Finite Group Databasebeta

← C2×#21444748 #29652102

Subgroups — C2×#21444748 #29652102

Order 15616.

1404 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839912C211yesmaximal, characteristic, complemented
2C2×#16839895C211yesmaximal, characteristic
3C2×#16839679C211yesmaximal, characteristic, complemented
4#21444748C218yesmaximal, direct product factor
5C2×#16839499C211yesmaximal, characteristic, complemented
6C2×#16839496C211yesmaximal, characteristic, complemented
7C2×#16839488C211yesmaximal, characteristic, complemented
8C2×C61×#539C211yesmaximal, characteristic, complemented
9C23×D244C2211yescharacteristic
10C22×#11758201—21no—
11C22×#11758199—21no—
12C22×#11758198—21no—
13C22×#11758198—21no—
14#16839912—22no—
15#16839912C2214yescomplemented
16#16839895—22no—
17#16839895C2214yes—
18C2×#14519697—21no—
19C2×#14519697—21no—
20C2×C22⋊#92418C2211yescharacteristic
21C2×C22⋊#92418C2211yescharacteristic
22#16839679—22no—
23#16839679C2214yescomplemented
24C2×#14519684C2211yescharacteristic
25#16839499C2214yescomplemented
26#16839496C2214yescomplemented
27#16839488C2214yescomplemented
28C61×#539—22no—
29C61×#539—22no—
30C61×#539—22no—
31C61×#539C2214yescomplemented
32C2×#126×C61—21no—
33C2×#125×C61—21no—
34C2×#123×C61—21no—
35C2×#123×C61—21no—
36C2×C22⋊Q8×C61—21no—
37C2×C22⋊Q8×C61C2211yescharacteristic
38C2×#121×C61C2211yescharacteristic
39C2×C4×D4×C61—21no—
40C22×C4⋊C4×C61C2211yescharacteristic
41C24×D61—21no—
42C22×D244—21no—
43C22×D244—21no—
44C22×D244—21no—
45C22×D244—21no—
46C22×D244—21no—
47C22×D244—44no—
48C22×D244C2312yes—
49C23×Dic61—21no—
50C2×#11758201—24no—
51C2×#11758201—44no—
52C2×#11758199—24no—
53C2×#11758199—44no—
54C22×#92418—21no—
55C22×#92418—21no—
56C2×#11758198—24no—
57C2×#11758198—24no—
58C2×#11758198—44no—
59C2×#11758198—44no—
60#14519697—24no—
61#14519697—24no—
62C22⋊#92418—21no—
63C22⋊#92418—21no—
64C22⋊#92418C2312yes—
65C22⋊#92418C2312yes—
66#14519684—21no—
67#14519684C2312yes—
68C22×Q8×C61D411yescharacteristic
69C22×D4×C61—21no—
70C22×D4×C61D411yescharacteristic
71C23×C4×C61—21no—
72C23×C4×C61D411yescharacteristic
73C23×C4×C61D411yescharacteristic
74C23×C4×C61C2311yescharacteristic
75#126×C61—24no—
76#126×C61—24no—
77#125×C61—24no—
78#125×C61—24no—
79#123×C61—24no—
80#123×C61—24no—
81#123×C61—24no—
82#123×C61—24no—
83C22⋊Q8×C61—24no—
84C22⋊Q8×C61—24no—
85C22⋊Q8×C61—21no—
86C22⋊Q8×C61—21no—
87C22⋊Q8×C61D412yes—
88C22⋊Q8×C61C2312yes—
89#121×C61—21no—
90#121×C61—21no—
91#121×C61D412yes—
92#121×C61C2312yes—
93C4×D4×C61—24no—
94C4×D4×C61—24no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61D412yes—
104C2×C4⋊C4×C61D411yescharacteristic
105C2×C4⋊C4×C61D411yescharacteristic
106C2×C4⋊C4×C61C2312yes—
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61—21no—
112C2×C42×C61—21no—
113C24×C61—21no—
114C24×C61C2×D411yescharacteristic
115C23×D61—24no—
116C23×D61—22no—
117C23×D61—42no—
118C23×D61—42no—
119C23×D61—42no—
120C23×D61—41no—
121C23×D61—41no—
122C23×D61—42no—
123C23×D61—42no—
124C2×Q8×C61—21no—
125C2×Q8×C61—42no—
126C2×Q8×C61C2×D412yes—
127C2×D4×C61—22no—
128C2×D4×C61—22no—
129C2×D4×C61—21no—
