Finite Group Databasebeta

← C2×#21444926 #29655755

Subgroups — C2×#21444926 #29655755

Order 15616.

1062 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840486C211yesmaximal, characteristic, complemented
2C2×#16839959C211yesmaximal, characteristic, complemented
3C2×#16839954C211yesmaximal, characteristic
4#21444926C218yesmaximal, direct product factor
5C2×#16839508C211yesmaximal, characteristic, complemented
6C2×#16839494C211yesmaximal, characteristic, complemented
7C2×#16839491C211yesmaximal, characteristic, complemented
8C2×C61×#486C211yesmaximal, characteristic, complemented
9C22×#11758200—21no—
10C22×#11758199—21no—
11#16840486—22no—
12#16840486—22no—
13#16840486—22no—
14#16840486C2214yescomplemented
15C2×#14519772—22no—
16C2×#14519766—21no—
17C2×#14519757—21no—
18C2×Q8×Dic61—21no—
19C2×C4×Dic122C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×#14519735—21no—
22#16839959—22no—
23#16839959C2214yescomplemented
24#16839954—22no—
25#16839954C2214yes—
26C2×C4⋊#92418C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519698—21no—
29C2×#14519698—21no—
30#16839508C2214yescomplemented
31#16839494C2214yescomplemented
32#16839491C2214yescomplemented
33C2×C4⋊Q8×C61C2211yescharacteristic
34C2×#127×C61C2211yescharacteristic
35C61×#486—22no—
36C61×#486C2214yescomplemented
37C2×#102×C61—22no—
38C2×C4×C8×C61C2211yescharacteristic
39C22×Dic122D411yescharacteristic
40C22×D244D411yescharacteristic
41C22×C4×D61—21no—
42C2×#11758200—24no—
43C2×#11758200—44no—
44C2×#11758199—24no—
45C2×#11758199—44no—
46C22×#92418—21no—
47C22×#92418—21no—
48#14519772—28no—
49#14519772—28no—
50#14519766—24no—
51#14519766—24no—
52#14519757—24no—
53#14519757—24no—
54Q8×Dic61—24no—
55Q8×Dic61—24no—
56C4×Dic122—21no—
57C4×Dic122—21no—
58C4×Dic122D412yes—
59C4×Dic122C2312yes—
60C4×D244—21no—
61C4×D244—21no—
62C4×D244D412yes—
63C4×D244C2312yes—
64#14519735—24no—
65#14519735—24no—
66C2×C4⋊Dic61—22no—
67C2×C4⋊Dic61D411yescharacteristic
68C2×C4⋊Dic61D411yescharacteristic
69C2×#11758196—21no—
70C2×#11758198—22no—
71C2×#11758198—22no—
72C2×#11758198—21no—
73C2×C4×Dic61—22no—
74C2×C4×Dic61—21no—
75C4⋊#92418—21no—
76C4⋊#92418—21no—
77C4⋊#92418C2312yes—
78C4⋊#92418C2312yes—
79#14519698—24no—
80#14519698—24no—
81C22×Q8×C61—21no—
82C22×D4×C61—21no—
83C22×D4×C61—21no—
84C22×D4×C61—21no—
85C22×C8×C61—21no—
86C4⋊Q8×C61—21no—
87C4⋊Q8×C61—21no—
88C4⋊Q8×C61D412yes—
89C4⋊Q8×C61C2312yes—
90#127×C61—21no—
91#127×C61—21no—
92#127×C61—21no—
93#127×C61C2312yes—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61D412yes—
96C2×C42×C61C2311yescharacteristic
97#102×C61—28no—
98C4×C8×C61—21no—
99C4×C8×C61C2312yes—
100C24×C61—41no—
101C23×D61—21no—
102C2×Q8×C61—22no—
103C2×Q8×C61—22no—
104C2×Q8×C61—42no—
105C2×Q8×C61—42no—
106C2×D4×C61—22no—
107C2×D4×C61—22no—
108C2×D4×C61—22no—
109C2×D4×C61—44no—
110C2×D4×C61—41no—
