Finite Group Databasebeta

← #29748544

Subgroups — #29748544

Order 15616.

804 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450353C211yesmaximal, characteristic, complemented
2#21448881C211yesmaximal, characteristic
3#21447233C211yesmaximal, characteristic, complemented
4#21447206C211yesmaximal, characteristic, complemented
5#21447051C211yesmaximal, characteristic
6#21447051C211yesmaximal, characteristic
7#21446504C211yesmaximal, characteristic, complemented
8#21446441C211yesmaximal, characteristic, complemented
9#21446410C211yesmaximal, characteristic, complemented
10#21446395C211yesmaximal, characteristic, complemented
11#21446373C211yesmaximal, characteristic, complemented
12#21446081C211yesmaximal, characteristic, complemented
13#21446080C211yesmaximal, characteristic, complemented
14#21445633C211yesmaximal, characteristic, complemented
15C61×#1804C211yesmaximal, characteristic, complemented
16C2×#14519773C2211yescharacteristic
17C2×#14519739C2211yescharacteristic
18C2×C4×C22⋊D61—21no—
19C2×#14519711C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21C2×#14519699C2211yescharacteristic
22C2×#14519699C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×C8×Dic61C2211yescharacteristic
28#16839702—21no—
29#16839696—21no—
30#16839665C2211yescharacteristic
31#16839664C2211yescharacteristic
32#16839662—21no—
33#16839661C2211yescharacteristic
34#16839660C2211yescharacteristic
35#16839658C2211yescharacteristic
36#16839658C2211yescharacteristic
37#16839644—21no—
38#16839641—21no—
39#16839638—21no—
40#16839626—21no—
41C4⋊C4×Dic61C2211yescharacteristic
42C4⋊C4×Dic61C2211yescharacteristic
43C4×#11758196C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C2×C4⋊C8×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C61×#382C2211yescharacteristic
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—22no—
67#14519739—22no—
68#14519739—41no—
69C4×C22⋊D61—44no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196D411yescharacteristic
78C2×#11758196D411yescharacteristic
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61C2311yescharacteristic
87C2×C4×Dic61C2311yescharacteristic
88#14519711—22no—
89#14519708—22no—
90#14519699—22no—
91#14519699—41no—
92#14519698—22no—
93#14519698—41no—
94#14519697—22no—
95#14519697—22no—
96C8×Dic61—41no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684D411yescharacteristic
104#14519684D411yescharacteristic
105C22×D4×C61C2311yescharacteristic
106C23×C4×C61—21no—
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C4×D4×C61—22no—
110C4×D4×C61—41no—
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C22⋊C4×C61—21no—
115C2×C42×C61C2311yescharacteristic
116C4⋊C8×C61—41no—
117#102×C61—22no—
118#102×C61—22no—
119#95×C61—21no—
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#4112yes—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—42no—
133C22×C4×C61—42no—
134C22×C4×C61—81no—
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C2×C22⋊D61—24no—
139C2×C22⋊D61—24no—
140C2×C22⋊D61—42no—
141C2×C22⋊D61—42no—
142C2×C22⋊D61—81no—
143C2×C22⋊D61—81no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
149C22×Dic61C2×D411yescharacteristic
150C22×Dic61C2×D411yescharacteristic
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244#4112yes—
157C2×C4×D61—42no—
158C2×C4×D61—42no—
159C2×C4×D61—81no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61#4112yes—
172C22⋊C4×C61—42no—
173C42×C61—21no—
174C42×C61—21no—
175C22⋊Dic61—42no—
176C22⋊Dic61—81no—
177#11758198—42no—
178#11758198—42no—
179#11758198—81no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—81no—
186C4⋊Dic61#4112yes—
187#11758196—22no—
188#11758196—22no—
189#11758196—42no—
190#11758196—81no—
191#11758196—81no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—42no—