130C2×D4×C61—42no—
131C2×D4×C61—42no—
132C2×D4×C61—42no—
133C2×D4×C61C2×D412yes—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—24no—
143C22×C4×C61—21no—
144C22×C4×C61—42no—
145C22×C4×C61—42no—
146C22×C4×C61—82no—
147C22×C4×C61C2×D412yes—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D412yes—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2411yescharacteristic
155C22×Dic61—22no—
156C22×Dic61—42no—
157C22×Dic61—42no—
158C22×Dic61—42no—
159C2×D244—24no—
160C2×D244—24no—
161C2×D244—22no—
162C2×D244—22no—
163C2×D244—44no—
164C2×D244—44no—
165C2×D244—44no—
166C2×D244—42no—
167C2×D244—42no—
168C2×D244—44no—
169C2×D244—41no—
170C2×D244—41no—
171C4⋊C4×C61—24no—
172C4⋊C4×C61—24no—
173C4⋊C4×C61—24no—
174C4⋊C4×C61—22no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61C2×D412yes—
183C4⋊C4×C61C2×D412yes—
184C22⋊C4×C61—24no—
185C22⋊C4×C61—24no—
186C22⋊C4×C61—24no—
187C22⋊C4×C61—22no—
188C22⋊C4×C61—22no—
189C22⋊C4×C61—22no—
190C22⋊C4×C61—22no—
191C42×C61—24no—
192#11758201—48no—
193#11758199—48no—
194#11758198—48no—
195#11758198—48no—
196C2×#92418—22no—
197C2×#92418—22no—
198C2×#92418—42no—
199C2×#92418—42no—
200C23×C61—22no—
201C23×C61—22no—
202C23×C61—22no—
203C23×C61—42no—
204C23×C61—42no—
205C23×C61—42no—
206C23×C61#12011yescharacteristic
207C23×C61#12011yescharacteristic
208C23×C61#13512yes—
209C23×C61AGL(1,ℤ/8)12yes—
210C23×C61C22×D411yescharacteristic
211C22×D61—24no—
212C22×D61—42no—
213C22×D61—44no—
214C22×D61—48no—
215C22×D61—48no—
216C22×D61—42no—
217C22×D61—42no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—44no—
222C22×D61—84no—
223C22×D61—84no—
224C22×D61—82no—
225C22×D61—82no—
226C22×D61—82no—
227C22×D61—82no—
228Q8×C61—42no—
229Q8×C61—81no—
230D4×C61—42no—
231D4×C61—42no—
232D4×C61—42no—
233D4×C61—44no—
234D4×C61—81no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61—42no—
254C2×C4×C61—42no—
255C2×C4×C61—81no—
256C2×C4×C61—84no—
257C2×C4×C61#12011yescharacteristic
258C2×C4×C61#12011yescharacteristic
259C2×C4×C61C22×D411yescharacteristic
260C2×C4×C61C22×D411yescharacteristic
261C2×Dic61—42no—
262C2×Dic61—42no—
263C2×Dic61—42no—
264C2×Dic61—84no—
265D244—24no—
266D244—24no—
267D244—42no—
268D244—42no—
269D244—44no—
270D244—44no—
271#92418—42no—
272#92418—42no—
273C2×#1597—611nomaximal, Sylow
274C22×C61—24no—
275C22×C61—24no—
276C22×C61—21no—
277C22×C61—21no—
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—42no—
281C22×C61—42no—
282C22×C61—42no—
283C22×C61—84no—
284C22×C61#44912yes—
285C22×C61#44912yes—
286C22×C61#45412yes—
287C22×C61B(4,𝔽2)12yes—
288C22×C61C2×#12011yescharacteristic
289C22×C61C2×#13511yescharacteristic
290C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
291C2×D61—44no—
292C2×D61—44no—
293C2×D61—44no—
294C2×D61—82no—
295C2×D61—82no—
296C2×D61—88no—
297C2×D61—88no—
298C2×D61—82no—
299C2×D61—82no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—21no—
303C4×C61—21no—
304C4×C61—42no—
305C4×C61—42no—
306C4×C61—42no—
307C4×C61—42no—
308C4×C61—42no—
309Dic61—82no—
310C2×#539D6111yescharacteristic, complemented
311C2×#450—611no—
312C2×#447—611no—
313C2×#394—611no—
