Finite Group Databasebeta

← C2×#21460903 #30606254

Subgroups — C2×#21460903 #30606254

Order 15616.

1202 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519837C211yesmaximal, characteristic
2C22×#14519835C211yesmaximal, characteristic
3#21460903C214yesmaximal, direct product factor
4C2×#16839641C211yesmaximal, characteristic
5C22×#11758217—21no—
6C22×C22⋊#6923—21no—
7C2×#14519837—22no—
8C2×#14519837—21no—
9C2×#14519837C414yescomplemented
10C2×#14519837C2212yes—
11C2×#14519835—21no—
12C2×#14519835—22no—
13C2×#14519835C414yescomplemented
14C2×#14519835C2212yes—
15C23×C22⋊D61C2211yescharacteristic
16C22×C22⋊Dic61C411yescharacteristic, complemented
17C22×#11758198—21no—
18#16839641—21no—
19#16839641—21no—
20#16839641C412yescomplemented
21#16839641C2212yes—
22C2×#14519684—21no—
23C24×C4×C61C411yescharacteristic, complemented
24C23×#6923—41no—
25C2×#11758217—24no—
26C2×#11758217—22no—
27C2×#11758217—41no—
28C2×#11758217—42no—
29C22×#92420—41no—
30C2×C22⋊#6923—24no—
31C2×C22⋊#6923—22no—
32C2×C22⋊#6923—41no—
33C2×C22⋊#6923—42no—
34#14519837—24no—
35#14519837—22no—
36#14519837C2×C414yescomplemented
37#14519835—24no—
38#14519835—22no—
39#14519835C2×C414yescomplemented
40C24×D61D411yescharacteristic
41C22×C22⋊D61—41no—
42C22×C22⋊D61—41no—
43C22×C22⋊D61—42no—
44C22×C22⋊D61C2×C411yescharacteristic
45C22×C22⋊D61C2×C412yes—
46C22×C22⋊D61C2×C412yes—
47C22×C22⋊D61D411yescharacteristic
48C22×C22⋊D61D412yes—
49C22×C22⋊D61D411yescharacteristic
50C22×C22⋊D61Q812yes—
51C22×C22⋊D61C2311yescharacteristic
52C23×Dic61—21no—
53C23×Dic61D411yescharacteristic
54C2×C22⋊Dic61—21no—
55C2×C22⋊Dic61—42no—
56C2×C22⋊Dic61C2×C412yescomplemented
57C2×#11758198—22no—
58C2×#11758198—22no—
59C2×#11758198—44no—
60#14519684—22no—
61#14519684—22no—
62C25×C61C2×C411yescharacteristic
63C23×C4×C61—21no—
64C23×C4×C61—21no—
65C23×C4×C61—44no—
66C23×C4×C61—41no—
67C23×C4×C61—41no—
68C23×C4×C61C2×C412yescomplemented
69C24×C61—21no—
70C24×C61—21no—
71C24×C61—22no—
72C24×C61—42no—
73C24×C61—42no—
74C24×C61C4212yes—
75C24×C61C22⋊C411yescharacteristic
76C24×C61C22⋊C411yescharacteristic
77C24×C61C4⋊C412yes—
78C24×C61C22×C411yescharacteristic
79C23×D61—21no—
80C23×D61—22no—
81C23×D61—21no—
82C23×D61—42no—
83C23×D61—42no—
84C23×D61C22⋊C411yescharacteristic
85C23×D61C22⋊C412yes—
86C23×D61C4⋊C412yes—
87C23×D61C2×D411yescharacteristic
88C22×#6923—44no—
89C22×#6923—42no—
90C22×#6923—82no—
91C22×#6923—82no—
92C22×C4×C61—24no—
93C22×C4×C61—22no—
94C22×C4×C61—44no—
95C22×C4×C61—44no—
96C22×C4×C61—42no—
97C22×C4×C61—42no—
98C22×C4×C61—48no—
99C22×C4×C61—44no—
100C22×C4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61—42no—
103C22×C4×C61—44no—
104C2×C22⋊D61—42no—
105C2×C22⋊D61—42no—
106C2×C22⋊D61—42no—
107C2×C22⋊D61—42no—
108C2×C22⋊D61—41no—
109C2×C22⋊D61—41no—
110C2×C22⋊D61—42no—
111C2×C22⋊D61—42no—
112C2×C22⋊D61—41no—
113C2×C22⋊D61—41no—
114C2×C22⋊D61—41no—
115C2×C22⋊D61—41no—
116C2×C22⋊D61—42no—
117C2×C22⋊D61—42no—
118C2×C22⋊D61—41no—
119C2×C22⋊D61—41no—
120C2×C22⋊D61C4212yes—
121C2×C22⋊D61C22⋊C412yes—
122C2×C22⋊D61C22⋊C412yes—
123C2×C22⋊D61C4⋊C412yes—
124C2×C22⋊D61C4⋊C412yes—
125C2×C22⋊D61C4⋊C412yes—
126C2×C22⋊D61C22×C411yescharacteristic
127C2×C22⋊D61C22×C411yescharacteristic
