Finite Group Databasebeta

← C2×#21444865 #29652261

Subgroups — C2×#21444865 #29652261

Order 15616.

1200 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840350C211yesmaximal, characteristic
2C2×#16840097C211yesmaximal, characteristic, complemented
3C2×#16840080C211yesmaximal, characteristic, complemented
4#21444865C218yesmaximal, direct product factor
5C2×#16839498C211yesmaximal, characteristic, complemented
6C2×#16839495C211yesmaximal, characteristic, complemented
7C2×#16839486C211yesmaximal, characteristic, complemented
8C2×C61×#399C211yesmaximal, characteristic, complemented
9#16840350—22no—
10#16840350—22no—
11#16840350—22no—
12#16840350C2214yes—
13C2×#14519770—21no—
14C2×#14519763—21no—
15C2×#14519759—21no—
16C2×#14519756C2211yescharacteristic
17C2×#14519751C2211yescharacteristic
18C2×#14519750—21no—
19C2×#14519746—21no—
20C2×C4×C22⋊D61—21no—
21#16840097—22no—
22#16840097C2214yescomplemented
23#16840080—22no—
24#16840080C2214yescomplemented
25C2×#14519710—21no—
26C2×#14519708—21no—
27C2×#14519700—21no—
28C2×#14519697—21no—
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31#16839498C2214yescomplemented
32#16839495C2214yescomplemented
33#16839486C2214yescomplemented
34C22×C4⋊C4×C61—21no—
35C22×C4⋊C4×C61C2211yescharacteristic
36C22×C22⋊C4×C61—21no—
37C22×C22⋊C4×C61C2211yescharacteristic
38C61×#399—22no—
39C61×#399C2214yescomplemented
40C2×#95×C61C2211yescharacteristic
41C22×Dic122D411yescharacteristic
42C22×D244D411yescharacteristic
43C22×C22⋊D61—21no—
44C22×C22⋊D61—21no—
45C22×C22⋊D61—21no—
46C22×C4×D61—21no—
47C22×#92418—21no—
48C22×#92418—21no—
49#14519770—24no—
50#14519770—24no—
51#14519763—24no—
52#14519763—24no—
53#14519759—24no—
54#14519759—24no—
55#14519756—21no—
56#14519756—21no—
57#14519756D412yes—
58#14519756C2312yes—
59#14519751—21no—
60#14519751—21no—
61#14519751D412yes—
62#14519751C2312yes—
63#14519750—24no—
64#14519750—24no—
65#14519746—24no—
66#14519746—24no—
67C4×C22⋊D61—24no—
68C4×C22⋊D61—24no—
69C2×C4⋊Dic61D411yescharacteristic
70C2×C4⋊Dic61D411yescharacteristic
71C2×#11758196—21no—
72C2×#11758196—21no—
73C2×C22⋊Dic61—21no—
74C2×C22⋊Dic61—21no—
75C2×C22⋊Dic61—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×C4×Dic61—21no—
79#14519710—24no—
80#14519708—24no—
81#14519700—24no—
82#14519697—24no—
83C22⋊#92418—21no—
84C22⋊#92418—21no—
85C22⋊#92418C2312yes—
86C22⋊#92418C2312yes—
87C25×C61D411yescharacteristic
88C23×C4×C61—21no—
89C23×C4×C61—21no—
90C23×C4×C61D411yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—24no—
98C2×C4⋊C4×C61—44no—
99C2×C4⋊C4×C61C2312yes—
100C2×C22⋊C4×C61—21no—
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61—21no—
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61—24no—
105C2×C22⋊C4×C61—44no—
106C2×C22⋊C4×C61D412yes—
107C2×C22⋊C4×C61C2312yes—
108#95×C61—21no—
109#95×C61C2312yes—
110C24×C61—21no—
111C24×C61—22no—
112C24×C61—21no—
113C24×C61—22no—
114C24×C61—42no—
115C24×C61—42no—
116C24×C61C2×D411yescharacteristic
117C24×C61C2×D412yes—
118C23×D61—21no—
119C22×C4×C61—24no—
120C22×C4×C61—21no—
