Finite Group Databasebeta

← C2×#21461801 #30615585

Subgroups — C2×#21461801 #30615585

Order 15616.

2050 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D61⋊M16C211yesmaximal, characteristic, complemented
2C22×#14519842C212yesmaximal, complemented
3C2×C4×C22⋊#6923C211yesmaximal, characteristic, complemented
4#21461801C218yesmaximal, direct product factor
5C2×#16840632C212yesmaximal, complemented
6C2×#16840275C211yesmaximal, characteristic
7C22×#11758213C2212yes—
8C2×D61⋊M16—28no—
9C2×D61⋊M16—22no—
10C2×D61⋊M16C2214yescomplemented
11C22×#11758217—21no—
12C22×D61⋊C8—21no—
13C22×C22⋊#6923—21no—
14C22×C4×#6923C2212yes—
15C2×#14519842—28no—
16C2×#14519842C2218yescomplemented
17C4×C22⋊#6923—22no—
18C4×C22⋊#6923C2214yescomplemented
19C2×(C2×#6923)⋊C4—21no—
20#16840632C2218yescomplemented
21C22×#11758226C2211yescharacteristic
22C23×C4×D61C2211yescharacteristic
23#16840275—22no—
24#16840275—22no—
25#16840275C414yescomplemented
26#16840275C2214yes—
27C2×#14519762—21no—
28C2×#14519753C411yescharacteristic, complemented
29C2×#14519752C411yescharacteristic, complemented
30C2×#14519751C411yescharacteristic, complemented
31C2×#14519747—21no—
32C2×#14519739—21no—
33C2×#14519737—21no—
34C2×#14519735C2211yescharacteristic
35C2×C22⋊Q8×C61C411yescharacteristic, complemented
36C23×#6923—22no—
37C2×#11758213—22no—
38C2×#11758213—24no—
39C2×#11758213D418yescomplemented
40C2×#11758213C2314yes—
41D61⋊M16—216no—
42D61⋊M16—216no—
43C2×#11758217—28no—
44C2×#11758217—24no—
45C2×D61⋊C8—28no—
46C2×D61⋊C8—24no—
47C22×#92420—22no—
48C2×C22⋊#6923—28no—
49C2×C22⋊#6923—24no—
50C2×C4×#6923—24no—
51C2×C4×#6923—24no—
52C2×C4×#6923—22no—
53C2×C4×#6923C2314yes—
54#14519842—216no—
55(C2×#6923)⋊C4—24no—
56C24×D61D411yescharacteristic
57C2×#11758226—21no—
58C2×#11758226—21no—
59C2×#11758226—24no—
60C2×#11758226—24no—
61C2×#11758226C2×C412yes—
62C2×#11758226C2312yes—
63C22×D244—21no—
64C22×D244—21no—
65C22×D244C2×C411yescharacteristic
66C22×C22⋊D61—21no—
67C23×Dic61D411yescharacteristic
68C22×C4×D61—24no—
69C22×C4×D61—24no—
70C22×C4×D61—21no—
71C22×C4×D61C2×C411yescharacteristic
72C22×C4×D61C2×C412yes—
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D412yes—
75C22×C4×D61D411yescharacteristic
76C22×C4×D61D412yes—
77C22×C4×D61C2312yes—
78C22×C4×D61C2311yescharacteristic
79#14519762—24no—
80#14519762—24no—
81#14519753—22no—
82#14519753C2×C414yescomplemented
83#14519752—22no—
84#14519752C2×C414yescomplemented
85#14519751—22no—
86#14519751C2×C414yescomplemented
87#14519747—24no—
88#14519747—24no—
89#14519739—24no—
90#14519739—24no—
91#14519737—24no—
92#14519737—24no—
93#14519735—21no—
94#14519735—21no—
95#14519735C2×C412yes—
96#14519735C2312yes—
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×#11758196—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×C4×Dic61—21no—
104C22×Q8×C61C2×C411yescharacteristic
105C23×C4×C61C2×C411yescharacteristic
106C22⋊Q8×C61—22no—
