Finite Group Databasebeta

← #29646774

Subgroups — #29646774

Order 15616.

1240 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840309C211yesmaximal, characteristic
2#21454450C211yesmaximal, characteristic, complemented
3#432×D61C211yesmaximal, characteristic, complemented
4#21444286C214yesmaximal, complemented
5#21444263C211yesmaximal, characteristic, complemented
6#21444262C211yesmaximal, characteristic, complemented
7#21444261C211yesmaximal, characteristic, complemented
8#21444216C214yesmaximal, complemented
9C61×#1490C211yesmaximal, characteristic, complemented
10C22×#11758222—21no—
11#16840309—21no—
12#16840309—21no—
13#16840309—21no—
14#16840309—21no—
15#16840309C412yes—
16#16840309C412yes—
17#16840309C2212yes—
18#16840309C2212yes—
19C2×#14519776C411yescharacteristic
20C2×#14519773C411yescharacteristic
21C2×#14519763—21no—
22C2×#14519752C411yescharacteristic
23C2×#14519750—21no—
24C2×#14519748C411yescharacteristic
25C2×C4×D244C2211yescharacteristic
26C2×C4×C22⋊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—
42#16839491C2214yescomplemented
43D4⋊#92418C2214yescomplemented
44#16839489C2214yescomplemented
45C2×C4×D4×C61C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C4×M16×C61C2211yescharacteristic
48C61×D4⋊C8C2214yescomplemented
49C2×#11758222—22no—
50C2×#11758222—22no—
51C2×#11758222—22no—
52C2×#11758222—22no—
53C2×#11758222—48no—
54C22×Dic122—21no—
55C22×D244—21no—
56C22×D244C2×C411yescharacteristic
57C22×C22⋊D61—21no—
58C22×C22⋊D61—21no—
59C22×C22⋊D61—21no—
60C22×C4×D61—21no—
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C2×#11758194—21no—
65C2×C8×D61—22no—
66#14519776—21no—
67#14519776—21no—
68#14519776C2×C412yes—
69#14519776C2×C412yes—
70#14519773—21no—
71#14519773—21no—
72#14519773C2×C412yes—
73#14519773C2×C412yes—
74#14519763—22no—
75#14519763—22no—
76#14519763—22no—
77#14519763—22no—
78#14519752—21no—
79#14519752—21no—
80#14519752C2×C412yes—
81#14519752C2×C412yes—
82#14519750—22no—
83#14519750—22no—
84#14519750—22no—
85#14519750—22no—
86#14519748—21no—
87#14519748—21no—
88#14519748C2×C412yes—
89#14519748C2×C412yes—
90C4×D244—21no—
91C4×D244—21no—
92C4×D244C2×C412yes—
93C4×D244C2312yes—
94C4×C22⋊D61—22no—
95C4×C22⋊D61—22no—
96C4×C22⋊D61—22no—
97C4×C22⋊D61—22no—
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×#11758196—21no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
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⋊#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×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×D61—21no—
143C23×D61C22⋊C411yescharacteristic
144C2×D4×C61—21no—
145C2×D4×C61—42no—
146C2×D4×C61C22×C412yes—
147C22×C4×C61—21no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—44no—
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—44no—
161C2×C22⋊D61—44no—
