Finite Group Databasebeta

← C2×#21444830 #29652252

Subgroups — C2×#21444830 #29652252

Order 15616.

1156 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840349C211yesmaximal, characteristic
2C2×#16840092C211yesmaximal, characteristic, complemented
3C2×#16839688C211yesmaximal, characteristic, complemented
4#21444830C218yesmaximal, direct product factor
5C2×#16839500C211yesmaximal, characteristic, complemented
6C2×#16839496C211yesmaximal, characteristic, complemented
7C2×#16839485C211yesmaximal, characteristic, complemented
8C2×C61×#480C211yesmaximal, characteristic, complemented
9#16840349—22no—
10#16840349—22no—
11#16840349—22no—
12#16840349C2214yes—
13C2×#14519772—21no—
14C2×#14519763—21no—
15C2×#14519761—21no—
16C2×#14519756C2211yescharacteristic
17C2×#14519749—21no—
18C2×#14519745—21no—
19C2×D4×Dic61—21no—
20C22×#11758198—21no—
21C22×#11758198C2211yescharacteristic
22#16840092—22no—
23#16840092C2214yescomplemented
24C2×#14519708—21no—
25C2×#14519700—21no—
26C2×C22⋊#92418C2211yescharacteristic
27#16839688—22no—
28#16839688C2214yescomplemented
29C2×#14519684—21no—
30C2×#14519684C2211yescharacteristic
31#16839500C2214yescomplemented
32#16839496C2214yescomplemented
33#16839485C2214yescomplemented
34C2×#121×C61C2211yescharacteristic
35C22×C4⋊C4×C61C2211yescharacteristic
36C61×#480—22no—
37C61×#480C2214yescomplemented
38C2×#107×C61—21no—
39C2×#102×C61—21no—
40C2×C22⋊C8×C61C2211yescharacteristic
41C24×D61D411yescharacteristic
42C22×Dic122D411yescharacteristic
43C22×C22⋊D61—21no—
44C22×C22⋊D61—21no—
45C23×Dic61—21no—
46C23×Dic61—21no—
47C23×Dic61D411yescharacteristic
48C22×#92418—21no—
49#14519772—24no—
50#14519772—24no—
51#14519763—24no—
52#14519763—24no—
53#14519761—24no—
54#14519761—24no—
55#14519756—21no—
56#14519756—21no—
57#14519756D412yes—
58#14519756C2312yes—
59#14519749—24no—
60#14519749—24no—
61#14519745—24no—
62#14519745—24no—
63D4×Dic61—24no—
64D4×Dic61—24no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61D411yescharacteristic
67C2×#11758196—21no—
68C2×C22⋊Dic61—21no—
69C2×C22⋊Dic61—21no—
70C2×#11758198—21no—
71C2×#11758198—21no—
72C2×#11758198—21no—
73C2×#11758198—21no—
74C2×#11758198—21no—
75C2×#11758198—21no—
76C2×#11758198—24no—
77C2×#11758198—44no—
78C2×#11758198D412yes—
79C2×#11758198C2312yes—
80C2×C4×Dic61—21no—
81#14519708—24no—
82#14519700—24no—
83C22⋊#92418—21no—
84C22⋊#92418C2312yes—
85#14519684—21no—
86#14519684—24no—
87#14519684C2312yes—
88C22×D4×C61—21no—
89C22×D4×C61D411yescharacteristic
90C23×C4×C61—21no—
91C23×C4×C61C2311yescharacteristic
92C22×C8×C61—21no—
93#121×C61—21no—
94#121×C61—21no—
95#121×C61D412yes—
96#121×C61C2312yes—
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#107×C61—24no—
106#102×C61—24no—
107C22⋊C8×C61—21no—
108C22⋊C8×C61C2312yes—
109C24×C61—21no—
110C24×C61C2×D411yescharacteristic
111C23×D61—21no—
112C23×D61—22no—
113C23×D61—21no—
114C23×D61—22no—
115C23×D61—42no—
116C23×D61—42no—
117C23×D61C2×D412yes—
118C2×D4×C61—22no—
119C2×D4×C61—22no—
120C2×D4×C61—21no—
121C2×D4×C61—42no—
122C2×D4×C61—42no—
