Finite Group Databasebeta

← #29601612

Subgroups — #29601612

Order 15616.

2390 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839663C211yesmaximal, characteristic
2C2×#16839640C212yesmaximal
3C2×C4×#11758198C212yesmaximal, complemented
4C2×#16839609C212yesmaximal, complemented
5#21444055C212yesmaximal, complemented
6#21444055C212yesmaximal, complemented
7#21444051C211yesmaximal, characteristic, complemented
8#95×Dic61C212yesmaximal, complemented
9C61×#1436C211yesmaximal, characteristic, complemented
10C23×D244C2211yescharacteristic
11C23×C4×D61C2212yes—
12C22×#11758198C2212yes—
13C22×#11758198C2212yes—
14C22×#11758198C2212yes—
15C22×#11758198C2212yes—
16C22×#11758198C2212yes—
17C22×C4×Dic61C2212yes—
18C22×C4×Dic61C2212yes—
19C22×C4×Dic61C2211yescharacteristic
20C22×C4×Dic61C2211yescharacteristic
21#16839663C418yescomplemented
22#16839640C4116yescomplemented
23C4×#11758198—28no—
24#16839609—28no—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2211yescharacteristic
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C22×C4⋊C4×C61C2211yescharacteristic
31C22×C42×C61C2211yescharacteristic
32C2×#95×C61C2212yes—
33C2×#95×C61C2211yescharacteristic
34C2×#95×C61C2212yes—
35C24×D61C2312yes—
36C22×D244—41no—
37C22×D244—41no—
38C22×D244—42no—
39C22×D244C2×C418yes—
40C22×D244C2×C414yes—
41C23×Dic61C2312yes—
42C23×Dic61C2312yes—
43C23×Dic61C2312yes—
44C22×C4×D61—24no—
45C22×C4×D61—24no—
46C22×C4×D61—24no—
47C22×C4×D61—24no—
48C22×C4×D61—42no—
49C22×C4×D61—42no—
50C22×C4×D61C2×C418yescomplemented
51C2×#11758198—24no—
52C2×#11758198—24no—
53C2×#11758198—24no—
54C2×#11758198—24no—
55C2×#11758198—24no—
56C2×#11758198—24no—
57C2×#11758198—24no—
58C2×#11758198—24no—
59C2×#11758198—42no—
60C2×#11758198—42no—
61C2×#11758198C2×C418yes—
62C2×#11758198C2×C418yes—
63C2×#11758198C2×C418yescomplemented
64C2×#11758198C2×C418yescomplemented
65C2×#11758198C2×C418yescomplemented
66C2×C4×Dic61—24no—
67C2×C4×Dic61—24no—
68C2×C4×Dic61—24no—
69C2×C4×Dic61—24no—
70C2×C4×Dic61—24no—
71C2×C4×Dic61—42no—
72C2×C4×Dic61—41no—
73C2×C4×Dic61—42no—
74C2×C4×Dic61—42no—
75C2×C4×Dic61C2×C414yescomplemented
76#14519684—24no—
77#14519684—24no—
78#14519684—41no—
79#14519684C2×C418yescomplemented
80#14519684D418yescomplemented
81C23×C4×C61C2312yes—
82C23×C4×C61C2311yescharacteristic
83C23×C4×C61C2311yescharacteristic
84C23×C4×C61C2311yescharacteristic
85C23×C4×C61C2312yes—
86C2×C4⋊C4×C61—41no—
87C2×C4⋊C4×C61—41no—
88C2×C4⋊C4×C61C2×C414yescomplemented
89C2×C42×C61—24no—
90C2×C42×C61—41no—
91#95×C61—24no—
92#95×C61—41no—
93#95×C61C2×C418yescomplemented
94C24×C61C2411yescharacteristic
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×D61—22no—
105C23×D61—22no—
106C23×D61—22no—
107C23×D61C22×C414yes—
108C23×D61C22×C414yes—
109C23×D61C22×C414yes—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—21no—
126C22×C4×C61—22no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—22no—
131C22×C4×C61C22×C414yes—
132C22×C4×C61C22×C412yes—
133C22×C4×C61C22×C412yes—
134C22×C4×C61C22×C414yes—
135C22×C4×C61C22×C412yes—
136C22×C4×C61C22×C414yes—
137C22×C4×C61C2×D414yes—
