Finite Group Databasebeta

← #29748085

Subgroups — #29748085

Order 15616.

874 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448833C211yesmaximal, characteristic, complemented
2#21447129C211yesmaximal, characteristic, complemented
3#21447008C211yesmaximal, characteristic, complemented
4#21446962C211yesmaximal, characteristic, complemented
5#21446815C211yesmaximal, characteristic
6#21446777C211yesmaximal, characteristic, complemented
7#21446505C211yesmaximal, characteristic, complemented
8#21446443C211yesmaximal, characteristic, complemented
9#21446427C211yesmaximal, characteristic, complemented
10#21446397C211yesmaximal, characteristic, complemented
11#21446170C211yesmaximal, characteristic, complemented
12#21446137C211yesmaximal, characteristic, complemented
13#21445907C211yesmaximal, characteristic, complemented
14C4×#14519697C211yesmaximal, characteristic, complemented
15C61×#2490C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×#14519751C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519737—21no—
20C22×C4⋊Dic61C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×C4×#92418C2211yescharacteristic
32#16839664C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839654—21no—
35#16839639—21no—
36#16839636—21no—
37C4×C4⋊Dic61C2211yescharacteristic
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×#125×C61C2211yescharacteristic
49C2×#121×C61C2211yescharacteristic
50C61×#397—21no—
51C61×#394—21no—
52C61×#390—21no—
53C61×#390C2211yescharacteristic
54C61×#390C2211yescharacteristic
55C61×#388—21no—
56C61×#380C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C22⋊D61—21no—
61C23×Dic61—21no—
62C22×C4×D61—21no—
63C2×#11758199—22no—
64C2×#11758199—41no—
65C2×#11758199—41no—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70#14519751—22no—
71#14519751—22no—
72C4×D244—22no—
73C4×D244—41no—
74#14519737—44no—
75C2×C4⋊Dic61—22no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—41no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×#11758196—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×C4×Dic61—21no—
87#14519708—22no—
88C4⋊#92418—41no—
89#14519698—22no—
90#14519698—22no—
91#14519698—41no—
92#14519697—22no—
93#14519697—22no—
94#14519697—41no—
95C22⋊#92418—41no—
96C22⋊#92418—41no—
97C4×#92418—41no—
98#14519684—21no—
99#14519684—21no—
100C22×D4×C61—21no—
101C22×D4×C61C2311yescharacteristic
102C23×C4×C61C2311yescharacteristic
103#125×C61—22no—
104#125×C61—41no—
105#121×C61—22no—
106#121×C61—41no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61D411yescharacteristic
119C2×C22⋊C4×C61D411yescharacteristic
120C2×C42×C61—21no—
121C2×C42×C61C2311yescharacteristic
122C2×C42×C61C2311yescharacteristic
123#95×C61—21no—
124#95×C61—21no—
125#95×C61D411yescharacteristic
126#95×C61D411yescharacteristic
127C24×C61—21no—
128C24×C61C2×D411yescharacteristic
129C23×D61—21no—
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—42no—
137C2×D4×C61—42no—
138C2×D4×C61—81no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2411yescharacteristic
154C2×C22⋊D61—24no—
155C2×C22⋊D61—42no—
156C2×C22⋊D61—42no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—42no—