123C2×D4×C61—42no—
124C2×D4×C61C2×D412yes—
125C22×C4×C61—21no—
126C22×C4×C61—22no—
127C22×C4×C61—42no—
128C22×C4×C61—41no—
129C22×C4×C61—41no—
130C22×C4×C61—42no—
131C22×C4×C61—42no—
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C2×C22⋊D61—24no—
139C2×C22⋊D61—24no—
140C2×C22⋊D61—82no—
141C2×C22⋊D61—82no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—24no—
146C22×Dic61—21no—
147C22×Dic61—22no—
148C22×Dic61—42no—
149C22×Dic61—42no—
150C22×Dic61—42no—
151C22×Dic61—42no—
152C22×Dic61—82no—
153C22×Dic61C2×D412yes—
154C2×Dic122—21no—
155C2×Dic122—42no—
156C2×Dic122C2×D412yes—
157C2×C8×C61—22no—
158C2×C8×C61—42no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—22no—
161C4⋊C4×C61—22no—
162C4⋊C4×C61—41no—
163C4⋊C4×C61—41no—
164C4⋊C4×C61C2×D412yes—
165C22⋊C4×C61—22no—
166C22⋊C4×C61—22no—
167C22⋊Dic61—24no—
168C22⋊Dic61—22no—
169C22⋊Dic61—22no—
170#11758198—24no—
171#11758198—24no—
172#11758198—22no—
173#11758198—22no—
174#11758198—22no—
175#11758198—22no—
176#11758198—48no—
177C4⋊Dic61—24no—
178C4⋊Dic61—21no—
179C4⋊Dic61C2×D412yes—
180#11758196—22no—
181#11758196—22no—
182C4×Dic61—24no—
183C2×#92418—22no—
184C2×#92418—42no—
185C23×C61—22no—
186C23×C61—22no—
187C23×C61—22no—
188C23×C61—42no—
189C23×C61—42no—
190C23×C61—42no—
191C23×C61#12011yescharacteristic
192C23×C61#12011yescharacteristic
193C23×C61#13512yes—
194C23×C61AGL(1,ℤ/8)12yes—
195C23×C61C22×D411yescharacteristic
196C22×D61—22no—
197C22×D61—22no—
198C22×D61—22no—
199C22×D61—42no—
200C22×D61—42no—
201C22×D61—48no—
202C22×D61—42no—
203C22×D61—42no—
204C22×D61—42no—
205C22×D61—42no—
206C22×D61—81no—
207C22×D61—81no—
208C22×D61—84no—
209D4×C61—42no—
210D4×C61—42no—
211D4×C61—42no—
212D4×C61—44no—
213D4×C61—81no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—82no—
226C2×C4×C61—82no—
227C2×C4×C61#12011yescharacteristic
228C2×C4×C61#12011yescharacteristic
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61C22×D411yescharacteristic
231C22⋊D61—84no—
232C22⋊D61—84no—
233C2×Dic61—22no—
234C2×Dic61—22no—
235C2×Dic61—22no—
236C2×Dic61—42no—
237C2×Dic61—42no—
238C2×Dic61—42no—
239C2×Dic61—42no—
240C2×Dic61—42no—
241C2×Dic61—42no—
242C2×Dic61—42no—
243C2×Dic61—81no—
244C2×Dic61—84no—
245C2×Dic61—84no—
246Dic122—42no—
247Dic122—81no—
248C8×C61—42no—
249#92418—42no—
250C2×#1612—611nomaximal, Sylow
251C22×C61—24no—
252C22×C61—24no—
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—42no—
258C22×C61—42no—
259C22×C61—42no—
260C22×C61—84no—
261C22×C61#44912yes—
262C22×C61#44912yes—
263C22×C61#45512yes—
264C22×C61#45812yes—
265C22×C61C2×#12011yescharacteristic
266C22×C61C2×#13511yescharacteristic
267C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
268C2×D61—44no—
269C2×D61—42no—
270C2×D61—42no—
271C2×D61—42no—
272C2×D61—84no—
273C2×D61—84no—
274C2×D61—82no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—42no—
280C4×C61—82no—
281Dic61—42no—
282Dic61—42no—
283Dic61—42no—
284Dic61—82no—
285C2×#538—611no—
286C2×#483—611no—
287C2×#480D6111yescharacteristic, complemented
288C2×#397—611no—
289#1612—618no—
