Finite Group Databasebeta

← #29608963

Subgroups — #29608963

Order 15616.

1918 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839663C211yesmaximal, characteristic
2C2×#16839640C212yesmaximal
3#21444072C211yesmaximal, characteristic, complemented
4#21444065C212yesmaximal, complemented
5#21444061C212yesmaximal, complemented
6#21444045C212yesmaximal, complemented
7#21444040C212yesmaximal, complemented
8#21444040C212yesmaximal, complemented
9C61×#1441C211yesmaximal, characteristic, complemented
10C23×D244C2211yescharacteristic
11C23×C4×D61C2212yes—
12C22×C4⋊Dic61C2211yescharacteristic
13C22×#11758198C2212yes—
14C22×#11758198C2212yes—
15C22×#11758198C2212yes—
16C22×#11758198C2212yes—
17C22×#11758198C2212yes—
18C22×C4×Dic61C2211yescharacteristic
19#16839663C418yescomplemented
20#16839640—28no—
21C2×#14519684C2212yes—
22C2×#14519684C2212yes—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2211yescharacteristic
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C22×C4⋊C4×C61C2211yescharacteristic
29C22×C4⋊C4×C61C2211yescharacteristic
30C2×#95×C61C2212yes—
31C2×#95×C61C2211yescharacteristic
32C2×#95×C61C2212yes—
33C24×D61C2312yes—
34C22×D244—41no—
35C22×D244—41no—
36C22×D244—41no—
37C22×D244—41no—
38C22×D244C2×C414yes—
39C22×D244D414yes—
40C22×D244Q814yes—
41C23×Dic61C2312yes—
42C23×Dic61C2312yes—
43C23×Dic61C2312yes—
44C22×C4×D61—24no—
45C22×C4×D61—24no—
46C22×C4×D61—24no—
47C22×C4×D61—42no—
48C22×C4×D61—42no—
49C22×C4×D61—42no—
50C22×C4×D61—42no—
51C2×C4⋊Dic61—42no—
52C2×C4⋊Dic61—41no—
53C2×#11758198—24no—
54C2×#11758198—24no—
55C2×#11758198—24no—
56C2×#11758198—24no—
57C2×#11758198—24no—
58C2×#11758198—42no—
59C2×#11758198—42no—
60C2×#11758198—42no—
61C2×#11758198—42no—
62C2×#11758198—42no—
63C2×#11758198—42no—
64C2×#11758198—42no—
65C2×#11758198—42no—
66C2×#11758198C2×C418yescomplemented
67C2×#11758198C2×C418yescomplemented
68C2×C4×Dic61—41no—
69C2×C4×Dic61—41no—
70C2×C4×Dic61C2×C414yescomplemented
71#14519684—24no—
72#14519684—24no—
73#14519684—24no—
74#14519684—41no—
75#14519684—42no—
76#14519684—42no—
77#14519684—42no—
78C23×C4×C61C2312yes—
79C23×C4×C61C2311yescharacteristic
80C23×C4×C61C2311yescharacteristic
81C23×C4×C61C2312yes—
82C23×C4×C61C2311yescharacteristic
83C2×C4⋊C4×C61—41no—
84C2×C4⋊C4×C61—41no—
85C2×C4⋊C4×C61—41no—
86C2×C4⋊C4×C61—42no—
87C2×C4⋊C4×C61C2×C414yescomplemented
88#95×C61—24no—
89#95×C61—41no—
90#95×C61—42no—
91C24×C61C2411yescharacteristic
92C23×D61—22no—
93C23×D61—22no—
94C23×D61—22no—
95C23×D61—22no—
96C23×D61—22no—
97C23×D61—22no—
98C23×D61—22no—
99C23×D61—22no—
100C23×D61—22no—
101C23×D61—22no—
102C23×D61—22no—
103C23×D61—22no—
104C23×D61C22×C414yes—
105C23×D61C2×D414yes—
106C23×D61C2×Q814yes—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—21no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—21no—
118C22×C4×C61—22no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—22no—
122C22×C4×C61—21no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61C22×C412yes—
133C22×C4×C61C22×C412yes—
134C22×C4×C61C22×C412yes—
135C22×C4×C61C2×D412yes—
136C22×C4×C61C2×Q812yes—
137C22×C4×C61#4114yes—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61—22no—
141C22×Dic61—22no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61C22×C414yes—