161C22×Dic61—42no—
162C22×Dic61—81no—
163C2×D244—21no—
164C2×D244—21no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244#4112yes—
169C2×C4×D61—42no—
170C2×C4×D61—42no—
171C2×C4×D61—81no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—42no—
178C4⋊C4×C61—42no—
179C4⋊C4×C61#4112yes—
180C22⋊C4×C61—22no—
181C22⋊C4×C61—22no—
182C22⋊C4×C61—42no—
183C22⋊C4×C61—42no—
184C22⋊C4×C61—81no—
185C22⋊C4×C61—81no—
186C22⋊C4×C61—81no—
187C22⋊C4×C61—81no—
188C42×C61—21no—
189C42×C61—21no—
190C42×C61—21no—
191C42×C61—21no—
192C42×C61—81no—
193#11758199—44no—
194#11758198—24no—
195#11758198—42no—
196#11758198—42no—
197#11758198—81no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—42no—
203C4⋊Dic61#4112yes—
204C4⋊Dic61#4112yes—
205#11758196—42no—
206C4×Dic61—42no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61#13512yes—
233C23×C61C22×D411yescharacteristic
234C22×D61—22no—
235C22×D61—41no—
236C22×D61—41no—
237C22×D61—41no—
238C22×D61—41no—
239C22×D61—41no—
240C22×D61—41no—
241D4×C61—41no—
242D4×C61—41no—
243D4×C61—41no—
244D4×C61—41no—
245D4×C61—84no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—22no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61AGL(1,ℤ/8)12yes—
274C2×C4×C61C2×#4111yescharacteristic
275C2×C4×C61C2×#4111yescharacteristic
276C2×C4×C61C2×#4111yescharacteristic
277C2×C4×C61C2×#4111yescharacteristic
278C2×C4×C61H(5,𝔽2)11yescharacteristic
279C2×C4×C61H(5,𝔽2)11yescharacteristic
280C22⋊D61—48no—
281C2×Dic61—22no—
282C2×Dic61—22no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—84no—
291D244—22no—
292D244—22no—
293D244—41no—
294D244—41no—
295C4×D61—84no—
296#92418—41no—
297#92418—41no—
298#92418—41no—
299#92418—41no—
300#26723—611nomaximal, Sylow
301C22×C61—22no—
302C22×C61—22no—
303C22×C61—22no—
304C22×C61—41no—
305C22×C61—41no—
306C22×C61—41no—
307C22×C61—41no—
308C22×C61—81no—
309C22×C61—81no—
310C22×C61—81no—
311C22×C61—81no—
312C22×C61—81no—
313C22×C61—81no—
314C22×C61—81no—
315C22×C61#52511yescharacteristic
316C22×C61#54611yescharacteristic
317C22×C61#54611yescharacteristic
318C22×C61C2×#13511yescharacteristic
319C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
320C22×C61#57611yescharacteristic
321C22×C61#57711yescharacteristic
322C2×D61—42no—
323C2×D61—42no—
324C2×D61—42no—
325C2×D61—81no—
326C2×D61—81no—
327C2×D61—81no—
328C2×D61—81no—
329C4×C61—22no—
330C4×C61—41no—
331C4×C61—41no—
332C4×C61—41no—
333C4×C61—42no—
334C4×C61—41no—
335C4×C61—81no—
336C4×C61—81no—
337C4×C61#52911yescharacteristic
338C4×C61#53811yescharacteristic
339C4×C61#55511yescharacteristic
340C4×C61#55911yescharacteristic
341Dic61—42no—
342Dic61—42no—
343Dic61—81no—
344#2490D6111yescharacteristic, complemented
345#2361—611no—
346#2054—611no—
347#2034—611no—
348#2025—611no—
349#1999—611no—
350#1989—611no—
351#1934—611no—
352#1926—611no—
353#1923—611no—
354#1919—611no—
355#1879—611no—
356#1874—611no—
357#1824—611no—
358C4×#102—611no—
359C2×C61—42no—
360C2×C61—161no—
361C2×C61#245911yescharacteristic
362C2×C61#310511yescharacteristic
363C2×C61#311911yescharacteristic
364C2×C61#329711yescharacteristic
365C2×C61#330111yescharacteristic
366C2×C61#331811yescharacteristic
