Finite Group Databasebeta

← C2×#21447018 #29707472

Subgroups — C2×#21447018 #29707472

Order 15616.

1662 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519757C211yesmaximal, characteristic
2C22×#14519708C211yesmaximal, characteristic, complemented
3C22×#14519702C211yesmaximal, characteristic, complemented
4C22×#14519700C211yesmaximal, characteristic, complemented
5C22×#14519689C211yesmaximal, characteristic
6C2×#16839619C211yesmaximal, characteristic
7#21447018C218yesmaximal, direct product factor
8C2×C61×#340C211yesmaximal, characteristic, complemented
9C23×Dic122C2211yescharacteristic
10C23×C4×D61C2211yescharacteristic
11C23×#92418C2211yescharacteristic
12C2×#14519757—24no—
13C2×#14519757—24no—
14C2×#14519757—22no—
15C2×#14519757C2214yes—
16C22×C4⋊Dic61—21no—
17C22×C4⋊Dic61C2211yescharacteristic
18C22×#11758198—21no—
19C22×#11758198—21no—
20C2×#14519708—24no—
21C2×#14519708C2214yescomplemented
22C2×#14519702—24no—
23C2×#14519702C2214yescomplemented
24C2×#14519700—24no—
25C2×#14519700C2214yescomplemented
26C2×#14519689—24no—
27C2×#14519689C2214yes—
28#16839619—22no—
29#16839619C2214yes—
30C2×#14519684—21no—
31C23×C8×C61C2211yescharacteristic
32C22×C4⋊C4×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C61×#340C2214yescomplemented
35C24×D61D411yescharacteristic
36C22×Dic122—22no—
37C22×Dic122—22no—
38C22×Dic122—22no—
39C22×Dic122—22no—
40C22×Dic122—21no—
41C22×Dic122—22no—
42C22×Dic122D414yes—
43C22×Dic122C2312yes—
44C23×Dic61—21no—
45C23×Dic61—21no—
46C23×Dic61D411yescharacteristic
47C22×C4×D61—22no—
48C22×C4×D61—22no—
49C22×C4×D61—22no—
50C22×C4×D61—22no—
51C22×C4×D61—22no—
52C22×C4×D61—22no—
53C22×C4×D61D412yes—
54C22×C4×D61C2312yes—
55C22×#92418—22no—
56C22×#92418—22no—
57C22×#92418D414yes—
58C22×#92418C2312yes—
59#14519757—216no—
60#14519757—28no—
61#14519757—28no—
62C2×C4⋊Dic61—28no—
63C2×C4⋊Dic61—24no—
64C2×C4⋊Dic61—22no—
65C2×C4⋊Dic61—22no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61C2312yes—
68C2×#11758198—28no—
69C2×#11758198—24no—
70C2×#11758198—24no—
71C2×#11758198—44no—
72#14519708—28no—
73#14519702—28no—
74#14519700—28no—
75#14519689—28no—
76#14519684—24no—
77C23×C4×C61—21no—
78C23×C4×C61—21no—
79C23×C4×C61C2311yescharacteristic
80C22×C8×C61—22no—
81C22×C8×C61—22no—
82C22×C8×C61—22no—
83C22×C8×C61C2312yes—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61—22no—
86C2×C4⋊C4×C61—22no—
87C2×C4⋊C4×C61—22no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61D414yes—
90C2×C4⋊C4×C61C2312yes—
91C2×C4⋊C4×C61C2312yes—
92C24×C61C2×D411yescharacteristic
93C23×D61—22no—
94C23×D61—22no—
95C23×D61—22no—
96C23×D61—22no—
97C23×D61—22no—
