Finite Group Databasebeta

← #30615567

Subgroups — #30615567

Order 15616.

1938 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D61⋊M16C211yesmaximal, characteristic, complemented
2C2×#16840735C212yesmaximal, complemented
3C22×#14519834C211yesmaximal, characteristic, complemented
4#21461799C212yesmaximal, complemented
5#21461797C212yesmaximal, complemented
6#21461795C212yesmaximal, complemented
7#21461793C212yesmaximal, complemented
8#21461485C212yesmaximal, complemented
9C2×#16840270C211yesmaximal, characteristic
10C22×#11758213C2212yes—
11C2×D61⋊M16—28no—
12C2×D61⋊M16—24no—
13C22×#11758217C2212yes—
14C22×D61⋊C8C2212yes—
15C23×#92420C2212yes—
16#16840735—28no—
17C2×#14519834—24no—
18C2×#14519834C2212yes—
19C2×#14519834C2212yes—
20C2×#14519834C2214yescomplemented
21C2×C22⋊#92420C2214yescomplemented
22#16840628C2214yescomplemented
23#16840628C2214yescomplemented
24C22×#11758224C2211yescharacteristic
25C23×C4×D61C2211yescharacteristic
26#16840270—24no—
27#16840270—24no—
28C2×#14519760C411yescharacteristic
29C2×#14519755C411yescharacteristic
30C2×#14519755C411yescharacteristic
31C2×#14519750C411yescharacteristic
32C2×#14519750C411yescharacteristic
33C2×#14519747C411yescharacteristic
34C2×#14519745C411yescharacteristic
35C2×#14519739C2211yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×#14519737C2211yescharacteristic
38C2×#14519737C2211yescharacteristic
39C2×#14519733C2211yescharacteristic
40C2×#123×C61C411yescharacteristic
41C2×#11758213—24no—
42C2×#11758213—28no—
43D61⋊M16—232no—
44C2×#11758217—24no—
45C2×#11758217—24no—
46C2×#11758217D418yescomplemented
47C2×D61⋊C8—24no—
48C2×D61⋊C8—28no—
49C22×#92420—24no—
50C22×#92420—24no—
51C22×#92420—24no—
52C22×#92420C2314yes—
53C22×#92420C2314yes—
54#14519834—24no—
55#14519834—24no—
56#14519834—28no—
57C22⋊#92420—28no—
58C24×D61C2×C411yescharacteristic
59C2×#11758224—24no—
60C2×#11758224—22no—
61C2×#11758224—22no—
62C2×#11758224—24no—
63C22×Dic122C2×C411yescharacteristic
64C22×D244C2×C411yescharacteristic
65C22×D244C2×C411yescharacteristic
66C22×C22⋊D61C2×C411yescharacteristic
67C22×C22⋊D61C2×C411yescharacteristic
68C22×C22⋊D61C2×C411yescharacteristic
69C22×C22⋊D61C2×C411yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C22×C4×D61—24no—
73C22×C4×D61—24no—
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61D414yes—
77C22×C4×D61D414yes—
78C22×C4×D61C2311yescharacteristic
79C22×C4×D61C2311yescharacteristic
80C22×C4×D61C2311yescharacteristic
81#14519760—24no—
82#14519755—24no—
83#14519755—24no—
84#14519750—24no—
85#14519750—24no—
86#14519747—24no—
87#14519745—24no—
88#14519739—22no—
89#14519739—22no—
90#14519739—22no—
91#14519739—22no—
92#14519737—22no—
93#14519737—22no—
94#14519737—22no—
95#14519737—22no—
96#14519733—22no—
97#14519733—22no—
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×C22⋊Dic61C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C22×D4×C61C2×C411yescharacteristic
