Finite Group Databasebeta

← C2×#21444449 #29648038

Subgroups — C2×#21444449 #29648038

Order 15616.

986 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840297C211yesmaximal, characteristic
2C2×#16839817C211yesmaximal, characteristic, complemented
3C2×#16839817C211yesmaximal, characteristic, complemented
4#21444449C218yesmaximal, direct product factor
5C2×#16839504C211yesmaximal, characteristic, complemented
6C2×#16839501C211yesmaximal, characteristic, complemented
7C2×#16839501C211yesmaximal, characteristic, complemented
8C2×C61×#330C211yesmaximal, characteristic, complemented
9#16840297—22no—
10#16840297—22no—
11#16840297C414yes—
12#16840297C2214yes—
13C2×#14519772—21no—
14C2×#14519765C2211yescharacteristic
15C2×#14519762—21no—
16C2×#14519757C411yescharacteristic
17C2×#14519752C411yescharacteristic
18C2×#14519742C411yescharacteristic
19C2×#14519739—21no—
20C2×#14519739C411yescharacteristic
21C2×#14519735—21no—
22C2×C42×D61C2211yescharacteristic
23#16839817—22no—
24#16839817—22no—
25#16839817C2214yescomplemented
26#16839817C2214yescomplemented
27C2×#14519706—21no—
28C2×#14519706—21no—
29C2×#14519689—21no—
30C2×#14519689—21no—
31C2×#14519688C2211yescharacteristic
32C2×#14519688C2211yescharacteristic
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—
49#14519772—24no—
50#14519772—24no—
51#14519765—21no—
52#14519765—21no—
53#14519765C2×C412yes—
54#14519765C2312yes—
55#14519762—24no—
56#14519762—24no—
57#14519757—22no—
58#14519757C2×C414yes—
59#14519752—22no—
60#14519752C2×C414yes—
61#14519742—22no—
62#14519742C2×C414yes—
63#14519739—24no—
64#14519739—24no—
65#14519739—22no—
66#14519739C2×C414yes—
67#14519735—24no—
68#14519735—24no—
69C2×C4⋊Dic61—21no—
70C2×#11758196—21no—
71C2×#11758198—21no—
72C2×#11758198—21no—
73C2×#11758198—21no—
74C2×#11758198—21no—
75C2×#11758198—21no—
76C2×C4×Dic61—21no—
77C2×C4×Dic61C2×C411yescharacteristic
78C2×C4×Dic61D411yescharacteristic
79C2×C4×Dic61D411yescharacteristic
80C42×D61C2×C412yes—
81C42×D61D412yes—
82C42×D61D412yes—
83C42×D61C2312yes—
84#14519706—24no—
85#14519706—24no—
86#14519689—24no—
87#14519689—24no—
88#14519688—21no—
89#14519688—21no—
90#14519688C2312yes—
91#14519688C2312yes—
92C22×C8×C61—21no—
93C22×C8×C61—21no—
94#125×C61—21no—
95#125×C61—21no—
96#125×C61C2×C412yes—
97#125×C61C2312yes—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61C2×C411yescharacteristic
101C2×C4⋊C4×C61C2×C411yescharacteristic
102C2×C42×C61C2311yescharacteristic
103#97×C61—21no—
104#97×C61—21no—
105#97×C61C2312yes—
106#97×C61C2312yes—
107C23×D61—21no—
108C23×D61C22⋊C411yescharacteristic
109C22×C4×C61—21no—
110C22×C4×C61—21no—
111C22×C4×C61C22×C411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×Dic61—21no—
