Finite Group Databasebeta

← #29601832

Subgroups — #29601832

Order 15616.

1790 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839688C211yesmaximal, characteristic
2C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
3C2×#16839609C212yesmaximal
4C2×#16839609C211yesmaximal, characteristic
5#21444079C212yesmaximal, complemented
6#21444075C211yesmaximal, characteristic, complemented
7#21444067C212yesmaximal
8#21444065C211yesmaximal, characteristic
9#95×Dic61C212yesmaximal, complemented
10#95×Dic61C211yesmaximal, characteristic, complemented
11C61×#1445C211yesmaximal, characteristic, complemented
12C23×C4×D61C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×#11758198C2212yes—
15C22×#11758198C2211yescharacteristic
16C22×#11758198C2211yescharacteristic
17C22×#11758198C2212yes—
18C22×C4×Dic61C2211yescharacteristic
19C22×C4×Dic61C2212yes—
20C22×C4×Dic61C2212yes—
21C22×C4×Dic61C2211yescharacteristic
22#16839688C418yescomplemented
23C4⋊C4×Dic61—24no—
24#16839609—24no—
25#16839609—28no—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2212yes—
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2212yes—
34C22×C4⋊C4×C61C2211yescharacteristic
35C2×#95×C61C2211yescharacteristic
36C2×#95×C61C2212yes—
37C2×#95×C61C2211yescharacteristic
38C2×#95×C61C2212yes—
39C24×D61C2311yescharacteristic
40C23×Dic61C2311yescharacteristic
41C23×Dic61C2312yes—
42C23×Dic61C2311yescharacteristic
43C23×Dic61C2312yes—
44C23×Dic61C2311yescharacteristic
45C22×C4×D61—22no—
46C22×C4×D61—22no—
47C22×C4×D61—24no—
48C22×C4×D61—24no—
49C22×C4×D61D414yes—
50C2×C4⋊Dic61—22no—
51C2×C4⋊Dic61—24no—
52C2×#11758198—24no—
53C2×#11758198—24no—
54C2×#11758198—22no—
55C2×#11758198—24no—
56C2×#11758198—22no—
57C2×#11758198—22no—
58C2×#11758198—22no—
59C2×#11758198—24no—
60C2×#11758198—22no—
61C2×#11758198—24no—
62C2×#11758198C2×C418yes—
63C2×#11758198C2×C414yes—
64C2×C4×Dic61—24no—
65C2×C4×Dic61—24no—
66C2×C4×Dic61—24no—
67C2×C4×Dic61—22no—
68C2×C4×Dic61—24no—
69C2×C4×Dic61—24no—
70C2×C4×Dic61—24no—
71C2×C4×Dic61—24no—
72C2×C4×Dic61—24no—
73C2×C4×Dic61D414yes—
74#14519684—24no—
75#14519684—24no—
76#14519684—24no—
77#14519684—22no—
78#14519684—24no—
79#14519684—24no—
80#14519684C2×C418yescomplemented
81#14519684C2×C414yescomplemented
82C23×C4×C61C2312yes—
83C23×C4×C61C2311yescharacteristic
84C23×C4×C61C2311yescharacteristic
85C23×C4×C61C2312yes—
86C23×C4×C61C2311yescharacteristic
87C2×C4⋊C4×C61—22no—
88C2×C4⋊C4×C61—22no—
89C2×C4⋊C4×C61C2×C414yescomplemented
90#95×C61—22no—
91#95×C61—24no—
92#95×C61—24no—
93#95×C61—22no—
94C24×C61C2411yescharacteristic
95C23×D61—21no—
96C23×D61—21no—
97C23×D61—22no—
98C23×D61—22no—
99C23×D61—21no—
100C23×D61—22no—
101C23×D61—22no—
102C23×D61—21no—
103C23×D61C22×C412yes—
104C23×D61C2×D412yes—
105C23×D61#4112yes—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—21no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—21no—
112C22×C4×C61—22no—
113C22×C4×C61—21no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
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—22no—
126C22×C4×C61—21no—
127C22×C4×C61—22no—
128C22×C4×C61C22×C414yes—
129C22×C4×C61C22×C412yes—
130C22×C4×C61C2×D412yes—
131C22×C4×C61C2×D412yes—
132C22×C4×C61#4112yes—
133C22×C4×C61#4114yes—
134C22×C4×C61#4112yes—
135C22×Dic61—22no—
136C22×Dic61—21no—