107C22⋊Q8×C61C2×C414yescomplemented
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61C2×C411yescharacteristic
110C2×C22⋊C4×C61—21no—
111C24×C61C22⋊C411yescharacteristic
112C23×D61—24no—
113C23×D61—24no—
114C23×D61—21no—
115C23×D61—42no—
116C23×D61C22⋊C412yes—
117C23×D61C22⋊C411yescharacteristic
118C23×D61C2×D412yes—
119C23×D61C2×D411yescharacteristic
120C22×#6923—28no—
121C22×#6923—24no—
122C22×#6923—44no—
123C22×#6923—44no—
124C2×Q8×C61—21no—
125C2×Q8×C61—24no—
126C2×Q8×C61C22×C412yes—
127C22×C4×C61—24no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61C22⋊C411yescharacteristic
131C22×C4×C61C22⋊C412yes—
132C22×C4×C61C22×C412yes—
133C22×C4×C61C22×C411yescharacteristic
134C2×C22⋊D61—24no—
135C2×C22⋊D61—44no—
136C22×Dic61—22no—
137C22×Dic61—22no—
138C22×Dic61—21no—
139C22×Dic61C22⋊C411yescharacteristic
140C22×Dic61C22⋊C412yes—
141C22×Dic61C2×D412yes—
142C22×Dic61C2×D411yescharacteristic
143#11758226—28no—
144#11758226—24no—
145#11758226—24no—
146#11758226—42no—
147#11758226—44no—
148#11758226—42no—
149C2×D244—24no—
150C2×D244—22no—
151C2×D244—24no—
152C2×D244—22no—
153C2×D244—21no—
154C2×D244—44no—
155C2×D244—44no—
156C2×D244C22×C412yes—
157C2×C4×D61—24no—
158C2×C4×D61—24no—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—28no—
162C2×C4×D61—24no—
163C2×C4×D61—28no—
164C2×C4×D61—24no—
165C2×C4×D61—24no—
166C2×C4×D61—24no—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—42no—
170C2×C4×D61—42no—
171C2×C4×D61C22⋊C412yes—
172C2×C4×D61C22⋊C412yes—
173C2×C4×D61C22⋊C412yes—
174C2×C4×D61C22×C412yes—
175C2×C4×D61C22×C411yescharacteristic
176C2×C4×D61C2×D412yes—
177C2×C4×D61C2×D412yes—
178C2×C4×D61C2×D414yes—
179C2×C4×D61C2×D411yescharacteristic
180C2×C4×D61C2×D411yescharacteristic
181C2×C4×D61#4114yes—
182C2×C4×D61C2411yescharacteristic
183C22⋊#6923—216no—
184#11758217—216no—
185C2×#92420—28no—
186C2×#92420—24no—
187C4×#6923—24no—
188C4×#6923—24no—
189C4×#6923—44no—
190#11758213—28no—
191#11758213—24no—
192#11758213C2×D418yescomplemented
193D61⋊C8—216no—
194C4⋊C4×C61—24no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61C22×C412yes—
197C22⋊C4×C61—24no—
198#11758198—22no—
199#11758198—24no—
200#11758198—22no—
201#11758198—24no—
202#11758198—24no—
203C4⋊Dic61—21no—
204C4⋊Dic61C22×C412yes—
205#11758196—24no—
206C4×Dic61—22no—
207C4×Dic61—22no—
208C23×C61—22no—
209C23×C61—22no—
210C23×C61—22no—
211C23×C61C2×C22⋊C412yes—
212C23×C61C2×C22⋊C411yescharacteristic
213C22×D61—22no—
214C22×D61—22no—
215C22×D61—22no—
216C22×D61—22no—
217C22×D61—24no—
218C22×D61—24no—
219C22×D61—24no—
220C22×D61—24no—
221C22×D61—22no—
222C22×D61—42no—
223C22×D61—42no—
224C22×D61—416no—
225C22×D61—42no—
226C22×D61—42no—
227C22×D61—42no—
228C22×D61#10414yescomplemented
229C22×D61C2×C22⋊C411yescharacteristic
230C22×D61C2×C22⋊C412yes—
231C22×D61#12114yes—
232C22×D61C22×D411yescharacteristic
233C2×#6923—28no—
234C2×#6923—416no—
235C2×#6923—44no—
236C2×#6923—44no—
237Q8×C61—24no—
