Finite Group Databasebeta

← C2×#21444436 #29647946

Subgroups — C2×#21444436 #29647946

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×#16840291C211yesmaximal, characteristic
2C2×#16839817C211yesmaximal, characteristic, complemented
3C2×#97×D61C211yesmaximal, characteristic, complemented
4#21444436C218yesmaximal, direct product factor
5C2×#16839503C211yesmaximal, characteristic, complemented
6C2×#16839503C211yesmaximal, characteristic, complemented
7C2×#16839502C211yesmaximal, characteristic, complemented
8C2×C61×#329C211yesmaximal, characteristic, complemented
9C22×C8×D61—21no—
10#16840291—22no—
11#16840291—22no—
12#16840291C414yes—
13#16840291C2214yes—
14C2×#14519770—21no—
15C2×#14519769C2211yescharacteristic
16C2×#14519759—21no—
17C2×#14519753C411yescharacteristic
18C2×#14519748C411yescharacteristic
19C2×Q8×Dic61C411yescharacteristic
20C2×D4×Dic61C411yescharacteristic
21C2×#14519737—21no—
22C2×#14519733—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#16839503C2214yescomplemented
34#16839503C2214yescomplemented
35#16839502C2214yescomplemented
36C2×#124×C61C2211yescharacteristic
37C2×#97×C61C2211yescharacteristic
38C2×#97×C61C2211yescharacteristic
39C61×#329C2214yescomplemented
40C22×C22⋊D61—21no—
41C23×Dic61—21no—
42C22×C4×D61C2×C411yescharacteristic
43C22×C4×D61D411yescharacteristic
44C22×C4×D61D411yescharacteristic
45C22×#92418—21no—
46C22×#92418—21no—
47C2×C8×D61—28no—
48C2×C8×D61—24no—
49#14519770—24no—
50#14519770—24no—
51#14519769—21no—
52#14519769—21no—
53#14519769C2×C412yes—
54#14519769C2312yes—
55#14519759—24no—
56#14519759—24no—
57#14519753—22no—
58#14519753C2×C414yes—
59#14519748—22no—
60#14519748C2×C414yes—
61Q8×Dic61—22no—
62Q8×Dic61C2×C414yes—
63D4×Dic61—22no—
64D4×Dic61C2×C414yes—
65#14519737—24no—
66#14519737—24no—
67#14519733—24no—
68#14519733—24no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61C2×C411yescharacteristic
71C2×C4⋊Dic61C2×C411yescharacteristic
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×C22⋊Dic61—21no—
76C2×C22⋊Dic61—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×Q8×C61C2×C411yescharacteristic
94C22×D4×C61C2×C411yescharacteristic
95C22×C8×C61—21no—
96C22×C8×C61—21no—
97#124×C61—21no—
98#124×C61—21no—
99#124×C61C2×C412yes—
100#124×C61C2312yes—
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61—21no—
103C2×C42×C61C2311yescharacteristic
104#97×C61—21no—
105#97×C61—21no—
106#97×C61C2312yes—
107#97×C61C2312yes—
108C24×C61—21no—
109C23×D61C22⋊C411yescharacteristic
110C2×Q8×C61—21no—
111C2×Q8×C61—42no—
112C2×Q8×C61C22×C412yes—
113C2×D4×C61—21no—
114C2×D4×C61—42no—
115C2×D4×C61C22×C412yes—
116C22×C4×C61—21no—
117C22×C4×C61C22×C411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C2×C22⋊D61—24no—
121C2×C22⋊D61—44no—
122C22×Dic61—21no—
123C22×Dic61—21no—
124C22×Dic61—24no—
125C22×Dic61—44no—
126C22×Dic61C22⋊C411yescharacteristic
127C22×Dic61C22⋊C411yescharacteristic
128C22×Dic61C22⋊C411yescharacteristic
129C2×C4×D61—24no—
130C2×C4×D61—42no—
131C2×C4×D61—42no—
132C2×C4×D61C22⋊C412yes—
133C2×C4×D61C22⋊C412yes—
134C2×C4×D61C22⋊C412yes—
135C2×C4×D61C22×C412yes—