314#1597—618no—
315C2×#328—611no—
316C2×#327—611no—
317C2×#324—611no—
318C2×C61—21no—
319C2×C61—21no—
320C2×C61—22no—
321C2×C61—82no—
322C2×C61#159714yescomplemented
323C2×C61C2×#44911yescharacteristic
324C2×C61C2×#45411yescharacteristic
325C2×C61C2×B(4,𝔽2)11yescharacteristic
326D61—84no—
327C23×D4—611no—
328C22×SD16—1221no—
329C22×D8—1221no—
330#539—22no—
331#539—22no—
332#539—22no—
333#539C2×D6114yescomplemented
334C2×#126—21no—
335C2×#125—21no—
336C2×#123—21no—
337C2×#123—21no—
338C2×C22⋊Q8—21no—
339C2×C22⋊Q8C2×D6111yescharacteristic
340C2×#121C2×D6111yescharacteristic
341C2×C4×D4—21no—
342C22×C4⋊C4C2×D6111yescharacteristic
343C22×C22⋊C4—1221no—
344C22×C22⋊C4—1221no—
345#450—614no—
346#450—1222no—
347#447—614no—
348#447—1222no—
349C2×#102—1221no—
350C2×#102—1221no—
351C2×C22⋊C8—611no—
352C2×C22⋊C8—611no—
353#394—614no—
354#394—1222no—
355C2×#95—611no—
356#328—614no—
357#327—614no—
358#324—614no—
359C61C2×#159711yescharacteristic, complemented, Sylow
360C25—1221no—
361C22×Q8C22⋊D6111yescharacteristic
362C22×D4—21no—
363C22×D4—612no—
364C22×D4—1221no—
365C22×D4—1221no—
366C22×D4—1221no—
367C22×D4—1221no—
368C22×D4—1221no—
369C22×D4—2444no—
370C22×D4C22⋊D6111yescharacteristic
371C23×C4—21no—
372C23×C4—1221no—
373C23×C4C22⋊D6111yescharacteristic
374C23×C4C22⋊D6111yescharacteristic
375C23×C4C22×D6111yescharacteristic
376C2×SD16—1224no—
377C2×SD16—2444no—
378C2×D8—1224no—
379C2×D8—2444no—
380C22×C8—1221no—
381C22×C8—1221no—
382#126—24no—
383#126—24no—
384#125—24no—
385#125—24no—
386#123—24no—
387#123—24no—
388#123—24no—
389#123—24no—
390C22⋊Q8—24no—
391C22⋊Q8—24no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8C22⋊D6112yes—
395C22⋊Q8C22×D6112yes—
396#121—21no—
397#121—21no—
398#121C22⋊D6112yes—
399#121C22×D6112yes—
400C4×D4—24no—
401C4×D4—24no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4C22⋊D6112yes—
411C2×C4⋊C4C22⋊D6111yescharacteristic
412C2×C4⋊C4C22⋊D6111yescharacteristic
413C2×C4⋊C4C22×D6112yes—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—1224no—
420C2×C22⋊C4—1224no—
421C2×C22⋊C4—2444no—
422C2×C22⋊C4—2444no—
423C2×C42—21no—
424#102—1224no—
425#102—1224no—
426C22⋊C8—612no—
427C22⋊C8—612no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430#95—612no—
431#95—1221no—
432C24—21no—
433C24—1224no—
434C24—1222no—
435C24—2442no—
436C24—2442no—
437C24—2442no—
438C24—2441no—
439C24—2441no—
440C24—2442no—
441C24—2442no—
442C24C2×C22⋊D6111yescharacteristic
443C2×Q8—21no—
444C2×Q8—42no—
445C2×Q8C2×C22⋊D6112yes—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4—1224no—
453C2×D4—1224no—
454C2×D4—1222no—
455C2×D4—1222no—
456C2×D4—2442no—
457C2×D4—2442no—
458C2×D4—2444no—
459C2×D4—2444no—
460C2×D4—2444no—
461C2×D4—2444no—
462C2×D4—2441no—
463C2×D4—2441no—
464C2×D4C2×C22⋊D6112yes—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—21no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—82no—
478C22×C4—1222no—
479C22×C4—2442no—
480C22×C4—2442no—
481C22×C4—2442no—
482C22×C4C2×C22⋊D6112yes—
483C22×C4C2×C22⋊D6111yescharacteristic
484C22×C4C2×C22⋊D6111yescharacteristic
485C22×C4C2×C22⋊D6112yes—
