Finite Group Databasebeta

← C2×#21444361 #29647267

Subgroups — C2×#21444361 #29647267

Order 15616.

1510 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840275C211yesmaximal, characteristic
2C2×#16839724C211yesmaximal, characteristic, complemented
3C2×#16839621C211yesmaximal, characteristic, complemented
4#21444361C218yesmaximal, direct product factor
5C2×#16839499C211yesmaximal, characteristic, complemented
6C2×#16839497C211yesmaximal, characteristic, complemented
7C2×#16839495C211yesmaximal, characteristic, complemented
8C2×C61×#328C211yesmaximal, characteristic, complemented
9C22×#11758226C411yescharacteristic, complemented
10C23×C4×D61C2211yescharacteristic
11C22×#11758189—21no—
12#16840275—22no—
13#16840275—22no—
14#16840275C414yescomplemented
15#16840275C2214yes—
16C2×#14519762—21no—
17C2×#14519753C411yescharacteristic, complemented
18C2×#14519752C411yescharacteristic, complemented
19C2×#14519751C2211yescharacteristic
20C2×#14519747—21no—
21C2×#14519739—21no—
22C2×#14519737—21no—
23C2×#14519735C411yescharacteristic, complemented
24C22×#11758196—21no—
25C22×#11758198—21no—
26#16839724—22no—
27#16839724C2214yescomplemented
28C2×C22⋊#92418C2211yescharacteristic
29C2×#14519689—21no—
30#16839621—22no—
31#16839621C2214yescomplemented
32C2×#14519684C2211yescharacteristic
33#16839499C2214yescomplemented
34#16839497C2214yescomplemented
35#16839495C2214yescomplemented
36C2×C22⋊Q8×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×#95×C61C2211yescharacteristic
39C61×#328C2214yescomplemented
40C24×D61D411yescharacteristic
41C2×#11758226—22no—
42C2×#11758226—44no—
43C2×#11758226C2×C414yescomplemented
44C22×D244—21no—
45C22×D244—21no—
46C22×D244C2×C411yescharacteristic
47C22×C22⋊D61—21no—
48C23×Dic61—21no—
49C23×Dic61D411yescharacteristic
50C22×C4×D61—21no—
51C22×C4×D61—44no—
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C412yes—
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D412yes—
57C22×C4×D61D411yescharacteristic
58C22×C4×D61D412yes—
59C22×C4×D61C2312yes—
60C2×#11758189—24no—
61C2×#11758189—44no—
62C22×#92418—21no—
63#14519762—24no—
64#14519762—24no—
65#14519753—22no—
66#14519753C2×C414yescomplemented
67#14519752—22no—
68#14519752C2×C414yescomplemented
69#14519751—21no—
70#14519751—21no—
71#14519751C2×C412yes—
72#14519751C2312yes—
73#14519747—24no—
74#14519747—24no—
75#14519739—24no—
76#14519739—24no—
77#14519737—24no—
78#14519737—24no—
79#14519735—22no—
80#14519735C2×C414yescomplemented
81C2×C4⋊Dic61C2×C411yescharacteristic
82C2×#11758196—21no—
83C2×#11758196—24no—
84C2×#11758196—44no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—24no—
90C2×#11758198—44no—
91C2×C4×Dic61—21no—
92C22⋊#92418—21no—
93C22⋊#92418C2312yes—
94#14519689—24no—
95#14519684—21no—
96#14519684C2312yes—
97C22×Q8×C61C2×C411yescharacteristic
98C23×C4×C61—21no—
99C23×C4×C61C2311yescharacteristic
