Finite Group Databasebeta

← C4×#16840752 #30614128

Subgroups — C4×#16840752 #30614128

Order 15616.

1670 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840752C212yesmaximal
2C2×C4×D61⋊C8C211yesmaximal, characteristic, complemented
3C4×#14519856C211yesmaximal, characteristic, complemented
4C4×#14519840C214yesmaximal, complemented
5C4×#14519839C214yesmaximal, complemented
6#21461504C212yesmaximal, complemented
7C4×#41×D61C211yesmaximal, characteristic
8C22×D61⋊C8C2212yes—
9C2×#14519856C2212yes—
10#16840752C4116yesdirect product factor
11C2×#14519840C2214yes—
12C2×#14519839C2214yes—
13C4×D61⋊C8—21no—
14C4×D61⋊C8—21no—
15C4×D61⋊C8C2214yes—
16C2×C4×#92420—22no—
17C4×C4⋊#6923C2214yes—
18C4×C22⋊#6923—22no—
19#16840698—21no—
20C42×#6923—21no—
21#16840635C2218yes—
22C2×#41×D61C2211yescharacteristic
23#41×Dic61C411yescharacteristic, complemented
24C4×#11758226C412yescomplemented
25C4×#11758222—21no—
26C4×#11758222C411yescharacteristic, complemented
27#16840230—21no—
28#16840230C411yescharacteristic, complemented
29C4×#11758224—22no—
30C4×#11758224C412yescomplemented
31C4×Q8×D61C2212yes—
32C4×D4×D61—22no—
33C4×D4×D61C2212yes—
34#117×D61—21no—
35#117×D61C2211yescharacteristic
36C2×C42×D61—21no—
37C2×C42×D61C2211yescharacteristic
38C4×#41×C61C411yescharacteristic, complemented
39C2×D61⋊C8—22no—
40C2×D61⋊C8—24no—
41C2×D61⋊C8C2×C418yescomplemented
42C2×D61⋊C8C2314yes—
43C22×#92420—22no—
44#14519856—24no—
45#14519856C2×C418yescomplemented
46C2×C4⋊#6923C2314yes—
47C2×C22⋊#6923—22no—
48C2×C4×#6923—22no—
49C2×C4×#6923—24no—
50#14519840C2×C4116yescomplemented
51#14519839C2×C4116yescomplemented
52C4×#92420—24no—
53C4×#92420—24no—
54(C2×#6923)⋊C4—24no—
55C2×#11758226C2×C411yescharacteristic
56C2×#11758222—21no—
57C2×#11758222C2×C411yescharacteristic
58C2×#11758224—21no—
59C2×#11758224C2×C411yescharacteristic
60#41×D61—24no—
61#41×D61C2×C418yes—
62C2×Q8×D61C2311yescharacteristic
63C2×D4×D61—21no—
64C2×D4×D61C2311yescharacteristic
65C22×C4×D61—21no—
66C22×C4×D61—22no—
67C22×C4×D61D412yes—
68C22×C4×D61C2311yescharacteristic
69Q8×Dic61C2×C412yes—
70C4×Dic122—22no—
71C4×Dic122C2×C412yes—
72#14519742—22no—
73#14519742C2×C412yes—
74C4×D244—22no—
75C4×D244C2×C412yes—
76D4×Dic61—22no—
77D4×Dic61C2×C412yes—
78#14519739—22no—
79#14519739C2×C412yes—
80C4×C22⋊D61—22no—
81C4×C22⋊D61—22no—
82C4×C22⋊D61—22no—
83#14519737—22no—
84#14519737—22no—
85#14519737—22no—
86#14519736—21no—
87#14519736C2×C411yescharacteristic
88#14519735—22no—
89#14519735C2×C412yes—
90#14519734—21no—
91#14519734—21no—
92#14519734—21no—
93#14519733—21no—
94#14519733—22no—
95C4⋊C4×D61—22no—
96C4⋊C4×D61C2312yes—
97C22⋊C4×D61—21no—
98C22⋊C4×D61—22no—
99C2×C4×Dic61—22no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61C2×C411yescharacteristic
102C2×C4×Dic61D412yes—
103C42×D61—21no—
104C42×D61—22no—
105C42×D61—21no—
106C42×D61—22no—
