Finite Group Databasebeta

← #29646480

Subgroups — #29646480

Order 15616.

1248 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758226C211yesmaximal, characteristic
2#21454450C211yesmaximal, characteristic, complemented
3#432×D61C211yesmaximal, characteristic, complemented
4#21444266C211yesmaximal, characteristic, complemented
5#21444263C211yesmaximal, characteristic, complemented
6#21444261C211yesmaximal, characteristic, complemented
7#21444252C214yesmaximal, complemented
8#21444205C214yesmaximal, complemented
9C61×#1491C211yesmaximal, characteristic, complemented
10C22×#11758226C411yescharacteristic
11C4×#11758226—21no—
12C4×#11758226—21no—
13C4×#11758226—21no—
14C4×#11758226—21no—
15C4×#11758226C412yes—
16C4×#11758226C412yes—
17C4×#11758226C2212yes—
18C4×#11758226C2212yes—
19C2×Q8×Dic61C411yescharacteristic
20C2×C4×D244—21no—
21C2×C4×D244C2211yescharacteristic
22C2×#14519739—21no—
23C2×#14519739C411yescharacteristic
24C2×#14519735—21no—
25C2×#14519735C411yescharacteristic
26C2×C42×D61—21no—
27C2×C42×D61C2211yescharacteristic
28#16839819C2211yescharacteristic
29#16839818C2212yescomplemented
30#16839817—21no—
31#16839817—21no—
32#16839817—21no—
33#16839816—21no—
34#16839813C2212yescomplemented
35#16839813C2212yescomplemented
36#16839785—21no—
37C4⋊C8×D61C2212yescomplemented
38#16839725—21no—
39C22⋊C8×D61—21no—
40C4×#11758194C2211yescharacteristic
41#97×D61—21no—
42Q8⋊#92418C2214yescomplemented
43#16839491C2214yescomplemented
44#16839489C2214yescomplemented
45C2×C4×Q8×C61C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C4×M16×C61C2211yescharacteristic
48C61×Q8⋊C8C2214yescomplemented
49C2×#11758226—28no—
50C2×#11758226—21no—
51C2×#11758226—21no—
52C2×#11758226C2×C412yes—
53C2×#11758226C2×C412yes—
54C22×D244—21no—
55C22×D244C2×C411yescharacteristic
56C22×C4×D61—21no—
57C22×C4×D61—21no—
58C22×C4×D61—21no—
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C2×#11758194—21no—
63C2×C8×D61—22no—
64Q8×Dic61—21no—
65Q8×Dic61—21no—
66Q8×Dic61C2×C412yes—
67Q8×Dic61C2×C412yes—
68C4×D244—22no—
69C4×D244—22no—
70C4×D244—22no—
71C4×D244—22no—
72C4×D244—21no—
73C4×D244—21no—
74C4×D244C2×C412yes—
75C4×D244C2312yes—
76#14519739—22no—
77#14519739—22no—
78#14519739—22no—
79#14519739—22no—
80#14519739—21no—
81#14519739—21no—
82#14519739C2×C412yes—
83#14519739C2×C412yes—
84#14519735—21no—
85#14519735—21no—
86#14519735—22no—
87#14519735—22no—
88#14519735—22no—
89#14519735—22no—
90#14519735C2×C412yes—
91#14519735C2×C412yes—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61C2×C411yescharacteristic
100C2×C4×Dic61D411yescharacteristic
101C2×C4×Dic61D411yescharacteristic
102C42×D61—22no—
103C42×D61—22no—
104C42×D61—22no—
105C42×D61—22no—
106C42×D61C2×C411yescharacteristic
107C42×D61C2×C411yescharacteristic
108C42×D61D411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61C2311yescharacteristic