112C23×C4×C61C2×C411yescharacteristic
113#123×C61—24no—
114C2×C4⋊C4×C61C2×C411yescharacteristic
115C2×C4⋊C4×C61C2×C411yescharacteristic
116C2×C22⋊C4×C61C2×C411yescharacteristic
117C2×C22⋊C4×C61C2×C411yescharacteristic
118C2×C22⋊C4×C61C2×C411yescharacteristic
119C24×C61C22×C411yescharacteristic
120C24×C61C22×C411yescharacteristic
121C23×D61—24no—
122C23×D61—24no—
123C23×D61—42no—
124C23×D61C22⋊C414yes—
125C23×D61C22×C411yescharacteristic
126C23×D61C22×C411yescharacteristic
127C23×D61C22×C411yescharacteristic
128C2×D4×C61—22no—
129C2×D4×C61—24no—
130C22×C4×C61—24no—
131C22×C4×C61C22⋊C414yes—
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C2×C22⋊D61—22no—
138C2×C22⋊D61—24no—
139C2×C22⋊D61—22no—
140C2×C22⋊D61—22no—
141C2×C22⋊D61—24no—
142C2×C22⋊D61—22no—
143C2×C22⋊D61—24no—
144C2×C22⋊D61—42no—
145C22×Dic61—22no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—22no—
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C411yescharacteristic
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C2×D412yes—
154C22×Dic61C2×D412yes—
155C22×Dic61C2×D414yes—
156C22×Dic61#4114yes—
157C22×Dic61C2411yescharacteristic
158#11758224—44no—
159#11758224—48no—
160#11758224—44no—
161C2×D244—22no—
162C2×D244—22no—
163C2×D244—24no—
164C2×D244—42no—
165C2×C4×D61—24no—
166C2×C4×D61—24no—
167C2×C4×D61—28no—
168C2×C4×D61—216no—
169C2×C4×D61—28no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—22no—
178C2×C4×D61C22⋊C414yes—
179C2×C4×D61C22⋊C414yes—
180C2×C4×D61C2×D412yes—
181C2×C4×D61C2×D412yes—
182C2×C4×D61C2×D412yes—
183C2×C4×D61C2×D412yes—
184C2×Dic122—22no—
185C2×Dic122—24no—
186#11758217—216no—
187C2×#92420—24no—
188C2×#92420—24no—
189C2×#92420—24no—
190C2×#92420—24no—
191C2×#92420—24no—
192C2×#92420—48no—
193C2×#92420C2×D418yes—
194#11758213—216no—
195D61⋊C8—216no—
196C4⋊C4×C61—22no—
197C4⋊C4×C61—22no—
198C22⋊C4×C61—22no—
199C22⋊C4×C61—22no—
200C22⋊C4×C61—22no—
201C22⋊Dic61—22no—
202#11758198—22no—
203#11758198—22no—
204#11758198—22no—
205#11758198—22no—
206#11758198—22no—
207#11758198—22no—
208#11758196—22no—
209#11758196—22no—
210#11758196—22no—
211#11758196—22no—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C23×C61—22no—
217C23×C61—22no—
218C23×C61—21no—
219C23×C61—22no—
220C23×C61—22no—
221C23×C61—22no—
222C23×C61C2×C22⋊C412yes—
223C23×C61C4×D414yes—
224C23×C61C23×C411yescharacteristic
225C22×D61—22no—
226C22×D61—22no—
227C22×D61—22no—
228C22×D61—22no—
229C22×D61—22no—
230C22×D61—28no—
231C22×D61—28no—
232C22×D61—21no—
233C22×D61—22no—
234C22×D61—22no—
235C22×D61—22no—
236C22×D61—44no—
237C22×D61—416no—
238C22×D61C2×C22⋊C412yes—
239C22×D61C2×C22⋊C412yes—
240C22×D61#13114yes—
241D4×C61—44no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—28no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—22no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61C2×C22⋊C412yes—