100C22×C8×C61—21no—
101C22⋊Q8×C61—21no—
102C22⋊Q8×C61—21no—
103C22⋊Q8×C61C2×C412yes—
104C22⋊Q8×C61C2312yes—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61C2×C411yescharacteristic
107C2×C22⋊C4×C61—21no—
108C22⋊C8×C61—21no—
109C22⋊C8×C61C2312yes—
110#95×C61—21no—
111#95×C61C2312yes—
112C24×C61C2×D411yescharacteristic
113C23×D61—22no—
114C23×D61—22no—
115C23×D61—21no—
116C23×D61—42no—
117C23×D61—42no—
118C23×D61C22⋊C411yescharacteristic
119C23×D61C22⋊C411yescharacteristic
120C23×D61C22⋊C412yes—
121C23×D61C2×D412yes—
122C2×Q8×C61—21no—
123C2×Q8×C61—42no—
124C2×Q8×C61C22×C412yes—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—22no—
128C22×C4×C61—42no—
129C22×C4×C61—42no—
130C22×C4×C61—42no—
131C22×C4×C61—42no—
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C2×C22⋊D61—22no—
139C2×C22⋊D61—22no—
140C2×C22⋊D61—42no—
141C2×C22⋊D61—42no—
142C22×Dic61—24no—
143C22×Dic61—21no—
144C22×Dic61—22no—
145C22×Dic61—42no—
146C22×Dic61—42no—
147C22×Dic61—42no—
148C22×Dic61C22⋊C411yescharacteristic
149C22×Dic61C22⋊C412yes—
150C22×Dic61C22⋊C411yescharacteristic
151C22×Dic61C2×D412yes—
152#11758226—48no—
153#11758226—48no—
154C2×D244—24no—
155C2×D244—24no—
156C2×D244—21no—
157C2×D244—42no—
158C2×D244—44no—
159C2×D244—44no—
160C2×D244C22×C412yes—
161C2×C4×D61—24no—
162C2×C4×D61—24no—
163C2×C4×D61—24no—
164C2×C4×D61—44no—
165C2×C4×D61—44no—
166C2×C4×D61—44no—
167C2×C4×D61—44no—
168C2×C4×D61—42no—
169C2×C4×D61—42no—
170C2×C4×D61—44no—
171C2×C4×D61C22⋊C412yes—
172C2×C4×D61C22⋊C412yes—
173C2×C4×D61C22⋊C412yes—
174C2×C4×D61C22⋊C412yes—
175C2×C4×D61C22×C412yes—
176C2×C4×D61C22×C412yes—
177C2×C4×D61C2×D412yes—
178C2×C4×D61C2×D412yes—
179C2×C8×C61—22no—
180C2×C8×C61—42no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61C22×C412yes—
185C22⋊C4×C61—22no—
186C22⋊C4×C61—22no—
187#11758198—24no—
188#11758198—24no—
189#11758198—22no—
190#11758198—22no—
191#11758198—24no—
192#11758198—48no—
193C4⋊Dic61—21no—
194C4⋊Dic61C22×C412yes—
195#11758196—24no—
196#11758196—48no—
197C4×Dic61—24no—
198C2×#92418—22no—
199C2×#92418—42no—
200#11758189—48no—
201C23×C61—22no—
202C23×C61—22no—
203C23×C61C2×C22⋊C411yescharacteristic
204C23×C61C2×C22⋊C411yescharacteristic
205C23×C61AGL(1,ℤ/8)12yes—
206C23×C61#13712yes—
207C23×C61C22×D411yescharacteristic
208C22×D61—22no—
209C22×D61—22no—
210C22×D61—22no—
211C22×D61—22no—
212C22×D61—24no—
213C22×D61—22no—
214C22×D61—22no—
215C22×D61—22no—
216C22×D61—22no—
217C22×D61—22no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—42no—
222C22×D61—48no—
223C22×D61—48no—
224C22×D61—42no—
225C22×D61—42no—
226C22×D61—42no—
227C22×D61C2×C22⋊C412yes—
228C22×D61C2×C22⋊C412yes—
229Q8×C61—42no—
230Q8×C61—42no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—84no—
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C23×C411yescharacteristic
