Finite Group Databasebeta

← #29747990

Subgroups — #29747990

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#21449585C211yesmaximal, characteristic
2#21448914C211yesmaximal, characteristic, complemented
3#21447323C211yesmaximal, characteristic, complemented
4#21447051C211yesmaximal, characteristic
5#21446964C211yesmaximal, characteristic, complemented
6#21446963C211yesmaximal, characteristic, complemented
7#21446744C211yesmaximal, characteristic
8#21446449C211yesmaximal, characteristic, complemented
9#21446437C211yesmaximal, characteristic, complemented
10#21446436C211yesmaximal, characteristic, complemented
11#21446393C211yesmaximal, characteristic, complemented
12#21446383C211yesmaximal, characteristic, complemented
13#21446079C211yesmaximal, characteristic, complemented
14#21445645C211yesmaximal, characteristic, complemented
15C61×#1936C211yesmaximal, characteristic, complemented
16C2×#14519773C2211yescharacteristic
17C2×#14519768C2211yescharacteristic
18C2×#14519759—21no—
19C2×C4×D244C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29#16839678—21no—
30#16839677—21no—
31#16839665C2211yescharacteristic
32#16839663C2211yescharacteristic
33#16839661C2211yescharacteristic
34#16839658C2211yescharacteristic
35#16839657—21no—
36#16839647—21no—
37#16839644—21no—
38#16839638—21no—
39C4⋊C4×Dic61—21no—
40C4⋊C4×Dic61C2211yescharacteristic
41C4⋊C4×Dic61C2211yescharacteristic
42C4×#11758196C2211yescharacteristic
43C4×C4⋊Dic61C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#102×C61C2211yescharacteristic
53C2×#102×C61C2211yescharacteristic
54C2×#97×C61C2211yescharacteristic
55C61×#390C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C22⋊D61—21no—
61C22×C22⋊D61—21no—
62C22×C4×D61—21no—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519773—22no—
66#14519773—41no—
67#14519768—22no—
68#14519768—22no—
69#14519759—44no—
70C4×D244—22no—
71C4×D244—41no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196D411yescharacteristic
80C2×#11758196D411yescharacteristic
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61C2311yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91#14519710—22no—
92#14519708—41no—
93#14519706—41no—
94#14519699—22no—
95#14519699—22no—
96#14519698—22no—
97#14519698—22no—
98#14519697—22no—
99#14519697—22no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684D411yescharacteristic
106#14519684D411yescharacteristic
107C22×D4×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C42×C61C2311yescharacteristic
117#102×C61—22no—
118#102×C61—41no—
119#97×C61—41no—
120#95×C61—21no—
121C24×C61—21no—
122C23×D61—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—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2411yescharacteristic
135C2×C22⋊D61—42no—
136C2×C22⋊D61—42no—
137C2×C22⋊D61—42no—
138C2×C22⋊D61—42no—
139C2×C22⋊D61—81no—
140C2×C22⋊D61—81no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61C2×D411yescharacteristic
145C22×Dic61C2×D411yescharacteristic
146C22×Dic61C2×D411yescharacteristic
147C22×Dic61C2×D411yescharacteristic
148C2×D244—21no—
149C2×D244—21no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244#4112yes—
154C2×C4×D61—42no—
155C2×C4×D61—42no—
156C2×C4×D61—81no—
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—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—42no—
169C4⋊C4×C61#4112yes—
170C22⋊C4×C61—42no—
171C22⋊C4×C61—81no—
172C42×C61—21no—
173C42×C61—21no—
174C22⋊Dic61—42no—
175C22⋊Dic61—81no—
176#11758198—42no—
177#11758198—42no—
178#11758198—81no—
179C4⋊Dic61—24no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—42no—
185C4⋊Dic61#4112yes—
186C4⋊Dic61#4112yes—
187#11758196—24no—
188#11758196—22no—
189#11758196—41no—
190#11758196—81no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—42no—
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—41no—
