Finite Group Databasebeta

← C2×#21446891 #29707043

Subgroups — C2×#21446891 #29707043

Order 15616.

2942 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D488C211yesmaximal, characteristic, complemented
2C23×#11758199C211yesmaximal, characteristic, complemented
3C22×#14519773C211yesmaximal, characteristic, complemented
4C22×#14519697C211yesmaximal, characteristic, complemented
5C2×#16839663C211yesmaximal, characteristic, complemented
6#21446891C218yesmaximal, direct product factor
7C2×#16839516C211yesmaximal, characteristic, complemented
8C22×#102×C61C211yesmaximal, characteristic, complemented
9C23×D244C2211yescharacteristic
10C23×D244C2211yescharacteristic
11C23×C22⋊D61—22no—
12C22×D488—24no—
13C22×D488—24no—
14C22×D488—24no—
15C22×D488C2214yescomplemented
16C22×#11758199—24no—
17C22×#11758199—24no—
18C22×#11758199—24no—
19C22×#11758199C2214yescomplemented
20C23×#92418C2211yescharacteristic
21C2×#14519773—22no—
22C2×#14519773—24no—
23C2×#14519773—24no—
24C2×#14519773C2214yescomplemented
25C22×#11758198—22no—
26C22×C4×Dic61C2211yescharacteristic
27C2×#14519697—24no—
28C2×#14519697C2214yescomplemented
29#16839663—22no—
30#16839663C2214yescomplemented
31#16839516C2214yescomplemented
32C23×D4×C61C2211yescharacteristic
33C23×C8×C61C2211yescharacteristic
34C22×C4⋊C4×C61C2211yescharacteristic
35C2×#102×C61—24no—
36C2×#102×C61C2214yescomplemented
37C24×D61—21no—
38C24×D61—21no—
39C22×D244—22no—
40C22×D244—22no—
41C22×D244—22no—
42C22×D244—22no—
43C22×D244—22no—
44C22×D244—22no—
45C22×D244—22no—
46C22×D244—22no—
47C22×D244—22no—
48C22×D244—21no—
49C22×D244—21no—
50C22×D244—22no—
51C22×D244D414yes—
52C22×D244D414yescomplemented
53C22×D244C2312yes—
54C22×D244C2312yes—
55C22×C22⋊D61—216no—
56C22×C22⋊D61—28no—
57C22×C22⋊D61—48no—
58C22×C22⋊D61—48no—
59C23×Dic61D412yes—
60C2×D488—232no—
61C2×D488—28no—
62C2×D488—28no—
63C2×D488—28no—
64C2×#11758199—232no—
65C2×#11758199—28no—
66C2×#11758199—28no—
67C2×#11758199—28no—
68C22×#92418—22no—
69C22×#92418—22no—
70C22×#92418D414yescomplemented
71C22×#92418C2312yes—
72#14519773—216no—
73#14519773—28no—
74#14519773—28no—
75C2×#11758198—28no—
76C2×#11758198—48no—
77C2×C4×Dic61—22no—
78C2×C4×Dic61—22no—
79C2×C4×Dic61D412yes—
80C2×C4×Dic61C2312yes—
81#14519697—28no—
82C25×C61—21no—
83C22×D4×C61—22no—
84C22×D4×C61—22no—
85C22×D4×C61—22no—
86C22×D4×C61—22no—
87C22×D4×C61—21no—
88C22×D4×C61—22no—
89C22×D4×C61D414yes—
90C22×D4×C61C2312yes—
91C23×C4×C61—21no—
92C23×C4×C61C2311yescharacteristic
93C22×C8×C61—22no—
94C22×C8×C61—22no—
95C22×C8×C61D414yescomplemented
96C22×C8×C61C2312yes—
97C2×C4⋊C4×C61—22no—
98C2×C4⋊C4×C61—22no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61C2312yes—
101#102×C61—28no—
102C24×C61—24no—
103C24×C61—22no—
104C24×C61—42no—
105C24×C61—42no—
106C24×C61—44no—
107C24×C61—44no—
108C24×C61C2×D411yescharacteristic
