Finite Group Databasebeta

← C2×#21444341 #29647137

Subgroups — C2×#21444341 #29647137

Order 15616.

1206 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840293C211yesmaximal, characteristic
2C2×#16839816C211yesmaximal, characteristic, complemented
3C2×#16839613C211yesmaximal, characteristic, complemented
4#21444341C218yesmaximal, direct product factor
5C2×#16839500C211yesmaximal, characteristic, complemented
6C2×#16839498C211yesmaximal, characteristic, complemented
7C2×#16839496C211yesmaximal, characteristic
8C2×C61×#327C211yesmaximal, characteristic
9#16840293—22no—
10#16840293—22no—
11#16840293C414yescomplemented
12#16840293C2214yes—
13C2×#14519770—21no—
14C2×#14519768C411yescharacteristic, complemented
15C2×#14519764C411yescharacteristic, complemented
16C2×#14519758—21no—
17C2×#14519756C2211yescharacteristic
18C2×#14519742C411yescharacteristic, complemented
19C2×D4×Dic61—21no—
20C2×D4×Dic61C411yescharacteristic, complemented
21C2×#14519733—21no—
22C22×#11758196—21no—
23C22×C4×Dic61—21no—
24C22×C4×Dic61C2211yescharacteristic
25#16839816—22no—
26#16839816C2214yescomplemented
27C2×#14519706—21no—
28C2×C22⋊#92418C2211yescharacteristic
29C2×#14519687—21no—
30#16839613—22no—
31#16839613C2214yescomplemented
32C2×#14519684C2211yescharacteristic
33#16839500C2214yescomplemented
34#16839498C2214yescomplemented
35#16839496C2214yes—
36C2×#121×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×#95×C61C2211yescharacteristic
39C61×#327C2214yes—
40C22×Dic122C2×C411yescharacteristic
41C23×Dic61—21no—
42C23×Dic61—21no—
43C23×Dic61D411yescharacteristic
44C23×Dic61D411yescharacteristic
45C22×#92418—21no—
46#14519770—24no—
47#14519770—24no—
48#14519768—22no—
49#14519768C2×C414yescomplemented
50#14519764—22no—
51#14519764C2×C414yescomplemented
52#14519758—24no—
53#14519758—24no—
54#14519756—21no—
55#14519756—21no—
56#14519756C2×C412yes—
57#14519756C2312yes—
58#14519742—22no—
59#14519742C2×C414yescomplemented
60D4×Dic61—24no—
61D4×Dic61—24no—
62D4×Dic61—22no—
63D4×Dic61C2×C414yescomplemented
64#14519733—24no—
65#14519733—24no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61C2×C411yescharacteristic
68C2×#11758196—28no—
69C2×#11758196—21no—
70C2×#11758196—21no—
71C2×#11758196—21no—
72C2×#11758196—24no—
73C2×C22⋊Dic61—21no—
74C2×C22⋊Dic61—21no—
75C2×C22⋊Dic61—21no—
76C2×C22⋊Dic61—21no—
77C2×C4×Dic61—21no—
78C2×C4×Dic61—24no—
79C2×C4×Dic61—44no—
80C2×C4×Dic61C2×C411yescharacteristic
81C2×C4×Dic61C2×C411yescharacteristic
82C2×C4×Dic61C2×C412yes—
83C2×C4×Dic61D412yes—
84C2×C4×Dic61D411yescharacteristic
85C2×C4×Dic61D411yescharacteristic
86C2×C4×Dic61D412yes—
87C2×C4×Dic61C2312yes—
88#14519706—24no—
89C22⋊#92418—21no—
90C22⋊#92418C2312yes—
91#14519687—24no—
92#14519684—21no—
93#14519684C2312yes—
94C22×D4×C61—21no—
95C22×D4×C61C2×C411yescharacteristic
96C23×C4×C61—21no—
97C23×C4×C61C2311yescharacteristic
98C22×C8×C61—21no—
99#121×C61—21no—
100#121×C61—21no—
101#121×C61C2×C412yes—
102#121×C61C2312yes—
103C2×C4⋊C4×C61C2×C411yescharacteristic
104C2×C22⋊C4×C61—21no—
105C22⋊C8×C61—21no—
106C22⋊C8×C61C2312yes—
107#95×C61—21no—
108#95×C61C2312yes—
109C24×C61—21no—
110C24×C61C2×D411yescharacteristic
111C2×D4×C61—22no—
112C2×D4×C61—22no—
