Finite Group Databasebeta

← C2×#21444857 #29652237

Subgroups — C2×#21444857 #29652237

Order 15616.

1264 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840339C211yesmaximal, characteristic
2C2×#16840081C211yesmaximal, characteristic, complemented
3C2×#16840078C211yesmaximal, characteristic, complemented
4C2×#16839702C211yesmaximal, characteristic, complemented
5#21444857C218yesmaximal, direct product factor
6C2×#16839495C211yesmaximal, characteristic, complemented
7C2×#16839487C211yesmaximal, characteristic, complemented
8C2×C61×#327C211yesmaximal, characteristic, complemented
9C22×#11758224—21no—
10#16840339—22no—
11#16840339—22no—
12#16840339—22no—
13#16840339C2214yes—
14C2×#14519755—21no—
15C2×#14519754—21no—
16C2×#14519751C2211yescharacteristic
17C2×#14519750—21no—
18C2×#14519749—21no—
19C2×#14519749—21no—
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22#16840081—22no—
23#16840081C2214yescomplemented
24#16840078—22no—
25#16840078C2214yescomplemented
26C2×#14519709—21no—
27C2×#14519708—21no—
28C2×#14519699—21no—
29C2×#14519698—21no—
30C2×C22⋊#92418C2211yescharacteristic
31#16839702—22no—
32#16839702C2214yescomplemented
33C2×#14519684—21no—
34C2×#14519684—21no—
35#16839495C2214yescomplemented
36#16839487C2214yescomplemented
37C2×#121×C61C2211yescharacteristic
38C2×C22⋊C8×C61C2211yescharacteristic
39C2×#95×C61C2211yescharacteristic
40C61×#327C2214yescomplemented
41C2×#11758224—24no—
42C2×#11758224—24no—
43C2×#11758224—44no—
44C2×#11758224—44no—
45C22×Dic122—21no—
46C22×D244D411yescharacteristic
47C22×C22⋊D61—21no—
48C22×C22⋊D61—21no—
49C22×C22⋊D61—21no—
50C23×Dic61—21no—
51C23×Dic61—21no—
52C23×Dic61D411yescharacteristic
53C23×Dic61D411yescharacteristic
54C22×C4×D61—21no—
55C22×#92418—21no—
56#14519755—24no—
57#14519755—24no—
58#14519754—24no—
59#14519754—24no—
60#14519751—21no—
61#14519751—21no—
62#14519751D412yes—
63#14519751C2312yes—
64#14519750—24no—
65#14519750—24no—
66#14519749—24no—
67#14519749—24no—
68#14519749—24no—
69#14519749—24no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61D411yescharacteristic
76C2×C4⋊Dic61C2312yes—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196D412yes—
83C2×#11758196C2312yes—
84C2×C22⋊Dic61—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87#14519709—24no—
88#14519708—24no—
89#14519699—24no—
90#14519698—24no—
91C22⋊#92418—21no—
92C22⋊#92418C2312yes—
93#14519684—24no—
94#14519684—24no—
95C22×D4×C61—21no—
96C22×D4×C61D411yescharacteristic
97C23×C4×C61—21no—
98C23×C4×C61C2311yescharacteristic
99C22×C8×C61—21no—
100#121×C61—21no—
101#121×C61—21no—
102#121×C61D412yes—
103#121×C61C2312yes—
104C2×C4⋊C4×C61D411yescharacteristic
105C2×C22⋊C4×C61—21no—
106C22⋊C8×C61—21no—
107C22⋊C8×C61C2312yes—
108#95×C61—21no—
109#95×C61C2312yes—
110C24×C61—21no—
111C24×C61C2×D411yescharacteristic
112C23×D61—21no—
113C2×D4×C61—22no—
114C2×D4×C61—22no—
115C2×D4×C61—21no—
116C2×D4×C61—42no—
117C2×D4×C61—42no—
118C2×D4×C61—42no—
119C2×D4×C61C2×D412yes—
120C22×C4×C61—21no—
121C22×C4×C61—22no—
122C22×C4×C61—42no—
123C22×C4×C61—42no—
124C22×C4×C61—42no—
125C22×C4×C61—42no—
