Finite Group Databasebeta

← C2×#21445000 #29655671

Subgroups — C2×#21445000 #29655671

Order 15616.

1690 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D244C211yesmaximal, characteristic
2C2×#16840109C211yesmaximal, characteristic, complemented
3C2×#16840043C211yesmaximal, characteristic, complemented
4C2×#16839967C211yesmaximal, characteristic, complemented
5#21445000C218yesmaximal, direct product factor
6C2×#16839505C211yesmaximal, characteristic, complemented
7C2×#16839491C211yesmaximal, characteristic, complemented
8C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
9C23×D244—21no—
10C22×D4×D61—21no—
11C22×#11758200—21no—
12D4×D244—22no—
13D4×D244—22no—
14D4×D244—22no—
15D4×D244C2214yes—
16C2×#14519777C2211yescharacteristic, complemented
17C2×#14519774C2211yescharacteristic
18C2×#14519752—21no—
19C2×#14519751—21no—
20C2×#14519747—22no—
21C2×C4×D244C2211yescharacteristic
22#16840109—22no—
23#16840109C2214yescomplemented
24#16840043—22no—
25#16840043C2214yescomplemented
26#16839967—22no—
27#16839967C2214yescomplemented
28C2×#14519711—21no—
29C2×C4⋊#92418C2211yescharacteristic, complemented
30C2×#14519700—21no—
31C2×#14519699—21no—
32C2×#14519699—22no—
33#16839505C2214yescomplemented
34#16839491C2214yescomplemented
35C2×C4×D4×C61C2211yescharacteristic
36C2×C4⋊C8×C61C2211yescharacteristic, complemented
37C2×C4×C8×C61C2211yescharacteristic, complemented
38C61×D4⋊C8C2214yescomplemented
39C24×D61—22no—
40C22×Dic122—21no—
41C22×D244—22no—
42C22×D244—24no—
43C22×D244—21no—
44C22×D244—21no—
45C22×D244—24no—
46C22×D244—44no—
47C22×D244—44no—
48C22×D244D411yescharacteristic
49C22×D244D412yes—
50C22×C22⋊D61—22no—
51C2×D4×D61—24no—
52C2×D4×D61—24no—
53C2×D4×D61—44no—
54C2×D4×D61—44no—
55C22×C4×D61—21no—
56C2×#11758200—24no—
57C2×#11758200—44no—
58C22×#92418—21no—
59#14519777—21no—
60#14519777—21no—
61#14519777—21no—
62#14519777C2312yescomplemented
63#14519774—21no—
64#14519774—21no—
65#14519774D412yes—
66#14519774C2312yes—
67#14519752—24no—
68#14519752—24no—
69#14519751—24no—
70#14519751—24no—
71#14519747—28no—
72#14519747—28no—
73C4×D244—21no—
74C4×D244—21no—
75C4×D244D412yes—
76C4×D244C2312yes—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61D411yescharacteristic
80C2×#11758198—22no—
81C2×#11758198—21no—
82#14519711—24no—
83C4⋊#92418—21no—
84C4⋊#92418C2312yescomplemented
85#14519700—24no—
86#14519699—24no—
87#14519699—28no—
88C22×D4×C61D411yescharacteristic
89C23×C4×C61—21no—
90C22×C8×C61—21no—
91C22×C8×C61—21no—
92C4×D4×C61—21no—
93C4×D4×C61—21no—
94C4×D4×C61D412yes—
95C4×D4×C61C2312yes—
96C2×C4⋊C4×C61D411yescharacteristic
97C2×C22⋊C4×C61—21no—
98C2×C42×C61C2311yescharacteristic
99C4⋊C8×C61—21no—
100C4⋊C8×C61C2312yescomplemented
101C4×C8×C61—21no—
102C4×C8×C61C2312yescomplemented
103C24×C61—21no—
104C23×D61—21no—
105C23×D61—22no—
106C23×D61—28no—
107C23×D61—48no—
108C23×D61—48no—
109C23×D61—84no—
110C2×D4×C61—21no—
111C2×D4×C61—22no—
112C2×D4×C61D814yes—
113C2×D4×C61C2×D412yes—
114C22×C4×C61—21no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—42no—
118C22×C4×C61—42no—
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C2×C22⋊D61—28no—
123C2×C22⋊D61—48no—
124C22×Dic61—21no—
125C22×Dic61—41no—
126D4×D61—48no—
127D4×D61—416no—