113C2×D4×C61—21no—
114C2×D4×C61—42no—
115C2×D4×C61—42no—
116C2×D4×C61—42no—
117C2×D4×C61C22×C412yes—
118C22×C4×C61—24no—
119C22×C4×C61—21no—
120C22×C4×C61—22no—
121C22×C4×C61—42no—
122C22×C4×C61—42no—
123C22×C4×C61—42no—
124C22×C4×C61C22×C411yescharacteristic
125C22×C4×C61C22×C411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2411yescharacteristic
130C22×Dic61—22no—
131C22×Dic61—22no—
132C22×Dic61—24no—
133C22×Dic61—24no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—22no—
137C22×Dic61—24no—
138C22×Dic61—42no—
139C22×Dic61—42no—
140C22×Dic61—44no—
141C22×Dic61C22⋊C411yescharacteristic
142C22×Dic61C22⋊C411yescharacteristic
143C22×Dic61C22⋊C411yescharacteristic
144C22×Dic61C22⋊C412yes—
145C22×Dic61C22⋊C412yes—
146C22×Dic61C22⋊C411yescharacteristic
147C22×Dic61C2×D412yes—
148C22×Dic61C2×D412yes—
149C2×Dic122—21no—
150C2×Dic122—42no—
151C2×Dic122C22×C412yes—
152C2×C8×C61—22no—
153C2×C8×C61—42no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61C22×C412yes—
156C22⋊C4×C61—22no—
157C22⋊C4×C61—22no—
158C22⋊Dic61—22no—
159C22⋊Dic61—22no—
160C22⋊Dic61—24no—
161C22⋊Dic61—24no—
162C22⋊Dic61—24no—
163C4⋊Dic61—21no—
164C4⋊Dic61—24no—
165C4⋊Dic61C22×C412yes—
166#11758196—216no—
167#11758196—22no—
168#11758196—22no—
169#11758196—24no—
170#11758196—24no—
171C4×Dic61—24no—
172C4×Dic61—48no—
173C4×Dic61C22⋊C412yes—
174C4×Dic61C22⋊C412yes—
175C4×Dic61C22⋊C412yes—
176C4×Dic61C22⋊C412yes—
177C4×Dic61C22×C412yes—
178C4×Dic61C22×C412yes—
179C4×Dic61C2×D412yes—
180C4×Dic61C2×D412yes—
181C2×#92418—22no—
182C2×#92418—42no—
183C23×C61—22no—
184C23×C61—22no—
185C23×C61—22no—
186C23×C61—42no—
187C23×C61—42no—
188C23×C61—42no—
189C23×C61C2×C22⋊C411yescharacteristic
190C23×C61C2×C22⋊C411yescharacteristic
191C23×C61AGL(1,ℤ/8)12yes—
192C23×C61#13712yes—
193C23×C61C22×D411yescharacteristic
194D4×C61—42no—
195D4×C61—42no—
196D4×C61—42no—
197D4×C61—42no—
198D4×C61—44no—
199C2×C4×C61—22no—
200C2×C4×C61—22no—
201C2×C4×C61—24no—
202C2×C4×C61—22no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61—41no—
207C2×C4×C61—42no—
208C2×C4×C61—48no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61C2×C22⋊C411yescharacteristic
212C2×C4×C61C2×C22⋊C411yescharacteristic
213C2×C4×C61C23×C411yescharacteristic
214C2×C4×C61C22×D411yescharacteristic
215C2×Dic61—22no—
216C2×Dic61—22no—
217C2×Dic61—24no—
218C2×Dic61—22no—
219C2×Dic61—22no—
220C2×Dic61—22no—
221C2×Dic61—24no—
222C2×Dic61—24no—
223C2×Dic61—24no—
224C2×Dic61—22no—
225C2×Dic61—22no—
226C2×Dic61—42no—
227C2×Dic61—48no—
228C2×Dic61—42no—
229C2×Dic61—42no—
230C2×Dic61—42no—
231C2×Dic61—48no—
232C2×Dic61#10414yes—
233C2×Dic61C2×C22⋊C412yes—
234C2×Dic61C2×C22⋊C412yes—
235C2×Dic61C2×C22⋊C412yes—
236C2×Dic61C2×C22⋊C412yes—
237Dic122—42no—
238Dic122—42no—
239C8×C61—42no—
240#92418—42no—
241C2×#1509—611nomaximal, Sylow
242C22×C61—21no—
243C22×C61—21no—
244C22×C61—21no—
245C22×C61—21no—
246C22×C61—24no—
247C22×C61—24no—
248C22×C61—42no—
249C22×C61—42no—
250C22×C61—42no—
251C22×C61—84no—
252C22×C61#41012yes—
253C22×C61#41712yes—
254C22×C61#41712yes—
255C22×C61C2×#10412yes—
256C22×C61C22×C22⋊C411yescharacteristic
257C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
258C22×C61C2×#13711yescharacteristic
