Finite Group Databasebeta

← #29752794

Subgroups — #29752794

Order 15616.

734 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450224C211yesmaximal, characteristic, complemented
2#21448856C211yesmaximal, characteristic
3#21447236C211yesmaximal, characteristic, complemented
4#21447208C211yesmaximal, characteristic, complemented
5#21447010C211yesmaximal, characteristic
6#21447004C211yesmaximal, characteristic
7#21446588C211yesmaximal, characteristic, complemented
8#21446549C211yesmaximal, characteristic, complemented
9#21446423C211yesmaximal, characteristic, complemented
10#21446403C211yesmaximal, characteristic, complemented
11#21446083C211yesmaximal, characteristic, complemented
12#21446019C211yesmaximal, characteristic, complemented
13#21445913C211yesmaximal, characteristic, complemented
14C4×#14519697C211yesmaximal, characteristic, complemented
15C61×#1920C211yesmaximal, characteristic, complemented
16C2×#14519752C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×#14519735C2211yescharacteristic
19C2×#14519710C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519709C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×C4×#92418C2211yescharacteristic
30#16839703—21no—
31#16839691—21no—
32#16839663—21no—
33#16839663C2211yescharacteristic
34#16839660C2211yescharacteristic
35#16839658C2211yescharacteristic
36#16839653—21no—
37#16839652—21no—
38#16839640—21no—
39#16839630—21no—
40#16839627C2211yescharacteristic
41#16839619C2211yescharacteristic
42#16839619C2211yescharacteristic
43C4⋊C4×Dic61C2211yescharacteristic
44C4×#11758198C2211yescharacteristic
45#16839609—21no—
46#16839525C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#106×C61C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C4×C4⋊C4×C61C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×D244—21no—
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519752—22no—
66#14519752—22no—
67C4×D244—22no—
68C4×D244—41no—
69#14519735—22no—
70#14519735—41no—
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198D411yescharacteristic
84C2×#11758198D411yescharacteristic
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61C2311yescharacteristic
88#14519710—22no—
89#14519710—41no—
90#14519709—22no—
91#14519706—22no—
92#14519699—22no—
93#14519699—41no—
94#14519697—22no—
95#14519697—22no—
96#14519689—22no—
97#14519689—41no—
98C4×#92418—41no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684D411yescharacteristic
107#14519684D411yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C42×C61—21no—
116C2×C42×C61C2311yescharacteristic
117#106×C61—22no—
118#95×C61—21no—
119#95×C61—21no—
120C23×D61—21no—
121C23×D61C2×D411yescharacteristic
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2411yescharacteristic
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61C2×D411yescharacteristic
133C22×Dic61C2×D411yescharacteristic
134C22×Dic61C2×D411yescharacteristic
135C2×D244—21no—
136C2×D244—21no—
137C2×D244—21no—
138C2×D244—21no—
139C2×D244—21no—
140C2×D244—24no—
141C2×D244—81no—
142C2×D244—81no—
143C2×D244#4112yes—
144C2×C4×D61—21no—
145C2×C4×D61—21no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61—42no—
151C2×C4×D61—42no—
152C2×C4×D61—81no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×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—81no—
167C4⋊C4×C61#4112yes—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61—42no—
171#11758198—24no—
172#11758198—22no—
173#11758198—41no—
174#11758198—42no—
175#11758198—42no—
176#11758198—42no—
177#11758198—42no—
178#11758198—81no—
179#11758198—81no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61#4112yes—
186#11758196—81no—
187#11758196—81no—
188C4×Dic61—21no—
189C4×Dic61—21no—
190C4×Dic61—42no—
191C4×Dic61—81no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418#4112yes—
198C23×C61C22×D411yescharacteristic
199C22×D61—22no—
200C22×D61—21no—