136C2×C4×D61C2×D412yes—
137C2×C4×D61C2×D412yes—
138C2×C8×C61—24no—
139C2×C8×C61—22no—
140C2×C8×C61—22no—
141C2×C8×C61—42no—
142C22⋊C4×C61—22no—
143C22⋊C4×C61—22no—
144C22⋊C4×C61—22no—
145C22⋊C4×C61—22no—
146C42×C61C22×C411yescharacteristic
147C42×C61C2×D411yescharacteristic
148C42×C61C2×D411yescharacteristic
149C42×C61C2411yescharacteristic
150C22⋊Dic61—24no—
151C22⋊Dic61—24no—
152#11758198—24no—
153C4⋊Dic61—21no—
154C4⋊Dic61—21no—
155C4⋊Dic61—24no—
156C4⋊Dic61C22×C412yes—
157C4⋊Dic61C22×C412yes—
158#11758196—22no—
159#11758196—22no—
160#11758196—22no—
161#11758196—22no—
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×C61—22no—
176C23×C61—42no—
177C23×C61—42no—
178C23×C61—42no—
179C23×C61C2×C22⋊C411yescharacteristic
180C22×D61—22no—
181C22×D61—22no—
182C22×D61#10414yes—
183C22×D61C2×C22⋊C412yes—
184Q8×C61—42no—
185Q8×C61—42no—
186D4×C61—42no—
187D4×C61—42no—
188C2×C4×C61—22no—
189C2×C4×C61—22no—
190C2×C4×C61—22no—
191C2×C4×C61—22no—
192C2×C4×C61—42no—
193C2×C4×C61C2×C22⋊C411yescharacteristic
194C2×C4×C61C2×C22⋊C411yescharacteristic
195C2×C4×C61C2×C22⋊C411yescharacteristic
196C2×C4×C61C23×C411yescharacteristic
197C2×C4×C61C22×D411yescharacteristic
198C2×C4×C61C22×D411yescharacteristic
199C22⋊D61—48no—
200C2×Dic61—22no—
201C2×Dic61—22no—
202C2×Dic61—22no—
203C2×Dic61—22no—
204C2×Dic61—22no—
205C2×Dic61—48no—
206C2×Dic61—42no—
207C2×Dic61—42no—
208C2×Dic61C2×C22⋊C412yes—
209C2×Dic61C2×C22⋊C412yes—
210C2×Dic61C2×C22⋊C412yes—
211C4×D61—24no—
212C4×D61—24no—
213C4×D61—42no—
214C4×D61—42no—
215C4×D61—42no—
216C4×D61—42no—
217C8×C61—24no—
218C8×C61—42no—
219#92418—24no—
220#92418—42no—
221C2×#1532—611nomaximal, Sylow
222C22×C61—42no—
223C22×C61—42no—
224C22×C61—42no—
225C22×C61—84no—
226C22×C61#41312yes—
227C22×C61C2×#10412yes—
228C22×C61#42112yes—
229C22×C61C22×C22⋊C411yescharacteristic
230C2×D61—22no—
231C2×D61—22no—
232C2×D61—28no—
233C2×D61C2×#10414yes—
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—21no—
240C4×C61—42no—
241Dic61—22no—
242Dic61—22no—
243Dic61—22no—
244Dic61—42no—
245Dic61—42no—
246C2×#529—611no—
247C2×#432—611no—
248C22×#97—611no—
249#1532—618no—
250C2×#330—611no—
251C2×#330—611no—
252C2×#329—611no—
253C2×#329D6111yescharacteristic, complemented
254C2×C61—82no—
255C2×C61#153214yescomplemented
256C2×C61C2×#41311yescharacteristic
257C2×C61C22×#10411yescharacteristic
258C2×C61C2×#42111yescharacteristic
259D61—24no—
260C23×C8—1221no—
261#529—614no—
262#529—614no—
263#529—1222no—
264#529—1222no—
265C2×#126—1221no—
266C2×#125—611no—
267C2×#124C2×D6111yescharacteristic
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#330—614no—
289#329—614no—
290#329C2×D6114yescomplemented
291C61C2×#153211yescharacteristic, complemented, Sylow
292C22×Q8C4×D6111yescharacteristic
293C22×D4—1221no—
294C22×D4C4×D6111yescharacteristic
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—612no—
308#125—612no—
309#125—1221no—
310#125—1221no—
311#124—21no—
312#124—21no—
313#124C4×D6112yes—
314#124C22×D6112yes—
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—611no—
330C2×C4⋊C4—611no—
331C2×C4⋊C4—1221no—
332C2×C4⋊C4—1221no—
