Finite Group Databasebeta

← #29647958

Subgroups — #29647958

Order 15616.

1316 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840311C211yesmaximal, characteristic
2#21454449C211yesmaximal, characteristic, complemented
3C4×M16×D61C211yesmaximal, characteristic, complemented
4#21444428C214yesmaximal, complemented
5#21444418C211yesmaximal, characteristic, complemented
6#21444417C211yesmaximal, characteristic, complemented
7#21444416C211yesmaximal, characteristic, complemented
8#21444409C214yesmaximal, complemented
9C61×#1527C211yesmaximal, characteristic, complemented
10C22×#11758226C411yescharacteristic
11C22×#11758224C411yescharacteristic
12C2×M16×D61—21no—
13#16840311—21no—
14#16840311—21no—
15#16840311—21no—
16#16840311—21no—
17#16840311C412yes—
18#16840311C412yes—
19#16840311C2212yes—
20#16840311C2212yes—
21C2×#14519775C411yescharacteristic
22C2×#14519773C411yescharacteristic
23C2×#14519765C2211yescharacteristic
24C2×#14519750—21no—
25C2×#14519750—21no—
26C2×#14519737—21no—
27C2×#14519737—21no—
28C2×C42×D61C2211yescharacteristic
29#16839819C2211yescharacteristic
30#16839817C2212yescomplemented
31#16839814—21no—
32#16839812—21no—
33#16839784—21no—
34#16839724—21no—
35C4×#11758194C2211yescharacteristic
36#16839714C2212yescomplemented
37#16839714C2212yescomplemented
38M16×Dic61—21no—
39C4×#11758189—21no—
40#97×D61C2212yescomplemented
41C4×C8×D61—21no—
42#16839502C2214yescomplemented
43#16839501C2214yescomplemented
44#16839501C2214yescomplemented
45C2×#124×C61C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C4×M16×C61C2211yescharacteristic
48C61×#329C2214yescomplemented
49C2×#11758226—21no—
50C2×#11758226—21no—
51C2×#11758226—44no—
52C2×#11758226C2×C412yes—
53C2×#11758226C2×C412yes—
54C2×#11758224—21no—
55C2×#11758224—21no—
56C2×#11758224—44no—
57C2×#11758224C2×C412yes—
58C2×#11758224C2×C412yes—
59C22×Dic122C2×C411yescharacteristic
60C22×D244—21no—
61C22×D244C2×C411yescharacteristic
62C22×C22⋊D61—21no—
63C22×C22⋊D61—21no—
64C22×C22⋊D61—21no—
65C23×Dic61—21no—
66C22×C4×D61—21no—
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C2×#11758194—21no—
71C2×#11758189—22no—
72C2×#11758189—22no—
73M16×D61—28no—
74C2×C8×D61—22no—
75#14519775—21no—
76#14519775—21no—
77#14519775C2×C412yes—
78#14519775C2×C412yes—
79#14519773—21no—
80#14519773—21no—
81#14519773C2×C412yes—
82#14519773C2×C412yes—
83#14519765—21no—
84#14519765—21no—
85#14519765C2×C412yes—
86#14519765C2312yes—
87#14519750—22no—
88#14519750—22no—
89#14519750—22no—
90#14519750—22no—
91#14519750—22no—
92#14519750—22no—
93#14519750—22no—
94#14519750—22no—
95#14519737—22no—
96#14519737—22no—
97#14519737—22no—
98#14519737—22no—
99#14519737—22no—
100#14519737—22no—
101#14519737—22no—
102#14519737—22no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C42×D61C2×C411yescharacteristic
111C42×D61C2×C411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61C2311yescharacteristic
117C42×D61C2311yescharacteristic
118C4⋊#92418—21no—
119#14519706—22no—
120C22⋊#92418—21no—
121#14519689—22no—
122#14519688C2312yes—
123#14519688C2312yes—
