Finite Group Databasebeta

← #29710865

Subgroups — #29710865

Order 15616.

794 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#21448556C211yesmaximal, characteristic, complemented
2#21448541C211yesmaximal, characteristic
3#21447391C211yesmaximal, characteristic, complemented
4#21447390C211yesmaximal, characteristic, complemented
5#21447226C211yesmaximal, characteristic, complemented
6#21447225C211yesmaximal, characteristic, complemented
7#21447052C211yesmaximal, characteristic
8#21447051C211yesmaximal, characteristic
9#21446964C211yesmaximal, characteristic, complemented
10#21446963C211yesmaximal, characteristic, complemented
11#21445645C211yesmaximal, characteristic, complemented
12C4×#14519697C211yesmaximal, characteristic, complemented
13C4×#14519698C211yesmaximal, characteristic, complemented
14#21445572C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C2×#14519773C2211yescharacteristic
17C2×#14519768C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519699C2211yescharacteristic
20C2×#14519699C2211yescharacteristic
21C2×#14519698C2211yescharacteristic
22C2×#14519698C2211yescharacteristic
23C2×#14519697C2211yescharacteristic
24C2×#14519697C2211yescharacteristic
25C2×C4×#92418C2211yescharacteristic
26#16839665C2211yescharacteristic
27#16839663C2211yescharacteristic
28#16839661C2211yescharacteristic
29#16839660—21no—
30#16839659—21no—
31#16839658C2211yescharacteristic
32#16839646—21no—
33#16839645—21no—
34#16839641—21no—
35#16839641—21no—
36#16839638—21no—
37#16839638—21no—
38#16839631C2211yescharacteristic
39#16839627C2211yescharacteristic
40C4×C4⋊Dic61C2211yescharacteristic
41#16839608C2211yescharacteristic
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C2×#102×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#97×C61C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
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#14519768—22no—
68#14519768—22no—
69C4×D244—22no—
70C4×D244—22no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61C2311yescharacteristic
87C2×C4×Dic61C2311yescharacteristic
88#14519699—22no—
89#14519699—22no—
90#14519698—22no—
91#14519698—22no—
92#14519697—22no—
93#14519697—22no—
94C4×#92418—22no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684D411yescharacteristic
101#14519684D411yescharacteristic
102#14519684D411yescharacteristic
103#14519684D411yescharacteristic
104C22×D4×C61C2311yescharacteristic
105C23×C4×C61—21no—
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C4×D4×C61—22no—
109C4×D4×C61—22no—
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C22⋊C4×C61—21no—
114C2×C42×C61—21no—
115C2×C42×C61C2311yescharacteristic
116#102×C61—22no—
117#102×C61—22no—
118#97×C61—22no—
119#95×C61—21no—
120C24×C61—21no—
121C23×D61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61#4112yes—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—42no—
132C22×C4×C61—81no—
133C22×C4×C61—81no—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2411yescharacteristic
137C2×C22⋊D61—24no—
138C2×C22⋊D61—24no—
139C2×C22⋊D61—81no—
140C2×C22⋊D61—81no—
141C2×C22⋊D61—81no—
142C2×C22⋊D61—81no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61C2×D411yescharacteristic
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
149C22×Dic61C2×D411yescharacteristic
150C2×D244—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244#4112yes—
156C2×C4×D61—42no—
157C2×C4×D61—81no—
158C2×C4×D61—81no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61#4112yes—
171C22⋊C4×C61—42no—
172C42×C61—81no—
173C42×C61#4112yes—
174C42×C61#4112yes—
175C22⋊Dic61—81no—
176C22⋊Dic61—81no—
177#11758198—42no—
178#11758198—81no—
179#11758198—81no—
180C4⋊Dic61—24no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—81no—
187C4⋊Dic61#4112yes—
188#11758196—24no—
