Finite Group Databasebeta

← C2×#21444354 #29647252

Subgroups — C2×#21444354 #29647252

Order 15616.

1098 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840293C211yesmaximal, characteristic
2C2×#16839816C211yesmaximal, characteristic, complemented
3C2×#16839626C211yesmaximal, characteristic, complemented
4#21444354C218yesmaximal, 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×Dic61C2211yescharacteristic
24#16839816—22no—
25#16839816C2214yescomplemented
26C2×#14519706—21no—
27C2×C22⋊#92418C2211yescharacteristic
28C2×#14519687—21no—
29#16839626—22no—
30#16839626C2214yescomplemented
31C2×#14519684—21no—
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—21no—
69C2×#11758196—21no—
70C2×#11758196—21no—
71C2×#11758196—24no—
72C2×#11758196—44no—
73C2×C22⋊Dic61—21no—
74C2×C22⋊Dic61—21no—
75C2×C22⋊Dic61—21no—
76C2×C22⋊Dic61—21no—
77C2×C4×Dic61—21no—
78C2×C4×Dic61C2×C411yescharacteristic
79C2×C4×Dic61C2×C411yescharacteristic
80C2×C4×Dic61C2×C412yes—
81C2×C4×Dic61D412yes—
82C2×C4×Dic61D411yescharacteristic
83C2×C4×Dic61D411yescharacteristic
84C2×C4×Dic61D412yes—
85C2×C4×Dic61C2312yes—
86#14519706—24no—
87C22⋊#92418—21no—
88C22⋊#92418C2312yes—
89#14519687—24no—
90#14519684—21no—
91#14519684—24no—
92#14519684C2312yes—
93C22×D4×C61—21no—
94C22×D4×C61C2×C411yescharacteristic
95C23×C4×C61—21no—
96C23×C4×C61C2311yescharacteristic
97C22×C8×C61—21no—
98#121×C61—21no—
99#121×C61—21no—
100#121×C61C2×C412yes—
101#121×C61C2312yes—
102C2×C4⋊C4×C61C2×C411yescharacteristic
103C2×C22⋊C4×C61—21no—
104C22⋊C8×C61—21no—
105C22⋊C8×C61C2312yes—
106#95×C61—21no—
107#95×C61C2312yes—
108C24×C61—21no—
109C24×C61C2×D411yescharacteristic
110C2×D4×C61—22no—
111C2×D4×C61—22no—
112C2×D4×C61—21no—
113C2×D4×C61—42no—
114C2×D4×C61—42no—
115C2×D4×C61—42no—
116C2×D4×C61C22×C412yes—
117C22×C4×C61—21no—
118C22×C4×C61—22no—
119C22×C4×C61—42no—
120C22×C4×C61—42no—
121C22×C4×C61—42no—
122C22×C4×C61—42no—
123C22×C4×C61C22×C411yescharacteristic
124C22×C4×C61C22×C411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2411yescharacteristic
129C22×Dic61—22no—
130C22×Dic61—22no—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—24no—
134C22×Dic61—22no—
135C22×Dic61—42no—
136C22×Dic61—44no—
137C22×Dic61—42no—
138C22×Dic61—42no—
139C22×Dic61—42no—
140C22×Dic61C22⋊C411yescharacteristic
141C22×Dic61C22⋊C411yescharacteristic
142C22×Dic61C22⋊C411yescharacteristic
143C22×Dic61C22⋊C411yescharacteristic
144C22×Dic61C22⋊C412yes—
145C22×Dic61C22⋊C412yes—
146C22×Dic61C2×D412yes—
147C22×Dic61C2×D412yes—
148C2×Dic122—21no—
149C2×Dic122—42no—
150C2×Dic122C22×C412yes—
151C2×C8×C61—22no—
152C2×C8×C61—42no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61C22×C412yes—
155C22⋊C4×C61—22no—
156C22⋊C4×C61—22no—
157C22⋊Dic61—22no—