107C42×D61—21no—
108C42×D61C2×C412yes—
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61C2312yes—
114C2×#41×C61C2×C411yescharacteristic
115C4×Q8×C61C2×C412yes—
116C4×D4×C61—22no—
117C4×D4×C61C2×C412yes—
118#117×C61—21no—
119#117×C61C2×C411yescharacteristic
120C2×C42×C61—21no—
121C2×C42×C61C2×C411yescharacteristic
122C23×D61—21no—
123C23×D61C2×D411yescharacteristic
124C22×#6923—24no—
125#41×C61—22no—
126#41×C61C4214yescomplemented
127C2×Q8×C61C22×C411yescharacteristic
128C2×D4×C61—21no—
129C2×D4×C61C22×C411yescharacteristic
130C22×C4×C61—21no—
131C22×C4×C61—22no—
132C22×C4×C61C22⋊C412yes—
133C22×C4×C61C22×C411yescharacteristic
134C2×C22⋊D61—21no—
135C2×C22⋊D61—21no—
136C2×C22⋊D61—21no—
137C22×Dic61—21no—
138C22×Dic61—22no—
139C22×Dic61C22⋊C412yes—
140C22×Dic61C2×D411yescharacteristic
141#11758226—22no—
142#11758226C4214yescomplemented
143Q8×D61—22no—
144Q8×D61C22×C414yes—
145#11758224—28no—
146#11758224—22no—
147#11758224C4214yescomplemented
148D4×D61—28no—
149D4×D61—22no—
150D4×D61C22×C414yes—
151#11758222—22no—
152#11758222—28no—
153#11758222C4214yescomplemented
154C2×D244—21no—
155C2×D244C22×C411yescharacteristic
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—28no—
160C2×C4×D61—28no—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—48no—
165C2×C4×D61C22⋊C412yes—
166C2×C4×D61C22⋊C412yes—
167C2×C4×D61C22×C411yescharacteristic
168C2×C4×D61C22×C414yes—
169C2×C4×D61C2×D412yes—
170C2×C4×D61C2×D411yescharacteristic
171C2×C4×D61C2×D411yescharacteristic
172C2×C4×D61C2×D412yes—
173C2×C4×D61#4114yes—
174C2×C4×D61C2411yescharacteristic
175C2×Dic122—21no—
176C2×Dic122C22×C411yescharacteristic
177C22⋊#6923—28no—
178C2×#92420—28no—
179C2×#92420—24no—
180C4⋊#6923—24no—
181C4⋊#6923C22×C418yes—
182C4×#6923—28no—
183C4×#6923—48no—
184D61⋊C8—28no—
185D61⋊C8—24no—
186D61⋊C8C22×C418yes—
187C4⋊C4×C61—22no—
188C4⋊C4×C61C22×C412yes—
189C22⋊C4×C61—21no—
190C22⋊C4×C61—22no—
191C42×C61—21no—
192C42×C61—22no—
193C42×C61C22⋊C411yescharacteristic
194C42×C61C22⋊C411yescharacteristic
195C42×C61C22×C412yes—
196C22⋊Dic61—21no—
197C22⋊Dic61—22no—
198#11758198—22no—
199#11758198—22no—
200#11758198—22no—
201C4⋊Dic61—22no—
202C4⋊Dic61C22×C412yes—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206C4×Dic61—21no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C4×Dic61C22⋊C412yes—
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C412yes—
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22×C412yes—
216C4×Dic61C2×D412yes—
217C4×Dic61C2×D412yes—
218C23×C61—21no—
219C23×C61C2×C22⋊C411yescharacteristic
220C22×D61—24no—
221C22×D61—21no—
222C22×D61—24no—
223C22×D61—44no—
224C22×D61C2×C22⋊C411yescharacteristic
225C22×D61C4×D414yes—
226C22×D61C22×D411yescharacteristic
227C2×#6923—28no—
228C2×#6923—48no—
229Q8×C61—21no—
230Q8×C61C2×C4212yes—
231D4×C61—24no—
232D4×C61—21no—
233D4×C61C2×C4212yes—
