Finite Group Databasebeta

← C2×#21444849 #29652160

Subgroups — C2×#21444849 #29652160

Order 15616.

1016 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840361C211yesmaximal, characteristic
2C2×#16840080C211yesmaximal, characteristic
3C2×#16839700C211yesmaximal, characteristic, complemented
4#21444849C218yesmaximal, direct product factor
5C2×#16839499C211yesmaximal, characteristic, complemented
6C2×#16839497C211yesmaximal, characteristic
7C2×#16839487C211yesmaximal, characteristic, complemented
8C2×C61×#484C211yesmaximal, 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×#11758196C2211yescharacteristic
21#16840080—22no—
22#16840080C2214yes—
23C2×#14519708—21no—
24C2×#14519697—21no—
25C2×C22⋊#92418C2211yescharacteristic
26#16839700—22no—
27#16839700C2214yescomplemented
28C2×#14519684—21no—
29C2×#14519684—21no—
30C2×#14519684C2211yescharacteristic
31#16839499C2214yescomplemented
32#16839497C2214yes—
33#16839487C2214yescomplemented
34C2×C22⋊Q8×C61C2211yescharacteristic
35C22×C4⋊C4×C61C2211yescharacteristic
36C61×#484—22no—
37C61×#484C2214yescomplemented
38C2×#107×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×#11758196D412yes—
73C2×#11758196C2312yes—
74C2×#11758198—21no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×C4×Dic61—21no—
79#14519708—24no—
80#14519697—24no—
81C22⋊#92418—21no—
82C22⋊#92418C2312yes—
83#14519684—21no—
84#14519684—24no—
85#14519684—24no—
86#14519684C2312yes—
87C22×Q8×C61D411yescharacteristic
88C23×C4×C61—21no—
89C23×C4×C61C2311yescharacteristic
90C22×C8×C61—21no—
91C22⋊Q8×C61—21no—
92C22⋊Q8×C61—21no—
93C22⋊Q8×C61D412yes—
94C22⋊Q8×C61C2312yes—
95C2×C4⋊C4×C61—21no—
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×C61D411yescharacteristic
102C2×C4⋊C4×C61C2312yes—
103C2×C22⋊C4×C61—21no—
104#107×C61—24no—
105#103×C61—24no—
106C22⋊C8×C61—21no—
107C22⋊C8×C61C2312yes—
108C24×C61C2×D411yescharacteristic
109C23×D61—21no—
110C2×Q8×C61—21no—
111C2×Q8×C61—42no—
112C2×Q8×C61C2×D412yes—
113C22×C4×C61—21no—
114C22×C4×C61—21no—
115C22×C4×C61—22no—
116C22×C4×C61—42no—
117C22×C4×C61—44no—
118C22×C4×C61—41no—
119C22×C4×C61—41no—
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2411yescharacteristic
126C2×C22⋊D61—22no—
127C2×C22⋊D61—22no—
128C2×C22⋊D61—42no—
129C2×C22⋊D61—42no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—22no—
135C22×Dic61—22no—
136C22×Dic61—21no—
137C22×Dic61—22no—
138C22×Dic61—42no—
139C22×Dic61—42no—
140C22×Dic61—42no—
141C22×Dic61—42no—
142C22×Dic61C2×D412yes—
143C22×Dic61C2×D412yes—
144C2×D244—21no—
145C2×D244—42no—
146C2×D244C2×D412yes—
147C2×C4×D61—24no—
148C2×C4×D61—82no—
149C2×C8×C61—22no—
150C2×C8×C61—42no—
151C4⋊C4×C61—22no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—22no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—41no—
157C4⋊C4×C61—41no—
158C4⋊C4×C61C2×D412yes—
159C22⋊C4×C61—22no—
160C22⋊C4×C61—22no—
161#11758198—24no—
162#11758198—24no—
163#11758198—24no—
164#11758198—22no—
165#11758198—22no—
166C4⋊Dic61—24no—
167C4⋊Dic61—24no—
168C4⋊Dic61—21no—
169C4⋊Dic61C2×D412yes—
170#11758196—24no—
171#11758196—22no—
172#11758196—22no—
173#11758196—22no—
174#11758196—22no—
175C4×Dic61—24no—
176C2×#92418—22no—
177C2×#92418—42no—
178C23×C61—22no—
179C23×C61—22no—
180C23×C61#12011yescharacteristic
181C23×C61#12011yescharacteristic
182C23×C61#13512yes—
183C23×C61#13712yes—
184C23×C61C22×D411yescharacteristic
185C22×D61—22no—
186C22×D61—42no—
187C22×D61—42no—
188C22×D61—42no—
189Q8×C61—42no—
190Q8×C61—81no—
191C2×C4×C61—22no—
192C2×C4×C61—22no—
193C2×C4×C61—22no—