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2411yescharacteristic
132C2×C22⋊D61—24no—
133C2×C22⋊D61—22no—
134C2×C22⋊D61—22no—
135C2×C22⋊D61—24no—
136C2×C22⋊D61—44no—
137C2×C22⋊D61—42no—
138C2×C22⋊D61—42no—
139C2×C22⋊D61—82no—
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—22no—
143C22×Dic61—24no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—22no—
148C22×Dic61—44no—
149C22×Dic61—42no—
150C22×Dic61—44no—
151C22×Dic61—41no—
152C22×Dic61—41no—
153C22×Dic61SD1614yes—
154C22×Dic61C2×D412yes—
155C22×Dic61C2×D412yes—
156#11758224—48no—
157#11758224—416no—
158#11758224—48no—
159C2×D244—21no—
160C2×D244—42no—
161C2×D244C2×D412yes—
162C2×C4×D61—24no—
163C2×C4×D61—44no—
164C2×Dic122—24no—
165C2×Dic122—44no—
166C2×C8×C61—22no—
167C2×C8×C61—42no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61C2×D412yes—
170C22⋊C4×C61—22no—
171C22⋊C4×C61—22no—
172C22⋊Dic61—24no—
173#11758198—24no—
174#11758198—22no—
175#11758198—22no—
176C4⋊Dic61—21no—
177C4⋊Dic61—22no—
178C4⋊Dic61—22no—
179C4⋊Dic61—41no—
180C4⋊Dic61—41no—
181C4⋊Dic61C2×D412yes—
182#11758196—24no—
183#11758196—22no—
184#11758196—22no—
185#11758196—22no—
186#11758196—22no—
187C2×#92418—22no—
188C2×#92418—42no—
189C23×C61—22no—
190C23×C61—22no—
191C23×C61—22no—
192C23×C61—42no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61#12011yescharacteristic
196C23×C61#12011yescharacteristic
197C23×C61C2×SD1612yes—
198C23×C61AGL(1,ℤ/8)12yes—
199C23×C61C22×D411yescharacteristic
200C22×D61—22no—
201C22×D61—42no—
202C22×D61—42no—
203C22×D61—42no—
204D4×C61—42no—
205D4×C61—42no—
206D4×C61—42no—
207D4×C61—44no—
208D4×C61—81no—
209C2×C4×C61—22no—
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—42no—
220C2×C4×C61—84no—
221C2×C4×C61#12011yescharacteristic
222C2×C4×C61#12011yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C22×D411yescharacteristic
225C22⋊D61—48no—
226C22⋊D61—42no—
227C22⋊D61—42no—
228C22⋊D61—44no—
229C22⋊D61—84no—
230C2×Dic61—22no—
231C2×Dic61—22no—
232C2×Dic61—24no—
233C2×Dic61—24no—
234C2×Dic61—22no—
235C2×Dic61—22no—
236C2×Dic61—48no—
237C2×Dic61—42no—
238C2×Dic61—42no—
239C2×Dic61—42no—
240C2×Dic61—44no—
241C2×Dic61—42no—
242C2×Dic61—81no—
243C2×Dic61—82no—
244C2×Dic61—82no—
245C2×Dic61C2×SD1614yes—
246D244—42no—
247D244—81no—
248C4×D61—48no—
249Dic122—48no—
250C8×C61—42no—
251#92418—42no—
252C2×#1616—611nomaximal, Sylow
253C22×C61—24no—
254C22×C61—24no—
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—42no—
260C22×C61—42no—
261C22×C61—42no—
262C22×C61—84no—
263C22×C61#45012yes—
264C22×C61#45012yes—
265C22×C61#45412yes—
266C22×C61#45812yes—
267C22×C61C2×#12011yescharacteristic
268C22×C61C22×SD1611yescharacteristic
269C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
270C2×D61—42no—
271C2×D61—42no—
272C2×D61—42no—
273C2×D61—84no—
274C4×C61—21no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—42no—
279C4×C61—82no—
280Dic61—24no—
281Dic61—42no—
282Dic61—42no—
283Dic61—82no—
284C2×#537—611no—
285C2×#481—611no—
286C2×#481—611no—
287C2×#400—611no—
288#1616—618no—
289C2×#327—611no—
290C2×#327D6111yescharacteristic, complemented