162C2×C22⋊D61—44no—
163C22×Dic61—21no—
164C22×Dic61C22⋊C411yescharacteristic
165C22×Dic61C22⋊C411yescharacteristic
166C22×Dic61C22⋊C411yescharacteristic
167#11758222—48no—
168#11758222—48no—
169#11758222—48no—
170#11758222—48no—
171C2×D244—22no—
172C2×D244—22no—
173C2×D244—21no—
174C2×D244—42no—
175C2×D244—44no—
176C2×D244C22×C412yes—
177C2×C4×D61—24no—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—42no—
181C2×C4×D61—42no—
182C2×C4×D61—44no—
183C2×C4×D61C22⋊C411yescharacteristic
184C2×C4×D61C22⋊C411yescharacteristic
185C2×C4×D61C22⋊C411yescharacteristic
186C2×C4×D61C22⋊C411yescharacteristic
187C2×C4×D61C22⋊C411yescharacteristic
188C2×C4×D61C22⋊C411yescharacteristic
189C2×C4×D61C22×C411yescharacteristic
190C2×C4×D61C22×C411yescharacteristic
191C2×C4×D61C2×D411yescharacteristic
192C2×C4×D61C2×D411yescharacteristic
193C2×C4×D61C2×D411yescharacteristic
194C2×C4×D61C2×D411yescharacteristic
195C2×Dic122—22no—
196C2×Dic122—22no—
197C2×Dic122—44no—
198M16×C61—42no—
199C2×C8×C61—22no—
200C2×C8×C61—22no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61C22×C412yes—
203C22⋊C4×C61—22no—
204C22⋊C4×C61—22no—
205C42×C61C22×C411yescharacteristic
206C42×C61C2×D411yescharacteristic
207C42×C61C2×D411yescharacteristic
208C42×C61C2411yescharacteristic
209C22⋊Dic61—22no—
210C22⋊Dic61—22no—
211#11758198—22no—
212#11758198—22no—
213#11758198—22no—
214#11758198—22no—
215C4⋊Dic61—21no—
216C4⋊Dic61C22×C412yes—
217#11758196—22no—
218#11758196—22no—
219C4×Dic61C22⋊C411yescharacteristic
220C4×Dic61C22⋊C411yescharacteristic
221C4×Dic61C22⋊C411yescharacteristic
222C4×Dic61C22⋊C411yescharacteristic
223C4×Dic61C22⋊C411yescharacteristic
224C4×Dic61C22⋊C411yescharacteristic
225C4×Dic61C22×C411yescharacteristic
226C4×Dic61C22×C411yescharacteristic
227C4×Dic61C2×D411yescharacteristic
228C4×Dic61C2×D411yescharacteristic
229C4×Dic61C2×D411yescharacteristic
230C4×Dic61C2×D411yescharacteristic
231#11758194—42no—
232C2×#92418—22no—
233C2×#92418—22no—
234C8×D61—44no—
235C23×C61—22no—
236C23×C61—42no—
237C23×C61—42no—
238C23×C61—42no—
239C23×C61C2×C22⋊C411yescharacteristic
240C22×D61—22no—
241C22×D61—22no—
242C22×D61—22no—
243C22×D61—41no—
244C22×D61—42no—
245C22×D61—42no—
246C22×D61—42no—
247C22×D61C2×C22⋊C411yescharacteristic
248C22×D61C2×C22⋊C411yescharacteristic
249D4×C61—24no—
250D4×C61—42no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61—44no—
256C2×C4×C61—42no—
257C2×C4×C61—44no—
258C2×C4×C61C2×C22⋊C411yescharacteristic
259C2×C4×C61C2×C22⋊C411yescharacteristic
260C2×C4×C61C2×C22⋊C411yescharacteristic
261C2×C4×C61C23×C411yescharacteristic
262C2×C4×C61C22×D411yescharacteristic
263C2×C4×C61C22×D411yescharacteristic
264C22⋊D61—44no—
265C22⋊D61—44no—
266C22⋊D61—44no—
267C22⋊D61—44no—
268C22⋊D61—44no—
269C22⋊D61—44no—
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—41no—
