Finite Group Databasebeta

← C2×#21444912 #29655739

Subgroups — C2×#21444912 #29655739

Order 15616.

1030 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840487C211yesmaximal, characteristic, complemented
2C2×#16839959C211yesmaximal, characteristic
3C2×#16839959C211yesmaximal, characteristic
4#21444912C218yesmaximal, direct product factor
5C2×#16839508C211yesmaximal, characteristic, complemented
6C2×#16839494C211yesmaximal, characteristic, complemented
7C2×#16839494C211yesmaximal, characteristic, complemented
8C2×C61×#486C211yesmaximal, characteristic
9C22×#11758200—21no—
10C22×#11758200—21no—
11#16840487—22no—
12#16840487—22no—
13#16840487—22no—
14#16840487C2214yescomplemented
15C2×#14519775—21no—
16C2×#14519768—21no—
17C2×#14519767—22no—
18C2×Q8×Dic61—21no—
19C2×C4×Dic122C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C2×#14519742—21no—
22#16839959—22no—
23#16839959—22no—
24#16839959C2214yes—
25#16839959C2214yes—
26C2×C4⋊#92418C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519698—21no—
29C2×#14519698—21no—
30#16839508C2214yescomplemented
31#16839494C2214yescomplemented
32#16839494C2214yescomplemented
33C2×C4⋊Q8×C61C2211yescharacteristic
34C2×#127×C61C2211yescharacteristic
35C61×#486—22no—
36C61×#486C2214yes—
37C2×#102×C61—22no—
38C2×C4×C8×C61C2211yescharacteristic
39C22×Dic122D411yescharacteristic
40C22×Dic122D411yescharacteristic
41C2×#11758200—24no—
42C2×#11758200—24no—
43C2×#11758200—44no—
44C2×#11758200—44no—
45C22×#92418—21no—
46C22×#92418—21no—
47#14519775—24no—
48#14519775—24no—
49#14519768—24no—
50#14519768—24no—
51#14519767—28no—
52#14519767—28no—
53Q8×Dic61—24no—
54Q8×Dic61—24no—
55C4×Dic122—21no—
56C4×Dic122—21no—
57C4×Dic122—21no—
58C4×Dic122—21no—
59C4×Dic122D412yes—
60C4×Dic122D412yes—
61C4×Dic122C2312yes—
62C4×Dic122C2312yes—
63#14519742—24no—
64#14519742—24no—
65C2×C4⋊Dic61—22no—
66C2×C4⋊Dic61D411yescharacteristic
67C2×C4⋊Dic61D411yescharacteristic
68C2×#11758196—22no—
69C2×#11758196—22no—
70C2×#11758196—21no—
71C2×#11758196—21no—
72C2×C4×Dic61—22no—
73C2×C4×Dic61—21no—
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—
101C2×Q8×C61—22no—
102C2×Q8×C61—22no—
103C2×Q8×C61—42no—
104C2×Q8×C61—42no—
105C2×D4×C61—22no—
106C2×D4×C61—22no—
107C2×D4×C61—22no—
108C2×D4×C61—44no—
109C2×D4×C61—41no—
110C2×D4×C61—41no—
111C2×D4×C61—41no—
112C2×D4×C61—42no—
113C2×D4×C61—42no—
114C2×D4×C61—42no—
115C2×D4×C61—42no—
116C22×C4×C61—22no—
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×Dic61—21no—
121C22×Dic61—21no—
122C22×Dic61—21no—
123C22×Dic61—21no—
124C2×Dic122—21no—
125C2×Dic122—22no—
126C2×Dic122—22no—
127C2×Dic122—22no—
128C2×Dic122—21no—
129C2×Dic122SD1614yescomplemented
130C2×Dic122C2×D412yes—
131C2×Dic122C2×D412yes—
132C2×C8×C61—22no—
133C2×C8×C61—42no—
134C4⋊C4×C61—22no—
135C4⋊C4×C61—22no—
136C4⋊C4×C61—22no—
137C4⋊C4×C61C2×D414yes—
138C42×C61C2×D411yescharacteristic
139C42×C61C2×D411yescharacteristic
140C42×C61C2×D411yescharacteristic
141C42×C61C2411yescharacteristic
142#11758200—48no—
143#11758200—48no—
144C4⋊Dic61—28no—
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61C2×D412yes—
148C4⋊Dic61C2×D412yes—
149#11758196—28no—
150#11758196—28no—
151#11758196—22no—
152#11758196—22no—
153#11758196—22no—
154#11758196—22no—
155C4×Dic61—28no—
156C4×Dic61—22no—
157C4×Dic61—22no—
158C4×Dic61—22no—
159C4×Dic61—22no—
160C2×#92418—22no—
161C2×#92418—22no—
162C2×#92418—42no—
163C2×#92418—42no—
164C23×C61—42no—
165C23×C61—82no—