158C22⋊Dic61—22no—
159C22⋊Dic61—24no—
160C22⋊Dic61—24no—
161C22⋊Dic61—24no—
162C4⋊Dic61—21no—
163C4⋊Dic61—24no—
164C4⋊Dic61C22×C412yes—
165#11758196—22no—
166#11758196—22no—
167#11758196—24no—
168#11758196—24no—
169#11758196—48no—
170C4×Dic61—24no—
171C4×Dic61C22⋊C412yes—
172C4×Dic61C22⋊C412yes—
173C4×Dic61C22⋊C412yes—
174C4×Dic61C22⋊C412yes—
175C4×Dic61C22×C412yes—
176C4×Dic61C22×C412yes—
177C4×Dic61C2×D412yes—
178C4×Dic61C2×D412yes—
179C2×#92418—22no—
180C2×#92418—42no—
181C23×C61—22no—
182C23×C61—22no—
183C23×C61—22no—
184C23×C61—42no—
185C23×C61—42no—
186C23×C61—42no—
187C23×C61C2×C22⋊C411yescharacteristic
188C23×C61C2×C22⋊C411yescharacteristic
189C23×C61AGL(1,ℤ/8)12yes—
190C23×C61#13712yes—
191C23×C61C22×D411yescharacteristic
192D4×C61—42no—
193D4×C61—42no—
194D4×C61—42no—
195D4×C61—42no—
196D4×C61—44no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—42no—
205C2×C4×C61—42no—
206C2×C4×C61—42no—
207C2×C4×C61—42no—
208C2×C4×C61—84no—
209C2×C4×C61C2×C22⋊C411yescharacteristic
210C2×C4×C61C2×C22⋊C411yescharacteristic
211C2×C4×C61C23×C411yescharacteristic
212C2×C4×C61C22×D411yescharacteristic
213C2×Dic61—22no—
214C2×Dic61—22no—
215C2×Dic61—24no—
216C2×Dic61—22no—
217C2×Dic61—22no—
218C2×Dic61—22no—
219C2×Dic61—22no—
220C2×Dic61—22no—
221C2×Dic61—22no—
222C2×Dic61—42no—
223C2×Dic61—42no—
224C2×Dic61—48no—
225C2×Dic61—42no—
226C2×Dic61—42no—
227C2×Dic61—42no—
228C2×Dic61—42no—
229C2×Dic61—42no—
230C2×Dic61—84no—
231C2×Dic61C2×C22⋊C412yes—
232C2×Dic61C2×C22⋊C412yes—
233C2×Dic61C2×C22⋊C412yes—
234C2×Dic61C2×C22⋊C412yes—
235Dic122—42no—
236Dic122—42no—
237C8×C61—42no—
238#92418—42no—
239C2×#1512—611nomaximal, Sylow
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—21no—
243C22×C61—21no—
244C22×C61—24no—
245C22×C61—24no—
246C22×C61—42no—
247C22×C61—42no—
248C22×C61—42no—
249C22×C61—84no—
250C22×C61#41012yes—
251C22×C61#41712yes—
252C22×C61#41712yes—
253C22×C61#42112yes—
254C22×C61C22×C22⋊C411yescharacteristic
255C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
256C22×C61C2×#13711yescharacteristic
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—42no—
262C4×C61—82no—
263Dic61—22no—
264Dic61—22no—
265Dic61—22no—
266Dic61—22no—
267Dic61—42no—
268Dic61—42no—
269Dic61—82no—
270C2×#529—611no—
271C2×#432—611no—
272C2×#382—611no—
273#1512—618no—
274C2×#328—611no—
275C2×#328—611no—
276C2×#327—611no—
277C2×#327D6111yescharacteristic
278C2×C61—21no—
279C2×C61—21no—
280C2×C61—22no—
281C2×C61—82no—
282C2×C61#151214yescomplemented
283C2×C61C2×#41011yescharacteristic
284C2×C61C2×#41711yescharacteristic
285C2×C61C2×#42111yescharacteristic
286#529—614no—
287#529—614no—
288#529—1222no—
289#529—1222no—
290C2×#126—1221no—
291C2×#125—611no—
292C2×#124—611no—
293C2×#123—1221no—
294C2×C22⋊Q8—611no—