121C22×C4×C61—22no—
122C22×C4×C61—21no—
123C22×C4×C61—22no—
124C22×C4×C61—42no—
125C22×C4×C61—42no—
126C22×C4×C61—42no—
127C22×C4×C61—42no—
128C22×C4×C61—42no—
129C22×C4×C61—42no—
130C22×C4×C61—41no—
131C22×C4×C61—41no—
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D412yes—
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C2×C22⋊D61—22no—
140C2×C22⋊D61—22no—
141C2×C22⋊D61—24no—
142C2×C22⋊D61—24no—
143C2×C22⋊D61—42no—
144C2×C22⋊D61—42no—
145C2×C22⋊D61—82no—
146C2×C22⋊D61—82no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C2×D244—21no—
151C2×D244—42no—
152C2×D244C2×D412yes—
153C2×C4×D61—24no—
154C2×C4×D61—82no—
155C2×Dic122—21no—
156C2×Dic122—42no—
157C2×Dic122C2×D412yes—
158C4⋊C4×C61—22no—
159C4⋊C4×C61—22no—
160C4⋊C4×C61—48no—
161C4⋊C4×C61—41no—
162C4⋊C4×C61—41no—
163C22⋊C4×C61—22no—
164C22⋊C4×C61—22no—
165C22⋊C4×C61—22no—
166C22⋊C4×C61—22no—
167C22⋊C4×C61—48no—
168C22⋊Dic61—24no—
169C22⋊Dic61—24no—
170C22⋊Dic61—22no—
171C22⋊Dic61—22no—
172#11758198—24no—
173#11758198—22no—
174#11758198—22no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61C2×D412yes—
178C4⋊Dic61C2×D412yes—
179#11758196—24no—
180#11758196—22no—
181#11758196—22no—
182C4×Dic61—24no—
183C2×#92418—22no—
184C2×#92418—22no—
185C2×#92418—42no—
186C2×#92418—42no—
187C23×C61—22no—
188C23×C61—22no—
189C23×C61—22no—
190C23×C61—22no—
191C23×C61—22no—
192C23×C61—42no—
193C23×C61—42no—
194C23×C61—48no—
195C23×C61—42no—
196C23×C61—42no—
197C23×C61—42no—
198C23×C61—42no—
199C23×C61—81no—
200C23×C61—81no—
201C23×C61—84no—
202C23×C61#12011yescharacteristic
203C23×C61#12011yescharacteristic
204C23×C61#13512yes—
205C23×C61#13712yes—
206C23×C61C22×D411yescharacteristic
207C22×D61—22no—
208C22×D61—42no—
209C22×D61—42no—
210C22×D61—42no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—24no—
214C2×C4×C61—22no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—48no—
220C2×C4×C61—42no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—81no—
228C2×C4×C61—82no—
229C2×C4×C61—82no—
230C2×C4×C61#12011yescharacteristic
231C2×C4×C61#12011yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C22×D411yescharacteristic
234C22⋊D61—42no—
235C22⋊D61—42no—
236C22⋊D61—44no—
237C22⋊D61—84no—
238C22⋊D61—84no—
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—22no—
242C2×Dic61—42no—
243C2×Dic61—42no—
244C2×Dic61—42no—
245D244—42no—
246D244—81no—
247C4×D61—84no—
248Dic122—42no—
249Dic122—81no—
250#92418—42no—
251#92418—42no—
252C2×#1618—611nomaximal, Sylow
253C22×C61—24no—
254C22×C61—24no—
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—44no—
260C22×C61—42no—
261C22×C61—42no—
262C22×C61—42no—
263C22×C61—82no—
264C22×C61—84no—
265C22×C61—84no—
266C22×C61#45212yes—
267C22×C61#45212yes—
268C22×C61#45312yes—
269C22×C61#45812yes—
270C22×C61C2×#12011yescharacteristic
271C22×C61C2×#13511yescharacteristic
272C22×C61C2×#13711yescharacteristic
273C2×D61—42no—
274C2×D61—42no—
275C2×D61—42no—
276C2×D61—84no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—21no—
280C4×C61—21no—
281C4×C61—44no—
282C4×C61—42no—
283C4×C61—82no—
