Finite Group Databasebeta

← C2×#21444415 #29647913

Subgroups — C2×#21444415 #29647913

Order 15616.

1394 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×#124×D61C211yesmaximal, characteristic
2C2×#16839817C211yesmaximal, characteristic, complemented
3C2×#16839714C211yesmaximal, characteristic, complemented
4#21444415C218yesmaximal, direct product factor
5C2×#16839502C211yesmaximal, characteristic, complemented
6C2×#16839501C211yesmaximal, characteristic, complemented
7C2×#16839501C211yesmaximal, characteristic, complemented
8C2×C61×#329C211yesmaximal, characteristic, complemented
9C22×Q8×D61C411yescharacteristic
10C22×D4×D61C411yescharacteristic
11C22×#11758189—21no—
12C2×#14519766C411yescharacteristic
13C2×#14519765C2211yescharacteristic
14C2×#14519764C411yescharacteristic
15C2×#14519763—21no—
16C2×#14519763—21no—
17#124×D61—22no—
18#124×D61—22no—
19#124×D61C414yes—
20#124×D61C2214yes—
21C2×C22⋊C4×D61—21no—
22C2×C22⋊C4×D61—21no—
23C2×C42×D61C2211yescharacteristic
24#16839817—22no—
25#16839817C2214yescomplemented
26C2×#14519706—21no—
27C2×#14519689—21no—
28#16839714—22no—
29#16839714C2214yescomplemented
30C2×#14519688C2211yescharacteristic, complemented
31C2×#14519688C2211yescharacteristic, complemented
32C2×C8×Dic61—21no—
33#16839502C2214yescomplemented
34#16839501C2214yescomplemented
35#16839501C2214yescomplemented
36C2×#124×C61C2211yescharacteristic
37C2×#97×C61C2211yescharacteristic, complemented
38C2×#97×C61C2211yescharacteristic, complemented
39C61×#329C2214yescomplemented
40C24×D61—21no—
41C22×Dic122—21no—
42C22×Dic122C2×C411yescharacteristic
43C2×Q8×D61—22no—
44C2×Q8×D61—44no—
45C2×Q8×D61C2×C414yes—
46C22×D244C2×C411yescharacteristic
47C22×C22⋊D61—21no—
48C2×D4×D61—22no—
49C2×D4×D61—44no—
50C2×D4×D61C2×C414yes—
51C22×C4×D61—21no—
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C2×#11758189—28no—
56C2×#11758189—24no—
57C22×#92418—21no—
58C22×#92418—21no—
59#14519766—22no—
60#14519766C2×C414yes—
61#14519765—21no—
62#14519765—21no—
63#14519765C2×C412yes—
64#14519765C2312yes—
65#14519764—22no—
66#14519764C2×C414yes—
67#14519763—24no—
68#14519763—24no—
69#14519763—24no—
70#14519763—24no—
71C2×C22⋊Dic61—21no—
72C2×C22⋊Dic61—21no—
73C2×#11758198—21no—
74C2×#11758198—21no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C22⋊C4×D61—24no—
78C22⋊C4×D61—24no—
79C22⋊C4×D61—24no—
80C22⋊C4×D61—24no—
81C2×C4×Dic61C2×C411yescharacteristic
82C2×C4×Dic61D411yescharacteristic
83C2×C4×Dic61D411yescharacteristic
84C42×D61C2×C412yes—
85C42×D61D412yes—
86C42×D61D412yes—
87C42×D61C2312yes—
88#14519706—24no—
89#14519689—24no—
90#14519688—21no—
91#14519688—21no—
92#14519688C2312yescomplemented
93#14519688C2312yescomplemented
94C8×Dic61—24no—
95C22×Q8×C61C2×C411yescharacteristic
96C22×D4×C61C2×C411yescharacteristic
97C22×C8×C61—21no—
98C22×C8×C61—21no—
99#124×C61—21no—
100#124×C61—21no—
101#124×C61C2×C412yes—
102#124×C61C2312yes—
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61—21no—
105C2×C42×C61C2311yescharacteristic
106#97×C61—21no—
107#97×C61—21no—
108#97×C61C2312yescomplemented
109#97×C61C2312yescomplemented
110C24×C61—21no—
111C23×D61—21no—
112C23×D61—24no—
113C23×D61—44no—
114C23×D61—44no—
115C23×D61—44no—
116C23×D61C22⋊C411yescharacteristic
