Finite Group Databasebeta

← C2×#21445046 #29655942

Subgroups — C2×#21445046 #29655942

Order 15616.

1042 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840477C211yesmaximal, characteristic
2C2×#16840114C211yesmaximal, characteristic, complemented
3C2×#16839964C211yesmaximal, characteristic, complemented
4#21445046C218yesmaximal, direct product factor
5C2×#16839510C211yesmaximal, characteristic, complemented
6C2×D4⋊#92418C211yesmaximal, characteristic, complemented
7C2×#16839489C211yesmaximal, characteristic, complemented
8C2×C61×#474C211yesmaximal, characteristic, complemented
9C22×#11758201—21no—
10#16840477—22no—
11#16840477—22no—
12#16840477—22no—
13#16840477C2214yes—
14C2×#14519777C2211yescharacteristic
15C2×#14519763—22no—
16C2×#14519751—21no—
17C2×#14519748—21no—
18C2×C4×D244C2211yescharacteristic
19C2×#14519736—21no—
20C2×#14519735—21no—
21#16840114—22no—
22#16840114C2214yescomplemented
23#16839964—22no—
24#16839964C2214yescomplemented
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519701—21no—
27C2×#14519700—22no—
28C2×C4×#92418C2211yescharacteristic
29#16839510C2214yescomplemented
30D4⋊#92418C2214yescomplemented
31#16839489C2214yescomplemented
32C2×C4⋊Q8×C61C2211yescharacteristic
33C2×C4×D4×C61C2211yescharacteristic
34C61×#474—22no—
35C61×#474C2214yescomplemented
36C2×#107×C61—21no—
37C2×C4⋊C8×C61C2211yescharacteristic
38C2×#102×C61—21no—
39C22×Dic122D412yes—
40C22×D244D411yescharacteristic
41C22×C22⋊D61—22no—
42C22×C4×D61—21no—
43C2×#11758201—24no—
44C2×#11758201—44no—
45C22×#92418—21no—
46C22×#92418—21no—
47#14519777—21no—
48#14519777—21no—
49#14519777D412yes—
50#14519777C2312yes—
51#14519763—28no—
52#14519763—28no—
53#14519751—24no—
54#14519751—24no—
55#14519748—24no—
56#14519748—24no—
57C4×D244—21no—
58C4×D244—21no—
59C4×D244D412yes—
60C4×D244C2312yes—
61#14519736—24no—
62#14519736—24no—
63#14519735—24no—
64#14519735—24no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61D411yescharacteristic
68C2×C22⋊Dic61—22no—
69C2×#11758198—22no—
70C2×#11758198—21no—
71C2×C4×Dic61—22no—
72C4⋊#92418—21no—
73C4⋊#92418C2312yes—
74#14519701—24no—
75#14519700—28no—
76C4×#92418—21no—
77C4×#92418C2312yes—
78C22×Q8×C61—21no—
79C22×D4×C61D411yescharacteristic
80C23×C4×C61—21no—
81C22×C8×C61—21no—
82C4⋊Q8×C61—21no—
83C4⋊Q8×C61—21no—
84C4⋊Q8×C61—21no—
85C4⋊Q8×C61C2312yes—
86C4×D4×C61—21no—
87C4×D4×C61—21no—
88C4×D4×C61D412yes—
89C4×D4×C61C2312yes—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61D411yescharacteristic
93C2×C22⋊C4×C61—21no—
94C2×C42×C61C2311yescharacteristic
95#107×C61—24no—
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2312yes—
98#102×C61—24no—
99C24×C61—21no—
100C23×D61—21no—
101C2×Q8×C61—22no—
102C2×Q8×C61—41no—
103C2×Q8×C61—42no—
104C2×Q8×C61—42no—
105C2×D4×C61—21no—
