Finite Group Databasebeta

← C2×#21447112 #29707881

Subgroups — C2×#21447112 #29707881

Order 15616.

1490 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519803C211yesmaximal, characteristic
2C22×#14519713C211yesmaximal, characteristic, complemented
3C2×#16839761C211yesmaximal, characteristic, complemented
4C22×#14519694C211yesmaximal, characteristic, complemented
5C2×#16839728C211yesmaximal, characteristic, complemented
6#21447112C218yesmaximal, direct product factor
7C2×#16839531C211yesmaximal, characteristic, complemented
8C22×#102×C61C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C2×#14519803—24no—
11C2×#14519803—24no—
12C2×#14519803—22no—
13C2×#14519803C2214yes—
14C22×#11758200—21no—
15C22×#11758199—21no—
16C22×#11758194C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C2×#14519713—24no—
20C2×#14519713C2214yescomplemented
21#16839761—22no—
22#16839761C2214yescomplemented
23C2×#14519700—21no—
24C2×#14519697—21no—
25C2×#14519694—24no—
26C2×#14519694C2214yescomplemented
27#16839728—22no—
28#16839728C2214yescomplemented
29C2×#14519689—22no—
30#16839531C2214yescomplemented
31C23×D4×C61C2211yescharacteristic
32C23×C8×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C2×#102×C61—22no—
35C2×#102×C61—22no—
36C2×#102×C61C2214yescomplemented
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—22no—
40C2×#11758222—22no—
41C2×#11758222—22no—
42C2×#11758222—22no—
43C2×#11758222D412yes—
44C2×#11758222C2312yes—
45C22×Dic122D411yescharacteristic
46C22×D244D411yescharacteristic
47C22×C22⋊D61—21no—
48C22×C4×D61—21no—
49#14519803—216no—
50#14519803—28no—
51#14519803—28no—
52C2×#11758200—28no—
53C2×#11758200—24no—
54C2×#11758199—28no—
55C2×#11758199—24no—
56C2×#11758194—22no—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—22no—
61C2×#11758194—22no—
62C2×#11758194—22no—
63C2×#11758194—22no—
64C2×#11758194D414yes—
65C2×#11758194C2312yes—
66C2×#11758194C2312yes—
67C2×#11758194C2312yes—
68C22×#92418—21no—
69C22×#92418—21no—
70C22×#92418—21no—
71#14519713—28no—
72#14519700—24no—
73#14519697—24no—
74#14519694—28no—
75#14519689—28no—
76C25×C61—21no—
77C22×D4×C61—21no—
78C22×D4×C61—22no—
79C22×D4×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61—22no—
83C22×D4×C61—22no—
84C22×D4×C61—21no—
85C22×D4×C61D414yes—
86C22×D4×C61C2312yes—
87C23×C4×C61—21no—
88C23×C4×C61C2311yescharacteristic
89C22×C8×C61—22no—
90C22×C8×C61—22no—
91C22×C8×C61D412yes—
92C22×C8×C61D412yes—
93C22×C8×C61C2312yes—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61C2312yes—
100#102×C61—28no—
101C24×C61—24no—
102C24×C61—22no—
103C24×C61—41no—
104C24×C61—41no—
105C24×C61—42no—
106C24×C61—82no—
107C24×C61—82no—
108C24×C61#4111yescharacteristic
109C23×D61—21no—
110C2×D4×C61—24no—
111C2×D4×C61—24no—
112C2×D4×C61—24no—
113C2×D4×C61—24no—
114C2×D4×C61—24no—
115C2×D4×C61—22no—
116C2×D4×C61—22no—
117C2×D4×C61—22no—
118C2×D4×C61—22no—
119C2×D4×C61—22no—
120C2×D4×C61—42no—
121C2×D4×C61—42no—
122C2×D4×C61—41no—
123C2×D4×C61—41no—
124C2×D4×C61—42no—
125C2×D4×C61—42no—
126C2×D4×C61—42no—
127C2×D4×C61C2×D414yes—
128C22×C4×C61—22no—
129C22×C4×C61—41no—
130C22×C4×C61—41no—
131C22×C4×C61—82no—
132C22×C4×C61C2×D412yes—
133C22×C4×C61C2×D412yes—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61#4112yes—
139C22×C4×C61#4111yescharacteristic
140C22×C4×C61#4112yes—
