Finite Group Databasebeta

← C2×#21444815 #29652152

Subgroups — C2×#21444815 #29652152

Order 15616.

1060 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840361C211yesmaximal, characteristic
2C2×#16840075C211yesmaximal, characteristic
3C2×#16839693C211yesmaximal, characteristic, complemented
4#21444815C218yesmaximal, direct product factor
5C2×#16839499C211yesmaximal, characteristic, complemented
6C2×#16839497C211yesmaximal, characteristic
7C2×#16839487C211yesmaximal, characteristic, complemented
8C2×C61×#483C211yesmaximal, characteristic, complemented
9#16840361—22no—
10#16840361—22no—
11#16840361—22no—
12#16840361C2214yes—
13C2×#14519772—21no—
14C2×#14519768—21no—
15C2×#14519762—21no—
16C2×#14519761—21no—
17C2×#14519753—21no—
18C2×#14519751C2211yescharacteristic
19C2×#14519737—21no—
20C22×#11758196—21no—
21C22×#11758196C2211yescharacteristic
22#16840075—22no—
23#16840075C2214yes—
24C2×#14519710—21no—
25C2×#14519697—21no—
26C2×C22⋊#92418C2211yescharacteristic
27#16839693—22no—
28#16839693C2214yescomplemented
29C2×#14519684—21no—
30C2×#14519684C2211yescharacteristic
31#16839499C2214yescomplemented
32#16839497C2214yes—
33#16839487C2214yescomplemented
34C2×C22⋊Q8×C61C2211yescharacteristic
35C22×C4⋊C4×C61C2211yescharacteristic
36C61×#483—22no—
37C61×#483C2214yescomplemented
38C2×#106×C61—21no—
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—
47C22×#92418—21no—
48#14519772—24no—
49#14519772—24no—
50#14519768—24no—
51#14519768—24no—
52#14519762—24no—
53#14519762—24no—
54#14519761—24no—
55#14519761—24no—
56#14519753—24no—
57#14519753—24no—
58#14519751—21no—
59#14519751—21no—
60#14519751D412yes—
61#14519751C2312yes—
62#14519737—24no—
63#14519737—24no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61D411yescharacteristic
67C2×#11758196—21no—
68C2×#11758196—21no—
69C2×#11758196—21no—
70C2×#11758196—21no—
71C2×#11758196—21no—
72C2×#11758196—24no—
73C2×#11758196—44no—
74C2×#11758196D412yes—
75C2×#11758196C2312yes—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×C4×Dic61—21no—
81#14519710—24no—
82#14519697—24no—
83C22⋊#92418—21no—
84C22⋊#92418C2312yes—
85#14519684—21no—
86#14519684—24no—
87#14519684C2312yes—
88C22×Q8×C61D411yescharacteristic
89C23×C4×C61—21no—
90C23×C4×C61C2311yescharacteristic
91C22×C8×C61—21no—
92C22⋊Q8×C61—21no—
93C22⋊Q8×C61—21no—
94C22⋊Q8×C61D412yes—
95C22⋊Q8×C61C2312yes—
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×C61D411yescharacteristic
103C2×C4⋊C4×C61C2312yes—
104C2×C22⋊C4×C61—21no—
105#106×C61—24no—
106#103×C61—24no—
107C22⋊C8×C61—21no—
108C22⋊C8×C61C2312yes—
109C24×C61C2×D411yescharacteristic
110C23×D61—21no—
111C2×Q8×C61—21no—
112C2×Q8×C61—42no—
113C2×Q8×C61C2×D412yes—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—22no—
117C22×C4×C61—42no—
118C22×C4×C61—41no—
119C22×C4×C61—41no—
120C22×C4×C61—42no—
121C22×C4×C61—42no—
