Finite Group Databasebeta

← #30616718

Subgroups — #30616718

Order 15616.

1186 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D61⋊M16C211yesmaximal, characteristic
2#21462268C211yesmaximal, characteristic
3#21462000C212yesmaximal, complemented
4#21461946C212yesmaximal, complemented
5#21461834C214yesmaximal
6#21461591C214yesmaximal, complemented
7#533×D61C211yesmaximal, characteristic
8C2×D61⋊M16C2212yes—
9C2×#14519856—21no—
10C2×#14519840C2218yes—
11C4×#11758213—21no—
12C4×#11758213—21no—
13C4×#11758217—21no—
14C4×#11758217—21no—
15#16840721C2212yes—
16C4×D61⋊C8C2212yes—
17#16840708C2212yes—
18#16840706—21no—
19#16840704—21no—
20#16840704C2212yes—
21C4×C4⋊#6923—21no—
22C4×C4⋊#6923C2212yes—
23#16840635C2218yes—
24#16840319C411yescharacteristic, complemented
25#16840318—21no—
26#16840317C411yescharacteristic, complemented
27#16840317C411yescharacteristic, complemented
28#16840316—21no—
29#16840316C412yescomplemented
30#16840315—21no—
31#16840314—21no—
32#16840314C412yescomplemented
33C4⋊Q8×D61C2211yescharacteristic
34C4⋊Q8×D61C2211yescharacteristic
35#125×D61—21no—
36C22⋊Q8×D61—21no—
37C22⋊Q8×D61C2212yes—
38C4×Q8×D61—21no—
39C4×Q8×D61C2212yes—
40#117×D61—21no—
41C2×C42×D61C2211yescharacteristic
42C61×#533C411yescharacteristic, complemented
43C2×#11758213—22no—
44D61⋊M16—28no—
45C2×#11758217—22no—
46C2×D61⋊C8C2314yes—
47#14519856—44no—
48C2×C4⋊#6923—22no—
49C2×C4⋊#6923—22no—
50C2×C4⋊#6923C2314yes—
51C2×C22⋊#6923—22no—
52C2×C4×#6923—22no—
53#14519840—216no—
54#14519832—22no—
55#14519832—22no—
56C4×#92420—22no—
57C4×#92420—22no—
58(C2×#6923)⋊C4—22no—
59(C2×#6923)⋊C4—22no—
60C2×Q8×D61—21no—
61C2×Q8×D61C2312yes—
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61C2311yescharacteristic
65#14519777C2×C411yescharacteristic
66#14519777C2×C411yescharacteristic
67#14519776—21no—
68#14519776—21no—
69#14519776—21no—
70#14519776C2×C412yes—
71#14519775—21no—
72#14519775C2×C412yes—
73#14519769—21no—
74#14519768—21no—
75#14519768—21no—
76#14519767—22no—
77#14519767—22no—
78#14519757—21no—
79#14519757C2×C412yes—
80#14519756—21no—
81#14519756C2×C412yes—
82#14519755—22no—
83#14519755—22no—
84#14519754—22no—
85#14519754—22no—
86#14519753—21no—
87#14519753C2×C412yes—
88Q8×Dic61—21no—
89Q8×Dic61C2×C412yes—
90C4×Dic122—21no—
91C4×Dic122—22no—
92C4×Dic122—22no—
93C4×Dic122C2×C412yes—
94#14519742—21no—
95#14519742—22no—
96#14519742—22no—
97#14519742C2×C412yes—
98#14519736—21no—
99#14519735—21no—
100#14519735—21no—
101#14519734—22no—
102#14519733—22no—
103C4⋊C4×D61—21no—
104C4⋊C4×D61—21no—
105C4⋊C4×D61—21no—
106C4⋊C4×D61—22no—
107C4⋊C4×D61—22no—
108C4⋊C4×D61C2312yes—
109C22⋊C4×D61—22no—
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C42×D61—22no—
114C42×D61C2×C411yescharacteristic
115C42×D61C2×C411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61D411yescharacteristic
120C42×D61C2311yescharacteristic
121C42×D61C2311yescharacteristic
122C4⋊Q8×C61C2×C411yescharacteristic
123C4⋊Q8×C61C2×C411yescharacteristic
124#125×C61—21no—
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61C2×C412yes—
127C4×Q8×C61—21no—
128C4×Q8×C61C2×C412yes—
129#117×C61—21no—
130C2×C42×C61C2×C411yescharacteristic