124#14519687—22no—
125C4×#92418—21no—
126C8×Dic61—22no—
127C8×Dic61—22no—
128C22×Q8×C61C2×C411yescharacteristic
129C22×D4×C61C2×C411yescharacteristic
130C2×M16×C61—21no—
131#124×C61—21no—
132#124×C61—21no—
133#124×C61C2×C412yes—
134#124×C61C2312yes—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—21no—
139C22⋊C8×C61—21no—
140#97×C61C2312yes—
141#97×C61C2312yes—
142C4×C8×C61—21no—
143C24×C61—21no—
144C23×D61—21no—
145C23×D61C22⋊C411yescharacteristic
146C2×Q8×C61—21no—
147C2×Q8×C61—42no—
148C2×Q8×C61C22×C412yes—
149C2×D4×C61—21no—
150C2×D4×C61—42no—
151C2×D4×C61C22×C412yes—
152C22×C4×C61—21no—
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—44no—
163C2×C22⋊D61—44no—
164C2×C22⋊D61—44no—
165C22×Dic61—21no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—44no—
169C22×Dic61C22⋊C411yescharacteristic
170C22×Dic61C22⋊C411yescharacteristic
171C22×Dic61C22⋊C411yescharacteristic
172#11758226—44no—
173#11758226—44no—
174#11758226—44no—
175#11758226—44no—
176#11758224—44no—
177#11758224—44no—
178#11758224—44no—
179#11758224—44no—
180C2×D244—22no—
181C2×D244—22no—
182C2×D244—21no—
183C2×D244—44no—
184C2×D244—42no—
185C2×D244C22×C412yes—
186C2×C4×D61—24no—
187C2×C4×D61—24no—
188C2×C4×D61—22no—
189C2×C4×D61—22no—
190C2×C4×D61—42no—
191C2×C4×D61—44no—
192C2×C4×D61C22⋊C411yescharacteristic
193C2×C4×D61C22⋊C411yescharacteristic
194C2×C4×D61C22⋊C411yescharacteristic
195C2×C4×D61C22⋊C411yescharacteristic
196C2×C4×D61C22⋊C411yescharacteristic
197C2×C4×D61C22⋊C411yescharacteristic
198C2×C4×D61C22×C411yescharacteristic
199C2×C4×D61C22×C411yescharacteristic
200C2×C4×D61C2×D411yescharacteristic
201C2×C4×D61C2×D411yescharacteristic
202C2×C4×D61C2×D411yescharacteristic
203C2×C4×D61C2×D411yescharacteristic
204C2×Dic122—21no—
205C2×Dic122—42no—
206C2×Dic122C22×C412yes—
207M16×C61—24no—
208C2×C8×C61—22no—
209C2×C8×C61—22no—
210C22⋊C4×C61—22no—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—22no—
214C42×C61C22×C411yescharacteristic
215C42×C61C2×D411yescharacteristic
216C42×C61C2×D411yescharacteristic
217C42×C61C2411yescharacteristic
218#11758198—22no—
219#11758198—22no—
220#11758198—22no—
221#11758198—22no—
222#11758196—22no—
223#11758196—22no—
224#11758196—22no—
225#11758196—22no—
226C4×Dic61C22⋊C411yescharacteristic
227C4×Dic61C22⋊C411yescharacteristic
228C4×Dic61C22⋊C411yescharacteristic
229C4×Dic61C22⋊C411yescharacteristic
230C4×Dic61C22⋊C411yescharacteristic
231C4×Dic61C22⋊C411yescharacteristic
232C4×Dic61C22×C411yescharacteristic
233C4×Dic61C22×C411yescharacteristic
234C4×Dic61C2×D411yescharacteristic
235C4×Dic61C2×D411yescharacteristic
236C4×Dic61C2×D411yescharacteristic
237C4×Dic61C2×D411yescharacteristic
238#11758194—24no—
239C2×#92418—22no—
240C2×#92418—22no—
241#11758189—28no—
242#11758189—44no—
243C8×D61—28no—
244C23×C61—22no—
245C23×C61—42no—
246C23×C61—42no—
247C23×C61—42no—
248C23×C61C2×C22⋊C411yescharacteristic
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—41no—
253C22×D61—42no—
254C22×D61—42no—
255C22×D61—42no—
256C22×D61C2×C22⋊C411yescharacteristic