141C22×C4×C61C2411yescharacteristic
142C2×C22⋊D61—22no—
143C2×C22⋊D61—22no—
144C2×C22⋊D61—42no—
145C2×C22⋊D61—42no—
146C22×Dic61—21no—
147#11758222—24no—
148#11758222—24no—
149#11758222—22no—
150#11758222—22no—
151#11758222—22no—
152#11758222—22no—
153#11758222—42no—
154#11758222—42no—
155#11758222—42no—
156#11758222—42no—
157C2×D244—22no—
158C2×D244—22no—
159C2×D244—21no—
160C2×D244C2×D412yes—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—42no—
164C2×C4×D61—42no—
165C2×Dic122—22no—
166C2×Dic122—22no—
167C2×Dic122—21no—
168C2×Dic122C2×D412yes—
169C2×C8×C61—24no—
170C2×C8×C61—24no—
171C2×C8×C61—22no—
172C2×C8×C61—22no—
173C2×C8×C61C2×D414yes—
174C4⋊C4×C61—22no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—41no—
178#11758200—216no—
179#11758199—216no—
180#11758194—24no—
181#11758194—22no—
182#11758194—22no—
183#11758194—22no—
184#11758194—22no—
185#11758194—22no—
186#11758194—42no—
187#11758194—42no—
188#11758194C2×D414yes—
189C2×#92418—24no—
190C2×#92418—22no—
191C2×#92418—22no—
192C2×#92418—22no—
193C2×#92418—42no—
194C2×#92418—42no—
195C23×C61—22no—
196C23×C61—22no—
197C23×C61—24no—
198C23×C61—42no—
199C23×C61—42no—
200C23×C61—44no—
201C23×C61—44no—
202C23×C61—88no—
203C23×C61—82no—
204C23×C61—82no—
205C23×C61—88no—
206C23×C61—82no—
207C23×C61—82no—
208C23×C61—82no—
209C23×C61—82no—
210C23×C61#12111yescharacteristic
211C23×C61#12111yescharacteristic
212C23×C61#12312yes—
213C23×C61#12412yes—
214C23×C61C2×#4111yescharacteristic
215C22×D61—22no—
216C22×D61—42no—
217C22×D61—42no—
218C22×D61—42no—
219D4×C61—24no—
220D4×C61—24no—
221D4×C61—42no—
222D4×C61—42no—
223D4×C61—44no—
224D4×C61—44no—
225C2×C4×C61—42no—
226C2×C4×C61—82no—
227C2×C4×C61—82no—
228C2×C4×C61—82no—
229C2×C4×C61#12012yes—
230C2×C4×C61#12012yes—
231C2×C4×C61#12112yes—
232C2×C4×C61#12112yes—
233C2×C4×C61#12112yes—
234C2×C4×C61#12112yes—
235C2×C4×C61#12111yescharacteristic
236C2×C4×C61#12111yescharacteristic
237C2×C4×C61#12312yes—
238C2×C4×C61#12312yes—
239C2×C4×C61#12312yes—
240C2×C4×C61#12412yes—
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C22⋊D61—42no—
248C22⋊D61—42no—
249C22⋊D61—44no—
250C2×Dic61—22no—
251C2×Dic61—42no—
252D244—22no—
253D244—22no—
254D244—42no—
255C4×D61—42no—
256C4×D61—42no—
257C4×D61—44no—
258Dic122—22no—
259Dic122—22no—
260Dic122—42no—
261C8×C61—24no—
262#92418—24no—
263#92418—42no—
264#92418—42no—
265C2×#2051—611nomaximal, Sylow
266C22×C61—24no—
267C22×C61—24no—
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—44no—
273C22×C61—84no—
274C22×C61—84no—
275C22×C61—88no—
276C22×C61—88no—
277C22×C61—82no—
278C22×C61—82no—
279C22×C61#39412yes—
280C22×C61#39412yes—
281C22×C61#47112yes—
282C22×C61#47212yes—
283C22×C61C2×#12111yescharacteristic
284C22×C61C2×#12311yescharacteristic
285C22×C61C2×#12411yescharacteristic
286C2×D61—42no—
287C2×D61—42no—
288C2×D61—42no—
289C2×D61—84no—
290C4×C61—82no—
291C4×C61#39412yes—
292C4×C61#39412yes—
293C4×C61C2×#12011yescharacteristic
294C4×C61C2×#12111yescharacteristic
295C4×C61C2×#12111yescharacteristic
296C4×C61C2×#12311yescharacteristic
297Dic61—42no—
298C22×AGL(1,ℤ/8)—611no—
299C22×#108—611no—
300C2×#417—611no—
301C22×#102D6111yescharacteristic, complemented
302C22×#100—611no—
303C2×#408—611no—
304#2051—618no—
305C2×#343—611no—
306C2×C61—21no—
307C2×C61—21no—
308C2×C61—22no—
309C2×C61—84no—
310C2×C61#205114yescomplemented