252C2×C4×C61C2×C22⋊C412yes—
253C22⋊D61—44no—
254C22⋊D61—44no—
255C22⋊D61—44no—
256C22⋊D61—44no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—41no—
264C2×Dic61—42no—
265C2×Dic61—41no—
266C2×Dic61C2×C22⋊C412yes—
267C2×Dic61C4×D414yes—
268C2×Dic61#12014yes—
269C2×Dic61#12118yes—
270C2×Dic61#12314yes—
271C2×Dic61C22×D412yes—
272C2×Dic61C22×D411yescharacteristic
273C2×Dic61C22×D411yescharacteristic
274C2×Dic61C2×#4112yes—
275D244—44no—
276D244—44no—
277C4×D61—22no—
278C4×D61—22no—
279C4×D61—24no—
280C4×D61—24no—
281C4×D61—22no—
282C4×D61—22no—
283C4×D61—28no—
284C4×D61—28no—
285C4×D61—41no—
286C4×D61—42no—
287C4×D61—41no—
288Dic122—44no—
289#92420—28no—
290#92420—44no—
291#20897—611nomaximal, Sylow
292C22×C61—22no—
293C22×C61—22no—
294C22×C61—28no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61—44no—
298C22×C61—41no—
299C22×C61#38614yes—
300C22×C61C22×C22⋊C411yescharacteristic
301C22×C61C2×C4×D412yes—
302C22×C61C2×#13112yes—
303C22×C61#56812yes—
304C2×D61—22no—
305C2×D61—28no—
306C2×D61—22no—
307C2×D61—22no—
308C2×D61—22no—
309C2×D61—22no—
310C2×D61—416no—
311C2×D61—44no—
312C2×D61—41no—
313C2×D61—41no—
314C2×D61—44no—
315C2×D61—41no—
316C2×D61#40814yescomplemented
317C4×C61—22no—
318C4×C61—22no—
319C4×C61—41no—
320C4×C61—41no—
321C4×C61—41no—
322Dic61—41no—
323Dic61—41no—
324Dic61—41no—
325Dic61#38614yes—
326Dic61C2×#12011yescharacteristic
327Dic61C2×#12112yes—
328Dic61C2×#12311yescharacteristic
329C23×M16—611no—
330C2×#525—611no—
331C2×#408—612no—
332C22×C22⋊C8—611no—
333#1870—612no—
334#1870—612no—
335#1869—612no—
336#1869—612no—
337#1729—612no—
338C2×C61—24no—
339C2×C61—81no—
340C2×C61C2×#38611yescharacteristic
341C2×C61C2×#40811yescharacteristic
342C2×C61#287911yescharacteristic
343C2×C61#293314yes—
344D61—24no—
345D61—42no—
346D61—81no—
347C22×#41—611no—
348C24×C4—611no—
349C22×M16—612no—
350C22×M16—612no—
351C22×M16—1228no—
352C22×M16—1224no—
353C23×C8—612no—
354C23×C8—612no—
355#525—1224no—
356#525—1224no—
357C2×#123—611no—
358C2×#123#692311yescharacteristic
359C2×C22⋊Q8—611no—
360C2×C22⋊Q8—611no—
361C2×#121—611no—
362C2×#121—611no—
363C2×#120—611no—
364C2×#120—611no—
365C2×C4×D4—611no—
366C2×C4×D4—611no—
367C2×C4×D4—611no—
368C2×C4×D4—611no—
369C2×#117—611no—
370#408—1228no—
371C2×C22⋊C8—614no—
372C2×C22⋊C8—612no—
373C2×C22⋊C8—612no—
374C2×C22⋊C8—614no—
375C2×C22⋊C8—1224no—
376#336—614no—
377#336—614no—
378C61#2089711yescharacteristic, complemented, Sylow
379C25—611no—
380C2×#41—1222no—
381C2×#41—1222no—
382C2×#41—1224no—
383C2×#41—1224no—
384C22×Q8—611no—
385C22×D4—611no—
386C22×D4—611no—
387C22×D4—611no—
388C22×D4—611no—
389C22×D4—611no—
390C22×D4—611no—
391C22×D4C2×#692311yescharacteristic
392C23×C4—611no—
393C23×C4—614no—
394C23×C4—614no—
395C23×C4—611no—
396C23×C4—611no—
