Finite Group Databasebeta

← #29779377

Subgroups — #29779377

Order 15616.

780 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#21450406C211yesmaximal, characteristic, complemented
2#21449663C211yesmaximal, characteristic, complemented
3#21447314C211yesmaximal, characteristic, complemented
4#21447225C211yesmaximal, characteristic, complemented
5#21447127C211yesmaximal, characteristic
6#21446953C211yesmaximal, characteristic, complemented
7#21446778C211yesmaximal, characteristic, complemented
8#21446686C211yesmaximal, characteristic
9#21446519C211yesmaximal, characteristic, complemented
10#21446518C211yesmaximal, characteristic, complemented
11#21446518C211yesmaximal, characteristic, complemented
12#21446412C211yesmaximal, characteristic, complemented
13#21445692C211yesmaximal, characteristic, complemented
14#21445644C211yesmaximal, characteristic, complemented
15C61×#1879C211yesmaximal, characteristic
16C2×#14519776C2211yescharacteristic
17C2×#14519770—21no—
18C2×#14519756—21no—
19C2×#14519711C2211yescharacteristic
20C2×#14519706C2211yescharacteristic
21C2×#14519698C2211yescharacteristic
22C2×#14519698C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519688C2211yescharacteristic
26C2×#14519687C2211yescharacteristic
27C2×C8×Dic61C2211yescharacteristic
28#16839690—21no—
29#16839685—21no—
30#16839685—21no—
31#16839674—21no—
32#16839665C2211yescharacteristic
33#16839665C2211yescharacteristic
34#16839665C2211yescharacteristic
35#16839665C2211yescharacteristic
36#16839661C2211yescharacteristic
37#16839661C2211yescharacteristic
38#16839660C2211yescharacteristic
39#16839650—21no—
40#16839635—21no—
41#16839631C2211yescharacteristic
42C4×#11758196C2211yescharacteristic
43C4×C4⋊Dic61C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52C22×D8×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×Dic122—21no—
60C22×#92418C2311yescharacteristic
61C22×#92418C2311yescharacteristic
62#14519776—22no—
63#14519776—41no—
64#14519770—44no—
65#14519756—44no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×#11758196—21no—
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×C22⋊Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61C2311yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89#14519711—22no—
90#14519706—22no—
91#14519698—22no—
92#14519698—22no—
93#14519698—22no—
94#14519698—41no—
95#14519688—41no—
96#14519687—22no—
97C8×Dic61—41no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684D411yescharacteristic
103#14519684D411yescharacteristic
104C22×D4×C61C2311yescharacteristic
105C22×D4×C61C2311yescharacteristic
106C23×C4×C61—21no—
107C2×D8×C61—22no—
108C2×D8×C61—22no—
109C2×D8×C61—41no—
110C22×C8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C4×D4×C61—22no—
113C4×D4×C61—41no—
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C42×C61C2311yescharacteristic
120#102×C61—22no—
121#102×C61—22no—
122C24×C61—21no—
123C24×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—21no—
135C2×D4×C61#4112yes—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—42no—
139C22×C4×C61—42no—
140C22×C4×C61—81no—
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2411yescharacteristic
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61C2×D411yescharacteristic
149C22×Dic61C2×D411yescharacteristic
150C22×Dic61C2×D411yescharacteristic
151C22×Dic61C2×D411yescharacteristic
152C2×Dic122—42no—
153C2×Dic122—42no—
154C2×Dic122—81no—
155D8×C61—44no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61#4112yes—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61#4112yes—
166C22⋊C4×C61—42no—
167C22⋊C4×C61—42no—
168C22⋊C4×C61—81no—
169C42×C61—21no—
170C42×C61—21no—
171C22⋊Dic61—42no—
172C22⋊Dic61—42no—
173C22⋊Dic61—42no—
174C22⋊Dic61—42no—
175C22⋊Dic61—42no—
176C22⋊Dic61—42no—
177C22⋊Dic61—81no—
178C22⋊Dic61—81no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—42no—