115C22×Dic61C22⋊C411yescharacteristic
116C22×Dic61C22⋊C411yescharacteristic
117C22×Dic61C22⋊C411yescharacteristic
118C2×D244—24no—
119C2×D244—21no—
120C2×D244—42no—
121C2×D244—44no—
122C2×D244C22×C412yes—
123C2×C4×D61—24no—
124C2×C4×D61—42no—
125C2×C4×D61—42no—
126C2×C4×D61—42no—
127C2×C4×D61—44no—
128C2×C4×D61C22⋊C412yes—
129C2×C4×D61C22⋊C412yes—
130C2×C4×D61C22⋊C412yes—
131C2×C4×D61C22×C412yes—
132C2×C4×D61C2×D412yes—
133C2×C4×D61C2×D412yes—
134C2×Dic122—21no—
135C2×Dic122—42no—
136C2×Dic122C22×C412yes—
137C2×C8×C61—22no—
138C2×C8×C61—22no—
139C2×C8×C61—42no—
140C2×C8×C61—42no—
141C4⋊C4×C61—22no—
142C4⋊C4×C61—22no—
143C4⋊C4×C61—21no—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—22no—
146C4⋊C4×C61—22no—
147C4⋊C4×C61C22×C412yes—
148C4⋊C4×C61C22×C412yes—
149C42×C61C22×C411yescharacteristic
150C42×C61C2×D411yescharacteristic
151C42×C61C2×D411yescharacteristic
152C42×C61C2411yescharacteristic
153#11758198—24no—
154#11758198—22no—
155#11758198—22no—
156#11758198—22no—
157#11758198—22no—
158#11758198—24no—
159#11758198—24no—
160C4⋊Dic61—24no—
161#11758196—24no—
162C4×Dic61—24no—
163C4×Dic61C22⋊C412yes—
164C4×Dic61C22⋊C412yes—
165C4×Dic61C22⋊C412yes—
166C4×Dic61C22×C412yes—
167C4×Dic61C2×D412yes—
168C4×Dic61C2×D412yes—
169C2×#92418—22no—
170C2×#92418—22no—
171C2×#92418—42no—
172C2×#92418—42no—
173C23×C61C2×C22⋊C411yescharacteristic
174C22×D61—22no—
175C22×D61—22no—
176C22×D61—22no—
177C22×D61—22no—
178C22×D61—42no—
179C22×D61—42no—
180C22×D61—42no—
181C22×D61C2×C22⋊C412yes—
182C2×C4×C61—22no—
183C2×C4×C61—22no—
184C2×C4×C61—22no—
185C2×C4×C61—22no—
186C2×C4×C61—22no—
187C2×C4×C61—42no—
188C2×C4×C61—42no—
189C2×C4×C61C2×C22⋊C411yescharacteristic
190C2×C4×C61C2×C22⋊C411yescharacteristic
191C2×C4×C61C2×C22⋊C411yescharacteristic
192C2×C4×C61C23×C411yescharacteristic
193C2×C4×C61C22×D411yescharacteristic
194C2×C4×C61C22×D411yescharacteristic
195C2×Dic61—22no—
196C2×Dic61—22no—
197C2×Dic61—22no—
198C2×Dic61—22no—
199C2×Dic61—42no—
200C2×Dic61C2×C22⋊C412yes—
201C2×Dic61C2×C22⋊C412yes—
202C2×Dic61C2×C22⋊C412yes—
203D244—42no—
204D244—42no—
205D244—48no—
206C4×D61—42no—
207C4×D61—42no—
208C4×D61—42no—
209C4×D61—42no—
210C4×D61—42no—
211C4×D61—42no—
212C4×D61—48no—
213Dic122—42no—
214Dic122—42no—
215C8×C61—42no—
216C8×C61—42no—
217#92418—42no—
218#92418—42no—
219C2×#1535—611nomaximal, Sylow
220C22×C61#41312yes—
221C22×C61#42112yes—
222C22×C61#42112yes—
223C22×C61C22×C22⋊C411yescharacteristic
224C2×D61—22no—
225C2×D61—22no—
226C2×D61—22no—
227C2×D61—44no—
228C2×D61—42no—
229C2×D61—42no—
230C2×D61—42no—
231C2×D61—84no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—21no—
238C4×C61—42no—
239C4×C61—42no—
240Dic61—22no—
241Dic61—22no—
242Dic61—22no—
243Dic61—42no—