128D4×D61—48no—
129C2×D244—21no—
130C2×D244—22no—
131C2×D244—28no—
132C2×D244—22no—
133C2×D244—22no—
134C2×D244—22no—
135C2×D244—22no—
136C2×D244—22no—
137C2×D244—48no—
138C2×D244—416no—
139C2×D244—48no—
140C2×D244—42no—
141C2×D244—42no—
142C2×D244—42no—
143C2×D244—42no—
144C2×D244—48no—
145C2×D244—44no—
146C2×D244SD1614yescomplemented
147C2×D244C2×D412yes—
148C2×D244C2×D414yes—
149C2×C4×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—42no—
152C2×C4×D61—42no—
153C2×Dic122—22no—
154C2×Dic122—42no—
155C2×Dic122—42no—
156C2×Dic122—41no—
157C2×C8×C61—22no—
158C2×C8×C61—22no—
159C2×C8×C61—42no—
160C2×C8×C61—42no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61C2×D412yes—
163C22⋊C4×C61—22no—
164C22⋊C4×C61—22no—
165C42×C61C2×D411yescharacteristic
166C42×C61C2×D411yescharacteristic
167C42×C61C2×D411yescharacteristic
168C42×C61C2411yescharacteristic
169#11758200—48no—
170#11758198—28no—
171#11758198—22no—
172#11758198—22no—
173C4⋊Dic61—21no—
174C4⋊Dic61—22no—
175C4⋊Dic61—22no—
176C4⋊Dic61—41no—
177C4⋊Dic61—41no—
178C4⋊Dic61C2×D412yes—
179C2×#92418—22no—
180C2×#92418—42no—
181C23×C61—22no—
182C23×C61—24no—
183C23×C61—42no—
184C23×C61—42no—
185C23×C61#12011yescharacteristic
186C22×D61—22no—
187C22×D61—24no—
188C22×D61—24no—
189C22×D61—416no—
190C22×D61—42no—
191C22×D61—42no—
192C22×D61—416no—
193C22×D61—44no—
194C22×D61—44no—
195C22×D61—44no—
196C22×D61—88no—
197C22×D61—832no—
198D4×C61—22no—
199D4×C61—24no—
200D4×C61C2×D814yes—
201C2×C4×C61—22no—
202C2×C4×C61—22no—
203C2×C4×C61—42no—
204C2×C4×C61—42no—
205C2×C4×C61—42no—
206C2×C4×C61—44no—
207C2×C4×C61#12011yescharacteristic
208C2×C4×C61#12011yescharacteristic
209C2×C4×C61#12011yescharacteristic
210C2×C4×C61C2×D812yes—
211C2×C4×C61C2×SD1612yes—
212C2×C4×C61AGL(1,ℤ/8)12yes—
213C2×C4×C61AGL(1,ℤ/8)12yes—
214C2×C4×C61C22×D411yescharacteristic
215C2×C4×C61C22×D411yescharacteristic
216C2×C4×C61C22×D411yescharacteristic
217C22⋊D61—416no—
218C2×Dic61—22no—
219C2×Dic61—42no—
220C2×Dic61—42no—
221C2×Dic61—82no—
222D244—22no—
223D244—24no—
224D244—44no—
225D244—416no—
226D244—42no—
227D244—42no—
228D244—42no—
229D244—42no—
230D244—44no—
231D244—44no—
232D244—82no—
233D244C2×SD1614yescomplemented
234C4×D61—42no—
235C4×D61—42no—
236C4×D61—44no—
237Dic122—42no—
238Dic122—42no—
239Dic122—82no—
240C8×C61—42no—
241C8×C61—42no—
242#92418—42no—
243C2×#1639—611nomaximal, Sylow
244C22×C61—24no—
245C22×C61—48no—
246C22×C61—42no—
247C22×C61—42no—
248C22×C61#44712yes—
249C22×C61#45012yes—
250C22×C61#45512yes—
251C22×C61C2×#12011yescharacteristic
252C2×D61—24no—
253C2×D61—48no—
254C2×D61—42no—
255C2×D61—42no—
256C2×D61—44no—
257C2×D61—44no—
258C2×D61—44no—
259C2×D61—832no—
260C2×D61—88no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—42no—
264C4×C61#44712yes—
265C4×C61#45012yes—
266C4×C61C22×D811yescharacteristic
267C4×C61C22×SD1611yescharacteristic
268C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
269C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
270Dic61—42no—
271Dic61—82no—
272C2×D42—611no—
273C2×#486—611no—
274C2×#474—611no—
275C2×#461—611no—
276#1639—618no—
277C2×#331—611no—
278C2×D4⋊C8—611no—
279C2×D4⋊C8D6111yescharacteristic, complemented
280C2×C61—44no—
281C2×C61#163914yescomplemented
