Finite Group Databasebeta

← #29647928

Subgroups — #29647928

Order 15616.

1068 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840291C211yesmaximal, characteristic
2#21454449C211yesmaximal, characteristic, complemented
3C4×M16×D61C211yesmaximal, characteristic, complemented
4#21444423C214yesmaximal, complemented
5#21444422C211yesmaximal, characteristic, complemented
6#21444420C211yesmaximal, characteristic, complemented
7#21444417C211yesmaximal, characteristic, complemented
8#21444404C214yesmaximal, complemented
9C61×#1527C211yesmaximal, characteristic, complemented
10C2×M16×D61—21no—
11#16840291—21no—
12#16840291—21no—
13#16840291—21no—
14#16840291—21no—
15#16840291C412yes—
16#16840291C412yes—
17#16840291C2212yes—
18#16840291C2212yes—
19C2×#14519770—21no—
20C2×#14519769C2211yescharacteristic
21C2×#14519759—21no—
22C2×#14519753C411yescharacteristic
23C2×#14519748C411yescharacteristic
24C2×Q8×Dic61C411yescharacteristic
25C2×D4×Dic61C411yescharacteristic
26C2×#14519737—21no—
27C2×#14519733—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#16839503C2214yescomplemented
43#16839503C2214yescomplemented
44#16839502C2214yescomplemented
45C2×#124×C61C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C4×M16×C61C2211yescharacteristic
48C61×#329C2214yescomplemented
49C22×C22⋊D61—21no—
50C23×Dic61—21no—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C2×#11758194—21no—
55C2×#11758189—22no—
56C2×#11758189—22no—
57M16×D61—28no—
58C2×C8×D61—22no—
59#14519770—22no—
60#14519770—22no—
61#14519770—22no—
62#14519770—22no—
63#14519769—21no—
64#14519769—21no—
65#14519769C2×C412yes—
66#14519769C2312yes—
67#14519759—22no—
68#14519759—22no—
69#14519759—22no—
70#14519759—22no—
71#14519753—21no—
72#14519753—21no—
73#14519753C2×C412yes—
74#14519753C2×C412yes—
75#14519748—21no—
76#14519748—21no—
77#14519748C2×C412yes—
78#14519748C2×C412yes—
79Q8×Dic61—21no—
80Q8×Dic61—21no—
81Q8×Dic61C2×C412yes—
82Q8×Dic61C2×C412yes—
83D4×Dic61—21no—
84D4×Dic61—21no—
85D4×Dic61C2×C412yes—
86D4×Dic61C2×C412yes—
87#14519737—22no—
88#14519737—22no—
89#14519737—22no—
90#14519737—22no—
91#14519733—22no—
92#14519733—22no—
93#14519733—22no—
94#14519733—22no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×#11758198—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61C2×C411yescharacteristic
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61D411yescharacteristic
108C42×D61C2×C411yescharacteristic
109C42×D61C2×C411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61C2311yescharacteristic
115C42×D61C2311yescharacteristic
116C4⋊#92418—21no—
117#14519706—22no—
118C22⋊#92418—21no—
119#14519689—22no—
120#14519688C2312yes—
121#14519688C2312yes—
122#14519687—22no—
123C4×#92418—21no—
124C8×Dic61—22no—
125C8×Dic61—22no—
126C22×Q8×C61C2×C411yescharacteristic
127C22×D4×C61C2×C411yescharacteristic
128C2×M16×C61—21no—
129#124×C61—21no—
130#124×C61—21no—
131#124×C61C2×C412yes—
132#124×C61C2312yes—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138#97×C61C2312yes—
139#97×C61C2312yes—
140C4×C8×C61—21no—
141C24×C61—21no—
142C23×D61C22⋊C411yescharacteristic
143C2×Q8×C61—21no—
144C2×Q8×C61—42no—
145C2×Q8×C61C22×C412yes—
146C2×D4×C61—21no—