234C2×C4×C61—21no—
235C2×C4×C61—24no—
236C2×C4×C61—24no—
237C2×C4×C61—22no—
238C2×C4×C61—44no—
239C2×C4×C61C2×C4212yes—
240C2×C4×C61C2×C22⋊C412yes—
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C2×C22⋊C412yes—
243C2×C4×C61#11712yes—
244C2×C4×C61C23×C411yescharacteristic
245C22⋊D61—24no—
246C22⋊D61—24no—
247C22⋊D61—24no—
248C2×Dic61—21no—
249C2×Dic61—24no—
250C2×Dic61—24no—
251C2×Dic61—22no—
252C2×Dic61—44no—
253C2×Dic61C2×C22⋊C412yes—
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C2×C22⋊C412yes—
256C2×Dic61C4×D414yes—
257C2×Dic61C22×D411yescharacteristic
258D244—24no—
259D244—21no—
260D244C2×C4212yes—
261C4×D61—24no—
262C4×D61—24no—
263C4×D61—24no—
264C4×D61—24no—
265C4×D61—24no—
266C4×D61—24no—
267C4×D61—44no—
268C4×D61—44no—
269C4×D61—44no—
270C4×D61C2×C4212yes—
271C4×D61#11712yes—
272C4×D61C4×D414yes—
273C4×D61C4×D414yes—
274C4×D61#13518yes—
275C4×D61C23×C412yes—
276C4×D61C2×#4112yes—
277Dic122—21no—
278Dic122—24no—
279Dic122C2×C4212yes—
280#92420—28no—
281C4×#416—611nomaximal, Sylow
282C22×C61—22no—
283C22×C61—22no—
284C22×C61—42no—
285C22×C61C4×C22⋊C412yes—
286C22×C61C22×C22⋊C411yescharacteristic
287C2×D61—22no—
288C2×D61—28no—
289C2×D61—22no—
290C2×D61—42no—
291C2×D61—48no—
292C2×D61C4×C22⋊C412yes—
293C2×D61C2×C4×D412yes—
294C2×D61C2×#13514yes—
295#6923—48no—
296C4×C61—22no—
297C4×C61—22no—
298C4×C61—42no—
299C4×C61C4×C22⋊C412yes—
300C4×C61#41614yescomplemented
301C4×C61C22×C4211yescharacteristic
302C4×C61C2×#11711yescharacteristic
303Dic61—22no—
304Dic61—22no—
305Dic61—42no—
306Dic61C4×C22⋊C412yes—
307Dic61#41614yescomplemented
308Dic61C2×C4×D412yes—
309C2×C4×#41—611no—
310C2×#416—612no—
311C22×C4×C8—611no—
312C4×#117—611no—
313C4×#103—614no—
314C4×#102—614no—
315#1735—612no—
316C2×C61—22no—
317C2×C61—42no—
318C2×C61C2×C4×C22⋊C411yescharacteristic
319C2×C61C2×#41612yes—
320D61—22no—
321D61—42no—
322D61C4×#13514yes—
323C22×#41—611no—
324C23×C8—612no—
325C4×#41—611no—
326C4×#41—612no—
327C4×#41—612no—
328C4×#41—611no—
329C4×#41—611no—
330C4×#41—1221no—
331C4×#41—1221no—
332C4×#41—1222no—
333C4×#41#692311yescharacteristic, complemented
334C2×C4×Q8—612no—
335C2×C4×D4—612no—
336C2×C4×D4—1222no—
337C2×#117—612no—
338C2×#117—611no—
339C2×#117—1221no—
340C22×C42—611no—
341C22×C42—1221no—
342#416—6116no—
343C2×#103—614no—
344C2×#102—614no—
345C2×C4×C8—614no—
346C2×C4×C8—1222no—
347C2×C4×C8—1221no—
348C2×C4×C8—1221no—
349C4×C4⋊C4—614no—
350C4×C22⋊C4—1222no—
351#376—1221no—
352C43—1221no—
353#340—618no—
354C61C4×#41611yescharacteristic, complemented, Sylow
355C2×#41—618no—
356C2×#41—611no—
357C2×#41—611no—
358C2×#41—611no—
359C2×#41—1221no—
360C2×#41—1221no—
361C2×#41—1224no—
362C2×#41C2×#692311yescharacteristic
363C22×Q8—611no—
364C22×D4—611no—
365C22×D4—1221no—
366C23×C4—611no—
367C23×C4—612no—
368C23×C4—1221no—
369C23×C4—1222no—
370C22×C8—618no—
371C22×C8—614no—