282C2×C61C2×#44711yescharacteristic
283C2×C61C2×#45011yescharacteristic
284C2×C61C2×#45511yescharacteristic
285D61—44no—
286D61—84no—
287C23×D4—1221no—
288C23×D4—1221no—
289C22×SD16—1221no—
290D42—614no—
291D42—1222no—
292D42—1222no—
293D42—1222no—
294C2×C4⋊Q8—611no—
295C2×#127—611no—
296C2×#121—1221no—
297C2×#121—1221no—
298C2×#120—1222no—
299C2×C4×D4—611no—
300C2×C4×D4C2×D6111yescharacteristic
301#486—614no—
302#486—1222no—
303#474—614no—
304#474—1222no—
305#461—614no—
306#461—1222no—
307C2×#107—1221no—
308C2×C4⋊C8—611no—
309C2×C4⋊C8C2×D6111yescharacteristic, complemented
310C2×#103—1221no—
311C2×#102—1222no—
312C2×#102—1221no—
313C2×C4×C8C2×D6111yescharacteristic, complemented
314#331—614no—
315D4⋊C8—614no—
316D4⋊C8C2×D6114yescomplemented
317C61C2×#163911yescharacteristic, complemented, Sylow
318C25—1222no—
319C22×Q8—1221no—
320C22×D4—611no—
321C22×D4—612no—
322C22×D4—1224no—
323C22×D4—1222no—
324C22×D4—1224no—
325C22×D4—1224no—
326C22×D4—1222no—
327C22×D4—1224no—
328C22×D4—1221no—
329C22×D4—1221no—
330C22×D4—2444no—
331C22×D4—2444no—
332C22×D4—2444no—
333C22×D4—2444no—
334C22×D4D24411yescharacteristic
335C23×C4—21no—
336C23×C4—1221no—
337C2×SD16—1224no—
338C2×SD16—2444no—
339C22×C8—21no—
340C22×C8—21no—
341C22×C8—1221no—
342C4⋊Q8—612no—
343C4⋊Q8—1221no—
344C4⋊Q8—1221no—
345C4⋊Q8—1221no—
346#127—612no—
347#127—612no—
348#127—1221no—
349#127—1221no—
350#121—1224no—
351#121—1224no—
352#121—1224no—
353#121—1224no—
354#120—1228no—
355#120—1228no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—612no—
359C4×D4—612no—
360C4×D4—1221no—
361C4×D4—1221no—
362C4×D4D24412yes—
363C4×D4C22×D6112yes—
364C2×C4⋊C4—611no—
365C2×C4⋊C4—1221no—
366C2×C4⋊C4—1221no—
367C2×C4⋊C4D24411yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—1222no—
370C2×C22⋊C4—1221no—
371C2×C42C22×D6111yescharacteristic
372#107—1224no—
373C4⋊C8—21no—
374C4⋊C8—612no—
375C4⋊C8—1221no—
376C4⋊C8C22×D6112yescomplemented
377#103—1224no—
378#102—1224no—
379#102—1228no—
380C4×C8—21no—
381C4×C8C22×D6112yescomplemented
382C24—21no—
383C24—1228no—
384C24—1221no—
385C24—1222no—
386C24—4884no—
387C24—2448no—
388C24—2448no—
389C2×Q8—1222no—
390C2×Q8—2442no—
391C2×Q8—2442no—
392C2×Q8—2441no—
393C2×D4—21no—
394C2×D4—22no—
395C2×D4—612no—
396C2×D4—614no—
397C2×D4—614no—
398C2×D4—1228no—
399C2×D4—1228no—
400C2×D4—1222no—
401C2×D4—1222no—
402C2×D4—1221no—
403C2×D4—1222no—
404C2×D4—1222no—
405C2×D4—1222no—
406C2×D4—1222no—
407C2×D4—2444no—
408C2×D4—2448no—
409C2×D4—2448no—
410C2×D4—24416no—
411C2×D4—2448no—
412C2×D4—2448no—
413C2×D4—24416no—
414C2×D4—2448no—
415C2×D4—2448no—
416C2×D4—2442no—
417C2×D4—2442no—
418C2×D4—2442no—
419C2×D4—2442no—
420C2×D4D48814yes—
421C2×D4C2×D24412yes—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—1221no—
428C22×C4—1222no—
429C22×C4—1222no—
430C22×C4—2441no—
431C22×C4—2442no—
432C22×C4—2442no—
433C22×C4C2×D24411yescharacteristic
434C22×C4D4×D6111yescharacteristic
435C22×C4D4×D6111yescharacteristic
436SD16—2448no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—42no—
440C2×C8—42no—
441C2×C8—1222no—
442C2×C8—2442no—
443C4⋊C4—21no—
444C4⋊C4—612no—
445C4⋊C4—1221no—
446C4⋊C4—1222no—
447C4⋊C4—1222no—
448C4⋊C4—2441no—
449C4⋊C4—2441no—
450C4⋊C4C2×D24412yes—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—1228no—