138C22×C4×C61#4114yes—
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×Dic61C22×C414yes—
154C22×Dic61C22×C414yes—
155C22×Dic61C22×C414yes—
156C22×Dic61C2×D414yes—
157C22×Dic61C2×D414yes—
158C22×Dic61#4114yes—
159C22×Dic61#4114yes—
160C2×D244—44no—
161C2×D244—44no—
162C2×D244—48no—
163C2×D244—48no—
164C2×D244C42116yescomplemented
165C2×C4×D61—216no—
166C2×C4×D61—216no—
167C2×C4×D61—48no—
168C2×C4×D61—48no—
169C2×C4×D61—48no—
170C2×C4×D61—48no—
171C2×C4×D61—48no—
172C4⋊C4×C61—44no—
173C42×C61—44no—
174#11758198—216no—
175#11758198—216no—
176#11758198—216no—
177#11758198—216no—
178#11758198—48no—
179C4×Dic61—44no—
180C4×Dic61—44no—
181C4×Dic61—48no—
182C4×Dic61—48no—
183C23×C61C23×C412yes—
184C23×C61C23×C411yescharacteristic
185C23×C61C22×D412yes—
186C23×C61C2×#4112yes—
187C23×C61C2×#4112yes—
188C23×C61C2×#4112yes—
189C23×C61H(5,𝔽2)11yescharacteristic
190C23×C61H(5,𝔽2)12yes—
191C23×C61H(5,𝔽2)11yescharacteristic
192C22×D61—24no—
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—42no—
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×D61C2×C4218yes—
227C2×C4×C61—24no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—24no—
231C2×C4×C61—24no—
232C2×C4×C61—24no—
233C2×C4×C61—24no—
234C2×C4×C61—24no—
235C2×C4×C61—24no—
236C2×C4×C61—24no—
237C2×C4×C61—24no—
238C2×C4×C61—24no—
239C2×C4×C61—24no—
240C2×C4×C61—24no—
241C2×C4×C61—24no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—42no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61C2×C4214yes—
255C2×C4×C61C4×D418yes—
256C2×Dic61—24no—
257C2×Dic61—24no—
258C2×Dic61—24no—
259C2×Dic61—24no—
260C2×Dic61—24no—
261C2×Dic61—24no—
262C2×Dic61—24no—
263C2×Dic61—24no—
264C2×Dic61—24no—
265C2×Dic61—24no—
266C2×Dic61—24no—
267C2×Dic61—24no—
268C2×Dic61—24no—
269C2×Dic61—24no—
270C2×Dic61—24no—
271C2×Dic61—42no—
272C2×Dic61—42no—
273C2×Dic61—42no—
274C2×Dic61—42no—
275C2×Dic61C4×D418yes—
276C2×Dic61C4×D418yes—
277D244—416no—
278C4×D61—432no—
279#13824—611nomaximal, Sylow
280C22×C61C22×C4211yescharacteristic
281C22×C61C2×C4×D412yes—
282C22×C61C2×C4×D412yes—
283C22×C61C2×C4×D412yes—
284C22×C61C4×#4112yes—
285C22×C61C4×#4112yes—
286C22×C61C4×#4112yes—
287C22×C61#51812yes—
288C22×C61#51812yes—
289C22×C61#51811yescharacteristic
290C22×C61#51811yescharacteristic
291C22×C61D4211yescharacteristic
292C22×C61#54612yes—
293C22×C61#54612yes—
294C22×C61#55012yes—
295C22×C61#55112yes—
296C22×C61#55312yes—
297C22×C61#55312yes—
298C22×C61#55511yescharacteristic
299C22×C61#55511yescharacteristic
300C22×C61#55911yescharacteristic
301C2×D61—28no—
302C2×D61—28no—
303C2×D61—28no—
304C2×D61—44no—
305C2×D61—44no—
306C2×D61—44no—
307C2×D61—44no—
308C2×D61—44no—
309C2×D61—44no—
310C2×D61—44no—
311C2×D61—44no—
312C2×D61—44no—
313C2×D61—44no—
314C2×D61—44no—
315C2×D61—44no—
316C4×C61—28no—
317C4×C61—24no—
318C4×C61—44no—
319C4×C61—42no—
320C4×C61—42no—
321Dic61—28no—
322Dic61—28no—
323Dic61—44no—
324C2×#390—611no—
325C2×#386—612no—
326C2×C4×C22⋊C4—612no—
327C2×C4×C22⋊C4—612no—
328#1437—612no—
329#1437—612no—
330#1436—611no—
331#1436D6111yescharacteristic, complemented
332C4×#95—612no—