98C23×D61—22no—
99C23×D61SD1614yes—
100C23×D61C2×D412yes—
101C22×C4×C61—24no—
102C22×C4×C61—22no—
103C22×C4×C61—22no—
104C22×C4×C61—42no—
105C22×C4×C61—42no—
106C22×C4×C61—42no—
107C22×C4×C61—42no—
108C22×C4×C61—42no—
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D412yes—
111C22×C4×C61C2×D412yes—
112C22×C4×C61C2×D412yes—
113C22×C4×C61#4112yes—
114C22×C4×C61#4112yes—
115C22×C4×C61#4112yes—
116C22×C4×C61C2411yescharacteristic
117C22×Dic61—22no—
118C22×Dic61—24no—
119C22×Dic61—22no—
120C22×Dic61—22no—
121C22×Dic61—22no—
122C22×Dic61—22no—
123C22×Dic61—42no—
124C22×Dic61—42no—
125C22×Dic61—42no—
126C22×Dic61—42no—
127C22×Dic61—42no—
128C22×Dic61C2×D412yes—
129C2×C4×D61—24no—
130C2×C4×D61—24no—
131C2×C4×D61—24no—
132C2×C4×D61—22no—
133C2×C4×D61—22no—
134C2×C4×D61—22no—
135C2×C4×D61—22no—
136C2×C4×D61—22no—
137C2×C4×D61—22no—
138C2×C4×D61—44no—
139C2×C4×D61—44no—
140C2×C4×D61—44no—
141C2×C4×D61—44no—
142C2×Dic122—28no—
143C2×Dic122—28no—
144C2×Dic122—22no—
145C2×Dic122—22no—
146C2×Dic122—22no—
147C2×Dic122—22no—
148C2×Dic122—24no—
149C2×Dic122—22no—
150C2×Dic122—44no—
151C2×Dic122—42no—
152C2×Dic122—42no—
153C2×Dic122—44no—
154C2×Dic122C2×D414yes—
155C2×C8×C61—22no—
156C2×C8×C61—22no—
157C2×C8×C61—22no—
158C2×C8×C61—44no—
159C4⋊C4×C61—24no—
160C4⋊C4×C61—22no—
161C4⋊C4×C61—22no—
162C4⋊C4×C61—22no—
163C4⋊C4×C61—42no—
164C4⋊C4×C61C2×D414yes—
165#11758198—216no—
166#11758198—48no—
167C4⋊Dic61—216no—
168C4⋊Dic61—22no—
169C4⋊Dic61—22no—
170C4⋊Dic61—42no—
171C2×#92418—28no—
172C2×#92418—22no—
173C2×#92418—22no—
174C2×#92418C2×D414yes—
175C23×C61#12012yes—
176C23×C61#12112yes—
177C23×C61#12312yes—
178C23×C61C2×SD1612yes—
179C23×C61#13512yes—
180C23×C61#13712yes—
181C23×C61#13712yes—
182C23×C61C22×D411yescharacteristic
183C22×D61—22no—
184C22×D61—22no—
185C22×D61—22no—
186C22×D61—22no—
187C22×D61—22no—
188C22×D61—22no—
189C22×D61—28no—
190C22×D61—28no—
191C22×D61—28no—
192C22×D61—44no—
193C22×D61—44no—
194C22×D61—44no—
195C22×D61—44no—
196C22×D61C2×SD1614yes—
197C2×C4×C61—24no—
198C2×C4×C61—42no—
199C2×C4×C61—42no—
200C2×C4×C61—48no—
201C2×C4×C61—42no—
202C2×C4×C61—42no—
203C2×C4×C61—42no—
204C2×C4×C61—84no—
205C2×C4×C61#12012yes—
206C2×C4×C61#12114yes—
207C2×C4×C61#12114yes—
208C2×C4×C61#12112yes—
209C2×C4×C61#12314yes—
210C2×C4×C61#12312yes—
211C2×C4×C61#12414yes—
212C2×C4×C61C22×D411yescharacteristic
213C2×C4×C61C22×D411yescharacteristic
214C2×C4×C61C22×D411yescharacteristic
215C2×C4×C61C2×#4111yescharacteristic
216C2×C4×C61C2×#4111yescharacteristic
217C2×C4×C61C2×#4111yescharacteristic
218C2×Dic61—22no—
219C2×Dic61—24no—
220C2×Dic61—22no—
221C2×Dic61—22no—