397C23×C4—611no—
398C23×C4—611no—
399C23×C4—611no—
400C23×C4—611no—
401C23×C4—1224no—
402C23×C4—1224no—
403C23×C4C2×#692311yescharacteristic
404C2×M16—618no—
405C2×M16—1228no—
406C2×M16—1224no—
407C2×M16—1224no—
408C2×M16—1224no—
409C2×M16—12232no—
410C22×C8—614no—
411C22×C8—614no—
412C22×C8—1228no—
413C22×C8—1224no—
414C22×C8—1224no—
415C22×C8—1224no—
416C22×C8—1224no—
417#123—24no—
418#123—1224no—
419C22⋊Q8—1224no—
420C22⋊Q8—1224no—
421#121—1224no—
422#121—1224no—
423#120—1224no—
424#120—1224no—
425C4×D4—1222no—
426C4×D4—1222no—
427C4×D4—1222no—
428C4×D4—1222no—
429C4×D4—1222no—
430C4×D4—1222no—
431C4×D4—1222no—
432C4×D4—1222no—
433#117—1222no—
434#117—1222no—
435C2×C4⋊C4—611no—
436C2×C4⋊C4—611no—
437C2×C4⋊C4—611no—
438C2×C4⋊C4—611no—
439C2×C4⋊C4C2×#692311yescharacteristic
440C2×C4⋊C4C2×#692311yescharacteristic
441C2×C22⋊C4—611no—
442C2×C22⋊C4—611no—
443C2×C22⋊C4—611no—
444C2×C22⋊C4—611no—
445C2×C22⋊C4—611no—
446C2×C22⋊C4—611no—
447C2×C22⋊C4—611no—
448C2×C22⋊C4C2×#692311yescharacteristic
449C2×C22⋊C4C2×#692311yescharacteristic
450C2×C22⋊C4C2×#692311yescharacteristic
451C2×C42—611no—
452C2×C42—611no—
453C22⋊C8—1228no—
454C22⋊C8—1228no—
455C22⋊C8—1224no—
456C22⋊C8—1224no—
457C24—611no—
458C24—611no—
459C24—614no—
460C24—611no—
461C24—1224no—
462C24—1224no—
463C24—2442no—
464C24C22×#692311yescharacteristic
465C24C22×#692311yescharacteristic
466#41—2444no—
467#41—2448no—
468#41—2444no—
469C2×Q8—1222no—
470C2×Q8—1224no—
471C2×D4—22no—
472C2×D4—24no—
473C2×D4—1222no—
474C2×D4—1222no—
475C2×D4—1224no—
476C2×D4—1222no—
477C2×D4—1224no—
478C2×D4—1222no—
479C2×D4—1222no—
480C2×D4—1224no—
481C2×D4—1222no—
482C2×D4—1224no—
483C2×D4—2442no—
484C2×D4—2442no—
485C22×C4—24no—
486C22×C4—612no—
487C22×C4—612no—
488C22×C4—614no—
489C22×C4—614no—
490C22×C4—611no—
491C22×C4—611no—
492C22×C4—612no—
493C22×C4—612no—
494C22×C4—612no—
495C22×C4—612no—
496C22×C4—614no—
497C22×C4—614no—
498C22×C4—611no—
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—1222no—
502C22×C4—1228no—
503C22×C4—1222no—
504C22×C4—12216no—
505C22×C4—1228no—
506C22×C4—1224no—
507C22×C4—1224no—
508C22×C4—1222no—
509C22×C4—1222no—
510C22×C4—1222no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1222no—
518C22×C4C22⋊#692314yes—
519C22×C4C22×#692311yescharacteristic
520C22×C4C22×#692311yescharacteristic
521C22×C4C22×#692311yescharacteristic
522C22×C4C22×#692311yescharacteristic
523C22×C4C22×#692311yescharacteristic
524M16—12216no—
525M16—12216no—
526C2×C8—618no—
527C2×C8—1224no—
528C2×C8—1224no—
529C2×C8—12216no—
530C2×C8—1224no—
531C2×C8—1224no—
532C2×C8—1224no—
533C2×C8—2448no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—1222no—
537C4⋊C4—1222no—
538C4⋊C4—1222no—
539C4⋊C4—1222no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—1222no—
544C22⋊C4—1222no—
545C22⋊C4—1222no—
546C22⋊C4—1222no—
547C22⋊C4—1222no—