290C2×#328—611no—
291C2×#327—611no—
292C2×#323—611no—
293C2×C61—21no—
294C2×C61—21no—
295C2×C61—22no—
296C2×C61—82no—
297C2×C61#161214yescomplemented
298C2×C61C2×#44911yescharacteristic
299C2×C61C2×#45511yescharacteristic
300C2×C61C2×#45811yescharacteristic
301D61—82no—
302#538—614no—
303#538—1222no—
304#538—1222no—
305#538—1222no—
306C2×#126—1221no—
307C2×#124—1221no—
308C2×#123—1221no—
309C2×C22⋊Q8—611no—
310C2×#121—1221no—
311C2×#121C2×D6111yescharacteristic
312C2×#120—1221no—
313C2×C4×D4—1221no—
314C22×C4⋊C4C2×D6111yescharacteristic
315C22×C22⋊C4—611no—
316C22×C22⋊C4—1221no—
317#483—614no—
318#483—1222no—
319#480—22no—
320#480C2×D6114yescomplemented
321C2×#107—21no—
322C2×#106—1221no—
323C2×#103—1221no—
324C2×#102—21no—
325C2×C22⋊C8—611no—
326C2×C22⋊C8C2×D6111yescharacteristic
327#397—614no—
328#397—1222no—
329C2×#95—611no—
330C2×#95—1221no—
331#328—614no—
332#327—614no—
333#323—614no—
334C61C2×#161211yescharacteristic, complemented, Sylow
335C25—611no—
336C22×Q8—611no—
337C22×D4—21no—
338C22×D4—1221no—
339C22×D4—1221no—
340C22×D4C22⋊D6111yescharacteristic
341C23×C4—21no—
342C23×C4—611no—
343C23×C4—1221no—
344C23×C4—1221no—
345C23×C4C22×D6111yescharacteristic
346C22×C8—21no—
347C22×C8—1221no—
348#126—1224no—
349#126—1224no—
350#124—1224no—
351#124—1224no—
352#123—1224no—
353#123—1224no—
354C22⋊Q8—612no—
355C22⋊Q8—612no—
356C22⋊Q8—1221no—
357C22⋊Q8—1221no—
358#121—21no—
359#121—21no—
360#121—1224no—
361#121—1224no—
362#121C22⋊D6112yes—
363#121C22×D6112yes—
364#120—1224no—
365#120—1224no—
366C4×D4—1224no—
367C4×D4—1224no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4C22⋊D6111yescharacteristic
377C2×C4⋊C4C22×D6112yes—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—612no—
380C2×C22⋊C4—612no—
381C2×C22⋊C4—1221no—
382C2×C22⋊C4—1221no—
383C2×C22⋊C4—1221no—
384C2×C22⋊C4—1221no—
385C2×C22⋊C4—1221no—
386C2×C22⋊C4—1221no—
387C2×C22⋊C4—1221no—
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1224no—
390C2×C22⋊C4—2444no—
391C2×C42—1221no—
392#107—24no—
393#106—1224no—
394#103—1224no—
395#102—24no—
396C22⋊C8—21no—
397C22⋊C8—612no—
398C22⋊C8—1221no—
399C22⋊C8C22×D6112yes—
400#95—612no—
401#95—1224no—
402#95—1221no—
403C24—21no—
404C24—612no—
405C24—1221no—
406C24—1222no—
407C24—1221no—
408C24—1222no—
409C24—2442no—
410C24—2442no—
411C24D4×D6111yescharacteristic
412C2×Q8—612no—
413C2×Q8—1221no—
414C2×Q8—2442no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—1224no—
422C2×D4—1224no—
423C2×D4—4882no—
424C2×D4—4882no—
425C2×D4C2×C22⋊D6112yes—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—42no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—612no—
434C22×C4—1224no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1222no—
440C22×C4—4882no—
441C22×C4—2442no—
442C22×C4—2442no—
443C22×C4—2442no—
444C22×C4—2442no—
445C22×C4D4×D6111yescharacteristic
446C22×C4D4×D6111yescharacteristic
447C22×C4D4×D6111yescharacteristic
448C22×C4C2×C22⋊D6111yescharacteristic
449C22×C4C2×C22⋊D6111yescharacteristic
450C22×C4C23×D6111yescharacteristic
451C2×C8—22no—