137C22×Dic61—22no—
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—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61C22×C414yes—
156C22×Dic61C22×C412yes—
157C22×Dic61C2×D412yes—
158C22×Dic61C2×D412yes—
159C22×Dic61C2×D412yes—
160C22×Dic61#4114yes—
161C22×Dic61#4112yes—
162C22×Dic61#4114yes—
163C22×Dic61#4114yes—
164C2×C4×D61—28no—
165C2×C4×D61—216no—
166C2×C4×D61—44no—
167C2×C4×D61—44no—
168C2×C4×D61—48no—
169C4⋊C4×C61—28no—
170#11758198—28no—
171#11758198—216no—
172#11758198—216no—
173#11758198—28no—
174C4⋊Dic61—28no—
175C4×Dic61—28no—
176C4×Dic61—48no—
177C4×Dic61—48no—
178C4×Dic61—44no—
179C23×C61C23×C411yescharacteristic
180C23×C61C22×D411yescharacteristic
181C23×C61C22×D411yescharacteristic
182C23×C61C2×#4111yescharacteristic
183C23×C61C2×#4111yescharacteristic
184C23×C61C2×#4111yescharacteristic
185C23×C61C2×#4112yes—
186C23×C61C2×#4112yes—
187C23×C61C2×#4112yes—
188C23×C61C2×#4111yescharacteristic
189C23×C61C2×#4112yes—
190C22×D61—22no—
191C22×D61—22no—
192C22×D61—24no—
193C22×D61—24no—
194C22×D61—22no—
195C22×D61—24no—
196C22×D61—24no—
197C22×D61—22no—
198C22×D61—22no—
199C22×D61—24no—
200C22×D61—24no—
201C22×D61—22no—
202C22×D61—41no—
203C22×D61—41no—
204C22×D61—41no—
205C22×D61—42no—
206C22×D61—42no—
207C22×D61—42no—
208C22×D61—42no—
209C22×D61—42no—
210C22×D61—42no—
211C22×D61—41no—
212C22×D61C4×D414yes—
213C2×C4×C61—24no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—24no—
217C2×C4×C61—24no—
218C2×C4×C61—24no—
219C2×C4×C61—24no—
220C2×C4×C61—22no—
221C2×C4×C61—24no—
222C2×C4×C61—24no—
223C2×C4×C61—22no—
224C2×C4×C61—24no—
225C2×C4×C61—24no—
226C2×C4×C61—24no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—42no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61C4×D414yes—
242C2×Dic61—24no—
243C2×Dic61—22no—
244C2×Dic61—24no—
245C2×Dic61—24no—
246C2×Dic61—24no—
247C2×Dic61—22no—
248C2×Dic61—24no—
249C2×Dic61—22no—
250C2×Dic61—24no—
251C2×Dic61—24no—
252C2×Dic61—22no—
253C2×Dic61—42no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61—42no—
257C2×Dic61—41no—
258C2×Dic61—42no—
259C2×Dic61—42no—
260C2×Dic61—42no—
261C2×Dic61—42no—
262C2×Dic61—42no—
263C2×Dic61—42no—
264C2×Dic61—42no—
265C2×Dic61—41no—
266C2×Dic61#12114yes—
267C2×Dic61#12314yes—
268C2×Dic61#12318yes—
269C2×Dic61#12414yes—
270C2×Dic61#12618yes—
271C4×D61—416no—
272C4×#397—611nomaximal, Sylow
273C22×C61C2×C4×D411yescharacteristic
274C22×C61C2×C4×D411yescharacteristic
275C22×C61C4×#4111yescharacteristic
276C22×C61C4×#4112yes—
277C22×C61C4×#4112yes—
278C22×C61C2×#12111yescharacteristic
279C22×C61C2×#12311yescharacteristic
280C22×C61C2×#12312yes—
281C22×C61#52511yescharacteristic
282C22×C61#52511yescharacteristic
283C22×C61#52512yes—
284C22×C61C2×#12411yescharacteristic
285C22×C61C2×#12612yes—
286C22×C61#52912yes—
287C22×C61#52912yes—
288C22×C61#52911yescharacteristic
289C22×C61#52912yes—
290C22×C61#52912yes—
291C22×C61#52912yes—
292C22×C61#52912yes—
293C22×C61#52912yes—
294C22×C61#53211yescharacteristic
295C22×C61#53211yescharacteristic
296C2×D61—24no—
297C2×D61—28no—
298C2×D61—44no—
299C2×D61—42no—
300C2×D61—42no—
301C2×D61—42no—
302C2×D61—44no—
303C2×D61—42no—
304C2×D61—44no—
305C2×D61—42no—
306C2×D61—42no—
307C4×C61—24no—
308C4×C61—42no—
309C4×C61—44no—
310C4×C61—42no—
311C4×C61—44no—
312Dic61—44no—