201C22×D61—21no—
202C22×D61—21no—
203C22×D61—21no—
204C22×D61—21no—
205C22×D61—21no—
206C22×D61—21no—
207C22×D61—41no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—41no—
211C22×D61—41no—
212C22×D61—41no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—22no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61#13512yes—
231C2×C4×C61C2×#4111yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61H(5,𝔽2)11yescharacteristic
236C2×C4×C612−1+411yescharacteristic
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—22no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255D244—22no—
256D244—22no—
257D244—41no—
258D244—41no—
259D244—84no—
260C4×D61—41no—
261C4×D61—41no—
262C4×D61—41no—
263C4×D61—41no—
264C4×D61—84no—
265C8×C61—41no—
266C8×C61—41no—
267#92418—22no—
268#92418—41no—
269#27038—611nomaximal, Sylow
270C22×C61#52511yescharacteristic
271C22×C61#54611yescharacteristic
272C22×C61#54711yescharacteristic
273C22×C61C2×#13511yescharacteristic
274C22×C61#57511yescharacteristic
275C22×C61#57611yescharacteristic
276C22×C61#57711yescharacteristic
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—42no—
281C2×D61—41no—
282C2×D61—42no—
283C2×D61—41no—
284C2×D61—42no—
285C2×D61—41no—
286C2×D61—41no—
287C2×D61—81no—
288C2×D61—81no—
289C2×D61—81no—
290C2×D61—81no—
291C4×C61—22no—
292C4×C61—42no—
293C4×C61—41no—
294C4×C61—81no—
295C4×C61—81no—
296C4×C61—81no—
297C4×C61#52911yescharacteristic
298C4×C61#53911yescharacteristic
299C4×C61#55311yescharacteristic
300C4×C61#55611yescharacteristic
301Dic61—41no—
302Dic61—41no—
303Dic61—41no—
304Dic61—42no—
305Dic61—81no—
306Dic61—81no—
307#2495—611no—
308#2363—611no—
309#2073—611no—
310#2067—611no—
311#2034—611no—
312#2033—611no—
313#1949—611no—
314#1942—611no—
315#1923—611no—
316#1920—611no—
317#1920D6111yescharacteristic, complemented
318#1864—611no—
319#1854—611no—
320#1825—611no—
321C4×#102—611no—
322C2×C61#246611yescharacteristic
323C2×C61#310211yescharacteristic
324C2×C61#311811yescharacteristic
325C2×C61#329611yescharacteristic
326C2×C61#330911yescharacteristic
327C2×C61#334111yescharacteristic
328C2×C61#335111yescharacteristic
329D61—81no—
330D61—82no—
331C2×#121—611no—
332C2×C4×D4—611no—
333C2×#117—611no—
334C2×#107—611no—
335C2×#107—611no—
336C2×#106—611no—
337C2×#106C2×D6111yescharacteristic
338C2×C4⋊C8—611no—
339C2×#102—611no—
340C2×#102—611no—
341C2×#102—611no—
342C2×#102—611no—
343C2×C22⋊C8—611no—
344C2×C22⋊C8—611no—
345C2×C4×C8—611no—
346#400—1221no—
347#397—1221no—
348#390—611no—
349#390—1221no—
350#389—611no—
351#389—611no—
352#389C2×D6111yescharacteristic
353#388—1221no—
354#388—1221no—
355#386—1221no—
356#383—1221no—
357#382—611no—
358#380—611no—
359#380—611no—
360C4×C4⋊C4—611no—
361C4×C4⋊C4C2×D6111yescharacteristic
362C4×C22⋊C4—611no—
363C4×C22⋊C4—1221no—
364#340—611no—
365#340—611no—
366#340—611no—
367#340—611no—
368#340—611no—
369#340C2×D6111yescharacteristic
370#340C2×D6111yescharacteristic
371#340C2×D6111yescharacteristic
372#336—611no—
373#336C2×D6111yescharacteristic
374C61#2703811yescharacteristic, complemented, Sylow
375C22×D4—611no—
376C22×D4—1221no—
377C23×C4—611no—
378C23×C4—1221no—
379C22×C8—611no—
380C22×C8—611no—
381C22×C8C22×D6111yescharacteristic
382C22×C8C22×D6111yescharacteristic
383#121—1222no—
384#121—1222no—
385C4×D4—1222no—
386C4×D4—2441no—
387#117—1222no—
388#117—2441no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4—1221no—
395C2×C4⋊C4C22×D6111yescharacteristic
396C2×C4⋊C4C22×D6111yescharacteristic
397C2×C4⋊C4C22×D6111yescharacteristic
398C2×C4⋊C4C22×D6111yescharacteristic
399C2×C22⋊C4—611no—
400C2×C22⋊C4—611no—
401C2×C22⋊C4—1221no—
402C2×C22⋊C4—1221no—
403C2×C22⋊C4—1221no—
404C2×C22⋊C4—1221no—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4—1221no—
407C2×C22⋊C4—1221no—
408C2×C42—21no—
409C2×C42—611no—
410C2×C42—1221no—
411C2×C42—1221no—
412C2×C42C22×D6111yescharacteristic