158C22×Dic61#4114yes—
159C2×D244—44no—
160C2×D244—44no—
161C2×D244—44no—
162C2×D244—44no—
163C2×D244—44no—
164C2×D244—44no—
165C2×D244C4⋊C4116yescomplemented
166C2×C4×D61—48no—
167C2×C4×D61—48no—
168C2×C4×D61—48no—
169C2×C4×D61—48no—
170C2×C4×D61—48no—
171C2×C4×D61—48no—
172C2×C4×D61—48no—
173C4⋊C4×C61—44no—
174C4⋊C4×C61—44no—
175#11758198—48no—
176#11758198—48no—
177#11758198—48no—
178#11758198—48no—
179#11758198—48no—
180C4⋊Dic61—44no—
181C4×Dic61—44no—
182C23×C61C23×C411yescharacteristic
183C23×C61C22×D411yescharacteristic
184C23×C61C22×Q811yescharacteristic
185C23×C61C2×#4112yes—
186C23×C61C2×#4112yes—
187C23×C61H(5,𝔽2)11yescharacteristic
188C23×C61H(5,𝔽2)11yescharacteristic
189C23×C61H(5,𝔽2)11yescharacteristic
190C23×C61H(5,𝔽2)11yescharacteristic
191C23×C61H(5,𝔽2)12yes—
192C23×C61H(5,𝔽2)12yes—
193C22×D61—24no—
194C22×D61—24no—
195C22×D61—24no—
196C22×D61—24no—
197C22×D61—24no—
198C22×D61—24no—
199C22×D61—24no—
200C22×D61—24no—
201C22×D61—24no—
202C22×D61—24no—
203C22×D61—24no—
204C22×D61—24no—
205C22×D61—24no—
206C22×D61—24no—
207C22×D61—24no—
208C22×D61—24no—
209C22×D61—24no—
210C22×D61—24no—
211C22×D61—42no—
212C22×D61—42no—
213C22×D61—42no—
214C22×D61—42no—
215C22×D61—42no—
216C22×D61—42no—
217C22×D61—42no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—42no—
222C22×D61—42no—
223C22×D61—42no—
224C22×D61—42no—
225C22×D61—42no—
226C22×D61—42no—
227C22×D61C2×C4⋊C418yes—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—24no—
235C2×C4×C61—24no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—24no—
239C2×C4×C61—24no—
240C2×C4×C61—24no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—42no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61—42no—
254C2×C4×C61—42no—
255C2×C4×C61—42no—
256C2×C4×C61—42no—
257C2×C4×C61—42no—
258C2×C4×C61C2×C4⋊C414yes—
259C2×Dic61—24no—
260C2×Dic61—24no—
261C2×Dic61—24no—
262C2×Dic61—24no—
263C2×Dic61—24no—
264C2×Dic61—24no—
265C2×Dic61—42no—
266C2×Dic61—42no—
267C2×Dic61—42no—
268C2×Dic61—42no—
269C2×Dic61—42no—
270C2×Dic61—42no—
271C2×Dic61—42no—
272C2×Dic61—42no—
273C2×Dic61—42no—
274C2×Dic61—42no—
275C2×Dic61—42no—
276C2×Dic61—42no—
277C2×Dic61—42no—
278C2×Dic61—42no—
279C2×Dic61—42no—
280D244—416no—
281C4×D61—432no—
282#14486—611nomaximal, Sylow
283C22×C61C22×C4⋊C411yescharacteristic
284C22×C61C4×#4112yes—
285C22×C61#51812yes—
286C22×C61#51811yescharacteristic
287C22×C61#51811yescharacteristic
288C22×C61#53411yescharacteristic
289C22×C61#53411yescharacteristic
290C22×C61#53812yes—
291C22×C61#53812yes—
292C22×C61#54012yes—
293C22×C61#54012yes—
294C22×C61#54311yescharacteristic
295C22×C61#54311yescharacteristic
296C22×C61#54612yes—
297C22×C61#54612yes—
298C22×C61#55112yes—
299C22×C61#55412yes—
300C22×C61#55412yes—
301C22×C61#55511yescharacteristic
302C22×C61#55511yescharacteristic
303C22×C61#56012yes—
304C22×C61#56011yescharacteristic
305C22×C61#56011yescharacteristic
306C2×D61—28no—
307C2×D61—28no—
308C2×D61—28no—
309C2×D61—44no—
310C2×D61—44no—
311C2×D61—44no—
312C2×D61—44no—
313C2×D61—44no—
314C2×D61—44no—
315C2×D61—44no—
316C2×D61—44no—
317C2×D61—44no—
318C2×D61—44no—
319C2×D61—44no—
320C2×D61—44no—
321C4×C61—24no—
322C4×C61—42no—
323C4×C61—42no—
324C4×C61—44no—
325C4×C61—82no—
326Dic61—44no—
327Dic61—44no—
328Dic61—82no—