244C2×#529—611no—
245C2×#432—611no—
246C2×#432—611no—
247#1535—618no—
248C2×#330—611no—
249C2×#330D6111yescharacteristic, complemented
250C2×#329—611no—
251C2×#329—611no—
252C2×C61#153514yescomplemented
253C2×C61C2×#41311yescharacteristic
254C2×C61C2×#42111yescharacteristic
255C2×C61C2×#42111yescharacteristic
256D61—42no—
257D61—82no—
258#529—614no—
259#529—614no—
260#529—1222no—
261#529—1222no—
262C2×#126—1221no—
263C2×#125C2×D6111yescharacteristic
264C2×#124—611no—
265C2×#123—1221no—
266C2×C22⋊Q8—611no—
267C2×#121—611no—
268C2×C4×Q8—611no—
269C2×C4×D4—611no—
270C2×C4×D4—1221no—
271C2×#117—1221no—
272C22×C42—611no—
273#432—614no—
274#432—614no—
275#432—1222no—
276#432—1222no—
277C2×C4⋊C8—1221no—
278C2×C4⋊C8—1221no—
279C2×C22⋊C8—1221no—
280C2×C22⋊C8—1221no—
281C2×#97—611no—
282C2×#97—611no—
283C2×#97C2×D6111yescharacteristic
284C2×#97C2×D6111yescharacteristic
285#330—614no—
286#330C2×D6114yescomplemented
287#329—614no—
288#329—614no—
289C61C2×#153511yescharacteristic, complemented, Sylow
290C22×Q8—611no—
291C22×D4—611no—
292C22×D4—1221no—
293C23×C4—611no—
294C23×C4—611no—
295C23×C4—611no—
296C23×C4—1221no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—1221no—
300C22×C8—1221no—
301#126—1224no—
302#126—1224no—
303#125—21no—
304#125—21no—
305#125C4×D6112yes—
306#125C22×D6112yes—
307#124—612no—
308#124—612no—
309#124—1221no—
310#124—1221no—
311#123—1224no—
312#123—1224no—
313C22⋊Q8—614no—
314C22⋊Q8—1222no—
315#121—614no—
316#121—1222no—
317C4×Q8—614no—
318C4×Q8—1222no—
319C4×D4—614no—
320C4×D4—1222no—
321C4×D4—1224no—
322C4×D4—1224no—
323#117—1224no—
324#117—1224no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—1221no—
328C2×C4⋊C4—1221no—
329C2×C4⋊C4C4×D6111yescharacteristic
330C2×C4⋊C4C4×D6111yescharacteristic
331C2×C22⋊C4—1221no—
332C2×C22⋊C4—1221no—
333C2×C22⋊C4—1221no—
334C2×C22⋊C4—1221no—
335C2×C22⋊C4—1221no—
336C2×C42—611no—
337C2×C42—611no—
338C2×C42—611no—
339C2×C42—612no—
340C2×C42—612no—
341C2×C42—612no—
342C2×C42—612no—
343C2×C42—1221no—
344C2×C42C22×D6111yescharacteristic
345C4⋊C8—1224no—
346C4⋊C8—1224no—
347C22⋊C8—1224no—
348C22⋊C8—1224no—
349#97—21no—
350#97—21no—
351#97—612no—
352#97—612no—
353#97—1221no—
354#97—1221no—
355#97C22×D6112yes—
356#97C22×D6112yes—
357C24—611no—
358C24—1221no—
359C2×Q8—612no—
360C2×Q8—1221no—
361C2×Q8—2442no—
362C2×D4—612no—
363C2×D4—1224no—
364C2×D4—1221no—
365C2×D4—2442no—
366C2×D4—2444no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—611no—
370C22×C4—611no—
371C22×C4—611no—
372C22×C4—612no—
373C22×C4—612no—
374C22×C4—612no—
375C22×C4—612no—
376C22×C4—612no—
377C22×C4—612no—
378C22×C4—1224no—
379C22×C4—1221no—
380C22×C4—2442no—
381C22×C4—2442no—
382C22×C4—2442no—
383C22×C4—2444no—
