Finite Group Databasebeta

← #29646420

Subgroups — #29646420

Order 15616.

1268 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758224C211yesmaximal, characteristic
2#21454451C211yesmaximal, characteristic, complemented
3#431×D61C211yesmaximal, characteristic, complemented
4#21444250C214yesmaximal, complemented
5#21444249C211yesmaximal, characteristic, complemented
6#21444247C211yesmaximal, characteristic, complemented
7#21444244C211yesmaximal, characteristic, complemented
8#21444198C214yesmaximal, complemented
9C61×#1486C211yesmaximal, characteristic, complemented
10C22×#11758224C411yescharacteristic
11C4×#11758224—21no—
12C4×#11758224—21no—
13C4×#11758224—21no—
14C4×#11758224—21no—
15C4×#11758224C412yes—
16C4×#11758224C412yes—
17C4×#11758224C2212yes—
18C4×#11758224C2212yes—
19C2×C4×Dic122C2211yescharacteristic
20C2×#14519742C411yescharacteristic
21C2×D4×Dic61C411yescharacteristic
22C2×C4×C22⋊D61—21no—
23C2×#14519737—21no—
24C2×#14519735C411yescharacteristic
25C2×#14519733—21no—
26C22×C4×Dic61—21no—
27C2×C42×D61C2211yescharacteristic
28#16839818—21no—
29#16839818C2212yescomplemented
30#16839815C2211yescharacteristic
31#16839814—21no—
32#16839814—21no—
33#16839814C2212yescomplemented
34#16839813C2212yescomplemented
35#16839812—21no—
36#16839786C2211yescharacteristic
37C4⋊C8×D61—21no—
38#16839725—21no—
39C22⋊C8×D61—21no—
40M16×Dic61—21no—
41C4×C8×D61C2212yescomplemented
42#16839494C2214yescomplemented
43#16839492C2214yescomplemented
44D4⋊#92418C2214yescomplemented
45C2×C4×D4×C61C2211yescharacteristic
46C61×#431C2211yescharacteristic
47C61×#423C2211yescharacteristic
48C61×D4⋊C8C2214yescomplemented
49C2×#11758224—28no—
50C2×#11758224—21no—
51C2×#11758224—21no—
52C2×#11758224C2×C412yes—
53C2×#11758224C2×C412yes—
54C22×Dic122C2×C411yescharacteristic
55C22×C22⋊D61—21no—
56C23×Dic61—21no—
57C23×Dic61—21no—
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C22×C4×D61D411yescharacteristic
61C2×#11758194—21no—
62C2×C8×D61—22no—
63C4×Dic122—21no—
64C4×Dic122—21no—
65C4×Dic122C2×C412yes—
66C4×Dic122C2312yes—
67#14519742—21no—
68#14519742—21no—
69#14519742C2×C412yes—
70#14519742C2×C412yes—
71D4×Dic61—21no—
72D4×Dic61—21no—
73D4×Dic61C2×C412yes—
74D4×Dic61C2×C412yes—
75C4×C22⋊D61—22no—
76C4×C22⋊D61—22no—
77C4×C22⋊D61—22no—
78C4×C22⋊D61—22no—
79#14519737—22no—
80#14519737—22no—
81#14519737—22no—
82#14519737—22no—
83#14519735—21no—
84#14519735—21no—
85#14519735C2×C412yes—
86#14519735C2×C412yes—
87#14519733—22no—
88#14519733—22no—
89#14519733—22no—
90#14519733—22no—
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×C22⋊Dic61—21no—
95C2×#11758198—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61—22no—
100C2×C4×Dic61—22no—
101C2×C4×Dic61—22no—
102C2×C4×Dic61—22no—
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61D411yescharacteristic
105C2×C4×Dic61D411yescharacteristic
106C42×D61C2×C411yescharacteristic
107C42×D61C2×C411yescharacteristic
108C42×D61D411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61C2311yescharacteristic
113C42×D61C2311yescharacteristic