413#107—1222no—
414#107—2441no—
415#106—22no—
416#106—1222no—
417C4⋊C8—1222no—
418#102—1222no—
419#102—1222no—
420#102—1222no—
421#102—2441no—
422C22⋊C8—1222no—
423C22⋊C8—2441no—
424C4×C8—2441no—
425#95—21no—
426#95—21no—
427#95—611no—
428#95—611no—
429#95—1221no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433#95—1221no—
434#95—1221no—
435#95—1221no—
436C24—611no—
437C24—1221no—
438C2×D4—612no—
439C2×D4—1224no—
440C2×D4—1221no—
441C2×D4—1221no—
442C2×D4—1221no—
443C2×D4—1221no—
444C2×D4—1221no—
445C2×D4—4881no—
446C2×D4—4881no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—4881no—
464C22×C4—2442no—
465C22×C4—2442no—
466C22×C4D4×D6111yescharacteristic
467C22×C4D4×D6111yescharacteristic
468C22×C4C23×D6111yescharacteristic
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—612no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—81no—
489C4⋊C4—612no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—4881no—
496C4⋊C4—4881no—
497C4⋊C4#1175822212yes—
498C22⋊C4—1224no—
499C22⋊C4—1222no—
500C22⋊C4—4881no—
501C22⋊C4—4881no—
502C22⋊C4—2441no—
503C22⋊C4—2442no—
504C22⋊C4—2442no—
505C22⋊C4—2442no—
506C22⋊C4—2442no—
507C42—21no—
508C42—21no—
509C42—42no—
510C42—1221no—
511C42—1221no—
512C42—4881no—
513C42—2442no—
514C23—1222no—
515C23—1221no—
516C23—1221no—
517C23—1221no—
518C23—1221no—
519C23—1221no—
520C23—1221no—
521C23—1221no—
522C23—2441no—
523C23—2441no—
524C23—2441no—
525C23—2441no—
526C23—2441no—
527C23—2441no—
528C23C2×D4×D6111yescharacteristic
529D4—1222no—
530D4—1222no—
531D4—4884no—
532D4—2441no—
533D4—2441no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1222no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—4884no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4#1451979812yes—
575C2×C4#41×D6111yescharacteristic
576C2×C4#41×D6111yescharacteristic
577C2×C4#41×D6111yescharacteristic
578C2×C4C2×#1175822211yescharacteristic
579C2×C4#1451982311yescharacteristic
580C2×C4#1451982511yescharacteristic
581C8—41no—
582C8—41no—
583C8—1222no—
584C8—2441no—
585C22—4881no—
586C22—4881no—
587C22—4881no—
588C22—4881no—
589C22—2441no—
590C22—2441no—
591C22—2442no—
592C22—2441no—
593C22—2442no—
594C22—2441no—
595C22—2441no—
596C22—2441no—
597C22—2442no—
598C22—2441no—
599C22#1684027111yescharacteristic
600C22#1684040411yescharacteristic
601C22#1684041411yescharacteristic
602C22C2×#1451979811yescharacteristic
603C22#1684055911yescharacteristic
604C22#1684056611yescharacteristic
605C22#1684057111yescharacteristic
606C4—22no—
607C4—42no—
608C4—41no—
609C4—81no—
610C4—81no—
611C4—81no—
612C4—4881no—
613C4—4881no—
614C4—2441no—
615C4—2441no—
616C4—2441no—
617C4—2442no—
618C4#1684029511yescharacteristic
619C4#1684036011yescharacteristic
620C4#1684045611yescharacteristic
621C4#1684048411yescharacteristic
622C2—4882no—
623C2—4881no—
624C2#2144985911yescharacteristic
625C2#2145583511yescharacteristic
626C2#2145600711yescharacteristic
627C2#2145765211yescharacteristic
628C2#2145782311yescharacteristic
629C2#2145824011yescharacteristic
630C2#2145837611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1920C2
socleC23×C61C22×D4
prime radicalC2×#14519752C22
hypercenter#1920D61
hypocenterC61#27038
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
1. #21450224C2semidirect
3. #21447236C2semidirect
4. #21447208C2semidirect
7. #21446588C2semidirect
8. #21446549C2semidirect
9. #21446423C2semidirect
10. #21446403C2semidirect
11. #21446083C2semidirect
12. #21446019C2semidirect
13. #21445913C2semidirect
14. C4×#14519697C2semidirect
15. C61×#1920C2semidirect
317. #1920D61semidirect
374. C61#27038semidirect

Maximal subgroups

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

subgroupindex
#214502242
#214488562
#214472362
#214472082
#214470102
#214470042
#214465882
#214465492
#214464232
#214464032
#214460832
#214460192
#214459132
C4×#145196972
C61×#19202
#2703861