Finite Group Databasebeta

← C2×#21447052 #29707680

Subgroups — C2×#21447052 #29707680

Order 15616.

2230 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519773C211yesmaximal, characteristic
2C22×#14519699C211yesmaximal, characteristic, complemented
3C22×#14519698C211yesmaximal, characteristic, complemented
4C22×#14519697C211yesmaximal, characteristic, complemented
5C2×#16839661C211yesmaximal, characteristic, complemented
6#21447052C218yesmaximal, direct product factor
7C2×#16839516C211yesmaximal, characteristic, complemented
8C22×#102×C61C211yesmaximal, characteristic, complemented
9C23×D244C2211yescharacteristic
10C23×C22⋊D61—21no—
11C23×C22⋊D61—21no—
12C23×#92418C2211yescharacteristic
13C2×#14519773—22no—
14C2×#14519773—24no—
15C2×#14519773—24no—
16C2×#14519773C2214yes—
17C22×C4⋊Dic61—21no—
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4×Dic61C2211yescharacteristic
20C2×#14519699—24no—
21C2×#14519699C2214yescomplemented
22C2×#14519698—24no—
23C2×#14519698C2214yescomplemented
24C2×#14519697—24no—
25C2×#14519697C2214yescomplemented
26#16839661—22no—
27#16839661C2214yescomplemented
28C2×#14519684—21no—
29#16839516C2214yescomplemented
30C23×D4×C61C2211yescharacteristic
31C23×C8×C61C2211yescharacteristic
32C22×C4⋊C4×C61C2211yescharacteristic
33C2×#102×C61—24no—
34C2×#102×C61C2214yescomplemented
35C24×D61—21no—
36C22×D244—22no—
37C22×D244—22no—
38C22×D244—22no—
39C22×D244—22no—
40C22×D244—22no—
41C22×D244—21no—
42C22×D244D414yes—
43C22×D244C2312yes—
44C22×C22⋊D61—28no—
45C22×C22⋊D61—28no—
46C22×C22⋊D61—24no—
47C22×C22⋊D61—24no—
48C22×C22⋊D61—44no—
49C22×C22⋊D61—44no—
50C22×C22⋊D61—44no—
51C22×C22⋊D61—44no—
52C23×Dic61—21no—
53C23×Dic61D411yescharacteristic
54C23×Dic61D411yescharacteristic
55C22×#92418—22no—
56C22×#92418—22no—
57C22×#92418—22no—
58C22×#92418C2312yes—
59#14519773—216no—
60#14519773—28no—
61#14519773—28no—
62C2×C4⋊Dic61—22no—
63C2×C4⋊Dic61—22no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61—24no—
66C2×C4⋊Dic61—44no—
67C2×C4⋊Dic61C2312yes—
68C2×C4×Dic61—22no—
69C2×C4×Dic61—22no—
70C2×C4×Dic61D412yes—
71C2×C4×Dic61C2312yes—
72#14519699—28no—
73#14519698—28no—
74#14519697—28no—
75#14519684—24no—
76C25×C61—21no—
77C22×D4×C61—22no—
78C22×D4×C61—21no—
79C22×D4×C61—22no—
80C22×D4×C61—22no—
81C22×D4×C61—22no—
82C22×D4×C61—22no—
83C22×D4×C61D414yes—
84C22×D4×C61C2312yes—
85C23×C4×C61—21no—
86C23×C4×C61C2311yescharacteristic
87C22×C8×C61—22no—
88C22×C8×C61—22no—
89C22×C8×C61—22no—
90C22×C8×C61C2312yes—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—22no—
93C2×C4⋊C4×C61D414yescomplemented
94C2×C4⋊C4×C61C2312yes—
95#102×C61—28no—
96C24×C61—24no—
97C24×C61—22no—
98C24×C61—42no—
99C24×C61—42no—
100C24×C61—42no—
101C24×C61—42no—
102C24×C61—42no—
103C24×C61—42no—
104C24×C61C2×D411yescharacteristic
105C23×D61—24no—
106C23×D61—22no—