372C22×C8—1222no—
373C22×C8—1224no—
374C22×C8—1222no—
375C4×Q8—612no—
376C4×Q8—612no—
377C4×Q8—612no—
378C4×Q8—1222no—
379C4×Q8—1222no—
380C4×Q8C2×#692312yes—
381C4×D4—22no—
382C4×D4—612no—
383C4×D4—612no—
384C4×D4—612no—
385C4×D4—1222no—
386C4×D4—1222no—
387C4×D4—1222no—
388C4×D4—1222no—
389C4×D4—1222no—
390C4×D4—1222no—
391C4×D4—1222no—
392C4×D4—1222no—
393C4×D4—1222no—
394C4×D4C2×#692312yes—
395#117—21no—
396#117—618no—
397#117—611no—
398#117—612no—
399#117—1221no—
400#117—1221no—
401#117—1222no—
402#117—1222no—
403#117—1221no—
404#117—1221no—
405#117—1224no—
406#117—1221no—
407#117C2×#692311yescharacteristic
408C2×C4⋊C4—614no—
409C2×C4⋊C4—612no—
410C2×C4⋊C4—1222no—
411C2×C22⋊C4—1222no—
412C2×C22⋊C4—1221no—
413C2×C22⋊C4—1222no—
414C2×C42—21no—
415C2×C42—612no—
416C2×C42—611no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—612no—
422C2×C42—612no—
423C2×C42—1221no—
424C2×C42—1222no—
425C2×C42—1221no—
426C2×C42—1222no—
427C2×C42—1222no—
428C2×C42—1221no—
429C2×C42—1222no—
430C2×C42—1221no—
431C2×C42—1224no—
432C2×C42C2×#692311yescharacteristic
433#103—6116no—
434#102—6116no—
435C4×C8—1224no—
436C4×C8—1224no—
437#95—1224no—
438C24—611no—
439C24—1221no—
440#41—22no—
441#41—614no—
442#41—614no—
443#41—614no—
444#41—1228no—
445#41—1228no—
446#41—1222no—
447#41—1222no—
448#41—1222no—
449#41C4×#692314yescomplemented
450C2×Q8—614no—
451C2×Q8—611no—
452C2×Q8—1221no—
453C2×Q8—1222no—
454C2×Q8C22×#692311yescharacteristic
455C2×D4—21no—
456C2×D4—614no—
457C2×D4—611no—
458C2×D4—1221no—
459C2×D4—1222no—
460C2×D4—1221no—
461C2×D4—1228no—
462C2×D4—1221no—
463C2×D4—1221no—
464C2×D4C22×#692311yescharacteristic
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—611no—
468C22×C4—614no—
469C22×C4—612no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—614no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—612no—
476C22×C4—612no—
477C22×C4—612no—
478C22×C4—612no—
479C22×C4—1221no—
480C22×C4—1228no—
481C22×C4—1228no—
482C22×C4—1222no—
483C22×C4—1221no—
484C22×C4—1222no—
485C22×C4—1221no—
486C22×C4—1222no—
487C22×C4—1221no—
488C22×C4—1224no—
489C22×C4—1222no—
490C22×C4—2448no—
491C22×C4C22⋊#692312yes—
492C22×C4C22×#692311yescharacteristic
493C2×C8—618no—
494C2×C8—1224no—
495C2×C8—1224no—
496C2×C8—1228no—
497C2×C8—1228no—
498C4⋊C4—22no—
499C4⋊C4—618no—
500C4⋊C4—612no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4—1224no—
505C4⋊C4—1222no—
506C4⋊C4C22×#692312yes—
507C22⋊C4—21no—
508C22⋊C4—22no—
509C22⋊C4—1222no—
510C22⋊C4—1222no—
511C22⋊C4—1222no—
512C22⋊C4—1228no—
513C22⋊C4—1221no—
514C22⋊C4—1222no—
515C42—21no—
516C42—22no—
517C42—612no—
518C42—612no—
519C42—612no—
520C42—611no—
521C42—612no—
522C42—611no—
523C42—612no—
524C42—1222no—
525C42—1222no—
526C42—1222no—
527C42—1228no—
528C42—1221no—
529C42—1222no—
530C42—2448no—
531C42C22⋊#692311yescharacteristic
532C42C22⋊#692311yescharacteristic