188C4⋊Dic61—42no—
189#11758196—22no—
190#11758196—22no—
191#11758196—42no—
192#11758196—42no—
193#11758196—42no—
194#11758196—81no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—42no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418#4112yes—
206C23×C61—22no—
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×C61—41no—
219C23×C61—41no—
220C23×C61C22×D411yescharacteristic
221D4×C61—22no—
222D4×C61—22no—
223D4×C61—41no—
224D4×C61—41no—
225D4×C61—41no—
226D4×C61—41no—
227D4×C61—41no—
228D4×C61—41no—
229C2×C4×C61—22no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
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×C61—41no—
241C2×C4×C61—84no—
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61H(5,𝔽2)11yescharacteristic
247C2×C4×C612−1+411yescharacteristic
248C2×Dic61—21no—
249C2×Dic61—21no—
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—41no—
259C2×Dic61—41no—
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×Dic61AGL(1,ℤ/8)12yes—
271C2×Dic61AGL(1,ℤ/8)12yes—
272Dic122—84no—
273C8×C61—22no—
274C8×C61—41no—
275#92418—22no—
276#92418—41no—
277#29095—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—81no—
286C22×C61—81no—
287C22×C61—81no—
288C22×C61—81no—
289C22×C61—81no—
290C22×C61—81no—
291C22×C61—81no—
292C22×C61#53211yescharacteristic
293C22×C61#54611yescharacteristic
294C22×C61#54811yescharacteristic
295C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
296C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C61#57611yescharacteristic
298C22×C61#57811yescharacteristic
299C4×C61—41no—
300C4×C61—42no—
301C4×C61—41no—
302C4×C61—81no—
303C4×C61#52911yescharacteristic
304C4×C61#53911yescharacteristic
305C4×C61#55111yescharacteristic
306C4×C61#55611yescharacteristic
307Dic61—22no—
308Dic61—22no—
309Dic61—41no—
310Dic61—41no—
311Dic61—81no—
312Dic61—81no—
313Dic61—81no—
314Dic61—81no—
315#2512—611no—
316#2452—611no—
317#2087—611no—
318#2071—611no—
319#2054—611no—
320#2023—611no—
321#1990—611no—
322#1970—611no—
323#1936—611no—
324#1936—611no—
325#1936—611no—
326#1921—611no—
327#1879D6111yescharacteristic
328#1771—611no—
329#1762—611no—
330C2×C61—82no—
331C2×C61—161no—
332C2×C61#256011yescharacteristic
333C2×C61#317511yescharacteristic
334C2×C61#318411yescharacteristic
335C2×C61#330811yescharacteristic
336C2×C61#331811yescharacteristic
337C2×C61#336611yescharacteristic
338C2×C61#336711yescharacteristic
339C22×D8C2×D6111yescharacteristic
340C2×C4⋊Q8—611no—
341C2×#126—1221no—
342C2×C22⋊Q8—1221no—
343C2×C4×D4C2×D6111yescharacteristic
344C2×#107—611no—
345C2×C4⋊C8—611no—
346C2×#102—611no—
347C2×#102—611no—
348C2×#102—611no—
349C2×#102—611no—
350C2×#102C2×D6111yescharacteristic
351C2×#102C2×D6111yescharacteristic
352C2×#97—611no—
353C2×#97—611no—
354C2×C4×C8—611no—
355#397—1221no—
356#396—1221no—
357#396—1221no—
358#393—1221no—
359#390—611no—
360#390—611no—
361#390—611no—
362#390—611no—
363#390C2×D6111yescharacteristic
364#389—611no—
365#389—611no—
366#389—611no—
367#388—1221no—
368#385—1221no—
369#384—611no—
370C4×C4⋊C4—611no—
371C4×C4⋊C4—611no—
372#340—611no—
373#340—611no—
374#340—611no—
375#340—611no—
376#340—611no—
377#340—611no—
378#340—611no—
379#340C2×D6111yescharacteristic
380#336—611no—
381#336C2×D6111yescharacteristic
382C61#2909511yescharacteristic, complemented, Sylow
383C22×Q8—1221no—
384C22×D4C22×D6111yescharacteristic
385C22×D4C22×D6111yescharacteristic
386C23×C4—21no—
387C2×D8—22no—
388C2×D8—22no—
389C2×D8—41no—
390C22×C8—611no—
391C22×C8—611no—
392C22×C8C22×D6111yescharacteristic
393C22×C8C22×D6111yescharacteristic
394C4⋊Q8—1222no—
395C4⋊Q8—2441no—
396#126—2444no—
397C22⋊Q8—2444no—
398C4×D4—22no—
399C4×D4—41no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4C22×D6111yescharacteristic
413C2×C4⋊C4C22×D6111yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—1221no—