311C2×C61C2×#39411yescharacteristic
312C2×C61C2×#47111yescharacteristic
313C2×C61C2×#47211yescharacteristic
314D61—82no—
315C22×#41—611no—
316C23×D4C2×D6111yescharacteristic
317C2×AGL(1,ℤ/8)—614no—
318C2×AGL(1,ℤ/8)—1224no—
319C2×AGL(1,ℤ/8)—1222no—
320C2×AGL(1,ℤ/8)—1224no—
321C22×SD16—1221no—
322C22×D8—1221no—
323C22×M16—611no—
324C22×M16—611no—
325C22×M16—611no—
326C23×C8C2×D6111yescharacteristic
327C22×C4⋊C4C2×D6111yescharacteristic
328C2×#108—614no—
329C2×#108—1224no—
330#417—614no—
331#417—1222no—
332C2×#103—1221no—
333C2×#102—22no—
334C2×#102—22no—
335C2×#102—1221no—
336C2×#102C2×D6114yescomplemented
337C2×#100—614no—
338C2×#100—1224no—
339#408—614no—
340#408—1222no—
341C2×C22⋊C8—1222no—
342#343—614no—
343C61C2×#205111yescharacteristic, complemented, Sylow
344C25—21no—
345C2×#41—612no—
346C2×#41—612no—
347C2×#41—1221no—
348C2×#41—1221no—
349C2×#41—1222no—
350C2×#41—1222no—
351C2×#41—1222no—
352C2×#41—1222no—
353C22×Q8—611no—
354C22×D4—22no—
355C22×D4—21no—
356C22×D4—21no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—611no—
363C22×D4—1221no—
364C22×D4D24414yes—
365C22×D4C22×D6112yes—
366C23×C4—21no—
367C23×C4—1221no—
368C23×C4C22×D6111yescharacteristic
369AGL(1,ℤ/8)—1228no—
370AGL(1,ℤ/8)—12216no—
371AGL(1,ℤ/8)—1228no—
372C2×SD16—1224no—
373C2×SD16—1228no—
374C2×D8—1224no—
375C2×D8—1228no—
376C2×M16—614no—
377C2×M16—612no—
378C2×M16—612no—
379C2×M16—612no—
380C2×M16—1222no—
381C2×M16—1221no—
382C2×M16—1221no—
383C2×M16—1221no—
384C2×M16—1222no—
385C2×M16—1222no—
386C2×M16—1222no—
387C2×M16—1222no—
388C22×C8—22no—
389C22×C8—22no—
390C22×C8—1221no—
391C22×C8—1221no—
392C22×C8—1221no—
393C22×C8C22⋊D6112yes—
394C22×C8C22⋊D6112yes—
395C22×C8C22×D6112yes—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4C22×D6112yes—
402#108—1228no—
403#103—1224no—
404#102—28no—
405#102—1224no—
406#100—1228no—
407C22⋊C8—1228no—
408C24—22no—
409C24—24no—
410C24—41no—
411C24—41no—
412C24—42no—
413C24—82no—
414C24—82no—
415C24—1221no—
416C24#1175822411yescharacteristic
417#41—1222no—
418#41—1222no—
419#41—1222no—
420#41—1222no—
421#41—1224no—
422#41—1224no—
423#41—2442no—
424#41—2442no—
425#41—2442no—
426#41—2442no—
427C2×Q8—612no—
428C2×Q8—1221no—
429C2×Q8—1222no—
430C2×Q8—1222no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—24no—
437C2×D4—24no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—24no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—42no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—612no—
449C2×D4—1222no—
450C2×D4—1222no—
451C2×D4—1222no—
452C2×D4—1221no—
453C2×D4—1222no—
454C2×D4—2442no—
455C2×D4—2442no—
456C2×D4C2×D24414yes—
457C22×C4—22no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—82no—
461C22×C4—1221no—
462C22×C4—1222no—
463C22×C4—1222no—
464C22×C4—2442no—
465C22×C4—2442no—
466C22×C4C2×D24412yes—
467C22×C4#1175822212yes—
468C22×C4D4×D6111yescharacteristic
469C22×C4D4×D6111yescharacteristic
470C22×C4D4×D6112yes—
471C22×C4#1175822412yes—
472C22×C4#1175822411yescharacteristic
473C22×C4C2×C22⋊D6111yescharacteristic
474C22×C4C2×C22⋊D6111yescharacteristic
475C22×C4C23×D6111yescharacteristic
476SD16—12216no—
477D8—12216no—
478M16—614no—
479M16—1222no—
480M16—1224no—
481M16—1222no—
482M16—1222no—
483M16—1222no—
484M16—1222no—
485M16—2442no—
486M16—2442no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—24no—