147C2×D4×C61—42no—
148C2×D4×C61C22×C412yes—
149C22×C4×C61—21no—
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C2×C22⋊D61—22no—
154C2×C22⋊D61—22no—
155C2×C22⋊D61—44no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—44no—
161C22×Dic61C22⋊C411yescharacteristic
162C22×Dic61C22⋊C411yescharacteristic
163C22×Dic61C22⋊C411yescharacteristic
164C2×C4×D61—24no—
165C2×C4×D61—42no—
166C2×C4×D61—42no—
167C2×C4×D61C22⋊C411yescharacteristic
168C2×C4×D61C22⋊C411yescharacteristic
169C2×C4×D61C22⋊C411yescharacteristic
170C2×C4×D61C22⋊C411yescharacteristic
171C2×C4×D61C22⋊C411yescharacteristic
172C2×C4×D61C22⋊C411yescharacteristic
173C2×C4×D61C22×C411yescharacteristic
174C2×C4×D61C22×C411yescharacteristic
175C2×C4×D61C2×D411yescharacteristic
176C2×C4×D61C2×D411yescharacteristic
177C2×C4×D61C2×D411yescharacteristic
178C2×C4×D61C2×D411yescharacteristic
179M16×C61—24no—
180C2×C8×C61—22no—
181C2×C8×C61—22no—
182C22⋊C4×C61—22no—
183C22⋊C4×C61—22no—
184C22⋊C4×C61—22no—
185C22⋊C4×C61—22no—
186C42×C61C22×C411yescharacteristic
187C42×C61C2×D411yescharacteristic
188C42×C61C2×D411yescharacteristic
189C42×C61C2411yescharacteristic
190C22⋊Dic61—22no—
191C22⋊Dic61—22no—
192C22⋊Dic61—22no—
193C22⋊Dic61—22no—
194#11758198—22no—
195#11758198—22no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—22no—
199C4⋊Dic61—22no—
200C4⋊Dic61C22×C412yes—
201C4⋊Dic61C22×C412yes—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208C4×Dic61—22no—
209C4×Dic61—22no—
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22×C411yescharacteristic
217C4×Dic61C22×C411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222#11758194—24no—
223C2×#92418—22no—
224C2×#92418—22no—
225#11758189—28no—
226#11758189—44no—
227C8×D61—28no—
228C23×C61—22no—
229C23×C61—42no—
230C23×C61—42no—
231C23×C61—42no—
232C23×C61C2×C22⋊C411yescharacteristic
233C22×D61—22no—
234C22×D61—22no—
235C22×D61—41no—
236C22×D61C2×C22⋊C411yescharacteristic
237C22×D61C2×C22⋊C411yescharacteristic
238Q8×C61—42no—
239Q8×C61—42no—
240D4×C61—42no—
241D4×C61—42no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—41no—
246C2×C4×C61—42no—
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C23×C411yescharacteristic
251C2×C4×C61C22×D411yescharacteristic
252C2×C4×C61C22×D411yescharacteristic
253C22⋊D61—44no—
254C22⋊D61—44no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—42no—
260C2×Dic61—42no—
261C2×Dic61—44no—
262C2×Dic61—44no—
263C2×Dic61#10414yes—
264C2×Dic61C2×C22⋊C411yescharacteristic
265C2×Dic61C2×C22⋊C411yescharacteristic
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C411yescharacteristic
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—22no—
273C4×D61—22no—
274C4×D61—22no—
275C4×D61—22no—
276C4×D61—22no—
277C4×D61—22no—
278C4×D61—41no—
279C4×D61—41no—
280C4×D61—41no—
281C4×D61—41no—
282C8×C61—24no—
283C8×C61—42no—
284#92418—24no—
285#92418—42no—
286#17642—611nomaximal, Sylow
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—42no—
290C22×C61—42no—
291C22×C61—42no—
292C22×C61—84no—
293C22×C61C2×#10412yes—
294C22×C61C22×C22⋊C411yescharacteristic
295C2×D61—21no—
296C2×D61—21no—
297C2×D61—21no—
298C2×D61—21no—
299C2×D61—21no—
300C2×D61—44no—
