Finite Group Databasebeta

← #29779374

Subgroups — #29779374

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#21450401C211yesmaximal, characteristic, complemented
2#21449671C211yesmaximal, characteristic, complemented
3#21447316C211yesmaximal, characteristic, complemented
4#21447128C211yesmaximal, characteristic
5#21446956C211yesmaximal, characteristic, complemented
6#21446779C211yesmaximal, characteristic, complemented
7#21446684C211yesmaximal, characteristic
8#21446518C211yesmaximal, characteristic, complemented
9#21446517C211yesmaximal, characteristic, complemented
10#21446514C211yesmaximal, characteristic, complemented
11#21446414C211yesmaximal, characteristic, complemented
12#21446165C211yesmaximal, characteristic
13#21445690C211yesmaximal, characteristic, complemented
14#21445646C211yesmaximal, characteristic, complemented
15C61×#2071C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×#14519777C2211yescharacteristic
18C2×#14519772—21no—
19C2×#14519754—21no—
20C2×D4×Dic61C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519687C2211yescharacteristic
28C2×#14519687C2211yescharacteristic
29C2×C4×#92418C2211yescharacteristic
30#16839688—21no—
31#16839685—21no—
32#16839684—21no—
33#16839674—21no—
34#16839665C2211yescharacteristic
35#16839664C2211yescharacteristic
36#16839663C2211yescharacteristic
37#16839663C2211yescharacteristic
38#16839661C2211yescharacteristic
39#16839661C2211yescharacteristic
40#16839658C2211yescharacteristic
41#16839652—21no—
42#16839637—21no—
43C4⋊C4×Dic61C2211yescharacteristic
44C4×#11758196C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#102×C61C2211yescharacteristic
53C2×#102×C61C2211yescharacteristic
54C61×#390C2211yescharacteristic
55C61×#384C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×Dic122—21no—
60C22×D244C2311yescharacteristic
61C23×Dic61—21no—
62C2×#11758199—22no—
63C2×#11758199—22no—
64C2×#11758199—41no—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519777—22no—
68#14519777—41no—
69#14519772—44no—
70#14519754—44no—
71D4×Dic61—22no—
72D4×Dic61—41no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×#11758196—21no—
80C2×#11758196D411yescharacteristic
81C2×#11758196D411yescharacteristic
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61C2311yescharacteristic
93C2×C4×Dic61C2311yescharacteristic
94#14519710—22no—
95#14519706—22no—
96#14519699—22no—
97#14519699—41no—
98#14519698—22no—
99#14519697—22no—
100#14519687—22no—
101#14519687—41no—
102C4×#92418—41no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684D411yescharacteristic
108#14519684D411yescharacteristic
109C22×D4×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C42×C61C2311yescharacteristic
120#102×C61—22no—
121#102×C61—22no—
122C24×C61—21no—
123C23×D61—21no—
124C2×D4×C61—21no—
125C2×D4×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—21no—
129C2×D4×C61#4112yes—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2411yescharacteristic
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—42no—
140C22×Dic61—42no—
141C22×Dic61—81no—
142C22×Dic61C2×D411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144C22×Dic61C2×D411yescharacteristic
145C22×Dic61C2×D411yescharacteristic
146C2×D244—21no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244—21no—
150C2×D244—21no—
151C2×D244—21no—
152C2×Dic122—42no—
153C2×Dic122—42no—
154C2×Dic122—81no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—42no—
168C4⋊C4×C61—81no—
169C22⋊C4×C61—42no—
170C22⋊C4×C61—42no—
171C42×C61—21no—
172C42×C61—21no—
173C22⋊Dic61—42no—
174C22⋊Dic61—42no—
175C22⋊Dic61—81no—
176#11758199—44no—
177#11758198—42no—
178#11758198—42no—
179#11758198—42no—
180#11758198—42no—
181#11758198—81no—
182#11758198—81no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—42no—
189C4⋊Dic61—42no—
190C4⋊Dic61—42no—
191C4⋊Dic61#4112yes—
192#11758196—22no—
193#11758196—22no—
194#11758196—42no—
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#4112yes—
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×C61C22×D411yescharacteristic
214C22×D61—41no—
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—41no—
218C22×D61—41no—
219C22×D61—41no—
220C22×D61—41no—
221D4×C61—22no—
222D4×C61—22no—
223D4×C61—41no—
224D4×C61—41no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—41no—
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×C61AGL(1,ℤ/8)12yes—
239C2×C4×C61AGL(1,ℤ/8)12yes—
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61H(5,𝔽2)11yescharacteristic
245C2×C4×C612−1+411yescharacteristic
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—22no—
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—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—84no—
268D244—41no—
269D244—41no—
270D244—41no—
271D244—41no—
272Dic122—84no—
273C8×C61—41no—
274C8×C61—41no—
275#92418—22no—
276#92418—22no—
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#53211yescharacteristic
286C22×C61#54611yescharacteristic
287C22×C61#54811yescharacteristic
288C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C61#57611yescharacteristic
291C22×C61#57811yescharacteristic
292C2×D61—81no—
293C2×D61—81no—
294C2×D61—81no—
295C2×D61—81no—
296C2×D61—81no—
297C2×D61—81no—
298C2×D61—81no—
299C4×C61—22no—
300C4×C61—22no—
301C4×C61—81no—
