Finite Group Databasebeta

← #29646747

Subgroups — #29646747

Order 15616.

958 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840316C211yesmaximal, characteristic
2#21454451C211yesmaximal, characteristic
3#21454447C211yesmaximal, characteristic
4#21444290C214yesmaximal, complemented
5#21444249C211yesmaximal, characteristic, complemented
6#21444248C211yesmaximal, characteristic, complemented
7#21444247C211yesmaximal, characteristic, complemented
8#21444238C214yesmaximal, complemented
9C61×#1487C211yesmaximal, characteristic, complemented
10#16840316—21no—
11#16840316—21no—
12#16840316—21no—
13#16840316—21no—
14#16840316C412yes—
15#16840316C412yes—
16#16840316C2212yes—
17#16840316C2212yes—
18C2×#14519776C411yescharacteristic
19C2×#14519775C411yescharacteristic
20C2×#14519767—21no—
21C2×#14519757C411yescharacteristic
22C2×#14519755—21no—
23C2×#14519753C411yescharacteristic
24C2×C4×Dic122—21no—
25C2×C4×Dic122C2211yescharacteristic
26C2×#14519734—21no—
27C2×C42×D61C2211yescharacteristic
28#16839818—21no—
29#16839818—21no—
30#16839818C2212yes—
31#16839816—21no—
32#16839815C2211yescharacteristic
33#16839814—21no—
34#16839814C2212yes—
35#16839813C2212yes—
36#16839786C2211yescharacteristic
37#16839784—21no—
38#16839725—21no—
39#16839724—21no—
40M16×Dic61—21no—
41C4×#11758189C2212yes—
42#16839494C2214yescomplemented
43Q8⋊#92418C2214yescomplemented
44#16839492C2214yescomplemented
45C2×C4×Q8×C61C2211yescharacteristic
46C61×#431C2211yescharacteristic
47C61×#423C2211yescharacteristic
48C61×Q8⋊C8C2214yescomplemented
49C22×Dic122—21no—
50C22×Dic122C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C2×#11758194—21no—
55C2×#11758189—22no—
56#14519776—21no—
57#14519776—21no—
58#14519776C2×C412yes—
59#14519776C2×C412yes—
60#14519775—21no—
61#14519775—21no—
62#14519775C2×C412yes—
63#14519775C2×C412yes—
64#14519767—22no—
65#14519767—22no—
66#14519767—22no—
67#14519767—22no—
68#14519757—21no—
69#14519757—21no—
70#14519757C2×C412yes—
71#14519757C2×C412yes—
72#14519755—22no—
73#14519755—22no—
74#14519755—22no—
75#14519755—22no—
76#14519753—21no—
77#14519753—21no—
78#14519753C2×C412yes—
79#14519753C2×C412yes—
80C4×Dic122—21no—
81C4×Dic122—21no—
82C4×Dic122—22no—
83C4×Dic122—22no—
84C4×Dic122—22no—
85C4×Dic122—22no—
86C4×Dic122C2×C412yes—
87C4×Dic122C2312yes—
88#14519734—22no—
89#14519734—22no—
90#14519734—22no—
91#14519734—22no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61D411yescharacteristic
104C2×C4×Dic61D411yescharacteristic
105C42×D61C2×C411yescharacteristic
106C42×D61C2×C411yescharacteristic
107C42×D61D411yescharacteristic
108C42×D61D411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61C2311yescharacteristic
112C42×D61C2311yescharacteristic
113C4⋊#92418—21no—
114C4⋊#92418—21no—
115C4⋊#92418C2312yes—
116#14519706—22no—
117C22⋊#92418—21no—
118#14519689—22no—
119#14519689—22no—
120#14519689—22no—
121#14519687—22no—
122#14519687—22no—
123C4×#92418C2312yes—
124C8×Dic61—22no—
125C22×Q8×C61C2×C411yescharacteristic
126C2×M16×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61C2×C412yes—