238Q8×C61—42no—
239C2×C4×C61—22no—
240C2×C4×C61—24no—
241C2×C4×C61—24no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61C2×C22⋊C412yes—
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C4×D414yes—
249C2×C4×C61C23×C411yescharacteristic
250C22⋊D61—48no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—24no—
255C2×Dic61—22no—
256C2×Dic61—42no—
257C2×Dic61C2×C22⋊C412yes—
258C2×Dic61C2×C22⋊C411yescharacteristic
259C2×Dic61#12012yes—
260C2×Dic61#12312yes—
261C2×Dic61C22×D411yescharacteristic
262D244—24no—
263D244—44no—
264D244—44no—
265D244—48no—
266D244—42no—
267C4×D61—24no—
268C4×D61—24no—
269C4×D61—24no—
270C4×D61—24no—
271C4×D61—22no—
272C4×D61—22no—
273C4×D61—24no—
274C4×D61—42no—
275C4×D61—42no—
276C4×D61—44no—
277C4×D61C4×D414yes—
278C4×D61#12012yes—
279C4×D61#12114yes—
280C4×D61#12312yes—
281C4×D61C22×D412yes—
282C4×D61C2×#4112yes—
283#92420—28no—
284C2×#1871—611nomaximal, Sylow
285C22×C61—22no—
286C22×C61—22no—
287C22×C61—22no—
288C22×C61—44no—
289C22×C61#38612yes—
290C22×C61C2×#10412yes—
291C22×C61#42112yes—
292C22×C61C22×C22⋊C411yescharacteristic
293C2×D61—28no—
294C2×D61—28no—
295C2×D61—21no—
296C2×D61—21no—
297C2×D61—21no—
298C2×D61—21no—
299C2×D61—22no—
300C2×D61—22no—
301C2×D61—48no—
302C2×D61—48no—
303C2×D61—42no—
304C2×D61—42no—
305C2×D61—42no—
306C2×D61—84no—
307C2×D61#38612yes—
308C2×D61C2×#10414yescomplemented
309C2×D61C2×#12112yes—
310#6923—48no—
311C4×C61—22no—
312C4×C61—42no—
313C4×C61—42no—
314C4×C61#38612yes—
315C4×C61C2×C4×D412yes—
316Dic61—22no—
317Dic61—42no—
318Dic61#38612yes—
319Dic61C2×#12011yescharacteristic
320Dic61C2×#12311yescharacteristic
321C23×M16—611no—
322C2×#525—611no—
323C22×#104—612no—
324C2×C4×C22⋊C4—611no—
325#1871—618no—
326C2×#339—612no—
327C2×C61—42no—
328C2×C61#187114yescomplemented
329C2×C61C2×#38611yescharacteristic
330C2×C61C22×#10411yescharacteristic
331C2×C61C2×#42111yescharacteristic
332D61—22no—
333D61—22no—
334D61—24no—
335D61—82no—
336C22×#41—611no—
337C24×C4—611no—
338C22×M16—612no—
339C22×M16—614no—
340C22×M16—1228no—
341C22×M16—1221no—
342C22×M16—1222no—
343C23×C8—1221no—
344#525—614no—
345#525—614no—
346#525—1222no—
347#525—1222no—
348C2×#123—1221no—
349C2×C22⋊Q8—611no—
350C2×C22⋊Q8#692311yescharacteristic, complemented
351C2×#121—611no—
352C2×#121—611no—
353C2×#120—1221no—
354C2×C4×D4—1221no—
355C2×C4×D4—1221no—
356C2×#117—611no—
357C22×C22⋊C4—1221no—
358C22×C42—612no—
359C2×#104—618no—
360C2×#104—1228no—
361C4×C22⋊C4—614no—
362C4×C22⋊C4—1222no—
363C2×#95—1221no—
364#339—618no—
365C61C2×#187111yescharacteristic, complemented, Sylow
366C25—611no—
367C2×#41—612no—
368C2×#41—612no—
369C2×#41—1221no—
370C2×#41—1221no—
371C2×#41—1224no—
372C2×#41—1224no—
373C22×Q8C2×#692311yescharacteristic
374C22×D4—611no—
375C22×D4—1221no—
376C22×D4—1221no—
377C22×D4—1221no—
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—612no—
383C23×C4—612no—
384C23×C4—611no—
385C23×C4—612no—