189#11758196—81no—
190#11758196—81no—
191#11758196—81no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—81no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C23×C61—22no—
204C23×C61—41no—
205C23×C61—41no—
206C23×C61—41no—
207C23×C61—41no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61C22×D411yescharacteristic
211C22×D61—22no—
212C22×D61—41no—
213C22×D61—41no—
214C22×D61—41no—
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—41no—
218D4×C61—22no—
219D4×C61—22no—
220D4×C61—41no—
221D4×C61—41no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—22no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
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—84no—
236C2×C4×C61#12412yes—
237C2×C4×C61#12412yes—
238C2×C4×C61C2×#4111yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
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—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—
267D244—22no—
268D244—22no—
269D244—41no—
270D244—41no—
271C4×D61—84no—
272C8×C61—41no—
273C8×C61—41no—
274#92418—41no—
275#92418—41no—
276#23830—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#52511yescharacteristic
285C22×C61#52511yescharacteristic
286C22×C61C2×#12411yescharacteristic
287C22×C61#57611yescharacteristic
288C22×C61#57611yescharacteristic
289C22×C61#57711yescharacteristic
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—22no—
299C4×C61—22no—
300C4×C61—42no—
301C4×C61—81no—
302C4×C61—81no—
303C4×C61#52911yescharacteristic
304C4×C61#52911yescharacteristic
305C4×C61#52911yescharacteristic
306C4×C61#52911yescharacteristic
307Dic61—41no—
308Dic61—41no—
309Dic61—42no—
310Dic61—41no—
311Dic61—41no—
312Dic61—81no—
313Dic61—81no—
314#2330—611no—
315#2328—611no—
316#2101—611no—
317#2101—611no—
318#2071—611no—
319#2071—611no—
320#2041—611no—
321#2041—611no—
322#2025—611no—
323#2025—611no—
324#1762—611no—
325#1762D6111yescharacteristic, complemented
326C4×#102—611no—
327C4×#102—611no—
328#1746—611no—
329C2×C61—82no—
330C2×C61#239811yescharacteristic
331C2×C61#311911yescharacteristic
332C2×C61#311911yescharacteristic
333C2×C61#312211yescharacteristic
334C2×C61#312311yescharacteristic
335C2×C61#313611yescharacteristic
336C2×C61#313611yescharacteristic
337D61—82no—
338C2×#127—611no—
339C2×#125—611no—
340C2×C4×D4—611no—
341C2×C4×D4C2×D6111yescharacteristic
342C2×#102—611no—
343C2×#102—611no—
344C2×#102—611no—
345C2×#102—611no—
346C2×#102—611no—
347C2×#102—611no—
348C2×#102C2×D6111yescharacteristic
349C2×#102C2×D6111yescharacteristic
350C2×#97C2×D6111yescharacteristic
351C2×C4×C8—611no—
352#390—611no—
353#390—611no—
354#389—611no—
355#389—611no—
356#389—1221no—
357#389—1221no—
358#387—1221no—
359#387—1221no—
360#386—1221no—
361#386—1221no—
362#386—1221no—
363#386—1221no—
364#384—611no—
365#382—611no—
366C4×C4⋊C4—611no—
367C4×C4⋊C4C2×D6111yescharacteristic
368#376—611no—
369#340—611no—
370#340—611no—
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#2383011yescharacteristic, complemented, Sylow
382C22×D4—611no—
383C22×D4—1221no—
384C22×D4—1221no—
385C22×D4C22×D6111yescharacteristic
386C23×C4—21no—
387C23×C4—1221no—
388C22×C8—611no—
389C22×C8—611no—
390C22×C8C22×D6111yescharacteristic
391C22×C8C22×D6111yescharacteristic
392#127—1222no—
393#127—1222no—
394#125—1222no—
395#125—1222no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—1222no—
399C4×D4—1222no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—1221no—
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×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—21no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—1221no—
422C2×C42C22×D6111yescharacteristic
423#102—22no—
424#102—22no—
425#102—1222no—
426#102—1222no—
427#102—1222no—
428#102—1222no—
429#102—1222no—
430#102—1222no—
431#97—22no—
