Finite Group Databasebeta

← #29646819

Subgroups — #29646819

Order 15616.

1078 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×#16840294C211yesmaximal, characteristic
2#432×D61C211yesmaximal, characteristic, complemented
3C4×M16×D61C211yesmaximal, characteristic, complemented
4#21444276C214yesmaximal, complemented
5#21444267C211yesmaximal, characteristic, complemented
6#21444265C211yesmaximal, characteristic, complemented
7#21444262C211yesmaximal, characteristic, complemented
8#21444229C214yesmaximal, complemented
9C61×#1490C211yesmaximal, characteristic, complemented
10C2×M16×D61—21no—
11#16840294—21no—
12#16840294—21no—
13#16840294—21no—
14#16840294—21no—
15#16840294C412yes—
16#16840294C412yes—
17#16840294C2212yes—
18#16840294C2212yes—
19C2×#14519770—21no—
20C2×#14519768C411yescharacteristic
21C2×#14519764C411yescharacteristic
22C2×#14519759—21no—
23C2×#14519757C411yescharacteristic
24C2×#14519748C411yescharacteristic
25C2×C4×Dic122C2211yescharacteristic
26C2×C4×C22⋊D61—21no—
27C2×#14519736—21no—
28C2×C42×D61C2211yescharacteristic
29#16839819C2211yescharacteristic
30#16839818C2212yescomplemented
31#16839817—21no—
32#16839816—21no—
33C4⋊C8×D61C2212yescomplemented
34C22⋊C8×D61—21no—
35C4×#11758194C2211yescharacteristic
36#16839714—21no—
37M16×Dic61—21no—
38C4×#11758189C2212yescomplemented
39#97×D61—21no—
40#97×D61—21no—
41C4×C8×D61C2212yescomplemented
42#16839494C2214yescomplemented
43#16839492C2214yescomplemented
44D4⋊#92418C2214yescomplemented
45C2×C4×D4×C61C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C4×M16×C61C2211yescharacteristic
48C61×D4⋊C8C2214yescomplemented
49C22×Dic122C2×C411yescharacteristic
50C22×C22⋊D61—21no—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C2×#11758194—21no—
55C2×#11758189—22no—
56M16×D61—28no—
57C2×C8×D61—22no—
58C2×C8×D61—22no—
59#14519770—22no—
60#14519770—22no—
61#14519770—22no—
62#14519770—22no—
63#14519768—21no—
64#14519768—21no—
65#14519768C2×C412yes—
66#14519768C2×C412yes—
67#14519764—21no—
68#14519764—21no—
69#14519764C2×C412yes—
70#14519764C2×C412yes—
71#14519759—22no—
72#14519759—22no—
73#14519759—22no—
74#14519759—22no—
75#14519757—21no—
76#14519757—21no—
77#14519757C2×C412yes—
78#14519757C2×C412yes—
79#14519748—21no—
80#14519748—21no—
81#14519748C2×C412yes—
82#14519748C2×C412yes—
83C4×Dic122—21no—
84C4×Dic122—21no—
85C4×Dic122C2×C412yes—
86C4×Dic122C2312yes—
87C4×C22⋊D61—22no—
88C4×C22⋊D61—22no—
89C4×C22⋊D61—22no—
90C4×C22⋊D61—22no—
91#14519736—22no—
92#14519736—22no—
93#14519736—22no—
94#14519736—22no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×C22⋊Dic61—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⋊#92418C2312yes—
117#14519706—22no—
118C22⋊#92418—21no—
119#14519689—22no—
120#14519688—21no—
121#14519688—21no—
122#14519687—22no—
123#14519687—22no—
124C4×#92418C2312yes—
125C8×Dic61—22no—
126C22×D4×C61C2×C411yescharacteristic
127C23×C4×C61—21no—
128C2×M16×C61—21no—
129C4×D4×C61—21no—
130C4×D4×C61—21no—
131C4×D4×C61C2×C412yes—
132C4×D4×C61C2312yes—
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61C2312yes—
137C22⋊C8×C61—21no—
138#97×C61—21no—
139#97×C61—21no—
140C4×C8×C61C2312yes—
141C24×C61—21no—
142C23×D61C22⋊C411yescharacteristic
143C2×D4×C61—21no—
144C2×D4×C61—42no—
145C2×D4×C61C22×C412yes—
146C22×C4×C61—21no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—44no—
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×Dic61C22⋊C411yescharacteristic
159C22×Dic61C22⋊C411yescharacteristic
160C22×Dic61C22⋊C411yescharacteristic
161C2×C4×D61—24no—
162C2×C4×D61—42no—
163C2×C4×D61—42no—
