Finite Group Databasebeta

← #29575582

Subgroups — #29575582

Order 15616.

694 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839812C211yesmaximal, characteristic, complemented
2#21454151C211yesmaximal, characteristic
3C2×#16839497C211yesmaximal, characteristic
4C2×#16839495C211yesmaximal, characteristic
5#21444043C211yesmaximal, characteristic, complemented
6#21443697C211yesmaximal, characteristic, complemented
7C61×#1294C211yesmaximal, characteristic, complemented
8C2×#14519761—21no—
9C2×#14519751C2211yescharacteristic
10C22×C4×Dic61C2211yescharacteristic
11#16839812—22no—
12#16839812—22no—
13C2×#14519706—21no—
14C2×C22⋊#92418C2211yescharacteristic
15C2×C8×Dic61—21no—
16#16839663C411yescharacteristic, complemented
17#16839663C411yescharacteristic, complemented
18#16839661C411yescharacteristic, complemented
19#16839661C411yescharacteristic, complemented
20#16839654—21no—
21#16839654—21no—
22#16839639—21no—
23C2×#14519684—21no—
24C2×#14519684—21no—
25C2×#14519684C2211yescharacteristic
26#16839497—22no—
27#16839495—22no—
28C2×C22⋊C8×C61C2211yescharacteristic
29C61×#380C2211yescharacteristic
30C2×#95×C61C2211yescharacteristic
31C22×D244C2×C411yescharacteristic
32C22×C22⋊D61—21no—
33C23×Dic61—21no—
34C23×Dic61D411yescharacteristic
35C23×Dic61D411yescharacteristic
36C22×#92418—21no—
37#14519761—42no—
38#14519761—42no—
39#14519751—21no—
40#14519751—21no—
41#14519751—21no—
42#14519751—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×C4×Dic61—21no—
52C2×C4×Dic61—21no—
53C2×C4×Dic61—21no—
54C2×C4×Dic61—21no—
55C2×C4×Dic61C2×C411yescharacteristic
56C2×C4×Dic61C2×C411yescharacteristic
57C2×C4×Dic61D411yescharacteristic
58C2×C4×Dic61D411yescharacteristic
59#14519706—24no—
60C22⋊#92418—21no—
61C22⋊#92418D412yes—
62C8×Dic61—24no—
63#14519684—24no—
64#14519684—21no—
65#14519684—21no—
66#14519684—21no—
67#14519684—21no—
68#14519684—42no—
69C23×C4×C61—21no—
70C23×C4×C61C2311yescharacteristic
71C22×C8×C61—21no—
72C2×C4⋊C4×C61C2×C411yescharacteristic
73C2×C4⋊C4×C61C2×C411yescharacteristic
74C2×C22⋊C4×C61—21no—
75C22⋊C8×C61—21no—
76C22⋊C8×C61D412yes—
77#95×C61—21no—
78#95×C61—21no—
79#95×C61—21no—
80C24×C61C2×D411yescharacteristic
81C23×D61—21no—
82C22×C4×C61—22no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61C22×C411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C22×C4×C61#4111yescharacteristic
99C2×C22⋊D61—41no—
100C2×C22⋊D61—41no—
101C2×C22⋊D61—41no—
102C2×C22⋊D61—41no—
103C2×C22⋊D61—41no—
104C2×C22⋊D61—41no—
105C22×Dic61—21no—
106C22×Dic61—21no—
107C22×Dic61—21no—
108C22×Dic61—21no—
109C22×Dic61—21no—
110C22×Dic61—21no—
111C22×Dic61—22no—
112C22×Dic61—22no—
113C22×Dic61—21no—
114C22×Dic61—41no—
115C22×Dic61—41no—
116C22×Dic61—41no—
117C22×Dic61—41no—
118C22×Dic61—41no—
119C22×Dic61—41no—
120C22×Dic61—41no—
121C22×Dic61C22⋊C411yescharacteristic