329C2×#390—611no—
330C2×#386—612no—
331#1441—611no—
332#1441D6111yescharacteristic, complemented
333#1439—612no—
334#1439—612no—
335#1434—612no—
336C22⋊#95—612no—
337C22⋊#95—612no—
338C2×C61#231511yescharacteristic
339C2×C61#233312yes—
340C2×C61#234912yes—
341C2×C61#237211yescharacteristic
342C2×C61#238011yescharacteristic
343C2×C61#269712yes—
344C2×C61#269911yescharacteristic
345C2×C61#269911yescharacteristic
346C2×C61#274812yes—
347C2×C61#278411yescharacteristic
348C2×C61#278411yescharacteristic
349D61—48no—
350C23×D4—611no—
351C24×C4—612no—
352C22×C4⋊C4—611no—
353C22×C4⋊C4C2×D6111yescharacteristic
354C22×C4⋊C4C2×D6111yescharacteristic
355C22×C22⋊C4—612no—
356C22×C22⋊C4—612no—
357C22×C22⋊C4—612no—
358C22×C22⋊C4—612no—
359C22×C22⋊C4—612no—
360C22×C42—611no—
361#390—618no—
362#386—1228no—
363C2×#95—612no—
364C2×#95—612no—
365C2×#95—612no—
366C2×#95—612no—
367C2×#95—611no—
368C2×#95—612no—
369C2×#95—612no—
370C2×#95C2×D6112yes—
371C2×#95C2×D6111yescharacteristic
372C2×#95C2×D6112yes—
373C61#1448611yescharacteristic, complemented, Sylow
374C25—612no—
375C22×D4—614no—
376C22×D4—614no—
377C22×D4—614no—
378C22×D4—2441no—
379C22×D4—2441no—
380C22×D4—2441no—
381C22×D4—2441no—
382C23×C4—612no—
383C23×C4—612no—
384C23×C4—612no—
385C23×C4—1224no—
386C23×C4—1224no—
387C23×C4—1224no—
388C23×C4—2442no—
389C23×C4—2442no—
390C23×C4—2442no—
391C23×C4—2442no—
392C23×C4C22×D6112yes—
393C23×C4C22×D6111yescharacteristic
394C23×C4C22×D6111yescharacteristic
395C23×C4C22×D6112yes—
396C23×C4C22×D6111yescharacteristic
397C2×C4⋊C4—41no—
398C2×C4⋊C4—41no—
399C2×C4⋊C4—42no—
400C2×C4⋊C4—41no—
401C2×C4⋊C4—2441no—
402C2×C4⋊C4—2442no—
403C2×C4⋊C4C4×D6114yescomplemented
404C2×C22⋊C4—618no—
405C2×C22⋊C4—618no—
406C2×C22⋊C4—1224no—
407C2×C22⋊C4—1224no—
408C2×C22⋊C4—1224no—
409C2×C22⋊C4—1224no—
410C2×C22⋊C4—1224no—
411C2×C22⋊C4—2442no—
412C2×C22⋊C4—2442no—
413C2×C22⋊C4—2442no—
414C2×C22⋊C4—2442no—
415C2×C22⋊C4—2442no—
416C2×C22⋊C4—2442no—
417C2×C22⋊C4—2442no—
418C2×C22⋊C4—2442no—
419C2×C42—614no—
420C2×C42—2441no—
421C2×C42—2441no—
422#95—24no—
423#95—42no—
424#95—41no—
425#95—1224no—
426#95—1224no—
427#95—1224no—
428#95—2441no—
429#95—2442no—
430#95—2442no—
431#95—2442no—
432C24—614no—
433C24—614no—
434C24—614no—
435C24—1222no—
436C24—1222no—
437C24—1222no—
438C24—1222no—
439C24—1222no—
440C24—1222no—
441C24—1222no—
442C24—1222no—
443C24—1222no—
444C24—1222no—
445C24—1222no—
446C24—1222no—
447C24C23×D6111yescharacteristic
448C2×D4—6116no—
449C2×D4—2444no—
450C2×D4—2444no—
451C2×D4—2444no—
452C2×D4—2444no—
453C2×D4—2444no—
454C2×D4—2444no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—614no—
481C22×C4—614no—
482C22×C4—1222no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—2448no—
502C22×C4—2448no—
503C22×C4—2448no—
504C22×C4—2448no—
505C22×C4—2448no—
506C22×C4—2448no—
507C22×C4—2448no—
508C22×C4C2×C4×D6112yes—
509C22×C4C2×C4×D6112yes—
510C22×C4C2×C4×D6112yes—
511C22×C4D4×D6112yes—
512C22×C4Q8×D6112yes—
513C22×C4#1175822614yes—
514C4⋊C4—44no—
515C4⋊C4—44no—
516C4⋊C4—2444no—
517C22⋊C4—2448no—
518C22⋊C4—2448no—
519C22⋊C4—2448no—
520C22⋊C4—2448no—
521C22⋊C4—2448no—
522C42—2444no—
523C23—618no—
524C23—1224no—
525C23—1224no—
526C23—1224no—
527C23—1224no—
528C23—1224no—
529C23—1224no—
530C23—1224no—
531C23—1224no—