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2411yescharacteristic
128C2×C22⋊D61—22no—
129C2×C22⋊D61—22no—
130C2×C22⋊D61—42no—
131C2×C22⋊D61—42no—
132C22×Dic61—24no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—22no—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61—21no—
141C22×Dic61—42no—
142C22×Dic61—42no—
143C22×Dic61—42no—
144C22×Dic61C2×D412yes—
145C22×Dic61C2×D412yes—
146C2×D244—21no—
147C2×D244—42no—
148C2×D244C2×D412yes—
149C2×C4×D61—24no—
150C2×C4×D61—82no—
151C2×C8×C61—22no—
152C2×C8×C61—42no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—22no—
157C4⋊C4×C61—22no—
158C4⋊C4×C61—41no—
159C4⋊C4×C61—41no—
160C4⋊C4×C61C2×D412yes—
161C22⋊C4×C61—22no—
162C22⋊C4×C61—22no—
163#11758198—24no—
164#11758198—24no—
165#11758198—24no—
166#11758198—22no—
167#11758198—22no—
168C4⋊Dic61—24no—
169C4⋊Dic61—24no—
170C4⋊Dic61—21no—
171C4⋊Dic61C2×D412yes—
172#11758196—24no—
173#11758196—22no—
174#11758196—22no—
175#11758196—22no—
176#11758196—22no—
177#11758196—48no—
178C4×Dic61—24no—
179C2×#92418—22no—
180C2×#92418—42no—
181C23×C61—22no—
182C23×C61—22no—
183C23×C61#12011yescharacteristic
184C23×C61#12011yescharacteristic
185C23×C61#13512yes—
186C23×C61AGL(1,ℤ/8)12yes—
187C23×C61C22×D411yescharacteristic
188C22×D61—22no—
189C22×D61—42no—
190C22×D61—42no—
191C22×D61—42no—
192Q8×C61—42no—
193Q8×C61—81no—
194C2×C4×C61—22no—
195C2×C4×C61—22no—
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—42no—
203C2×C4×C61—42no—
204C2×C4×C61—42no—
205C2×C4×C61—42no—
206C2×C4×C61—42no—
207C2×C4×C61—82no—
208C2×C4×C61—82no—
209C2×C4×C61#12011yescharacteristic
210C2×C4×C61#12011yescharacteristic
211C2×C4×C61C22×D411yescharacteristic
212C2×C4×C61C22×D411yescharacteristic
213C22⋊D61—42no—
214C22⋊D61—42no—
215C22⋊D61—44no—
216C2×Dic61—24no—
217C2×Dic61—22no—
218C2×Dic61—22no—
219C2×Dic61—22no—
220C2×Dic61—22no—
221C2×Dic61—22no—
222C2×Dic61—48no—
223C2×Dic61—42no—
224C2×Dic61—42no—
225C2×Dic61—42no—
226C2×Dic61—42no—
227C2×Dic61—42no—
228C2×Dic61—42no—
229C2×Dic61—42no—
230C2×Dic61—81no—
231D244—42no—
232D244—81no—
233C4×D61—84no—
234C8×C61—42no—
235#92418—42no—
236C2×#1609—611nomaximal, Sylow
237C22×C61—24no—
238C22×C61—24no—
239C22×C61—21no—
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—21no—
243C22×C61#44912yes—
244C22×C61#44912yes—
245C22×C61#45612yes—
246C22×C61#45812yes—
247C22×C61C2×#12011yescharacteristic
248C22×C61C2×#13511yescharacteristic
249C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
250C2×D61—42no—
251C2×D61—42no—
252C2×D61—42no—
253C2×D61—84no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—21no—
257C4×C61—21no—
258C4×C61—42no—
259C4×C61—42no—
260C4×C61—82no—
261Dic61—44no—
262Dic61—42no—
263Dic61—42no—
264Dic61—42no—
265C2×#539—611no—
266C2×#483D6111yescharacteristic, complemented
267C2×#480—611no—
268C2×#398—611no—
269#1609—618no—
270C2×#328—611no—
271C2×#327—611no—
272C2×#324—611no—
