no—
607C23—2444no—
608C23#1451974512yes—
609C23#1451974711yescharacteristic
610C23#1451974711yescharacteristic
611C23#1451975012yes—
612C23C2×D4×D6111yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—42no—
616Q8—1224no—
617Q8—1224no—
618Q8—2442no—
619Q8—2442no—
620Q8—2444no—
621Q8—2444no—
622D4—22no—
623D4—22no—
624D4—42no—
625D4—42no—
626D4—44no—
627D4—42no—
628D4—48816no—
629D4—2442no—
630D4—2442no—
631D4—2442no—
632D4—2442no—
633D4—2444no—
634D4—2444no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—44no—
638C2×C4—48no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—44no—
643C2×C4—1224no—
644C2×C4—1224no—
645C2×C4—2444no—
646C2×C4—2442no—
647C2×C4—2442no—
648C2×C4—2444no—
649C2×C4—2444no—
650C2×C4#1451974512yes—
651C2×C4#1451974712yes—
652C2×C4#1451974712yes—
653C2×C4#1451974711yescharacteristic
654C2×C4#1451974711yescharacteristic
655C2×C4#1451975012yes—
656C2×C4#1451975012yes—
657C2×C4#1451975012yes—
658C2×C4#1451975112yes—
659C2×C4#1451975112yes—
660C2×C4#1451977312yes—
661C2×C4#1451977312yes—
662C2×C4C2×D4×D6111yescharacteristic
663C2×C4C2×D4×D6111yescharacteristic
664C2×C4C2×D4×D6111yescharacteristic
665C2×C4C22×C22⋊D6111yescharacteristic
666C2×C4C22×D24411yescharacteristic
667C2×C4C2×#1175822211yescharacteristic
668C8—42no—
669C8—1224no—
670C22—22no—
671C22—22no—
672C22—24no—
673C22—24no—
674C22—44no—
675C22—42no—
676C22—84no—
677C22—4884no—
678C22—4888no—
679C22—4888no—
680C22—2448no—
681C22—2448no—
682C22—2444no—
683C22#1683967112yes—
684C22#1683967112yes—
685C22#1683994114yes—
686C22C2×#1451974511yescharacteristic
687C22C2×#1451974711yescharacteristic
688C22C2×#1451975011yescharacteristic
689C4—44no—
690C4—42no—
691C4—2444no—
692C4—2444no—
693C4#1683967112yes—
694C4#1683967112yes—
695C4C2×#1451974711yescharacteristic
696C4C2×#1451975011yescharacteristic
697C4C2×#1451975111yescharacteristic
698C4C2×#1451977311yescharacteristic
699C2—21no—
700C2—21no—
701C2—22no—
702C2—82no—
703C2—4884no—
704C2#2144684714yesdirect product factor
705C2C2×#1683967111yescharacteristic
706C2C2×#1683994112yes—
subgroupG/H
centerC23#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#104×C61C2
socleC23×C61#120
prime radicalC2×#16840326C2
hypercenterC22×#104D61
hypocenterC61C2×#2004
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
1. C22×#14519807C2semidirect
3. C22×#14519765C2semidirect
4. C2×#16839772C2semidirect
5. C22×#14519693C2semidirect
6. #21446847C2direct (N × H)
7. C2×#16839522C2semidirect
8. C22×#104×C61C2semidirect
14. C2×#14519807C22semidirect
27. C2×#14519765C22semidirect
33. #16839772C22semidirect
36. C2×#14519693C22semidirect
37. #16839522C22semidirect
42. C2×#104×C61C22semidirect
52. C22×Dic122D4semidirect
75. C2×#11758194D4semidirect
122. C2×C42×C61D4semidirect
216. C2×Dic122C2×D4semidirect
224. C42×C61C2×D4semidirect
237. #11758194C2×D4semidirect
349. C22×#104D61semidirect
358. C2×C61#2004semidirect
389. C2×#104C2×D61semidirect
396. C61C2×#2004semidirect
474. C2×C42C22⋊D61semidirect
593. C42C2×C22⋊D61semidirect
704. C2#21446847direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198072
C2×#168403262
C22×#145197652
C2×#168397722
C22×#145196932
#214468472
C2×#168395222
C22×#104×C612
C2×#200461