114C4⋊#92418—21no—
115C4⋊#92418—21no—
116C4⋊#92418C2312yes—
117#14519706—22no—
118C22⋊#92418—21no—
119#14519689—22no—
120#14519689—22no—
121#14519689—22no—
122#14519687—22no—
123C4×#92418C2312yes—
124C8×Dic61—22no—
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×C61—21no—
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2312yes—
139C22⋊C8×C61—21no—
140C4×C8×C61C2312yes—
141C24×C61—21no—
142C23×D61C22⋊C411yescharacteristic
143C2×D4×C61—24no—
144C2×D4×C61—21no—
145C2×D4×C61C22×C412yes—
146C22×C4×C61—21no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—42no—
150C22×C4×C61—42no—
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C2×C22⋊D61—28no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C22×Dic61—28no—
158C22×Dic61—21no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—21no—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—44no—
165C22×Dic61C22⋊C411yescharacteristic
166C22×Dic61C22⋊C411yescharacteristic
167C22×Dic61C22⋊C411yescharacteristic
168#11758224—28no—
169#11758224—28no—
170#11758224—24no—
171#11758224—24no—
172#11758224—24no—
173#11758224M1618yescomplemented
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—24no—
177C2×C4×D61—42no—
178C2×C4×D61C22⋊C411yescharacteristic
179C2×C4×D61C22⋊C411yescharacteristic
180C2×C4×D61C22⋊C411yescharacteristic
181C2×C4×D61C22⋊C411yescharacteristic
182C2×C4×D61C22⋊C411yescharacteristic
183C2×C4×D61C22⋊C411yescharacteristic
184C2×C4×D61C22×C411yescharacteristic
185C2×C4×D61C22×C411yescharacteristic
186C2×C4×D61C2×D411yescharacteristic
187C2×C4×D61C2×D411yescharacteristic
188C2×C4×D61C2×D411yescharacteristic
189C2×C4×D61C2×D411yescharacteristic
190C2×Dic122—21no—
191C2×Dic122—24no—
192C2×Dic122C22×C412yes—
193M16×C61—42no—
194C2×C8×C61—22no—
195C2×C8×C61—22no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61C22×C412yes—
198C22⋊C4×C61—22no—
199C22⋊C4×C61—22no—
200C42×C61C22×C411yescharacteristic
201C42×C61C2×D411yescharacteristic
202C42×C61C2×D411yescharacteristic
203C42×C61C2411yescharacteristic
204C22⋊Dic61—22no—
205C22⋊Dic61—22no—
206#11758198—22no—
207#11758198—22no—
208C4⋊Dic61—21no—
209C4⋊Dic61C22×C412yes—
210#11758196—22no—
211#11758196—22no—
212#11758196—22no—
213#11758196—22no—
214C4×Dic61—22no—
215C4×Dic61—22no—
216C4×Dic61—22no—
217C4×Dic61—22no—
218C4×Dic61—22no—
219C4×Dic61—22no—
220C4×Dic61C22⋊C411yescharacteristic
221C4×Dic61C22⋊C411yescharacteristic
222C4×Dic61C22⋊C411yescharacteristic
223C4×Dic61C22⋊C411yescharacteristic
224C4×Dic61C22⋊C411yescharacteristic
225C4×Dic61C22⋊C411yescharacteristic
226C4×Dic61C22×C411yescharacteristic
227C4×Dic61C22×C411yescharacteristic
228C4×Dic61C2×D411yescharacteristic
229C4×Dic61C2×D411yescharacteristic
230C4×Dic61C2×D411yescharacteristic
231C4×Dic61C2×D411yescharacteristic
232#11758194—42no—
233C2×#92418—22no—
234C2×#92418—22no—
235C8×D61—44no—
236C23×C61—24no—
237C23×C61—22no—
238C23×C61—42no—
239C23×C61—42no—
240C23×C61C2×C22⋊C411yescharacteristic
241C22×D61—22no—
242C22×D61—22no—
243C22×D61—41no—
244C22×D61C2×C22⋊C411yescharacteristic