248C2×C4×C61C22×D411yescharacteristic
249C22⋊D61—42no—
250C22⋊D61—42no—
251C22⋊D61—44no—
252C2×Dic61—22no—
253C2×Dic61—24no—
254C2×Dic61—24no—
255C2×Dic61—22no—
256C2×Dic61—42no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—42no—
260C2×Dic61—84no—
261C2×Dic61#9914yes—
262C2×Dic61C2×C22⋊C412yes—
263C2×Dic61C2×C22⋊C412yes—
264D244—42no—
265D244—42no—
266D244—48no—
267D244—48no—
268C4×D61—24no—
269C4×D61—24no—
270C4×D61—24no—
271C4×D61—24no—
272C4×D61—42no—
273C4×D61—42no—
274C4×D61—42no—
275C4×D61—42no—
276C4×D61—48no—
277C8×C61—42no—
278#92418—42no—
279C2×#1513—611nomaximal, Sylow
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—24no—
285C22×C61—24no—
286C22×C61C2×#9912yes—
287C22×C61#41712yes—
288C22×C61#41712yes—
289C22×C61#42112yes—
290C22×C61C22×C22⋊C411yescharacteristic
291C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
292C22×C61C2×#13711yescharacteristic
293C2×D61—22no—
294C2×D61—22no—
295C2×D61—22no—
296C2×D61—22no—
297C2×D61—22no—
298C2×D61—22no—
299C2×D61—44no—
300C2×D61—44no—
301C2×D61—48no—
302C2×D61—44no—
303C2×D61—44no—
304C2×D61—42no—
305C2×D61—42no—
306C2×D61—42no—
307C2×D61—84no—
308C4×C61—21no—
309C4×C61—21no—
310C4×C61—21no—
311C4×C61—21no—
312C4×C61—42no—
313C4×C61—42no—
314C4×C61—82no—
315Dic61—22no—
316Dic61—42no—
317Dic61—82no—
318Dic61C2×#9914yes—
319C2×#525—611no—
320C2×#407—611no—
321C2×#380—611no—
322#1513—618no—
323C2×#328—611no—
324C2×#328D6111yescharacteristic, complemented
325C2×#327—611no—
326C2×#327—611no—
327C2×C61—21no—
328C2×C61—21no—
329C2×C61—22no—
330C2×C61#151314yescomplemented
331C2×C61C22×#9911yescharacteristic
332C2×C61C2×#41711yescharacteristic
333C2×C61C2×#42111yescharacteristic
334D61—42no—
335D61—42no—
336D61—82no—
337C22×#41—611no—
338C24×C4—611no—
339C22×M16—1221no—
340#525—614no—
341#525—614no—
342#525—1222no—
343#525—1222no—
344C2×#123—1221no—
345C2×C22⋊Q8—611no—
346C2×C22⋊Q8C2×D6111yescharacteristic
347C2×#121—611no—
348C2×#121—611no—
349C2×#120—1221no—
350C2×C4×D4—1221no—
351C2×C4×D4—1221no—
352C2×#117—611no—
353C22×C4⋊C4—1221no—
354C22×C22⋊C4—1221no—
355#407—614no—
356#407—1222no—
357C2×C22⋊C8—611no—
358C2×C22⋊C8—1221no—
359C2×C22⋊C8C2×D6111yescharacteristic
360#380—614no—
361#380—1222no—
362C2×#95—611no—
363C2×#95C2×D6111yescharacteristic
364#328—614no—
365#328C2×D6114yescomplemented
366#327—614no—
367#327—614no—
368C61C2×#151311yescharacteristic, complemented, Sylow
369C25—611no—
370C2×#41—614no—
371C2×#41—1222no—
372C2×#41—2444no—
373C22×Q8C4×D6111yescharacteristic
374C22×D4—611no—
375C22×D4—1221no—
376C22×D4—1221no—
377C22×D4—1221no—
378C23×C4—21no—
379C23×C4—611no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—612no—
384C23×C4—611no—
385C23×C4—612no—
386C23×C4—612no—
387C23×C4—612no—
388C23×C4—1221no—
389C23×C4—1221no—
390C23×C4—2444no—
391C23×C4C22×D6111yescharacteristic
392C2×M16—1224no—
393C2×M16—2444no—
