Finite Group Databasebeta

← C2×#21444781 #29652109

Subgroups — C2×#21444781 #29652109

Order 15616.

1232 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840361C211yesmaximal, characteristic
2C2×#16839901C211yesmaximal, characteristic
3C2×#16839681C211yesmaximal, characteristic, complemented
4#21444781C218yesmaximal, direct product factor
5C2×#16839499C211yesmaximal, characteristic, complemented
6C2×#16839497C211yesmaximal, characteristic
7C2×#16839487C211yesmaximal, characteristic, complemented
8C2×C61×#451C211yesmaximal, characteristic, complemented
9C22×#11758201—21no—
10#16840361—22no—
11#16840361—22no—
12#16840361—22no—
13#16840361C2214yes—
14C2×#14519772—21no—
15C2×#14519768—21no—
16C2×#14519762—21no—
17C2×#14519761—21no—
18C2×#14519753—21no—
19C2×#14519751C2211yescharacteristic
20C2×#14519737—21no—
21C22×#11758196—21no—
22C22×#11758196C2211yescharacteristic
23#16839901—22no—
24#16839901C2214yes—
25C2×#14519701—21no—
26C2×C22⋊#92418C2211yescharacteristic
27#16839681—22no—
28#16839681C2214yescomplemented
29C2×#14519684—21no—
30C2×#14519684C2211yescharacteristic
31#16839499C2214yescomplemented
32#16839497C2214yes—
33#16839487C2214yescomplemented
34C23×Q8×C61C2211yescharacteristic
35C22×Q16×C61—21no—
36C2×C22⋊Q8×C61C2211yescharacteristic
37C61×#451—22no—
38C61×#451C2214yescomplemented
39C2×#103×C61—21no—
40C2×C22⋊C8×C61C2211yescharacteristic
41C22×D244D411yescharacteristic
42C22×C22⋊D61—21no—
43C23×Dic61—21no—
44C23×Dic61D411yescharacteristic
45C23×Dic61D411yescharacteristic
46C22×C4×D61—21no—
47C2×#11758201—24no—
48C2×#11758201—44no—
49C22×#92418—21no—
50#14519772—24no—
51#14519772—24no—
52#14519768—24no—
53#14519768—24no—
54#14519762—24no—
55#14519762—24no—
56#14519761—24no—
57#14519761—24no—
58#14519753—24no—
59#14519753—24no—
60#14519751—21no—
61#14519751—21no—
62#14519751D412yes—
63#14519751C2312yes—
64#14519737—24no—
65#14519737—24no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61D411yescharacteristic
69C2×#11758196—21no—
70C2×#11758196—21no—
71C2×#11758196—21no—
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196—24no—
75C2×#11758196—44no—
76C2×#11758196D412yes—
77C2×#11758196C2312yes—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×C4×Dic61—21no—
83#14519701—24no—
84C22⋊#92418—21no—
85C22⋊#92418C2312yes—
86#14519684—21no—
87#14519684—24no—
88#14519684C2312yes—
89C22×Q8×C61—21no—
90C22×Q8×C61—21no—
91C22×Q8×C61—21no—
92C22×Q8×C61—21no—
93C22×Q8×C61—21no—
94C22×Q8×C61—44no—
95C22×Q8×C61D411yescharacteristic
96C22×Q8×C61C2312yes—
97C23×C4×C61—21no—
98C23×C4×C61C2311yescharacteristic
99C2×Q16×C61—24no—
100C2×Q16×C61—44no—
101C22×C8×C61—21no—
102C22⋊Q8×C61—21no—
103C22⋊Q8×C61—21no—
104C22⋊Q8×C61D412yes—
105C22⋊Q8×C61C2312yes—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61D411yescharacteristic
108C2×C22⋊C4×C61—21no—
109#103×C61—24no—
110C22⋊C8×C61—21no—
111C22⋊C8×C61C2312yes—
112C24×C61C2×D411yescharacteristic
113C23×D61—21no—
114C2×Q8×C61—21no—
115C2×Q8×C61—24no—
116C2×Q8×C61—24no—
117C2×Q8×C61—22no—