128C2×C22⋊D61C2×D411yescharacteristic
129C2×C22⋊D61C2×Q811yescharacteristic
130C22×Dic61—21no—
131C22×Dic61—22no—
132C22×Dic61—21no—
133C22×Dic61—22no—
134C22×Dic61—42no—
135C22×Dic61—42no—
136C22×Dic61—42no—
137C22×Dic61C22⋊C411yescharacteristic
138C22×Dic61C22⋊C412yes—
139C22×Dic61C4⋊C412yes—
140C22×Dic61C2×D411yescharacteristic
141C22⋊#6923—24no—
142C22⋊#6923—44no—
143C22⋊#6923—42no—
144#11758217—24no—
145#11758217—44no—
146#11758217—42no—
147C2×#92420—44no—
148C2×#92420—42no—
149C22⋊Dic61—42no—
150C22⋊Dic61—42no—
151#11758198—44no—
152#11758198—44no—
153C23×C61—22no—
154C23×C61—22no—
155C23×C61—22no—
156C23×C61—22no—
157C23×C61—22no—
158C23×C61—22no—
159C23×C61—21no—
160C23×C61—21no—
161C23×C61—21no—
162C23×C61—21no—
163C23×C61—42no—
164C23×C61—42no—
165C23×C61—48no—
166C23×C61—41no—
167C23×C61—41no—
168C23×C61—44no—
169C23×C61—41no—
170C23×C61—44no—
171C23×C61—41no—
172C23×C61—42no—
173C23×C61—42no—
174C23×C61#9512yes—
175C23×C61#9512yes—
176C23×C61#9911yescharacteristic
177C23×C61#9912yes—
178C23×C61#9911yescharacteristic
179C23×C61C2×C4211yescharacteristic
180C23×C61C2×C22⋊C411yescharacteristic
181C23×C61C2×C4⋊C411yescharacteristic
182C22×D61—22no—
183C22×D61—22no—
184C22×D61—21no—
185C22×D61—21no—
186C22×D61—22no—
187C22×D61—22no—
188C22×D61—21no—
189C22×D61—21no—
190C22×D61—42no—
191C22×D61—42no—
192C22×D61—41no—
193C22×D61—41no—
194C22×D61—41no—
195C22×D61—44no—
196C22×D61—44no—
197C22×D61—41no—
198C22×D61—81no—
199C22×D61—81no—
200C22×D61—84no—
201C22×D61#9512yes—
202C22×D61C2×C22⋊C411yescharacteristic
203C22×D61C2×C4⋊C411yescharacteristic
204C2×#6923—44no—
205C2×#6923—82no—
206C2×#6923—82no—
207C2×#6923—88no—
208C2×C4×C61—24no—
209C2×C4×C61—42no—
210C2×C4×C61—44no—
211C2×C4×C61—48no—
212C2×C4×C61—44no—
213C2×C4×C61—44no—
214C2×C4×C61—42no—
215C2×C4×C61—44no—
216C22⋊D61—42no—
217C22⋊D61—42no—
218C22⋊D61—42no—
219C22⋊D61—42no—
220C22⋊D61—42no—
221C22⋊D61—42no—
222C22⋊D61—41no—
223C22⋊D61—41no—
224C22⋊D61—41no—
225C22⋊D61—41no—
226C2×Dic61—22no—
227C2×Dic61—22no—
228C2×Dic61—22no—
229C2×Dic61—22no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—42no—
235C2×Dic61—42no—
236C2×Dic61—42no—
237C2×Dic61—84no—
238C2×Dic61#9512yes—
239C2×Dic61C2×C22⋊C411yescharacteristic
240C2×Dic61C2×C4⋊C411yescharacteristic
241#92420—44no—
242C2×#1390—611nomaximal, Sylow
243C22×C61—21no—
244C22×C61—21no—
245C22×C61—21no—
246C22×C61—21no—
247C22×C61—24no—
248C22×C61—24no—
249C22×C61—22no—
250C22×C61—21no—
251C22×C61—21no—
252C22×C61—42no—
253C22×C61—41no—
254C22×C61—41no—
255C22×C61—42no—
256C22×C61—42no—
257C22×C61—44no—
258C22×C61—44no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—44no—
264C22×C61—44no—
265C22×C61#34212yes—
266C22×C61#34212yes—
267C22×C61AΣL(1,𝔽16)12yes—
268C22×C61#35212yes—
269C22×C61C2×#9511yescharacteristic
270C22×C61C2×#9911yescharacteristic
271C22×C61C2×#9911yescharacteristic
272C2×D61—21no—
273C2×D61—22no—
274C2×D61—21no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—44no—
280C2×D61—44no—
281C2×D61—42no—
282C2×D61—41no—
283C2×D61—41no—
284C2×D61—81no—
285C2×D61—82no—
286C2×D61—81no—
287C2×D61—82no—
288#6923—84no—
289C4×C61—44no—
290Dic61—21no—
291Dic61—22no—
292Dic61—21no—
293Dic61—82no—
294C22×#100—611no—
