Finite Group Databasebeta

← C2×#21444438 #29647948

Subgroups — C2×#21444438 #29647948

Order 15616.

1082 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840297C211yesmaximal, characteristic
2C2×#16839817C211yesmaximal, characteristic, complemented
3C2×#97×D61C211yesmaximal, characteristic, complemented
4#21444438C218yesmaximal, direct product factor
5C2×#16839504C211yesmaximal, characteristic, complemented
6C2×#16839501C211yesmaximal, characteristic, complemented
7C2×#16839501C211yesmaximal, characteristic, complemented
8C2×C61×#330C211yesmaximal, characteristic, complemented
9C22×C8×D61—21no—
10#16840297—22no—
11#16840297—22no—
12#16840297C414yes—
13#16840297C2214yes—
14C2×#14519772—21no—
15C2×#14519765C2211yescharacteristic
16C2×#14519762—21no—
17C2×#14519757C411yescharacteristic
18C2×#14519752C411yescharacteristic
19C2×#14519742C411yescharacteristic
20C2×#14519739—21no—
21C2×#14519739C411yescharacteristic
22C2×#14519735—21no—
23C2×C42×D61C2211yescharacteristic
24#16839817—22no—
25#16839817C2214yescomplemented
26C2×#14519706—21no—
27C2×#14519689—21no—
28C2×#14519688C2211yescharacteristic
29C2×#14519688C2211yescharacteristic
30C2×#14519687—21no—
31#97×D61—22no—
32#97×D61C2214yescomplemented
33#16839504C2214yescomplemented
34#16839501C2214yescomplemented
35#16839501C2214yescomplemented
36C2×#125×C61C2211yescharacteristic
37C2×#97×C61C2211yescharacteristic
38C2×#97×C61C2211yescharacteristic
39C61×#330C2214yescomplemented
40C22×Dic122C2×C411yescharacteristic
41C22×D244—21no—
42C22×D244C2×C411yescharacteristic
43C22×C4×D61—21no—
44C22×C4×D61C2×C411yescharacteristic
45C22×C4×D61D411yescharacteristic
46C22×C4×D61D411yescharacteristic
47C22×#92418—21no—
48C22×#92418—21no—
49C2×C8×D61—28no—
50C2×C8×D61—24no—
51#14519772—24no—
52#14519772—24no—
53#14519765—21no—
54#14519765—21no—
55#14519765C2×C412yes—
56#14519765C2312yes—
57#14519762—24no—
58#14519762—24no—
59#14519757—22no—
60#14519757C2×C414yes—
61#14519752—22no—
62#14519752C2×C414yes—
63#14519742—22no—
64#14519742C2×C414yes—
65#14519739—24no—
66#14519739—24no—
67#14519739—22no—
68#14519739C2×C414yes—
69#14519735—24no—
70#14519735—24no—
71C2×C4⋊Dic61—21no—
72C2×#11758196—21no—
73C2×#11758198—21no—
74C2×#11758198—21no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×C4×Dic61—21no—
79C2×C4×Dic61C2×C411yescharacteristic
80C2×C4×Dic61D411yescharacteristic
81C2×C4×Dic61D411yescharacteristic
82C42×D61C2×C412yes—
83C42×D61D412yes—
84C42×D61D412yes—
85C42×D61C2312yes—
86#14519706—24no—
87#14519689—24no—
88#14519688—21no—
89#14519688—21no—
90#14519688C2312yes—
91#14519688C2312yes—
92#14519687—24no—
93C22×C8×C61—21no—
94C22×C8×C61—21no—
95#125×C61—21no—
96#125×C61—21no—
97#125×C61C2×C412yes—
98#125×C61C2312yes—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61C2×C411yescharacteristic
102C2×C4⋊C4×C61C2×C411yescharacteristic
103C2×C42×C61C2311yescharacteristic