301C2×D61#42112yes—
302C4×C61—21no—
303C4×C61—21no—
304C4×C61—21no—
305C4×C61—21no—
306C4×C61—21no—
307C4×C61—42no—
308C4×C61#41312yes—
309Dic61—21no—
310Dic61—21no—
311Dic61—21no—
312Dic61—21no—
313Dic61—42no—
314Dic61—42no—
315Dic61C2×#10412yes—
316Dic61C2×#10412yes—
317C2×#529—611no—
318#2920—611no—
319C2×C4×M16—611no—
320#1529—614no—
321#1528—611no—
322#1528—611no—
323#1527—611no—
324#1527D6111yescharacteristic, complemented
325#1524—614no—
326C2×C61—22no—
327C2×C61—82no—
328C2×C61C2×#41311yescharacteristic
329C2×C61C22×#10411yescharacteristic
330C2×C61C2×#42111yescharacteristic
331D61—22no—
332D61—41no—
333C22×M16—1221no—
334#529—612no—
335#529—612no—
336#529—612no—
337#529—612no—
338#529—1221no—
339#529—1221no—
340#529—1221no—
341#529—1221no—
342C2×#126—1221no—
343C2×#125—611no—
344C2×#124C2×D6111yescharacteristic
345C2×#123—1221no—
346C2×C22⋊Q8—611no—
347C2×#121—611no—
348C2×C4×Q8—611no—
349C2×C4×D4—611no—
350C2×C4×D4—1221no—
351C2×#117—1221no—
352C22×C42—611no—
353#432—611no—
354#432—612no—
355#432C2×D6111yescharacteristic
356#431—1221no—
357#431—1221no—
358#423—1221no—
359#407—1221no—
360C4×M16—611no—
361C4×M16—612no—
362C4×M16—612no—
363C4×M16—1221no—
364C4×M16—1221no—
365C4×M16C2×D6111yescharacteristic
366C2×#97—612no—
367C2×C4×C8—1221no—
368#330—614no—
369#330—614no—
370#329—614no—
371#329C2×D6114yescomplemented
372C61#1764211yescharacteristic, complemented, Sylow
373C22×Q8C4×D6111yescharacteristic
374C22×D4—1221no—
375C22×D4C4×D6111yescharacteristic
376C23×C4—611no—
377C23×C4—611no—
378C23×C4—611no—
379C23×C4—1221no—
380C2×M16—21no—
381C2×M16—1222no—
382C2×M16—1222no—
383C2×M16—1228no—
384C2×M16—1221no—
385C22×C8—1222no—
386#126—1222no—
387#126—1222no—
388#126—1222no—
389#126—1222no—
390#125—612no—
391#125—612no—
392#125—1221no—
393#125—1221no—
394#124—21no—
395#124—21no—
396#124C4×D6112yes—
397#124C22×D6112yes—
398#123—1222no—
399#123—1222no—
400#123—1222no—
401#123—1222no—
402C22⋊Q8—612no—
403C22⋊Q8—612no—
404C22⋊Q8—1221no—
405C22⋊Q8—1221no—
406#121—612no—
407#121—612no—
408#121—1221no—
409#121—1221no—
410C4×Q8—612no—
411C4×Q8—612no—
412C4×Q8—1221no—
413C4×Q8—1221no—
414C4×D4—612no—
415C4×D4—612no—
416C4×D4—1221no—
417C4×D4—1221no—
418C4×D4—1222no—
419C4×D4—1222no—
420C4×D4—1222no—
421C4×D4—1222no—
422#117—1222no—
423#117—1222no—
424#117—1222no—
425#117—1222no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—611no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4—1221no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—1221no—
435C2×C22⋊C4—1221no—
436C2×C22⋊C4—1221no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—1221no—
449C2×C42C22×D6111yescharacteristic
450C4⋊C8—21no—
451C4⋊C8—1222no—
452C4⋊C8—1221no—
453C22⋊C8—21no—
454C22⋊C8—1222no—
455C22⋊C8—1221no—
456#97—612no—
457#97—612no—
458#97—1222no—
459#97C22×D6112yes—
460#97C22×D6112yes—
461C4×C8—21no—
462C4×C8—1222no—
463C4×C8—1222no—
464C4×C8—1221no—
465C24—21no—
466C24—611no—
467C2×Q8—21no—
468C2×Q8—42no—
469C2×Q8C2×C4×D6112yes—
470C2×D4—21no—
471C2×D4—42no—
472C2×D4—1222no—
473C2×D4—1222no—
474C2×D4—2444no—
475C2×D4C2×C4×D6112yes—
476C22×C4—21no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—611no—
