Finite Group Databasebeta

← #29747989

Subgroups — #29747989

Order 15616.

772 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21449580C211yesmaximal, characteristic
2#21448917C211yesmaximal, characteristic, complemented
3#21447317C211yesmaximal, characteristic, complemented
4#21447050C211yesmaximal, characteristic
5#21446963C211yesmaximal, characteristic, complemented
6#21446963C211yesmaximal, characteristic, complemented
7#21446518C211yesmaximal, characteristic, complemented
8#21446448C211yesmaximal, characteristic, complemented
9#21446442C211yesmaximal, characteristic, complemented
10#21446442C211yesmaximal, characteristic, complemented
11#21446390C211yesmaximal, characteristic, complemented
12#21446380C211yesmaximal, characteristic, complemented
13#21446082C211yesmaximal, characteristic, complemented
14#21445646C211yesmaximal, characteristic, complemented
15C61×#1982C211yesmaximal, characteristic
16C2×#14519768C2211yescharacteristic
17C2×#14519758—21no—
18C2×D4×Dic61C2211yescharacteristic
19C2×#14519710C2211yescharacteristic
20C2×#14519709C2211yescharacteristic
21C2×#14519698C2211yescharacteristic
22C2×#14519698C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519687C2211yescharacteristic
26#16839676—21no—
27#16839676—21no—
28#16839665C2211yescharacteristic
29#16839665C2211yescharacteristic
30#16839665C2211yescharacteristic
31#16839661C2211yescharacteristic
32#16839660C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839659—21no—
35#16839646—21no—
36#16839645—21no—
37#16839642—21no—
38C4⋊C4×Dic61C2211yescharacteristic
39C4⋊C4×Dic61C2211yescharacteristic
40C4×#11758196C2211yescharacteristic
41C4×C4⋊Dic61—21no—
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#127×C61C2211yescharacteristic
53C2×C4⋊C8×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C23×Dic61—21no—
60C22×#92418C2311yescharacteristic
61C22×#92418C2311yescharacteristic
62#14519768—22no—
63#14519768—22no—
64#14519758—44no—
65D4×Dic61—22no—
66D4×Dic61—41no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196D411yescharacteristic
77C2×#11758196D411yescharacteristic
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61C2311yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89#14519710—22no—
90#14519709—41no—
91#14519698—22no—
92#14519698—22no—
93#14519698—22no—
94#14519698—41no—
95#14519687—41no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684D411yescharacteristic
102#14519684D411yescharacteristic
103C22×D4×C61—21no—
104C22×D4×C61—21no—
105C22×D4×C61C2311yescharacteristic
106C22×D4×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109#127×C61—22no—
110#127×C61—41no—
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C42×C61—21no—
114C2×C42×C61C2311yescharacteristic
115C4⋊C8×C61—41no—
116#102×C61—22no—
117#102×C61—22no—
118#102×C61—22no—
119#102×C61—22no—
120#95×C61—21no—
121C24×C61—21no—
122C24×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—21no—
129C2×D4×C61—21no—
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—42no—
135C2×D4×C61—42no—
136C2×D4×C61—42no—
137C2×D4×C61—42no—
138C2×D4×C61—81no—
139C2×D4×C61—81no—
140C2×D4×C61#4112yes—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2411yescharacteristic
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—42no—
151C22×Dic61—42no—
152C22×Dic61—81no—
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61#4112yes—
166C4⋊C4×C61#4112yes—
167C42×C61—21no—
168C42×C61—21no—
169C42×C61—42no—
170C22⋊Dic61—42no—
171C22⋊Dic61—42no—
172C22⋊Dic61—42no—
173C22⋊Dic61—42no—
174C22⋊Dic61—81no—
175C22⋊Dic61—81no—
176C22⋊Dic61—81no—
177C4⋊Dic61—24no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—42no—
186C4⋊Dic61#4112yes—
187#11758196—24no—
188#11758196—22no—
189#11758196—41no—
190#11758196—42no—