104#97×C61—21no—
105#97×C61—21no—
106#97×C61C2312yes—
107#97×C61C2312yes—
108C23×D61—21no—
109C23×D61C22⋊C411yescharacteristic
110C22×C4×C61—21no—
111C22×C4×C61—21no—
112C22×C4×C61C22×C411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×Dic61—21no—
116C22×Dic61C22⋊C411yescharacteristic
117C22×Dic61C22⋊C411yescharacteristic
118C22×Dic61C22⋊C411yescharacteristic
119C2×D244—24no—
120C2×D244—21no—
121C2×D244—42no—
122C2×D244—44no—
123C2×D244C22×C412yes—
124C2×C4×D61—24no—
125C2×C4×D61—24no—
126C2×C4×D61—42no—
127C2×C4×D61—42no—
128C2×C4×D61—44no—
129C2×C4×D61C22⋊C412yes—
130C2×C4×D61C22⋊C412yes—
131C2×C4×D61C22⋊C412yes—
132C2×C4×D61C22×C412yes—
133C2×C4×D61C2×D412yes—
134C2×C4×D61C2×D412yes—
135C2×Dic122—21no—
136C2×Dic122—42no—
137C2×Dic122C22×C412yes—
138C2×C8×C61—24no—
139C2×C8×C61—22no—
140C2×C8×C61—22no—
141C2×C8×C61—42no—
142C4⋊C4×C61—22no—
143C4⋊C4×C61—22no—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—22no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61C22×C412yes—
149C4⋊C4×C61C22×C412yes—
150C42×C61C22×C411yescharacteristic
151C42×C61C2×D411yescharacteristic
152C42×C61C2×D411yescharacteristic
153C42×C61C2411yescharacteristic
154#11758198—24no—
155#11758198—22no—
156#11758198—22no—
157#11758198—22no—
158#11758198—22no—
159#11758198—24no—
160#11758198—24no—
161C4⋊Dic61—24no—
162#11758196—24no—
163C4×Dic61—24no—
164C4×Dic61C22⋊C412yes—
165C4×Dic61C22⋊C412yes—
166C4×Dic61C22⋊C412yes—
167C4×Dic61C22×C412yes—
168C4×Dic61C2×D412yes—
169C4×Dic61C2×D412yes—
170C2×#92418—24no—
171C2×#92418—22no—
172C2×#92418—22no—
173C2×#92418—42no—
174C8×D61—216no—
175C23×C61C2×C22⋊C411yescharacteristic
176C22×D61—22no—
177C22×D61—22no—
178C22×D61—22no—
179C22×D61—42no—
180C22×D61—42no—
181C22×D61—42no—
182C22×D61#10414yes—
183C22×D61C2×C22⋊C412yes—
184C2×C4×C61—22no—
185C2×C4×C61—22no—
186C2×C4×C61—22no—
187C2×C4×C61—22no—
188C2×C4×C61—22no—
189C2×C4×C61—42no—
190C2×C4×C61—42no—
191C2×C4×C61C2×C22⋊C411yescharacteristic
192C2×C4×C61C2×C22⋊C411yescharacteristic
193C2×C4×C61C2×C22⋊C411yescharacteristic
194C2×C4×C61C23×C411yescharacteristic
195C2×C4×C61C22×D411yescharacteristic
196C2×C4×C61C22×D411yescharacteristic
197C2×Dic61—22no—
198C2×Dic61—22no—
199C2×Dic61—22no—
200C2×Dic61—22no—
201C2×Dic61—42no—
202C2×Dic61C2×C22⋊C412yes—
203C2×Dic61C2×C22⋊C412yes—
204C2×Dic61C2×C22⋊C412yes—
205D244—42no—
206D244—42no—
207D244—48no—
208C4×D61—24no—
209C4×D61—24no—
210C4×D61—42no—
211C4×D61—42no—
212C4×D61—42no—
213C4×D61—42no—
214C4×D61—48no—
215Dic122—42no—
216Dic122—42no—
217C8×C61—24no—
218C8×C61—42no—
219#92418—24no—
220#92418—42no—
221C2×#1532—611nomaximal, Sylow
222C22×C61#41312yes—
223C22×C61C2×#10412yes—
224C22×C61#42112yes—
225C22×C61C22×C22⋊C411yescharacteristic
226C2×D61—22no—
227C2×D61—22no—
228C2×D61—28no—
229C2×D61—42no—
230C2×D61—42no—
231C2×D61—42no—
232C2×D61—84no—
233C2×D61C2×#10414yes—