111C2×D4×C61—41no—
112C2×D4×C61—41no—
113C2×D4×C61—42no—
114C2×D4×C61—42no—
115C2×D4×C61—42no—
116C2×D4×C61—42no—
117C22×C4×C61—22no—
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×Dic61—21no—
122C22×Dic61—21no—
123C22×Dic61—21no—
124C2×D244—22no—
125C2×D244—22no—
126C2×D244—21no—
127C2×D244C2×D412yes—
128C2×C4×D61—22no—
129C2×C4×D61—22no—
130C2×C4×D61—42no—
131C2×C4×D61—42no—
132C2×Dic122—22no—
133C2×Dic122—22no—
134C2×Dic122—21no—
135C2×Dic122C2×D412yes—
136C2×C8×C61—22no—
137C2×C8×C61—42no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61—22no—
140C4⋊C4×C61—22no—
141C4⋊C4×C61C2×D414yes—
142C42×C61C2×D411yescharacteristic
143C42×C61C2×D411yescharacteristic
144C42×C61C2×D411yescharacteristic
145C42×C61C2411yescharacteristic
146#11758200—48no—
147#11758199—48no—
148#11758198—28no—
149#11758198—28no—
150#11758198—22no—
151#11758198—22no—
152C4⋊Dic61—28no—
153C4⋊Dic61—21no—
154C4⋊Dic61—21no—
155C4⋊Dic61C2×D412yes—
156C4⋊Dic61C2×D412yes—
157#11758196—22no—
158#11758196—22no—
159C4×Dic61—28no—
160C4×Dic61—22no—
161C4×Dic61—22no—
162C2×#92418—22no—
163C2×#92418—22no—
164C2×#92418—42no—
165C2×#92418—42no—
166C23×C61—42no—
167C23×C61—82no—
168C23×C61—82no—
169C23×C61—82no—
170C23×C61#12011yescharacteristic
171C22×D61—22no—
172C22×D61—42no—
173C22×D61—42no—
174C22×D61—42no—
175Q8×C61—42no—
176Q8×C61—42no—
177Q8×C61—44no—
178D4×C61—44no—
179D4×C61—42no—
180D4×C61—42no—
181D4×C61—42no—
182D4×C61—42no—
183D4×C61—82no—
184D4×C61—82no—
185D4×C61—82no—
186C2×C4×C61—22no—
187C2×C4×C61—24no—
188C2×C4×C61—44no—
189C2×C4×C61#12011yescharacteristic
190C2×C4×C61#12011yescharacteristic
191C2×C4×C61#12011yescharacteristic
192C2×C4×C61#13512yes—
193C2×C4×C61#13512yes—
194C2×C4×C61AGL(1,ℤ/8)12yes—
195C2×C4×C61AGL(1,ℤ/8)12yes—
196C2×C4×C61C22×D411yescharacteristic
197C2×C4×C61C22×D411yescharacteristic
198C2×C4×C61C22×D411yescharacteristic
199C2×Dic61—22no—
200C2×Dic61—22no—
201C2×Dic61—22no—
202C2×Dic61—42no—
203C2×Dic61—42no—
204C2×Dic61—42no—
205D244—22no—
206D244—22no—
207D244—42no—
208C4×D61—42no—
209C4×D61—42no—
210C4×D61—44no—
211Dic122—22no—
212Dic122—22no—
213Dic122—42no—
214C8×C61—42no—
215#92418—42no—
216#92418—42no—
217C2×#1628—611nomaximal, Sylow
218C22×C61—82no—
219C22×C61—82no—
220C22×C61—82no—
221C22×C61—164no—
222C22×C61#44912yes—
223C22×C61#44912yes—
224C22×C61#45412yes—
225C22×C61C2×#12011yescharacteristic
226C2×D61—42no—
227C2×D61—42no—
228C2×D61—42no—
229C2×D61—84no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—44no—
233C4×C61#44912yes—
234C4×C61#44912yes—
235C4×C61C2×#13511yescharacteristic
236C4×C61C2×#13511yescharacteristic
237C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
238C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
239Dic61—42no—
240Dic61—42no—
241Dic61—42no—
242C2×#556—611no—
243C2×#486D6111yescharacteristic, complemented