191#11758196—81no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—81no—
197C4×Dic61—81no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C23×C61—22no—
205C23×C61—41no—
206C23×C61—41no—
207C23×C61—41no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61—41no—
212C23×C61—41no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61—41no—
216C23×C61—41no—
217C23×C61—41no—
218C23×C61C22×D411yescharacteristic
219D4×C61—22no—
220D4×C61—22no—
221D4×C61—41no—
222D4×C61—41no—
223D4×C61—41no—
224D4×C61—41no—
225D4×C61—41no—
226D4×C61—41no—
227D4×C61—84no—
228D4×C61—84no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—22no—
232C2×C4×C61—21no—
233C2×C4×C61—22no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61AGL(1,ℤ/8)12yes—
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61H(5,𝔽2)11yescharacteristic
246C2×C4×C612−1+411yescharacteristic
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—22no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—84no—
272C8×C61—41no—
273C8×C61—41no—
274#92418—41no—
275#92418—41no—
276#26716—611nomaximal, Sylow
277C22×C61—42no—
278C22×C61—42no—
279C22×C61—42no—
280C22×C61—81no—
281C22×C61—81no—
282C22×C61—81no—
283C22×C61—81no—
284C22×C61—81no—
285C22×C61—81no—
286C22×C61—81no—
287C22×C61—81no—
288C22×C61—81no—
289C22×C61—81no—
290C22×C61—81no—
291C22×C61#52511yescharacteristic
292C22×C61#54611yescharacteristic
293C22×C61#54811yescharacteristic
294C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
295C22×C61#57511yescharacteristic
296C22×C61#57611yescharacteristic
297C22×C61#57711yescharacteristic
298C4×C61—22no—
299C4×C61—42no—
300C4×C61—42no—
301C4×C61—41no—
302C4×C61#52911yescharacteristic
303C4×C61#54211yescharacteristic
304C4×C61#55211yescharacteristic
305C4×C61#55911yescharacteristic
306Dic61—41no—
307Dic61—41no—
308Dic61—42no—
309Dic61—41no—
310Dic61—41no—
311Dic61—81no—
312Dic61—81no—
313Dic61—81no—
314#2445—611no—
315#2370—611no—
316#2088—611no—
317#2041—611no—
318#2025—611no—
319#2025—611no—
320#1982D6111yescharacteristic
321#1936—611no—
322#1926—611no—
323#1925—611no—
324#1925—611no—
325#1918—611no—
326#1917—611no—
327#1864—611no—
328#1762—611no—
329C2×C61—82no—
330C2×C61—161no—
331C2×C61#245811yescharacteristic
332C2×C61#311511yescharacteristic
333C2×C61#311911yescharacteristic
334C2×C61#331011yescharacteristic
335C2×C61#332211yescharacteristic
336C2×C61#336611yescharacteristic
337C2×C61#337111yescharacteristic
338C2×#127C2×D6111yescharacteristic
339C2×#125—611no—
340C2×#123—1221no—
341C2×C4×D4—611no—
342C2×#107—611no—
343C2×#106—611no—
344C2×C4⋊C8C2×D6111yescharacteristic
345C2×#102—611no—
346C2×#102—611no—
347C2×#102—611no—
348C2×#102—611no—
349C2×#102C2×D6111yescharacteristic
350C2×#102C2×D6111yescharacteristic
351C2×#102C2×D6111yescharacteristic
352C2×#102C2×D6111yescharacteristic
353C2×#97—611no—
354#394—1221no—
355#394—1221no—
356#390—611no—
357#390—611no—
358#390—611no—
359#389—611no—
360#389—611no—
361#389—611no—
362#389—1221no—
363#387—1221no—
364#387—1221no—
365#386—1221no—
366C4×C4⋊C4—611no—
367C4×C4⋊C4—611no—
368C4×C4⋊C4—611no—
369C4×C4⋊C4—1221no—
370C4×C4⋊C4C2×D6111yescharacteristic
371#340—611no—
372#340—611no—
373#340—611no—
374#340—611no—
375#340—611no—
376#340—611no—
377#336—611no—
378#336—611no—
379#336—611no—
380#336—611no—
381C61#2671611yescharacteristic, complemented, Sylow
382C22×D4—21no—
383C22×D4—21no—
384C22×D4C22×D6111yescharacteristic
385C22×D4C22×D6111yescharacteristic
386C23×C4—1221no—
387C22×C8—611no—
388C22×C8—611no—
389C22×C8C22×D6111yescharacteristic
390C22×C8C22×D6111yescharacteristic
391#127—22no—
392#127—41no—
393#125—1222no—
394#125—1222no—
395#123—2444no—
396C4×D4—1222no—
397C4×D4—2441no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4C22×D6111yescharacteristic