122C22×Dic61C22⋊C411yescharacteristic
123C22×Dic61C22⋊C411yescharacteristic
124C22×Dic61C22⋊C411yescharacteristic
125C22×Dic61D812yes—
126C22×Dic61SD1612yes—
127C2×D244—21no—
128C2×D244—21no—
129C2×D244—41no—
130C2×D244—41no—
131C2×C8×C61—22no—
132C2×C8×C61—41no—
133C2×C8×C61—41no—
134C4⋊C4×C61—41no—
135C4⋊C4×C61—41no—
136C22⋊C4×C61—41no—
137C22⋊C4×C61—41no—
138#11758198—42no—
139#11758198—41no—
140#11758198—41no—
141#11758198—42no—
142#11758198—42no—
143#11758198—42no—
144C4⋊Dic61—21no—
145C4⋊Dic61—21no—
146C4⋊Dic61—42no—
147C4⋊Dic61—42no—
148C4×Dic61—21no—
149C4×Dic61—21no—
150C4×Dic61—21no—
151C4×Dic61—21no—
152C4×Dic61—21no—
153C4×Dic61—21no—
154C4×Dic61—21no—
155C4×Dic61—21no—
156C2×#92418—22no—
157C2×#92418—41no—
158C2×#92418—41no—
159C23×C61—21no—
160C23×C61—21no—
161C23×C61—21no—
162C23×C61—21no—
163C23×C61C2×C22⋊C411yescharacteristic
164C23×C61#12111yescharacteristic
165C23×C61#12111yescharacteristic
166C23×C61C2×D811yescharacteristic
167C23×C61C2×SD1611yescharacteristic
168C23×C61#13511yescharacteristic
169C23×C61#13511yescharacteristic
170C22×D61—41no—
171C22×D61—41no—
172C22×D61—41no—
173C22×D61—41no—
174C22×D61—41no—
175C22×D61—41no—
176C22×D61—41no—
177C2×C4×C61—21no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61—21no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61—81no—
195C2×C4×C61—81no—
196C2×C4×C61—81no—
197C2×C4×C61—81no—
198C2×C4×C61C4×D411yescharacteristic
199C2×C4×C61C4×D411yescharacteristic
200C2×C4×C61#12011yescharacteristic
201C2×C4×C61#12311yescharacteristic
202C22⋊D61—81no—
203C22⋊D61—81no—
204C22⋊D61—81no—
205C22⋊D61—81no—
206C2×Dic61—21no—
207C2×Dic61—21no—
208C2×Dic61—21no—
209C2×Dic61—21no—
210C2×Dic61—21no—
211C2×Dic61—21no—
212C2×Dic61—22no—
213C2×Dic61—22no—
214C2×Dic61—22no—
215C2×Dic61—22no—
216C2×Dic61—21no—
217C2×Dic61—21no—
218C2×Dic61—21no—
219C2×Dic61—42no—
220C2×Dic61—42no—
221C2×Dic61—42no—
222C2×Dic61—42no—
223C2×Dic61—42no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226C2×Dic61—41no—
227C2×Dic61—81no—
228C2×Dic61—81no—
229C2×Dic61—81no—
230C2×Dic61—81no—
231C2×Dic61#10212yes—
232C2×Dic61#10212yes—
233C2×Dic61#10412yes—
234D244—81no—
235D244—81no—
236C8×C61—42no—
237#92418—42no—
238#9114—611nomaximal, Sylow
239C22×C61—21no—
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—21no—
243C22×C61—21no—
244C22×C61—21no—
245C22×C61—21no—
246C22×C61—21no—
247C22×C61—21no—
248C22×C61—21no—
249C22×C61—21no—
250C22×C61—21no—
251C22×C61#38611yescharacteristic
252C22×C61#41011yescharacteristic
253C22×C61#41011yescharacteristic
254C22×C61C2×#10211yescharacteristic
255C22×C61#41611yescharacteristic
256C22×C61C2×#10411yescharacteristic
257C22×C61#42111yescharacteristic
258C22×C61#46511yescharacteristic
259C22×C61#46511yescharacteristic
260C22×C61#46611yescharacteristic
261C22×C61#46611yescharacteristic
