Finite Group Databasebeta

← #29679944

Subgroups — #29679944

Order 15616.

1866 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2#21448197C212yesmaximal, complemented
3#21445893C211yesmaximal, characteristic, complemented
4#21445806C214yesmaximal, complemented
5#21445733C212yesmaximal
6#21445606C214yesmaximal, complemented
7C61×#1819C211yesmaximal, characteristic, complemented
8C23×C22⋊D61C2211yescharacteristic
9C24×Dic61C2211yescharacteristic
10C23×C4×D61C411yescharacteristic, complemented
11C2×#14519737—22no—
12C2×#14519737—22no—
13C2×#14519737—22no—
14C2×#14519737—22no—
15C2×#14519737C412yescomplemented
16C2×#14519737C412yescomplemented
17C2×#14519737C2212yes—
18C2×#14519737C2212yes—
19C2×#14519733—22no—
20C22×#11758196C411yescharacteristic, complemented
21C22×#11758198C411yescharacteristic, complemented
22C22×C4×Dic61C411yescharacteristic, complemented
23C2×#14519691C2218yes—
24#16839623—22no—
25#16839620—22no—
26#16839620C2214yescomplemented
27#16839618C2212yes—
28C22⋊C4×Dic61—22no—
29C22⋊C4×Dic61C2214yescomplemented
30#16839529C2214yescomplemented
31C22×C22⋊C4×C61C2211yescharacteristic
32C61×#379C2212yes—
33C61×#342C2214yescomplemented
34C24×D61C2×C411yescharacteristic
35C22×C22⋊D61—22no—
36C22×C22⋊D61—22no—
37C22×C22⋊D61—28no—
38C22×C22⋊D61C2×C412yes—
39C22×C22⋊D61C2312yes—
40C23×Dic61—44no—
41C23×Dic61C2×C411yescharacteristic
42C23×Dic61C2×C411yescharacteristic
43C23×Dic61C2×C411yescharacteristic
44C23×Dic61C2×C411yescharacteristic
45C23×Dic61C2×C411yescharacteristic
46C23×Dic61D412yes—
47C23×Dic61D412yes—
48C23×Dic61D412yes—
49C23×Dic61D412yes—
50C23×Dic61C2311yescharacteristic
51C23×Dic61C2311yescharacteristic
52C22×C4×D61—21no—
53C22×C4×D61—21no—
54C22×C4×D61—21no—
55C22×C4×D61—21no—
56C22×C4×D61—44no—
57C22×C4×D61C2×C412yes—
58C22×C4×D61C2×C412yes—
59#14519737—24no—
60#14519737—24no—
61#14519737—24no—
62#14519737—24no—
63#14519737—24no—
64#14519737—24no—
65#14519737—24no—
66#14519737—24no—
67#14519733—48no—
68C2×#11758196—22no—
69C2×#11758196—22no—
70C2×#11758196—24no—
71C2×#11758196C2×C412yes—
72C2×#11758196C2×C412yes—
73C2×C22⋊Dic61—22no—
74C2×C22⋊Dic61—22no—
75C2×C22⋊Dic61C2314yes—
76C2×#11758198—22no—
77C2×#11758198—22no—
78C2×#11758198C2×C412yes—
79C2×#11758198C2×C412yes—
80C2×C4×Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—24no—
85C2×C4×Dic61C2×C412yes—
86C2×C4×Dic61C2×C412yes—
87#14519691—216no—
88#14519684—24no—
89#14519684—24no—
90C25×C61C2311yescharacteristic
91C23×C4×C61C2×C411yescharacteristic
92C23×C4×C61C2×C411yescharacteristic
93C2×C22⋊C4×C61—22no—
94C2×C22⋊C4×C61—22no—
95C2×C22⋊C4×C61—22no—
96C2×C22⋊C4×C61—22no—
97C2×C22⋊C4×C61C2×C412yes—
98C2×C22⋊C4×C61C2314yes—
99C2×C22⋊C4×C61C2312yes—
100C24×C61—24no—
101C24×C61—42no—
102C24×C61—42no—
103C24×C61C22×C411yescharacteristic
104C24×C61C22×C411yescharacteristic
105C24×C61C2×D412yes—
106C24×C61C2×D412yes—
107C24×C61C2411yescharacteristic
108C23×D61—21no—
109C23×D61—21no—
110C23×D61—24no—
111C23×D61—42no—
112C23×D61—42no—
113C23×D61C22×C412yes—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61—24no—
119C22×C4×C61—42no—
120C22×C4×C61—42no—
121C22×C4×C61C22×C412yes—
122C22×C4×C61C22×C412yes—
123C2×C22⋊D61—216no—
124C2×C22⋊D61—216no—
125C2×C22⋊D61—24no—
126C2×C22⋊D61—24no—
127C2×C22⋊D61—24no—
128C2×C22⋊D61—24no—
129C2×C22⋊D61—24no—
130C2×C22⋊D61#4118yes—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—24no—