113C42×D61C2311yescharacteristic
114C4⋊#92418C2312yes—
115#14519706—22no—
116#14519706—22no—
117#14519706—22no—
118C22⋊#92418—21no—
119#14519689—22no—
120#14519689—22no—
121#14519689—22no—
122#14519688—21no—
123#14519688—21no—
124#14519687—22no—
125C4×#92418C2312yes—
126C22×Q8×C61C2×C411yescharacteristic
127C2×M16×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130C4×Q8×C61C2×C412yes—
131C4×Q8×C61C2312yes—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C42×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61C2312yes—
137C22⋊C8×C61—21no—
138#97×C61—21no—
139#97×C61—21no—
140C4×C8×C61C2312yes—
141C23×D61—21no—
142C23×D61C22⋊C411yescharacteristic
143C2×Q8×C61—24no—
144C2×Q8×C61—21no—
145C2×Q8×C61C22×C412yes—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×Dic61—21no—
152C22×Dic61C22⋊C411yescharacteristic
153C22×Dic61C22⋊C411yescharacteristic
154C22×Dic61C22⋊C411yescharacteristic
155#11758226—28no—
156#11758226—28no—
157#11758226—24no—
158#11758226—24no—
159#11758226—24no—
160#11758226M1618yescomplemented
161C2×D244—28no—
162C2×D244—22no—
163C2×D244—22no—
164C2×D244—21no—
165C2×D244—24no—
166C2×D244C22×C412yes—
167C2×C4×D61—28no—
168C2×C4×D61—22no—
169C2×C4×D61—22no—
170C2×C4×D61—24no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—42no—
176C2×C4×D61—42no—
177C2×C4×D61—44no—
178C2×C4×D61—44no—
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×D61C22×C411yescharacteristic
187C2×C4×D61C2×D411yescharacteristic
188C2×C4×D61C2×D411yescharacteristic
189C2×C4×D61C2×D411yescharacteristic
190C2×C4×D61C2×D411yescharacteristic
191M16×C61—42no—
192C2×C8×C61—22no—
193C2×C8×C61—22no—
194C4⋊C4×C61—22no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—22no—
197C4⋊C4×C61C22×C412yes—
198C42×C61—22no—
199C42×C61—22no—
200C42×C61C22×C411yescharacteristic
201C42×C61C2×D411yescharacteristic
202C42×C61C2×D411yescharacteristic
203C42×C61C2411yescharacteristic
204#11758198—22no—
205#11758198—22no—
206#11758198—22no—
207#11758198—22no—
208#11758198—22no—
209#11758198—22no—
210C4⋊Dic61—21no—
211C4⋊Dic61—22no—
212C4⋊Dic61—22no—
213C4⋊Dic61C22×C412yes—
214C4×Dic61—22no—
215C4×Dic61—22no—
216C4×Dic61—22no—
217C4×Dic61—22no—
218C4×Dic61C22⋊C411yescharacteristic
219C4×Dic61C22⋊C411yescharacteristic
220C4×Dic61C22⋊C411yescharacteristic
221C4×Dic61C22⋊C411yescharacteristic
222C4×Dic61C22⋊C411yescharacteristic
223C4×Dic61C22⋊C411yescharacteristic
224C4×Dic61C22×C411yescharacteristic
225C4×Dic61C22×C411yescharacteristic
226C4×Dic61C2×D411yescharacteristic
227C4×Dic61C2×D411yescharacteristic
228C4×Dic61C2×D411yescharacteristic
229C4×Dic61C2×D411yescharacteristic
230#11758194—42no—
231C2×#92418—22no—
232C2×#92418—22no—
233C8×D61—44no—
234C23×C61C2×C22⋊C411yescharacteristic
235C22×D61—24no—
236C22×D61—22no—
237C22×D61—22no—
238C22×D61—22no—