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—44no—
264C4×C61—42no—
265Dic61—22no—
266Dic61—22no—
267Dic61—22no—
268Dic61—44no—
269Dic61—42no—
270Dic61—42no—
271Dic61C2×#10414yes—
272C2×#529—611no—
273C2×#432—611no—
274C2×C4×C4⋊C4—611no—
275#1509—618no—
276C2×#328—611no—
277C2×#328—611no—
278C2×#327—611no—
279C2×#327D6111yescharacteristic
280C2×C61—21no—
281C2×C61—21no—
282C2×C61—22no—
283C2×C61—82no—
284C2×C61#150914yescomplemented
285C2×C61C2×#41011yescharacteristic
286C2×C61C2×#41711yescharacteristic
287C2×C61C22×#10411yescharacteristic
288#529—614no—
289#529—614no—
290#529—1222no—
291#529—1222no—
292C2×#126—1221no—
293C2×#125—611no—
294C2×#124—611no—
295C2×#123—1221no—
296C2×C22⋊Q8—611no—
297C2×#121C2×D6111yescharacteristic
298C2×C4×Q8—611no—
299C2×C4×D4—611no—
300C2×C4×D4—1221no—
301C2×#117—1221no—
302C22×C4⋊C4—1221no—
303C22×C42—611no—
304C22×C42—1221no—
305#432—614no—
306#432—1222no—
307C2×C4⋊C8—1221no—
308C2×C22⋊C8—611no—
309C2×C22⋊C8C2×D6111yescharacteristic
310C2×#97—1221no—
311C4×C4⋊C4—614no—
312C4×C4⋊C4—1222no—
313C2×#95—611no—
314C2×#95C2×D6111yescharacteristic
315#328—614no—
316#328—614no—
317#327—614no—
318#327C2×D6114yes—
319C61C2×#150911yescharacteristic, complemented, Sylow
320C22×Q8—611no—
321C22×D4—21no—
322C22×D4C4×D6111yescharacteristic
323C23×C4—21no—
324C23×C4—611no—
325C23×C4—611no—
326C23×C4—1221no—
327C23×C4—1221no—
328C23×C4C22×D6111yescharacteristic
329C22×C8—21no—
330C22×C8—1221no—
331#126—1224no—
332#126—1224no—
333#125—614no—
334#125—1222no—
335#124—614no—
336#124—1222no—
337#123—1224no—
338#123—1224no—
339C22⋊Q8—612no—
340C22⋊Q8—612no—
341C22⋊Q8—1221no—
342C22⋊Q8—1221no—
343#121—21no—
344#121—21no—
345#121C4×D6112yes—
346#121C22×D6112yes—
347C4×Q8—614no—
348C4×Q8—1222no—
349C4×D4—614no—
350C4×D4—1222no—
351C4×D4—1224no—
352C4×D4—1224no—
353#117—1224no—
354#117—1224no—
355C2×C4⋊C4—611no—
356C2×C4⋊C4—1224no—
357C2×C4⋊C4—1221no—
358C2×C4⋊C4—1221no—
359C2×C4⋊C4—1221no—
360C2×C4⋊C4—1228no—
361C2×C4⋊C4—1221no—
362C2×C4⋊C4C4×D6111yescharacteristic
363C2×C22⋊C4—21no—
364C2×C22⋊C4—1221no—
365C2×C22⋊C4—1221no—
366C2×C22⋊C4—1221no—
367C2×C22⋊C4—1221no—
368C2×C42—611no—
369C2×C42—611no—
370C2×C42—612no—
371C2×C42—611no—
372C2×C42—611no—
373C2×C42—612no—
374C2×C42—612no—
375C2×C42—612no—
376C2×C42—1221no—
377C2×C42—1224no—
378C2×C42—2444no—
379C4⋊C8—1224no—
380C22⋊C8—21no—
381C22⋊C8—612no—
382C22⋊C8—1221no—
383C22⋊C8C22×D6112yes—
384#97—1224no—
385#95—21no—
386#95—612no—
387#95—1221no—
388#95C22×D6112yes—
389C24—21no—
390C24D4×D6111yescharacteristic
391C2×Q8—612no—
392C2×Q8—1221no—
393C2×Q8—2442no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—21no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4C2×C4×D6112yes—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—611no—
408C22×C4—612no—
409C22×C4—612no—
410C22×C4—612no—
411C22×C4—612no—
412C22×C4—611no—
413C22×C4—611no—
414C22×C4—611no—
415C22×C4—1224no—
416C22×C4—1224no—
417C22×C4—1222no—
418C22×C4—1222no—
419C22×C4—1224no—
420C22×C4—1222no—
421C22×C4—1221no—
422C22×C4—1221no—
423C22×C4—2444no—
424C22×C4—2442no—
425C22×C4—2442no—
426C22×C4C2×C4×D6111yescharacteristic
427C22×C4C2×C4×D6111yescharacteristic
428C22×C4D4×D6111yescharacteristic