313Dic61—42no—
314Dic61—44no—
315Dic61—42no—
316Dic61#39718yescomplemented
317C2×#397—611no—
318C2×C4×C4⋊C4—611no—
319C2×C4×C22⋊C4—611no—
320C2×C4×C22⋊C4—612no—
321#1445D6111yescharacteristic, complemented
322#1443—612no—
323#1442—611no—
324#1440—612no—
325#1439—611no—
326C4×#95—611no—
327C4×#95—612no—
328C2×C61C4×#12111yescharacteristic
329C2×C61C4×#12311yescharacteristic
330C2×C61C4×#12312yes—
331C2×C61C4×#12411yescharacteristic
332C2×C61C4×#12612yes—
333C2×C61C2×#39711yescharacteristic
334C2×C61#239211yescharacteristic
335C2×C61#239511yescharacteristic
336C2×C61#239512yes—
337C2×C61#239811yescharacteristic
338C2×C61#240112yes—
339D61—44no—
340C24×C4—611no—
341C22×C4⋊C4—611no—
342C22×C4⋊C4C2×D6111yescharacteristic
343C22×C22⋊C4—611no—
344C22×C22⋊C4—612no—
345C22×C22⋊C4—612no—
346C22×C22⋊C4—611no—
347C22×C42—611no—
348C22×C42—611no—
349C22×C42—612no—
350C22×C42—612no—
351#397—618no—
352C4×C4⋊C4—1224no—
353C4×C22⋊C4—1224no—
354C4×C22⋊C4—1228no—
355C2×#95—611no—
356C2×#95—612no—
357C2×#95—612no—
358C2×#95—612no—
359C2×#95—612no—
360C2×#95—612no—
361C2×#95—612no—
362C2×#95—611no—
363C2×#95C2×D6111yescharacteristic
364C2×#95C2×D6112yes—
365C2×#95C2×D6111yescharacteristic
366C2×#95C2×D6112yes—
367C61C4×#39711yescharacteristic, complemented, Sylow
368C25—611no—
369C23×C4—611no—
370C23×C4—612no—
371C23×C4—612no—
372C23×C4—611no—
373C23×C4—611no—
374C23×C4—614no—
375C23×C4—1222no—
376C23×C4—1224no—
377C23×C4—1224no—
378C23×C4—1222no—
379C23×C4C22×D6112yes—
380C23×C4C22×D6111yescharacteristic
381C23×C4C22×D6111yescharacteristic
382C23×C4C22×D6112yes—
383C23×C4C22×D6111yescharacteristic
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—1224no—
387C2×C4⋊C4—1222no—
388C2×C4⋊C4C4×D6114yescomplemented
389C2×C22⋊C4—618no—
390C2×C22⋊C4—614no—
391C2×C22⋊C4—1222no—
392C2×C22⋊C4—1224no—
393C2×C22⋊C4—1224no—
394C2×C22⋊C4—1224no—
395C2×C22⋊C4—1224no—
396C2×C22⋊C4—1222no—
397C2×C22⋊C4—1222no—
398C2×C22⋊C4—1222no—
399C2×C22⋊C4—1222no—
400C2×C22⋊C4—1224no—
401C2×C42—614no—
402C2×C42—1224no—
403C2×C42—1222no—
404C2×C42—1224no—
405C2×C42—1224no—
406C2×C42—1224no—
407C2×C42—1224no—
408C2×C42—1224no—
409C2×C42—1224no—
410C2×C42—1224no—
411#95—22no—
412#95—24no—
413#95—24no—
414#95—22no—
415#95—618no—
416#95—614no—
417#95—1222no—
418#95—1224no—
419#95—1224no—
420#95—1224no—
421#95—1224no—
422#95—1224no—
423C24—612no—
424C24—612no—
425C24—612no—
426C24—1221no—
427C24—1222no—
428C24—1221no—
429C24—1222no—
430C24—1222no—
431C24—1221no—
432C24—1221no—
433C24—1222no—
434C24C23×D6111yescharacteristic
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—612no—
458C22×C4—612no—
459C22×C4—612no—
460C22×C4—614no—
461C22×C4—614no—
462C22×C4—614no—
463C22×C4—612no—
464C22×C4—612no—
465C22×C4—614no—
466C22×C4—1228no—
467C22×C4—12216no—
468C22×C4—1222no—
469C22×C4—1221no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1221no—
480C22×C4—1222no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—2444no—
489C22×C4—2444no—
490C22×C4—2448no—
491C22×C4C2×C4×D6114yes—
492C22×C4C2×C4×D6112yes—
493C22×C4D4×D6112yes—
494C22×C4D4×D6112yes—
495C22×C4#1175822412yes—
496C22×C4#1175822412yes—
497C22×C4#1175822614yes—
498C4⋊C4—28no—
499C4⋊C4—1228no—
500C22⋊C4—12216no—
501C22⋊C4—1228no—
502C22⋊C4—12216no—
503C22⋊C4—1228no—
504C42—1228no—
505C42—2448no—
