Finite Group Databasebeta

← #29753174

Subgroups — #29753174

Order 15616.

848 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450394C211yesmaximal, characteristic, complemented
2#21447352C211yesmaximal, characteristic, complemented
3#21447136C211yesmaximal, characteristic, complemented
4#21447050C211yesmaximal, characteristic
5#21446907C211yesmaximal, characteristic
6#21446672C211yesmaximal, characteristic, complemented
7#21446453C211yesmaximal, characteristic, complemented
8#21446443C211yesmaximal, characteristic, complemented
9#21446404C211yesmaximal, characteristic, complemented
10#21446378C211yesmaximal, characteristic, complemented
11#21446153C211yesmaximal, characteristic, complemented
12#21446153C211yesmaximal, characteristic, complemented
13#21445819C211yesmaximal, characteristic, complemented
14C4×#14519698C211yesmaximal, characteristic, complemented
15C61×#2366C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×#14519708C2211yescharacteristic
19C2×#14519708C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519700C2211yescharacteristic
22C2×#14519700C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×C4×#92418C2211yescharacteristic
30#16839704—21no—
31#16839701—21no—
32#16839668C2211yescharacteristic
33#16839668C2211yescharacteristic
34#16839668C2211yescharacteristic
35#16839660C2211yescharacteristic
36#16839648—21no—
37#16839645—21no—
38#16839632C2211yescharacteristic
39C4×C4⋊Dic61C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839517C2211yescharacteristic
45#16839517C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×#127×C61C2211yescharacteristic
49C2×C4×D4×C61—21no—
50C2×C4×D4×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C61×#390—21no—
53C61×#390C2211yescharacteristic
54C61×#390C2211yescharacteristic
55C61×#386—21no—
56C61×#386—21no—
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C22×Dic122C2311yescharacteristic
60C2×#11758200—22no—
61C2×#11758200—22no—
62C2×#11758200—22no—
63C2×#11758200—41no—
64C2×#11758200—41no—
65C2×#11758200—41no—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×C4×Dic61—21no—
77#14519708—22no—
78#14519708—41no—
79C4⋊#92418—41no—
80#14519700—22no—
81#14519700—41no—
82#14519698—22no—
83#14519698—22no—
84#14519698—22no—
85#14519698—41no—
86#14519698—41no—
87#14519698—41no—
88C4×#92418—41no—
89#14519684—21no—
90#14519684—21no—
91#14519684—21no—
92#14519684—21no—
93#14519684—21no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97C22×D4×C61—21no—
98C22×D4×C61—21no—
99C22×D4×C61C2311yescharacteristic
100C22×D4×C61C2311yescharacteristic
101C23×C4×C61—21no—
102C23×C4×C61—21no—
103#127×C61—22no—
104#127×C61—22no—
105C4×D4×C61—22no—
106C4×D4×C61—22no—
107C4×D4×C61—41no—
108C4×D4×C61—41no—
109C4×D4×C61—44no—
110C2×C4⋊C4×C61D411yescharacteristic
111C2×C4⋊C4×C61D411yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C42×C61—21no—
121C2×C42×C61C2311yescharacteristic
122C2×C42×C61C2311yescharacteristic
123C2×C42×C61C2311yescharacteristic
124#95×C61—21no—
125#95×C61D411yescharacteristic
126#95×C61D411yescharacteristic
127C24×C61—21no—
128C24×C61—21no—
129C2×D4×C61—24no—
130C2×D4×C61—24no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—42no—
142C2×D4×C61—42no—
143C2×D4×C61—81no—
144C2×D4×C61—81no—
145C2×D4×C61#4112yes—
146C2×D4×C61#4112yes—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—42no—
150C22×C4×C61—42no—
151C22×C4×C61—42no—
152C22×C4×C61—42no—
153C22×C4×C61—81no—
154C22×C4×C61—81no—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2411yescharacteristic
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×Dic122—21no—
169C2×Dic122—21no—
170C2×Dic122—21no—
171C2×Dic122—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61SD1614yescomplemented
177C4⋊C4×C61#4112yes—
178C22⋊C4×C61—42no—
179C22⋊C4×C61—42no—
180C22⋊C4×C61—42no—
181C22⋊C4×C61—42no—
182C22⋊C4×C61—81no—
183C22⋊C4×C61—81no—
184C42×C61—21no—
185C42×C61—21no—
186C42×C61—21no—
187C42×C61—21no—
188C42×C61—21no—
189C42×C61—21no—
190C42×C61—42no—
191#11758200—44no—
192#11758200—44no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—42no—
200C4⋊Dic61—81no—
201#11758196—81no—
