Finite Group Databasebeta

← C2×#21444808 #29652138

Subgroups — C2×#21444808 #29652138

Order 15616.

1136 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840387C211yesmaximal, characteristic
2C2×#16840092C211yesmaximal, characteristic, complemented
3C2×#16839688C211yesmaximal, characteristic
4#21444808C218yesmaximal, direct product factor
5C2×#16839500C211yesmaximal, characteristic, complemented
6C2×#16839499C211yesmaximal, characteristic, complemented
7C2×#16839485C211yesmaximal, characteristic
8C2×C61×#483C211yesmaximal, characteristic, complemented
9#16840387—22no—
10#16840387—22no—
11#16840387—22no—
12#16840387C2214yes—
13C2×#14519757—21no—
14C2×#14519756C2211yescharacteristic
15C2×#14519755—21no—
16C2×#14519755—21no—
17C2×#14519754—21no—
18C2×#14519753—21no—
19C22×#11758198—21no—
20C22×#11758198C2211yescharacteristic
21C2×C22⋊C4×D61—21no—
22#16840092—22no—
23#16840092C2214yescomplemented
24C2×#14519708—21no—
25C2×#14519700—21no—
26C2×C22⋊#92418C2211yescharacteristic
27#16839688—22no—
28#16839688C2214yes—
29C2×#14519684—21no—
30C2×#14519684C2211yescharacteristic
31#16839500C2214yescomplemented
32#16839499C2214yescomplemented
33#16839485C2214yes—
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
41C24×D61D411yescharacteristic
42C22×Dic122—21no—
43C22×Dic122D411yescharacteristic
44C23×Dic61—21no—
45C23×Dic61D411yescharacteristic
46C22×C4×D61—21no—
47C22×C4×D61—21no—
48C22×#92418—21no—
49#14519757—24no—
50#14519757—24no—
51#14519756—21no—
52#14519756—21no—
53#14519756D412yes—
54#14519756C2312yes—
55#14519755—24no—
56#14519755—24no—
57#14519755—24no—
58#14519755—24no—
59#14519754—24no—
60#14519754—24no—
61#14519753—24no—
62#14519753—24no—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61D411yescharacteristic
65C2×#11758196—21no—
66C2×#11758196—21no—
67C2×#11758196—21no—
68C2×C22⋊Dic61—21no—
69C2×#11758198—21no—
70C2×#11758198—21no—
71C2×#11758198—21no—
72C2×#11758198—21no—
73C2×#11758198—21no—
74C2×#11758198—21no—
75C2×#11758198—24no—
76C2×#11758198—44no—
77C2×#11758198D412yes—
78C2×#11758198C2312yes—
79C22⋊C4×D61—24no—
80C22⋊C4×D61—24no—
81#14519708—24no—
82#14519700—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—
111C23×D61—21no—
112C23×D61—22no—
113C23×D61—42no—
114C23×D61—42no—
115C23×D61SD1614yes—
116C23×D61C2×D412yes—
117C2×Q8×C61—21no—
118C2×Q8×C61—42no—
119C2×Q8×C61C2×D412yes—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—22no—
123C22×C4×C61—42no—
124C22×C4×C61—41no—
125C22×C4×C61—41no—
126C22×C4×C61—42no—
127C22×C4×C61—42no—
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2411yescharacteristic
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—22no—
139C22×Dic61—42no—
140C22×Dic61—42no—
141C22×Dic61—42no—
142C22×Dic61—42no—
143C22×Dic61C2×D412yes—
144C2×C4×D61—24no—
145C2×C4×D61—24no—