118C2×Q8×C61—22no—
119C2×Q8×C61—44no—
120C2×Q8×C61—42no—
121C2×Q8×C61—42no—
122C2×Q8×C61—44no—
123C2×Q8×C61—42no—
124C2×Q8×C61—44no—
125C2×Q8×C61—44no—
126C2×Q8×C61—41no—
127C2×Q8×C61—41no—
128C2×Q8×C61C2×D412yes—
129C22×C4×C61—24no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—42no—
134C22×C4×C61—42no—
135C22×C4×C61—41no—
136C22×C4×C61—41no—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2411yescharacteristic
143C2×C22⋊D61—22no—
144C2×C22⋊D61—22no—
145C2×C22⋊D61—42no—
146C2×C22⋊D61—42no—
147C22×Dic61—24no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—21no—
156C22×Dic61—42no—
157C22×Dic61—42no—
158C22×Dic61—42no—
159C22×Dic61C2×D412yes—
160C22×Dic61C2×D412yes—
161C2×D244—21no—
162C2×D244—42no—
163C2×D244C2×D412yes—
164C2×C4×D61—24no—
165C2×C4×D61—82no—
166Q16×C61—48no—
167C2×C8×C61—22no—
168C2×C8×C61—42no—
169C4⋊C4×C61—22no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61C2×D412yes—
173C22⋊C4×C61—22no—
174C22⋊C4×C61—22no—
175#11758201—48no—
176#11758198—24no—
177#11758198—24no—
178#11758198—24no—
179#11758198—22no—
180#11758198—22no—
181C4⋊Dic61—24no—
182C4⋊Dic61—24no—
183C4⋊Dic61—21no—
184C4⋊Dic61C2×D412yes—
185#11758196—24no—
186#11758196—22no—
187#11758196—22no—
188#11758196—22no—
189#11758196—22no—
190#11758196—48no—
191C4×Dic61—24no—
192C2×#92418—22no—
193C2×#92418—42no—
194C23×C61—22no—
195C23×C61—22no—
196C23×C61#12011yescharacteristic
197C23×C61#12011yescharacteristic
198C23×C61#13512yes—
199C23×C61#13712yes—
200C23×C61C22×D411yescharacteristic
201C22×D61—22no—
202C22×D61—42no—
203C22×D61—42no—
204C22×D61—42no—
205Q8×C61—24no—
206Q8×C61—24no—
207Q8×C61—42no—
208Q8×C61—42no—
209Q8×C61—44no—
210Q8×C61—44no—
211Q8×C61—42no—
212Q8×C61—81no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—24no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—42no—
223C2×C4×C61—44no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—44no—
228C2×C4×C61#12011yescharacteristic
229C2×C4×C61#12011yescharacteristic
230C2×C4×C61C22×D411yescharacteristic
231C2×C4×C61C22×D411yescharacteristic
232C22⋊D61—42no—
233C22⋊D61—42no—
234C22⋊D61—44no—
235C2×Dic61—24no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—42no—
242C2×Dic61—48no—
243C2×Dic61—42no—
244C2×Dic61—42no—
245C2×Dic61—42no—
246C2×Dic61—42no—
247C2×Dic61—42no—
248C2×Dic61—42no—
249C2×Dic61—81no—
250D244—42no—
251D244—81no—
252C4×D61—84no—
253C8×C61—42no—
254#92418—42no—
255C2×#1603—611nomaximal, Sylow
256C22×C61—24no—
257C22×C61—24no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61#45212yes—
263C22×C61#45212yes—
264C22×C61#45612yes—
265C22×C61B(4,𝔽2)12yes—
266C22×C61C2×#12011yescharacteristic
267C22×C61C2×#13511yescharacteristic
268C22×C61C2×#13711yescharacteristic
269C2×D61—42no—
270C2×D61—42no—
271C2×D61—42no—
272C2×D61—84no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—42no—
278C4×C61—42no—
279C4×C61—44no—
280Dic61—44no—
281Dic61—42no—
282Dic61—42no—
283Dic61—42no—
284C2×#539—611no—
285C2×#451D6111yescharacteristic, complemented
286C2×#448—611no—
287C2×#395—611no—