107C23×D61—42no—
108C23×D61—42no—
109C23×D61—42no—
110C23×D61—42no—
111C23×D61—42no—
112C23×D61—42no—
113C2×D4×C61—24no—
114C2×D4×C61—28no—
115C2×D4×C61—28no—
116C2×D4×C61—22no—
117C2×D4×C61—22no—
118C2×D4×C61—22no—
119C2×D4×C61—22no—
120C2×D4×C61—22no—
121C2×D4×C61—44no—
122C2×D4×C61—42no—
123C2×D4×C61—44no—
124C2×D4×C61—42no—
125C2×D4×C61C2×D414yes—
126C22×C4×C61—24no—
127C22×C4×C61—22no—
128C22×C4×C61—42no—
129C22×C4×C61—42no—
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D412yes—
132C22×C4×C61C2×D412yes—
133C22×C4×C61C2×D412yes—
134C22×C4×C61#4112yes—
135C22×C4×C61#4112yes—
136C22×C4×C61#4112yes—
137C22×C4×C61C2411yescharacteristic
138C2×C22⋊D61—216no—
139C2×C22⋊D61—216no—
140C2×C22⋊D61—48no—
141C2×C22⋊D61—48no—
142C2×C22⋊D61—432no—
143C2×C22⋊D61—432no—
144C2×C22⋊D61—48no—
145C2×C22⋊D61—48no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—42no—
152C22×Dic61—42no—
153C22×Dic61—42no—
154C22×Dic61D814yes—
155C22×Dic61SD1614yes—
156C22×Dic61C2×D412yes—
157C22×Dic61C2×D412yes—
158C2×D244—28no—
159C2×D244—28no—
160C2×D244—22no—
161C2×D244—22no—
162C2×D244—22no—
163C2×D244—22no—
164C2×D244—24no—
165C2×D244—22no—
166C2×D244—44no—
167C2×D244—42no—
168C2×D244—44no—
169C2×D244—42no—
170C2×D244C2×D414yes—
171C2×C8×C61—22no—
172C2×C8×C61—22no—
173C2×C8×C61—22no—
174C2×C8×C61—44no—
175C4⋊C4×C61—24no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61C2×D414yescomplemented
178C4⋊Dic61—22no—
179C4⋊Dic61—22no—
180C4⋊Dic61—42no—
181C4⋊Dic61—48no—
182C4×Dic61—24no—
183C4×Dic61—22no—
184C4×Dic61—22no—
185C2×#92418—22no—
186C2×#92418—22no—
187C2×#92418—22no—
188C2×#92418—44no—
189C23×C61—24no—
190C23×C61—42no—
191C23×C61—42no—
192C23×C61—42no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61—42no—
196C23×C61—48no—
197C23×C61—48no—
198C23×C61—48no—
199C23×C61—84no—
200C23×C61—84no—
201C23×C61—84no—
202C23×C61—84no—
203C23×C61#12012yes—
204C23×C61#12112yes—
205C23×C61#12412yes—
206C23×C61C2×D812yes—
207C23×C61C2×SD1612yes—
208C23×C61AGL(1,ℤ/8)12yes—
209C23×C61AGL(1,ℤ/8)12yes—
210C23×C61C22×D411yescharacteristic
211C22×D61—24no—
212C22×D61—42no—
213C22×D61—42no—
214C22×D61—42no—
215C22×D61—42no—
216C22×D61—42no—
217C22×D61—42no—
218C22×D61—48no—
219C22×D61—48no—
220C22×D61—48no—
221C22×D61—84no—
222C22×D61—84no—
223C22×D61—84no—
224C22×D61—84no—
225D4×C61—24no—
226D4×C61—24no—
227D4×C61—42no—
228D4×C61—42no—
229D4×C61—48no—
230C2×C4×C61—24no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—48no—
234C2×C4×C61#12012yes—
235C2×C4×C61#12114yes—
236C2×C4×C61#12114yes—
237C2×C4×C61#12112yes—
238C2×C4×C61#12314yes—
239C2×C4×C61#12314yes—
240C2×C4×C61#12412yes—
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C22⋊D61—432no—
248C22⋊D61—432no—
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—28no—
254C2×Dic61—28no—
255C2×Dic61—42no—
256C2×Dic61—42no—