333C2×C61C42×D412yes—
334C2×C61#227311yescharacteristic
335C2×C61#235812yes—
336C2×C61#236312yes—
337C2×C61#236312yes—
338C2×C61#236412yes—
339C2×C61#236611yescharacteristic
340C2×C61#237211yescharacteristic
341C2×C61#237412yes—
342D61—48no—
343C23×D4—611no—
344C24×C4—612no—
345C22×C4⋊C4C2×D6111yescharacteristic
346C22×C22⋊C4—612no—
347C22×C22⋊C4—612no—
348C22×C22⋊C4—612no—
349C22×C22⋊C4—612no—
350C22×C22⋊C4—612no—
351C22×C42—611no—
352C22×C42—612no—
353C22×C42—612no—
354C22×C42—611no—
355C22×C42C2×D6111yescharacteristic
356#390—618no—
357#386—6116no—
358C4×C22⋊C4—1228no—
359C4×C22⋊C4—1228no—
360C2×#95—612no—
361C2×#95—612no—
362C2×#95—612no—
363C2×#95—612no—
364C2×#95—611no—
365C2×#95C2×D6112yes—
366C2×#95C2×D6111yescharacteristic
367C2×#95C2×D6112yes—
368C61#1382411yescharacteristic, complemented, Sylow
369C25—612no—
370C22×D4—618no—
371C22×D4—614no—
372C22×D4—2441no—
373C22×D4—2441no—
374C22×D4—2442no—
375C23×C4—612no—
376C23×C4—612no—
377C23×C4—612no—
378C23×C4—618no—
379C23×C4—1224no—
380C23×C4—1224no—
381C23×C4—1224no—
382C23×C4—1224no—
383C23×C4—2442no—
384C23×C4—2442no—
385C23×C4C22×D6111yescharacteristic
386C23×C4C22×D6111yescharacteristic
387C23×C4C22×D6112yes—
388C23×C4C22×D6111yescharacteristic
389C23×C4C22×D6112yes—
390C2×C4⋊C4—41no—
391C2×C4⋊C4—41no—
392C2×C4⋊C4C4×D6114yescomplemented
393C2×C22⋊C4—618no—
394C2×C22⋊C4—618no—
395C2×C22⋊C4—618no—
396C2×C22⋊C4—618no—
397C2×C22⋊C4—618no—
398C2×C22⋊C4—1224no—
399C2×C22⋊C4—1224no—
400C2×C22⋊C4—1224no—
401C2×C22⋊C4—1224no—
402C2×C22⋊C4—1224no—
403C2×C22⋊C4—1224no—
404C2×C22⋊C4—1224no—
405C2×C22⋊C4—1224no—
406C2×C22⋊C4—2442no—
407C2×C22⋊C4—2442no—
408C2×C42—24no—
409C2×C42—41no—
410C2×C42—614no—
411C2×C42—1224no—
412C2×C42—1224no—
413C2×C42—1224no—
414C2×C42—1224no—
415C2×C42—1224no—
416C2×C42—2442no—
417C2×C42—2442no—
418C2×C42—2441no—
419C2×C42—2442no—
420#95—24no—
421#95—41no—
422#95—618no—
423#95—618no—
424#95—1224no—
425#95—1224no—
426#95—2441no—
427#95C4×D6118yescomplemented
428C24—614no—
429C24—614no—
430C24—614no—
431C24—1222no—
432C24—1222no—
433C24—1222no—
434C24—1222no—
435C24—1222no—
436C24—1222no—
437C24—1222no—
438C24—1222no—
439C24—1222no—
440C24—1222no—
441C24—1222no—
442C24—1222no—
443C24C23×D6111yescharacteristic
444C2×D4—6116no—
445C2×D4—2448no—
446C2×D4—2448no—
447C2×D4—2444no—
448C2×D4—2444no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—614no—
471C22×C4—614no—
472C22×C4—614no—
473C22×C4—614no—
474C22×C4—614no—
475C22×C4—614no—
476C22×C4—614no—
477C22×C4—12216no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—1222no—
481C22×C4—1222no—
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—12216no—
493C22×C4—2448no—
494C22×C4—2448no—
495C22×C4—2448no—
496C22×C4—2448no—
497C22×C4—2448no—
498C22×C4C2×C4×D6114yes—
499C22×C4C2×C4×D6112yes—
500C22×C4C2×C4×D6112yes—
501C22×C4C2×C4×D6114yes—
502C22×C4C2×C4×D6112yes—
503C22×C4C2×C4×D6114yes—
504C22×C4D4×D6114yes—
505C22×C4#1175822614yes—
506C4⋊C4—44no—
507C22⋊C4—12216no—
508C22⋊C4—12216no—
509C22⋊C4—12216no—
510C22⋊C4—12216no—
511C22⋊C4—2448no—
512C42—44no—
513C42—2444no—
514C42—2448no—