202C4×Dic61—81no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418#4112yes—
215C23×C61—22no—
216C23×C61—22no—
217C23×C61—41no—
218C23×C61—41no—
219C23×C61—41no—
220C23×C61—41no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61C22×D411yescharacteristic
230D4×C61—22no—
231D4×C61—22no—
232D4×C61—22no—
233D4×C61—22no—
234D4×C61—48no—
235D4×C61—41no—
236D4×C61—41no—
237D4×C61—41no—
238D4×C61—41no—
239D4×C61—84no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—22no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—84no—
262C2×C4×C61—84no—
263C2×C4×C61C2×SD1612yes—
264C2×C4×C61C2×SD1612yes—
265C2×C4×C61C2×SD1612yes—
266C2×C4×C61C2×#4111yescharacteristic
267C2×C4×C61C2×#4111yescharacteristic
268C2×C4×C61C2×#4111yescharacteristic
269C2×C4×C61C2×#4111yescharacteristic
270C2×C4×C61H(5,𝔽2)11yescharacteristic
271C2×C4×C61H(5,𝔽2)11yescharacteristic
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284Dic122—41no—
285Dic122—41no—
286Dic122—41no—
287Dic122—41no—
288#92418—22no—
289#92418—41no—
290#92418—41no—
291#92418—41no—
292#27064—611nomaximal, Sylow
293C22×C61—42no—
294C22×C61—42no—
295C22×C61—42no—
296C22×C61—42no—
297C22×C61—42no—
298C22×C61—42no—
299C22×C61—81no—
300C22×C61—81no—
301C22×C61—81no—
302C22×C61—81no—
303C22×C61—81no—
304C22×C61—81no—
305C22×C61—81no—
306C22×C61—81no—
307C22×C61#52511yescharacteristic
308C22×C61#54611yescharacteristic
309C22×C61#55011yescharacteristic
310C22×C61C22×SD1611yescharacteristic
311C22×C61#57511yescharacteristic
312C22×C61#57611yescharacteristic
313C22×C61#57711yescharacteristic
314C4×C61—22no—
315C4×C61—22no—
316C4×C61—22no—
317C4×C61—41no—
318C4×C61—42no—
319C4×C61—41no—
320C4×C61—41no—
321C4×C61—81no—
322C4×C61#52911yescharacteristic
323C4×C61#53811yescharacteristic
324C4×C61#55111yescharacteristic
325C4×C61#55311yescharacteristic
326Dic61—81no—
327Dic61—81no—
328Dic61—81no—
329Dic61—81no—
330#2511—611no—
331#2366D6111yescharacteristic
332#2094—611no—
333#2055—611no—
334#2041—611no—
335#2014—611no—
336#1968—611no—
337#1927—611no—
338#1926—611no—
339#1920—611no—
340#1916—611no—
341#1877—611no—
342#1877—611no—
343#1802—611no—
344C4×#102—611no—
345C2×C61—82no—
346C2×C61—82no—
347C2×C61#246711yescharacteristic
348C2×C61#310111yescharacteristic
349C2×C61#311811yescharacteristic
350C2×C61#329511yescharacteristic
351C2×C61#331711yescharacteristic
352C2×C61#339211yescharacteristic
353C2×C61#340311yescharacteristic
354C22×SD16—611no—
355C22×SD16—611no—
356C2×#127C2×D6111yescharacteristic
357C2×C4×D4—21no—
358C2×C4×D4C2×D6111yescharacteristic
359C2×C4×D4C2×D6111yescharacteristic
360C2×#106—611no—
361C2×#106—611no—
362C2×C4⋊C8—611no—
363C2×#103—611no—
364C2×#103—611no—
365C2×#102—611no—
366C2×#102—611no—
367C2×#102—611no—
368C2×#102—611no—
369C2×#102—611no—
370C2×#102—611no—
371C2×C4×C8—611no—
372#400—1221no—
373#400—1221no—
374#391—611no—
375#391—611no—
376#391—611no—
377#390—21no—
378#390C2×D6111yescharacteristic
379#390C2×D6111yescharacteristic
380#389—611no—
381#387—1221no—
382#387—1221no—
383#386—21no—
384#386—21no—
385#384—611no—
386C4×C4⋊C4—611no—
387C4×C4⋊C4C2×D6111yescharacteristic
388C4×C4⋊C4C2×D6111yescharacteristic
389#340—611no—
390#340—611no—
391#340—611no—
392#340—611no—
393#336—611no—
394#336—611no—
395#336—611no—
396#336—611no—
397C61#2706411yescharacteristic, complemented, Sylow
398C22×Q8—611no—
399C22×D4—21no—
400C22×D4—21no—
401C22×D4C22×D6111yescharacteristic
402C22×D4C22×D6111yescharacteristic
403C23×C4—21no—
404C23×C4—21no—
405C2×SD16—1222no—
406C2×SD16—1222no—
407C2×SD16—1222no—
408C2×SD16—2441no—
409C2×SD16—2441no—
410C2×SD16—2441no—
411C22×C8—611no—
412C22×C8—611no—
413C22×C8—611no—
414C22×C8—611no—
415#127—22no—
416#127—22no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—41no—
420C4×D4—41no—
421C4×D4—44no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4C22⋊D6111yescharacteristic
429C2×C4⋊C4C22⋊D6111yescharacteristic
430C2×C4⋊C4C22×D6111yescharacteristic
431C2×C4⋊C4C22×D6111yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C42—21no—
439C2×C42—1221no—
440C2×C42C22×D6111yescharacteristic
441C2×C42C22×D6111yescharacteristic
442C2×C42C22×D6111yescharacteristic
443#106—1222no—
444#106—2441no—