291C2×#324—611no—
292C2×C61—21no—
293C2×C61—21no—
294C2×C61—22no—
295C2×C61—82no—
296C2×C61#161614yescomplemented
297C2×C61C2×#45011yescharacteristic
298C2×C61C2×#45411yescharacteristic
299C2×C61C2×#45811yescharacteristic
300D61—82no—
301C22×#41—1221no—
302#537—614no—
303#537—1222no—
304#537—1222no—
305#537—1222no—
306C2×C22⋊Q8—1221no—
307C2×C22⋊Q8—1221no—
308C2×#121—611no—
309C2×#121—1221no—
310C2×#121—1221no—
311C2×#121—1221no—
312C2×#121C2×D6111yescharacteristic
313C22×C4⋊C4—611no—
314C22×C4⋊C4—611no—
315#481—614no—
316#481—614no—
317#481—1222no—
318#481—1222no—
319C2×#106—1221no—
320C2×#106—1221no—
321C2×#102—1221no—
322C2×#102—1221no—
323C2×C22⋊C8—611no—
324C2×C22⋊C8C2×D6111yescharacteristic
325#400—614no—
326#400—1222no—
327C2×#95—1221no—
328C2×#95—1221no—
329C2×#95C2×D6111yescharacteristic
330#327—614no—
331#327C2×D6114yescomplemented
332#324—614no—
333C61C2×#161611yescharacteristic, complemented, Sylow
334C2×#41—1224no—
335C2×#41—1224no—
336C2×#41—2444no—
337C2×#41—2444no—
338C22×Q8—1221no—
339C22×D4—21no—
340C22×D4—611no—
341C22×D4—1221no—
342C22×D4—1221no—
343C22×D4—1221no—
344C22×D4D24411yescharacteristic
345C23×C4—21no—
346C23×C4—611no—
347C23×C4—611no—
348C23×C4—1221no—
349C23×C4—1221no—
350C23×C4—1221no—
351C23×C4C22×D6111yescharacteristic
352C22×C8—21no—
353C22×C8—1221no—
354C22⋊Q8—1224no—
355C22⋊Q8—1224no—
356C22⋊Q8—1224no—
357C22⋊Q8—1224no—
358#121—21no—
359#121—21no—
360#121—612no—
361#121—612no—
362#121—1224no—
363#121—1224no—
364#121—1224no—
365#121—1224no—
366#121—1224no—
367#121—1224no—
368#121—1221no—
369#121—1221no—
370#121D24412yes—
371#121C22×D6112yes—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—612no—
374C2×C4⋊C4—612no—
375C2×C4⋊C4—612no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4—1221no—
378C2×C4⋊C4—1221no—
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⋊C4D24411yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1221no—
390C2×C22⋊C4—1221no—
391#106—1224no—
392#106—1224no—
393#102—1224no—
394#102—1224no—
395C22⋊C8—21no—
396C22⋊C8—612no—
397C22⋊C8—1221no—
398C22⋊C8C22×D6112yes—
399#95—21no—
400#95—1224no—
401#95—1224no—
402#95C22×D6112yes—
403C24—21no—
404C24—1221no—
405C24D4×D6111yescharacteristic
406#41—2448no—
407#41—2448no—
408#41—24416no—
409C2×Q8—1224no—
410C2×Q8—2444no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—21no—
414C2×D4—42no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—612no—
418C2×D4—1224no—
419C2×D4—1224no—
420C2×D4—1222no—
421C2×D4—1222no—
422C2×D4—1221no—
423C2×D4—4882no—
424C2×D4—2442no—
425C2×D4—2444no—
426C2×D4—2442no—
427C2×D4—2442no—
428C2×D4C2×D24412yes—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—612no—
436C22×C4—614no—
437C22×C4—612no—
438C22×C4—1224no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4—1222no—
442C22×C4—1221no—
443C22×C4—1224no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1222no—
447C22×C4—2444no—
448C22×C4—2444no—
449C22×C4—2444no—
450C22×C4—2441no—
451C22×C4—2441no—
452C22×C4—2442no—
453C22×C4C2×D24411yescharacteristic
454C22×C4C2×D24411yescharacteristic