257C2×Dic61—42no—
258C2×Dic61—84no—
259C2×Dic61C2×D814yes—
260C2×Dic61C2×SD1614yes—
261D244—24no—
262D244—24no—
263D244—42no—
264D244—42no—
265D244—48no—
266C8×C61—42no—
267#92418—42no—
268C2×#2041—611nomaximal, Sylow
269C22×C61—44no—
270C22×C61—44no—
271C22×C61—44no—
272C22×C61—82no—
273C22×C61—82no—
274C22×C61—82no—
275C22×C61—82no—
276C22×C61—816no—
277C22×C61#39414yes—
278C22×C61#44714yes—
279C22×C61#45014yes—
280C22×C61#45914yes—
281C22×C61#46014yes—
282C22×C61#48614yes—
283C22×C61#49014yes—
284C22×C61C2×#12011yescharacteristic
285C22×C61C2×#12111yescharacteristic
286C22×C61C2×#12411yescharacteristic
287C22×C61C22×D811yescharacteristic
288C22×C61C22×SD1611yescharacteristic
289C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
291C2×D61—44no—
292C2×D61—44no—
293C2×D61—44no—
294C2×D61—82no—
295C2×D61—82no—
296C2×D61—82no—
297C2×D61—82no—
298C2×D61—816no—
299C4×C61—44no—
300C4×C61#39414yes—
301C4×C61C2×#12111yescharacteristic
302C4×C61C2×#12111yescharacteristic
303C4×C61C2×#12311yescharacteristic
304C4×C61C2×#12311yescharacteristic
305Dic61—24no—
306Dic61—24no—
307Dic61—82no—
308C22×#127—611no—
309C22×#102—611no—
310C22×#102—611no—
311C22×#102—611no—
312C22×#102D6111yescharacteristic, complemented
313C2×#389—611no—
314#2041—618no—
315C2×#336—611no—
316C2×C61—84no—
317C2×C61#204118yescomplemented
318C2×C61C2×#39411yescharacteristic
319C2×C61C2×#44711yescharacteristic
320C2×C61C2×#45011yescharacteristic
321C2×C61C2×#45911yescharacteristic
322C2×C61C2×#46011yescharacteristic
323C2×C61C2×#48611yescharacteristic
324C2×C61C2×#49011yescharacteristic
325D61—84no—
326C23×D4—611no—
327C23×D4—1221no—
328C23×D4—1221no—
329C23×D4C2×D6111yescharacteristic
330C23×C8—611no—
331C23×C8C2×D6111yescharacteristic
332C2×#127—614no—
333C2×#127—1222no—
334C2×#127—1224no—
335C2×#127—1224no—
336C22×C4⋊C4—611no—
337C22×C4⋊C4—1221no—
338C22×C4⋊C4C2×D6111yescharacteristic
339C22×C42—611no—
340C2×#102—24no—
341C2×#102—614no—
342C2×#102—614no—
343C2×#102—614no—
344C2×#102—1224no—
345C2×#102—1224no—
346C2×#102—1224no—
347C2×#102C2×D6114yescomplemented
348#389—614no—
349#389—1222no—
350C2×#95—1221no—
351#336—614no—
352C61C2×#204111yescharacteristic, complemented, Sylow
353C25—21no—
354C25—1221no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—21no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—614no—
362C22×D4—612no—
363C22×D4—1224no—
364C22×D4—1224no—
365C22×D4—1228no—
366C22×D4—1228no—
367C22×D4—1222no—
368C22×D4—1222no—
369C22×D4—1221no—
370C22×D4—1222no—
371C22×D4—1222no—
372C22×D4—1222no—
373C22×D4—2444no—
374C22×D4—2444no—
375C22×D4—2444no—
376C22×D4—2444no—
377C22×D4D24414yes—
378C22×D4C22×D6112yes—
379C23×C4—21no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—1221no—
383C23×C4C22×D6111yescharacteristic
384C22×C8—22no—
385C22×C8—22no—
386C22×C8—22no—