109C23×D61—24no—
110C23×D61—24no—
111C23×D61—22no—
112C23×D61—22no—
113C23×D61—42no—
114C23×D61—42no—
115C23×D61—42no—
116C23×D61—42no—
117C23×D61—44no—
118C23×D61—44no—
119C23×D61—44no—
120C23×D61—44no—
121C2×D4×C61—28no—
122C2×D4×C61—24no—
123C2×D4×C61—28no—
124C2×D4×C61—22no—
125C2×D4×C61—22no—
126C2×D4×C61—22no—
127C2×D4×C61—22no—
128C2×D4×C61—22no—
129C2×D4×C61—44no—
130C2×D4×C61—44no—
131C2×D4×C61—42no—
132C2×D4×C61—42no—
133C2×D4×C61C2×D414yes—
134C22×C4×C61—22no—
135C22×C4×C61—42no—
136C22×C4×C61—44no—
137C22×C4×C61C2×D412yes—
138C22×C4×C61C2×D412yes—
139C22×C4×C61C2×D412yes—
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D412yes—
142C22×C4×C61C2×D412yes—
143C22×C4×C61#4112yes—
144C22×C4×C61C2411yescharacteristic
145C2×C22⋊D61—232no—
146C2×C22⋊D61—416no—
147C2×C22⋊D61—464no—
148C2×C22⋊D61—416no—
149C22×Dic61—24no—
150C22×Dic61—24no—
151C22×Dic61D818yescomplemented
152C22×Dic61C2×D414yes—
153C2×D244—28no—
154C2×D244—28no—
155C2×D244—28no—
156C2×D244—28no—
157C2×D244—22no—
158C2×D244—22no—
159C2×D244—22no—
160C2×D244—22no—
161C2×D244—22no—
162C2×D244—22no—
163C2×D244—22no—
164C2×D244—22no—
165C2×D244—24no—
166C2×D244—24no—
167C2×D244—22no—
168C2×D244—22no—
169C2×D244—44no—
170C2×D244—42no—
171C2×D244—44no—
172C2×D244—44no—
173C2×D244—44no—
174C2×D244—42no—
175C2×D244—42no—
176C2×D244—42no—
177C2×D244C2×D414yes—
178C2×D244C2×D414yescomplemented
179C2×C8×C61—28no—
180C2×C8×C61—22no—
181C2×C8×C61—22no—
182C2×C8×C61C2×D414yescomplemented
183C4⋊C4×C61—22no—
184C4⋊C4×C61—22no—
185C4⋊C4×C61—42no—
186#11758199—232no—
187#11758198—416no—
188C4×Dic61—24no—
189C4×Dic61—22no—
190C4×Dic61—22no—
191C2×#92418—28no—
192C2×#92418—22no—
193C2×#92418—22no—
194C2×#92418C2×D414yescomplemented
195D488—232no—
196C23×C61—24no—
197C23×C61—42no—
198C23×C61—42no—
199C23×C61—44no—
200C23×C61—44no—
201C23×C61—48no—
202C23×C61—416no—
203C23×C61—88no—
204C23×C61—84no—
205C23×C61—84no—
206C23×C61#12012yes—
207C23×C61#12112yes—
208C23×C61#12712yes—
209C23×C61C2×D814yes—
210C23×C61AGL(1,ℤ/8)14yes—
211C23×C61C22×D411yescharacteristic
212C22×D61—24no—
213C22×D61—24no—
214C22×D61—42no—
215C22×D61—42no—
216C22×D61—42no—
217C22×D61—42no—
218C22×D61—44no—
219C22×D61—44no—
220C22×D61—44no—
221C22×D61—44no—
222C22×D61—48no—
223C22×D61—48no—
224C22×D61—416no—
225C22×D61—416no—
226C22×D61—88no—
227C22×D61—88no—
228C22×D61—84no—
229C22×D61—84no—
230C22×D61—84no—
231C22×D61—84no—
232D4×C61—24no—
233D4×C61—24no—
234D4×C61—42no—
235D4×C61—42no—
236D4×C61—48no—
237C2×C4×C61—42no—
238C2×C4×C61—44no—
239C2×C4×C61—84no—
240C2×C4×C61#12014yes—
241C2×C4×C61#12014yes—
242C2×C4×C61#12012yes—
243C2×C4×C61#12114yes—
244C2×C4×C61#12114yes—
245C2×C4×C61#12112yes—
246C2×C4×C61#12712yes—
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61C22×D411yescharacteristic
250C2×C4×C61C22×D411yescharacteristic