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—21no—
240C4×C61—42no—
241C4×C61—42no—
242Dic61—22no—
243Dic61—22no—
244Dic61—22no—
245Dic61—42no—
246C2×#529—611no—
247C2×#432—611no—
248C22×#97—611no—
249#1532—618no—
250C2×#330—611no—
251C2×#330D6111yescharacteristic, complemented
252C2×#329—611no—
253C2×#329—611no—
254C2×C61#153214yescomplemented
255C2×C61C2×#41311yescharacteristic
256C2×C61C22×#10411yescharacteristic
257C2×C61C2×#42111yescharacteristic
258D61—24no—
259D61—82no—
260C23×C8—1221no—
261#529—614no—
262#529—614no—
263#529—1222no—
264#529—1222no—
265C2×#126—1221no—
266C2×#125C2×D6111yescharacteristic
267C2×#124—611no—
268C2×#123—1221no—
269C2×C22⋊Q8—611no—
270C2×#121—611no—
271C2×C4×Q8—611no—
272C2×C4×D4—611no—
273C2×C4×D4—1221no—
274C2×#117—1221no—
275C22×C42—611no—
276#432—614no—
277#432—1222no—
278C2×C4⋊C8—1221no—
279C2×C22⋊C8—1221no—
280C2×#97—611no—
281C2×#97—611no—
282C2×#97—614no—
283C2×#97—1222no—
284C2×#97—1221no—
285C2×#97C2×D6111yescharacteristic
286C2×#97C2×D6111yescharacteristic
287#330—614no—
288#330C2×D6114yescomplemented
289#329—614no—
290#329—614no—
291C61C2×#153211yescharacteristic, complemented, Sylow
292C22×Q8—611no—
293C22×D4—611no—
294C22×D4—1221no—
295C23×C4—611no—
296C23×C4—611no—
297C23×C4—611no—
298C23×C4—1221no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—1224no—
302C22×C8—1228no—
303C22×C8—1221no—
304C22×C8—1221no—
305#126—1224no—
306#126—1224no—
307#125—21no—
308#125—21no—
309#125C4×D6112yes—
310#125C22×D6112yes—
311#124—612no—
312#124—612no—
313#124—1221no—
314#124—1221no—
315#123—1224no—
316#123—1224no—
317C22⋊Q8—614no—
318C22⋊Q8—1222no—
319#121—614no—
320#121—1222no—
321C4×Q8—614no—
322C4×Q8—1222no—
323C4×D4—614no—
324C4×D4—1222no—
325C4×D4—1224no—
326C4×D4—1224no—
327#117—1224no—
328#117—1224no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—1221no—
332C2×C4⋊C4—1221no—
333C2×C4⋊C4C4×D6111yescharacteristic
334C2×C4⋊C4C4×D6111yescharacteristic
335C2×C22⋊C4—1221no—
336C2×C22⋊C4—1221no—
337C2×C22⋊C4—1221no—
338C2×C22⋊C4—1221no—
339C2×C22⋊C4—1221no—
340C2×C42—611no—
341C2×C42—611no—
342C2×C42—611no—
343C2×C42—612no—
344C2×C42—612no—
345C2×C42—612no—
346C2×C42—612no—
347C2×C42—1221no—
348C2×C42C22×D6111yescharacteristic
349C4⋊C8—1224no—
350C22⋊C8—1224no—
351#97—21no—
352#97—21no—
353#97—612no—
354#97—612no—
355#97—1224no—
356#97—1221no—
357#97—1221no—
358#97C22×D6112yes—
359#97C22×D6112yes—
360C24—611no—
361C24—1221no—
362C2×Q8—612no—
363C2×Q8—1221no—
364C2×Q8—2442no—
365C2×D4—612no—
366C2×D4—1224no—
367C2×D4—1221no—
368C2×D4—2442no—
369C2×D4—2444no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—612no—
376C22×C4—612no—
377C22×C4—612no—
378C22×C4—612no—
379C22×C4—612no—
380C22×C4—612no—
381C22×C4—1224no—
382C22×C4—1224no—
383C22×C4—1221no—
384C22×C4—2442no—
385C22×C4—2442no—
386C22×C4—2444no—
387C22×C4C2×C4×D6111yescharacteristic