387C22×C8—612no—
388C22×C8—1222no—
389C22×C8—1222no—
390C22×C8—1222no—
391C22×C8C22×D6112yes—
392#127—1228no—
393#127—12216no—
394#127—1228no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—612no—
398C2×C4⋊C4—1222no—
399C2×C4⋊C4—1222no—
400C2×C4⋊C4—1224no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—2444no—
403C2×C4⋊C4C22⋊D6114yescomplemented
404C2×C4⋊C4C22×D6112yes—
405C2×C42—612no—
406C2×C42—612no—
407C2×C42—1222no—
408C2×C42—1222no—
409#102—28no—
410#102—1228no—
411#102—1228no—
412#102—1228no—
413#95—1224no—
414C24—22no—
415C24—24no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—1222no—
423C24—1224no—
424C24—2442no—
425C24—2442no—
426C24—2442no—
427C24—2442no—
428C24—2442no—
429C24—2442no—
430C24D4×D6111yescharacteristic
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—24no—
437C2×D4—28no—
438C2×D4—28no—
439C2×D4—44no—
440C2×D4—42no—
441C2×D4—44no—
442C2×D4—42no—
443C2×D4—614no—
444C2×D4—12216no—
445C2×D4—12216no—
446C2×D4—1222no—
447C2×D4—1222no—
448C2×D4—1222no—
449C2×D4—1222no—
450C2×D4—1222no—
451C2×D4—1224no—
452C2×D4—1228no—
453C2×D4—1228no—
454C2×D4—2448no—
455C2×D4—2448no—
456C2×D4—2448no—
457C2×D4—2448no—
458C2×D4—24432no—
459C2×D4—24432no—
460C2×D4—2442no—
461C2×D4—2444no—
462C2×D4—2444no—
463C2×D4—2442no—
464C2×D4C2×D24414yes—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—612no—
470C22×C4—612no—
471C22×C4—614no—
472C22×C4—614no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—2442no—
479C22×C4—2442no—
480C22×C4—2442no—
481C22×C4C2×D24412yes—
482C22×C4#1175822212yes—
483C22×C4D4×D6112yes—
484C22×C4D4×D6111yescharacteristic
485C22×C4#1175822412yes—
486C22×C4#1175822412yes—
487C22×C4C2×C22⋊D6112yes—
488C22×C4C23×D6111yescharacteristic
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—44no—
493C2×C8—1222no—
494C2×C8—1222no—
495C2×C8—1222no—
496C2×C8—2444no—
497C4⋊C4—22no—
498C4⋊C4—24no—
499C4⋊C4—1222no—
500C4⋊C4—1222no—
501C4⋊C4—2448no—
502C4⋊C4—2442no—
503C4⋊C4C2×C22⋊D6114yescomplemented
504C42—1222no—
505C42—1222no—
506C42—1224no—
507C23—24no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—48no—
515C23—48no—
516C23—48no—
517C23—84no—
518C23—84no—
519C23—84no—
520C23—84no—
521C23—1224no—
522C23—4884no—
523C23—4884no—
524C23—4884no—
525C23—4884no—
526C23—2442no—
527C23—2442no—
528C23—2442no—
529C23—2442no—
530C23—2442no—
531C23—2442no—
532C23—2448no—
533C23—2448no—
534C23—2448no—
535C23#1451974712yes—
536C23#1451974912yes—
537C23#1451976312yes—
538C23D8×D6112yes—
539C23SD16×D6112yes—
540C23#1451980112yes—
541C23#1451980412yes—
542C23C2×D4×D6111yescharacteristic
543D4—24no—
544D4—24no—
545D4—42no—
546D4—42no—
547D4—48no—
548D4—1224no—
549D4—1224no—
550D4—24432no—
551D4—24432no—
552D4—2442no—
553D4—2442no—
554D4—2448no—
555C2×C4—24no—
556C2×C4—48no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—614no—