130C4×Q8×C61C2312yes—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C42×C61—21no—
134C2×C42×C61C2311yescharacteristic
135C4⋊C8×C61—21no—
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2312yes—
138C22⋊C8×C61—21no—
139C4×C8×C61C2312yes—
140C23×D61C22⋊C411yescharacteristic
141C2×Q8×C61—21no—
142C2×Q8×C61—42no—
143C2×Q8×C61C22×C412yes—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61C22⋊C411yescharacteristic
152C22×Dic61C22⋊C411yescharacteristic
153C22×Dic61C22⋊C411yescharacteristic
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—42no—
157C2×C4×D61—42no—
158C2×C4×D61C22⋊C411yescharacteristic
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22⋊C411yescharacteristic
161C2×C4×D61C22⋊C411yescharacteristic
162C2×C4×D61C22⋊C411yescharacteristic
163C2×C4×D61C22⋊C411yescharacteristic
164C2×C4×D61C22×C411yescharacteristic
165C2×C4×D61C22×C411yescharacteristic
166C2×C4×D61C2×D411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61C2×D411yescharacteristic
170C2×Dic122—21no—
171C2×Dic122—22no—
172C2×Dic122—22no—
173C2×Dic122—42no—
174C2×Dic122—44no—
175C2×Dic122C22×C412yes—
176M16×C61—42no—
177C2×C8×C61—22no—
178C2×C8×C61—22no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61C22×C412yes—
183C42×C61—22no—
184C42×C61—22no—
185C42×C61C22×C411yescharacteristic
186C42×C61C2×D411yescharacteristic
187C42×C61C2×D411yescharacteristic
188C42×C61C2411yescharacteristic
189#11758198—22no—
190#11758198—22no—
191#11758198—22no—
192#11758198—22no—
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—
205#11758196—22no—
206#11758196—22no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22×C411yescharacteristic
216C4×Dic61C22×C411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221#11758194—42no—
222C2×#92418—22no—
223C2×#92418—22no—
224#11758189—44no—
225C23×C61C2×C22⋊C411yescharacteristic
226C22×D61—22no—
227C22×D61—41no—
228C22×D61—41no—
229C22×D61C2×C22⋊C411yescharacteristic
230C22×D61C2×C22⋊C411yescharacteristic
231Q8×C61—24no—
232Q8×C61—42no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—41no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61#13712yes—
243C2×C4×C61#13712yes—
244C2×C4×C61C23×C411yescharacteristic
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—41no—
252C2×Dic61—42no—
253C2×Dic61—42no—
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C2×C22⋊C411yescharacteristic
256C2×Dic61C2×C22⋊C411yescharacteristic
257C2×Dic61C2×C22⋊C411yescharacteristic
258C2×Dic61C2×C22⋊C411yescharacteristic
259C2×Dic61C2×C22⋊C411yescharacteristic
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—21no—
263C4×D61—21no—
264C4×D61—21no—
265C4×D61—21no—
266C4×D61—22no—
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—41no—
271C4×D61—41no—
272C4×D61—41no—
273C4×D61—41no—
274Dic122—24no—
275Dic122—44no—
276Dic122—42no—
277Dic122—44no—
278C8×C61—42no—
279C8×C61—42no—
280#92418—42no—
281#92418—42no—
282#17491—611nomaximal, Sylow
283C22×C61—21no—
284C22×C61—21no—
285C22×C61#41912yes—
286C22×C61C22×C22⋊C411yescharacteristic
287C2×D61—21no—
288C2×D61—21no—
289C2×D61—21no—
290C2×D61—21no—
291C2×D61—21no—