532C23—1224no—
533C23—1224no—
534C23—1224no—
535C23—1224no—
536C23—1224no—
537C23—1224no—
538C23—1224no—
539C23—1224no—
540C23—1224no—
541C23—1224no—
542C23—2442no—
543C23—2442no—
544C23—2442no—
545C23—2442no—
546C23—2442no—
547C23—2442no—
548C23—2442no—
549C23—2442no—
550C23—2442no—
551C23—2442no—
552C23—2442no—
553C23—2442no—
554C23—2442no—
555C23—2442no—
556C23—2442no—
557C23—2442no—
558C23C22×C4×D6111yescharacteristic
559C23C2×D4×D6111yescharacteristic
560C23C2×Q8×D6111yescharacteristic
561C23#41×D6112yes—
562C23C2×#1175822612yes—
563C23#1451982212yes—
564C23#1451982211yescharacteristic
565C23#1451982211yescharacteristic
566C23#1451982312yes—
567C23#1451982311yescharacteristic
568C23#1451982311yescharacteristic
569D4—24416no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—1224no—
601C2×C4—1224no—
602C2×C4—1224no—
603C2×C4—1224no—
604C2×C4—1224no—
605C2×C4—1224no—
606C2×C4—24432no—
607C2×C4—2442no—
608C2×C4—2442no—
609C2×C4—2442no—
610C2×C4—2442no—
611C2×C4—2442no—
612C2×C4—2442no—
613C2×C4—2442no—
614C2×C4—2442no—
615C2×C4—2442no—
616C2×C4—2442no—
617C2×C4—2442no—
618C2×C4—2442no—
619C2×C4—2442no—
620C2×C4—2442no—
621C2×C4—2442no—
622C2×C4C4⋊C4×D6114yes—
623C22—1228no—
624C22—1228no—
625C22—1228no—
626C22—2444no—
627C22—2444no—
628C22—2444no—
629C22—2444no—
630C22—2444no—
631C22—2444no—
632C22—2444no—
633C22—2444no—
634C22—2444no—
635C22—2444no—
636C22—2444no—
637C22—2444no—
638C22C2×C4⋊C4×D6111yescharacteristic
639C22C4×#1175822612yes—
640C22#1684023412yes—
641C22#1684023511yescharacteristic
642C22#1684023611yescharacteristic
643C22#1684032011yescharacteristic
644C22#1684032011yescharacteristic
645C22#1684035112yes—
646C22#1684035212yes—
647C22#1684036412yes—
648C22#1684036812yes—
649C22#1684038711yescharacteristic
650C22#1684038711yescharacteristic
651C22#1684040312yes—
652C22#1684040912yes—
653C22#1684043912yes—
654C22#1684046812yes—
655C22#1684047312yes—
656C22#1684047411yescharacteristic
657C22#1684047811yescharacteristic
658C22#1684050012yes—
659C22#1684050111yescharacteristic
660C22#1684050211yescharacteristic
661C4—24no—
662C4—42no—
663C4—42no—
664C4—44no—
665C4—82no—
666C4—4882no—
667C4—2444no—
668C4—2444no—
669C2—2448no—
670C2#2144843211yescharacteristic
671C2#2144858312yes—
672C2#2144872812yes—
673C2#2144893011yescharacteristic
674C2#2144899411yescharacteristic
675C2#2145237712yes—
676C2#2145240111yescharacteristic
677C2#2145240511yescharacteristic
678C2#2145303112yes—
679C2#2145351911yescharacteristic
680C2#2145352211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1441C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1441D61
hypocenterC61#14486
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. #21444072C2semidirect
4. #21444065C2semidirect
5. #21444061C2semidirect
6. #21444045C2semidirect
7. #21444040C2semidirect
8. #21444040C2semidirect
9. C61×#1441C2semidirect
19. #16839663C4semidirect
66. C2×#11758198C2×C4semidirect
67. C2×#11758198C2×C4semidirect
70. C2×C4×Dic61C2×C4semidirect
87. C2×C4⋊C4×C61C2×C4semidirect
165. C2×D244C4⋊C4semidirect
332. #1441D61semidirect
373. C61#14486semidirect
403. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396632
C2×#168396402
#214440722
#214440652
#214440612
#214440452
#214440402
C61×#14412
#1448661