560C2×C4—614no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—1228no—
566C2×C4—1228no—
567C2×C4—4884no—
568C2×C4—2442no—
569C2×C4—2442no—
570C2×C4—2442no—
571C2×C4#1451974712yes—
572C2×C4#1451974814yes—
573C2×C4#1451974912yes—
574C2×C4#1451975114yes—
575C2×C4#1451975914yes—
576C2×C4#1451976114yes—
577C2×C4#1451976312yes—
578C2×C4C2×D4×D6111yescharacteristic
579C2×C4C22×C22⋊D6111yescharacteristic
580C2×C4C22×D24411yescharacteristic
581C2×C4C2×#1175822411yescharacteristic
582C2×C4C2×#1175822411yescharacteristic
583C2×C4C2×#1175822211yescharacteristic
584C8—42no—
585C8—2442no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—82no—
590C22—82no—
591C22—816no—
592C22—82no—
593C22—82no—
594C22—4882no—
595C22—4882no—
596C22—48816no—
597C22—4882no—
598C22—4882no—
599C22—2444no—
600C22—2444no—
601C22—2444no—
602C22#1683967814yes—
603C22#1683989714yes—
604C22#1683991414yes—
605C22#1683995514yes—
606C22#1683996014yes—
607C22#1684010714yes—
608C22#1684012514yes—
609C22C2×#1451974711yescharacteristic
610C22C2×#1451974911yescharacteristic
611C22C2×#1451976311yescharacteristic
612C22C2×D8×D6111yescharacteristic
613C22C2×SD16×D6111yescharacteristic
614C22C2×#1451980111yescharacteristic
615C22C2×#1451980411yescharacteristic
616C4—44no—
617C4—1224no—
618C4—1224no—
619C4—4882no—
620C4#1683967814yes—
621C4C2×#1451974811yescharacteristic
622C4C2×#1451975111yescharacteristic
623C4C2×#1451975911yescharacteristic
624C4C2×#1451976111yescharacteristic
625C2—84no—
626C2—4884no—
627C2#2144705218yesdirect product factor
628C2C2×#1683967811yescharacteristic
629C2C2×#1683989711yescharacteristic
630C2C2×#1683991411yescharacteristic
631C2C2×#1683995511yescharacteristic
632C2C2×#1683996011yescharacteristic
633C2C2×#1684010711yescharacteristic
634C2C2×#1684012511yescharacteristic
subgroupG/H
centerC24D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#102×C61C2
socleC24×C61C2×D4
prime radicalC22×#14519773C2
hypercenterC22×#102D61
hypocenterC61C2×#2041
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#14519699C2semidirect
3. C22×#14519698C2semidirect
4. C22×#14519697C2semidirect
5. C2×#16839661C2semidirect
6. #21447052C2direct (N × H)
7. C2×#16839516C2semidirect
8. C22×#102×C61C2semidirect
21. C2×#14519699C22semidirect
23. C2×#14519698C22semidirect
25. C2×#14519697C22semidirect
27. #16839661C22semidirect
29. #16839516C22semidirect
34. C2×#102×C61C22semidirect
93. C2×C4⋊C4×C61D4semidirect
177. C4⋊C4×C61C2×D4semidirect
312. C22×#102D61semidirect
317. C2×C61#2041semidirect
347. C2×#102C2×D61semidirect
352. C61C2×#2041semidirect
403. C2×C4⋊C4C22⋊D61semidirect
503. C4⋊C4C2×C22⋊D61semidirect
627. C2#21447052direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197732
C22×#145196992
C22×#145196982
C22×#145196972
C2×#168396612
#214470522
C2×#168395162
C22×#102×C612
C2×#204161