515C42—2444no—
516C42—2448no—
517C23—618no—
518C23—1224no—
519C23—1224no—
520C23—1224no—
521C23—1224no—
522C23—1224no—
523C23—1224no—
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—2442no—
537C23—2442no—
538C23—2442no—
539C23—2442no—
540C23—2442no—
541C23—2442no—
542C23—2442no—
543C23—2442no—
544C23—2442no—
545C23—2442no—
546C23—2442no—
547C23—2442no—
548C23—2442no—
549C23—2442no—
550C23—2442no—
551C23—2442no—
552C23C22×C4×D6111yescharacteristic
553C23C22×C4×D6112yes—
554C23C2×D4×D6112yes—
555C23#41×D6112yes—
556C23#41×D6112yes—
557C23C2×#1175822612yes—
558C23#1451982211yescharacteristic
559C23#1451982211yescharacteristic
560C23#1451982312yes—
561D4—24416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—618no—
590C2×C4—618no—
591C2×C4—1224no—
592C2×C4—1224no—
593C2×C4—1224no—
594C2×C4—1224no—
595C2×C4—1224no—
596C2×C4—1224no—
597C2×C4—1224no—
598C2×C4—1224no—
599C2×C4—1224no—
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×C4C42×D6114yes—
612C2×C4#1451973918yes—
613C22—1228no—
614C22—1228no—
615C22—1228no—
616C22—2444no—
617C22—2444no—
618C22—2444no—
619C22—2444no—
620C22—2444no—
621C22—2444no—
622C22—2444no—
623C22—2444no—
624C22—2444no—
625C22—2444no—
626C22—2444no—
627C22—2444no—
628C22C2×C42×D6111yescharacteristic
629C22C4×D4×D6112yes—
630C22C4×D4×D6112yes—
631C22C2×#1451973912yes—
632C22#1684023012yes—
633C22C4×#1175822612yes—
634C22C4×#1175822612yes—
635C22#1684023412yes—
636C22#1684023412yes—
637C22#1684023511yescharacteristic
638C22#1684023611yescharacteristic
639C22#1684039411yescharacteristic
640C22#1684040312yes—
641C22#1684040412yes—
642C22#1684043012yes—
643C22#1684043912yes—
644C22#1684046312yes—
645C22#1684046512yes—
646C22#1684047411yescharacteristic
647C22#1684047811yescharacteristic
648C22#1684049611yescharacteristic
649C4—28no—
650C4—24no—
651C4—44no—
652C4—42no—
653C4—42no—
654C4—1228no—
655C4—1228no—
656C4—2444no—
657C2—2448no—
658C2C4×#1451973912yes—
659C2#2144817111yescharacteristic
660C2#2144879512yes—
661C2#2144885212yes—
662C2#2144885612yes—
663C2#2144886512yes—
664C2#2144888211yescharacteristic
665C2#2144893011yescharacteristic
666C2#2144895112yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×#1436C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1436D61
hypocenterC61#13824
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11758198C2semidirect
4. C2×#16839609C2semidirect
5. #21444055C2semidirect
6. #21444055C2semidirect
7. #21444051C2semidirect
8. #95×Dic61C2semidirect
9. C61×#1436C2semidirect
21. #16839663C4semidirect
22. #16839640C4semidirect
50. C22×C4×D61C2×C4semidirect
63. C2×#11758198C2×C4semidirect
64. C2×#11758198C2×C4semidirect
65. C2×#11758198C2×C4semidirect
75. C2×C4×Dic61C2×C4semidirect
79. #14519684C2×C4semidirect
80. #14519684D4semidirect
88. C2×C4⋊C4×C61C2×C4semidirect
93. #95×C61C2×C4semidirect
164. C2×D244C42semidirect
331. #1436D61semidirect
368. C61#13824semidirect
392. C2×C4⋊C4C4×D61semidirect
427. #95C4×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
C2×C4×#117581982
C2×#168396092
#214440552
#214440512
#95×Dic612
C61×#14362
#1382461