244C2×#460—611no—
245C2×#459—611no—
246#1628—618no—
247C2×#332—611no—
248C2×Q8⋊C8—611no—
249C2×D4⋊C8—611no—
250C2×C61—162no—
251C2×C61#162814yescomplemented
252C2×C61C2×#44911yescharacteristic
253C2×C61C2×#44911yescharacteristic
254C2×C61C2×#45411yescharacteristic
255D61—82no—
256C22×SD16—1221no—
257C22×D8—1221no—
258#556—614no—
259#556—1222no—
260#556—1222no—
261#556—1222no—
262C2×C4⋊Q8C2×D6111yescharacteristic
263C2×#127C2×D6111yescharacteristic
264C2×#126—1222no—
265C2×#124—1221no—
266C2×C22⋊Q8—1221no—
267C2×C4×Q8—611no—
268C2×C4×Q8—1221no—
269C2×C4×D4—611no—
270C2×#117—1221no—
271#486—22no—
272#486C2×D6114yescomplemented
273#460—614no—
274#460—1222no—
275#459—614no—
276#459—1222no—
277C2×C4⋊C8—611no—
278C2×C4⋊C8—611no—
279C2×#102—22no—
280C2×#102—1221no—
281C2×#102—1221no—
282C2×C4×C8C2×D6111yescharacteristic
283#332—614no—
284Q8⋊C8—614no—
285D4⋊C8—614no—
286C61C2×#162811yescharacteristic, complemented, Sylow
287C22×Q8—21no—
288C22×Q8—611no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4—611no—
293C23×C4—1221no—
294C2×SD16—1224no—
295C2×SD16—2444no—
296C2×D8—1224no—
297C2×D8—2444no—
298C22×C8—21no—
299C22×C8—1221no—
300C22×C8—1221no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8C22⋊D6112yes—
304C4⋊Q8C22×D6112yes—
305#127—21no—
306#127—21no—
307#127—21no—
308#127C22×D6112yes—
309#126—1228no—
310#126—1228no—
311#124—1224no—
312#124—1224no—
313C22⋊Q8—1224no—
314C22⋊Q8—1224no—
315C4×Q8—612no—
316C4×Q8—612no—
317C4×Q8—1224no—
318C4×Q8—1224no—
319C4×Q8—1221no—
320C4×Q8—1221no—
321C4×D4—612no—
322C4×D4—612no—
323C4×D4—1221no—
324C4×D4—1221no—
325#117—1224no—
326#117—1224no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—611no—
329C2×C4⋊C4—611no—
330C2×C4⋊C4—1222no—
331C2×C4⋊C4—1221no—
332C2×C4⋊C4C22⋊D6112yes—
333C2×C22⋊C4—1222no—
334C2×C22⋊C4—1222no—
335C2×C22⋊C4—1221no—
336C2×C42—1222no—
337C2×C42—1221no—
338C2×C42C22×D6111yescharacteristic
339C4⋊C8—612no—
340C4⋊C8—612no—
341C4⋊C8—1221no—
342C4⋊C8—1221no—
343#102—28no—
344#102—1224no—
345#102—1224no—
346C4×C8—21no—
347C4×C8C22×D6112yes—
348C24—41no—
349C24—1221no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—42no—
353C2×Q8—42no—
354C2×Q8—612no—
355C2×Q8—1221no—
356C2×Q8—1222no—
357C2×Q8—1222no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—44no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4—612no—
370C2×D4—1221no—
371C2×D4—1222no—
372C2×D4—1222no—
373C22×C4—22no—
374C22×C4—1221no—
375C22×C4—1221no—
376C22×C4—1221no—
377C22×C4—1222no—
378C22×C4—1222no—
379C22×C4—2442no—
380C22×C4—2442no—
381C22×C4D4×D6111yescharacteristic
382C22×C4D4×D6111yescharacteristic
383C22×C4C2×C22⋊D6111yescharacteristic
384SD16—2448no—
385D8—2448no—
386C2×C8—22no—
387C2×C8—42no—
388C2×C8—1222no—
389C2×C8—1222no—
390C2×C8—2442no—
391C2×C8—2442no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—612no—