273C2×C61—21no—
274C2×C61—21no—
275C2×C61—22no—
276C2×C61#160914yescomplemented
277C2×C61C2×#44911yescharacteristic
278C2×C61C2×#45611yescharacteristic
279C2×C61C2×#45811yescharacteristic
280D61—82no—
281#539—614no—
282#539—1222no—
283#539—1222no—
284#539—1222no—
285C2×#126—1221no—
286C2×#125—1221no—
287C2×#123—1221no—
288C2×#123—1221no—
289C2×C22⋊Q8—1221no—
290C2×C22⋊Q8C2×D6111yescharacteristic
291C2×#121—611no—
292C2×C4×D4—1221no—
293C22×C4⋊C4—611no—
294C22×C4⋊C4—1221no—
295C22×C4⋊C4C2×D6111yescharacteristic
296#483—22no—
297#483C2×D6114yescomplemented
298#480—614no—
299#480—1222no—
300C2×#107—1221no—
301C2×#106—21no—
302C2×#103—21no—
303C2×#102—1221no—
304C2×C22⋊C8—611no—
305C2×C22⋊C8C2×D6111yescharacteristic
306#398—614no—
307#398—1222no—
308C2×#95—611no—
309C2×#95—1221no—
310#328—614no—
311#327—614no—
312#324—614no—
313C61C2×#160911yescharacteristic, complemented, Sylow
314C22×Q8C22⋊D6111yescharacteristic
315C22×D4—611no—
316C22×D4—1221no—
317C23×C4—21no—
318C23×C4—611no—
319C23×C4—611no—
320C23×C4—1221no—
321C23×C4—1221no—
322C23×C4C22×D6111yescharacteristic
323C22×C8—21no—
324C22×C8—1221no—
325#126—1224no—
326#126—1224no—
327#125—1224no—
328#125—1224no—
329#123—1224no—
330#123—1224no—
331#123—1224no—
332#123—1224no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—1224no—
336C22⋊Q8—1224no—
337C22⋊Q8C22⋊D6112yes—
338C22⋊Q8C22×D6112yes—
339#121—612no—
340#121—612no—
341#121—1221no—
342#121—1221no—
343C4×D4—1224no—
344C4×D4—1224no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—611no—
352C2×C4⋊C4—612no—
353C2×C4⋊C4—612no—
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1221no—
356C2×C4⋊C4—1221no—
357C2×C4⋊C4—1221no—
358C2×C4⋊C4—1221no—
359C2×C4⋊C4—1221no—
360C2×C4⋊C4—1221no—
361C2×C4⋊C4—1224no—
362C2×C4⋊C4—2444no—
363C2×C4⋊C4C22⋊D6111yescharacteristic
364C2×C4⋊C4C22×D6112yes—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—1221no—
367C2×C22⋊C4—1221no—
368C2×C22⋊C4—1221no—
369C2×C22⋊C4—1221no—
370C2×C42—1221no—
371#107—1224no—
372#106—24no—
373#103—24no—
374#102—1224no—
375C22⋊C8—21no—
376C22⋊C8—612no—
377C22⋊C8—1221no—
378C22⋊C8C22×D6112yes—
379#95—612no—
380#95—1224no—
381#95—1221no—
382C24—1221no—
383C24D4×D6111yescharacteristic
384C2×Q8—21no—
385C2×Q8—42no—
386C2×Q8C2×C22⋊D6112yes—
387C2×D4—612no—
388C2×D4—1222no—
389C2×D4—1222no—
390C2×D4—1221no—
391C2×D4—2442no—
392C2×D4—2442no—
393C2×D4—2442no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—42no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—612no—
403C22×C4—612no—
404C22×C4—1224no—
405C22×C4—1221no—
406C22×C4—1224no—
407C22×C4—1222no—
408C22×C4—1221no—
409C22×C4—1221no—
410C22×C4—1221no—
411C22×C4—1221no—
412C22×C4—1222no—
413C22×C4—1222no—
414C22×C4—4882no—
415C22×C4—2442no—
416C22×C4—2442no—
417C22×C4—2442no—
418C22×C4D4×D6111yescharacteristic
419C22×C4D4×D6111yescharacteristic
420C22×C4D4×D6111yescharacteristic