295C2×#121C2×D6111yescharacteristic
296C2×C4×Q8—611no—
297C2×C4×D4—611no—
298C2×C4×D4—1221no—
299C2×#117—1221no—
300C22×C4⋊C4—1221no—
301C22×C42—611no—
302#432—614no—
303#432—1222no—
304C2×C4⋊C8—1221no—
305C2×C22⋊C8—611no—
306C2×C22⋊C8C2×D6111yescharacteristic
307C2×#97—1221no—
308#382—614no—
309#382—1222no—
310C2×#95—611no—
311C2×#95—1221no—
312C2×#95C2×D6111yescharacteristic
313#328—614no—
314#328—614no—
315#327—614no—
316#327C2×D6114yes—
317C61C2×#151211yescharacteristic, complemented, Sylow
318C22×Q8—611no—
319C22×D4—21no—
320C22×D4C4×D6111yescharacteristic
321C23×C4—21no—
322C23×C4—611no—
323C23×C4—611no—
324C23×C4—1221no—
325C23×C4—1221no—
326C23×C4C22×D6111yescharacteristic
327C22×C8—21no—
328C22×C8—1221no—
329#126—1224no—
330#126—1224no—
331#125—614no—
332#125—1222no—
333#124—614no—
334#124—1222no—
335#123—1224no—
336#123—1224no—
337C22⋊Q8—612no—
338C22⋊Q8—612no—
339C22⋊Q8—1221no—
340C22⋊Q8—1221no—
341#121—21no—
342#121—21no—
343#121C4×D6112yes—
344#121C22×D6112yes—
345C4×Q8—614no—
346C4×Q8—1222no—
347C4×D4—614no—
348C4×D4—1222no—
349C4×D4—1224no—
350C4×D4—1224no—
351#117—1224no—
352#117—1224no—
353C2×C4⋊C4—611no—
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1221no—
356C2×C4⋊C4—1221no—
357C2×C4⋊C4—1221no—
358C2×C4⋊C4—1224no—
359C2×C4⋊C4—2444no—
360C2×C4⋊C4C4×D6111yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—1221no—
363C2×C22⋊C4—1221no—
364C2×C22⋊C4—1221no—
365C2×C22⋊C4—1221no—
366C2×C42—611no—
367C2×C42—611no—
368C2×C42—612no—
369C2×C42—611no—
370C2×C42—611no—
371C2×C42—612no—
372C2×C42—612no—
373C2×C42—612no—
374C2×C42—1221no—
375C4⋊C8—1224no—
376C22⋊C8—21no—
377C22⋊C8—612no—
378C22⋊C8—1221no—
379C22⋊C8C22×D6112yes—
380#97—1224no—
381#95—21no—
382#95—612no—
383#95—1224no—
384#95—1221no—
385#95C22×D6112yes—
386C24—21no—
387C24D4×D6111yescharacteristic
388C2×Q8—612no—
389C2×Q8—1221no—
390C2×Q8—2442no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—42no—
397C2×D4C2×C4×D6112yes—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—612no—
405C22×C4—612no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—611no—
409C22×C4—611no—
410C22×C4—612no—
411C22×C4—612no—
412C22×C4—1224no—
413C22×C4—1222no—
414C22×C4—1222no—
415C22×C4—1221no—
416C22×C4—1221no—
417C22×C4—1222no—
418C22×C4—2442no—
419C22×C4—2444no—
420C22×C4—2442no—
421C22×C4—2442no—
422C22×C4—2442no—
423C22×C4C2×C4×D6111yescharacteristic
424C22×C4C2×C4×D6111yescharacteristic
425C22×C4D4×D6111yescharacteristic
426C22×C4D4×D6111yescharacteristic
427C22×C4D4×D6111yescharacteristic
428C22×C4C23×D6111yescharacteristic
429C2×C8—22no—
430C2×C8—42no—
431C2×C8—1222no—
432C2×C8—2442no—
433C4⋊C4—21no—
434C4⋊C4—612no—
435C4⋊C4—1224no—
436C4⋊C4—1224no—
437C4⋊C4—1224no—
438C4⋊C4—1222no—
439C4⋊C4—1221no—