492C22×C4—1224no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4—2442no—
498C22×C4—2442no—
499C22×C4—2444no—
500C22×C4C2×C4×D6111yescharacteristic
501C22×C4D4×D6111yescharacteristic
502C22×C4D4×D6111yescharacteristic
503M16—24no—
504M16—1228no—
505M16—1224no—
506M16—2444no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—1228no—
510C2×C8—1222no—
511C2×C8—1222no—
512C4⋊C4—612no—
513C4⋊C4—612no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—1222no—
523C4⋊C4—1222no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—1222no—
529C22⋊C4—1222no—
530C22⋊C4—1222no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—611no—
545C42—611no—
546C42—1222no—
547C42—1222no—
548C42C2×C4×D6111yescharacteristic
549C42D4×D6111yescharacteristic
550C42D4×D6111yescharacteristic
551C42C23×D6111yescharacteristic
552C23—22no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—611no—
557C23—611no—
558C23—1222no—
559C23—1222no—
560C23—2441no—
561C23C22⋊C4×D6111yescharacteristic
562Q8—42no—
563Q8—42no—
564D4—42no—
565D4—42no—
566D4—2444no—
567D4—2444no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—611no—
574C2×C4—611no—
575C2×C4—614no—
576C2×C4—611no—
577C2×C4—611no—
578C2×C4—611no—
579C2×C4—611no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1222no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2444no—
595C2×C4—2444no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2442no—
599C2×C4—2442no—
600C2×C4C22⋊C4×D6111yescharacteristic
601C2×C4C22⋊C4×D6111yescharacteristic
602C2×C4C22⋊C4×D6111yescharacteristic
603C2×C4C22×C4×D6111yescharacteristic
604C2×C4C2×D4×D6111yescharacteristic
605C2×C4C2×D4×D6111yescharacteristic
606C8—24no—
607C8—42no—
608C8—1224no—
609C8—2442no—
610C22—21no—
611C22—21no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—84no—
616C22—612no—
617C22—1221no—
618C22—1221no—
619C22—1221no—
620C22—1221no—
621C22—1221no—
622C22—2444no—
623C22#104×D6112yes—
624C22C2×C22⋊C4×D6111yescharacteristic
625C4—21no—
626C4—21no—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—42no—
631C4—612no—
632C4—612no—
633C4—1221no—
634C4—1221no—
635C4—1221no—
636C4—1221no—
637C4—2442no—
638C4—2442no—
639C4#1683974312yes—
640C2—22no—
641C2—82no—
642C2—1222no—
643C2—2441no—
644C2C2×#1683974311yescharacteristic
645C2C2×#104×D6111yescharacteristic
646C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1527C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519748C4
cosocleC42×C61C24
hypercenter#1527D61
hypocenterC61#17642
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. #21444423C2semidirect
5. #21444422C2semidirect
6. #21444420C2semidirect
7. #21444417C2semidirect
8. #21444404C2semidirect
9. C61×#1527C2semidirect
30. #16839817C22semidirect
36. #16839714C22semidirect
37. #16839714C22semidirect
40. #97×D61C22semidirect
42. #16839503C22semidirect
43. #16839503C22semidirect
44. #16839502C22semidirect
48. C61×#329C22semidirect
324. #1527D61semidirect
371. #329C2×D61semidirect
372. C61#17642semidirect

Maximal subgroups

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

subgroupindex
C2×#168402912
#214544492
C4×M16×D612
#214444232
#214444222
#214444202
#214444172
#214444042
C61×#15272
#1764261