386C23×C4—612no—
387C23×C4—1224no—
388C23×C4—1224no—
389C23×C4—1221no—
390C23×C4—1222no—
391C23×C4C2×#692311yescharacteristic
392C2×M16—614no—
393C2×M16—618no—
394C2×M16—12216no—
395C2×M16—1224no—
396C2×M16—1222no—
397C2×M16—1224no—
398C2×M16—1228no—
399C2×M16—12216no—
400C22×C8—1222no—
401C22×C8—1224no—
402C22×C8—1228no—
403#123—1224no—
404#123—1224no—
405C22⋊Q8—22no—
406C22⋊Q8—614no—
407C22⋊Q8—1222no—
408C22⋊Q8C2×#692314yescomplemented
409#121—614no—
410#121—614no—
411#121—1222no—
412#121—1222no—
413#120—1224no—
414#120—1224no—
415C4×D4—1224no—
416C4×D4—1224no—
417C4×D4—1224no—
418C4×D4—1224no—
419#117—612no—
420#117—612no—
421#117—1221no—
422#117—1221no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4C2×#692311yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—1221no—
429C2×C22⋊C4—1221no—
430C2×C22⋊C4—1221no—
431C2×C22⋊C4—1224no—
432C2×C22⋊C4—1228no—
433C2×C22⋊C4—1221no—
434C2×C42—614no—
435C2×C42—1221no—
436C2×C42—1224no—
437C2×C42—1224no—
438C2×C42—1222no—
439#104—12216no—
440#95—1224no—
441C24—611no—
442C24—611no—
443C24—612no—
444C24—612no—
445C24—1224no—
446C24—1224no—
447C24—1221no—
448C24—2442no—
449C24C22⋊#692311yescharacteristic
450#41—1224no—
451#41—1228no—
452#41—1224no—
453#41—2442no—
454#41—2444no—
455#41—2442no—
456C2×Q8—21no—
457C2×Q8—24no—
458C2×Q8C22×#692312yes—
459C2×D4—612no—
460C2×D4—1224no—
461C2×D4—1222no—
462C2×D4—1222no—
463C2×D4—1224no—
464C2×D4—1221no—
465C2×D4—1224no—
466C2×D4—2444no—
467C2×D4—2444no—
468C2×D4—2444no—
469C22×C4—24no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—614no—
476C22×C4—614no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—612no—
480C22×C4—612no—
481C22×C4—611no—
482C22×C4—612no—
483C22×C4—612no—
484C22×C4—612no—
485C22×C4—612no—
486C22×C4—612no—
487C22×C4—612no—
488C22×C4—1222no—
489C22×C4—1224no—
490C22×C4—1224no—
491C22×C4—1222no—
492C22×C4—1228no—
493C22×C4—1224no—
494C22×C4—1228no—
495C22×C4—1224no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1224no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—1224no—
502C22×C4—1224no—
503C22×C4—1228no—
504C22×C4—1221no—
505C22×C4—2442no—
506C22×C4—2442no—
507C22×C4—2444no—
508C22×C4—2444no—
509C22×C4C22⋊#692312yes—
510C22×C4C22⋊#692311yescharacteristic
511C22×C4C22×#692312yes—
512C22×C4C22×#692311yescharacteristic
513M16—618no—
514M16—1228no—
515M16—1224no—
516M16—12216no—
517C2×C8—1228no—
518C2×C8—1224no—
519C2×C8—12216no—
520C4⋊C4—24no—
521C4⋊C4—21no—
522C4⋊C4—612no—
523C4⋊C4—1224no—
524C4⋊C4—1221no—
525C4⋊C4C22×#692312yes—
526C22⋊C4—24no—
527C22⋊C4—1224no—
528C22⋊C4—1222no—
529C22⋊C4—1222no—
530C22⋊C4—1224no—
531C22⋊C4—12216no—
532C22⋊C4—1224no—
533C42—1222no—
534C42—1222no—
535C42—1224no—
536C42—1224no—
537C42—2444no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—614no—
542C23—614no—
543C23—612no—
544C23—611no—
545C23—611no—
546C23—1224no—
547C23—1224no—
548C23—1224no—
549C23—1224no—
550C23—1222no—
551C23—1222no—