410C2×C4⋊C4C22×D6111yescharacteristic
411C2×C22⋊C4—1221no—
412C2×C22⋊C4—1221no—
413C2×C22⋊C4—1221no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C42—21no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—1221no—
422C2×C42—1221no—
423C2×C42C22×D6111yescharacteristic
424#107—1222no—
425#106—2441no—
426C4⋊C8—41no—
427#102—22no—
428#102—22no—
429#102—22no—
430#102—22no—
431#102—1222no—
432#102—1222no—
433#102—1222no—
434#102—2441no—
435#97—2441no—
436#95—21no—
437#95—611no—
438#95—611no—
439#95—1221no—
440#95—1221no—
441#95—1221no—
442#95—1221no—
443#95—1221no—
444C24—21no—
445C24—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—42no—
460C2×D4—42no—
461C2×D4—81no—
462C2×D4—81no—
463C2×D4#1175822212yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—4881no—
475C22×C4—2442no—
476C22×C4—2442no—
477C22×C4D4×D6111yescharacteristic
478C22×C4D4×D6111yescharacteristic
479C22×C4C23×D6111yescharacteristic
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—612no—
495C4⋊C4—1224no—
496C4⋊C4—1224no—
497C4⋊C4—1221no—
498C4⋊C4—1222no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—4881no—
506C4⋊C4—2441no—
507C4⋊C4—2442no—
508C4⋊C4—2442no—
509C4⋊C4#1175822412yes—
510C4⋊C4#1175822412yes—
511C22⋊C4—4881no—
512C22⋊C4—4881no—
513C22⋊C4—4881no—
514C22⋊C4—2442no—
515C22⋊C4—2442no—
516C22⋊C4—2442no—
517C22⋊C4—2442no—
518C42—21no—
519C42—21no—
520C42—42no—
521C42—1221no—
522C42—1221no—
523C42—1221no—
524C42—1221no—
525C42—4881no—
526C42—4881no—
527C23—22no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23C2×D4×D6111yescharacteristic
542D4—22no—
543D4—22no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—84no—
551D4—84no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1222no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—4884no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4#1451980112yes—
589C2×C4#41×D6111yescharacteristic
590C2×C4C2×#1175822411yescharacteristic
591C2×C4C2×#1175822411yescharacteristic
592C2×C4C2×#1175822211yescharacteristic
593C2×C4#1451982211yescharacteristic
594C2×C4#1451982411yescharacteristic
595C8—41no—
596C8—41no—
597C8—2441no—
598C8—2441no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22#1684027211yescharacteristic
614C22#1684040211yescharacteristic
615C22#1684041811yescharacteristic
616C22C2×#1451980111yescharacteristic
617C22#1684055811yescharacteristic
618C22#1684056611yescharacteristic
619C22#1684056811yescharacteristic
620C4—22no—
621C4—42no—
622C4—41no—
623C4—42no—
624C4—4881no—
625C4—4881no—
626C4—4881no—
627C4—2441no—
628C4—2441no—
629C4—2441no—
630C4—2442no—
631C4—2441no—
632C4#1684029211yescharacteristic
633C4#1684037611yescharacteristic
634C4#1684045211yescharacteristic
635C4#1684049811yescharacteristic
636C2—82no—
637C2—161no—
638C2#2144974611yescharacteristic
639C2#2145596711yescharacteristic
640C2#2145601711yescharacteristic
641C2#2145783611yescharacteristic
642C2#2145801611yescharacteristic
643C2#2145853011yescharacteristic
644C2#2145858011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1982C2
socleC23×C61C22×D4
prime radicalC2×#127×C61C22
hypercenter#1982D61
hypocenterC61#26716
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. #21448917C2semidirect
3. #21447317C2semidirect
5. #21446963C2semidirect
6. #21446963C2semidirect
7. #21446518C2semidirect
8. #21446448C2semidirect
9. #21446442C2semidirect
10. #21446442C2semidirect
11. #21446390C2semidirect
12. #21446380C2semidirect
13. #21446082C2semidirect
14. #21445646C2semidirect
381. C61#26716semidirect

Maximal subgroups

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

subgroupindex
#214495802
#214489172
#214473172
#214470502
#214469632
#214465182
#214464482
#214464422
#214463902
#214463802
#214460822
#214456462
C61×#19822
#2671661