222C2×Dic61—42no—
223C2×Dic61—42no—
224C2×Dic61—48no—
225C2×Dic61—44no—
226C2×Dic61—42no—
227C2×Dic61—42no—
228C2×Dic61—42no—
229C2×Dic61—84no—
230C4×D61—42no—
231C4×D61—42no—
232C4×D61—42no—
233C4×D61—42no—
234C4×D61—48no—
235Dic122—24no—
236Dic122—24no—
237Dic122—42no—
238Dic122—42no—
239Dic122—48no—
240C8×C61—42no—
241#92418—24no—
242C2×#2035—611nomaximal, Sylow
243C22×C61#39414yes—
244C22×C61#44814yes—
245C22×C61#45214yes—
246C22×C61#46514yes—
247C22×C61#47014yes—
248C22×C61#48314yes—
249C22×C61#48514yes—
250C22×C61C2×#12011yescharacteristic
251C22×C61C2×#12111yescharacteristic
252C22×C61C2×#12311yescharacteristic
253C22×C61C22×SD1611yescharacteristic
254C22×C61C2×#13511yescharacteristic
255C22×C61C2×#13711yescharacteristic
256C22×C61C2×#13711yescharacteristic
257C2×D61—24no—
258C2×D61—24no—
259C2×D61—24no—
260C2×D61—42no—
261C2×D61—42no—
262C2×D61—42no—
263C2×D61—42no—
264C2×D61—416no—
265C4×C61—44no—
266C4×C61—82no—
267C4×C61#39414yes—
268C4×C61C2×#12111yescharacteristic
269C4×C61C2×#12111yescharacteristic
270C4×C61C2×#12311yescharacteristic
271C4×C61C2×#12411yescharacteristic
272Dic61—44no—
273Dic61—42no—
274Dic61—82no—
275C22×C22⋊Q8—611no—
276C22×#106—611no—
277C22×#103—611no—
278C22×#103—611no—
279C22×C22⋊C8—611no—
280C2×#380—611no—
281#2035—618no—
282C2×#340D6111yescharacteristic, complemented
283C2×C61#203518yescomplemented
284C2×C61C2×#39411yescharacteristic
285C2×C61C2×#44811yescharacteristic
286C2×C61C2×#45211yescharacteristic
287C2×C61C2×#46511yescharacteristic
288C2×C61C2×#47011yescharacteristic
289C2×C61C2×#48311yescharacteristic
290C2×C61C2×#48511yescharacteristic
291D61—44no—
292C23×Q8—611no—
293C24×C4—611no—
294C23×C8—611no—
295C23×C8C2×D6111yescharacteristic
296C2×C22⋊Q8—614no—
297C2×C22⋊Q8—1222no—
298C2×C22⋊Q8—1224no—
299C2×C22⋊Q8—1224no—
300C22×C4⋊C4—611no—
301C22×C4⋊C4—1221no—
302C22×C4⋊C4C2×D6111yescharacteristic
303C22×C4⋊C4C2×D6111yescharacteristic
304C22×C22⋊C4—1221no—
305C22×C22⋊C4—1221no—
306C2×#106—614no—
307C2×#106—1224no—
308C2×#103—614no—
309C2×#103—614no—
310C2×#103—1224no—
311C2×#103—1224no—
312C2×C22⋊C8—614no—
313C2×C22⋊C8—1224no—
314#380—614no—
315#380—1222no—
316C2×#95—1221no—
317#340C2×D6114yescomplemented
318C61C2×#203511yescharacteristic, complemented, Sylow
319C25—611no—
320C22×Q8—614no—
321C22×Q8—612no—
322C22×Q8—1222no—
323C22×Q8—1221no—
324C22×Q8—1222no—
325C22×Q8—1222no—
326C22×Q8—1222no—
327C22×Q8—1222no—
328C23×C4—21no—
329C23×C4—21no—
330C23×C4—611no—
331C23×C4—612no—
332C23×C4—612no—
333C23×C4—1221no—
334C23×C4—1222no—
335C23×C4—1222no—
336C23×C4—1222no—
337C23×C4—1222no—
338C23×C4—1222no—
339C23×C4—1222no—
340C23×C4—1221no—