245C22×D61C2×C22⋊C411yescharacteristic
246D4×C61—24no—
247D4×C61—22no—
248D4×C61C2×M1614yes—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—41no—
252C2×C4×C61—42no—
253C2×C4×C61—42no—
254C2×C4×C61—42no—
255C2×C4×C61—44no—
256C2×C4×C61C2×C22⋊C411yescharacteristic
257C2×C4×C61C2×C22⋊C411yescharacteristic
258C2×C4×C61C2×C22⋊C411yescharacteristic
259C2×C4×C61#13512yes—
260C2×C4×C61#13512yes—
261C2×C4×C61C23×C411yescharacteristic
262C2×C4×C61C22×D411yescharacteristic
263C2×C4×C61C22×D411yescharacteristic
264C22⋊D61—28no—
265C22⋊D61—28no—
266C2×Dic61—24no—
267C2×Dic61—28no—
268C2×Dic61—22no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—28no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—44no—
275C2×Dic61—42no—
276C2×Dic61—44no—
277C2×Dic61C2×C22⋊C411yescharacteristic
278C2×Dic61C2×C22⋊C411yescharacteristic
279C2×Dic61C2×C22⋊C411yescharacteristic
280C2×Dic61C2×C22⋊C411yescharacteristic
281C2×Dic61C2×C22⋊C411yescharacteristic
282C2×Dic61C2×C22⋊C411yescharacteristic
283C4×D61—22no—
284C4×D61—22no—
285C4×D61—21no—
286C4×D61—21no—
287C4×D61—21no—
288C4×D61—21no—
289C4×D61—22no—
290C4×D61—22no—
291C4×D61—22no—
292C4×D61—22no—
293C4×D61—22no—
294C4×D61—41no—
295C4×D61—41no—
296C4×D61C2×M1614yes—
297Dic122—24no—
298Dic122—22no—
299Dic122C2×M1614yes—
300C8×C61—42no—
301C8×C61—42no—
302#92418—42no—
303#92418—42no—
304#17443—611nomaximal, Sylow
305C22×C61—21no—
306C22×C61—21no—
307C22×C61—24no—
308C22×C61—48no—
309C22×C61—42no—
310C22×C61—42no—
311C22×C61#41612yes—
312C22×C61C22×C22⋊C411yescharacteristic
313C2×D61—21no—
314C2×D61—21no—
315C2×D61—21no—
316C2×D61—21no—
317C2×D61—21no—
318C2×D61—44no—
319C2×D61#40712yes—
320C4×C61—21no—
321C4×C61—21no—
322C4×C61—21no—
323C4×C61—42no—
324C4×C61#41612yes—
325C4×C61C22×M1612yes—
326C4×C61C2×#13511yescharacteristic
327C4×C61C2×#13511yescharacteristic
328Dic61—24no—
329Dic61—21no—
330Dic61—21no—
331Dic61—21no—
332Dic61—21no—
333Dic61—42no—
334Dic61#40712yes—
335Dic61#42112yes—
336C2×C4×#41—611no—
337#2920—611no—
338C2×#431—611no—
339#1488—614no—
340#1487—611no—
341#1487—611no—
342#1486—611no—
343#1486D6111yescharacteristic, complemented
344#1476—614no—
345C2×C61—22no—
346C2×C61—44no—
347C2×C61C2×#40711yescharacteristic
348C2×C61C2×#41611yescharacteristic
349C2×C61C2×#42111yescharacteristic
350D61—22no—
351D61—41no—
352C22×#41—611no—
353C4×#41—612no—
354C4×#41—612no—
355C4×#41—612no—
356C4×#41—612no—
357C4×#41—1221no—
358C4×#41—1221no—
359C4×#41—1221no—
360C4×#41—1221no—
361C2×C4×Q8—611no—
362C2×C4×Q8—611no—
363C2×C4×D4—611no—
364C2×C4×D4—1221no—
365C2×C4×D4—1221no—
366C2×C4×D4C2×D6111yescharacteristic
367C2×#117—611no—
368C2×#117—1221no—
369C22×C42—611no—
370C22×C42—1221no—
371#432—612no—
372#432—1221no—
373#431—611no—
374#431—612no—
375#431—612no—
376#431—1221no—
377#431—1221no—
378#431—1221no—
379#431C2×D6111yescharacteristic
380#423—611no—
381#423C2×D6111yescharacteristic
382C2×C4⋊C8—1221no—
383#407—1221no—
384C2×C22⋊C8—1221no—
385C4×M16—1221no—
386C2×C4×C8—612no—
387Q8⋊C8—614no—
388Q8⋊C8—614no—
389D4⋊C8—614no—