455C22×C4D4×D6111yescharacteristic
456C22×C4D4×D6111yescharacteristic
457C22×C4D4×D6111yescharacteristic
458C22×C4C23×D6111yescharacteristic
459C2×C8—22no—
460C2×C8—42no—
461C2×C8—1222no—
462C2×C8—2442no—
463C4⋊C4—21no—
464C4⋊C4—612no—
465C4⋊C4—1224no—
466C4⋊C4—1222no—
467C4⋊C4—1222no—
468C4⋊C4—1222no—
469C4⋊C4—1222no—
470C4⋊C4—1221no—
471C4⋊C4—1222no—
472C4⋊C4—1222no—
473C4⋊C4—2441no—
474C4⋊C4—2441no—
475C4⋊C4C2×D24412yes—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—1224no—
479C22⋊C4—1224no—
480C22⋊C4—1222no—
481C22⋊C4—1222no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—1222no—
489C23—2442no—
490C23—2442no—
491C23—2442no—
492C23#1451974711yescharacteristic
493C23#1451974711yescharacteristic
494C23SD16×D6112yes—
495C23#1451980112yes—
496C23C2×D4×D6111yescharacteristic
497Q8—2448no—
498D4—42no—
499D4—42no—
500D4—42no—
501D4—44no—
502D4—81no—
503D4—4881no—
504D4—4884no—
505D4—2442no—
506D4—2448no—
507D4—2442no—
508D4—2442no—
509D4—2444no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—84no—
522C2×C4—614no—
523C2×C4—1222no—
524C2×C4—1222no—
525C2×C4—1224no—
526C2×C4—1224no—
527C2×C4—1222no—
528C2×C4—1222no—
529C2×C4—4882no—
530C2×C4—4882no—
531C2×C4—4881no—
532C2×C4—2448no—
533C2×C4—2448no—
534C2×C4—2444no—
535C2×C4—2442no—
536C2×C4—2442no—
537C2×C4—2442no—
538C2×C4—2442no—
539C2×C4#1451974711yescharacteristic
540C2×C4#1451974711yescharacteristic
541C2×C4C2×D4×D6111yescharacteristic
542C2×C4C22×D24411yescharacteristic
543C8—42no—
544C8—2442no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—24no—
550C22—24no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—84no—
555C22—4884no—
556C22—2442no—
557C22—2442no—
558C22—2442no—
559C22#1683991412yes—
560C22#1683991412yes—
561C22#1683993612yes—
562C22#1683995312yes—
563C22C2×#1451974711yescharacteristic
564C22C2×SD16×D6111yescharacteristic
565C22C2×#1451980111yescharacteristic
566C4—21no—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—42no—
571C4—82no—
572C4—1224no—
573C4—4882no—
574C4—2442no—
575C4—2442no—
576C2—21no—
577C2—21no—
578C2—22no—
579C2—82no—
580C2—4882no—
581C2#2144485714yesdirect product factor
582C2C2×#1683991411yescharacteristic
583C2C2×#1683993611yescharacteristic
584C2C2×#1683995311yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#327C2
socleC23×C61#120
prime radicalC2×#16840339C2
hypercenterC2×#327D61
hypocenterC61C2×#1616
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#16840081C2semidirect
3. C2×#16840078C2semidirect
4. C2×#16839702C2semidirect
5. #21444857C2direct (N × H)
6. C2×#16839495C2semidirect
7. C2×#16839487C2semidirect
8. C2×C61×#327C2semidirect
23. #16840081C22semidirect
25. #16840078C22semidirect
32. #16839702C22semidirect
35. #16839495C22semidirect
36. #16839487C22semidirect
40. C61×#327C22semidirect
290. C2×#327D61semidirect
296. C2×C61#1616semidirect
331. #327C2×D61semidirect
333. C61C2×#1616semidirect
581. C2#21444857direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403392
C2×#168400812
C2×#168400782
C2×#168397022
#214448572
C2×#168394952
C2×#168394872
C2×C61×#3272
C2×#161661