292C2×D61—21no—
293C2×D61—44no—
294C4×C61—21no—
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—42no—
298C4×C61—42no—
299C4×C61#41912yes—
300C4×C61#56812yes—
301C4×C61C2×#13711yescharacteristic
302C4×C61C2×#13711yescharacteristic
303Dic61—21no—
304Dic61—21no—
305Dic61—21no—
306Dic61—21no—
307Dic61—21no—
308Dic61—42no—
309Dic61—42no—
310Dic61#42112yes—
311C2×#533—611no—
312#2920—611no—
313#2920—611no—
314#1497—614no—
315#1487—611no—
316#1487—611no—
317#1487—611no—
318#1487D6111yescharacteristic, complemented
319#1485—614no—
320C2×C61—22no—
321C2×C61#287911yescharacteristic
322C2×C61C2×#41911yescharacteristic
323C2×C61C2×#42111yescharacteristic
324D61—41no—
325D61—41no—
326#533—612no—
327#533—612no—
328#533—612no—
329#533—612no—
330#533—1221no—
331#533—1221no—
332#533—1221no—
333#533—1221no—
334C2×C4⋊Q8—611no—
335C2×C4⋊Q8—611no—
336C2×#125—1221no—
337C2×C22⋊Q8—611no—
338C2×C22⋊Q8—611no—
339C2×C22⋊Q8—1221no—
340C2×C4×Q8—611no—
341C2×C4×Q8—1221no—
342C2×C4×Q8C2×D6111yescharacteristic
343C2×#117—1221no—
344C22×C42—611no—
345#432—612no—
346#432—1221no—
347#432—1221no—
348#432—1221no—
349#431—611no—
350#431—612no—
351#431—612no—
352#431—1221no—
353#431C2×D6111yescharacteristic
354#423—611no—
355#423—1221no—
356#423C2×D6111yescharacteristic
357#407—1221no—
358#407—1221no—
359C4×M16—612no—
360C4×M16—1221no—
361Q8⋊C8—614no—
362Q8⋊C8—614no—
363Q8⋊C8—614no—
364Q8⋊C8C2×D6114yescomplemented
365C61#1749111yescharacteristic, complemented, Sylow
366C22×Q8—611no—
367C22×Q8—1221no—
368C22×Q8C4×D6111yescharacteristic
369C23×C4—611no—
370C23×C4—611no—
371C23×C4—611no—
372C2×M16—21no—
373C2×M16—1222no—
374C2×M16—1221no—
375C4⋊Q8—612no—
376C4⋊Q8—612no—
377C4⋊Q8—612no—
378C4⋊Q8—612no—
379C4⋊Q8—1221no—
380C4⋊Q8—1221no—
381C4⋊Q8—1221no—
382C4⋊Q8—1221no—
383#125—1222no—
384#125—1222no—
385#125—1222no—
386#125—1222no—
387C22⋊Q8—612no—
388C22⋊Q8—612no—
389C22⋊Q8—612no—
390C22⋊Q8—612no—
391C22⋊Q8—1221no—
392C22⋊Q8—1221no—
393C22⋊Q8—1222no—
394C22⋊Q8—1222no—
395C22⋊Q8—1222no—
396C22⋊Q8—1222no—
397C22⋊Q8—1221no—
398C22⋊Q8—1221no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8—612no—
402C4×Q8—612no—
403C4×Q8—1222no—
404C4×Q8—1222no—
405C4×Q8—1222no—
406C4×Q8—1222no—
407C4×Q8—1221no—
408C4×Q8—1221no—
409C4×Q8C4×D6112yes—
410C4×Q8C22×D6112yes—
411#117—1222no—
412#117—1222no—
413#117—1222no—
414#117—1222no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—1221no—
418C2×C4⋊C4—1221no—
419C2×C4⋊C4—1221no—
420C2×C4⋊C4—1221no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4C4×D6111yescharacteristic
424C2×C22⋊C4—1221no—
425C2×C22⋊C4—1221no—
426C2×C42—21no—
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—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—1221no—
439C2×C42C22×D6111yescharacteristic
440C4⋊C8—21no—
441C4⋊C8—21no—
442C4⋊C8—612no—
443C4⋊C8—1222no—
444C4⋊C8—1221no—
445C4⋊C8—1221no—
446C4⋊C8C22×D6112yes—
447C22⋊C8—21no—
448C22⋊C8—1222no—
449C22⋊C8—1222no—
450C22⋊C8—1222no—
451C22⋊C8—1221no—
452#97—1222no—
453#97—1222no—
454C4×C8—612no—
455C4×C8—1222no—
456C4×C8C22×D6112yes—
457C24—611no—
458C2×Q8—21no—
459C2×Q8—42no—