341C23×C4C22×D6111yescharacteristic
342C22×C8—22no—
343C22×C8—22no—
344C22×C8—22no—
345C22×C8—614no—
346C22×C8—612no—
347C22×C8—1222no—
348C22×C8—1222no—
349C22×C8C22×D6112yes—
350C22⋊Q8—1228no—
351C22⋊Q8—12216no—
352C22⋊Q8—1228no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—612no—
359C2×C4⋊C4—1224no—
360C2×C4⋊C4—1228no—
361C2×C4⋊C4—1222no—
362C2×C4⋊C4—1222no—
363C2×C4⋊C4—1221no—
364C2×C4⋊C4D24414yes—
365C2×C4⋊C4C22×D6112yes—
366C2×C4⋊C4C22×D6112yes—
367C2×C22⋊C4—1224no—
368C2×C22⋊C4—1228no—
369C2×C22⋊C4—1224no—
370C2×C22⋊C4—2444no—
371#106—1228no—
372#103—1228no—
373#103—1228no—
374C22⋊C8—1228no—
375#95—1224no—
376C24—612no—
377C24—614no—
378C24—1222no—
379C24—1222no—
380C24—1222no—
381C24—1222no—
382C24—1222no—
383C24—1222no—
384C24D4×D6111yescharacteristic
385C2×Q8—614no—
386C2×Q8—1222no—
387C2×Q8—1224no—
388C2×Q8—1222no—
389C2×Q8—1222no—
390C2×Q8—1222no—
391C2×Q8—1222no—
392C2×Q8—1228no—
393C2×Q8—1228no—
394C2×Q8—2442no—
395C2×Q8—2444no—
396C2×Q8—2442no—
397C2×Q8—2444no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—612no—
407C22×C4—1222no—
408C22×C4—1224no—
409C22×C4—1222no—
410C22×C4—1222no—
411C22×C4—1222no—
412C22×C4—1222no—
413C22×C4—1222no—
414C22×C4—1222no—
415C22×C4—1222no—
416C22×C4—1222no—
417C22×C4—1222no—
418C22×C4—1224no—
419C22×C4—1224no—
420C22×C4—1224no—
421C22×C4—1222no—
422C22×C4—2442no—
423C22×C4—2442no—
424C22×C4—2442no—
425C22×C4—2442no—
426C22×C4—2442no—
427C22×C4—2444no—
428C22×C4—2444no—
429C22×C4—2444no—
430C22×C4—2444no—
431C22×C4C2×D24412yes—
432C22×C4#1175822212yes—
433C22×C4#1175822212yes—
434C22×C4D4×D6112yes—
435C22×C4D4×D6112yes—
436C22×C4D4×D6111yescharacteristic
437C22×C4#1175822612yes—
438C22×C4C23×D6111yescharacteristic
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—44no—
443C2×C8—614no—
444C2×C8—1222no—
445C2×C8—1222no—
446C2×C8—1228no—
447C4⋊C4—22no—
448C4⋊C4—24no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—42no—
452C4⋊C4—12216no—
453C4⋊C4—1222no—
454C4⋊C4—1222no—
455C4⋊C4—2442no—
456C4⋊C4C2×D24414yes—
457C22⋊C4—12216no—
458C22⋊C4—2448no—
459C23—614no—
460C23—1228no—
461C23—1222no—
462C23—1222no—
463C23—1222no—
464C23—1222no—
465C23—1222no—
466C23—1222no—
467C23—1228no—
468C23—1228no—
469C23—2444no—
470C23—2444no—
471C23—2444no—
472C23—2444no—
473C23#1451974712yes—
474C23#1451975012yes—
475C23#1451976212yes—
476C23SD16×D6112yes—
477C23#1451979612yes—
478C23#1451980612yes—
479C23#1451980912yes—
480C23C2×D4×D6111yescharacteristic
481Q8—1224no—
482Q8—1224no—
483Q8—2448no—
484Q8—2442no—
485Q8—2442no—
486C2×C4—24no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—48no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—84no—