166C23×C61—82no—
167C23×C61—82no—
168C23×C61#12011yescharacteristic
169Q8×C61—42no—
170Q8×C61—42no—
171Q8×C61—44no—
172D4×C61—44no—
173D4×C61—42no—
174D4×C61—42no—
175D4×C61—42no—
176D4×C61—42no—
177D4×C61—82no—
178D4×C61—82no—
179D4×C61—82no—
180C2×C4×C61—22no—
181C2×C4×C61—24no—
182C2×C4×C61—44no—
183C2×C4×C61#12011yescharacteristic
184C2×C4×C61#12011yescharacteristic
185C2×C4×C61#12011yescharacteristic
186C2×C4×C61C2×SD1612yes—
187C2×C4×C61#13512yes—
188C2×C4×C61AGL(1,ℤ/8)12yes—
189C2×C4×C61#13712yes—
190C2×C4×C61C22×D411yescharacteristic
191C2×C4×C61C22×D411yescharacteristic
192C2×C4×C61C22×D411yescharacteristic
193C2×Dic61—22no—
194C2×Dic61—24no—
195C2×Dic61—22no—
196C2×Dic61—22no—
197C2×Dic61—22no—
198C2×Dic61—42no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201Dic122—22no—
202Dic122—24no—
203Dic122—22no—
204Dic122—22no—
205Dic122—42no—
206Dic122C2×SD1614yescomplemented
207C8×C61—42no—
208#92418—42no—
209#92418—42no—
210C2×#1626—611nomaximal, Sylow
211C22×C61—82no—
212C22×C61—82no—
213C22×C61—82no—
214C22×C61—164no—
215C22×C61#44812yes—
216C22×C61#44912yes—
217C22×C61#45412yes—
218C22×C61C2×#12011yescharacteristic
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—44no—
222C4×C61#44812yes—
223C4×C61#44912yes—
224C4×C61C22×SD1611yescharacteristic
225C4×C61C2×#13511yescharacteristic
226C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
227C4×C61C2×#13711yescharacteristic
228Dic61—24no—
229Dic61—42no—
230Dic61—42no—
231Dic61—42no—
232C2×#557—611no—
233C2×#486D6111yescharacteristic
234C2×#460—611no—
235C2×#460—611no—
236#1626—618no—
237C2×#332—611no—
238C2×Q8⋊C8—611no—
239C2×Q8⋊C8—611no—
240C2×C61—162no—
241C2×C61#162614yescomplemented
242C2×C61C2×#44811yescharacteristic
243C2×C61C2×#44911yescharacteristic
244C2×C61C2×#45411yescharacteristic
245C22×SD16—1221no—
246C22×SD16—1221no—
247#557—614no—
248#557—1222no—
249#557—1222no—
250#557—1222no—
251C2×C4⋊Q8—1221no—
252C2×C4⋊Q8C2×D6111yescharacteristic
253C2×#127C2×D6111yescharacteristic
254C2×#125—1221no—
255C2×#125—1222no—
256C2×C4×Q8—611no—
257C2×C4×Q8—611no—
258C2×C4×Q8—1221no—
259C2×C4×Q8—1221no—
260#486—22no—
261#486C2×D6114yes—
262#460—614no—
263#460—614no—
264#460—1222no—
265#460—1222no—
266C2×C4⋊C8—611no—
267C2×C4⋊C8—611no—
268C2×#102—22no—
269C2×#102—1221no—
270C2×#102—1221no—
271C2×C4×C8C2×D6111yescharacteristic
272#332—614no—
273Q8⋊C8—614no—
274Q8⋊C8—614no—
275C61C2×#162611yescharacteristic, complemented, Sylow
276C22×Q8—21no—
277C22×Q8—611no—
278C22×Q8—611no—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—21no—
282C2×SD16—1224no—
283C2×SD16—1224no—
284C2×SD16—2444no—
285C2×SD16—2444no—
286C22×C8—21no—
287C22×C8—1221no—
288C22×C8—1221no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—1224no—
292C4⋊Q8—1224no—
293C4⋊Q8C22⋊D6112yes—
294C4⋊Q8C22×D6112yes—
295#127—21no—
296#127—21no—
297#127—21no—
298#127C22×D6112yes—
299#125—1224no—
300#125—1228no—
301#125—1224no—
302#125—1228no—
303C4×Q8—612no—
304C4×Q8—612no—
305C4×Q8—612no—
306C4×Q8—612no—
307C4×Q8—1224no—
308C4×Q8—1224no—
309C4×Q8—1224no—
310C4×Q8—1224no—
311C4×Q8—1221no—
312C4×Q8—1221no—
313C4×Q8—1221no—
314C4×Q8—1221no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—611no—
317C2×C4⋊C4—611no—
318C2×C4⋊C4—1222no—
319C2×C4⋊C4—1222no—
320C2×C4⋊C4—1222no—
321C2×C4⋊C4—1221no—
322C2×C4⋊C4—1221no—
323C2×C4⋊C4C22⋊D6112yes—
324C2×C42—1222no—
325C2×C42—1221no—
326C2×C42—1221no—
327C2×C42C22×D6111yescharacteristic