131C23×D61C2×D411yescharacteristic
132C22×#6923—24no—
133C2×Q8×C61—21no—
134C2×Q8×C61C22×C412yes—
135C22×C4×C61C22⋊C411yescharacteristic
136C22×C4×C61C22⋊C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×Dic61C22⋊C411yescharacteristic
139C22×Dic61C22⋊C411yescharacteristic
140C22×Dic61C2×D411yescharacteristic
141Q8×D61—28no—
142Q8×D61—42no—
143Q8×D61—42no—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—24no—
147C2×C4×D61—24no—
148C2×C4×D61—22no—
149C2×C4×D61—22no—
150C2×C4×D61C22⋊C411yescharacteristic
151C2×C4×D61C22⋊C411yescharacteristic
152C2×C4×D61C22⋊C411yescharacteristic
153C2×C4×D61C22⋊C411yescharacteristic
154C2×C4×D61C22×C411yescharacteristic
155C2×C4×D61C2×D411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61C2×D411yescharacteristic
158C2×C4×D61C2×D411yescharacteristic
159C2×C4×D61C2×D411yescharacteristic
160C2×C4×D61C2×D411yescharacteristic
161C2×C4×D61C2411yescharacteristic
162C2×Dic122—21no—
163C2×Dic122—22no—
164C2×Dic122—22no—
165C2×Dic122C22×C412yes—
166C22⋊#6923—44no—
167#11758217—28no—
168C2×#92420—24no—
169C4⋊#6923—28no—
170C4⋊#6923—44no—
171C4⋊#6923—44no—
172C4×#6923—44no—
173#11758213—28no—
174D61⋊C8—24no—
175D61⋊C8#4118yes—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61C22×C412yes—
182C22⋊C4×C61—22no—
183C42×C61—22no—
184C42×C61C22⋊C411yescharacteristic
185C42×C61C22⋊C411yescharacteristic
186C42×C61C22×C411yescharacteristic
187C42×C61C22×C411yescharacteristic
188C22⋊Dic61—22no—
189#11758198—22no—
190#11758198—22no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—22no—
195C4⋊Dic61—22no—
196C4⋊Dic61C22×C412yes—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205C4×Dic61—22no—
206C4×Dic61—22no—
207C4×Dic61—22no—
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22×C411yescharacteristic
215C4×Dic61C22×C411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C23×C61C2×C22⋊C411yescharacteristic
221C22×D61—22no—
222C22×D61—21no—
223C22×D61—22no—
224C22×D61—21no—
225C22×D61C2×C22⋊C411yescharacteristic
226C22×D61C22×D411yescharacteristic
227C2×#6923—44no—
228C2×#6923—44no—
229C2×#6923—44no—
230Q8×C61—24no—
231Q8×C61—42no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C23×C411yescharacteristic
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61C2×C22⋊C411yescharacteristic
249C2×Dic61C2×C22⋊C411yescharacteristic
250C2×Dic61C2×C22⋊C411yescharacteristic
251C2×Dic61C2×C22⋊C411yescharacteristic
252C2×Dic61C2×C22⋊C411yescharacteristic
253C2×Dic61C22×D411yescharacteristic
254C4×D61—22no—
255C4×D61—21no—
256C4×D61—22no—
257C4×D61—21no—
258C4×D61—22no—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—22no—
264C4×D61—44no—
265C4×D61—42no—
266C4×D61—42no—
267C4×D61AGL(1,ℤ/8)12yes—
268C4×D61#13712yes—
269C4×D61#13714yes—
270C4×D61C2×#4114yes—
271Dic122—24no—
272Dic122—42no—
273Dic122—44no—
274Dic122—44no—
275#92420—28no—
276#21409—611nomaximal, Sylow
277C22×C61—21no—
278C22×C61—21no—
279C22×C61—21no—
280C22×C61C22×C22⋊C411yescharacteristic
281C2×D61—21no—
282C2×D61—21no—
283C2×D61—21no—
284C2×D61—42no—
285C2×D61—42no—
286C2×D61#53212yes—
287C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
288C2×D61C2×#13712yes—
289C2×D61C2×#13711yescharacteristic