284Dic61—42no—
285Dic61—42no—
286Dic61—42no—
287C2×#538—611no—
288C2×#484—611no—
289C2×#481—611no—
290C2×#399D6111yescharacteristic, complemented
291#1618—618no—
292C2×#328—611no—
293C2×#327—611no—
294C2×#323—611no—
295C2×C61—21no—
296C2×C61—21no—
297C2×C61—22no—
298C2×C61—82no—
299C2×C61#161814yescomplemented
300C2×C61C2×#45211yescharacteristic
301C2×C61C2×#45311yescharacteristic
302C2×C61C2×#45811yescharacteristic
303D61—82no—
304#538—614no—
305#538—1222no—
306#538—1222no—
307#538—1222no—
308C2×#126—1221no—
309C2×#124—1221no—
310C2×#123—1221no—
311C2×C22⋊Q8—611no—
312C2×#121—611no—
313C2×#121—1221no—
314C2×#120—1221no—
315C2×C4×D4—1221no—
316C22×C4⋊C4—21no—
317C22×C4⋊C4C2×D6111yescharacteristic
318C22×C22⋊C4—21no—
319C22×C22⋊C4C2×D6111yescharacteristic
320#484—614no—
321#484—1222no—
322#481—614no—
323#481—1222no—
324C2×#107—1221no—
325C2×#106—1221no—
326C2×#103—1221no—
327C2×#102—1221no—
328C2×C22⋊C8—611no—
329C2×C22⋊C8—611no—
330#399—22no—
331#399C2×D6114yescomplemented
332C2×#95C2×D6111yescharacteristic
333#328—614no—
334#327—614no—
335#323—614no—
336C61C2×#161811yescharacteristic, complemented, Sylow
337C25C22⋊D6111yescharacteristic
338C22×Q8—611no—
339C22×D4—611no—
340C22×D4—1221no—
341C22×D4—1221no—
342C22×D4—1221no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—1221no—
346C23×C4C22⋊D6111yescharacteristic
347C23×C4C22×D6111yescharacteristic
348C22×C8—1221no—
349C22×C8—1221no—
350#126—1224no—
351#126—1224no—
352#124—1224no—
353#124—1224no—
354#123—1224no—
355#123—1224no—
356C22⋊Q8—612no—
357C22⋊Q8—612no—
358C22⋊Q8—1221no—
359C22⋊Q8—1221no—
360#121—612no—
361#121—612no—
362#121—1224no—
363#121—1224no—
364#121—1221no—
365#121—1221no—
366#120—1224no—
367#120—1224no—
368C4×D4—1224no—
369C4×D4—1224no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—611no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4C22×D6112yes—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1221no—
390C2×C22⋊C4—1221no—
391C2×C22⋊C4—1221no—
392C2×C22⋊C4—1221no—
393C2×C22⋊C4C22⋊D6112yes—
394C2×C22⋊C4C22×D6112yes—
395C2×C42—1221no—
396#107—1224no—
397#106—1224no—
398#103—1224no—
399#102—1224no—
400C22⋊C8—612no—
401C22⋊C8—612no—
402C22⋊C8—1221no—
403C22⋊C8—1221no—
404#95—21no—
405#95C22×D6112yes—
406C24—22no—
407C24—21no—
408C24—21no—
409C24—22no—
410C24—42no—
411C24—42no—
412C24—1221no—
413C24C2×C22⋊D6111yescharacteristic
414C24C2×C22⋊D6112yes—
415C2×Q8—612no—
416C2×Q8—1221no—
417C2×Q8—2442no—
418C2×D4—612no—
419C2×D4—1224no—
420C2×D4—1224no—
421C2×D4—1222no—
422C2×D4—1222no—
423C2×D4—1221no—
424C2×D4—4882no—
425C2×D4—4882no—
426C2×D4—2442no—
427C2×D4—2442no—
428C2×D4—2442no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—1224no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—4882no—
447C22×C4D4×D6111yescharacteristic
448C22×C4D4×D6111yescharacteristic
449C22×C4D4×D6111yescharacteristic
450C22×C4D4×D6111yescharacteristic
451C22×C4C2×C22⋊D6112yes—
452C22×C4C2×C22⋊D6111yescharacteristic
453C22×C4C23×D6111yescharacteristic
454C2×C8—1222no—
455C2×C8—1222no—
456C2×C8—2442no—