506C42—2448no—
507C42—2444no—
508C23—614no—
509C23—1222no—
510C23—1222no—
511C23—1224no—
512C23—1224no—
513C23—1222no—
514C23—1224no—
515C23—1222no—
516C23—1224no—
517C23—1222no—
518C23—1224no—
519C23—1224no—
520C23—1222no—
521C23—2441no—
522C23—2441no—
523C23—2441no—
524C23—2442no—
525C23—2442no—
526C23—2442no—
527C23—2442no—
528C23—2442no—
529C23—2442no—
530C23—2441no—
531C23C22×C4×D6111yescharacteristic
532C23C2×D4×D6111yescharacteristic
533C23C2×D4×D6111yescharacteristic
534C23#41×D6111yescharacteristic
535C23#41×D6111yescharacteristic
536C23#41×D6112yes—
537C23#41×D6112yes—
538C23#41×D6112yes—
539C23C2×#1175822411yescharacteristic
540C23C2×#1175822411yescharacteristic
541C23C2×#1175822612yes—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—614no—
571C2×C4—614no—
572C2×C4—618no—
573C2×C4—614no—
574C2×C4—618no—
575C2×C4—1224no—
576C2×C4—1222no—
577C2×C4—1224no—
578C2×C4—1224no—
579C2×C4—1224no—
580C2×C4—1222no—
581C2×C4—1224no—
582C2×C4—1222no—
583C2×C4—1224no—
584C2×C4—1224no—
585C2×C4—1222no—
586C2×C4—24416no—
587C2×C4—2442no—
588C2×C4—2442no—
589C2×C4—2442no—
590C2×C4—2442no—
591C2×C4—2441no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4—2442no—
596C2×C4—2442no—
597C2×C4—2442no—
598C2×C4—2442no—
599C2×C4—2441no—
600C2×C4#1451973714yes—
601C22—1224no—
602C22—1228no—
603C22—2442no—
604C22—2442no—
605C22—2442no—
606C22—2444no—
607C22—2442no—
608C22—2442no—
609C22—2444no—
610C22—2442no—
611C22—2444no—
612C22C4×D4×D6111yescharacteristic
613C22C2×#1451973711yescharacteristic
614C22C4×#1175822411yescharacteristic
615C22#1684023012yes—
616C22C4×#1175822612yes—
617C22#121×D6111yescharacteristic
618C22#123×D6111yescharacteristic
619C22#123×D6112yes—
620C22#1684027011yescharacteristic
621C22#1684027211yescharacteristic
622C22#1684027512yes—
623C22#124×D6111yescharacteristic
624C22#126×D6112yes—
625C22#1684028912yes—
626C22#1684028912yes—
627C22#1684029111yescharacteristic
628C22#1684029512yes—
629C22#1684029712yes—
630C22#1684029712yes—
631C22#1684029812yes—
632C22#1684029812yes—
633C22#1684031011yescharacteristic
634C22#1684031311yescharacteristic
635C4—24no—
636C4—42no—
637C4—44no—
638C4—44no—
639C4—42no—
640C4—618no—
641C4—2444no—
642C4—2442no—
643C4—2444no—
644C4—2442no—
645C2—2444no—
646C2#2144833511yescharacteristic
647C2#2144833611yescharacteristic
648C2#2144834012yes—
649C2#2144836211yescharacteristic
650C2#2144836912yes—
651C2#397×D6111yescharacteristic
652C2#2144906011yescharacteristic
653C2#2144908311yescharacteristic
654C2#2144908412yes—
655C2#2144910411yescharacteristic
656C2#2144911812yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1445C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenter#1445D61
hypocenterC61C4×#397
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic61C2semidirect
5. #21444079C2semidirect
6. #21444075C2semidirect
9. #95×Dic61C2semidirect
10. #95×Dic61C2semidirect
11. C61×#1445C2semidirect
22. #16839688C4semidirect
80. #14519684C2×C4semidirect
81. #14519684C2×C4semidirect
89. C2×C4⋊C4×C61C2×C4semidirect
316. Dic61#397semidirect
321. #1445D61semidirect
367. C61C4×#397semidirect
388. 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×#168396882
C2×C4⋊C4×Dic612
C2×#168396092
#214440792
#214440752
#214440672
#214440652
#95×Dic612
C61×#14452
C4×#39761