262C2×D61—81no—
263C2×D61—81no—
264C2×D61—81no—
265C2×D61—81no—
266C2×D61—81no—
267C2×D61—81no—
268C2×D61—81no—
269C4×C61—21no—
270C4×C61—21no—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—82no—
274C4×C61—81no—
275C4×C61—81no—
276Dic61—22no—
277Dic61—22no—
278Dic61—22no—
279Dic61—41no—
280Dic61—82no—
281Dic61—81no—
282C2×#431—611no—
283#2854—611no—
284C2×#327—611no—
285C2×#327—611no—
286#1434—611no—
287#1294—611no—
288#1294D6111yescharacteristic, complemented
289C2×C61—21no—
290C2×C61—21no—
291C2×C61—21no—
292C2×C61—21no—
293C2×C61#150011yescharacteristic
294C2×C61#150211yescharacteristic
295C2×C61#151711yescharacteristic
296C2×C61#152111yescharacteristic
297C2×C61#187111yescharacteristic
298C2×C61#189311yescharacteristic
299C2×C61#189911yescharacteristic
300D61—161no—
301C2×#123—1221no—
302C2×#121—611no—
303C22×C42—611no—
304#431—1222no—
305#431—1222no—
306C2×C4⋊C8—1221no—
307C2×C22⋊C8—611no—
308C2×C22⋊C8C2×D6111yescharacteristic
309C2×C4×C8—1221no—
310#390—611no—
311#390—611no—
312#389—611no—
313#389—611no—
314#388—1221no—
315#388—1221no—
316#386—1221no—
317#380C2×D6111yescharacteristic
318C2×#95—611no—
319C2×#95—1221no—
320C2×#95—1221no—
321C2×#95C2×D6111yescharacteristic
322#327—1222no—
323#327—1222no—
324C61#911411yescharacteristic, complemented, Sylow
325C22×D4—611no—
326C22×D4—1221no—
327C23×C4—21no—
328C23×C4—611no—
329C23×C4—611no—
330C23×C4—1221no—
331C23×C4C22×D6111yescharacteristic
332C22×C8—21no—
333C22×C8—1221no—
334#123—2442no—
335#123—2442no—
336#121—1221no—
337#121—1221no—
338#121—1221no—
339#121—1221no—
340C2×C4⋊C4—611no—
341C2×C4⋊C4—1221no—
342C2×C4⋊C4—1221no—
343C2×C4⋊C4C4×D6111yescharacteristic
344C2×C4⋊C4C4×D6111yescharacteristic
345C2×C22⋊C4—21no—
346C2×C22⋊C4—1221no—
347C2×C22⋊C4—1221no—
348C2×C22⋊C4—1221no—
349C2×C22⋊C4—1221no—
350C2×C22⋊C4—1221no—
351C2×C42—611no—
352C2×C42—611no—
353C2×C42—611no—
354C2×C42—611no—
355C2×C42—1221no—
356C2×C42—1221no—
357C2×C42—1221no—
358C2×C42—1221no—
359C4⋊C8—1224no—
360C22⋊C8—21no—
361C22⋊C8—612no—
362C22⋊C8—1221no—
363C22⋊C8D24412yes—
364C4×C8—1224no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—1221no—
369#95—1221no—
370#95—1224no—
371#95—1221no—
372#95—1221no—
373#95—2442no—
374C24—1221no—
375C24D4×D6111yescharacteristic
376C2×D4—1221no—
377C2×D4—1221no—
378C2×D4—2441no—
379C2×D4—2441no—
380C2×D4—2441no—
381C2×D4—2441no—
382C2×D4—2441no—
383C2×D4—2441no—
384C2×D4—2441no—
385C2×D4—2441no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—611no—
400C22×C4—612no—
401C22×C4—612no—
402C22×C4—611no—
403C22×C4—1222no—
404C22×C4—1221no—
405C22×C4—1221no—
406C22×C4—1221no—
407C22×C4—1221no—
408C22×C4—1221no—
409C22×C4—1221no—
410C22×C4—1222no—
411C22×C4—1221no—
412C22×C4—2441no—
413C22×C4—2441no—
414C22×C4—2441no—
415C22×C4—2441no—
416C22×C4—2441no—
417C22×C4—2441no—
418C22×C4—2441no—