457C2×C8—2442no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—48no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—612no—
464C4⋊C4—612no—
465C4⋊C4—1224no—
466C4⋊C4—1222no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1222no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—48no—
475C22⋊C4—1224no—
476C22⋊C4—1224no—
477C22⋊C4—1224no—
478C22⋊C4—1222no—
479C22⋊C4—1222no—
480C22⋊C4—1222no—
481C22⋊C4—1222no—
482C42—1224no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—42no—
489C23—42no—
490C23—48no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—81no—
496C23—81no—
497C23—84no—
498C23—1222no—
499C23—2442no—
500C23—2442no—
501C23—2442no—
502C23#1451974511yescharacteristic
503C23#1451974511yescharacteristic
504C23#1451979712yes—
505C23#1451980812yes—
506C23C22×C22⋊D6111yescharacteristic
507Q8—4881no—
508Q8—2442no—
509D4—4881no—
510D4—4884no—
511D4—4884no—
512D4—2442no—
513D4—2442no—
514D4—2442no—
515D4—2444no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—48no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—81no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4—1222no—
536C2×C4—1222no—
537C2×C4—1222no—
538C2×C4—4884no—
539C2×C4—2442no—
540C2×C4—2442no—
541C2×C4—2442no—
542C2×C4#1451974511yescharacteristic
543C2×C4#1451974511yescharacteristic
544C2×C4C2×D4×D6111yescharacteristic
545C2×C4C2×D4×D6111yescharacteristic
546C8—2442no—
547C8—2442no—
548C22—24no—
549C22—24no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—44no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—82no—
559C22—84no—
560C22—84no—
561C22—4884no—
562C22—2442no—
563C22—2442no—
564C22—2442no—
565C22#1683992212yes—
566C22#1683992212yes—
567C22#1683992912yes—
568C22#1683995112yes—
569C22C2×#1451974511yescharacteristic
570C22C2×#1451979711yescharacteristic
571C22C2×#1451980811yescharacteristic
572C4—21no—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—44no—
577C4—42no—
578C4—82no—
579C4—2442no—
580C4—2442no—
581C4—2442no—
582C2—21no—
583C2—21no—
584C2—22no—
585C2—82no—
586C2—4882no—
587C2#2144486514yesdirect product factor
588C2C2×#1683992211yescharacteristic
589C2C2×#1683992911yescharacteristic
590C2C2×#1683995111yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#399C2
socleC23×C61#120
prime radicalC2×#16840350C2
hypercenterC2×#399D61
hypocenterC61C2×#1618
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
2. C2×#16840097C2semidirect
3. C2×#16840080C2semidirect
4. #21444865C2direct (N × H)
5. C2×#16839498C2semidirect
6. C2×#16839495C2semidirect
7. C2×#16839486C2semidirect
8. C2×C61×#399C2semidirect
22. #16840097C22semidirect
24. #16840080C22semidirect
31. #16839498C22semidirect
32. #16839495C22semidirect
33. #16839486C22semidirect
39. C61×#399C22semidirect
290. C2×#399D61semidirect
299. C2×C61#1618semidirect
331. #399C2×D61semidirect
336. C61C2×#1618semidirect
587. C2#21444865direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403502
C2×#168400972
C2×#168400802
#214448652
C2×#168394982
C2×#168394952
C2×#168394862
C2×C61×#3992
C2×#161861