390D4⋊C8C2×D6114yescomplemented
391C61#1744311yescharacteristic, complemented, Sylow
392C2×#41—612no—
393C2×#41—612no—
394C2×#41—1221no—
395C2×#41—1221no—
396C2×#41—1228no—
397C22×Q8—611no—
398C22×D4—1221no—
399C22×D4C4×D6111yescharacteristic
400C23×C4—21no—
401C23×C4—611no—
402C23×C4—611no—
403C23×C4—611no—
404C23×C4—1221no—
405C23×C4—1221no—
406C2×M16—21no—
407C2×M16—1221no—
408C22×C8—1222no—
409C4×Q8—612no—
410C4×Q8—612no—
411C4×Q8—612no—
412C4×Q8—612no—
413C4×Q8—1221no—
414C4×Q8—1221no—
415C4×Q8—1221no—
416C4×Q8—1221no—
417C4×D4—21no—
418C4×D4—21no—
419C4×D4—612no—
420C4×D4—612no—
421C4×D4—1221no—
422C4×D4—1221no—
423C4×D4—1222no—
424C4×D4—1222no—
425C4×D4—1222no—
426C4×D4—1222no—
427C4×D4—1222no—
428C4×D4—1222no—
429C4×D4—1222no—
430C4×D4—1222no—
431C4×D4C4×D6112yes—
432C4×D4C22×D6112yes—
433#117—612no—
434#117—612no—
435#117—1222no—
436#117—1222no—
437#117—1222no—
438#117—1222no—
439#117—1221no—
440#117—1221no—
441C2×C4⋊C4—611no—
442C2×C4⋊C4—1221no—
443C2×C4⋊C4—1221no—
444C2×C4⋊C4C4×D6111yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—1221no—
447C2×C22⋊C4—1221no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—611no—
452C2×C42—611no—
453C2×C42—611no—
454C2×C42—611no—
455C2×C42—611no—
456C2×C42—611no—
457C2×C42—611no—
458C2×C42—611no—
459C2×C42—1222no—
460C2×C42—1222no—
461C2×C42—1222no—
462C2×C42—1222no—
463C2×C42—1221no—
464C2×C42—1221no—
465C2×C42—1221no—
466C2×C42C22×D6111yescharacteristic
467C4⋊C8—21no—
468C4⋊C8—21no—
469C4⋊C8—612no—
470C4⋊C8—1222no—
471C4⋊C8—1221no—
472C4⋊C8—1221no—
473C4⋊C8C22×D6112yes—
474C22⋊C8—21no—
475C22⋊C8—1222no—
476C22⋊C8—1222no—
477C22⋊C8—1222no—
478C22⋊C8—1221no—
479#97—1222no—
480C4×C8—612no—
481C4×C8—1222no—
482C4×C8—1222no—
483C4×C8C22×D6112yes—
484C24—21no—
485C24—611no—
486#41—618no—
487#41—1224no—
488#41—1224no—
489#41—1228no—
490#41—1228no—
491#41—1224no—
492C2×Q8—612no—
493C2×Q8—1224no—
494C2×Q8—1221no—
495C2×D4—24no—
496C2×D4—21no—
497C2×D4—1222no—
498C2×D4—1222no—
499C2×D4—1228no—
500C2×D4C2×C4×D6112yes—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—611no—
511C22×C4—611no—
512C22×C4—611no—
513C22×C4—611no—
514C22×C4—611no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—1224no—
522C22×C4—1222no—
523C22×C4—1222no—
524C22×C4—1222no—
525C22×C4—1222no—
526C22×C4—1228no—
527C22×C4—1221no—
528C22×C4—1222no—
529C22×C4—1222no—
530C22×C4—1221no—
531C22×C4—2442no—
532C22×C4—2444no—
533C22×C4C2×C4×D6111yescharacteristic
534C22×C4D4×D6111yescharacteristic
535C22×C4D4×D6111yescharacteristic
536M16—42no—
537M16—2442no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—1222no—
541C2×C8—1222no—
542C2×C8—2444no—
543C4⋊C4—21no—
544C4⋊C4—612no—
545C4⋊C4—1222no—
546C4⋊C4—1222no—
547C4⋊C4—1222no—
548C4⋊C4—1221no—
549C4⋊C4—1222no—
550C4⋊C4C2×C4×D6112yes—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—1222no—
554C22⋊C4—1222no—
555C22⋊C4—1222no—
556C22⋊C4—1222no—
557C42—611no—
558C42—611no—
559C42—611no—
560C42—611no—
561C42—611no—
562C42—611no—
563C42—611no—
564C42—611no—
565C42—611no—
566C42—611no—