274C2×Dic61—42no—
275C2×Dic61C2×C22⋊C411yescharacteristic
276C2×Dic61C2×C22⋊C411yescharacteristic
277C2×Dic61C2×C22⋊C411yescharacteristic
278C2×Dic61C2×C22⋊C411yescharacteristic
279C2×Dic61C2×C22⋊C411yescharacteristic
280C2×Dic61C2×C22⋊C411yescharacteristic
281D244—24no—
282D244—42no—
283D244—44no—
284D244—44no—
285C4×D61—22no—
286C4×D61—22no—
287C4×D61—22no—
288C4×D61—22no—
289C4×D61—22no—
290C4×D61—41no—
291C4×D61—41no—
292C4×D61—41no—
293C4×D61—41no—
294C4×D61—41no—
295C4×D61—41no—
296C4×D61—44no—
297C4×D61—44no—
298C4×D61AGL(1,ℤ/8)14yes—
299Dic122—44no—
300Dic122—44no—
301C8×C61—42no—
302C8×C61—42no—
303#92418—42no—
304#92418—42no—
305#17495—611nomaximal, Sylow
306C22×C61—21no—
307C22×C61—21no—
308C22×C61—42no—
309C22×C61—42no—
310C22×C61—42no—
311C22×C61—84no—
312C22×C61#42112yes—
313C22×C61C22×C22⋊C411yescharacteristic
314C2×D61—21no—
315C2×D61—21no—
316C2×D61—21no—
317C2×D61—21no—
318C2×D61—21no—
319C2×D61—44no—
320C2×D61—42no—
321C2×D61—42no—
322C2×D61—42no—
323C2×D61—84no—
324C2×D61#41812yes—
325C4×C61—21no—
326C4×C61—21no—
327C4×C61—21no—
328C4×C61—21no—
329C4×C61—42no—
330C4×C61#56812yes—
331C4×C61C2×AGL(1,ℤ/8)12yes—
332Dic61—21no—
333Dic61—21no—
334Dic61—21no—
335Dic61—21no—
336Dic61—21no—
337Dic61—42no—
338Dic61#41812yes—
339C2×#532—611no—
340#2920—611no—
341C2×#432—611no—
342#1496—614no—
343#1490—611no—
344#1490—611no—
345#1490—611no—
346#1490D6111yescharacteristic, complemented
347#1480—614no—
348C2×C61—22no—
349C2×C61—82no—
350C2×C61#287911yescharacteristic
351C2×C61C2×#41811yescharacteristic
352C2×C61C2×#42111yescharacteristic
353D61—22no—
354D61—41no—
355D61—82no—
356C22×#41—1221no—
357#532—612no—
358#532—612no—
359#532—612no—
360#532—612no—
361#532—1221no—
362#532—1221no—
363#532—1221no—
364#532—1221no—
365C2×C4⋊Q8—611no—
366C2×#127—611no—
367C2×#124—1221no—
368C2×#121—611no—
369C2×#121—611no—
370C2×#121—1221no—
371C2×C4×D4—611no—
372C2×C4×D4—1221no—
373C2×C4×D4C2×D6111yescharacteristic
374C22×C42—611no—
375#432—611no—
376#432—612no—
377#432—1221no—
378#432—1221no—
379#432—1221no—
380#432—1221no—
381#432C2×D6111yescharacteristic
382#431—612no—
383#431—612no—
384#423—1221no—
385C2×C4⋊C8—612no—
386#407—1221no—
387C2×C22⋊C8—1221no—
388C4×M16—611no—
389C4×M16C2×D6111yescharacteristic
390C2×#97—1221no—
391D4⋊C8—614no—
392D4⋊C8—614no—
393D4⋊C8—614no—
394D4⋊C8C2×D6114yescomplemented
395C61#1749511yescharacteristic, complemented, Sylow
396C2×#41—1222no—
397C2×#41—1222no—
398C2×#41—1222no—
399C2×#41—1222no—
400C2×#41—2448no—
401C22×Q8—1221no—
402C22×D4—611no—
403C22×D4—1221no—
404C22×D4—1221no—
405C22×D4—1221no—
406C22×D4—1221no—
407C22×D4C4×D6111yescharacteristic
408C23×C4—21no—
409C23×C4—611no—
410C23×C4—611no—
411C23×C4—611no—
412C23×C4—1221no—
413C2×M16—21no—
414C2×M16—1221no—
415C22×C8—1222no—
416C4⋊Q8—612no—
417C4⋊Q8—612no—