548C22⋊C4—1222no—
549C22⋊C4—1222no—
550C42—1221no—
551C42—1221no—
552C42—1221no—
553C42—1221no—
554C23—22no—
555C23—22no—
556C23—21no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—612no—
561C23—614no—
562C23—612no—
563C23—1228no—
564C23—1222no—
565C23—1222no—
566C23—1228no—
567C23—1222no—
568C23—1222no—
569C23—1222no—
570C23—1221no—
571C23—1222no—
572C23—1222no—
573C23—1222no—
574C23—2444no—
575C23—24416no—
576C23C2×C22⋊#692312yes—
577C23D4×#692314yes—
578C23C23×#692311yescharacteristic
579Q8—2444no—
580D4—44no—
581D4—2444no—
582D4—2444no—
583D4—2444no—
584D4—2444no—
585D4—2444no—
586D4—2444no—
587C2×C4—28no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—614no—
597C2×C4—618no—
598C2×C4—614no—
599C2×C4—612no—
600C2×C4—611no—
601C2×C4—611no—
602C2×C4—614no—
603C2×C4—612no—
604C2×C4—612no—
605C2×C4—1222no—
606C2×C4—1222no—
607C2×C4—1224no—
608C2×C4—1224no—
609C2×C4—1222no—
610C2×C4—1222no—
611C2×C4—1228no—
612C2×C4—1228no—
613C2×C4—1221no—
614C2×C4—1221no—
615C2×C4—1221no—
616C2×C4—1222no—
617C2×C4—1222no—
618C2×C4—1222no—
619C2×C4—2441no—
620C2×C4—2442no—
621C2×C4—2441no—
622C2×C4—2441no—
623C2×C4—2442no—
624C2×C4—2441no—
625C2×C4C2×C22⋊#692312yes—
626C2×C4C2×C22⋊#692312yes—
627C8—1228no—
628C8—2444no—
629C22—28no—
630C22—22no—
631C22—22no—
632C22—44no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—614no—
637C22—1228no—
638C22—1222no—
639C22—1222no—
640C22—1222no—
641C22—1222no—
642C22—1222no—
643C22—24416no—
644C22—2444no—
645C22—2441no—
646C22—2441no—
647C22—2441no—
648C22—2444no—
649C22#1684071014yes—
650C22C22×C22⋊#692311yescharacteristic
651C22C2×D4×#692312yes—
652C22D61⋊#13112yes—
653C22#1684084112yes—
654C4—22no—
655C4—22no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—611no—
660C4—612no—
661C4—611no—
662C4—614no—
663C4—2441no—
664C4—2441no—
665C4—2441no—
666C2—24no—
667C2—81no—
668C2—1224no—
669C2—4881no—
670C2—2442no—
671C2C2×#1684071011yescharacteristic
672C2D61⋊#40811yescharacteristic
673C2#2146240411yescharacteristic
674C2#2146255314yes—
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC2×#123×C61C4
prime radicalC2×#16840270C2
cosocleC22×Dic61C24
hypercenterC2×#123#6923
hypocenterC61#20897
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C22×D61⋊M16C2semidirect
2. C2×#16840735C2semidirect
3. C22×#14519834C2semidirect
4. #21461799C2semidirect
5. #21461797C2semidirect
6. #21461795C2semidirect
7. #21461793C2semidirect
8. #21461485C2semidirect
20. C2×#14519834C22semidirect
21. C2×C22⋊#92420C22semidirect
22. #16840628C22semidirect
23. #16840628C22semidirect
46. C2×#11758217D4semidirect
316. C2×D61#408semidirect
378. C61#20897semidirect

Maximal subgroups

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

subgroupindex
C22×D61⋊M162
C2×#168407352
C22×#145198342
#214617992
#214617972
#214617952
#214617932
#214614852
C2×#168402702
#2089761