251C2×C4×C61C22×D411yescharacteristic
252C2×C4×C61C2×#4111yescharacteristic
253C22⋊D61—464no—
254C2×Dic61—24no—
255C2×Dic61—24no—
256C2×Dic61—216no—
257C2×Dic61C2×D818yescomplemented
258D244—24no—
259D244—24no—
260D244—24no—
261D244—24no—
262D244—42no—
263D244—42no—
264D244—42no—
265D244—42no—
266D244—48no—
267D244—48no—
268C8×C61—24no—
269#92418—24no—
270C2×#2011—611nomaximal, Sylow
271C22×C61—44no—
272C22×C61—48no—
273C22×C61—82no—
274C22×C61—82no—
275C22×C61—84no—
276C22×C61—816no—
277C22×C61#39214yes—
278C22×C61#44718yes—
279C22×C61#45918yes—
280C22×C61#49314yes—
281C22×C61#49614yes—
282C22×C61C2×#12011yescharacteristic
283C22×C61C2×#12111yescharacteristic
284C22×C61C2×#12711yescharacteristic
285C22×C61C22×D812yes—
286C22×C61C2×AGL(1,ℤ/8)12yes—
287C2×D61—44no—
288C2×D61—44no—
289C2×D61—48no—
290C2×D61—48no—
291C2×D61—82no—
292C2×D61—82no—
293C2×D61—82no—
294C2×D61—82no—
295C2×D61—84no—
296C2×D61—84no—
297C2×D61—816no—
298C2×D61—816no—
299C4×C61—82no—
300C4×C61#39214yes—
301C4×C61C2×#12011yescharacteristic
302C4×C61C2×#12011yescharacteristic
303C4×C61C2×#12111yescharacteristic
304C4×C61C2×#12111yescharacteristic
305Dic61—28no—
306C23×D8—611no—
307C23×D8—611no—
308C22×#127—611no—
309C22×#102—611no—
310C22×#102D6111yescharacteristic, complemented
311C2×#390—611no—
312#2011—618no—
313C2×#336—611no—
314C2×C61—84no—
315C2×C61#201118yescomplemented
316C2×C61C2×#39211yescharacteristic
317C2×C61C2×#44712yes—
318C2×C61C2×#45912yes—
319C2×C61C2×#49311yescharacteristic
320C2×C61C2×#49611yescharacteristic
321D61—84no—
322D61—84no—
323C23×D4—611no—
324C23×D4—611no—
325C23×D4—1222no—
326C23×D4C2×D6111yescharacteristic
327C22×D8—614no—
328C22×D8—614no—
329C22×D8—1224no—
330C22×D8—1224no—
331C22×D8—1224no—
332C22×D8—1224no—
333C22×D8—1224no—
334C22×D8—1224no—
335C23×C8—611no—
336C23×C8C2×D6111yescharacteristic
337C2×#127—614no—
338C2×#127—1222no—
339C2×#127—1224no—
340C2×#127—1224no—
341C22×C4⋊C4C2×D6111yescharacteristic
342C22×C22⋊C4—1222no—
343C22×C42—611no—
344C2×#102—24no—
345C2×#102—614no—
346C2×#102—1224no—
347C2×#102C2×D6114yescomplemented
348#390—614no—
349#390—1222no—
350#336—614no—
351C61C2×#201111yescharacteristic, complemented, Sylow
352C25—21no—
353C25—1221no—
354C25—1221no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—21no—
360C22×D4—22no—
361C22×D4—614no—
362C22×D4—614no—
363C22×D4—612no—
364C22×D4—612no—
365C22×D4—1228no—
366C22×D4—12216no—
367C22×D4—1222no—
368C22×D4—1222no—
369C22×D4—1222no—
370C22×D4—1222no—
371C22×D4—1222no—
372C22×D4—1222no—
373C22×D4—1222no—
374C22×D4—1222no—
375C22×D4—1221no—
376C22×D4—1221no—
377C22×D4—1222no—
378C22×D4—1222no—
379C22×D4—2448no—
380C22×D4—2448no—
381C22×D4D24414yes—
382C22×D4C22×D6112yes—
383C23×C4—21no—
384C23×C4—612no—
385C23×C4C22×D6111yescharacteristic
386C2×D8—1228no—
387C2×D8—1228no—