205C23×C61—41no—
206C23×C61—41no—
207C23×C61—41no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61C22×D411yescharacteristic
212C22×D61—22no—
213C22×D61—41no—
214C22×D61—41no—
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—41no—
218C22×D61—41no—
219D4×C61—41no—
220D4×C61—41no—
221D4×C61—41no—
222D4×C61—41no—
223C2×C4×C61—22no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61C2×#4111yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61H(5,𝔽2)11yescharacteristic
243C2×C4×C612−1+411yescharacteristic
244C22⋊D61—84no—
245C22⋊D61—84no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—22no—
251C2×Dic61—21no—
252C2×Dic61—22no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61AGL(1,ℤ/8)12yes—
267D244—22no—
268D244—22no—
269D244—41no—
270D244—41no—
271C4×D61—84no—
272C8×C61—41no—
273C8×C61—41no—
274#92418—41no—
275#92418—41no—
276#26716—611nomaximal, Sylow
277C22×C61—81no—
278C22×C61—81no—
279C22×C61—81no—
280C22×C61—81no—
281C22×C61—81no—
282C22×C61—81no—
283C22×C61—81no—
284C22×C61#52511yescharacteristic
285C22×C61#54611yescharacteristic
286C22×C61#54811yescharacteristic
287C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
288C22×C61#57511yescharacteristic
289C22×C61#57611yescharacteristic
290C22×C61#57711yescharacteristic
291C2×D61—42no—
292C2×D61—42no—
293C2×D61—42no—
294C2×D61—81no—
295C2×D61—81no—
296C2×D61—81no—
297C2×D61—81no—
298C4×C61—42no—
299C4×C61—41no—
300C4×C61—41no—
301C4×C61—81no—
302C4×C61—81no—
303C4×C61#52911yescharacteristic
304C4×C61#54211yescharacteristic
305C4×C61#55211yescharacteristic
306C4×C61#55911yescharacteristic
307Dic61—22no—
308Dic61—42no—
309Dic61—41no—
310Dic61—41no—
311Dic61—42no—
312Dic61—41no—
313Dic61—81no—
314#2445—611no—
315#2370—611no—
316#2088—611no—
317#2041—611no—
318#2025—611no—
319#2025—611no—
320#1982—611no—
321#1936D6111yescharacteristic, complemented
322#1926—611no—
323#1925—611no—
324#1925—611no—
325#1918—611no—
326#1917—611no—
327#1864—611no—
328#1762—611no—
329C2×C61—161no—
330C2×C61#245811yescharacteristic
331C2×C61#311511yescharacteristic
332C2×C61#311911yescharacteristic
333C2×C61#331011yescharacteristic
334C2×C61#332211yescharacteristic
335C2×C61#336611yescharacteristic
336C2×C61#337111yescharacteristic
337D61—82no—
338C2×#127—611no—
339C2×#125—611no—
340C2×#123—1221no—
341C2×C4×D4—611no—
342C2×#107—611no—
343C2×#106—611no—
344C2×C4⋊C8—611no—
345C2×#102—611no—
346C2×#102—611no—
347C2×#102—611no—
348C2×#102—611no—
349C2×#102—611no—
350C2×#102—611no—
351C2×#102C2×D6111yescharacteristic
352C2×#102C2×D6111yescharacteristic
353C2×#97C2×D6111yescharacteristic
354#394—1221no—
355#394—1221no—
356#390—611no—
357#390—611no—
358#390C2×D6111yescharacteristic
359#389—611no—
360#389—611no—
361#389—1221no—
362#389C2×D6111yescharacteristic
363#387—1221no—
364#387—1221no—
365#386—1221no—
366C4×C4⋊C4—611no—
367C4×C4⋊C4—611no—
368C4×C4⋊C4—611no—
369C4×C4⋊C4—611no—
370C4×C4⋊C4—1221no—
371#340—611no—
372#340—611no—
373#340—611no—
374#340—611no—
375#340C2×D6111yescharacteristic
376#340C2×D6111yescharacteristic
377#336—611no—
378#336—611no—
379#336—611no—
380#336—611no—
381C61#2671611yescharacteristic, complemented, Sylow
382C22×D4—611no—
383C22×D4—1221no—
384C22×D4—1221no—
385C22×D4C22×D6111yescharacteristic
386C23×C4—1221no—
387C22×C8—611no—
388C22×C8—611no—
389C22×C8C22×D6111yescharacteristic
390C22×C8C22×D6111yescharacteristic
391#127—1222no—
392#127—2441no—
393#125—1222no—
394#125—1222no—
395#123—2444no—
396C4×D4—1222no—
397C4×D4—2441no—
398C2×C4⋊C4—21no—
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⋊C4C22×D6111yescharacteristic
409C2×C4⋊C4C22×D6111yescharacteristic
410C2×C4⋊C4C22×D6111yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—1221no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C42—611no—
419C2×C42—611no—