388C22×C4D4×D6111yescharacteristic
389C22×C4D4×D6111yescharacteristic
390C2×C8—24no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—42no—
394C2×C8—12216no—
395C2×C8—1224no—
396C2×C8—1222no—
397C2×C8—1222no—
398C2×C8—2442no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—1224no—
406C4⋊C4—1224no—
407C4⋊C4C2×C4×D6112yes—
408C4⋊C4C2×C4×D6112yes—
409C22⋊C4—1224no—
410C22⋊C4—1224no—
411C22⋊C4—1224no—
412C22⋊C4—1222no—
413C22⋊C4—1222no—
414C22⋊C4—1222no—
415C22⋊C4—1222no—
416C42—612no—
417C42—612no—
418C42—612no—
419C42—612no—
420C42—612no—
421C42—612no—
422C42—1224no—
423C42C2×C4×D6111yescharacteristic
424C42D4×D6111yescharacteristic
425C42D4×D6111yescharacteristic
426C42C23×D6111yescharacteristic
427C23—612no—
428C23—614no—
429C23—1222no—
430C23—1222no—
431C23—1222no—
432C23—2442no—
433C23—2442no—
434C23—2442no—
435C23C22⋊C4×D6111yescharacteristic
436Q8—2442no—
437Q8—2442no—
438D4—2442no—
439D4—2442no—
440D4—2448no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—612no—
449C2×C4—612no—
450C2×C4—612no—
451C2×C4—1224no—
452C2×C4—1224no—
453C2×C4—1222no—
454C2×C4—1222no—
455C2×C4—1222no—
456C2×C4—1222no—
457C2×C4—2442no—
458C2×C4—2442no—
459C2×C4—2442no—
460C2×C4—2442no—
461C2×C4—2448no—
462C2×C4—2442no—
463C2×C4C22⋊C4×D6111yescharacteristic
464C2×C4C22⋊C4×D6111yescharacteristic
465C2×C4C22⋊C4×D6111yescharacteristic
466C2×C4C22×C4×D6111yescharacteristic
467C2×C4C2×D4×D6111yescharacteristic
468C2×C4C2×D4×D6111yescharacteristic
469C8—24no—
470C8—42no—
471C8—1224no—
472C8—2442no—
473C22—614no—
474C22—1222no—
475C22—1228no—
476C22—1222no—
477C22—4884no—
478C22—2442no—
479C22—2442no—
480C22—2442no—
481C22#1683974512yes—
482C22#104×D6112yes—
483C22#1683977712yes—
484C22C2×C22⋊C4×D6111yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—42no—
492C4—42no—
493C4—1222no—
494C4—1222no—
495C4—1222no—
496C4—2442no—
497C2—1224no—
498C2—4882no—
499C2#2144443814yesdirect product factor
500C2C2×#1683974511yescharacteristic
501C2C2×#104×D6111yescharacteristic
502C2C2×#1683977711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC2×C61×#330C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C4
cosocleC42×C61C24
hypercenterC2×#330D61
hypocenterC61C2×#1532
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
2. C2×#16839817C2semidirect
3. C2×#97×D61C2semidirect
4. #21444438C2direct (N × H)
5. C2×#16839504C2semidirect
6. C2×#16839501C2semidirect
7. C2×#16839501C2semidirect
8. C2×C61×#330C2semidirect
25. #16839817C22semidirect
32. #97×D61C22semidirect
33. #16839504C22semidirect
34. #16839501C22semidirect
35. #16839501C22semidirect
39. C61×#330C22semidirect
251. C2×#330D61semidirect
254. C2×C61#1532semidirect
288. #330C2×D61semidirect
291. C61C2×#1532semidirect
499. C2#21444438direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402972
C2×#168398172
C2×#97×D612
#214444382
C2×#168395042
C2×#168395012
C2×C61×#3302
C2×#153261