257C22×D61C2×C22⋊C411yescharacteristic
258Q8×C61—42no—
259Q8×C61—42no—
260D4×C61—42no—
261D4×C61—42no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—41no—
266C2×C4×C61—42no—
267C2×C4×C61C2×C22⋊C411yescharacteristic
268C2×C4×C61C2×C22⋊C411yescharacteristic
269C2×C4×C61C2×C22⋊C411yescharacteristic
270C2×C4×C61C23×C411yescharacteristic
271C2×C4×C61C22×D411yescharacteristic
272C2×C4×C61C22×D411yescharacteristic
273C22⋊D61—44no—
274C22⋊D61—44no—
275C22⋊D61—44no—
276C22⋊D61—44no—
277C22⋊D61—44no—
278C22⋊D61—44no—
279C2×Dic61—22no—
280C2×Dic61—22no—
281C2×Dic61—22no—
282C2×Dic61—44no—
283C2×Dic61—42no—
284C2×Dic61—44no—
285C2×Dic61#10414yes—
286C2×Dic61C2×C22⋊C411yescharacteristic
287C2×Dic61C2×C22⋊C411yescharacteristic
288C2×Dic61C2×C22⋊C411yescharacteristic
289C2×Dic61C2×C22⋊C411yescharacteristic
290C2×Dic61C2×C22⋊C411yescharacteristic
291C2×Dic61C2×C22⋊C411yescharacteristic
292D244—42no—
293D244—44no—
294D244—44no—
295D244—42no—
296C4×D61—22no—
297C4×D61—22no—
298C4×D61—22no—
299C4×D61—22no—
300C4×D61—22no—
301C4×D61—22no—
302C4×D61—22no—
303C4×D61—22no—
304C4×D61—22no—
305C4×D61—41no—
306C4×D61—41no—
307C4×D61—44no—
308C4×D61—44no—
309C4×D61#10014yes—
310Dic122—42no—
311Dic122—42no—
312C8×C61—24no—
313C8×C61—42no—
314#92418—24no—
315#92418—42no—
316#17647—611nomaximal, Sylow
317C22×C61—21no—
318C22×C61—21no—
319C22×C61—42no—
320C22×C61—42no—
321C22×C61—42no—
322C22×C61—84no—
323C22×C61C2×#10412yes—
324C22×C61C22×C22⋊C411yescharacteristic
325C2×D61—21no—
326C2×D61—21no—
327C2×D61—21no—
328C2×D61—21no—
329C2×D61—21no—
330C2×D61—44no—
331C2×D61—42no—
332C2×D61—42no—
333C2×D61—42no—
334C2×D61—84no—
335C2×D61C2×#10012yes—
336C4×C61—21no—
337C4×C61—21no—
338C4×C61—21no—
339C4×C61—21no—
340C4×C61—21no—
341C4×C61—42no—
342C4×C61C2×#10012yes—
343Dic61—21no—
344Dic61—21no—
345Dic61—42no—
346Dic61C2×#10012yes—
347Dic61C2×#10412yes—
348Dic61C2×#10412yes—
349Dic61#42112yes—
350C2×#532—611no—
351#2920—611no—
352C2×C4×M16—611no—
353#1530—614no—
354#1527—611no—
355#1527—611no—
356#1527—611no—
357#1527D6111yescharacteristic, complemented
358#1525—614no—
359C2×C61—22no—
360C2×C61—82no—
361C2×C61C22×#10011yescharacteristic
362C2×C61C22×#10411yescharacteristic
363C2×C61C2×#42111yescharacteristic
364D61—22no—
365D61—41no—
366D61—82no—
367C22×#41—611no—
368C22×#41—611no—
369C22×M16—1221no—
370#532—612no—
371#532—612no—
372#532—612no—
373#532—612no—
374#532—1221no—
375#532—1221no—
376#532—1221no—
377#532—1221no—
378C2×C4⋊Q8—611no—
379C2×#127—611no—
380C2×#124—611no—
381C2×#124C2×D6111yescharacteristic
382C2×#121—1221no—
383C2×#121—1221no—
384C2×C4×D4—1221no—
385C2×C4×D4—1221no—
386C22×C42—611no—
387#432—611no—
388#432—612no—
389#432C2×D6111yescharacteristic
390#431—1221no—
391#431—1221no—
392#423—1221no—
393#407—1221no—
394C4×M16—611no—
395C4×M16—612no—
396C4×M16—612no—
397C4×M16—1221no—
398C4×M16—1221no—
399C4×M16C2×D6111yescharacteristic
400C2×#97—612no—
401C2×C4×C8—1221no—
402#329—614no—
403#329—614no—
404#329—614no—
405#329C2×D6114yescomplemented
406C61#1764711yescharacteristic, complemented, Sylow
407C2×#41—612no—