106C2×D4×C61—22no—
107C2×D4×C61—22no—
108C2×D4×C61C2×D412yes—
109C22×C4×C61—21no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—42no—
113C22×C4×C61—42no—
114C22×C4×C61—41no—
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C2×C22⋊D61—28no—
119C2×C22⋊D61—84no—
120C22×Dic61—21no—
121C22×Dic61—22no—
122C2×D244—22no—
123C2×D244—22no—
124C2×D244—21no—
125C2×D244C2×D412yes—
126C2×C4×D61—22no—
127C2×C4×D61—22no—
128C2×C4×D61—42no—
129C2×C4×D61—42no—
130C2×Dic122—22no—
131C2×Dic122—44no—
132C2×Dic122C2×D414yes—
133C2×C8×C61—22no—
134C2×C8×C61—42no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61—22no—
137C4⋊C4×C61—22no—
138C4⋊C4×C61—41no—
139C4⋊C4×C61—41no—
140C4⋊C4×C61C2×D412yes—
141C22⋊C4×C61—22no—
142C22⋊C4×C61—22no—
143C42×C61C2×D411yescharacteristic
144C42×C61C2×D411yescharacteristic
145C42×C61C2×D411yescharacteristic
146C42×C61C2411yescharacteristic
147C22⋊Dic61—28no—
148#11758201—48no—
149#11758198—28no—
150#11758198—22no—
151#11758198—22no—
152C4⋊Dic61—22no—
153C4⋊Dic61—22no—
154C4⋊Dic61—21no—
155C4⋊Dic61—22no—
156C4⋊Dic61—22no—
157C4⋊Dic61C2×D412yes—
158C4×Dic61—28no—
159C2×#92418—22no—
160C2×#92418—22no—
161C2×#92418—42no—
162C2×#92418—42no—
163C23×C61—22no—
164C23×C61—42no—
165C23×C61—42no—
166C23×C61—42no—
167C23×C61#12011yescharacteristic
168C22×D61—22no—
169C22×D61—42no—
170C22×D61—42no—
171C22×D61—42no—
172Q8×C61—42no—
173Q8×C61—42no—
174Q8×C61—82no—
175D4×C61—22no—
176D4×C61—22no—
177D4×C61—42no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61—44no—
184C2×C4×C61—42no—
185C2×C4×C61—82no—
186C2×C4×C61#12011yescharacteristic
187C2×C4×C61#12011yescharacteristic
188C2×C4×C61#12011yescharacteristic
189C2×C4×C61#13512yes—
190C2×C4×C61#13512yes—
191C2×C4×C61AGL(1,ℤ/8)12yes—
192C2×C4×C61#13712yes—
193C2×C4×C61C22×D411yescharacteristic
194C2×C4×C61C22×D411yescharacteristic
195C2×C4×C61C22×D411yescharacteristic
196C22⋊D61—88no—
197C2×Dic61—22no—
198C2×Dic61—24no—
199C2×Dic61—42no—
200C2×Dic61—44no—
201D244—22no—
202D244—22no—
203D244—42no—
204C4×D61—42no—
205C4×D61—42no—
206C4×D61—44no—
207Dic122—44no—
208Dic122—82no—
209C8×C61—42no—
210#92418—42no—
211#92418—42no—
212C2×#1646—611nomaximal, Sylow
213C22×C61—42no—
214C22×C61—42no—
215C22×C61—42no—
216C22×C61—84no—
217C22×C61#44912yes—
218C22×C61#45212yes—
219C22×C61#45512yes—
220C22×C61C2×#12011yescharacteristic
221C2×D61—42no—
222C2×D61—42no—
223C2×D61—42no—
224C2×D61—84no—
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—42no—
228C4×C61—82no—
229C4×C61#44912yes—
230C4×C61#45212yes—
231C4×C61C2×#13511yescharacteristic
232C4×C61C2×#13511yescharacteristic
233C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
234C4×C61C2×#13711yescharacteristic
235Dic61—42no—
236Dic61—44no—
237C2×#555—611no—
238C2×#487—611no—