388C2×D8—12232no—
389C2×D8—1228no—
390C2×D8—1228no—
391C2×D8—12232no—
392C2×D8—1228no—
393C2×D8—1228no—
394C22×C8—22no—
395C22×C8—22no—
396C22×C8—614no—
397C22×C8—612no—
398C22×C8—1222no—
399C22×C8—1222no—
400C22×C8C22⋊D6114yescomplemented
401C22×C8C22×D6112yes—
402#127—1228no—
403#127—12216no—
404#127—1228no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4C22×D6112yes—
409C2×C22⋊C4—1228no—
410C2×C22⋊C4—2448no—
411C2×C42—612no—
412C2×C42—612no—
413C2×C42—1222no—
414C2×C42—1222no—
415#102—28no—
416#102—1228no—
417C24—22no—
418C24—24no—
419C24—42no—
420C24—42no—
421C24—44no—
422C24—44no—
423C24—1222no—
424C24—1222no—
425C24—1224no—
426C24—1224no—
427C24—2442no—
428C24—2442no—
429C24—2442no—
430C24—2442no—
431C24—2444no—
432C24—2444no—
433C24—2444no—
434C24—2444no—
435C24D4×D6111yescharacteristic
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—28no—
442C2×D4—24no—
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—614no—
449C2×D4—614no—
450C2×D4—12232no—
451C2×D4—1222no—
452C2×D4—1222no—
453C2×D4—1222no—
454C2×D4—1222no—
455C2×D4—1222no—
456C2×D4—1222no—
457C2×D4—1222no—
458C2×D4—1222no—
459C2×D4—1222no—
460C2×D4—1222no—
461C2×D4—1228no—
462C2×D4—1228no—
463C2×D4—1228no—
464C2×D4—1224no—
465C2×D4—1228no—
466C2×D4—1224no—
467C2×D4—24416no—
468C2×D4—24416no—
469C2×D4—24464no—
470C2×D4—2444no—
471C2×D4—2442no—
472C2×D4—2444no—
473C2×D4—2442no—
474C2×D4—2444no—
475C2×D4—2444no—
476C2×D4—2442no—
477C2×D4—2442no—
478C2×D4C2×D24414yes—
479C22×C4—22no—
480C22×C4—42no—
481C22×C4—44no—
482C22×C4—614no—
483C22×C4—618no—
484C22×C4—1224no—
485C22×C4—1224no—
486C22×C4C2×D24412yes—
487C22×C4#1175822212yes—
488C22×C4D4×D6112yes—
489C22×C4D4×D6112yes—
490C22×C4D4×D6112yes—
491C22×C4D4×D6111yescharacteristic
492C22×C4C2×C22⋊D6112yes—
493C22×C4C23×D6111yescharacteristic
494D8—12232no—
495D8—12232no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—28no—
499C2×C8—614no—
500C2×C8—1222no—
501C2×C8—1222no—
502C2×C8—1228no—
503C2×C8C2×C22⋊D6114yescomplemented
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—42no—
507C22⋊C4—24416no—
508C42—1222no—
509C42—1222no—
510C42—1224no—
511C23—24no—
512C23—42no—
513C23—44no—
514C23—44no—
515C23—42no—
516C23—416no—
517C23—48no—
518C23—88no—
519C23—84no—
520C23—84no—
521C23—1224no—
522C23—1224no—
523C23—4888no—
524C23—4884no—
525C23—4884no—
526C23—4884no—
527C23—4884no—
528C23—4888no—
529C23—24416no—
530C23—2442no—
531C23—2442no—
532C23—2444no—
533C23—2444no—
534C23—2444no—
535C23—2444no—
536C23—2442no—
537C23—2442no—
538C23—24416no—
539C23—2448no—
540C23—2448no—
541C23#1451974712yes—
542C23#1451975012yes—
543C23#1451977312yes—
544C23D8×D6114yes—
545C23#1451980414yes—
546C23C2×D4×D6111yescharacteristic
547D4—24no—
548D4—24no—
549D4—42no—
550D4—42no—
551D4—48no—
552D4—1224no—
553D4—1224no—
554D4—1224no—
555D4—1224no—