146C2×C4×D61—82no—
147C2×C4×D61—82no—
148C2×Dic122—24no—
149C2×Dic122—21no—
150C2×Dic122—42no—
151C2×Dic122—82no—
152C2×Dic122C2×D412yes—
153C2×C8×C61—22no—
154C2×C8×C61—42no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—22no—
158C4⋊C4×C61—22no—
159C4⋊C4×C61—22no—
160C4⋊C4×C61—41no—
161C4⋊C4×C61—41no—
162C4⋊C4×C61C2×D412yes—
163C22⋊C4×C61—22no—
164C22⋊C4×C61—22no—
165C22⋊Dic61—22no—
166C22⋊Dic61—22no—
167#11758198—24no—
168#11758198—24no—
169#11758198—22no—
170#11758198—22no—
171#11758198—22no—
172#11758198—22no—
173#11758198—48no—
174C4⋊Dic61—24no—
175C4⋊Dic61—21no—
176C4⋊Dic61C2×D412yes—
177#11758196—24no—
178#11758196—24no—
179#11758196—22no—
180#11758196—22no—
181C2×#92418—22no—
182C2×#92418—42no—
183C23×C61—22no—
184C23×C61—22no—
185C23×C61#12011yescharacteristic
186C23×C61#12011yescharacteristic
187C23×C61C2×SD1612yes—
188C23×C61#13712yes—
189C23×C61C22×D411yescharacteristic
190C22×D61—22no—
191C22×D61—24no—
192C22×D61—22no—
193C22×D61—24no—
194C22×D61—42no—
195C22×D61—42no—
196C22×D61—48no—
197C22×D61—42no—
198C22×D61—42no—
199C22×D61—84no—
200C22×D61—81no—
201C22×D61—81no—
202C22×D61C2×SD1614yes—
203Q8×C61—42no—
204Q8×C61—81no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—82no—
219C2×C4×C61—82no—
220C2×C4×C61#12011yescharacteristic
221C2×C4×C61#12011yescharacteristic
222C2×C4×C61C22×D411yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C2×Dic61—22no—
225C2×Dic61—22no—
226C2×Dic61—22no—
227C2×Dic61—42no—
228C2×Dic61—42no—
229C2×Dic61—42no—
230C2×Dic61—42no—
231C2×Dic61—42no—
232C2×Dic61—42no—
233C2×Dic61—42no—
234C2×Dic61—81no—
235C2×Dic61—84no—
236C4×D61—84no—
237C4×D61—84no—
238Dic122—42no—
239Dic122—81no—
240Dic122—84no—
241C8×C61—42no—
242#92418—42no—
243C2×#1608—611nomaximal, Sylow
244C22×C61—24no—
245C22×C61—24no—
246C22×C61—21no—
247C22×C61—21no—
248C22×C61—21no—
249C22×C61—21no—
250C22×C61#44812yes—
251C22×C61#44812yes—
252C22×C61#45512yes—
253C22×C61#45812yes—
254C22×C61C2×#12011yescharacteristic
255C22×C61C22×SD1611yescharacteristic
256C22×C61C2×#13711yescharacteristic
257C2×D61—24no—
258C2×D61—48no—
259C2×D61—42no—
260C2×D61—42no—
261C2×D61—44no—
262C2×D61—82no—
263C2×D61—84no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—42no—
269C4×C61—42no—
270C4×C61—82no—
271Dic61—42no—
272Dic61—42no—
273Dic61—42no—
274Dic61—82no—
275C2×#543—611no—
276C2×#483—611no—
277C2×#483D6111yescharacteristic, complemented
278C2×#397—611no—
279#1608—618no—
280C2×#328—611no—
281C2×#328—611no—
282C2×#323—611no—
283C2×C61—21no—
284C2×C61—21no—
285C2×C61—22no—
286C2×C61#160814yescomplemented
287C2×C61C2×#44811yescharacteristic
288C2×C61C2×#45511yescharacteristic
289C2×C61C2×#45811yescharacteristic
290D61—44no—
291#543—614no—
292#543—1222no—
293#543—1222no—
294#543—1222no—
295C2×C22⋊Q8—611no—
296C2×C22⋊Q8—1221no—