452C2×C8—42no—
453C2×C8—1222no—
454C2×C8—2442no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—612no—
461C4⋊C4—1224no—
462C4⋊C4—1222no—
463C4⋊C4—1221no—
464C4⋊C4—1222no—
465C4⋊C4C2×C22⋊D6112yes—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—1224no—
469C22⋊C4—1224no—
470C22⋊C4—1224no—
471C22⋊C4—1222no—
472C22⋊C4—1222no—
473C22⋊C4—1222no—
474C22⋊C4—1222no—
475C22⋊C4—1222no—
476C22⋊C4—1222no—
477C22⋊C4—2448no—
478C42—1224no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—1222no—
486C23—1222no—
487C23—1222no—
488C23—4884no—
489C23—4881no—
490C23—4881no—
491C23—2448no—
492C23—2442no—
493C23—2442no—
494C23—2442no—
495C23—2442no—
496C23—2442no—
497C23—2442no—
498C23#1451974511yescharacteristic
499C23#1451974511yescharacteristic
500C23#1451979612yes—
501C23#1451980112yes—
502C23C2×D4×D6111yescharacteristic
503Q8—4881no—
504Q8—2442no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—44no—
509D4—81no—
510D4—4884no—
511D4—4884no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4—1222no—
526C2×C4—1222no—
527C2×C4—1222no—
528C2×C4—4884no—
529C2×C4—4881no—
530C2×C4—4884no—
531C2×C4—2442no—
532C2×C4—2442no—
533C2×C4—2442no—
534C2×C4—2442no—
535C2×C4—2442no—
536C2×C4—2442no—
537C2×C4—2442no—
538C2×C4#1451974511yescharacteristic
539C2×C4#1451974511yescharacteristic
540C2×C4C2×D4×D6111yescharacteristic
541C2×C4C22×C22⋊D6111yescharacteristic
542C8—42no—
543C8—2442no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—24no—
549C22—24no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—84no—
554C22—4882no—
555C22—4884no—
556C22—4884no—
557C22—2444no—
558C22—2442no—
559C22—2442no—
560C22—2442no—
561C22#1683990412yes—
562C22#1683990412yes—
563C22#1683993812yes—
564C22#1683995112yes—
565C22C2×#1451974511yescharacteristic
566C22C2×#1451979611yescharacteristic
567C22C2×#1451980111yescharacteristic
568C4—21no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—42no—
573C4—82no—
574C4—4882no—
575C4—2442no—
576C4—2442no—
577C4—2442no—
578C2—21no—
579C2—21no—
580C2—22no—
581C2—82no—
582C2—4882no—
583C2#2144483014yesdirect product factor
584C2C2×#1683990411yescharacteristic
585C2C2×#1683993811yescharacteristic
586C2C2×#1683995111yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#480C2
socleC23×C61#120
prime radicalC2×#16840349C2
hypercenterC2×#480D61
hypocenterC61C2×#1612
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C2×#16840092C2semidirect
3. C2×#16839688C2semidirect
4. #21444830C2direct (N × H)
5. C2×#16839500C2semidirect
6. C2×#16839496C2semidirect
7. C2×#16839485C2semidirect
8. C2×C61×#480C2semidirect
23. #16840092C22semidirect
28. #16839688C22semidirect
31. #16839500C22semidirect
32. #16839496C22semidirect
33. #16839485C22semidirect
37. C61×#480C22semidirect
287. C2×#480D61semidirect
297. C2×C61#1612semidirect
320. #480C2×D61semidirect
334. C61C2×#1612semidirect
583. C2#21444830direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403492
C2×#168400922
C2×#168396882
#214448302
C2×#168395002
C2×#168394962
C2×#168394852
C2×C61×#4802
C2×#161261