197C4×Dic61—42no—
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×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—22no—
220D4×C61—22no—
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×C61—84no—
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61H(5,𝔽2)11yescharacteristic
244C2×C4×C612−1+411yescharacteristic
245C22⋊D61—48no—
246C22⋊D61—84no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—22no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61#13512yes—
267C2×Dic61AGL(1,ℤ/8)12yes—
268D244—22no—
269D244—22no—
270D244—41no—
271D244—41no—
272C4×D61—84no—
273C8×C61—41no—
274C8×C61—41no—
275#92418—41no—
276#92418—41no—
277#26753—611nomaximal, Sylow
278C22×C61—42no—
279C22×C61—42no—
280C22×C61—42no—
281C22×C61—81no—
282C22×C61—81no—
283C22×C61—81no—
284C22×C61—81no—
285C22×C61#52511yescharacteristic
286C22×C61#54611yescharacteristic
287C22×C61#54811yescharacteristic
288C22×C61C2×#13511yescharacteristic
289C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C61#57611yescharacteristic
291C22×C61#57711yescharacteristic
292C2×D61—42no—
293C2×D61—42no—
294C2×D61—42no—
295C2×D61—81no—
296C2×D61—81no—
297C2×D61—81no—
298C2×D61—81no—
299C4×C61—41no—
300C4×C61—42no—
301C4×C61—41no—
302C4×C61—81no—
303C4×C61—81no—
304C4×C61#52911yescharacteristic
305C4×C61#53911yescharacteristic
306C4×C61#55211yescharacteristic
307C4×C61#55311yescharacteristic
308Dic61—22no—
309Dic61—22no—
310Dic61—42no—
311Dic61—41no—
312Dic61—41no—
313Dic61—81no—
314Dic61—81no—
315#2508—611no—
316#2366—611no—
317#2073—611no—
318#2067—611no—
319#2041—611no—
320#2041—611no—
321#1934—611no—
322#1925—611no—
323#1921—611no—
324#1919—611no—
325#1916—611no—
326#1864—611no—
327#1864—611no—
328#1804D6111yescharacteristic, complemented
329C4×#102—611no—
330C2×C61—82no—
331C2×C61#246011yescharacteristic
332C2×C61#310511yescharacteristic
333C2×C61#311811yescharacteristic
334C2×C61#330511yescharacteristic
335C2×C61#331011yescharacteristic
336C2×C61#336511yescharacteristic
337C2×C61#336611yescharacteristic
338D61—82no—
339C2×#127—611no—
340C2×C4×D4—611no—
341C2×C4×D4—1221no—
342C2×C4×D4C2×D6111yescharacteristic
343C2×#107—611no—
344C2×#106—611no—
345C2×C4⋊C8C2×D6111yescharacteristic
346C2×#102—611no—
347C2×#102—611no—
348C2×#102—611no—
349C2×#102—611no—
350C2×#102—611no—
351C2×#102—611no—
352C2×#102C2×D6111yescharacteristic
353C2×#102C2×D6111yescharacteristic
354C2×C4×C8—611no—
355#400—1221no—
356#398—1221no—
357#390—611no—
358#390—611no—
359#390—1221no—
360#389—611no—
361#389—611no—
362#389—611no—
363#389—611no—
364#387—1221no—
365#386—1221no—
366#386—1221no—
367#382—1221no—
368#382C2×D6111yescharacteristic
369C4×C4⋊C4—611no—
370C4×C4⋊C4—611no—
371C4×C4⋊C4—611no—
372#340—611no—
373#340—611no—
374#340—611no—
375#340—611no—
376#340C2×D6111yescharacteristic
377#340C2×D6111yescharacteristic
378#336—611no—
379#336—611no—
380#336—611no—
381#336—611no—
382C61#2675311yescharacteristic, complemented, Sylow
383C22×D4—611no—
384C22×D4—1221no—
385C22×D4—1221no—
386C22×D4C22×D6111yescharacteristic
387C23×C4—21no—
388C23×C4—1221no—
389C22×C8—611no—
390C22×C8—611no—
391C22×C8C22×D6111yescharacteristic
392C22×C8C22×D6111yescharacteristic
393#127—1222no—
394#127—1222no—
395C4×D4—22no—
396C4×D4—41no—
397C4×D4—1222no—
398C4×D4—2441no—
399C4×D4—2444no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—611no—
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×C4⋊C4C22×D6111yescharacteristic
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×C42C22×D6111yescharacteristic
423#107—1222no—
424#106—1222no—
425C4⋊C8—41no—
426#102—22no—
427#102—22no—
428#102—1222no—
429#102—1222no—
430#102—1222no—
431#102—1222no—
432#102—2441no—
433#102—2441no—