297C2×C22⋊Q8—1221no—
298C2×C22⋊Q8—1221no—
299C2×C22⋊Q8—1221no—
300C2×C22⋊Q8—1221no—
301C2×C22⋊Q8C2×D6111yescharacteristic
302C22×C4⋊C4C2×D6111yescharacteristic
303C22×C22⋊C4—611no—
304C22×C22⋊C4—1221no—
305C22×C22⋊C4—1221no—
306#483—22no—
307#483—614no—
308#483—1222no—
309#483C2×D6114yescomplemented
310C2×#106—21no—
311C2×#106—1221no—
312C2×#103—21no—
313C2×#103—1221no—
314C2×C22⋊C8—611no—
315C2×C22⋊C8C2×D6111yescharacteristic
316#397—614no—
317#397—1222no—
318C2×#95—611no—
319C2×#95—1221no—
320#328—614no—
321#328—614no—
322#323—614no—
323C61C2×#160811yescharacteristic, complemented, Sylow
324C25—611no—
325C22×Q8—611no—
326C22×Q8—1221no—
327C22×Q8C22⋊D6111yescharacteristic
328C23×C4—21no—
329C23×C4—611no—
330C23×C4—1221no—
331C23×C4—1221no—
332C23×C4—1221no—
333C23×C4C22×D6111yescharacteristic
334C22×C8—21no—
335C22×C8—1221no—
336C22⋊Q8—21no—
337C22⋊Q8—21no—
338C22⋊Q8—612no—
339C22⋊Q8—612no—
340C22⋊Q8—1224no—
341C22⋊Q8—1224no—
342C22⋊Q8—1224no—
343C22⋊Q8—1224no—
344C22⋊Q8—1224no—
345C22⋊Q8—1224no—
346C22⋊Q8—1224no—
347C22⋊Q8—1224no—
348C22⋊Q8—1224no—
349C22⋊Q8—1221no—
350C22⋊Q8—1221no—
351C22⋊Q8—1224no—
352C22⋊Q8C22⋊D6112yes—
353C22⋊Q8C22×D6112yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—611no—
361C2×C4⋊C4—1221no—
362C2×C4⋊C4—1221no—
363C2×C4⋊C4—1221no—
364C2×C4⋊C4—1221no—
365C2×C4⋊C4C22⋊D6111yescharacteristic
366C2×C4⋊C4C22×D6112yes—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—612no—
369C2×C22⋊C4—612no—
370C2×C22⋊C4—1224no—
371C2×C22⋊C4—1224no—
372C2×C22⋊C4—1221no—
373C2×C22⋊C4—1221no—
374C2×C22⋊C4—1221no—
375C2×C22⋊C4—1221no—
376C2×C22⋊C4—1221no—
377C2×C22⋊C4—1221no—
378C2×C22⋊C4—1221no—
379C2×C22⋊C4—1224no—
380C2×C22⋊C4—2444no—
381#106—24no—
382#106—1224no—
383#103—24no—
384#103—1224no—
385C22⋊C8—21no—
386C22⋊C8—612no—
387C22⋊C8—1221no—
388C22⋊C8C22×D6112yes—
389#95—612no—
390#95—1224no—
391#95—1221no—
392C24—612no—
393C24—614no—
394C24—1221no—
395C24—1222no—
396C24—1221no—
397C24—2442no—
398C24—2442no—
399C24D4×D6111yescharacteristic
400C2×Q8—21no—
401C2×Q8—42no—
402C2×Q8—612no—
403C2×Q8—1224no—
404C2×Q8—1221no—
405C2×Q8—4882no—
406C2×Q8—2442no—
407C2×Q8C2×C22⋊D6112yes—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—42no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—612no—
417C22×C4—1224no—
418C22×C4—1224no—
419C22×C4—1221no—
420C22×C4—1221no—
421C22×C4—1221no—
422C22×C4—1221no—
423C22×C4—1222no—
424C22×C4—4882no—
425C22×C4—4882no—
426C22×C4—2442no—
427C22×C4—2442no—
428C22×C4—2442no—
429C22×C4—2442no—
430C22×C4D4×D6111yescharacteristic
431C22×C4D4×D6111yescharacteristic
432C22×C4D4×D6111yescharacteristic
433C22×C4C2×C22⋊D6111yescharacteristic
434C22×C4C2×C22⋊D6111yescharacteristic
435C22×C4C23×D6111yescharacteristic
436C2×C8—22no—
437C2×C8—42no—
438C2×C8—1222no—