418C4⋊Q8—1221no—
419C4⋊Q8—1221no—
420#127—612no—
421#127—612no—
422#127—1221no—
423#127—1221no—
424#124—1222no—
425#124—1222no—
426#124—1222no—
427#124—1222no—
428#121—612no—
429#121—612no—
430#121—612no—
431#121—612no—
432#121—1222no—
433#121—1222no—
434#121—1222no—
435#121—1222no—
436#121—1221no—
437#121—1221no—
438#121—1221no—
439#121—1221no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4—612no—
443C4×D4—612no—
444C4×D4—1222no—
445C4×D4—1222no—
446C4×D4—1222no—
447C4×D4—1222no—
448C4×D4—1221no—
449C4×D4—1221no—
450C4×D4C4×D6112yes—
451C4×D4C22×D6112yes—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—1221no—
454C2×C4⋊C4C4×D6111yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—1221no—
457C2×C22⋊C4—1221no—
458C2×C22⋊C4—1221no—
459C2×C42—611no—
460C2×C42—611no—
461C2×C42—611no—
462C2×C42—611no—
463C2×C42—611no—
464C2×C42—611no—
465C2×C42—611no—
466C2×C42—611no—
467C2×C42—611no—
468C2×C42—611no—
469C2×C42—611no—
470C2×C42C22×D6111yescharacteristic
471C4⋊C8—612no—
472C4⋊C8—1222no—
473C4⋊C8—1222no—
474C4⋊C8—1222no—
475C4⋊C8C22×D6112yes—
476C22⋊C8—21no—
477C22⋊C8—1222no—
478C22⋊C8—1222no—
479C22⋊C8—1222no—
480C22⋊C8—1221no—
481#97—21no—
482#97—21no—
483#97—1222no—
484#97—1221no—
485#97—1221no—
486C4×C8—612no—
487C4×C8C22×D6112yes—
488C24—21no—
489C24—611no—
490C24—1221no—
491#41—2448no—
492#41—2448no—
493#41—2448no—
494#41—2448no—
495C2×Q8—1222no—
496C2×Q8—1222no—
497C2×Q8—2444no—
498C2×D4—21no—
499C2×D4—42no—
500C2×D4—612no—
501C2×D4—1222no—
502C2×D4—1222no—
503C2×D4—1222no—
504C2×D4—1222no—
505C2×D4—1222no—
506C2×D4—1222no—
507C2×D4—1222no—
508C2×D4—1222no—
509C2×D4—1221no—
510C2×D4—2442no—
511C2×D4—2444no—
512C2×D4—2444no—
513C2×D4—2444no—
514C2×D4—2444no—
515C2×D4C2×C4×D6112yes—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—44no—
520C22×C4—611no—
521C22×C4—611no—
522C22×C4—611no—
523C22×C4—611no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—1224no—
536C22×C4—1221no—
537C22×C4—1222no—
538C22×C4—1222no—
539C22×C4—2442no—
540C22×C4—2442no—
541C22×C4—2444no—
542C22×C4C2×C4×D6111yescharacteristic
543C22×C4D4×D6111yescharacteristic
544C22×C4D4×D6111yescharacteristic
545M16—42no—
546M16—2442no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—1222no—
550C2×C8—1222no—
551C2×C8—2444no—
552C4⋊C4—21no—
553C4⋊C4—612no—
554C4⋊C4—1222no—
555C4⋊C4—1222no—
556C4⋊C4—1221no—
557C4⋊C4C2×C4×D6112yes—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—1222no—
561C22⋊C4—1222no—
562C22⋊C4—1222no—
563C22⋊C4—1222no—
564C22⋊C4—1222no—
565C22⋊C4—1222no—
566C42—611no—
567C42—611no—
568C42—611no—
569C42—611no—
570C42—611no—
571C42—611no—
572C42—611no—
573C42—611no—
574C42—611no—
575C42—611no—
576C42—611no—
577C42—611no—
578C42C2×C4×D6111yescharacteristic
579C42D4×D6111yescharacteristic
580C42D4×D6111yescharacteristic