295C22×#99—611no—
296C2×#386—611no—
297#1390—614no—
298C2×C61—21no—
299C2×C61—21no—
300C2×C61—22no—
301C2×C61—42no—
302C2×C61—41no—
303C2×C61—41no—
304C2×C61#139014yescomplemented
305C2×C61C2×#34211yescharacteristic
306C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
307C2×C61C2×#35211yescharacteristic
308D61—41no—
309D61—42no—
310D61—41no—
311C23×D4—611no—
312C24×C4#692311yescharacteristic, complemented
313C22×M16—1221no—
314C22×C22⋊C4—611no—
315C22×C22⋊C4—1221no—
316C22×C22⋊C4—1221no—
317C2×#100—614no—
318C2×#100—612no—
319C2×#100—1222no—
320C2×#100—1221no—
321C2×#99—614no—
322C2×#99—612no—
323C2×#99—1222no—
324C2×#99—1221no—
325#386—612no—
326#386—612no—
327#386—1221no—
328#386—1221no—
329C2×#95—1221no—
330C61C2×#139011yescharacteristic, complemented, Sylow
331C25—611no—
332C25C2×#692311yescharacteristic
333C22×D4—612no—
334C22×D4—612no—
335C22×D4—612no—
336C22×D4—612no—
337C22×D4—611no—
338C22×D4—611no—
339C22×D4—611no—
340C22×D4—611no—
341C22×D4—2441no—
342C22×D4—2441no—
343C22×D4—2442no—
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—44no—
347C23×C4—41no—
348C23×C4—41no—
349C23×C4—611no—
350C23×C4—1221no—
351C23×C4—2441no—
352C23×C4C2×#692312yescomplemented
353C2×M16—1224no—
354C2×M16—1222no—
355C2×M16—2441no—
356C2×M16—2442no—
357C22×C8—2441no—
358C2×C22⋊C4—612no—
359C2×C22⋊C4—1224no—
360C2×C22⋊C4—1222no—
361C2×C22⋊C4—1222no—
362C2×C22⋊C4—1222no—
363C2×C22⋊C4—1221no—
364C2×C22⋊C4—2444no—
365C2×C22⋊C4—2441no—
366C2×C22⋊C4—2442no—
367C2×C22⋊C4—2442no—
368#100—614no—
369#100—1224no—
370#100—1222no—
371#99—614no—
372#99—1224no—
373#99—1222no—
374#95—1222no—
375#95—1222no—
376C24—21no—
377C24—21no—
378C24—22no—
379C24—42no—
380C24—42no—
381C24—612no—
382C24—612no—
383C24—611no—
384C24—611no—
385C24—1221no—
386C24—1222no—
387C24—1221no—
388C24—2442no—
389C24—2442no—
390C24C4×#692312yes—
391C24C4⋊#692312yes—
392C24C22⋊#692311yescharacteristic
393C24C22⋊#692311yescharacteristic
394C24C22×#692311yescharacteristic
395C2×D4—612no—
396C2×D4—612no—
397C2×D4—612no—
398C2×D4—612no—
399C2×D4—611no—
400C2×D4—611no—
401C2×D4—612no—
402C2×D4—611no—
403C2×D4—612no—
404C2×D4—611no—
405C2×D4—2441no—
406C2×D4—2441no—
407C2×D4—2441no—
408C2×D4—2441no—
409C2×D4—2441no—
410C2×D4—2441no—
411C2×D4—2441no—
412C2×D4—2441no—
413C2×D4—2442no—
414C2×D4—2442no—
415C2×D4—2442no—
416C2×D4—2442no—
417C2×D4—2442no—
418C2×D4—2442no—
419C2×D4—2442no—
420C2×D4—2442no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—44no—
424C22×C4—44no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—48no—
428C22×C4—44no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—42no—
432C22×C4—44no—
433C22×C4—612no—
434C22×C4—612no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1222no—
440C22×C4—1222no—
441C22×C4—4882no—
442C22×C4—4882no—
443C22×C4—2442no—
444C22×C4—2442no—
445C22×C4—2442no—
446C22×C4—2444no—
447C22×C4—2442no—
448M16—1224no—
449M16—2442no—
450M16—2444no—
451C2×C8—2442no—
452C2×C8—2444no—
453C22⋊C4—1224no—
454C22⋊C4—2444no—
455C22⋊C4—2444no—
456C22⋊C4—2442no—
457C22⋊C4—2442no—
458C22⋊C4—2444no—
459C22⋊C4—2442no—
460C23—22no—
461C23—22no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—22no—
470C23—41no—
471C23—41no—
472C23—44no—
473C23—44no—