164C2×C4×D61C22⋊C411yescharacteristic
165C2×C4×D61C22⋊C411yescharacteristic
166C2×C4×D61C22⋊C411yescharacteristic
167C2×C4×D61C22⋊C411yescharacteristic
168C2×C4×D61C22⋊C411yescharacteristic
169C2×C4×D61C22⋊C411yescharacteristic
170C2×C4×D61C22×C411yescharacteristic
171C2×C4×D61C22×C411yescharacteristic
172C2×C4×D61C2×D411yescharacteristic
173C2×C4×D61C2×D411yescharacteristic
174C2×C4×D61C2×D411yescharacteristic
175C2×C4×D61C2×D411yescharacteristic
176C2×Dic122—21no—
177C2×Dic122—42no—
178C2×Dic122C22×C412yes—
179M16×C61—24no—
180C2×C8×C61—22no—
181C2×C8×C61—22no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61C22×C412yes—
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—
194C22⋊Dic61—22no—
195C22⋊Dic61—22no—
196#11758198—22no—
197#11758198—22no—
198C4⋊Dic61—21no—
199C4⋊Dic61—22no—
200C4⋊Dic61—22no—
201C4⋊Dic61—22no—
202C4⋊Dic61—22no—
203C4⋊Dic61C22×C412yes—
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—
226C8×D61—28no—
227C8×D61—44no—
228C23×C61—22no—
229C23×C61—42no—
230C23×C61—42no—
231C23×C61—42no—
232C23×C61C2×C22⋊C411yescharacteristic
233C22×D61—41no—
234C22×D61—41no—
235C22×D61#10414yes—
236C22×D61C2×C22⋊C411yescharacteristic
237C22×D61C2×C22⋊C411yescharacteristic
238D4×C61—24no—
239D4×C61—42no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—44no—
245C2×C4×C61—42no—
246C2×C4×C61—44no—
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—22no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—42no—
261C2×Dic61—42no—
262C2×Dic61C2×C22⋊C411yescharacteristic
263C2×Dic61C2×C22⋊C411yescharacteristic
264C2×Dic61C2×C22⋊C411yescharacteristic
265C2×Dic61C2×C22⋊C411yescharacteristic
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61C2×C22⋊C411yescharacteristic
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—22no—
273C4×D61—22no—
274C4×D61—22no—
275C4×D61—22no—
276C4×D61—41no—
277C4×D61—41no—
278C4×D61—41no—
279C4×D61—41no—
280Dic122—24no—
281Dic122—42no—
282C8×C61—24no—
283C8×C61—42no—
284#92418—24no—
285#92418—42no—
286#17502—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—44no—
300C2×D61C2×#10412yes—
301C2×D61C2×#10412yes—
302C4×C61—21no—
303C4×C61—21no—
304C4×C61—21no—
305C4×C61—21no—
306C4×C61—42no—
307C4×C61#56812yes—
308C4×C61#57512yes—
309Dic61—21no—
310Dic61—21no—
311Dic61—21no—
312Dic61—21no—
313Dic61—21no—
314Dic61—21no—
315Dic61—42no—
316Dic61—42no—
317C2×#529—611no—
318C2×#432—611no—
319C2×C4×M16—611no—
320#1494—614no—
321#1491—611no—
322#1491—611no—
323#1490—611no—
324#1490D6111yescharacteristic, complemented
325#1483—614no—
326C2×C61—22no—
327C2×C61—82no—
328C2×C61#287911yescharacteristic
329C2×C61#289611yescharacteristic
330C2×C61C22×#10411yescharacteristic
331D61—22no—
332D61—22no—
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×#124—611no—
345C2×#123—1221no—
346C2×C22⋊Q8—611no—
347C2×#121—611no—
348C2×C4×Q8—611no—
349C2×C4×D4—1221no—
350C2×C4×D4C2×D6111yescharacteristic
351C2×#117—1221no—
352C22×C42—611no—
353#432—611no—
354#432—612no—
355#432—1221no—
356#432—1221no—
357#432C2×D6111yescharacteristic
358C2×C4⋊C8—612no—
359C2×C22⋊C8—1221no—
360C4×M16—611no—
361C4×M16—612no—
362C4×M16—1221no—
363C4×M16—1221no—
364C4×M16C2×D6111yescharacteristic
365C2×#97—1221no—
366C2×#97—1221no—
367C2×C4×C8—612no—
368Q8⋊C8—614no—
369Q8⋊C8—614no—
370D4⋊C8—614no—
371D4⋊C8C2×D6114yescomplemented
372C61#1750211yescharacteristic, complemented, Sylow
373C22×Q8—611no—
374C22×D4—1221no—
375C22×D4C4×D6111yescharacteristic
376C23×C4—21no—
377C23×C4—611no—
378C23×C4—611no—
379C23×C4—611no—
380C2×M16—21no—
381C2×M16—1222no—
382C2×M16—1228no—
383C2×M16—1221no—
384C22×C8—1222no—