533C42C22×#692312yes—
534C23—21no—
535C23—611no—
536C23—611no—
537C23—614no—
538C23—1224no—
539C23—1224no—
540C23—1221no—
541C23—2444no—
542C23C2×C22⋊#692311yescharacteristic
543Q8—21no—
544Q8—612no—
545Q8—1224no—
546Q8—1221no—
547Q8C2×C4×#692312yes—
548D4—24no—
549D4—21no—
550D4—612no—
551D4—1224no—
552D4—1224no—
553D4—1224no—
554D4—1224no—
555D4—1221no—
556D4C2×C4×#692312yes—
557C2×C4—21no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—44no—
562C2×C4—612no—
563C2×C4—611no—
564C2×C4—611no—
565C2×C4—614no—
566C2×C4—618no—
567C2×C4—612no—
568C2×C4—612no—
569C2×C4—612no—
570C2×C4—612no—
571C2×C4—614no—
572C2×C4—614no—
573C2×C4—612no—
574C2×C4—1224no—
575C2×C4—1224no—
576C2×C4—1224no—
577C2×C4—1224no—
578C2×C4—1224no—
579C2×C4—1224no—
580C2×C4—1221no—
581C2×C4—1224no—
582C2×C4—1224no—
583C2×C4—1228no—
584C2×C4—1222no—
585C2×C4—2444no—
586C2×C4—2444no—
587C2×C4—2444no—
588C2×C4—2448no—
589C2×C4—2444no—
590C2×C4C2×C4×#692312yes—
591C2×C4C2×C22⋊#692312yes—
592C2×C4C2×C22⋊#692312yes—
593C2×C4C2×C22⋊#692311yescharacteristic
594C2×C4#1451985612yes—
595C2×C4C23×#692311yescharacteristic
596C8—1228no—
597C22—22no—
598C22—22no—
599C22—42no—
600C22—614no—
601C22—612no—
602C22—612no—
603C22—1228no—
604C22—1222no—
605C22—1222no—
606C22—2448no—
607C22—2442no—
608C22C4×C22⋊#692312yes—
609C22C22×C22⋊#692311yescharacteristic
610C4—22no—
611C4—22no—
612C4—42no—
613C4—614no—
614C4—612no—
615C4—612no—
616C4—1222no—
617C4—1222no—
618C4—2448no—
619C4—2442no—
620C4C4×C22⋊#692312yes—
621C4#1684075214yesdirect product factor
622C4C22×C4×#692311yescharacteristic
623C4C2×#1451985611yescharacteristic
624C2—22no—
625C2—42no—
626C2—614no—
627C2—1222no—
628C2—2442no—
629C2C2×C4×C22⋊#692311yescharacteristic
630C2C2×#1684075212yes—
subgroupG/H
centerC42C22⋊#6923
commutatorC4×C61C22×C42
FrattiniC2×C4C23×#6923
FittingC4×#41×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenterC4×#41#6923
hypocenterC61C4×#416
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. C2×C4×D61⋊C8C2semidirect
3. C4×#14519856C2semidirect
4. C4×#14519840C2semidirect
5. C4×#14519839C2semidirect
6. #21461504C2semidirect
10. #16840752C4direct (N × H)
23. #41×Dic61C4semidirect
24. C4×#11758226C4semidirect
26. C4×#11758222C4semidirect
28. #16840230C4semidirect
30. C4×#11758224C4semidirect
38. C4×#41×C61C4semidirect
41. C2×D61⋊C8C2×C4semidirect
45. #14519856C2×C4semidirect
50. #14519840C2×C4semidirect
51. #14519839C2×C4semidirect
126. #41×C61C42semidirect
142. #11758226C42semidirect
147. #11758224C42semidirect
153. #11758222C42semidirect
300. C4×C61#416semidirect
307. Dic61#416semidirect
333. C4×#41#6923semidirect
354. C61C4×#416semidirect
449. #41C4×#6923semidirect
621. C4#16840752direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407522
C2×C4×D61⋊C82
C4×#145198562
C4×#145198402
C4×#145198392
#214615042
C4×#41×D612
C4×#41661