194C2×C4×C61—22no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—42no—
200C2×C4×C61—42no—
201C2×C4×C61—44no—
202C2×C4×C61—42no—
203C2×C4×C61—82no—
204C2×C4×C61—82no—
205C2×C4×C61#12011yescharacteristic
206C2×C4×C61#12011yescharacteristic
207C2×C4×C61C22×D411yescharacteristic
208C2×C4×C61C22×D411yescharacteristic
209C22⋊D61—42no—
210C22⋊D61—42no—
211C22⋊D61—44no—
212C2×Dic61—22no—
213C2×Dic61—22no—
214C2×Dic61—22no—
215C2×Dic61—22no—
216C2×Dic61—22no—
217C2×Dic61—42no—
218C2×Dic61—42no—
219C2×Dic61—42no—
220C2×Dic61—42no—
221C2×Dic61—42no—
222C2×Dic61—42no—
223C2×Dic61—42no—
224C2×Dic61—42no—
225C2×Dic61—81no—
226C2×Dic61—84no—
227D244—42no—
228D244—81no—
229C4×D61—84no—
230C8×C61—42no—
231#92418—42no—
232C2×#1615—611nomaximal, Sylow
233C22×C61—24no—
234C22×C61—24no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—21no—
238C22×C61—21no—
239C22×C61#45212yes—
240C22×C61#45212yes—
241C22×C61#45412yes—
242C22×C61#45812yes—
243C22×C61C2×#12011yescharacteristic
244C22×C61C2×#13511yescharacteristic
245C22×C61C2×#13711yescharacteristic
246C2×D61—42no—
247C2×D61—42no—
248C2×D61—42no—
249C2×D61—84no—
250C4×C61—21no—
251C4×C61—21no—
252C4×C61—21no—
253C4×C61—21no—
254C4×C61—42no—
255C4×C61—42no—
256C4×C61—82no—
257Dic61—42no—
258Dic61—42no—
259Dic61—42no—
260Dic61—82no—
261C2×#539—611no—
262C2×#484D6111yescharacteristic, complemented
263C2×#481—611no—
264C2×#400—611no—
265#1615—618no—
266C2×#328—611no—
267C2×#327—611no—
268C2×#324—611no—
269C2×C61—21no—
270C2×C61—21no—
271C2×C61—22no—
272C2×C61#161514yescomplemented
273C2×C61C2×#45211yescharacteristic
274C2×C61C2×#45411yescharacteristic
275C2×C61C2×#45811yescharacteristic
276D61—82no—
277#539—614no—
278#539—1222no—
279#539—1222no—
280#539—1222no—
281C2×#126—1221no—
282C2×#125—1221no—
283C2×#123—1221no—
284C2×#123—1221no—
285C2×C22⋊Q8—1221no—
286C2×C22⋊Q8C2×D6111yescharacteristic
287C2×#121—611no—
288C2×C4×D4—1221no—
289C22×C4⋊C4—611no—
290C22×C4⋊C4C2×D6111yescharacteristic
291#484—22no—
292#484C2×D6114yescomplemented
293#481—614no—
294#481—1222no—
295C2×#107—21no—
296C2×#106—1221no—
297C2×#103—21no—
298C2×#102—1221no—
299C2×C22⋊C8—611no—
300C2×C22⋊C8C2×D6111yescharacteristic
301#400—614no—
302#400—1222no—
303C2×#95—611no—
304C2×#95—1221no—
305C2×#95—1221no—
306#328—614no—
307#327—614no—
308#324—614no—
309C61C2×#161511yescharacteristic, complemented, Sylow
310C22×Q8C22⋊D6111yescharacteristic
311C22×D4—611no—
312C22×D4—1221no—
313C23×C4—21no—
314C23×C4—611no—
315C23×C4—611no—
316C23×C4—1221no—
317C23×C4—1221no—
318C23×C4C22×D6111yescharacteristic
319C22×C8—21no—
320C22×C8—1221no—
321#126—1224no—
322#126—1224no—
323#125—1224no—
324#125—1224no—
325#123—1224no—
326#123—1224no—
327#123—1224no—
328#123—1224no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—1224no—
332C22⋊Q8—1224no—
333C22⋊Q8C22⋊D6112yes—
334C22⋊Q8C22×D6112yes—
335#121—612no—
336#121—612no—
337#121—1221no—
338#121—1221no—
339C4×D4—1224no—
340C4×D4—1224no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—611no—
348C2×C4⋊C4—612no—
349C2×C4⋊C4—612no—
350C2×C4⋊C4—1221no—
351C2×C4⋊C4—1221no—
352C2×C4⋊C4—1221no—
353C2×C4⋊C4—1221no—
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1221no—
356C2×C4⋊C4—1221no—
357C2×C4⋊C4C22⋊D6111yescharacteristic
358C2×C4⋊C4C22×D6112yes—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—1221no—
361C2×C22⋊C4—1221no—
362C2×C22⋊C4—1221no—
363C2×C22⋊C4—1221no—
364C2×C42—1221no—
365#107—24no—
366#106—1224no—
367#103—24no—
368#102—1224no—
369C22⋊C8—21no—
370C22⋊C8—612no—
371C22⋊C8—1221no—
372C22⋊C8C22×D6112yes—
373#95—612no—
374#95—1224no—