394C22×C8—21no—
395C22×C8—1221no—
396#123—1224no—
397#123—1224no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—614no—
401C22⋊Q8—1222no—
402C22⋊Q8C4×D6112yes—
403C22⋊Q8C22×D6112yes—
404#121—612no—
405#121—612no—
406#121—614no—
407#121—1222no—
408#121—1221no—
409#121—1221no—
410#120—1224no—
411#120—1224no—
412C4×D4—1224no—
413C4×D4—1224no—
414C4×D4—1224no—
415C4×D4—1224no—
416#117—614no—
417#117—1222no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—1221no—
421C2×C4⋊C4—1224no—
422C2×C4⋊C4—2444no—
423C2×C4⋊C4C4×D6111yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—1221no—
426C2×C22⋊C4—1221no—
427C2×C22⋊C4—1221no—
428C2×C22⋊C4—1221no—
429C2×C22⋊C4—1224no—
430C2×C22⋊C4—2444no—
431C2×C42—1221no—
432C22⋊C8—21no—
433C22⋊C8—612no—
434C22⋊C8—1224no—
435C22⋊C8—1221no—
436C22⋊C8C22×D6112yes—
437#95—21no—
438#95—612no—
439#95—1221no—
440#95C22×D6112yes—
441C24—611no—
442C24—611no—
443C24—612no—
444C24—612no—
445C24—1222no—
446C24—1222no—
447C24—1221no—
448C24—2442no—
449C24—2442no—
450C24D4×D6111yescharacteristic
451#41—2448no—
452#41—2448no—
453C2×Q8—21no—
454C2×Q8—42no—
455C2×Q8C2×C4×D6112yes—
456C2×D4—612no—
457C2×D4—1224no—
458C2×D4—1224no—
459C2×D4—1222no—
460C2×D4—1222no—
461C2×D4—1221no—
462C2×D4—2442no—
463C2×D4—2444no—
464C2×D4—2444no—
465C2×D4—2442no—
466C2×D4—2442no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—611no—
475C22×C4—612no—
476C22×C4—612no—
477C22×C4—611no—
478C22×C4—612no—
479C22×C4—612no—
480C22×C4—612no—
481C22×C4—612no—
482C22×C4—612no—
483C22×C4—612no—
484C22×C4—612no—
485C22×C4—612no—
486C22×C4—1224no—
487C22×C4—1224no—
488C22×C4—1224no—
489C22×C4—1224no—
490C22×C4—1221no—
491C22×C4—1222no—
492C22×C4—2442no—
493C22×C4—2442no—
494C22×C4—2444no—
495C22×C4—2444no—
496C22×C4—2444no—
497C22×C4—2444no—
498C22×C4—2444no—
499C22×C4—2442no—
500C22×C4—2442no—
501C22×C4—2442no—
502C22×C4C2×C4×D6111yescharacteristic
503C22×C4C2×C4×D6111yescharacteristic
504C22×C4D4×D6111yescharacteristic
505C22×C4D4×D6111yescharacteristic
506C22×C4D4×D6111yescharacteristic
507C22×C4C23×D6111yescharacteristic
508M16—2448no—
509C2×C8—22no—
510C2×C8—42no—
511C2×C8—1222no—
512C2×C8—2442no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—612no—
517C4⋊C4—1224no—
518C4⋊C4—1221no—
519C4⋊C4—2448no—
520C4⋊C4C2×C4×D6112yes—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—1224no—
524C22⋊C4—1224no—
525C22⋊C4—1224no—
526C22⋊C4—1222no—
527C22⋊C4—1222no—
528C22⋊C4—2448no—
529C42—1224no—
530C23—22no—
531C23—22no—
532C23—612no—
533C23—612no—
534C23—1222no—
535C23—1222no—
536C23—1224no—
537C23—1222no—
538C23—1222no—
539C23—1222no—
540C23—1222no—
541C23—1222no—
542C23—1222no—
543C23—1222no—
544C23—2442no—
545C23—2442no—
546C23—2442no—
547C23—2442no—
548C23—2448no—
549C23—2448no—
550C23—2442no—
551C23—2442no—
552C23—2442no—
553C23C22⋊C4×D6111yescharacteristic