396C4⋊C4—612no—
397C4⋊C4—1228no—
398C4⋊C4—1222no—
399C4⋊C4—1221no—
400C4⋊C4—1221no—
401C4⋊C4—1222no—
402C4⋊C4C2×C22⋊D6114yes—
403C22⋊C4—1228no—
404C22⋊C4—1228no—
405C22⋊C4—1222no—
406C22⋊C4—1222no—
407C42—1228no—
408C42—1222no—
409C42—1222no—
410C42D4×D6111yescharacteristic
411C42D4×D6111yescharacteristic
412C42C2×C22⋊D6111yescharacteristic
413C42C23×D6111yescharacteristic
414C23—42no—
415C23—82no—
416C23—82no—
417C23—82no—
418C23—1222no—
419C23—2442no—
420C23—2442no—
421C23—2442no—
422C23#1451974511yescharacteristic
423Q8—42no—
424Q8—42no—
425Q8—44no—
426Q8—1222no—
427Q8—1222no—
428Q8—2442no—
429D4—44no—
430D4—42no—
431D4—42no—
432D4—42no—
433D4—42no—
434D4—82no—
435D4—82no—
436D4—82no—
437D4—1222no—
438D4—1222no—
439D4—2442no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—44no—
443C2×C4—1222no—
444C2×C4—1222no—
445C2×C4—1222no—
446C2×C4—2442no—
447C2×C4—2442no—
448C2×C4—2442no—
449C2×C4—2442no—
450C2×C4—2442no—
451C2×C4—2444no—
452C2×C4#1451974511yescharacteristic
453C2×C4#1451974511yescharacteristic
454C2×C4#1451974511yescharacteristic
455C2×C4#1451979612yes—
456C2×C4#1451979812yes—
457C2×C4#1451980112yes—
458C2×C4#1451980412yes—
459C2×C4C2×D4×D6111yescharacteristic
460C2×C4C2×D4×D6111yescharacteristic
461C2×C4C22×C22⋊D6111yescharacteristic
462C8—42no—
463C8—2442no—
464C8—2442no—
465C22—82no—
466C22—82no—
467C22—82no—
468C22—164no—
469C22—4884no—
470C22—2442no—
471C22—2442no—
472C22—2442no—
473C22#1683990412yes—
474C22#1683990612yes—
475C22#1683993412yes—
476C22C2×#1451974511yescharacteristic
477C4—21no—
478C4—21no—
479C4—44no—
480C4—2442no—
481C4—2442no—
482C4—2442no—
483C4#1683990412yes—
484C4#1683990612yes—
485C4C2×#1451979611yescharacteristic
486C4C2×#1451979811yescharacteristic
487C4C2×#1451980111yescharacteristic
488C4C2×#1451980411yescharacteristic
489C2—162no—
490C2—4882no—
491C2#2144492614yesdirect product factor
492C2C2×#1683990411yescharacteristic
493C2C2×#1683990611yescharacteristic
494C2C2×#1683993411yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#486C2
socleC23×C61#120
prime radicalC2×#16839954C2
hypercenterC2×#486D61
hypocenterC61C2×#1628
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×#16840486C2semidirect
2. C2×#16839959C2semidirect
4. #21444926C2direct (N × H)
5. C2×#16839508C2semidirect
6. C2×#16839494C2semidirect
7. C2×#16839491C2semidirect
8. C2×C61×#486C2semidirect
14. #16840486C22semidirect
23. #16839959C22semidirect
30. #16839508C22semidirect
31. #16839494C22semidirect
32. #16839491C22semidirect
36. C61×#486C22semidirect
243. C2×#486D61semidirect
251. C2×C61#1628semidirect
272. #486C2×D61semidirect
286. C61C2×#1628semidirect
491. C2#21444926direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404862
C2×#168399592
C2×#168399542
#214449262
C2×#168395082
C2×#168394942
C2×#168394912
C2×C61×#4862
C2×#162861