418C2×C22⋊C4—1221no—
419C2×C22⋊C4—1221no—
420C2×C22⋊C4—1221no—
421C2×C22⋊C4—1221no—
422C2×C22⋊C4—1221no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—1221no—
428C2×C42C22×D6111yescharacteristic
429#107—1222no—
430C4⋊C8—1222no—
431#102—22no—
432#102—22no—
433#102—1222no—
434#102—1222no—
435#102—1222no—
436#102—2441no—
437#97—1222no—
438#97—2441no—
439C4×C8—2441no—
440#95—611no—
441#95—611no—
442#95—1221no—
443#95—1221no—
444#95—1221no—
445#95—1221no—
446C24—21no—
447C24—21no—
448C2×Q8—4881no—
449C2×Q8—2442no—
450C2×Q8—2442no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4#1175822412yes—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—81no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4D4×D6111yescharacteristic
477C22×C4D4×D6111yescharacteristic
478C22×C4C23×D6111yescharacteristic
479D8—44no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—612no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8#1175822212yes—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—1222no—
496C4⋊C4—1222no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—4881no—
506C4⋊C4—2442no—
507C4⋊C4—2442no—
508C4⋊C4—2442no—
509C4⋊C4—2442no—
510C4⋊C4—2442no—
511C4⋊C4#1175822412yes—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—81no—
515C22⋊C4—4881no—
516C22⋊C4—4881no—
517C22⋊C4—2442no—
518C22⋊C4—2442no—
519C22⋊C4—2442no—
520C22⋊C4—2442no—
521C22⋊C4—2442no—
522C22⋊C4—2442no—
523C42—21no—
524C42—21no—
525C42—1221no—
526C42—1221no—
527C42—1221no—
528C42—1221no—
529C42—2442no—
530C23—22no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23C2×D4×D6111yescharacteristic
545Q8—4884no—
546D4—22no—
547D4—22no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—84no—
567C2×C4—612no—
568C2×C4—612no—
569C2×C4—1221no—
570C2×C4—1221no—
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—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—2441no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4#41×D6111yescharacteristic
592C2×C4C2×#1175822411yescharacteristic
593C2×C4C2×#1175822411yescharacteristic
594C2×C4C2×#1175822211yescharacteristic
595C2×C4#1451982211yescharacteristic
596C2×C4#1451982411yescharacteristic
597C8—22no—
598C8—41no—
599C8—1222no—
600C8—2441no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22#1684030911yescharacteristic
616C22#1684039911yescharacteristic
617C22#1684041811yescharacteristic
618C22AGL(1,ℤ/8)×D6111yescharacteristic
619C22AGL(1,ℤ/8)×D6111yescharacteristic
620C22#1684056311yescharacteristic
621C22#1684057611yescharacteristic
622C4—41no—
623C4—42no—
624C4—41no—
625C4—81no—
626C4—1222no—
627C4—1222no—
628C4—4881no—
629C4—4881no—
630C4—4881no—
631C4—4881no—
632C4—2441no—
633C4—2441no—
634C4#1684029311yescharacteristic
635C4#1684035511yescharacteristic
636C4#1684043811yescharacteristic
637C4#1684048211yescharacteristic
638C2—82no—
639C2—161no—
640C2#2145096711yescharacteristic
641C2#2145645411yescharacteristic
642C2#2145655411yescharacteristic
643C2#2145780311yescharacteristic
644C2#2145795311yescharacteristic
645C2#2145852111yescharacteristic
646C2#2145853211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1879C2
socleC23×C61C22×D4
prime radicalC22×D8×C61C22
hypercenter#1879D61
hypocenterC61#29095
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
1. #21450406C2semidirect
2. #21449663C2semidirect
3. #21447314C2semidirect
4. #21447225C2semidirect
6. #21446953C2semidirect
7. #21446778C2semidirect
9. #21446519C2semidirect
10. #21446518C2semidirect
11. #21446518C2semidirect
12. #21446412C2semidirect
13. #21445692C2semidirect
14. #21445644C2semidirect
382. C61#29095semidirect

Maximal subgroups

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

subgroupindex
#214504062
#214496632
#214473142
#214472252
#214471272
#214469532
#214467782
#214466862
#214465192
#214465182
#214464122
#214456922
#214456442
C61×#18792
#2909561