408C2×#41—612no—
409C2×#41—612no—
410C2×#41—612no—
411C2×#41—1221no—
412C2×#41—1221no—
413C2×#41—1221no—
414C2×#41—1221no—
415C2×#41—2444no—
416C2×#41—2444no—
417C22×Q8—611no—
418C22×Q8C4×D6111yescharacteristic
419C22×D4—611no—
420C22×D4—1221no—
421C22×D4—1221no—
422C22×D4—1221no—
423C22×D4—1221no—
424C22×D4C4×D6111yescharacteristic
425C23×C4—611no—
426C23×C4—611no—
427C23×C4—611no—
428C23×C4—1221no—
429C23×C4—1221no—
430C2×M16—21no—
431C2×M16—1222no—
432C2×M16—1222no—
433C2×M16—1228no—
434C2×M16—1221no—
435C22×C8—1222no—
436C4⋊Q8—612no—
437C4⋊Q8—612no—
438C4⋊Q8—1221no—
439C4⋊Q8—1221no—
440#127—612no—
441#127—612no—
442#127—1221no—
443#127—1221no—
444#124—21no—
445#124—21no—
446#124—612no—
447#124—612no—
448#124—1221no—
449#124—1221no—
450#124C4×D6112yes—
451#124C22×D6112yes—
452#121—1222no—
453#121—1222no—
454#121—1222no—
455#121—1222no—
456#121—1222no—
457#121—1222no—
458#121—1222no—
459#121—1222no—
460C4×D4—1222no—
461C4×D4—1222no—
462C4×D4—1222no—
463C4×D4—1222no—
464C4×D4—1222no—
465C4×D4—1222no—
466C4×D4—1222no—
467C4×D4—1222no—
468C2×C4⋊C4—1221no—
469C2×C4⋊C4—1221no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—1221no—
473C2×C22⋊C4—1221no—
474C2×C42—611no—
475C2×C42—611no—
476C2×C42—611no—
477C2×C42—611no—
478C2×C42—611no—
479C2×C42—611no—
480C2×C42—611no—
481C2×C42—611no—
482C2×C42—611no—
483C2×C42—611no—
484C2×C42—611no—
485C2×C42C22×D6111yescharacteristic
486C4⋊C8—21no—
487C4⋊C8—1222no—
488C4⋊C8—1221no—
489C22⋊C8—21no—
490C22⋊C8—1222no—
491C22⋊C8—1221no—
492#97—612no—
493#97—612no—
494#97—1222no—
495#97C22×D6112yes—
496#97C22×D6112yes—
497C4×C8—21no—
498C4×C8—1222no—
499C4×C8—1222no—
500C4×C8—1221no—
501C24—21no—
502C24—611no—
503C24—1221no—
504#41—2444no—
505#41—2444no—
506#41—2444no—
507#41—2444no—
508#41—2444no—
509#41—2444no—
510#41—2444no—
511#41—2444no—
512C2×Q8—21no—
513C2×Q8—42no—
514C2×Q8—612no—
515C2×Q8—1221no—
516C2×Q8—2442no—
517C2×Q8C2×C4×D6112yes—
518C2×D4—21no—
519C2×D4—42no—
520C2×D4—612no—
521C2×D4—1222no—
522C2×D4—1222no—
523C2×D4—1222no—
524C2×D4—1222no—
525C2×D4—1222no—
526C2×D4—1222no—
527C2×D4—1222no—
528C2×D4—1222no—
529C2×D4—1221no—
530C2×D4—2442no—
531C2×D4—2444no—
532C2×D4—2444no—
533C2×D4—2444no—
534C2×D4—2444no—
535C2×D4C2×C4×D6112yes—
536C22×C4—21no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—1224no—
553C22×C4—1224no—
554C22×C4—1222no—
555C22×C4—1222no—
556C22×C4—1222no—
557C22×C4—1222no—
558C22×C4—1221no—
559C22×C4—2442no—
560C22×C4—2444no—
561C22×C4—2444no—
562C22×C4C2×C4×D6111yescharacteristic
563C22×C4D4×D6111yescharacteristic
564C22×C4D4×D6111yescharacteristic
565M16—24no—
566M16—1228no—
567M16—1224no—
568M16—2444no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—1228no—
572C2×C8—1222no—
573C2×C8—1222no—
574C4⋊C4—1222no—
575C4⋊C4—1222no—
576C4⋊C4—1222no—
577C4⋊C4—1222no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—1222no—
583C22⋊C4—1222no—
584C22⋊C4—1222no—
585C22⋊C4—1222no—
586C42—611no—
587C42—611no—
588C42—611no—
589C42—611no—
590C42—611no—
591C42—611no—
592C42—611no—
593C42—611no—
594C42—611no—