333C2×C4⋊C4—1221no—
334C2×C4⋊C4—1221no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
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—21no—
361C24—611no—
362C2×Q8—21no—
363C2×Q8—42no—
364C2×Q8C2×C4×D6112yes—
365C2×D4—21no—
366C2×D4—42no—
367C2×D4—1224no—
368C2×D4—2444no—
369C2×D4C2×C4×D6112yes—
370C22×C4—21no—
371C22×C4—611no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—612no—
375C22×C4—612no—
376C22×C4—612no—
377C22×C4—612no—
378C22×C4—612no—
379C22×C4—612no—
380C22×C4—1224no—
381C22×C4—1224no—
382C22×C4—1221no—
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—612no—
400C4⋊C4—612no—
401C4⋊C4—1224no—
402C4⋊C4—1224no—
403C4⋊C4—1222no—
404C4⋊C4—1222no—
405C4⋊C4—1221no—
406C4⋊C4—1221no—
407C4⋊C4—1222no—
408C4⋊C4—1222no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—1224no—
414C22⋊C4—1224no—
415C22⋊C4—1224no—
416C42—612no—
417C42—612no—
418C42—612no—
419C42—612no—
420C42—612no—
421C42—612no—
422C42—1224no—
423C42C2×C4×D6111yescharacteristic
424C42D4×D6111yescharacteristic
425C42D4×D6111yescharacteristic
426C42C23×D6111yescharacteristic
427C23—22no—
428C23—42no—
429C23—42no—
430C23—42no—
431C23—612no—
432C23—614no—
433C23—1222no—
434C23—1222no—
435C23C22⋊C4×D6111yescharacteristic
436Q8—42no—
437Q8—42no—
438D4—42no—
439D4—42no—
440D4—2448no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—42no—
446C2×C4—612no—
447C2×C4—612no—
448C2×C4—612no—
449C2×C4—1224no—
450C2×C4—1224no—
451C2×C4—1222no—
452C2×C4—1222no—
453C2×C4—1222no—
454C2×C4—1222no—
455C2×C4—1222no—
456C2×C4—2442no—
457C2×C4—2442no—
458C2×C4—2442no—
459C2×C4—2442no—
460C2×C4—2448no—
461C2×C4—2442no—
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—42no—
474C22—42no—
475C22—42no—
476C22—84no—
477C22—614no—
478C22—1222no—
479C22—1228no—
480C22—1222no—
481C22#1683974312yes—
482C22#104×D6112yes—
483C22#1683977712yes—
484C22C2×C22⋊C4×D6111yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—42no—
492C4—1222no—
493C4—1222no—
494C4—1222no—
495C4—2442no—
496C4—2442no—
497C2—82no—
498C2—1224no—
499C2#2144443614yesdirect product factor
500C2C2×#1683974311yescharacteristic
501C2C2×#104×D6111yescharacteristic
502C2C2×#1683977711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC2×C61×#329C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C4
cosocleC42×C61C24
hypercenterC2×#329D61
hypocenterC61C2×#1532
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

Complements

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

NH ≅ G/Ntype
2. C2×#16839817C2semidirect
3. C2×#97×D61C2semidirect
4. #21444436C2direct (N × H)
5. C2×#16839503C2semidirect
6. C2×#16839503C2semidirect
7. C2×#16839502C2semidirect
8. C2×C61×#329C2semidirect
25. #16839817C22semidirect
32. #97×D61C22semidirect
33. #16839503C22semidirect
34. #16839503C22semidirect
35. #16839502C22semidirect
39. C61×#329C22semidirect
253. C2×#329D61semidirect
255. C2×C61#1532semidirect
290. #329C2×D61semidirect
291. C61C2×#1532semidirect
499. C2#21444436direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402912
C2×#168398172
C2×#97×D612
#214444362
C2×#168395032
C2×#168395022
C2×C61×#3292
C2×#153261