384C22×C4C2×C4×D6111yescharacteristic
385C22×C4D4×D6111yescharacteristic
386C22×C4D4×D6111yescharacteristic
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—42no—
390C2×C8—42no—
391C2×C8—1222no—
392C2×C8—1222no—
393C2×C8—2442no—
394C2×C8—2442no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—1224no—
402C4⋊C4—1224no—
403C4⋊C4C2×C4×D6112yes—
404C4⋊C4C2×C4×D6112yes—
405C22⋊C4—1224no—
406C22⋊C4—1224no—
407C22⋊C4—1224no—
408C22⋊C4—1222no—
409C22⋊C4—1222no—
410C22⋊C4—1222no—
411C22⋊C4—1222no—
412C42—612no—
413C42—612no—
414C42—612no—
415C42—612no—
416C42—612no—
417C42—612no—
418C42—1224no—
419C42C2×C4×D6111yescharacteristic
420C42D4×D6111yescharacteristic
421C42D4×D6111yescharacteristic
422C42C23×D6111yescharacteristic
423C23—612no—
424C23—1222no—
425C23—1222no—
426C23—1222no—
427C23—1222no—
428C23—2442no—
429C23—2442no—
430C23—2442no—
431C23C22⋊C4×D6111yescharacteristic
432Q8—2442no—
433Q8—2442no—
434D4—2442no—
435D4—2442no—
436D4—2448no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—612no—
445C2×C4—612no—
446C2×C4—612no—
447C2×C4—1222no—
448C2×C4—1222no—
449C2×C4—1222no—
450C2×C4—1222no—
451C2×C4—2442no—
452C2×C4—2442no—
453C2×C4—2442no—
454C2×C4—2442no—
455C2×C4—2442no—
456C2×C4—2442no—
457C2×C4—2448no—
458C2×C4—2442no—
459C2×C4C22⋊C4×D6111yescharacteristic
460C2×C4C22⋊C4×D6111yescharacteristic
461C2×C4C22⋊C4×D6111yescharacteristic
462C2×C4C22×C4×D6111yescharacteristic
463C2×C4C2×D4×D6111yescharacteristic
464C2×C4C2×D4×D6111yescharacteristic
465C8—42no—
466C8—42no—
467C8—2442no—
468C8—2442no—
469C22—1222no—
470C22—1222no—
471C22—1222no—
472C22—4884no—
473C22—2442no—
474C22—2442no—
475C22—2442no—
476C22—2444no—
477C22#1683974512yes—
478C22#1683977712yes—
479C22#1683977712yes—
480C22C2×C22⋊C4×D6111yescharacteristic
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—42no—
488C4—42no—
489C4—1222no—
490C4—1222no—
491C4—1222no—
492C4—2442no—
493C2—4882no—
494C2—2442no—
495C2#2144444914yesdirect product factor
496C2C2×#1683974511yescharacteristic
497C2C2×#1683977711yescharacteristic
498C2C2×#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×#1535
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×#16839817C2semidirect
4. #21444449C2direct (N × H)
5. C2×#16839504C2semidirect
6. C2×#16839501C2semidirect
7. C2×#16839501C2semidirect
8. C2×C61×#330C2semidirect
25. #16839817C22semidirect
26. #16839817C22semidirect
33. #16839504C22semidirect
34. #16839501C22semidirect
35. #16839501C22semidirect
39. C61×#330C22semidirect
249. C2×#330D61semidirect
252. C2×C61#1535semidirect
286. #330C2×D61semidirect
289. C61C2×#1535semidirect
495. C2#21444449direct (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
#214444492
C2×#168395042
C2×#168395012
C2×C61×#3302
C2×#153561