290#6923—84no—
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—21no—
294C4×C61—42no—
295C4×C61—42no—
296C4×C61#41712yes—
297C4×C61#41912yes—
298C4×C61C4×#4112yes—
299Dic61—21no—
300Dic61—21no—
301Dic61—21no—
302Dic61—42no—
303Dic61—42no—
304Dic61#41712yes—
305Dic61#41912yes—
306Dic61#52512yes—
307C2×#533—611no—
308C2×C4×M16—611no—
309#2285—611no—
310#1990—612no—
311#1956—612no—
312#1894—614no—
313#1763—614no—
314C2×C61—41no—
315C2×C61#229711yescharacteristic
316C2×C61C2×#41911yescharacteristic
317C2×C61C2×#41711yescharacteristic
318D61—41no—
319D61#318212yes—
320D61#318512yes—
321C22×M16—612no—
322#533—611no—
323#533—611no—
324#533—612no—
325#533—612no—
326#533—611no—
327#533—1221no—
328#533—1221no—
329#533—1221no—
330#533—1221no—
331#533#692311yescharacteristic, complemented
332C2×C4⋊Q8—611no—
333C2×C4⋊Q8—611no—
334C2×#125—1221no—
335C2×C22⋊Q8—612no—
336C2×C22⋊Q8—1221no—
337C2×C4×Q8—612no—
338C2×C4×Q8—1221no—
339C2×#117—1221no—
340C2×#117—1221no—
341C22×C42—611no—
342C2×#103—618no—
343C4×M16—1221no—
344C4×M16—1221no—
345C4×M16—1221no—
346C4×M16—1221no—
347C2×#97—612no—
348C2×C4×C8—612no—
349#384—612no—
350#382—1221no—
351#380—612no—
352#380—1221no—
353C4×C4⋊C4—612no—
354C4×C4⋊C4—1221no—
355#340—618no—
356C61#2140911yescharacteristic, complemented, Sylow
357C22×Q8—612no—
358C22×Q8—1221no—
359C23×C4—611no—
360C23×C4—611no—
361C23×C4—611no—
362C2×M16—1228no—
363C2×M16—1222no—
364C2×M16—1222no—
365C22×C8—614no—
366C4⋊Q8—612no—
367C4⋊Q8—612no—
368C4⋊Q8—611no—
369C4⋊Q8—611no—
370C4⋊Q8—1221no—
371C4⋊Q8—1221no—
372C4⋊Q8—1221no—
373C4⋊Q8—1221no—
374C4⋊Q8C2×#692311yescharacteristic
375C4⋊Q8C2×#692311yescharacteristic
376#125—21no—
377#125—1222no—
378#125—1222no—
379#125—1221no—
380#125—1221no—
381#125—1221no—
382C22⋊Q8—21no—
383C22⋊Q8—612no—
384C22⋊Q8—612no—
385C22⋊Q8—612no—
386C22⋊Q8—1222no—
387C22⋊Q8—1222no—
388C22⋊Q8—1222no—
389C22⋊Q8—1222no—
390C22⋊Q8—1221no—
391C22⋊Q8—1221no—
392C22⋊Q8—1221no—
393C22⋊Q8C2×#692312yes—
394C4×Q8—21no—
395C4×Q8—612no—
396C4×Q8—612no—
397C4×Q8—612no—
398C4×Q8—1222no—
399C4×Q8—1222no—
400C4×Q8—1222no—
401C4×Q8—1221no—
402C4×Q8—1222no—
403C4×Q8—1221no—
404C4×Q8—1221no—
405C4×Q8C2×#692312yes—
406#117—21no—
407#117—1222no—
408#117—1222no—
409#117—1221no—
410#117—1221no—
411#117—1221no—
412#117—2444no—
413C2×C4⋊C4—612no—
414C2×C4⋊C4—614no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4—1221no—
417C2×C4⋊C4—1222no—
418C2×C4⋊C4—1222no—
419C2×C4⋊C4—1221no—
420C2×C4⋊C4—1222no—
421C2×C4⋊C4—1222no—
422C2×C22⋊C4—1222no—
423C2×C22⋊C4—1222no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—1222no—
436C2×C42—1222no—
437C2×C42C2×#692311yescharacteristic
438#103—12216no—
439#97—1222no—
440#97—1222no—
441C4×C8—1222no—
442C4×C8—1222no—
443#95—1222no—
444#95—1222no—
445C24—611no—
446C2×Q8—21no—
447C2×Q8—612no—
448C2×Q8—1222no—
449C2×Q8—1222no—
450C2×Q8—1228no—
451C2×Q8—1221no—
452C2×Q8—2442no—
453C2×Q8—2442no—
454C2×Q8C22×#692312yes—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—1222no—
471C22×C4—1224no—
472C22×C4—1222no—
473C22×C4—1224no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1224no—
477C22×C4C22⋊#692311yescharacteristic