239C22×D61—41no—
240C22×D61—42no—
241C22×D61—42no—
242C22×D61C2×C22⋊C411yescharacteristic
243C22×D61C2×C22⋊C411yescharacteristic
244Q8×C61—24no—
245Q8×C61—22no—
246Q8×C61C2×M1614yes—
247C2×C4×C61—24no—
248C2×C4×C61—22no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—42no—
254C2×C4×C61C2×C22⋊C411yescharacteristic
255C2×C4×C61C2×C22⋊C411yescharacteristic
256C2×C4×C61C2×C22⋊C411yescharacteristic
257C2×C4×C61C23×C411yescharacteristic
258C2×C4×C61C22×D411yescharacteristic
259C2×C4×C61C22×D411yescharacteristic
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—41no—
264C2×Dic61—42no—
265C2×Dic61C2×C22⋊C411yescharacteristic
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271D244—28no—
272D244—24no—
273D244—28no—
274D244—22no—
275D244C2×M1614yes—
276C4×D61—28no—
277C4×D61—22no—
278C4×D61—22no—
279C4×D61—22no—
280C4×D61—22no—
281C4×D61—28no—
282C4×D61—22no—
283C4×D61—41no—
284C4×D61—41no—
285C4×D61—41no—
286C4×D61—41no—
287C4×D61—41no—
288C4×D61—41no—
289C4×D61—44no—
290C4×D61—44no—
291C4×D61—44no—
292C4×D61—44no—
293C4×D61C2×M1614yes—
294C8×C61—42no—
295C8×C61—42no—
296#92418—42no—
297#92418—42no—
298#17452—611nomaximal, Sylow
299C22×C61—21no—
300C22×C61—21no—
301C22×C61#42112yes—
302C22×C61C22×C22⋊C411yescharacteristic
303C2×D61—21no—
304C2×D61—21no—
305C2×D61—21no—
306C2×D61—24no—
307C2×D61—21no—
308C2×D61—21no—
309C2×D61—44no—
310C2×D61—48no—
311C2×D61—42no—
312C2×D61—42no—
313C2×D61#40712yes—
314C4×C61—24no—
315C4×C61—21no—
316C4×C61—21no—
317C4×C61—21no—
318C4×C61—21no—
319C4×C61—42no—
320C4×C61C22×M1612yes—
321C4×C61#57512yes—
322Dic61—21no—
323Dic61—21no—
324Dic61—21no—
325Dic61—21no—
326Dic61—21no—
327Dic61—42no—
328Dic61#40712yes—
329C2×C4×#41—611no—
330#2920—611no—
331C2×#432—611no—
332#1491—611no—
333#1491D6111yescharacteristic, complemented
334#1490—611no—
335#1490—611no—
336#1488—614no—
337#1477—614no—
338C2×C61—22no—
339C2×C61C2×#40711yescharacteristic
340C2×C61#289611yescharacteristic
341C2×C61C2×#42111yescharacteristic
342D61—22no—
343D61—41no—
344D61—44no—
345C22×#41—611no—
346C4×#41—612no—
347C4×#41—612no—
348C4×#41—612no—
349C4×#41—612no—
350C4×#41—1221no—
351C4×#41—1221no—
352C4×#41—1221no—
353C4×#41—1221no—
354C2×C4×Q8—611no—
355C2×C4×Q8C2×D6111yescharacteristic
356C2×C4×D4—611no—
357C2×C4×D4—611no—
358C2×C4×D4—1221no—
359C2×C4×D4—1221no—
360C2×#117—611no—
361C2×#117—1221no—
362C22×C42—611no—
363C22×C42—1221no—
364#432—611no—
365#432—612no—
366#432—1221no—
367#432—1221no—
368#432—1221no—
369#432—1221no—
370#432C2×D6111yescharacteristic
371#431—612no—
372#431—612no—
373#423—1221no—
374C2×C4⋊C8—612no—
375#407—1221no—
376C2×C22⋊C8—1221no—
377C4×M16—611no—
378C4×M16C2×D6111yescharacteristic
379C2×#97—1221no—
380Q8⋊C8—614no—
381Q8⋊C8C2×D6114yescomplemented
382D4⋊C8—614no—
383D4⋊C8—614no—
384C61#1745211yescharacteristic, complemented, Sylow