486C22×C4C2×C22⋊D6111yescharacteristic
487C22×C4C2×C22⋊D6111yescharacteristic
488C22×C4C2×C22⋊D6111yescharacteristic
489C22×C4C23×D6111yescharacteristic
490SD16—2448no—
491D8—2448no—
492C2×C8—1222no—
493C2×C8—1222no—
494C2×C8—2442no—
495C2×C8—2442no—
496C4⋊C4—24no—
497C4⋊C4—24no—
498C4⋊C4—24no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4C2×C22⋊D6112yes—
508C4⋊C4C2×C22⋊D6112yes—
509C22⋊C4—24no—
510C22⋊C4—24no—
511C22⋊C4—24no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—2448no—
517C22⋊C4—2448no—
518C42—24no—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—1224no—
526C23—4882no—
527C23—4884no—
528C23—4884no—
529C23—4882no—
530C23—4882no—
531C23—4882no—
532C23—2442no—
533C23—2444no—
534C23—2442no—
535C23—2442no—
536C23—2448no—
537C23—2448no—
538C23—2444no—
539C23—2442no—
540C23—2442no—
541C23—2442no—
542C23#1451974611yescharacteristic
543C23#1451974611yescharacteristic
544C23#1451979712yes—
545C23#1451980212yes—
546C23C22×C22⋊D6111yescharacteristic
547Q8—42no—
548Q8—81no—
549D4—42no—
550D4—42no—
551D4—42no—
552D4—44no—
553D4—81no—
554D4—1224no—
555D4—1224no—
556D4—2442no—
557D4—2442no—
558D4—2444no—
559D4—2444no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—81no—
581C2×C4—84no—
582C2×C4—4884no—
583C2×C4—2442no—
584C2×C4—2442no—
585C2×C4—2442no—
586C2×C4#1451974611yescharacteristic
587C2×C4#1451974611yescharacteristic
588C2×C4C22×C22⋊D6111yescharacteristic
589C2×C4C22×C22⋊D6111yescharacteristic
590C8—2442no—
591C8—2442no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—24no—
597C22—24no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—84no—
602C22—4882no—
603C22—4888no—
604C22—4882no—
605C22—4882no—
606C22—4888no—
607C22—4882no—
608C22—2444no—
609C22—2444no—
610C22—2444no—
611C22#1683990712yes—
612C22#1683990712yes—
613C22#1683993512yes—
614C22#1683994912yes—
615C22C2×#1451974611yescharacteristic
616C22C2×#1451979711yescharacteristic
617C22C2×#1451980211yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—42no—
623C4—42no—
624C4—42no—
625C4—42no—
626C4—42no—
627C4—4882no—
628C2—21no—
629C2—22no—
630C2—21no—
631C2—82no—
632C2—4884no—
633C2#2144474814yesdirect product factor
634C2C2×#1683990711yescharacteristic
635C2C2×#1683993511yescharacteristic
636C2C2×#1683994911yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#539C2
socleC23×C61#120
prime radicalC2×#16839895C2
hypercenterC2×#539D61
hypocenterC61C2×#1597
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. C2×#16839912C2semidirect
3. C2×#16839679C2semidirect
4. #21444748C2direct (N × H)
5. C2×#16839499C2semidirect
6. C2×#16839496C2semidirect
7. C2×#16839488C2semidirect
8. C2×C61×#539C2semidirect
15. #16839912C22semidirect
23. #16839679C22semidirect
25. #16839499C22semidirect
26. #16839496C22semidirect
27. #16839488C22semidirect
31. C61×#539C22semidirect
310. C2×#539D61semidirect
322. C2×C61#1597semidirect
333. #539C2×D61semidirect
359. C61C2×#1597semidirect
633. C2#21444748direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168399122
C2×#168398952
C2×#168396792
#214447482
C2×#168394992
C2×#168394962
C2×#168394882
C2×C61×#5392
C2×#159761