445C4⋊C8—2441no—
446#103—1222no—
447#103—2441no—
448#102—1222no—
449#102—1222no—
450#102—1222no—
451#102—2441no—
452#102—2441no—
453#102—2441no—
454C4×C8—2441no—
455#95—21no—
456#95—1221no—
457#95—1221no—
458#95—1221no—
459#95—1221no—
460#95—1221no—
461#95—1221no—
462#95—1221no—
463#95—1221no—
464#95C22⋊D6111yescharacteristic
465#95C22⋊D6111yescharacteristic
466C24—21no—
467C24—21no—
468C2×Q8—1221no—
469C2×Q8—1221no—
470C2×Q8—1221no—
471C2×Q8—1221no—
472C2×Q8—1221no—
473C2×Q8—1221no—
474C2×D4—24no—
475C2×D4—24no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—81no—
489C2×D4—81no—
490C2×D4#1175822212yes—
491C2×D4#1175822212yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—81no—
499C22×C4—81no—
500C22×C4—1221no—
501C22×C4—1221no—
502C22×C4—1221no—
503C22×C4—1221no—
504C22×C4C2×C22⋊D6111yescharacteristic
505C22×C4C2×C22⋊D6111yescharacteristic
506C22×C4C2×C22⋊D6111yescharacteristic
507C22×C4C2×C22⋊D6111yescharacteristic
508C22×C4C2×C22⋊D6111yescharacteristic
509C22×C4C2×C22⋊D6111yescharacteristic
510C22×C4C23×D6111yescharacteristic
511SD16—2444no—
512SD16—2444no—
513C2×C8—612no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C2×C8—1221no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—41no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—1221no—
532C4⋊C4—1221no—
533C4⋊C4—1221no—
534C4⋊C4—1221no—
535C4⋊C4—4881no—
536C4⋊C4—4881no—
537C4⋊C4—2442no—
538C4⋊C4#1175820014yescomplemented
539C4⋊C4#1175822412yes—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—81no—
545C22⋊C4—81no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—42no—
553C42—4881no—
554C23—22no—
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23C22×C22⋊D6111yescharacteristic
569Q8—2441no—
570Q8—2441no—
571Q8—2441no—
572Q8—2441no—
573D4—22no—
574D4—22no—
575D4—22no—
576D4—22no—
577D4—48no—
578D4—41no—
579D4—41no—
580D4—41no—
581D4—41no—
582D4—84no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—84no—
605C2×C4—84no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4C2×#1175820012yes—
619C2×C4C2×#1175820012yes—
620C2×C4C2×#1175820012yes—
621C2×C4#41×D6111yescharacteristic
622C2×C4C2×#1175822411yescharacteristic
623C2×C4C2×#1175822211yescharacteristic
624C2×C4C2×#1175822211yescharacteristic
625C2×C4#1451982211yescharacteristic
626C2×C4#1451982311yescharacteristic
627C8—1222no—
628C8—2441no—
629C8—2441no—
630C8—2441no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22#1684027311yescharacteristic
646C22#1684040611yescharacteristic
647C22#1684043111yescharacteristic
648C22C22×#1175820011yescharacteristic
649C22#1684056011yescharacteristic
650C22#1684056511yescharacteristic
651C22#1684057311yescharacteristic
652C4—22no—
653C4—22no—
654C4—22no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—42no—
659C4—81no—
660C4—4881no—
661C4—4881no—
662C4—4881no—
663C4—4881no—
664C4#1684029211yescharacteristic
665C4#1684034511yescharacteristic
666C4#1684044111yescharacteristic
667C4#1684045811yescharacteristic
668C2—82no—
669C2—82no—
670C2#2144986411yescharacteristic
671C2#2145582711yescharacteristic
672C2#2145600311yescharacteristic
673C2#2145764311yescharacteristic
674C2#2145794511yescharacteristic
675C2#2145880011yescharacteristic
676C2#2145890311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2366C2
socleC23×C61C22×D4
prime radicalC2×#127×C61C22
hypercenter#2366D61
hypocenterC61#27064
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2366

Complements

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

NH ≅ G/Ntype
1. #21450394C2semidirect
2. #21447352C2semidirect
3. #21447136C2semidirect
6. #21446672C2semidirect
7. #21446453C2semidirect
8. #21446443C2semidirect
9. #21446404C2semidirect
10. #21446378C2semidirect
11. #21446153C2semidirect
12. #21446153C2semidirect
13. #21445819C2semidirect
14. C4×#14519698C2semidirect
176. C4⋊C4×C61SD16semidirect
397. C61#27064semidirect
538. C4⋊C4#11758200semidirect

Maximal subgroups

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

subgroupindex
#214503942
#214473522
#214471362
#214470502
#214469072
#214466722
#214464532
#214464432
#214464042
#214463782
#214461532
#214458192
C4×#145196982
C61×#23662
#2706461