494C2×C4—1224no—
495C2×C4—1222no—
496C2×C4—1222no—
497C2×C4—1222no—
498C2×C4—4884no—
499C2×C4—2442no—
500C2×C4—2442no—
501C2×C4—2442no—
502C2×C4—2444no—
503C2×C4—2448no—
504C2×C4—2442no—
505C2×C4—2442no—
506C2×C4—2448no—
507C2×C4—2442no—
508C2×C4—2442no—
509C2×C4—2442no—
510C2×C4—2442no—
511C2×C4#1451974712yes—
512C2×C4#1451975012yes—
513C2×C4#1451975014yes—
514C2×C4#1451975214yes—
515C2×C4#1451976212yes—
516C2×C4#1451976214yes—
517C2×C4#1451976514yes—
518C2×C4C2×D4×D6111yescharacteristic
519C2×C4C2×D4×D6111yescharacteristic
520C2×C4C22×D24411yescharacteristic
521C2×C4C2×#1175822211yescharacteristic
522C2×C4C2×#1175822211yescharacteristic
523C2×C4C2×#1175822611yescharacteristic
524C8—42no—
525C8—1224no—
526C22—1224no—
527C22—1224no—
528C22—1224no—
529C22—2442no—
530C22—2442no—
531C22—2442no—
532C22—24416no—
533C22—2442no—
534C22#1683968014yes—
535C22#1683990214yes—
536C22#1683992514yes—
537C22#1683999014yes—
538C22#1684001914yes—
539C22#1684009414yes—
540C22#1684010514yes—
541C22C2×#1451974711yescharacteristic
542C22C2×#1451975011yescharacteristic
543C22C2×#1451976211yescharacteristic
544C22C2×SD16×D6111yescharacteristic
545C22C2×#1451979611yescharacteristic
546C22C2×#1451980611yescharacteristic
547C22C2×#1451980911yescharacteristic
548C4—44no—
549C4—82no—
550C4—4882no—
551C4—2442no—
552C4—2444no—
553C4#1683968014yes—
554C4C2×#1451975011yescharacteristic
555C4C2×#1451975211yescharacteristic
556C4C2×#1451976211yescharacteristic
557C4C2×#1451976511yescharacteristic
558C2—2444no—
559C2#2144701818yesdirect product factor
560C2C2×#1683968011yescharacteristic
561C2C2×#1683990211yescharacteristic
562C2C2×#1683992511yescharacteristic
563C2C2×#1683999011yescharacteristic
564C2C2×#1684001911yescharacteristic
565C2C2×#1684009411yescharacteristic
566C2C2×#1684010511yescharacteristic
subgroupG/H
centerC24D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#340C2
socleC24×C61C2×D4
prime radicalC24×D61D4
hypercenterC2×#340D61
hypocenterC61C2×#2035
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×#14519708C2semidirect
3. C22×#14519702C2semidirect
4. C22×#14519700C2semidirect
7. #21447018C2direct (N × H)
8. C2×C61×#340C2semidirect
21. C2×#14519708C22semidirect
23. C2×#14519702C22semidirect
25. C2×#14519700C22semidirect
34. C61×#340C22semidirect
282. C2×#340D61semidirect
283. C2×C61#2035semidirect
317. #340C2×D61semidirect
318. C61C2×#2035semidirect
559. C2#21447018direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197572
C22×#145197082
C22×#145197022
C22×#145197002
C22×#145196892
C2×#168396192
#214470182
C2×C61×#3402
C2×#203561