385C2×#41—612no—
386C2×#41—612no—
387C2×#41—1221no—
388C2×#41—1221no—
389C2×#41—1228no—
390C22×Q8C4×D6111yescharacteristic
391C22×D4—611no—
392C22×D4—1221no—
393C23×C4—611no—
394C23×C4—611no—
395C23×C4—611no—
396C23×C4—1221no—
397C23×C4—1221no—
398C23×C4—1221no—
399C2×M16—21no—
400C2×M16—1221no—
401C22×C8—1222no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8—612no—
405C4×Q8—612no—
406C4×Q8—1221no—
407C4×Q8—1221no—
408C4×Q8C4×D6112yes—
409C4×Q8C22×D6112yes—
410C4×D4—612no—
411C4×D4—612no—
412C4×D4—612no—
413C4×D4—612no—
414C4×D4—1222no—
415C4×D4—1222no—
416C4×D4—1222no—
417C4×D4—1222no—
418C4×D4—1221no—
419C4×D4—1221no—
420C4×D4—1222no—
421C4×D4—1222no—
422C4×D4—1222no—
423C4×D4—1222no—
424C4×D4—1221no—
425C4×D4—1221no—
426#117—612no—
427#117—612no—
428#117—1222no—
429#117—1222no—
430#117—1222no—
431#117—1222no—
432#117—1221no—
433#117—1221no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—611no—
436C2×C4⋊C4—1221no—
437C2×C4⋊C4C4×D6111yescharacteristic
438C2×C22⋊C4—1221no—
439C2×C22⋊C4—1221no—
440C2×C22⋊C4—1221no—
441C2×C42—21no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—611no—
452C2×C42—611no—
453C2×C42—1222no—
454C2×C42—1222no—
455C2×C42—1222no—
456C2×C42—1222no—
457C2×C42—1221no—
458C2×C42—1221no—
459C2×C42C22×D6111yescharacteristic
460C4⋊C8—612no—
461C4⋊C8—1222no—
462C4⋊C8—1222no—
463C4⋊C8—1222no—
464C4⋊C8C22×D6112yes—
465C22⋊C8—21no—
466C22⋊C8—1222no—
467C22⋊C8—1222no—
468C22⋊C8—1222no—
469C22⋊C8—1221no—
470#97—21no—
471#97—21no—
472#97—1222no—
473#97—1221no—
474#97—1221no—
475C4×C8—612no—
476C4×C8C22×D6112yes—
477C24—611no—
478C24—1221no—
479#41—618no—
480#41—1224no—
481#41—1224no—
482#41—1228no—
483#41—1228no—
484#41—1224no—
485C2×Q8—24no—
486C2×Q8—21no—
487C2×Q8C2×C4×D6112yes—
488C2×D4—612no—
489C2×D4—1224no—
490C2×D4—1222no—
491C2×D4—1222no—
492C2×D4—1228no—
493C2×D4—1221no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—611no—
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—611no—
511C22×C4—1222no—
512C22×C4—1222no—
513C22×C4—1224no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1228no—
517C22×C4—1221no—
518C22×C4—1222no—
519C22×C4—1222no—
520C22×C4—2442no—
521C22×C4—2442no—
522C22×C4—2444no—
523C22×C4—2444no—
524C22×C4C2×C4×D6111yescharacteristic
525C22×C4D4×D6111yescharacteristic
526C22×C4D4×D6111yescharacteristic
527M16—42no—
528M16—2442no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—1222no—
532C2×C8—1222no—
533C2×C8—2444no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—21no—
537C4⋊C4—612no—
538C4⋊C4—1222no—
539C4⋊C4—1222no—
540C4⋊C4—1221no—
541C4⋊C4C2×C4×D6112yes—
542C22⋊C4—1222no—
543C22⋊C4—1222no—
544C22⋊C4—1222no—
545C22⋊C4—1222no—
546C22⋊C4—1222no—
547C22⋊C4—1222no—
548C42—22no—
549C42—22no—
550C42—611no—
551C42—611no—
552C42—611no—
553C42—611no—
554C42—611no—
555C42—611no—