429C22×C4D4×D6111yescharacteristic
430C22×C4D4×D6111yescharacteristic
431C22×C4C23×D6111yescharacteristic
432C2×C8—22no—
433C2×C8—42no—
434C2×C8—1222no—
435C2×C8—2442no—
436C4⋊C4—21no—
437C4⋊C4—612no—
438C4⋊C4—1224no—
439C4⋊C4—1224no—
440C4⋊C4—1224no—
441C4⋊C4—12216no—
442C4⋊C4—1222no—
443C4⋊C4—1221no—
444C4⋊C4—1222no—
445C4⋊C4C2×C4×D6112yes—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—1224no—
449C22⋊C4—1224no—
450C22⋊C4—1224no—
451C22⋊C4—1222no—
452C22⋊C4—1222no—
453C42—612no—
454C42—612no—
455C42—612no—
456C42—612no—
457C42—612no—
458C42—612no—
459C42—612no—
460C42—612no—
461C42—1224no—
462C42—2448no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23C22⋊C4×D6111yescharacteristic
470C23C22⋊C4×D6111yescharacteristic
471C23#1451980112yes—
472C23#1451980612yes—
473C23C2×D4×D6111yescharacteristic
474Q8—2442no—
475Q8—2442no—
476D4—42no—
477D4—42no—
478D4—44no—
479D4—42no—
480D4—42no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—48no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—612no—
494C2×C4—614no—
495C2×C4—612no—
496C2×C4—612no—
497C2×C4—612no—
498C2×C4—1224no—
499C2×C4—1224no—
500C2×C4—1224no—
501C2×C4—1222no—
502C2×C4—1222no—
503C2×C4—1222no—
504C2×C4—1222no—
505C2×C4—1222no—
506C2×C4—1224no—
507C2×C4—1222no—
508C2×C4—1222no—
509C2×C4—2448no—
510C2×C4—2442no—
511C2×C4—2448no—
512C2×C4—2442no—
513C2×C4—2442no—
514C2×C4—2442no—
515C2×C4C22⋊C4×D6111yescharacteristic
516C2×C4C22⋊C4×D6111yescharacteristic
517C2×C4C22×C4×D6111yescharacteristic
518C2×C4C2×D4×D6111yescharacteristic
519C8—42no—
520C8—2442no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—24no—
526C22—24no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—84no—
531C22#1683973412yes—
532C22#1683976012yes—
533C22#1683976012yes—
534C22#104×D6112yes—
535C22C2×C22⋊C4×D6111yescharacteristic
536C22C2×#1451980111yescharacteristic
537C22C2×#1451980611yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—44no—
543C4—42no—
544C4—614no—
545C4—1222no—
546C4—1222no—
547C4—1222no—
548C4—2444no—
549C4—2442no—
550C4—2442no—
551C2—21no—
552C2—22no—
553C2—21no—
554C2—82no—
555C2#2144434114yesdirect product factor
556C2C2×#1683973411yescharacteristic
557C2C2×#1683976011yescharacteristic
558C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#327C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#121×C61C22
cosocleC22×C4×C61C24
hypercenterC2×#327D61
hypocenterC61C2×#1509
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#16839816C2semidirect
3. C2×#16839613C2semidirect
4. #21444341C2direct (N × H)
5. C2×#16839500C2semidirect
6. C2×#16839498C2semidirect
11. #16840293C4semidirect
14. C2×#14519768C4semidirect
15. C2×#14519764C4semidirect
18. C2×#14519742C4semidirect
20. C2×D4×Dic61C4semidirect
26. #16839816C22semidirect
31. #16839613C22semidirect
33. #16839500C22semidirect
34. #16839498C22semidirect
49. #14519768C2×C4semidirect
51. #14519764C2×C4semidirect
59. #14519742C2×C4semidirect
63. D4×Dic61C2×C4semidirect
284. C2×C61#1509semidirect
319. C61C2×#1509semidirect
555. C2#21444341direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402932
C2×#168398162
C2×#168396132
#214443412
C2×#168395002
C2×#168394982
C2×#168394962
C2×C61×#3272
C2×#150961