288#1603—618no—
289C2×#328—611no—
290C2×#327—611no—
291C2×#324—611no—
292C2×C61—21no—
293C2×C61—21no—
294C2×C61—22no—
295C2×C61#160314yescomplemented
296C2×C61C2×#45211yescharacteristic
297C2×C61C2×#45611yescharacteristic
298C2×C61C2×B(4,𝔽2)11yescharacteristic
299D61—82no—
300C23×Q8C2×D6111yescharacteristic
301C22×Q16—21no—
302C22×SD16—1221no—
303#539—614no—
304#539—1222no—
305#539—1222no—
306#539—1222no—
307C2×#126—1221no—
308C2×#125—1221no—
309C2×#123—1221no—
310C2×#123—1221no—
311C2×C22⋊Q8—1221no—
312C2×C22⋊Q8C2×D6111yescharacteristic
313C2×#121—611no—
314C2×C4×D4—1221no—
315C22×C4⋊C4—611no—
316C22×C4⋊C4—1221no—
317#451—22no—
318#451C2×D6114yescomplemented
319#448—614no—
320#448—1222no—
321C2×#103—21no—
322C2×#103—1221no—
323C2×C22⋊C8—611no—
324C2×C22⋊C8C2×D6111yescharacteristic
325#395—614no—
326#395—1222no—
327C2×#95—611no—
328C2×#95—1221no—
329#328—614no—
330#327—614no—
331#324—614no—
332C61C2×#160311yescharacteristic, complemented, Sylow
333C22×Q8—21no—
334C22×Q8—21no—
335C22×Q8—21no—
336C22×Q8—21no—
337C22×Q8—21no—
338C22×Q8—44no—
339C22×Q8C22⋊D6111yescharacteristic
340C22×Q8C22×D6112yes—
341C22×D4—611no—
342C22×D4—1221no—
343C23×C4—21no—
344C23×C4—611no—
345C23×C4—611no—
346C23×C4—1221no—
347C23×C4—1221no—
348C23×C4C22×D6111yescharacteristic
349C2×Q16—24no—
350C2×Q16—44no—
351C2×SD16—1224no—
352C2×SD16—2444no—
353C22×C8—21no—
354C22×C8—1221no—
355#126—1224no—
356#126—1224no—
357#125—1224no—
358#125—1224no—
359#123—1224no—
360#123—1224no—
361#123—1224no—
362#123—1224no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—1224no—
366C22⋊Q8—1224no—
367C22⋊Q8C22⋊D6112yes—
368C22⋊Q8C22×D6112yes—
369#121—612no—
370#121—612no—
371#121—1221no—
372#121—1221no—
373C4×D4—1224no—
374C4×D4—1224no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—612no—
378C2×C4⋊C4—612no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4—1221no—
385C2×C4⋊C4—1221no—
386C2×C4⋊C4—1224no—
387C2×C4⋊C4—2444no—
388C2×C4⋊C4C22⋊D6111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—1221no—
391C2×C22⋊C4—1221no—
392C2×C22⋊C4—1221no—
393C2×C22⋊C4—1221no—
394C2×C42—1221no—
395#103—24no—
396#103—1224no—
397C22⋊C8—21no—
398C22⋊C8—612no—
399C22⋊C8—1221no—
400C22⋊C8C22×D6112yes—
401#95—612no—
402#95—1224no—
403#95—1221no—
404C24—1221no—
405C24D4×D6111yescharacteristic
406C2×Q8—21no—
407C2×Q8—24no—
408C2×Q8—24no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—44no—
412C2×Q8—42no—
413C2×Q8—42no—
414C2×Q8—44no—
415C2×Q8—42no—
416C2×Q8—44no—
417C2×Q8—44no—
418C2×Q8—41no—
419C2×Q8—41no—
420C2×Q8C2×C22⋊D6112yes—
421C2×D4—612no—
422C2×D4—1222no—
423C2×D4—1222no—
424C2×D4—1221no—
425C2×D4—2442no—
426C2×D4—2442no—
427C2×D4—2442no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—612no—
437C22×C4—612no—
438C22×C4—1224no—
439C22×C4—1221no—
440C22×C4—1224no—
441C22×C4—1222no—
442C22×C4—1222no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4—1222no—
448C22×C4—4882no—
449C22×C4—2442no—
450C22×C4—2442no—
451C22×C4—2442no—
452C22×C4D4×D6111yescharacteristic