134C22×Dic61—28no—
135C22×Dic61—24no—
136C22×Dic61—24no—
137C22×Dic61—42no—
138C22×Dic61—42no—
139C22×Dic61—44no—
140C22×Dic61—44no—
141C22×Dic61—42no—
142C22×Dic61—42no—
143C22×Dic61—42no—
144C22×Dic61—44no—
145C22×Dic61C22⋊C411yescharacteristic
146C22×Dic61C22⋊C411yescharacteristic
147C22×Dic61C22⋊C411yescharacteristic
148C22×Dic61C22⋊C412yes—
149C22×Dic61C22⋊C412yes—
150C22×Dic61C22⋊C412yes—
151C22×Dic61C22⋊C412yes—
152C22×Dic61C22⋊C412yes—
153C22×Dic61C22⋊C412yes—
154C22×Dic61C22⋊C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157C22×Dic61C22×C412yes—
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C2×D412yes—
161C22×Dic61C2×D412yes—
162C22×Dic61C2×D412yes—
163C22×Dic61C2×D412yes—
164C2×C4×D61—22no—
165C2×C4×D61—22no—
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61—44no—
169C2×C4×D61—44no—
170C2×C4×D61—44no—
171C2×C4×D61—44no—
172C2×C4×D61—44no—
173C2×C4×D61—44no—
174C22⋊C4×C61—24no—
175C22⋊C4×C61—24no—
176C22⋊C4×C61—28no—
177C22⋊C4×C61—44no—
178C22⋊C4×C61—44no—
179C22⋊Dic61—28no—
180C22⋊Dic61—44no—
181C22⋊Dic61—44no—
182#11758198—24no—
183#11758198—24no—
184#11758196—24no—
185#11758196—24no—
186#11758196—48no—
187C4×Dic61—22no—
188C4×Dic61—22no—
189C4×Dic61—22no—
190C4×Dic61—22no—
191C4×Dic61—48no—
192C23×C61—22no—
193C23×C61—22no—
194C23×C61—22no—
195C23×C61—22no—
196C23×C61—24no—
197C23×C61—24no—
198C23×C61—24no—
199C23×C61—24no—
200C23×C61—41no—
201C23×C61—42no—
202C23×C61—41no—
203C23×C61—41no—
204C23×C61—42no—
205C23×C61—41no—
206C23×C61—416no—
207C23×C61C2×C22⋊C412yes—
208C23×C61C2×C22⋊C411yescharacteristic
209C23×C61C2×C22⋊C411yescharacteristic
210C23×C61C23×C411yescharacteristic
211C23×C61C22×D412yes—
212C23×C61C2×#4114yes—
213C22×D61—24no—
214C22×D61—24no—
215C22×D61—22no—
216C22×D61—22no—
217C22×D61—42no—
218C22×D61—416no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—42no—
222C22×D61—42no—
223C22×D61—42no—
224C22×D61#11714yescomplemented
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—44no—
234C2×C4×C61—44no—
235C2×C4×C61—44no—
236C22⋊D61—216no—
237C22⋊D61—216no—
238C2×Dic61—24no—
239C2×Dic61—24no—
240C2×Dic61—22no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—24no—
244C2×Dic61—24no—
245C2×Dic61—24no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—24no—
251C2×Dic61—24no—
252C2×Dic61—42no—
253C2×Dic61—42no—
254C2×Dic61—42no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—44no—
260C2×Dic61—44no—
261C2×Dic61—44no—
262C2×Dic61#9914yescomplemented
263C2×Dic61C2×C22⋊C411yescharacteristic
264C2×Dic61C2×C22⋊C411yescharacteristic
265C2×Dic61C2×C22⋊C412yes—
266C2×Dic61C2×C22⋊C412yes—
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61#11714yescomplemented
270C4×D61—44no—
271C4×D61—44no—
272C4×D61—44no—
273C4×D61—44no—
274#20722—611nomaximal, Sylow
275C22×C61—28no—
276C22×C61—22no—
277C22×C61—21no—
278C22×C61—21no—
279C22×C61—22no—
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—22no—
285C22×C61—22no—
286C22×C61—22no—
287C22×C61—44no—
288C22×C61—48no—
289C22×C61—48no—
290C22×C61—44no—
291C22×C61C2×#9912yes—
292C22×C61#41012yes—
293C22×C61C22×C22⋊C411yescharacteristic
294C22×C61C2×#11712yes—
295C22×C61#52514yes—
296C2×D61—24no—
297C2×D61—44no—
298C2×D61—48no—
299C2×D61—48no—
300C2×D61—42no—
301C2×D61—42no—
302C2×D61—44no—
303C4×C61—42no—
304C4×C61—42no—
305C4×C61—84no—
306Dic61—21no—
307Dic61—21no—