460C2×Q8—612no—
461C2×Q8—1222no—
462C2×Q8—1222no—
463C2×Q8—1221no—
464C2×Q8—2442no—
465C2×Q8—2444no—
466C2×Q8C2×C4×D6112yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—2442no—
489C22×C4—2442no—
490C22×C4C2×C4×D6111yescharacteristic
491C22×C4D4×D6111yescharacteristic
492C22×C4D4×D6111yescharacteristic
493M16—42no—
494M16—2444no—
495M16—2442no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—1222no—
499C2×C8—1222no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—612no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—1221no—
516C4⋊C4—1222no—
517C4⋊C4C2×C4×D6112yes—
518C22⋊C4—1222no—
519C22⋊C4—1222no—
520C22⋊C4—1222no—
521C22⋊C4—1222no—
522C42—22no—
523C42—22no—
524C42—611no—
525C42—611no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—611no—
532C42—611no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—1222no—
537C42—1222no—
538C42C2×C4×D6111yescharacteristic
539C42D4×D6111yescharacteristic
540C42D4×D6111yescharacteristic
541C42C23×D6111yescharacteristic
542C23—611no—
543C23—611no—
544C23—1222no—
545C23—2441no—
546C23—2441no—
547C23C22⋊C4×D6111yescharacteristic
548Q8—24no—
549Q8—42no—
550Q8—1224no—
551Q8—2442no—
552Q8—2444no—
553Q8—2444no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—611no—
561C2×C4—611no—
562C2×C4—611no—
563C2×C4—611no—
564C2×C4—611no—
565C2×C4—611no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2442no—
586C2×C4—2442no—
587C2×C4C22⋊C4×D6111yescharacteristic
588C2×C4C22⋊C4×D6111yescharacteristic
589C2×C4C22⋊C4×D6111yescharacteristic
590C2×C4#1451980612yes—
591C2×C4#1451980912yes—
592C2×C4C22×C4×D6111yescharacteristic
593C2×C4C2×D4×D6111yescharacteristic
594C2×C4C2×D4×D6111yescharacteristic
595C8—42no—
596C8—42no—
597C8—2442no—
598C8—2442no—
599C22—21no—
600C22—21no—
601C22—1221no—
602C22—1221no—
603C22—1221no—
604C22—1221no—
605C22—1221no—
606C22—1221no—
607C22—2444no—
608C22#1683976912yes—
609C22C2×C22⋊C4×D6111yescharacteristic
610C4—21no—
611C4—21no—
612C4—21no—
613C4—42no—
614C4—42no—
615C4—612no—
616C4—1221no—
617C4—1221no—
618C4—1221no—
619C4—1221no—
620C4—1221no—
621C4—2442no—
622C4—2442no—
623C4#1683976912yes—
624C4#1684052812yes—
625C4C2×#1451980611yescharacteristic
626C4C2×#1451980911yescharacteristic
627C2—22no—
628C2—2441no—
629C2—2441no—
630C2#2145426211yescharacteristic
631C2C2×#1683976911yescharacteristic
632C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1487C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC42×C61C24
hypercenter#1487D61
hypocenterC61#17491
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
4. #21444290C2semidirect
5. #21444249C2semidirect
6. #21444248C2semidirect
7. #21444247C2semidirect
8. #21444238C2semidirect
9. C61×#1487C2semidirect
42. #16839494C22semidirect
43. Q8⋊#92418C22semidirect
44. #16839492C22semidirect
48. C61×Q8⋊C8C22semidirect
318. #1487D61semidirect
364. Q8⋊C8C2×D61semidirect
365. C61#17491semidirect

Maximal subgroups

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

subgroupindex
C2×#168403162
#214544512
#214544472
#214442902
#214442492
#214442482
#214442472
#214442382
C61×#14872
#1749161