554C23C22⋊C4×D6111yescharacteristic
555C23#1451980412yes—
556C23#1451980912yes—
557C23C2×D4×D6111yescharacteristic
558Q8—42no—
559Q8—42no—
560D4—2442no—
561D4—2442no—
562D4—2448no—
563D4—2448no—
564D4—2444no—
565D4—2442no—
566D4—2442no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—84no—
581C2×C4—612no—
582C2×C4—614no—
583C2×C4—612no—
584C2×C4—1224no—
585C2×C4—1224no—
586C2×C4—1224no—
587C2×C4—1224no—
588C2×C4—1224no—
589C2×C4—1224no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—4884no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4—2442no—
596C2×C4—2442no—
597C2×C4—2448no—
598C2×C4—2442no—
599C2×C4—2442no—
600C2×C4—2442no—
601C2×C4—2442no—
602C2×C4C22⋊C4×D6111yescharacteristic
603C2×C4C22⋊C4×D6111yescharacteristic
604C2×C4C22×C4×D6111yescharacteristic
605C2×C4C2×D4×D6111yescharacteristic
606C8—42no—
607C8—2442no—
608C22—24no—
609C22—24no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—1222no—
615C22—1222no—
616C22—1222no—
617C22—1222no—
618C22—1222no—
619C22—1222no—
620C22—4884no—
621C22—2444no—
622C22—2448no—
623C22—2444no—
624C22—2442no—
625C22—2442no—
626C22—2442no—
627C22—2444no—
628C22—2444no—
629C22#99×D6112yes—
630C22#1683976212yes—
631C22#1683976212yes—
632C22#1683977712yes—
633C22C2×C22⋊C4×D6111yescharacteristic
634C22C2×#1451980411yescharacteristic
635C22C2×#1451980911yescharacteristic
636C4—21no—
637C4—21no—
638C4—21no—
639C4—21no—
640C4—42no—
641C4—42no—
642C4—82no—
643C4—614no—
644C4—1222no—
645C4—4882no—
646C4—2442no—
647C2—21no—
648C2—22no—
649C2—21no—
650C2—4882no—
651C2—2442no—
652C2—2442no—
653C2#2144436114yesdirect product factor
654C2C2×#99×D6111yescharacteristic
655C2C2×#1683976211yescharacteristic
656C2C2×#1683977711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#328C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840275C2
cosocleC22×C4×C61C24
hypercenterC2×#328D61
hypocenterC61C2×#1513
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. C2×#16839724C2semidirect
3. C2×#16839621C2semidirect
4. #21444361C2direct (N × H)
5. C2×#16839499C2semidirect
6. C2×#16839497C2semidirect
7. C2×#16839495C2semidirect
8. C2×C61×#328C2semidirect
9. C22×#11758226C4semidirect
14. #16840275C4semidirect
17. C2×#14519753C4semidirect
18. C2×#14519752C4semidirect
23. C2×#14519735C4semidirect
27. #16839724C22semidirect
31. #16839621C22semidirect
33. #16839499C22semidirect
34. #16839497C22semidirect
35. #16839495C22semidirect
39. C61×#328C22semidirect
43. C2×#11758226C2×C4semidirect
66. #14519753C2×C4semidirect
68. #14519752C2×C4semidirect
80. #14519735C2×C4semidirect
324. C2×#328D61semidirect
330. C2×C61#1513semidirect
365. #328C2×D61semidirect
368. C61C2×#1513semidirect
653. C2#21444361direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402752
C2×#168397242
C2×#168396212
#214443612
C2×#168394992
C2×#168394972
C2×#168394952
C2×C61×#3282
C2×#151361