308Dic61—22no—
309Dic61—22no—
310Dic61—24no—
311Dic61—84no—
312Dic61C2×#9912yes—
313Dic61C2×#9912yes—
314C22×C4×D4—611no—
315#2280—612no—
316#1819—611no—
317#1819D6111yescharacteristic, complemented
318#1799—614no—
319#1781—612no—
320C4×#99—614no—
321C2×C61—24no—
322C2×C61—22no—
323C2×C61—22no—
324C2×C61—22no—
325C2×C61—42no—
326C2×C61#228011yescharacteristic
327C2×C61C22×#9911yescharacteristic
328C2×C61C2×#41011yescharacteristic
329D61—44no—
330C23×D4—611no—
331C24×C4—611no—
332C24×C4—611no—
333C2×C4×D4—612no—
334C2×C4×D4—612no—
335C2×C4×D4—612no—
336C2×C4×D4—612no—
337C2×C4×D4—1222no—
338C2×C4×D4—1222no—
339C2×C4×D4—1222no—
340C2×C4×D4—1222no—
341C2×#117—1222no—
342C22×C4⋊C4—611no—
343C22×C22⋊C4—611no—
344C22×C22⋊C4C2×D6111yescharacteristic
345C22×C42—611no—
346C2×#99—618no—
347#381—1222no—
348#380—614no—
349#380—1222no—
350#379—612no—
351#379C2×D6112yes—
352C4×C22⋊C4—614no—
353C4×C22⋊C4—1222no—
354#342—614no—
355#342C2×D6114yescomplemented
356C61#2072211yescharacteristic, complemented, Sylow
357C25—611no—
358C25C22×D6111yescharacteristic
359C22×D4—612no—
360C22×D4—612no—
361C22×D4—1228no—
362C22×D4—1222no—
363C22×D4—1222no—
364C23×C4—611no—
365C23×C4—612no—
366C23×C4—611no—
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—612no—
370C23×C4—612no—
371C23×C4—612no—
372C23×C4—611no—
373C23×C4—611no—
374C23×C4—611no—
375C23×C4—612no—
376C23×C4—612no—
377C23×C4—1221no—
378C23×C4—1221no—
379C23×C4—1221no—
380C23×C4—1221no—
381C23×C4—2444no—
382C23×C4—2444no—
383C23×C4C4×D6111yescharacteristic
384C23×C4C4×D6111yescharacteristic
385C4×D4—1224no—
386C4×D4—1224no—
387C4×D4—1224no—
388C4×D4—1224no—
389C4×D4—1224no—
390C4×D4—1224no—
391C4×D4—1224no—
392C4×D4—1224no—
393#117—2448no—
394C2×C4⋊C4—612no—
395C2×C4⋊C4—612no—
396C2×C4⋊C4—1222no—
397C2×C4⋊C4—1222no—
398C2×C4⋊C4—1224no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—612no—
404C2×C22⋊C4—612no—
405C2×C22⋊C4—614no—
406C2×C22⋊C4—1222no—
407C2×C22⋊C4—1222no—
408C2×C22⋊C4—1222no—
409C2×C22⋊C4—1222no—
410C2×C22⋊C4C4×D6112yes—
411C2×C22⋊C4C22×D6114yes—
412C2×C22⋊C4C22×D6112yes—
413C2×C42—612no—
414C2×C42—612no—
415C2×C42—1221no—
416C2×C42—1221no—
417C2×C42—1221no—
418C2×C42—1221no—
419C2×C42—1224no—
420#99—12216no—
421#95—1224no—
422#95—1224no—
423C24—24no—
424C24—42no—
425C24—42no—
426C24—612no—
427C24—1224no—
428C24—1221no—
429C24—1221no—
430C24—2442no—
431C24—2442no—
432C24C2×C4×D6111yescharacteristic
433C24C2×C4×D6111yescharacteristic
434C24D4×D6112yes—
435C24D4×D6112yes—
436C24C23×D6111yescharacteristic
437C2×D4—618no—
438C2×D4—1224no—
439C2×D4—1224no—
440C2×D4—12216no—
441C2×D4—12216no—
442C2×D4—1224no—
443C2×D4—1224no—
444C2×D4—1224no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—24no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—611no—
453C22×C4—612no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—612no—
457C22×C4—612no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—612no—
462C22×C4—612no—
463C22×C4—612no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—612no—
467C22×C4—612no—
468C22×C4—612no—
469C22×C4—612no—
470C22×C4—612no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—1228no—
476C22×C4—1224no—
477C22×C4—1224no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1224no—
481C22×C4—2444no—
482C22×C4—2444no—
483C22×C4—2444no—
484C22×C4—2444no—
485C22×C4—2444no—
486C22×C4—2444no—