421C22×C4C2×C22⋊D6111yescharacteristic
422C22×C4C2×C22⋊D6111yescharacteristic
423C22×C4C23×D6111yescharacteristic
424C2×C8—22no—
425C2×C8—42no—
426C2×C8—1222no—
427C2×C8—2442no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—41no—
434C4⋊C4—41no—
435C4⋊C4—612no—
436C4⋊C4—1224no—
437C4⋊C4—1224no—
438C4⋊C4—1224no—
439C4⋊C4—1222no—
440C4⋊C4—1222no—
441C4⋊C4—1222no—
442C4⋊C4—1222no—
443C4⋊C4—1221no—
444C4⋊C4—2448no—
445C4⋊C4C2×C22⋊D6112yes—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—1224no—
449C22⋊C4—1224no—
450C22⋊C4—1224no—
451C22⋊C4—1222no—
452C22⋊C4—1222no—
453C42—1224no—
454C23—22no—
455C23—22no—
456C23—1222no—
457C23—2442no—
458C23—2442no—
459C23—2442no—
460C23#1451974511yescharacteristic
461C23#1451974511yescharacteristic
462C23#1451979812yes—
463C23#1451980412yes—
464C23C2×D4×D6111yescharacteristic
465Q8—42no—
466Q8—81no—
467D4—4881no—
468D4—2442no—
469D4—2442no—
470D4—2442no—
471D4—2444no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—82no—
486C2×C4—82no—
487C2×C4—1224no—
488C2×C4—1222no—
489C2×C4—1222no—
490C2×C4—1222no—
491C2×C4—1222no—
492C2×C4—1222no—
493C2×C4—4884no—
494C2×C4—4881no—
495C2×C4—2442no—
496C2×C4—2448no—
497C2×C4—2442no—
498C2×C4—2442no—
499C2×C4—2442no—
500C2×C4—2442no—
501C2×C4—2442no—
502C2×C4—2442no—
503C2×C4#1451974511yescharacteristic
504C2×C4#1451974511yescharacteristic
505C2×C4C2×D4×D6111yescharacteristic
506C2×C4C22×C22⋊D6111yescharacteristic
507C8—42no—
508C8—2442no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—24no—
514C22—24no—
515C22—4884no—
516C22—2442no—
517C22—2442no—
518C22—2442no—
519C22#1683990612yes—
520C22#1683990612yes—
521C22#1683994312yes—
522C22#1683995112yes—
523C22C2×#1451974511yescharacteristic
524C22C2×#1451979811yescharacteristic
525C22C2×#1451980411yescharacteristic
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—42no—
531C4—42no—
532C4—82no—
533C4—2444no—
534C4—2442no—
535C4—2442no—
536C4—2442no—
537C2—21no—
538C2—21no—
539C2—22no—
540C2—4882no—
541C2#2144481514yesdirect product factor
542C2C2×#1683990611yescharacteristic
543C2C2×#1683994311yescharacteristic
544C2C2×#1683995111yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#483C2
socleC23×C61#120
prime radicalC2×#14519751C22
hypercenterC2×#483D61
hypocenterC61C2×#1609
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
3. C2×#16839693C2semidirect
4. #21444815C2direct (N × H)
5. C2×#16839499C2semidirect
7. C2×#16839487C2semidirect
8. C2×C61×#483C2semidirect
28. #16839693C22semidirect
31. #16839499C22semidirect
33. #16839487C22semidirect
37. C61×#483C22semidirect
266. C2×#483D61semidirect
276. C2×C61#1609semidirect
297. #483C2×D61semidirect
313. C61C2×#1609semidirect
541. C2#21444815direct (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×#168400752
C2×#168396932
#214448152
C2×#168394992
C2×#168394972
C2×#168394872
C2×C61×#4832
C2×#160961