478C22×C4C22⋊#692311yescharacteristic
479C22×C4C22×#692311yescharacteristic
480M16—1228no—
481M16—1228no—
482C2×C8—618no—
483C2×C8—1224no—
484C2×C8—1224no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—612no—
491C4⋊C4—1222no—
492C4⋊C4—1222no—
493C4⋊C4—1222no—
494C4⋊C4—1222no—
495C4⋊C4—1222no—
496C4⋊C4—1222no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—1228no—
500C4⋊C4—1222no—
501C4⋊C4—1222no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—2444no—
506C4⋊C4—2444no—
507C4⋊C4C22×#692312yes—
508C22⋊C4—22no—
509C22⋊C4—1222no—
510C22⋊C4—1222no—
511C22⋊C4—1222no—
512C22⋊C4—2444no—
513C42—22no—
514C42—611no—
515C42—611no—
516C42—611no—
517C42—611no—
518C42—611no—
519C42—611no—
520C42—611no—
521C42—611no—
522C42—611no—
523C42—611no—
524C42—611no—
525C42—611no—
526C42—1222no—
527C42—1222no—
528C42—1222no—
529C42—2444no—
530C42C22⋊#692311yescharacteristic
531C42C22⋊#692311yescharacteristic
532C42C22×#692311yescharacteristic
533C42C22×#692311yescharacteristic
534C23—611no—
535C23—611no—
536C23—1221no—
537C23—1222no—
538C23—1222no—
539C23—1221no—
540C23C2×C22⋊#692311yescharacteristic
541Q8—24no—
542Q8—42no—
543Q8—1224no—
544Q8—2444no—
545Q8—2444no—
546Q8—2442no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—611no—
553C2×C4—611no—
554C2×C4—611no—
555C2×C4—612no—
556C2×C4—612no—
557C2×C4—614no—
558C2×C4—614no—
559C2×C4—611no—
560C2×C4—611no—
561C2×C4—611no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—1221no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1221no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—2444no—
578C2×C4—2442no—
579C2×C4—2442no—
580C2×C4—2444no—
581C2×C4—2444no—
582C2×C4—2444no—
583C2×C4C2×C22⋊#692311yescharacteristic
584C2×C4C2×C22⋊#692311yescharacteristic
585C2×C4C2×C22⋊#692311yescharacteristic
586C2×C4C2×C22⋊#692311yescharacteristic
587C2×C4C2×C22⋊#692311yescharacteristic
588C2×C4C23×#692311yescharacteristic
589C8—1228no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—612no—
594C22—612no—
595C22—611no—
596C22—611no—
597C22—1221no—
598C22—1221no—
599C22—1221no—
600C22—2442no—
601C22—2442no—
602C22C22×C22⋊#692311yescharacteristic
603C4—21no—
604C4—21no—
605C4—21no—
606C4—42no—
607C4—42no—
608C4—612no—
609C4—612no—
610C4—612no—
611C4—1221no—
612C4—1221no—
613C4—1221no—
614C4—4884no—
615C4—2442no—
616C4—2442no—
617C4#1684075312yes—
618C4#1684075512yes—
619C4#41×#692312yes—
620C2—41no—
621C2—612no—
622C2—612no—
623C2—2441no—
624C2#2146228011yescharacteristic
625C2C2×#1684075511yescharacteristic
626C2C2×#1684075311yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#533C4
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenter#533#6923
hypocenterC61#21409
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #21462000C2semidirect
4. #21461946C2semidirect
6. #21461591C2semidirect
24. #16840319C4semidirect
26. #16840317C4semidirect
27. #16840317C4semidirect
29. #16840316C4semidirect
32. #16840314C4semidirect
42. C61×#533C4semidirect
331. #533#6923semidirect
356. C61#21409semidirect

Maximal subgroups

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

subgroupindex
C4×D61⋊M162
#214622682
#214620002
#214619462
#214618342
#214615912
#533×D612
#2140961