556D4—24464no—
557D4—2442no—
558D4—2442no—
559D4—2442no—
560D4—2442no—
561D4—2448no—
562D4—2448no—
563C2×C4—44no—
564C2×C4—42no—
565C2×C4—84no—
566C2×C4—618no—
567C2×C4—1224no—
568C2×C4—1224no—
569C2×C4—12216no—
570C2×C4#1451974514yes—
571C2×C4#1451974714yes—
572C2×C4#1451974712yes—
573C2×C4#1451975014yes—
574C2×C4#1451975012yes—
575C2×C4#1451975114yes—
576C2×C4#1451977312yes—
577C2×C4C2×D4×D6111yescharacteristic
578C2×C4C2×D4×D6111yescharacteristic
579C2×C4C2×D4×D6111yescharacteristic
580C2×C4C22×C22⋊D6111yescharacteristic
581C2×C4C22×D24411yescharacteristic
582C2×C4C2×#1175822211yescharacteristic
583C8—24no—
584C8—1224no—
585C22—44no—
586C22—48no—
587C22—82no—
588C22—82no—
589C22—84no—
590C22—816no—
591C22—4882no—
592C22—4882no—
593C22—4882no—
594C22—4882no—
595C22—4884no—
596C22—4884no—
597C22—48816no—
598C22—48816no—
599C22—2444no—
600C22—2444no—
601C22—2448no—
602C22—2448no—
603C22#1683967114yes—
604C22#1683989718yes—
605C22#1683995618yes—
606C22#1684013714yes—
607C22#1684014814yes—
608C22C2×#1451974711yescharacteristic
609C22C2×#1451975011yescharacteristic
610C22C2×#1451977311yescharacteristic
611C22C2×D8×D6112yes—
612C22C2×#1451980412yes—
613C4—82no—
614C4—1228no—
615C4#1683967114yes—
616C4C2×#1451974511yescharacteristic
617C4C2×#1451974711yescharacteristic
618C4C2×#1451975011yescharacteristic
619C4C2×#1451975111yescharacteristic
620C2—84no—
621C2—4884no—
622C2—4884no—
623C2#2144689118yesdirect product factor
624C2C2×#1683967111yescharacteristic
625C2C2×#1683989712yes—
626C2C2×#1683995612yes—
627C2C2×#1684013711yescharacteristic
628C2C2×#1684014811yescharacteristic
subgroupG/H
centerC24D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#102×C61C2
socleC24×C61C2×D4
hypercenterC22×#102D61
hypocenterC61C2×#2011
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
1. C23×D488C2semidirect
2. C23×#11758199C2semidirect
3. C22×#14519773C2semidirect
4. C22×#14519697C2semidirect
5. C2×#16839663C2semidirect
6. #21446891C2direct (N × H)
7. C2×#16839516C2semidirect
8. C22×#102×C61C2semidirect
15. C22×D488C22semidirect
19. C22×#11758199C22semidirect
24. C2×#14519773C22semidirect
28. C2×#14519697C22semidirect
30. #16839663C22semidirect
31. #16839516C22semidirect
36. C2×#102×C61C22semidirect
52. C22×D244D4semidirect
70. C22×#92418D4semidirect
95. C22×C8×C61D4semidirect
151. C22×Dic61D8semidirect
178. C2×D244C2×D4semidirect
182. C2×C8×C61C2×D4semidirect
194. C2×#92418C2×D4semidirect
257. C2×Dic61C2×D8semidirect
310. C22×#102D61semidirect
315. C2×C61#2011semidirect
347. C2×#102C2×D61semidirect
351. C61C2×#2011semidirect
400. C22×C8C22⋊D61semidirect
503. C2×C8C2×C22⋊D61semidirect
623. C2#21446891direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D4882
C23×#117581992
C22×#145197732
C22×#145196972
C2×#168396632
#214468912
C2×#168395162
C22×#102×C612
C2×#201161