595C42—611no—
596C42—611no—
597C42—611no—
598C42C2×C4×D6111yescharacteristic
599C42D4×D6111yescharacteristic
600C42D4×D6111yescharacteristic
601C42C23×D6111yescharacteristic
602C23—22no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—611no—
607C23—611no—
608C23—1222no—
609C23—1222no—
610C23—1222no—
611C23—2441no—
612C23—2442no—
613C23—2442no—
614C23—2442no—
615C23C22⋊C4×D6111yescharacteristic
616Q8—42no—
617Q8—42no—
618Q8—2442no—
619Q8—2442no—
620D4—42no—
621D4—42no—
622D4—2442no—
623D4—2444no—
624D4—2444no—
625D4—2444no—
626D4—2444no—
627D4—2444no—
628D4—2444no—
629D4—2444no—
630D4—2444no—
631D4—2442no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—611no—
638C2×C4—611no—
639C2×C4—611no—
640C2×C4—611no—
641C2×C4—614no—
642C2×C4—614no—
643C2×C4—611no—
644C2×C4—611no—
645C2×C4—1222no—
646C2×C4—1222no—
647C2×C4—1222no—
648C2×C4—1222no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1222no—
652C2×C4—1222no—
653C2×C4—1222no—
654C2×C4—1222no—
655C2×C4—1222no—
656C2×C4—1222no—
657C2×C4—2441no—
658C2×C4—2441no—
659C2×C4—2444no—
660C2×C4—2444no—
661C2×C4—2444no—
662C2×C4—2444no—
663C2×C4—2442no—
664C2×C4C22⋊C4×D6111yescharacteristic
665C2×C4C22⋊C4×D6111yescharacteristic
666C2×C4C22⋊C4×D6111yescharacteristic
667C2×C4C22×C4×D6111yescharacteristic
668C2×C4C2×D4×D6111yescharacteristic
669C2×C4C2×D4×D6111yescharacteristic
670C8—24no—
671C8—42no—
672C8—1224no—
673C8—2442no—
674C22—21no—
675C22—21no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—84no—
680C22—612no—
681C22—1221no—
682C22—1221no—
683C22—1221no—
684C22—1221no—
685C22—1221no—
686C22—4884no—
687C22—2444no—
688C22—2442no—
689C22—2442no—
690C22—2442no—
691C22#104×D6112yes—
692C22C2×C22⋊C4×D6111yescharacteristic
693C4—21no—
694C4—21no—
695C4—21no—
696C4—21no—
697C4—21no—
698C4—42no—
699C4—612no—
700C4—612no—
701C4—612no—
702C4—612no—
703C4—1221no—
704C4—1221no—
705C4—2442no—
706C4#100×D6112yes—
707C2—22no—
708C2—82no—
709C2—1222no—
710C2—4882no—
711C2—2441no—
712C2C2×#100×D6111yescharacteristic
713C2C2×#104×D6111yescharacteristic
714C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1527C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840311C2
cosocleC42×C61C24
hypercenter#1527D61
hypocenterC61#17647
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1527

Complements

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

NH ≅ G/Ntype
2. #21454449C2semidirect
3. C4×M16×D61C2semidirect
4. #21444428C2semidirect
5. #21444418C2semidirect
6. #21444417C2semidirect
7. #21444416C2semidirect
8. #21444409C2semidirect
9. C61×#1527C2semidirect
30. #16839817C22semidirect
36. #16839714C22semidirect
37. #16839714C22semidirect
40. #97×D61C22semidirect
42. #16839502C22semidirect
43. #16839501C22semidirect
44. #16839501C22semidirect
48. C61×#329C22semidirect
357. #1527D61semidirect
405. #329C2×D61semidirect
406. C61#17647semidirect

Maximal subgroups

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

subgroupindex
C2×#168403112
#214544492
C4×M16×D612
#214444282
#214444182
#214444172
#214444162
#214444092
C61×#15272
#1764761