432C4×C8—1222no—
433#95—21no—
434#95—611no—
435#95—611no—
436#95—611no—
437#95—611no—
438#95—1221no—
439#95—1221no—
440#95—1221no—
441#95—1221no—
442#95—1221no—
443C24—21no—
444C24—1221no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—612no—
451C2×D4—1224no—
452C2×D4—1224no—
453C2×D4—1221no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—4881no—
459C2×D4—4881no—
460C2×D4—4881no—
461C2×D4—4881no—
462C2×D4#1175822212yes—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—42no—
467C22×C4—81no—
468C22×C4—81no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—4881no—
477C22×C4—4881no—
478C22×C4—2442no—
479C22×C4D4×D6111yescharacteristic
480C22×C4D4×D6111yescharacteristic
481C22×C4C23×D6111yescharacteristic
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—612no—
500C4⋊C4—1224no—
501C4⋊C4—1224no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—4881no—
508C4⋊C4—4881no—
509C4⋊C4—4881no—
510C4⋊C4—4881no—
511C4⋊C4#1175822212yes—
512C22⋊C4—42no—
513C22⋊C4—4881no—
514C22⋊C4—4881no—
515C22⋊C4—4881no—
516C22⋊C4—4881no—
517C22⋊C4—2442no—
518C42—81no—
519C42—1221no—
520C42—1221no—
521C42—1221no—
522C42—1221no—
523C42—4881no—
524C42#1175822212yes—
525C42#1175822412yes—
526C23—22no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—1222no—
534C23—2441no—
535C23—2441no—
536C23—2441no—
537C23—2441no—
538C23—2441no—
539C23—2441no—
540C23C2×D4×D6111yescharacteristic
541D4—22no—
542D4—22no—
543D4—41no—
544D4—41no—
545D4—1222no—
546D4—1222no—
547D4—4884no—
548D4—4884no—
549D4—2441no—
550D4—2441no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—84no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1222no—
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—4884no—
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#1451976312yes—
588C2×C4#1451976312yes—
589C2×C4#41×D6111yescharacteristic
590C2×C4#41×D6111yescharacteristic
591C2×C4C2×#1175822411yescharacteristic
592C2×C4C2×#1175822211yescharacteristic
593C2×C4C2×#1175822211yescharacteristic
594C2×C4C2×#1175822211yescharacteristic
595C8—41no—
596C8—41no—
597C8—2441no—
598C8—2441no—
599C22—42no—
600C22—42no—
601C22—42no—
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#1684027111yescharacteristic
615C22C2×#1451976311yescharacteristic
616C22#1684056611yescharacteristic
617C22#1684056611yescharacteristic
618C22#1684057111yescharacteristic
619C22#1684057211yescharacteristic
620C4—22no—
621C4—22no—
622C4—42no—
623C4—81no—
624C4—81no—
625C4—4881no—
626C4—4881no—
627C4—2441no—
628C4—2442no—
629C4—2441no—
630C4—2441no—
631C4—2441no—
632C4#1684029011yescharacteristic
633C4#1684029211yescharacteristic
634C4#1684029411yescharacteristic
635C4#1684029611yescharacteristic
636C2—82no—
637C2—4882no—
638C2#2144910611yescharacteristic
639C2#2145601611yescharacteristic
640C2#2145602211yescharacteristic
641C2#2145606111yescharacteristic
642C2#2145607011yescharacteristic
643C2#2145616911yescharacteristic
644C2#2145617611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1762C2
socleC23×C61C22×D4
prime radicalC2×#14519773C22
hypercenter#1762D61
hypocenterC61#23830
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
1. #21448556C2semidirect
3. #21447391C2semidirect
4. #21447390C2semidirect
5. #21447226C2semidirect
6. #21447225C2semidirect
9. #21446964C2semidirect
10. #21446963C2semidirect
11. #21445645C2semidirect
12. C4×#14519697C2semidirect
13. C4×#14519698C2semidirect
14. #21445572C2semidirect
15. C61×#1762C2semidirect
325. #1762D61semidirect
381. C61#23830semidirect

Maximal subgroups

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

subgroupindex
#214485562
#214485412
#214473912
#214473902
#214472262
#214472252
#214470522
#214470512
#214469642
#214469632
#214456452
C4×#145196972
C4×#145196982
#214455722
C61×#17622
#2383061