117C2×Q8×C61—21no—
118C2×Q8×C61—42no—
119C2×Q8×C61C22×C412yes—
120C2×D4×C61—21no—
121C2×D4×C61—42no—
122C2×D4×C61C22×C412yes—
123C22×C4×C61—21no—
124C22×C4×C61C22×C411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C2×C22⋊D61—24no—
128C2×C22⋊D61—44no—
129C22×Dic61—21no—
130C22×Dic61C22⋊C411yescharacteristic
131C22×Dic61C22⋊C411yescharacteristic
132C22×Dic61C22⋊C411yescharacteristic
133Q8×D61—48no—
134Q8×D61—48no—
135D4×D61—48no—
136D4×D61—48no—
137C2×D244—21no—
138C2×D244—42no—
139C2×D244C22×C412yes—
140C2×C4×D61—24no—
141C2×C4×D61—24no—
142C2×C4×D61—24no—
143C2×C4×D61—42no—
144C2×C4×D61—44no—
145C2×C4×D61C22⋊C412yes—
146C2×C4×D61C22⋊C412yes—
147C2×C4×D61C22⋊C412yes—
148C2×C4×D61C22×C412yes—
149C2×C4×D61C2×D412yes—
150C2×C4×D61C2×D412yes—
151C2×Dic122—21no—
152C2×Dic122—24no—
153C2×Dic122—44no—
154C2×Dic122—42no—
155C2×Dic122C22×C412yes—
156C2×C8×C61—24no—
157C2×C8×C61—22no—
158C2×C8×C61—22no—
159C2×C8×C61—42no—
160C22⋊C4×C61—22no—
161C22⋊C4×C61—22no—
162C22⋊C4×C61—22no—
163C22⋊C4×C61—22no—
164C42×C61C22×C411yescharacteristic
165C42×C61C2×D411yescharacteristic
166C42×C61C2×D411yescharacteristic
167C42×C61C2411yescharacteristic
168C22⋊Dic61—24no—
169C22⋊Dic61—24no—
170#11758198—22no—
171#11758198—22no—
172#11758198—22no—
173#11758198—22no—
174#11758198—24no—
175#11758198—24no—
176C4×Dic61C22⋊C412yes—
177C4×Dic61C22⋊C412yes—
178C4×Dic61C22⋊C412yes—
179C4×Dic61C22×C412yes—
180C4×Dic61C2×D412yes—
181C4×Dic61C2×D412yes—
182C2×#92418—24no—
183C2×#92418—22no—
184C2×#92418—22no—
185C2×#92418—42no—
186#11758189—216no—
187C23×C61—22no—
188C23×C61—42no—
189C23×C61—42no—
190C23×C61—42no—
191C23×C61C2×C22⋊C411yescharacteristic
192C22×D61—22no—
193C22×D61—22no—
194C22×D61—22no—
195C22×D61—48no—
196C22×D61—48no—
197C22×D61—42no—
198C22×D61—42no—
199C22×D61—42no—
200C22×D61—48no—
201C22×D61—816no—
202C22×D61#10414yes—
203C22×D61C2×C22⋊C412yes—
204Q8×C61—42no—
205Q8×C61—42no—
206D4×C61—42no—
207D4×C61—42no—
208C2×C4×C61—22no—
209C2×C4×C61—22no—
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61—42no—
213C2×C4×C61C2×C22⋊C411yescharacteristic
214C2×C4×C61C2×C22⋊C411yescharacteristic
215C2×C4×C61C2×C22⋊C411yescharacteristic
216C2×C4×C61C23×C411yescharacteristic
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C22⋊D61—48no—
220C2×Dic61—22no—
221C2×Dic61—22no—
222C2×Dic61—22no—
223C2×Dic61—42no—
224C2×Dic61#10014yes—
225C2×Dic61C2×C22⋊C412yes—
226C2×Dic61C2×C22⋊C412yes—
227C2×Dic61C2×C22⋊C412yes—
228D244—42no—
229D244—42no—
230C4×D61—24no—
231C4×D61—24no—
232C4×D61—24no—
233C4×D61—24no—
234C4×D61—42no—
235C4×D61—42no—
236C4×D61—48no—
237Dic122—42no—
238Dic122—48no—
239Dic122—42no—
240C8×C61—24no—
241C8×C61—42no—
242#92418—24no—
243#92418—42no—
244C2×#1527—611nomaximal, Sylow
245C22×C61—42no—
246C22×C61—42no—
247C22×C61—42no—
248C22×C61—84no—
249C22×C61C2×#10012yes—
250C22×C61C2×#10412yes—
251C22×C61#42112yes—
252C22×C61C22×C22⋊C411yescharacteristic
253C2×D61—22no—
254C2×D61—22no—
255C2×D61—28no—
256C2×D61—42no—
257C2×D61—42no—
258C2×D61—42no—
259C2×D61—816no—
260C2×D61—84no—
261C2×D61C2×#10414yes—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—42no—
269Dic61—22no—
270Dic61—22no—
271Dic61—42no—
272Dic61C2×#10014yes—
273C22×#124—611no—
274C2×#432—611no—
275C2×C4×M16—611no—