434C4×C8—2441no—
435#95—21no—
436#95—21no—
437#95—611no—
438#95—611no—
439#95—1221no—
440#95—1221no—
441#95—1221no—
442#95—1221no—
443#95—1221no—
444#95—1221no—
445C24—21no—
446C24—1221no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—612no—
453C2×D4—1224no—
454C2×D4—1224no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—1221no—
460C2×D4—4881no—
461C2×D4—4881no—
462C2×D4—2442no—
463C2×D4—2442no—
464C2×D4#1175822412yes—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—81no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—4881no—
479C22×C4—2442no—
480C22×C4—2442no—
481C22×C4D4×D6111yescharacteristic
482C22×C4D4×D6111yescharacteristic
483C22×C4C23×D6111yescharacteristic
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—612no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—1221no—
508C4⋊C4—1221no—
509C4⋊C4—4881no—
510C4⋊C4—4881no—
511C4⋊C4—4881no—
512C4⋊C4—2442no—
513C4⋊C4#1175822212yes—
514C22⋊C4—42no—
515C22⋊C4—4881no—
516C22⋊C4—4881no—
517C22⋊C4—2442no—
518C22⋊C4—2442no—
519C22⋊C4—2442no—
520C42—21no—
521C42—21no—
522C42—1221no—
523C42—1221no—
524C42—1221no—
525C42—1221no—
526C42—2442no—
527C42—2442no—
528C23—22no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—1222no—
536C23—2441no—
537C23—2441no—
538C23—2441no—
539C23—2441no—
540C23—2441no—
541C23—2441no—
542C23C2×D4×D6111yescharacteristic
543D4—22no—
544D4—22no—
545D4—41no—
546D4—41no—
547D4—1222no—
548D4—1222no—
549D4—4884no—
550D4—2448no—
551D4—2441no—
552D4—2441no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—84no—
569C2×C4—612no—
570C2×C4—612no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—1222no—
582C2×C4—4884no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4#41×D6111yescharacteristic
592C2×C4#41×D6111yescharacteristic
593C2×C4C2×#1175822411yescharacteristic
594C2×C4C2×#1175822211yescharacteristic
595C2×C4#1451982211yescharacteristic
596C2×C4#1451982511yescharacteristic
597C8—41no—
598C8—41no—
599C8—2441no—
600C8—2441no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—4881no—
609C22—4881no—
610C22—4881no—
611C22—4881no—
612C22—2442no—
613C22—2442no—
614C22—2442no—
615C22#1684027211yescharacteristic
616C22#1684040211yescharacteristic
617C22#1684042211yescharacteristic
618C22#135×D6111yescharacteristic
619C22AGL(1,ℤ/8)×D6111yescharacteristic
620C22#1684056411yescharacteristic
621C22#1684057211yescharacteristic
622C4—41no—
623C4—41no—
624C4—42no—
625C4—81no—
626C4—81no—
627C4—1222no—
628C4—1222no—
629C4—4881no—
630C4—4881no—
631C4—2442no—
632C4—2441no—
633C4—2441no—
634C4#1684029011yescharacteristic
635C4#1684035811yescharacteristic
636C4#1684044711yescharacteristic
637C4#1684045511yescharacteristic
638C2—82no—
639C2—4882no—
640C2#2144977611yescharacteristic
641C2#2145586511yescharacteristic
642C2#2145600011yescharacteristic
643C2#2145776511yescharacteristic
644C2#2145784111yescharacteristic
645C2#2145851811yescharacteristic
646C2#2145852911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1804C2
socleC23×C61C22×D4
prime radicalC2×#14519773C22
hypercenter#1804D61
hypocenterC61#26753
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
1. #21450353C2semidirect
3. #21447233C2semidirect
4. #21447206C2semidirect
7. #21446504C2semidirect
8. #21446441C2semidirect
9. #21446410C2semidirect
10. #21446395C2semidirect
11. #21446373C2semidirect
12. #21446081C2semidirect
13. #21446080C2semidirect
14. #21445633C2semidirect
15. C61×#1804C2semidirect
328. #1804D61semidirect
382. C61#26753semidirect

Maximal subgroups

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

subgroupindex
#214503532
#214488812
#214472332
#214472062
#214470512
#214465042
#214464412
#214464102
#214463952
#214463732
#214460812
#214460802
#214456332
C61×#18042
#2675361