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—612no—
395#124—612no—
396#124—1221no—
397#124—1221no—
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—21no—
415C4×D4—21no—
416C4×D4—1222no—
417C4×D4—1222no—
418C4×D4—1222no—
419C4×D4—1222no—
420C4×D4C4×D6112yes—
421C4×D4C22×D6112yes—
422#117—1222no—
423#117—1222no—
424#117—1222no—
425#117—1222no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4C4×D6111yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—1221no—
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—612no—
451C4⋊C8—1222no—
452C4⋊C8C22×D6112yes—
453C22⋊C8—21no—
454C22⋊C8—1222no—
455C22⋊C8—1221no—
456#97—21no—
457#97—21no—
458#97—1222no—
459#97—1222no—
460#97—1221no—
461#97—1221no—
462C4×C8—612no—
463C4×C8—1222no—
464C4×C8C22×D6112yes—
465C24—21no—
466C24—611no—
467C2×Q8—612no—
468C2×Q8—1221no—
469C2×Q8—2442no—
470C2×D4—21no—
471C2×D4—42no—
472C2×D4—1222no—
473C2×D4—1222no—
474C2×D4—2444no—
475C2×D4C2×C4×D6112yes—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—44no—
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—611no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—1224no—
496C22×C4—1221no—
497C22×C4—1221no—
498C22×C4—2442no—
499C22×C4—2442no—
500C22×C4C2×C4×D6111yescharacteristic
501C22×C4D4×D6111yescharacteristic
502C22×C4D4×D6111yescharacteristic
503M16—24no—
504M16—1228no—
505M16—1224no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—1228no—
509C2×C8—1222no—
510C2×C8—1222no—
511C2×C8—2444no—
512C4⋊C4—21no—
513C4⋊C4—612no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—1222no—
521C4⋊C4—1221no—
522C4⋊C4—1222no—
523C4⋊C4C2×C4×D6112yes—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—1222no—
527C22⋊C4—1222no—
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—614no—
559C23—2441no—
560C23—2441no—
561C23C22⋊C4×D6111yescharacteristic
562Q8—1224no—
563Q8—2442no—
564D4—24no—
565D4—42no—
566D4—2444no—
567D4—2444no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—44no—
573C2×C4—42no—
574C2×C4—44no—
575C2×C4—611no—
576C2×C4—611no—
577C2×C4—611no—
578C2×C4—611no—
579C2×C4—611no—
580C2×C4—611no—
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—1222no—
591C2×C4—1222no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2441no—
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—612no—
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—42no—
630C4—1221no—
631C4—1221no—
632C4—1221no—
633C4—1221no—
634C4—1221no—
635C4—1221no—
636C4—2442no—
637C4—2442no—
638C4#1684052812yes—
639C4#1684055812yes—
640C2—22no—
641C2—82no—
642C2—1222no—
643C2—1222no—
644C2#2145426211yescharacteristic
645C2#2145433311yescharacteristic
646C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1490C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519748C4
cosocleC42×C61C24
hypercenter#1490D61
hypocenterC61#17502
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
2. #432×D61C2semidirect
3. C4×M16×D61C2semidirect
4. #21444276C2semidirect
5. #21444267C2semidirect
6. #21444265C2semidirect
7. #21444262C2semidirect
8. #21444229C2semidirect
9. C61×#1490C2semidirect
30. #16839818C22semidirect
33. C4⋊C8×D61C22semidirect
38. C4×#11758189C22semidirect
41. C4×C8×D61C22semidirect
42. #16839494C22semidirect
43. #16839492C22semidirect
44. D4⋊#92418C22semidirect
48. C61×D4⋊C8C22semidirect
324. #1490D61semidirect
371. D4⋊C8C2×D61semidirect
372. C61#17502semidirect

Maximal subgroups

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

subgroupindex
C2×#168402942
#432×D612
C4×M16×D612
#214442762
#214442672
#214442652
#214442622
#214442292
C61×#14902
#1750261