276#1527—618no—
277C2×#329—611no—
278C2×#329—611no—
279C2×#329—611no—
280C2×#329D6111yescharacteristic, complemented
281C2×C61—82no—
282C2×C61#152714yescomplemented
283C2×C61C22×#10011yescharacteristic
284C2×C61C22×#10411yescharacteristic
285C2×C61C2×#42111yescharacteristic
286D61—24no—
287D61—82no—
288C23×Q8—611no—
289C23×D4—611no—
290C22×M16—1221no—
291C2×#124—611no—
292C2×#124—611no—
293C2×#124—614no—
294C2×#124—614no—
295C2×#124—611no—
296C2×#124—1221no—
297C2×#124—1221no—
298C2×#124—1222no—
299C2×#124—1222no—
300C2×#124C2×D6111yescharacteristic
301C22×C22⋊C4—1221no—
302C22×C22⋊C4—1221no—
303C22×C42—611no—
304#432—614no—
305#432—1222no—
306C2×C4⋊C8—1221no—
307C2×C22⋊C8—1221no—
308C4×M16—614no—
309C4×M16—1222no—
310C2×#97—611no—
311C2×#97—611no—
312C2×#97C2×D6111yescharacteristic, complemented
313C2×#97C2×D6111yescharacteristic, complemented
314C2×C4×C8—1221no—
315#329—614no—
316#329—614no—
317#329—614no—
318#329C2×D6114yescomplemented
319C61C2×#152711yescharacteristic, complemented, Sylow
320C25—1221no—
321C22×Q8—614no—
322C22×Q8—611no—
323C22×Q8—1221no—
324C22×Q8—1222no—
325C22×Q8—2444no—
326C22×Q8C4×D6111yescharacteristic
327C22×D4—614no—
328C22×D4—611no—
329C22×D4—1222no—
330C22×D4—1221no—
331C22×D4—2444no—
332C22×D4C4×D6111yescharacteristic
333C23×C4—611no—
334C23×C4—611no—
335C23×C4—611no—
336C23×C4—1221no—
337C2×M16—1224no—
338C2×M16—1228no—
339C22×C8—21no—
340C22×C8—21no—
341C22×C8—1221no—
342C22×C8—1221no—
343#124—21no—
344#124—21no—
345#124—614no—
346#124—614no—
347#124—612no—
348#124—612no—
349#124—1224no—
350#124—1224no—
351#124—1224no—
352#124—1224no—
353#124—1222no—
354#124—1222no—
355#124—1221no—
356#124—1221no—
357#124C4×D6112yes—
358#124C22×D6112yes—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—1224no—
362C2×C22⋊C4—1224no—
363C2×C22⋊C4—1224no—
364C2×C22⋊C4—1224no—
365C2×C22⋊C4—1221no—
366C2×C22⋊C4—1221no—
367C2×C22⋊C4—1221no—
368C2×C22⋊C4—1221no—
369C2×C22⋊C4—1221no—
370C2×C22⋊C4—1221no—
371C2×C42—611no—
372C2×C42—611no—
373C2×C42—611no—
374C2×C42—612no—
375C2×C42—612no—
376C2×C42—612no—
377C2×C42—612no—
378C2×C42C22×D6111yescharacteristic
379C4⋊C8—1224no—
380C22⋊C8—1224no—
381#97—21no—
382#97—21no—
383#97—612no—
384#97—612no—
385#97—1221no—
386#97—1221no—
387#97C22×D6112yescomplemented
388#97C22×D6112yescomplemented
389C4×C8—1224no—
390C24—21no—
391C24—611no—
392C24—1224no—
393C24—1221no—
394C24—2444no—
395C24—2444no—
396C24—2444no—
397C2×Q8—21no—
398C2×Q8—42no—
399C2×Q8—612no—
400C2×Q8—1224no—
401C2×Q8—1221no—
402C2×Q8—2442no—
403C2×Q8—2444no—
404C2×Q8—2448no—
405C2×Q8—2448no—
406C2×Q8C2×C4×D6112yes—
407C2×D4—21no—
408C2×D4—42no—
409C2×D4—612no—
410C2×D4—1224no—
411C2×D4—1221no—
412C2×D4—2442no—
413C2×D4—2444no—
414C2×D4—2448no—
415C2×D4—2448no—
416C2×D4C2×C4×D6112yes—
417C22×C4—21no—
418C22×C4—611no—
419C22×C4—611no—
420C22×C4—611no—
421C22×C4—612no—
422C22×C4—612no—
423C22×C4—612no—
424C22×C4—612no—
425C22×C4—612no—
426C22×C4—612no—
427C22×C4—1224no—
428C22×C4—1224no—
429C22×C4—1224no—
430C22×C4—1221no—
431C22×C4—2442no—
432C22×C4—2444no—
433C22×C4C2×C4×D6111yescharacteristic
434C22×C4D4×D6111yescharacteristic
435C22×C4D4×D6111yescharacteristic
436M16—12216no—
437C2×C8—24no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—42no—