490C2×C8—24no—
491C2×C8—1222no—
492C2×C8—1224no—
493C2×C8—1222no—
494C2×C8—1222no—
495C2×C8—2442no—
496C2×C8—2442no—
497C2×C8C2×C22⋊D6114yes—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C23—22no—
503C23—22no—
504C23—24no—
505C23—42no—
506C23—42no—
507C23—44no—
508C23—44no—
509C23—82no—
510C23—82no—
511C23—88no—
512C23—82no—
513C23—82no—
514C23—88no—
515C23—82no—
516C23—82no—
517C23—1222no—
518C23—2442no—
519C23—2442no—
520C23—2442no—
521C23#1451974811yescharacteristic
522C23#1451974811yescharacteristic
523C23#1451976112yes—
524C23#1451976312yes—
525C23C2×#1175822411yescharacteristic
526Q8—1222no—
527Q8—1222no—
528Q8—2442no—
529D4—24no—
530D4—24no—
531D4—42no—
532D4—42no—
533D4—44no—
534D4—44no—
535D4—1222no—
536D4—1222no—
537D4—2442no—
538D4—2442no—
539D4—2444no—
540D4—2442no—
541C2×C4—42no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—1222no—
546C2×C4—2442no—
547C2×C4—2442no—
548C2×C4—2442no—
549C2×C4—2444no—
550C2×C4#1451974712yes—
551C2×C4#1451974712yes—
552C2×C4#1451974811yescharacteristic
553C2×C4#1451974811yescharacteristic
554C2×C4#1451974912yes—
555C2×C4#1451974912yes—
556C2×C4#1451975112yes—
557C2×C4#1451975112yes—
558C2×C4#1451975912yes—
559C2×C4#1451975912yes—
560C2×C4#1451976112yes—
561C2×C4#1451976312yes—
562C2×C4C2×D4×D6111yescharacteristic
563C2×C4C2×D4×D6111yescharacteristic
564C2×C4C22×C22⋊D6111yescharacteristic
565C2×C4C22×D24411yescharacteristic
566C2×C4C2×#1175822411yescharacteristic
567C2×C4C2×#1175822211yescharacteristic
568C8—24no—
569C8—1224no—
570C8—2442no—
571C8—2442no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—24no—
577C22—24no—
578C22—44no—
579C22—84no—
580C22—84no—
581C22—88no—
582C22—82no—
583C22—82no—
584C22—88no—
585C22—4884no—
586C22—2442no—
587C22—2442no—
588C22—2442no—
589C22#1683967812yes—
590C22#1683967812yes—
591C22#1684002212yes—
592C22#1684002912yes—
593C22C2×#1451974811yescharacteristic
594C22C2×#1451976111yescharacteristic
595C22C2×#1451976311yescharacteristic
596C4—82no—
597C4—2442no—
598C4#1683967812yes—
599C4#1683967812yes—
600C4C2×#1451974711yescharacteristic
601C4C2×#1451974911yescharacteristic
602C4C2×#1451975111yescharacteristic
603C4C2×#1451975911yescharacteristic
604C2—21no—
605C2—21no—
606C2—22no—
607C2—84no—
608C2—4882no—
609C2#2144711214yesdirect product factor
610C2C2×#1683967811yescharacteristic
611C2C2×#1684002211yescharacteristic
612C2C2×#1684002911yescharacteristic
subgroupG/H
centerC23#14519748
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#102×C61C2
socleC23×C61#121
prime radicalC22×#14519803C2
hypercenterC22×#102D61
hypocenterC61C2×#2051
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#14519713C2semidirect
3. C2×#16839761C2semidirect
4. C22×#14519694C2semidirect
5. C2×#16839728C2semidirect
6. #21447112C2direct (N × H)
7. C2×#16839531C2semidirect
8. C22×#102×C61C2semidirect
20. C2×#14519713C22semidirect
22. #16839761C22semidirect
26. C2×#14519694C22semidirect
28. #16839728C22semidirect
30. #16839531C22semidirect
36. C2×#102×C61C22semidirect
301. C22×#102D61semidirect
310. C2×C61#2051semidirect
336. C2×#102C2×D61semidirect
343. C61C2×#2051semidirect
609. C2#21447112direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198032
C22×#145197132
C2×#168397612
C22×#145196942
C2×#168397282
#214471122
C2×#168395312
C22×#102×C612
C2×#205161