367C2×C61#333211yescharacteristic
368D61—82no—
369C22×D8—611no—
370C2×#125C2×D6111yescharacteristic
371C2×#121—611no—
372C2×#121C2×D6111yescharacteristic
373C2×C4×D4—611no—
374C2×C4×D4—1221no—
375C22×C4⋊C4—611no—
376C2×#106—611no—
377C2×C4⋊C8—611no—
378C2×#102—611no—
379C2×#102—611no—
380C2×#102—611no—
381C2×#102—611no—
382C2×#102—611no—
383C2×#102—611no—
384C2×C22⋊C8—611no—
385C2×C22⋊C8—611no—
386C2×C4×C8—611no—
387#397—21no—
388#394—21no—
389#390—21no—
390#390—611no—
391#390C2×D6111yescharacteristic
392#390C2×D6111yescharacteristic
393#389—611no—
394#388—21no—
395#388—1221no—
396#386—1221no—
397#385—1221no—
398#380C2×D6111yescharacteristic
399C4×C4⋊C4—611no—
400C4×C4⋊C4C2×D6111yescharacteristic
401C4×C22⋊C4C2×D6111yescharacteristic
402#340—611no—
403#340—611no—
404#340—611no—
405#340—611no—
406#340—611no—
407#340—611no—
408#340—611no—
409#340—611no—
410#336—611no—
411#336—611no—
412C61#2672311yescharacteristic, complemented, Sylow
413C22×D4—21no—
414C22×D4—611no—
415C22×D4—1221no—
416C22×D4C22×D6111yescharacteristic
417C23×C4—1221no—
418C23×C4—1221no—
419C23×C4C22×D6111yescharacteristic
420C2×D8—1222no—
421C2×D8—2441no—
422C2×D8—2441no—
423C22×C8—611no—
424C22×C8—611no—
425C22×C8—611no—
426C22×C8—611no—
427#125—22no—
428#125—41no—
429#121—22no—
430#121—41no—
431#121—1222no—
432#121—1222no—
433C4×D4—1222no—
434C4×D4—2441no—
435C4×D4—2444no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—611no—
439C2×C4⋊C4—611no—
440C2×C4⋊C4—611no—
441C2×C4⋊C4—1222no—
442C2×C4⋊C4—1221no—
443C2×C4⋊C4—1221no—
444C2×C4⋊C4—2441no—
445C2×C4⋊C4C22×D6111yescharacteristic
446C2×C4⋊C4C22×D6111yescharacteristic
447C2×C4⋊C4C22×D6111yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—1221no—
455C2×C22⋊C4—1221no—
456C2×C22⋊C4—1221no—
457C2×C22⋊C4—1221no—
458C2×C22⋊C4C22⋊D6111yescharacteristic
459C2×C22⋊C4C22⋊D6111yescharacteristic
460C2×C42—21no—
461C2×C42—1221no—
462C2×C42C22×D6111yescharacteristic
463C2×C42C22×D6111yescharacteristic
464#106—1222no—
465C4⋊C8—2441no—
466#102—1222no—
467#102—1222no—
468#102—1222no—
469#102—1222no—
470#102—2441no—
471#102—2441no—
472C22⋊C8—2441no—
473C22⋊C8—2441no—
474C4×C8—2441no—
475#95—21no—
476#95—21no—
477#95—1221no—
478#95—1221no—
479#95C22⋊D6111yescharacteristic
480#95C22⋊D6111yescharacteristic
481C24—21no—
482C24—1221no—
483C24C2×C22⋊D6111yescharacteristic
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—81no—
493C2×D4—612no—
494C2×D4—1224no—
495C2×D4—1221no—
496C2×D4—1221no—
497C2×D4—1221no—
498C2×D4—1221no—
499C2×D4—1221no—
500C2×D4—2442no—
501C2×D4—2442no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—1221no—
514C22×C4—4881no—
515C22×C4—4881no—
516C22×C4—2442no—
517C22×C4—2442no—
518C22×C4—2442no—
519C22×C4—2442no—
520C22×C4C2×C22⋊D6111yescharacteristic
521C22×C4C2×C22⋊D6111yescharacteristic
522C22×C4C2×C22⋊D6111yescharacteristic
523C22×C4C2×C22⋊D6111yescharacteristic
524C22×C4C2×C22⋊D6111yescharacteristic
525C22×C4C23×D6111yescharacteristic
526D8—2444no—
527C2×C8—1221no—
528C2×C8—1221no—
529C2×C8—1221no—
530C2×C8—1221no—
531C2×C8—1221no—
532C2×C8—1221no—
533C2×C8—1221no—
534C2×C8—1221no—
535C2×C8—1221no—
536C2×C8—1221no—
537C2×C8—1221no—