420C2×C42—1221no—
421C2×C42—1221no—
422C2×C42—1221no—
423C2×C42C22×D6111yescharacteristic
424#107—1222no—
425#106—2441no—
426C4⋊C8—2441no—
427#102—22no—
428#102—41no—
429#102—1222no—
430#102—1222no—
431#102—1222no—
432#102—1222no—
433#102—1222no—
434#102—1222no—
435#97—41no—
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—1221no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—612no—
453C2×D4—1221no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—4881no—
459C2×D4—4881no—
460C2×D4—2442no—
461C2×D4—2442no—
462C2×D4—2442no—
463C2×D4—2442no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
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—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—42no—
498C4⋊C4—612no—
499C4⋊C4—612no—
500C4⋊C4—1222no—
501C4⋊C4—1224no—
502C4⋊C4—1224no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—4881no—
508C4⋊C4—2441no—
509C4⋊C4—2442no—
510C4⋊C4#1175822212yes—
511C22⋊C4—42no—
512C22⋊C4—81no—
513C22⋊C4—4881no—
514C22⋊C4—4881no—
515C22⋊C4—2442no—
516C22⋊C4—2442no—
517C22⋊C4—2442no—
518C42—21no—
519C42—21no—
520C42—1221no—
521C42—1221no—
522C42—1221no—
523C42—1221no—
524C42—4881no—
525C42—4881no—
526C42—2442no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—1222no—
535C23—2441no—
536C23—2441no—
537C23—2441no—
538C23—2441no—
539C23—2441no—
540C23—2441no—
541C23C2×D4×D6111yescharacteristic
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—1222no—
547D4—1222no—
548D4—4884no—
549D4—4884no—
550D4—2441no—
551D4—2441no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—612no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1222no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1222no—
581C2×C4—4884no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4#41×D6111yescharacteristic
590C2×C4#41×D6111yescharacteristic
591C2×C4#41×D6111yescharacteristic
592C2×C4C2×#1175822211yescharacteristic
593C2×C4#1451982211yescharacteristic
594C2×C4#1451982411yescharacteristic
595C8—41no—
596C8—41no—
597C8—2441no—
598C8—2441no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—4881no—
607C22—4881no—
608C22—4881no—
609C22—4881no—
610C22—2442no—
611C22—2442no—
612C22—2442no—
613C22#1684027111yescharacteristic
614C22#1684040111yescharacteristic
615C22#1684042011yescharacteristic
616C22AGL(1,ℤ/8)×D6111yescharacteristic
617C22#1684055811yescharacteristic
618C22#1684056611yescharacteristic
619C22#1684057111yescharacteristic
620C4—42no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—81no—
625C4—1222no—
626C4—4881no—
627C4—2442no—
628C4—2441no—
629C4—2441no—
630C4—2441no—
631C4—2442no—
632C4#1684029511yescharacteristic
633C4#1684038011yescharacteristic
634C4#1684045111yescharacteristic
635C4#1684049511yescharacteristic
636C2—161no—
637C2—4882no—
638C2#2144974711yescharacteristic
639C2#2145596611yescharacteristic
640C2#2145601611yescharacteristic
641C2#2145783511yescharacteristic
642C2#2145801511yescharacteristic
643C2#2145852311yescharacteristic
644C2#2145858611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1936C2
socleC23×C61C22×D4
prime radicalC2×#14519773C22
hypercenter#1936D61
hypocenterC61#26716
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
2. #21448914C2semidirect
3. #21447323C2semidirect
5. #21446964C2semidirect
6. #21446963C2semidirect
8. #21446449C2semidirect
9. #21446437C2semidirect
10. #21446436C2semidirect
11. #21446393C2semidirect
12. #21446383C2semidirect
13. #21446079C2semidirect
14. #21445645C2semidirect
15. C61×#1936C2semidirect
321. #1936D61semidirect
381. C61#26716semidirect

Maximal subgroups

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

subgroupindex
#214495852
#214489142
#214473232
#214470512
#214469642
#214469632
#214467442
#214464492
#214464372
#214464362
#214463932
#214463832
#214460792
#214456452
C61×#19362
#2671661