581C42C23×D6111yescharacteristic
582C23—22no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—611no—
587C23—611no—
588C23—1222no—
589C23—1222no—
590C23—1222no—
591C23—2441no—
592C23—2442no—
593C23—2442no—
594C23—2442no—
595C23C22⋊C4×D6111yescharacteristic
596Q8—2444no—
597Q8—2444no—
598D4—24no—
599D4—42no—
600D4—1224no—
601D4—2442no—
602D4—2444no—
603D4—2444no—
604D4—2444no—
605D4—2444no—
606D4—2444no—
607D4—2444no—
608D4—2444no—
609D4—2444no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—44no—
615C2×C4—42no—
616C2×C4—44no—
617C2×C4—611no—
618C2×C4—614no—
619C2×C4—611no—
620C2×C4—611no—
621C2×C4—611no—
622C2×C4—611no—
623C2×C4—611no—
624C2×C4—1222no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—1222no—
628C2×C4—1222no—
629C2×C4—1222no—
630C2×C4—1222no—
631C2×C4—1222no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2441no—
636C2×C4—2441no—
637C2×C4—2441no—
638C2×C4—2444no—
639C2×C4—2441no—
640C2×C4—2442no—
641C2×C4—2444no—
642C2×C4C22⋊C4×D6111yescharacteristic
643C2×C4C22⋊C4×D6111yescharacteristic
644C2×C4C22⋊C4×D6111yescharacteristic
645C2×C4C22×C4×D6111yescharacteristic
646C2×C4C2×D4×D6111yescharacteristic
647C2×C4C2×D4×D6111yescharacteristic
648C8—42no—
649C8—42no—
650C8—2442no—
651C8—2442no—
652C22—21no—
653C22—21no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—84no—
658C22—612no—
659C22—1221no—
660C22—1221no—
661C22—1221no—
662C22—1221no—
663C22—1221no—
664C22—4884no—
665C22—2444no—
666C22—2442no—
667C22—2442no—
668C22—2442no—
669C22#1683977712yes—
670C22C2×C22⋊C4×D6111yescharacteristic
671C4—21no—
672C4—21no—
673C4—21no—
674C4—21no—
675C4—42no—
676C4—612no—
677C4—1221no—
678C4—1221no—
679C4—1221no—
680C4—1221no—
681C4—1221no—
682C4—2442no—
683C4#1684052812yes—
684C4AGL(1,ℤ/8)×D6112yes—
685C2—22no—
686C2—82no—
687C2—1222no—
688C2—4882no—
689C2—2441no—
690C2#2145426211yescharacteristic
691C2#418×D6111yescharacteristic
692C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1490C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840309C2
cosocleC42×C61C24
hypercenter#1490D61
hypocenterC61#17495
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. #21454450C2semidirect
3. #432×D61C2semidirect
4. #21444286C2semidirect
5. #21444263C2semidirect
6. #21444262C2semidirect
7. #21444261C2semidirect
8. #21444216C2semidirect
9. C61×#1490C2semidirect
29. #16839818C22semidirect
34. #16839813C22semidirect
35. #16839813C22semidirect
37. C4⋊C8×D61C22semidirect
42. #16839491C22semidirect
43. D4⋊#92418C22semidirect
44. #16839489C22semidirect
48. C61×D4⋊C8C22semidirect
346. #1490D61semidirect
394. D4⋊C8C2×D61semidirect
395. C61#17495semidirect

Maximal subgroups

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

subgroupindex
C2×#168403092
#214544502
#432×D612
#214442862
#214442632
#214442622
#214442612
#214442162
C61×#14902
#1749561