538C2×C8—1221no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—612no—
547C4⋊C4—612no—
548C4⋊C4—1221no—
549C4⋊C4—1221no—
550C4⋊C4—1221no—
551C4⋊C4—1221no—
552C4⋊C4—2442no—
553C4⋊C4—2442no—
554C4⋊C4#1175822412yes—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C22⋊C4—1224no—
564C22⋊C4—4881no—
565C22⋊C4—2442no—
566C22⋊C4—2442no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—81no—
572C42—2442no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—1222no—
587C23—2441no—
588C23—2441no—
589C23—2441no—
590C23—2441no—
591C23—2441no—
592C23—2441no—
593C23#1451979712yes—
594C23C22×C22⋊D6111yescharacteristic
595D4—41no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—84no—
600D4—1222no—
601D4—1222no—
602D4—2448no—
603D4—2441no—
604D4—2441no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—1222no—
633C2×C4—1222no—
634C2×C4—4884no—
635C2×C4—4884no—
636C2×C4—2441no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4—2441no—
643C2×C4#1451980212yes—
644C2×C4#41×D6111yescharacteristic
645C2×C4#41×D6111yescharacteristic
646C2×C4#41×D6111yescharacteristic
647C2×C4C2×#1175822411yescharacteristic
648C2×C4#1451982211yescharacteristic
649C2×C4#1451982311yescharacteristic
650C8—2441no—
651C8—2441no—
652C8—2441no—
653C8—2441no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—4881no—
669C22—4881no—
670C22—4881no—
671C22—4881no—
672C22—2442no—
673C22—2442no—
674C22—2442no—
675C22#1684026911yescharacteristic
676C22#1684040011yescharacteristic
677C22#1684040611yescharacteristic
678C22C2×#1451979711yescharacteristic
679C22C2×#1451980211yescharacteristic
680C22#1684056511yescharacteristic
681C22#1684057311yescharacteristic
682C4—22no—
683C4—41no—
684C4—42no—
685C4—41no—
686C4—41no—
687C4—41no—
688C4—81no—
689C4—81no—
690C4—4881no—
691C4—2442no—
692C4—2442no—
693C4#1684029111yescharacteristic
694C4#1684034611yescharacteristic
695C4#1684047411yescharacteristic
696C4#1684049411yescharacteristic
697C2—42no—
698C2—161no—
699C2—4882no—
700C2#2144975211yescharacteristic
701C2#2145586211yescharacteristic
702C2#2145601211yescharacteristic
703C2#2145766911yescharacteristic
704C2#2145771511yescharacteristic
705C2#2145795411yescharacteristic
706C2#2145814611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2490C2
socleC23×C61C22×D4
prime radical#21446815C2
hypercenter#2490D61
hypocenterC61#26723
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2490

Complements

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

NH ≅ G/Ntype
1. #21448833C2semidirect
2. #21447129C2semidirect
3. #21447008C2semidirect
4. #21446962C2semidirect
6. #21446777C2semidirect
7. #21446505C2semidirect
8. #21446443C2semidirect
9. #21446427C2semidirect
10. #21446397C2semidirect
11. #21446170C2semidirect
12. #21446137C2semidirect
13. #21445907C2semidirect
14. C4×#14519697C2semidirect
15. C61×#2490C2semidirect
344. #2490D61semidirect
412. C61#26723semidirect

Maximal subgroups

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

subgroupindex
#214488332
#214471292
#214470082
#214469622
#214468152
#214467772
#214465052
#214464432
#214464272
#214463972
#214461702
#214461372
#214459072
C4×#145196972
C61×#24902
#2672361