328C4⋊C8—612no—
329C4⋊C8—612no—
330C4⋊C8—1221no—
331C4⋊C8—1221no—
332#102—28no—
333#102—1224no—
334#102—1224no—
335C4×C8—21no—
336C4×C8C22×D6112yes—
337C24—41no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—42no—
341C2×Q8—42no—
342C2×Q8—612no—
343C2×Q8—612no—
344C2×Q8—614no—
345C2×Q8—1221no—
346C2×Q8—1221no—
347C2×Q8—1222no—
348C2×Q8—1222no—
349C2×Q8—1222no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—44no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4—42no—
361C22×C4—22no—
362C22×C4—1221no—
363C22×C4—1221no—
364C22×C4—1221no—
365C22×C4—1221no—
366C22×C4D4×D6111yescharacteristic
367C22×C4D4×D6111yescharacteristic
368C22×C4C2×C22⋊D6111yescharacteristic
369SD16—2448no—
370SD16—2448no—
371C2×C8—22no—
372C2×C8—42no—
373C2×C8—1222no—
374C2×C8—1222no—
375C2×C8—2442no—
376C2×C8—2442no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—612no—
381C4⋊C4—612no—
382C4⋊C4—1228no—
383C4⋊C4—1228no—
384C4⋊C4—1228no—
385C4⋊C4—1222no—
386C4⋊C4—1222no—
387C4⋊C4—1221no—
388C4⋊C4—1221no—
389C4⋊C4—1222no—
390C4⋊C4—1222no—
391C4⋊C4C2×C22⋊D6114yes—
392C42—1228no—
393C42—1222no—
394C42—1222no—
395C42—1222no—
396C42—1222no—
397C42D4×D6111yescharacteristic
398C42D4×D6111yescharacteristic
399C42C2×C22⋊D6111yescharacteristic
400C42C23×D6111yescharacteristic
401C23—42no—
402C23—82no—
403C23—82no—
404C23—82no—
405C23#1451974511yescharacteristic
406Q8—42no—
407Q8—42no—
408Q8—44no—
409Q8—614no—
410Q8—1222no—
411Q8—1224no—
412Q8—1222no—
413Q8—1222no—
414Q8—2442no—
415D4—44no—
416D4—42no—
417D4—42no—
418D4—42no—
419D4—42no—
420D4—82no—
421D4—82no—
422D4—82no—
423C2×C4—22no—
424C2×C4—24no—
425C2×C4—44no—
426C2×C4—1222no—
427C2×C4—1224no—
428C2×C4—1222no—
429C2×C4—1222no—
430C2×C4—1222no—
431C2×C4—2442no—
432C2×C4—2442no—
433C2×C4—2442no—
434C2×C4#1451974511yescharacteristic
435C2×C4#1451974511yescharacteristic
436C2×C4#1451974511yescharacteristic
437C2×C4SD16×D6112yes—
438C2×C4#1451979612yes—
439C2×C4#1451980112yes—
440C2×C4#1451980612yes—
441C2×C4C2×D4×D6111yescharacteristic
442C2×C4C2×D4×D6111yescharacteristic
443C2×C4C22×C22⋊D6111yescharacteristic
444C8—42no—
445C8—2442no—
446C8—2442no—
447C22—82no—
448C22—82no—
449C22—82no—
450C22—164no—
451C22#1683989912yes—
452C22#1683990412yes—
453C22#1683993412yes—
454C22C2×#1451974511yescharacteristic
455C4—21no—
456C4—21no—
457C4—44no—
458C4—1224no—
459C4—2442no—
460C4—2442no—
461C4—2442no—
462C4#1683989912yes—
463C4#1683990412yes—
464C4C2×SD16×D6111yescharacteristic
465C4C2×#1451979611yescharacteristic
466C4C2×#1451980111yescharacteristic
467C4C2×#1451980611yescharacteristic
468C2—162no—
469C2#2144491214yesdirect product factor
470C2C2×#1683989911yescharacteristic
471C2C2×#1683990411yescharacteristic
472C2C2×#1683993411yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#486C2
socleC23×C61#120
prime radicalC2×#127×C61C22
hypercenterC2×#486D61
hypocenterC61C2×#1626
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×#16840487C2semidirect
4. #21444912C2direct (N × H)
5. C2×#16839508C2semidirect
6. C2×#16839494C2semidirect
7. C2×#16839494C2semidirect
14. #16840487C22semidirect
30. #16839508C22semidirect
31. #16839494C22semidirect
32. #16839494C22semidirect
129. C2×Dic122SD16semidirect
206. Dic122C2×SD16semidirect
241. C2×C61#1626semidirect
275. C61C2×#1626semidirect
469. C2#21444912direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404872
C2×#168399592
#214449122
C2×#168395082
C2×#168394942
C2×C61×#4862
C2×#162661