552C23—1222no—
553C23—1222no—
554C23—1222no—
555C23—2442no—
556C23—2442no—
557C23—24416no—
558C23—2442no—
559C23—2442no—
560C23—2442no—
561C23C2×C22⋊#692312yes—
562C23C2×C22⋊#692311yescharacteristic
563Q8—24no—
564Q8—42no—
565D4—1224no—
566D4—2448no—
567D4—2444no—
568D4—2444no—
569D4—2448no—
570D4—2442no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—612no—
579C2×C4—612no—
580C2×C4—611no—
581C2×C4—611no—
582C2×C4—612no—
583C2×C4—614no—
584C2×C4—612no—
585C2×C4—614no—
586C2×C4—612no—
587C2×C4—612no—
588C2×C4—612no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—1224no—
592C2×C4—1224no—
593C2×C4—1224no—
594C2×C4—1222no—
595C2×C4—1222no—
596C2×C4—1224no—
597C2×C4—1222no—
598C2×C4—1224no—
599C2×C4—1224no—
600C2×C4—1228no—
601C2×C4—1222no—
602C2×C4—2442no—
603C2×C4—2442no—
604C2×C4—2444no—
605C2×C4—2444no—
606C2×C4—24416no—
607C2×C4—2444no—
608C2×C4—2442no—
609C2×C4C2×C22⋊#692312yes—
610C2×C4C2×C22⋊#692311yescharacteristic
611C2×C4D4×#692314yes—
612C2×C4C23×#692311yescharacteristic
613C8—1228no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—44no—
618C22—614no—
619C22—612no—
620C22—612no—
621C22—1228no—
622C22—1228no—
623C22—1221no—
624C22—1221no—
625C22—1221no—
626C22—1221no—
627C22—1222no—
628C22—1222no—
629C22—4884no—
630C22—2448no—
631C22—2448no—
632C22—2442no—
633C22—2442no—
634C22—2442no—
635C22#1684071012yes—
636C22D61⋊#10412yes—
637C22#1684076112yes—
638C22C22×C22⋊#692311yescharacteristic
639C4—22no—
640C4—42no—
641C4—42no—
642C4—611no—
643C4—611no—
644C4—612no—
645C4—1222no—
646C4—2448no—
647C4—2442no—
648C4#1684071012yes—
649C4C2×D4×#692312yes—
650C2—42no—
651C2—1222no—
652C2—1224no—
653C2—1222no—
654C2—4882no—
655C2#2146180114yesdirect product factor
656C2C2×#1684071011yescharacteristic
657C2C2×D61⋊#10411yescharacteristic
658C2C2×#1684076111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840275C2
cosocleC2×C4×D61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61C2×#1871
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×D61⋊M16C2semidirect
2. C22×#14519842C2semidirect
3. C2×C4×C22⋊#6923C2semidirect
4. #21461801C2direct (N × H)
5. C2×#16840632C2semidirect
10. C2×D61⋊M16C22semidirect
16. C2×#14519842C22semidirect
18. C4×C22⋊#6923C22semidirect
20. #16840632C22semidirect
25. #16840275C4semidirect
28. C2×#14519753C4semidirect
29. C2×#14519752C4semidirect
30. C2×#14519751C4semidirect
35. C2×C22⋊Q8×C61C4semidirect
39. C2×#11758213D4semidirect
82. #14519753C2×C4semidirect
84. #14519752C2×C4semidirect
86. #14519751C2×C4semidirect
107. C22⋊Q8×C61C2×C4semidirect
192. #11758213C2×D4semidirect
228. C22×D61#104semidirect
308. C2×D61C2×#104semidirect
328. C2×C61#1871semidirect
350. C2×C22⋊Q8#6923semidirect
365. C61C2×#1871semidirect
408. C22⋊Q8C2×#6923semidirect
655. C2#21461801direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D61⋊M162
C22×#145198422
C2×C4×C22⋊#69232
#214618012
C2×#168406322
C2×#168402752
C2×#187161