375#95—1224no—
376#95—1221no—
377C24—1221no—
378C24D4×D6111yescharacteristic
379C2×Q8—21no—
380C2×Q8—42no—
381C2×Q8C2×C22⋊D6112yes—
382C2×D4—612no—
383C2×D4—1222no—
384C2×D4—1222no—
385C2×D4—1221no—
386C2×D4—2442no—
387C2×D4—2442no—
388C2×D4—2442no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—42no—
393C22×C4—44no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—612no—
397C22×C4—612no—
398C22×C4—1224no—
399C22×C4—1221no—
400C22×C4—1222no—
401C22×C4—1221no—
402C22×C4—1221no—
403C22×C4—1221no—
404C22×C4—1221no—
405C22×C4—1222no—
406C22×C4—1222no—
407C22×C4—4882no—
408C22×C4—2442no—
409C22×C4—2442no—
410C22×C4—2442no—
411C22×C4—2442no—
412C22×C4D4×D6111yescharacteristic
413C22×C4D4×D6111yescharacteristic
414C22×C4D4×D6111yescharacteristic
415C22×C4C2×C22⋊D6111yescharacteristic
416C22×C4C2×C22⋊D6111yescharacteristic
417C22×C4C23×D6111yescharacteristic
418C2×C8—22no—
419C2×C8—42no—
420C2×C8—1222no—
421C2×C8—2442no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—612no—
430C4⋊C4—1224no—
431C4⋊C4—1224no—
432C4⋊C4—1224no—
433C4⋊C4—1222no—
434C4⋊C4—1222no—
435C4⋊C4—1222no—
436C4⋊C4—1222no—
437C4⋊C4—1221no—
438C4⋊C4C2×C22⋊D6112yes—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—1224no—
442C22⋊C4—1224no—
443C22⋊C4—1224no—
444C22⋊C4—1222no—
445C22⋊C4—1222no—
446C42—1224no—
447C23—22no—
448C23—22no—
449C23—1222no—
450C23—2442no—
451C23—2442no—
452C23—2442no—
453C23#1451974511yescharacteristic
454C23#1451974511yescharacteristic
455C23#1451980012yes—
456C23#1451980912yes—
457C23C2×D4×D6111yescharacteristic
458Q8—42no—
459Q8—81no—
460D4—4881no—
461D4—2442no—
462D4—2442no—
463D4—2442no—
464D4—2444no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—82no—
478C2×C4—82no—
479C2×C4—1222no—
480C2×C4—1222no—
481C2×C4—1222no—
482C2×C4—1222no—
483C2×C4—1222no—
484C2×C4—4884no—
485C2×C4—4884no—
486C2×C4—4881no—
487C2×C4—2442no—
488C2×C4—2442no—
489C2×C4—2442no—
490C2×C4—2442no—
491C2×C4—2442no—
492C2×C4—2442no—
493C2×C4—2442no—
494C2×C4—2442no—
495C2×C4#1451974511yescharacteristic
496C2×C4#1451974511yescharacteristic
497C2×C4C2×D4×D6111yescharacteristic
498C2×C4C22×C22⋊D6111yescharacteristic
499C8—42no—
500C8—2442no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—24no—
506C22—24no—
507C22—4884no—
508C22—2442no—
509C22—2442no—
510C22—2442no—
511C22#1683992312yes—
512C22#1683992312yes—
513C22#1683993312yes—
514C22#1683995112yes—
515C22C2×#1451974511yescharacteristic
516C22C2×#1451980011yescharacteristic
517C22C2×#1451980911yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—42no—
524C4—82no—
525C4—4882no—
526C4—2442no—
527C4—2442no—
528C4—2442no—
529C2—21no—
530C2—21no—
531C2—22no—
532C2—4882no—
533C2#2144484914yesdirect product factor
534C2C2×#1683992311yescharacteristic
535C2C2×#1683993311yescharacteristic
536C2C2×#1683995111yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#484C2
socleC23×C61#120
prime radicalC2×#14519751C22
hypercenterC2×#484D61
hypocenterC61C2×#1615
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. C2×#16839700C2semidirect
4. #21444849C2direct (N × H)
5. C2×#16839499C2semidirect
7. C2×#16839487C2semidirect
8. C2×C61×#484C2semidirect
27. #16839700C22semidirect
31. #16839499C22semidirect
33. #16839487C22semidirect
37. C61×#484C22semidirect
262. C2×#484D61semidirect
272. C2×C61#1615semidirect
292. #484C2×D61semidirect
309. C61C2×#1615semidirect
533. C2#21444849direct (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×#168400802
C2×#168397002
#214448492
C2×#168394992
C2×#168394972
C2×#168394872
C2×C61×#4842
C2×#161561