567C42—611no—
568C42—611no—
569C42—1222no—
570C42—1222no—
571C42—1222no—
572C42—1222no—
573C42—1222no—
574C42—1222no—
575C42C2×C4×D6111yescharacteristic
576C42D4×D6111yescharacteristic
577C42D4×D6111yescharacteristic
578C42C23×D6111yescharacteristic
579C23—24no—
580C23—22no—
581C23—42no—
582C23—42no—
583C23—611no—
584C23—611no—
585C23—1222no—
586C23—1222no—
587C23—2441no—
588C23C22⋊C4×D6111yescharacteristic
589Q8—614no—
590Q8—1224no—
591Q8—1222no—
592D4—24no—
593D4—22no—
594D4—1228no—
595D4—1228no—
596D4M16×D6114yes—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—44no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—611no—
605C2×C4—611no—
606C2×C4—614no—
607C2×C4—611no—
608C2×C4—611no—
609C2×C4—611no—
610C2×C4—611no—
611C2×C4—1222no—
612C2×C4—1222no—
613C2×C4—1222no—
614C2×C4—1222no—
615C2×C4—1222no—
616C2×C4—1222no—
617C2×C4—1228no—
618C2×C4—1224no—
619C2×C4—1228no—
620C2×C4—1222no—
621C2×C4—1222no—
622C2×C4—1222no—
623C2×C4—1222no—
624C2×C4—1222no—
625C2×C4—1221no—
626C2×C4—1221no—
627C2×C4—1221no—
628C2×C4—1221no—
629C2×C4—1222no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2444no—
633C2×C4—2444no—
634C2×C4—2442no—
635C2×C4C22⋊C4×D6111yescharacteristic
636C2×C4C22⋊C4×D6111yescharacteristic
637C2×C4C22⋊C4×D6111yescharacteristic
638C2×C4#1451979612yes—
639C2×C4#1451979812yes—
640C2×C4C22×C4×D6111yescharacteristic
641C2×C4C2×D4×D6111yescharacteristic
642C2×C4C2×D4×D6111yescharacteristic
643C8—42no—
644C8—42no—
645C8—2442no—
646C8—2442no—
647C22—21no—
648C22—21no—
649C22—24no—
650C22—48no—
651C22—42no—
652C22—42no—
653C22—612no—
654C22—1221no—
655C22—1221no—
656C22—1221no—
657C22—1221no—
658C22—1221no—
659C22—2444no—
660C22#1683975512yes—
661C22C2×C22⋊C4×D6111yescharacteristic
662C4—21no—
663C4—21no—
664C4—21no—
665C4—42no—
666C4—612no—
667C4—612no—
668C4—1221no—
669C4—1221no—
670C4—1224no—
671C4—1221no—
672C4—1221no—
673C4—2442no—
674C4#1683975512yes—
675C4C2×M16×D6112yes—
676C4C2×#1451979611yescharacteristic
677C4C2×#1451979811yescharacteristic
678C2—22no—
679C2—44no—
680C2—1222no—
681C2—2441no—
682C2#407×D6111yescharacteristic
683C2C2×#1683975511yescharacteristic
684C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1486C2
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758224C4
cosocleC42×C61C24
hypercenter#1486D61
hypocenterC61#17443
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #21454451C2semidirect
3. #431×D61C2semidirect
4. #21444250C2semidirect
5. #21444249C2semidirect
6. #21444247C2semidirect
7. #21444244C2semidirect
8. #21444198C2semidirect
9. C61×#1486C2semidirect
29. #16839818C22semidirect
33. #16839814C22semidirect
34. #16839813C22semidirect
41. C4×C8×D61C22semidirect
42. #16839494C22semidirect
43. #16839492C22semidirect
44. D4⋊#92418C22semidirect
48. C61×D4⋊C8C22semidirect
173. #11758224M16semidirect
343. #1486D61semidirect
390. D4⋊C8C2×D61semidirect
391. C61#17443semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582242
#214544512
#431×D612
#214442502
#214442492
#214442472
#214442442
#214441982
C61×#14862
#1744361