556C42—611no—
557C42—611no—
558C42—611no—
559C42—611no—
560C42—611no—
561C42—611no—
562C42—1222no—
563C42—1222no—
564C42—1222no—
565C42—1222no—
566C42C2×C4×D6111yescharacteristic
567C42D4×D6111yescharacteristic
568C42D4×D6111yescharacteristic
569C42C23×D6111yescharacteristic
570C23—611no—
571C23—611no—
572C23—1222no—
573C23—1224no—
574C23—1222no—
575C23—1222no—
576C23—2441no—
577C23—2442no—
578C23—2442no—
579C23C22⋊C4×D6111yescharacteristic
580Q8—24no—
581Q8—22no—
582Q8M16×D6114yes—
583D4—614no—
584D4—1228no—
585D4—1228no—
586D4—1224no—
587D4—1222no—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—42no—
595C2×C4—611no—
596C2×C4—614no—
597C2×C4—611no—
598C2×C4—611no—
599C2×C4—611no—
600C2×C4—611no—
601C2×C4—611no—
602C2×C4—1222no—
603C2×C4—1228no—
604C2×C4—1222no—
605C2×C4—1228no—
606C2×C4—1222no—
607C2×C4—1222no—
608C2×C4—1222no—
609C2×C4—1222no—
610C2×C4—1222no—
611C2×C4—1222no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2444no—
619C2×C4—2444no—
620C2×C4—2444no—
621C2×C4—2441no—
622C2×C4—2442no—
623C2×C4—2444no—
624C2×C4C22⋊C4×D6111yescharacteristic
625C2×C4C22⋊C4×D6111yescharacteristic
626C2×C4C22⋊C4×D6111yescharacteristic
627C2×C4C22×C4×D6111yescharacteristic
628C2×C4C2×D4×D6111yescharacteristic
629C2×C4C2×D4×D6111yescharacteristic
630C8—42no—
631C8—42no—
632C8—2442no—
633C8—2442no—
634C22—21no—
635C22—21no—
636C22—612no—
637C22—1221no—
638C22—1221no—
639C22—1221no—
640C22—1221no—
641C22—1224no—
642C22—1221no—
643C22—2444no—
644C22—2448no—
645C22—2442no—
646C22—2442no—
647C22#1683977712yes—
648C22C2×C22⋊C4×D6111yescharacteristic
649C4—21no—
650C4—21no—
651C4—21no—
652C4—24no—
653C4—21no—
654C4—42no—
655C4—612no—
656C4—1221no—
657C4—1221no—
658C4—1221no—
659C4—1221no—
660C4—1221no—
661C4—2442no—
662C4C2×M16×D6112yes—
663C4#1684056112yes—
664C2—22no—
665C2—1222no—
666C2—2441no—
667C2—2444no—
668C2#407×D6111yescharacteristic
669C2#2145433711yescharacteristic
670C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1491C2
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758226C4
cosocleC42×C61C24
hypercenter#1491D61
hypocenterC61#17452
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
2. #21454450C2semidirect
3. #432×D61C2semidirect
4. #21444266C2semidirect
5. #21444263C2semidirect
6. #21444261C2semidirect
7. #21444252C2semidirect
8. #21444205C2semidirect
9. C61×#1491C2semidirect
29. #16839818C22semidirect
34. #16839813C22semidirect
35. #16839813C22semidirect
37. C4⋊C8×D61C22semidirect
42. Q8⋊#92418C22semidirect
43. #16839491C22semidirect
44. #16839489C22semidirect
48. C61×Q8⋊C8C22semidirect
160. #11758226M16semidirect
333. #1491D61semidirect
381. Q8⋊C8C2×D61semidirect
384. C61#17452semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582262
#214544502
#432×D612
#214442662
#214442632
#214442612
#214442522
#214442052
C61×#14912
#1745261