239C2×#474D6111yescharacteristic, complemented
240C2×#461—611no—
241#1646—618no—
242C2×#333—611no—
243C2×D4⋊C8—611no—
244C2×D4⋊C8—611no—
245C2×C61—82no—
246C2×C61#164614yescomplemented
247C2×C61C2×#44911yescharacteristic
248C2×C61C2×#45211yescharacteristic
249C2×C61C2×#45511yescharacteristic
250D61—82no—
251C22×SD16—1221no—
252#555—614no—
253#555—1222no—
254#555—1222no—
255#555—1222no—
256C2×C4⋊Q8—611no—
257C2×C4⋊Q8C2×D6111yescharacteristic
258C2×#124—1222no—
259C2×#121—1221no—
260C2×#121—1221no—
261C2×C4×D4—611no—
262C2×C4×D4C2×D6111yescharacteristic
263C2×#117—1221no—
264C2×#117—1221no—
265#487—614no—
266#487—1222no—
267#474—22no—
268#474C2×D6114yescomplemented
269#461—614no—
270#461—1222no—
271C2×#107—21no—
272C2×C4⋊C8—611no—
273C2×C4⋊C8C2×D6111yescharacteristic
274C2×#103—1222no—
275C2×#103—1221no—
276C2×#102—21no—
277C2×C4×C8—611no—
278#333—614no—
279D4⋊C8—614no—
280D4⋊C8—614no—
281C61C2×#164611yescharacteristic, complemented, Sylow
282C22×Q8—21no—
283C22×Q8—612no—
284C22×D4—611no—
285C22×D4—1222no—
286C22×D4C22⋊D6111yescharacteristic
287C23×C4—21no—
288C23×C4—1221no—
289C2×SD16—1224no—
290C2×SD16—2444no—
291C22×C8—21no—
292C22×C8—1221no—
293C22×C8—1221no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8—612no—
298C4⋊Q8—612no—
299C4⋊Q8—1221no—
300C4⋊Q8—1221no—
301C4⋊Q8C22×D6112yes—
302#124—1228no—
303#124—1228no—
304#121—1224no—
305#121—1224no—
306#121—1224no—
307#121—1224no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4—612no—
311C4×D4—612no—
312C4×D4—1221no—
313C4×D4—1221no—
314C4×D4C22⋊D6112yes—
315C4×D4C22×D6112yes—
316#117—1224no—
317#117—1224no—
318#117—1224no—
319#117—1224no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—611no—
323C2×C4⋊C4—1221no—
324C2×C4⋊C4—1221no—
325C2×C4⋊C4C22⋊D6111yescharacteristic
326C2×C22⋊C4—21no—
327C2×C22⋊C4—1222no—
328C2×C22⋊C4—1222no—
329C2×C22⋊C4—1221no—
330C2×C42—1222no—
331C2×C42C22×D6111yescharacteristic
332#107—24no—
333C4⋊C8—21no—
334C4⋊C8—612no—
335C4⋊C8—1221no—
336C4⋊C8C22×D6112yes—
337#103—1228no—
338#103—1224no—
339#102—24no—
340C4×C8—612no—
341C4×C8—1221no—
342C24—21no—
343C24—1221no—
344C2×Q8—22no—
345C2×Q8—41no—
346C2×Q8—42no—
347C2×Q8—42no—
348C2×Q8—614no—
349C2×Q8—1222no—
350C2×Q8—2444no—
351C2×D4—22no—
352C2×D4—21no—
353C2×D4—22no—
354C2×D4—612no—
355C2×D4—1228no—
356C2×D4—1221no—
357C2×D4—1222no—
358C2×D4—1222no—
359C2×D4—4884no—
360C2×D4C2×C22⋊D6112yes—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—41no—
367C22×C4—1221no—
368C22×C4—1222no—
369C22×C4—1222no—
370C22×C4—1222no—
371C22×C4—2442no—
372C22×C4—2442no—
373C22×C4D4×D6111yescharacteristic
374C22×C4D4×D6111yescharacteristic
375C22×C4C2×C22⋊D6111yescharacteristic
376SD16—2448no—
377C2×C8—22no—
378C2×C8—42no—
379C2×C8—1222no—
380C2×C8—1222no—
381C2×C8—2442no—