440C4⋊C4—1222no—
441C4⋊C4—2448no—
442C4⋊C4C2×C4×D6112yes—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—1224no—
446C22⋊C4—1224no—
447C22⋊C4—1224no—
448C22⋊C4—1222no—
449C22⋊C4—1222no—
450C42—612no—
451C42—612no—
452C42—612no—
453C42—612no—
454C42—612no—
455C42—612no—
456C42—612no—
457C42—612no—
458C42—1224no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23C22⋊C4×D6111yescharacteristic
466C23C22⋊C4×D6111yescharacteristic
467C23#1451980112yes—
468C23#1451980612yes—
469C23C2×D4×D6111yescharacteristic
470Q8—2442no—
471Q8—2442no—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—42no—
476D4—42no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—84no—
489C2×C4—612no—
490C2×C4—612no—
491C2×C4—612no—
492C2×C4—612no—
493C2×C4—1224no—
494C2×C4—1222no—
495C2×C4—1222no—
496C2×C4—1222no—
497C2×C4—1222no—
498C2×C4—1222no—
499C2×C4—1222no—
500C2×C4—1222no—
501C2×C4—1222no—
502C2×C4—4884no—
503C2×C4—2442no—
504C2×C4—2442no—
505C2×C4—2448no—
506C2×C4—2442no—
507C2×C4—2442no—
508C2×C4—2442no—
509C2×C4—2442no—
510C2×C4—2442no—
511C2×C4C22⋊C4×D6111yescharacteristic
512C2×C4C22⋊C4×D6111yescharacteristic
513C2×C4C22×C4×D6111yescharacteristic
514C2×C4C2×D4×D6111yescharacteristic
515C8—42no—
516C8—2442no—
517C22—24no—
518C22—24no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—84no—
527C22#1683973412yes—
528C22#1683976012yes—
529C22#1683976012yes—
530C22#1683977712yes—
531C22C2×C22⋊C4×D6111yescharacteristic
532C22C2×#1451980111yescharacteristic
533C22C2×#1451980611yescharacteristic
534C4—21no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—42no—
539C4—82no—
540C4—1222no—
541C4—1222no—
542C4—1222no—
543C4—1222no—
544C4—4882no—
545C4—2442no—
546C4—2442no—
547C2—21no—
548C2—22no—
549C2—21no—
550C2—82no—
551C2#2144435414yesdirect product factor
552C2C2×#1683973411yescharacteristic
553C2C2×#1683976011yescharacteristic
554C2C2×#1683977711yescharacteristic
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×#1512
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×#16839626C2semidirect
4. #21444354C2direct (N × H)
5. C2×#16839500C2semidirect
6. C2×#16839498C2semidirect
11. #16840293C4semidirect
14. C2×#14519768C4semidirect
15. C2×#14519764C4semidirect
18. C2×#14519742C4semidirect
20. C2×D4×Dic61C4semidirect
25. #16839816C22semidirect
30. #16839626C22semidirect
33. #16839500C22semidirect
34. #16839498C22semidirect
49. #14519768C2×C4semidirect
51. #14519764C2×C4semidirect
59. #14519742C2×C4semidirect
63. D4×Dic61C2×C4semidirect
282. C2×C61#1512semidirect
317. C61C2×#1512semidirect
551. C2#21444354direct (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×#168396262
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C2×#168395002
C2×#168394982
C2×#168394962
C2×C61×#3272
C2×#151261