441C2×C8—1224no—
442C2×C8—1222no—
443C2×C8—1222no—
444C2×C8—2442no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—1224no—
450C22⋊C4—1224no—
451C22⋊C4—1224no—
452C22⋊C4—1224no—
453C22⋊C4—1222no—
454C22⋊C4—1222no—
455C22⋊C4—1222no—
456C22⋊C4—1222no—
457C42—612no—
458C42—612no—
459C42—612no—
460C42—612no—
461C42—612no—
462C42—612no—
463C42C2×C4×D6111yescharacteristic
464C42D4×D6111yescharacteristic
465C42D4×D6111yescharacteristic
466C42C23×D6111yescharacteristic
467C23—22no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—612no—
472C23—614no—
473C23—1222no—
474C23—1222no—
475C23—1222no—
476C23—48816no—
477C23—2448no—
478C23—2448no—
479C23—2448no—
480C23—2442no—
481C23—2442no—
482C23—2442no—
483C23C22⋊C4×D6111yescharacteristic
484Q8—42no—
485Q8—42no—
486Q8—2442no—
487Q8—2442no—
488Q8—2448no—
489D4—42no—
490D4—42no—
491D4—2442no—
492D4—2442no—
493D4—2448no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—42no—
499C2×C4—612no—
500C2×C4—614no—
501C2×C4—612no—
502C2×C4—612no—
503C2×C4—1224no—
504C2×C4—1224no—
505C2×C4—1224no—
506C2×C4—1224no—
507C2×C4—1222no—
508C2×C4—1222no—
509C2×C4—1222no—
510C2×C4—2442no—
511C2×C4—2442no—
512C2×C4—2448no—
513C2×C4—2442no—
514C2×C4C22⋊C4×D6111yescharacteristic
515C2×C4C22⋊C4×D6111yescharacteristic
516C2×C4C22⋊C4×D6111yescharacteristic
517C2×C4C22×C4×D6111yescharacteristic
518C2×C4C2×D4×D6111yescharacteristic
519C2×C4C2×D4×D6111yescharacteristic
520C8—24no—
521C8—42no—
522C8—1224no—
523C8—2442no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—84no—
528C22—614no—
529C22—1222no—
530C22—1228no—
531C22—1222no—
532C22—48816no—
533C22—4884no—
534C22—2442no—
535C22—2442no—
536C22—2442no—
537C22#100×D6112yes—
538C22#104×D6112yes—
539C22#1683977712yes—
540C22C2×C22⋊C4×D6111yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—42no—
548C4—614no—
549C4—1222no—
550C4—1222no—
551C4—2442no—
552C2—82no—
553C2—1224no—
554C2—4882no—
555C2#2144441514yesdirect product factor
556C2C2×#100×D6111yescharacteristic
557C2C2×#104×D6111yescharacteristic
558C2C2×#1683977711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC2×C61×#329C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×D61C4
cosocleC42×C61C24
hypercenterC2×#329D61
hypocenterC61C2×#1527
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×#16839714C2semidirect
4. #21444415C2direct (N × H)
5. C2×#16839502C2semidirect
6. C2×#16839501C2semidirect
7. C2×#16839501C2semidirect
8. C2×C61×#329C2semidirect
25. #16839817C22semidirect
29. #16839714C22semidirect
30. C2×#14519688C22semidirect
31. C2×#14519688C22semidirect
33. #16839502C22semidirect
34. #16839501C22semidirect
35. #16839501C22semidirect
37. C2×#97×C61C22semidirect
38. C2×#97×C61C22semidirect
39. C61×#329C22semidirect
92. #14519688C23semidirect
93. #14519688C23semidirect
108. #97×C61C23semidirect
109. #97×C61C23semidirect
280. C2×#329D61semidirect
282. C2×C61#1527semidirect
312. C2×#97C2×D61semidirect
313. C2×#97C2×D61semidirect
318. #329C2×D61semidirect
319. C61C2×#1527semidirect
387. #97C22×D61semidirect
388. #97C22×D61semidirect
555. C2#21444415direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#124×D612
C2×#168398172
C2×#168397142
#214444152
C2×#168395022
C2×#168395012
C2×C61×#3292
C2×#152761