454C22⋊C4—1222no—
455C22⋊C4—1222no—
456C42C2×D24411yescharacteristic
457C42D4×D6111yescharacteristic
458C42D4×D6111yescharacteristic
459C42C23×D6111yescharacteristic
460C23—22no—
461C23—24no—
462C23—42no—
463C23—42no—
464C23—1222no—
465C23—1224no—
466C23—1224no—
467C23—48832no—
468C23—4888no—
469C23—24416no—
470C23—24416no—
471C23—2444no—
472C23—2444no—
473C23—2444no—
474C23—2442no—
475C23—2442no—
476C23#1451974711yescharacteristic
477Q8—4882no—
478Q8—2442no—
479Q8—2442no—
480D4—22no—
481D4—24no—
482D4—614no—
483D4—1222no—
484D4—1224no—
485D4—4882no—
486D4—2444no—
487D4—24416no—
488D4—24416no—
489D4—2442no—
490D4—2442no—
491D4—2442no—
492D4—2442no—
493D4—2444no—
494D4—2444no—
495D4C2×D48814yes—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—44no—
502C2×C4—1222no—
503C2×C4—4882no—
504C2×C4—2442no—
505C2×C4—2442no—
506C2×C4—2442no—
507C2×C4—2442no—
508C2×C4—2444no—
509C2×C4#1451974711yescharacteristic
510C2×C4#1451974711yescharacteristic
511C2×C4#1451974711yescharacteristic
512C2×C4C2×D48812yes—
513C2×C4SD16×D6112yes—
514C2×C4#1451980112yes—
515C2×C4#1451980512yes—
516C2×C4C2×D4×D6111yescharacteristic
517C2×C4C2×D4×D6111yescharacteristic
518C2×C4C22×D24411yescharacteristic
519C8—42no—
520C8—42no—
521C8—2442no—
522C22—24no—
523C22—42no—
524C22—48no—
525C22—42no—
526C22—1224no—
527C22—48832no—
528C22—4888no—
529C22—2444no—
530C22—2444no—
531C22—2444no—
532C22—2442no—
533C22—2448no—
534C22—2442no—
535C22#1683989812yes—
536C22#1683991412yes—
537C22#1683994112yes—
538C22C2×#1451974711yescharacteristic
539C4—21no—
540C4—21no—
541C4—42no—
542C4—4882no—
543C4—2442no—
544C4#1683989812yes—
545C4#1683991412yes—
546C4C22×D48811yescharacteristic
547C4C2×SD16×D6111yescharacteristic
548C4C2×#1451980111yescharacteristic
549C4C2×#1451980511yescharacteristic
550C2—44no—
551C2—4884no—
552C2—2444no—
553C2#2144500014yesdirect product factor
554C2C2×#1683989811yescharacteristic
555C2C2×#1683991411yescharacteristic
556C2C2×#1683994111yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61#120
prime radicalC2×D4×D244C2
hypercenterC2×D4⋊C8D61
hypocenterC61C2×#1639
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#16840109C2semidirect
3. C2×#16840043C2semidirect
4. C2×#16839967C2semidirect
5. #21445000C2direct (N × H)
6. C2×#16839505C2semidirect
7. C2×#16839491C2semidirect
8. C2×C61×D4⋊C8C2semidirect
16. C2×#14519777C22semidirect
23. #16840109C22semidirect
25. #16840043C22semidirect
27. #16839967C22semidirect
29. C2×C4⋊#92418C22semidirect
33. #16839505C22semidirect
34. #16839491C22semidirect
36. C2×C4⋊C8×C61C22semidirect
37. C2×C4×C8×C61C22semidirect
38. C61×D4⋊C8C22semidirect
62. #14519777C23semidirect
84. C4⋊#92418C23semidirect
100. C4⋊C8×C61C23semidirect
102. C4×C8×C61C23semidirect
146. C2×D244SD16semidirect
233. D244C2×SD16semidirect
279. C2×D4⋊C8D61semidirect
281. C2×C61#1639semidirect
309. C2×C4⋊C8C2×D61semidirect
313. C2×C4×C8C2×D61semidirect
316. D4⋊C8C2×D61semidirect
317. C61C2×#1639semidirect
376. C4⋊C8C22×D61semidirect
381. C4×C8C22×D61semidirect
553. C2#21445000direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×D2442
C2×#168401092
C2×#168400432
C2×#168399672
#214450002
C2×#168395052
C2×#168394912
C2×C61×D4⋊C82
C2×#163961