487C22×C4—2442no—
488C22×C4—2444no—
489C22×C4—2442no—
490C22×C4—2444no—
491C22×C4—2442no—
492C22×C4—2442no—
493C22×C4—2442no—
494C22×C4—2444no—
495C22×C4C2×C4×D6112yes—
496C22×C4C2×C4×D6112yes—
497C4⋊C4—1224no—
498C4⋊C4—1224no—
499C4⋊C4—2448no—
500C22⋊C4—24no—
501C22⋊C4—24no—
502C22⋊C4—28no—
503C22⋊C4—44no—
504C22⋊C4—44no—
505C22⋊C4—1224no—
506C22⋊C4—1224no—
507C22⋊C4—1228no—
508C22⋊C4—2444no—
509C22⋊C4—2444no—
510C42—1222no—
511C42—1222no—
512C42—1222no—
513C42—1222no—
514C42—2448no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—41no—
524C23—42no—
525C23—41no—
526C23—41no—
527C23—42no—
528C23—41no—
529C23—416no—
530C23—614no—
531C23—1224no—
532C23—1224no—
533C23—1222no—
534C23—1222no—
535C23—2442no—
536C23—2442no—
537C23—2442no—
538C23—24416no—
539C23—2442no—
540C23—2442no—
541C23—2442no—
542C23C22⋊C4×D6112yes—
543C23C22⋊C4×D6111yescharacteristic
544C23C22⋊C4×D6111yescharacteristic
545C23C22×C4×D6111yescharacteristic
546C23C2×D4×D6112yes—
547C23#41×D6114yes—
548D4—12216no—
549D4—12216no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—611no—
562C2×C4—611no—
563C2×C4—614no—
564C2×C4—611no—
565C2×C4—611no—
566C2×C4—612no—
567C2×C4—612no—
568C2×C4—614no—
569C2×C4—1224no—
570C2×C4—1224no—
571C2×C4—1224no—
572C2×C4—1224no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1224no—
578C2×C4—1224no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1224no—
582C2×C4—1222no—
583C2×C4—2444no—
584C2×C4—2444no—
585C2×C4—2444no—
586C2×C4—2444no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2442no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2444no—
595C2×C4—2444no—
596C2×C4—2444no—
597C22—28no—
598C22—21no—
599C22—21no—
600C22—22no—
601C22—21no—
602C22—21no—
603C22—22no—
604C22—21no—
605C22—21no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—44no—
610C22—48no—
611C22—48no—
612C22—44no—
613C22—1224no—
614C22—2444no—
615C22—2444no—
616C22—2448no—
617C22—2448no—
618C22—2442no—
619C22—2442no—
620C22#99×D6112yes—
621C22#1683973412yes—
622C22C2×C22⋊C4×D6111yescharacteristic
623C22#117×D6112yes—
624C22#1684027014yes—
625C4—42no—
626C4—42no—
627C4—84no—
628C4—612no—
629C4—612no—
630C4—1224no—
631C4—1222no—
632C4—1222no—
633C4—1221no—
634C4—1221no—
635C4—4884no—
636C2—24no—
637C2—22no—
638C2—22no—
639C2—22no—
640C2—42no—
641C2—2444no—
642C2#2144819911yescharacteristic
643C2C2×#99×D6111yescharacteristic
644C2C2×#1683973411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1819C2
socleC22×C61C22×C22⋊C4
prime radicalC23×C22⋊D61C22
cosocleC24×C61C24
hypercenter#1819D61
hypocenterC61#20722
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
2. #21448197C2semidirect
3. #21445893C2semidirect
4. #21445806C2semidirect
6. #21445606C2semidirect
7. C61×#1819C2semidirect
10. C23×C4×D61C4semidirect
15. C2×#14519737C4semidirect
16. C2×#14519737C4semidirect
20. C22×#11758196C4semidirect
21. C22×#11758198C4semidirect
22. C22×C4×Dic61C4semidirect
26. #16839620C22semidirect
29. C22⋊C4×Dic61C22semidirect
30. #16839529C22semidirect
33. C61×#342C22semidirect
224. C22×D61#117semidirect
262. C2×Dic61#99semidirect
269. C2×Dic61#117semidirect
317. #1819D61semidirect
355. #342C2×D61semidirect
356. C61#20722semidirect

Maximal subgroups

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

subgroupindex
C22×#145197372
#214481972
#214458932
#214458062
#214457332
#214456062
C61×#18192
#2072261