474C23—41no—
475C23—41no—
476C23—42no—
477C23—42no—
478C23—48no—
479C23—42no—
480C23—42no—
481C23—612no—
482C23—611no—
483C23—611no—
484C23—1221no—
485C23—1221no—
486C23—1222no—
487C23—1222no—
488C23—1221no—
489C23—1221no—
490C23—1222no—
491C23—1222no—
492C23—4881no—
493C23—4881no—
494C23—4884no—
495C23—2441no—
496C23—2441no—
497C23—2441no—
498C23—2441no—
499C23—2444no—
500C23—2444no—
501C23—2442no—
502C23—2442no—
503C23(C2×#6923)⋊C412yes—
504C23(C2×#6923)⋊C412yes—
505C23#1451983511yescharacteristic
506C23#1451983511yescharacteristic
507C23#1451983612yes—
508C23C2×C4×#692311yescharacteristic
509C23C2×C22⋊#692311yescharacteristic
510C23C2×C4⋊#692311yescharacteristic
511D4—2442no—
512D4—2441no—
513D4—2441no—
514D4—2442no—
515D4—2442no—
516D4—2442no—
517D4—2441no—
518D4—2442no—
519D4—2442no—
520D4—2441no—
521C2×C4—24no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—48no—
525C2×C4—44no—
526C2×C4—42no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—612no—
530C2×C4—611no—
531C2×C4—611no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1222no—
537C2×C4—1222no—
538C2×C4—1222no—
539C2×C4—1222no—
540C2×C4—4884no—
541C2×C4—4882no—
542C2×C4—4882no—
543C2×C4—4888no—
544C2×C4—2442no—
545C2×C4—2442no—
546C2×C4—2444no—
547C2×C4—2442no—
548C8—2444no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—24no—
554C22—24no—
555C22—22no—
556C22—21no—
557C22—21no—
558C22—42no—
559C22—41no—
560C22—41no—
561C22—42no—
562C22—42no—
563C22—44no—
564C22—44no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—44no—
570C22—44no—
571C22—1221no—
572C22—1222no—
573C22—1221no—
574C22—4881no—
575C22—4881no—
576C22—4882no—
577C22—4882no—
578C22—2441no—
579C22—2442no—
580C22—2441no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22—2441no—
585C22—2444no—
586C22—2444no—
587C22#1684064012yes—
588C22#1684064012yes—
589C22#1684066212yes—
590C22#1684066412yes—
591C22C2×(C2×#6923)⋊C411yescharacteristic
592C22C2×#1451983511yescharacteristic
593C22C2×#1451983611yescharacteristic
594C4—44no—
595C4—1221no—
596C4—1222no—
597C4—1221no—
598C4—4882no—
599C4—4884no—
600C2—21no—
601C2—22no—
602C2—21no—
603C2—42no—
604C2—41no—
605C2—41no—
606C2—2441no—
607C2—2441no—
608C2—2442no—
609C2#2146090314yesdirect product factor
610C2C2×#1684064011yescharacteristic
611C2C2×#1684066211yescharacteristic
612C2C2×#1684066411yescharacteristic
subgroupG/H
centerC23#14519835
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC24×C4×C61C4
socleC23×C61#99
prime radicalC23×C22⋊D61C22
cosocleC22×C22⋊D61C23
hypercenterC24×C4#6923
hypocenterC61C2×#1390
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24 ◁ C25 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
3. #21460903C2direct (N × H)
9. C2×#14519837C4semidirect
13. C2×#14519835C4semidirect
16. C22×C22⋊Dic61C4semidirect
20. #16839641C4semidirect
23. C24×C4×C61C4semidirect
36. #14519837C2×C4semidirect
39. #14519835C2×C4semidirect
56. C2×C22⋊Dic61C2×C4semidirect
68. C23×C4×C61C2×C4semidirect
304. C2×C61#1390semidirect
312. C24×C4#6923semidirect
330. C61C2×#1390semidirect
352. C23×C4C2×#6923semidirect
609. C2#21460903direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198372
C22×#145198352
#214609032
C2×#168396412
C2×#139061