302C4×C61—81no—
303C4×C61—81no—
304C4×C61#52911yescharacteristic
305C4×C61#53911yescharacteristic
306C4×C61#55111yescharacteristic
307C4×C61#55611yescharacteristic
308Dic61—41no—
309Dic61—41no—
310Dic61—41no—
311Dic61—42no—
312Dic61—41no—
313Dic61—81no—
314Dic61—81no—
315#2512—611no—
316#2452—611no—
317#2087—611no—
318#2071D6111yescharacteristic, complemented
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#1879—611no—
328#1771—611no—
329#1762—611no—
330C2×C61—82no—
331C2×C61#256011yescharacteristic
332C2×C61#317511yescharacteristic
333C2×C61#318411yescharacteristic
334C2×C61#330811yescharacteristic
335C2×C61#331811yescharacteristic
336C2×C61#336611yescharacteristic
337C2×C61#336711yescharacteristic
338D61—161no—
339C22×D8—611no—
340C2×C4⋊Q8—611no—
341C2×#126—1221no—
342C2×C22⋊Q8—1221no—
343C2×C4×D4—611no—
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#384C2×D6111yescharacteristic
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#340C2×D6111yescharacteristic
379#340C2×D6111yescharacteristic
380#336—611no—
381#336C2×D6111yescharacteristic
382C61#2909511yescharacteristic, complemented, Sylow
383C22×Q8—1221no—
384C22×D4—611no—
385C22×D4C22×D6111yescharacteristic
386C23×C4—1221no—
387C2×D8—1222no—
388C2×D8—1222no—
389C2×D8—2441no—
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—1222no—
399C4×D4—2441no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—611no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4C22×D6111yescharacteristic
412C2×C4⋊C4C22×D6111yescharacteristic
413C2×C4⋊C4C22×D6111yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—1221no—
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—1221no—
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—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—1221no—
460C2×D4—1221no—
461C2×D4—1221no—
462C2×D4#1175822412yes—
463C22×C4—21no—
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—4881no—
474C22×C4—2442no—
475C22×C4—2442no—
476C22×C4D4×D6111yescharacteristic
477C22×C4D4×D6111yescharacteristic
478C22×C4C23×D6111yescharacteristic
479D8—2444no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—612no—
487C2×C8—612no—
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—21no—
498C4⋊C4—42no—
499C4⋊C4—81no—
500C4⋊C4—612no—
501C4⋊C4—1221no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—1221no—
508C4⋊C4—2442no—
509C4⋊C4—2442no—
510C4⋊C4—2442no—
511C4⋊C4—2442no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—4881no—
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—2441no—
538C23—2441no—
539C23—2441no—
540C23—2441no—
541C23—2441no—
542C23—2441no—
543C23—2441no—
544C23C2×D4×D6111yescharacteristic
545Q8—4884no—
546D4—22no—
547D4—22no—
548D4—41no—
549D4—41no—
550D4—2441no—
551D4—2441no—
552D4—2441no—
553D4—2441no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
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—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—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1222no—
580C2×C4—4884no—
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#1451980112yes—
590C2×C4#1451980412yes—
591C2×C4#41×D6111yescharacteristic
592C2×C4#41×D6111yescharacteristic
593C2×C4#41×D6111yescharacteristic
594C2×C4C2×#1175822411yescharacteristic
595C2×C4#1451982311yescharacteristic
596C2×C4#1451982411yescharacteristic
597C8—41no—
598C8—41no—
599C8—1222no—
600C8—1222no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—4881no—
609C22—4881no—
610C22—4881no—
611C22—4881no—
612C22—4881no—
613C22—4881no—
614C22—4881no—
615C22#1684031111yescharacteristic
616C22#1684040411yescharacteristic
617C22#1684041811yescharacteristic
618C22C2×#1451980111yescharacteristic
619C22C2×#1451980411yescharacteristic
620C22#1684056611yescharacteristic
621C22#1684057811yescharacteristic
622C4—22no—
623C4—22no—
624C4—81no—
625C4—81no—
626C4—81no—
627C4—4881no—
628C4—4881no—
629C4—2441no—
630C4—2442no—
631C4—2441no—
632C4—2441no—
633C4—2441no—
634C4#1684028911yescharacteristic
635C4#1684035311yescharacteristic
636C4#1684043511yescharacteristic
637C4#1684047911yescharacteristic
638C2—82no—
639C2—9761no—
640C2#2145096411yescharacteristic
641C2#2145645711yescharacteristic
642C2#2145655611yescharacteristic
643C2#2145780811yescharacteristic
644C2#2145795811yescharacteristic
645C2#2145853011yescharacteristic
646C2#2145854111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2071C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenter#2071D61
hypocenterC61#29095
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2071

Complements

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

NH ≅ G/Ntype
1. #21450401C2semidirect
2. #21449671C2semidirect
3. #21447316C2semidirect
5. #21446956C2semidirect
6. #21446779C2semidirect
8. #21446518C2semidirect
9. #21446517C2semidirect
10. #21446514C2semidirect
11. #21446414C2semidirect
13. #21445690C2semidirect
14. #21445646C2semidirect
15. C61×#2071C2semidirect
318. #2071D61semidirect
382. C61#29095semidirect

Maximal subgroups

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

subgroupindex
#214504012
#214496712
#214473162
#214471282
#214469562
#214467792
#214466842
#214465182
#214465172
#214465142
#214464142
#214461652
#214456902
#214456462
C61×#20712
#2909561