453C22×C4D4×D6111yescharacteristic
454C22×C4D4×D6111yescharacteristic
455C22×C4C2×C22⋊D6111yescharacteristic
456C22×C4C2×C22⋊D6111yescharacteristic
457C22×C4C23×D6111yescharacteristic
458Q16—48no—
459SD16—2448no—
460C2×C8—22no—
461C2×C8—42no—
462C2×C8—1222no—
463C2×C8—2442no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—612no—
468C4⋊C4—1224no—
469C4⋊C4—1224no—
470C4⋊C4—1224no—
471C4⋊C4—1222no—
472C4⋊C4—1222no—
473C4⋊C4—1222no—
474C4⋊C4—1222no—
475C4⋊C4—1221no—
476C4⋊C4—2448no—
477C4⋊C4C2×C22⋊D6112yes—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—1224no—
481C22⋊C4—1224no—
482C22⋊C4—1224no—
483C22⋊C4—1222no—
484C22⋊C4—1222no—
485C42—1224no—
486C23—22no—
487C23—22no—
488C23—1222no—
489C23—2442no—
490C23—2442no—
491C23—2442no—
492C23#1451974511yescharacteristic
493C23#1451974511yescharacteristic
494C23#1451980012yes—
495C23#1451980912yes—
496C23C2×D4×D6111yescharacteristic
497Q8—24no—
498Q8—24no—
499Q8—42no—
500Q8—42no—
501Q8—42no—
502Q8—44no—
503Q8—44no—
504Q8—81no—
505D4—4881no—
506D4—2442no—
507D4—2442no—
508D4—2442no—
509D4—2444no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—42no—
522C2×C4—44no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—1224no—
526C2×C4—1222no—
527C2×C4—1222no—
528C2×C4—1222no—
529C2×C4—1222no—
530C2×C4—1222no—
531C2×C4—4884no—
532C2×C4—4881no—
533C2×C4—2442no—
534C2×C4—2448no—
535C2×C4—2442no—
536C2×C4—2442no—
537C2×C4—2442no—
538C2×C4—2442no—
539C2×C4—2442no—
540C2×C4—2442no—
541C2×C4#1451974511yescharacteristic
542C2×C4#1451974511yescharacteristic
543C2×C4C2×D4×D6111yescharacteristic
544C2×C4C22×C22⋊D6111yescharacteristic
545C8—42no—
546C8—2442no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—24no—
552C22—24no—
553C22—4884no—
554C22—2442no—
555C22—2442no—
556C22—2442no—
557C22#1683992312yes—
558C22#1683992312yes—
559C22#1683994312yes—
560C22#1683994812yes—
561C22C2×#1451974511yescharacteristic
562C22C2×#1451980011yescharacteristic
563C22C2×#1451980911yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—42no—
569C4—44no—
570C4—42no—
571C4—2444no—
572C4—2442no—
573C4—2442no—
574C4—2442no—
575C2—21no—
576C2—21no—
577C2—22no—
578C2—4882no—
579C2#2144478114yesdirect product factor
580C2C2×#1683992311yescharacteristic
581C2C2×#1683994311yescharacteristic
582C2C2×#1683994811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#451C2
socleC23×C61#120
prime radicalC2×#14519751C22
hypercenterC2×#451D61
hypocenterC61C2×#1603
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. C2×#16839681C2semidirect
4. #21444781C2direct (N × H)
5. C2×#16839499C2semidirect
7. C2×#16839487C2semidirect
8. C2×C61×#451C2semidirect
28. #16839681C22semidirect
31. #16839499C22semidirect
33. #16839487C22semidirect
38. C61×#451C22semidirect
285. C2×#451D61semidirect
295. C2×C61#1603semidirect
318. #451C2×D61semidirect
332. C61C2×#1603semidirect
579. C2#21444781direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403612
C2×#168399012
C2×#168396812
#214447812
C2×#168394992
C2×#168394972
C2×#168394872
C2×C61×#4512
C2×#160361