382C2×C8—2442no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—612no—
389C4⋊C4—1222no—
390C4⋊C4—1222no—
391C4⋊C4—1221no—
392C4⋊C4—1222no—
393C4⋊C4—1222no—
394C4⋊C4C2×C22⋊D6112yes—
395C22⋊C4—22no—
396C22⋊C4—22no—
397C22⋊C4—1228no—
398C22⋊C4—1228no—
399C22⋊C4—1222no—
400C22⋊C4—1222no—
401C42—1228no—
402C42D4×D6111yescharacteristic
403C42D4×D6111yescharacteristic
404C42C2×C22⋊D6111yescharacteristic
405C42C23×D6111yescharacteristic
406C23—22no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—1222no—
411C23—2442no—
412C23—2442no—
413C23—2442no—
414C23#1451974511yescharacteristic
415Q8—42no—
416Q8—42no—
417Q8—82no—
418Q8—4882no—
419Q8—2444no—
420D4—22no—
421D4—22no—
422D4—42no—
423D4—1222no—
424D4—1222no—
425D4—4888no—
426D4—2442no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—82no—
435C2×C4—1222no—
436C2×C4—1224no—
437C2×C4—2444no—
438C2×C4—2442no—
439C2×C4—2442no—
440C2×C4—2442no—
441C2×C4—2444no—
442C2×C4#1451974511yescharacteristic
443C2×C4#1451974511yescharacteristic
444C2×C4#1451974511yescharacteristic
445C2×C4#1451979612yes—
446C2×C4#1451979712yes—
447C2×C4#1451980112yes—
448C2×C4#1451980812yes—
449C2×C4C2×D4×D6111yescharacteristic
450C2×C4C2×D4×D6111yescharacteristic
451C2×C4C22×C22⋊D6111yescharacteristic
452C8—42no—
453C8—2442no—
454C8—2442no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—84no—
459C22—4884no—
460C22—2442no—
461C22—2442no—
462C22—2442no—
463C22#1683990412yes—
464C22#1683992212yes—
465C22#1683993812yes—
466C22C2×#1451974511yescharacteristic
467C4—21no—
468C4—21no—
469C4—42no—
470C4—82no—
471C4—2444no—
472C4—2442no—
473C4#1683990412yes—
474C4#1683992212yes—
475C4C2×#1451979611yescharacteristic
476C4C2×#1451979711yescharacteristic
477C4C2×#1451980111yescharacteristic
478C4C2×#1451980811yescharacteristic
479C2—82no—
480C2—4882no—
481C2#2144504614yesdirect product factor
482C2C2×#1683990411yescharacteristic
483C2C2×#1683992211yescharacteristic
484C2C2×#1683993811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#474C2
socleC23×C61#120
prime radicalC2×#16840477C2
hypercenterC2×#474D61
hypocenterC61C2×#1646
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
2. C2×#16840114C2semidirect
3. C2×#16839964C2semidirect
4. #21445046C2direct (N × H)
5. C2×#16839510C2semidirect
6. C2×D4⋊#92418C2semidirect
7. C2×#16839489C2semidirect
8. C2×C61×#474C2semidirect
22. #16840114C22semidirect
24. #16839964C22semidirect
29. #16839510C22semidirect
30. D4⋊#92418C22semidirect
31. #16839489C22semidirect
35. C61×#474C22semidirect
239. C2×#474D61semidirect
246. C2×C61#1646semidirect
268. #474C2×D61semidirect
281. C61C2×#1646semidirect
481. C2#21445046direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404772
C2×#168401142
C2×#168399642
#214450462
C2×#168395102
C2×D4⋊#924182
C2×#168394892
C2×C61×#4742
C2×#164661