439C2×C8—2442no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C4⋊C4—612no—
448C4⋊C4—1224no—
449C4⋊C4—1224no—
450C4⋊C4—1224no—
451C4⋊C4—1222no—
452C4⋊C4—1221no—
453C4⋊C4—1222no—
454C4⋊C4C2×C22⋊D6112yes—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—1224no—
458C22⋊C4—1224no—
459C22⋊C4—1222no—
460C22⋊C4—1222no—
461C22⋊C4—1222no—
462C22⋊C4—1222no—
463C22⋊C4—1222no—
464C22⋊C4—1222no—
465C22⋊C4—2448no—
466C23—22no—
467C23—22no—
468C23—614no—
469C23—1222no—
470C23—1224no—
471C23—1222no—
472C23—1224no—
473C23—4881no—
474C23—4881no—
475C23—4884no—
476C23—2442no—
477C23—2442no—
478C23—2448no—
479C23—2442no—
480C23—2442no—
481C23#1451974511yescharacteristic
482C23#1451974511yescharacteristic
483C23SD16×D6112yes—
484C23#1451980612yes—
485C23C2×D4×D6111yescharacteristic
486Q8—42no—
487Q8—81no—
488Q8—4881no—
489Q8—4884no—
490Q8—2442no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—82no—
505C2×C4—82no—
506C2×C4—1222no—
507C2×C4—1222no—
508C2×C4—1222no—
509C2×C4—4884no—
510C2×C4—4884no—
511C2×C4—4884no—
512C2×C4—4881no—
513C2×C4—2442no—
514C2×C4—2442no—
515C2×C4—2442no—
516C2×C4—2442no—
517C2×C4—2442no—
518C2×C4—2442no—
519C2×C4—2442no—
520C2×C4#1451974511yescharacteristic
521C2×C4#1451974511yescharacteristic
522C2×C4C2×D4×D6111yescharacteristic
523C2×C4C22×C22⋊D6111yescharacteristic
524C8—42no—
525C8—2442no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—24no—
531C22—24no—
532C22—1224no—
533C22—4882no—
534C22—4884no—
535C22—2444no—
536C22—2442no—
537C22—2442no—
538C22—2448no—
539C22#1683989912yes—
540C22#1683989912yes—
541C22#1683993812yes—
542C22#1683995112yes—
543C22C2×#1451974511yescharacteristic
544C22C2×SD16×D6111yescharacteristic
545C22C2×#1451980611yescharacteristic
546C4—21no—
547C4—21no—
548C4—21no—
549C4—21no—
550C4—42no—
551C4—42no—
552C4—82no—
553C4—4882no—
554C4—2442no—
555C4—2442no—
556C4—2442no—
557C2—21no—
558C2—21no—
559C2—22no—
560C2—2444no—
561C2#2144480814yesdirect product factor
562C2C2×#1683989911yescharacteristic
563C2C2×#1683993811yescharacteristic
564C2C2×#1683995111yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#483C2
socleC23×C61#120
prime radicalC24×D61D4
hypercenterC2×#483D61
hypocenterC61C2×#1608
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
2. C2×#16840092C2semidirect
4. #21444808C2direct (N × H)
5. C2×#16839500C2semidirect
6. C2×#16839499C2semidirect
8. C2×C61×#483C2semidirect
23. #16840092C22semidirect
31. #16839500C22semidirect
32. #16839499C22semidirect
37. C61×#483C22semidirect
277. C2×#483D61semidirect
286. C2×C61#1608semidirect
309. #483C2×D61semidirect
323. C61C2×#1608semidirect
561. C2#21444808direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403872
C2×#168400922
C2×#168396882
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C2×#168395002
C2×#168394992
C2×#168394852
C2×C61×#4832
C2×#160861