419C22×C4C2×C4×D6111yescharacteristic
420C22×C4C2×D24411yescharacteristic
421C22×C4#1175822211yescharacteristic
422C22×C4D4×D6111yescharacteristic
423C22×C4D4×D6111yescharacteristic
424C22×C4#1175822611yescharacteristic
425C2×C8—22no—
426C2×C8—41no—
427C2×C8—41no—
428C2×C8—1222no—
429C2×C8—2441no—
430C2×C8—2441no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—1221no—
434C4⋊C4—1221no—
435C4⋊C4—2442no—
436C4⋊C4—2442no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—2442no—
440C22⋊C4—2442no—
441C22⋊C4—2442no—
442C22⋊C4—2442no—
443C22⋊C4—2441no—
444C22⋊C4—2441no—
445C42—1221no—
446C42—1221no—
447C42—1221no—
448C42—1221no—
449C42—1221no—
450C42—1221no—
451C42—1221no—
452C42—1221no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—2441no—
458C23—2441no—
459C23—2441no—
460C23—2441no—
461C23—2441no—
462C23—2441no—
463C23—2441no—
464C23C22⋊C4×D6111yescharacteristic
465C23#1451975011yescharacteristic
466C23#1451975211yescharacteristic
467C23D8×D6111yescharacteristic
468C23SD16×D6111yescharacteristic
469C23#1451979811yescharacteristic
470C23#1451980011yescharacteristic
471D4—4881no—
472D4—4881no—
473D4—4881no—
474D4—4881no—
475D4—4881no—
476D4—4881no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—81no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4—81no—
498C2×C4—612no—
499C2×C4—612no—
500C2×C4—612no—
501C2×C4—1222no—
502C2×C4—1222no—
503C2×C4—1222no—
504C2×C4—1222no—
505C2×C4—1221no—
506C2×C4—1221no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—4881no—
515C2×C4—4881no—
516C2×C4—4881no—
517C2×C4—4881no—
518C2×C4—2442no—
519C2×C4—2442no—
520C2×C4—2442no—
521C2×C4—2442no—
522C2×C4—2442no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4—2441no—
526C2×C4#1451973911yescharacteristic
527C2×C4C4×D24411yescharacteristic
528C2×C4#1451974711yescharacteristic
529C2×C4#1451976211yescharacteristic
530C8—42no—
531C8—2442no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—4881no—
545C22—4881no—
546C22—4881no—
547C22—4881no—
548C22—4881no—
549C22—4881no—
550C22—4881no—
551C22#1683964011yescharacteristic
552C22#1683973411yescharacteristic
553C22#1683973411yescharacteristic
554C22#102×D6111yescharacteristic
555C22#1683975711yescharacteristic
556C22#104×D6111yescharacteristic
557C22#1683977711yescharacteristic
558C22#1683999211yescharacteristic
559C22#1683999411yescharacteristic
560C22#1683999711yescharacteristic
561C22#1683999911yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—82no—
567C4—81no—
568C4—81no—
569C4—1222no—
570C4—1222no—
571C4—1222no—
572C4—4882no—
573C4—4881no—
574C4—2441no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—9761no—
580C2#2144430411yescharacteristic
581C2#2144431211yescharacteristic
582C2#2144437711yescharacteristic
583C2#2144439511yescharacteristic
584C2#2144612011yescharacteristic
585C2#2144624611yescharacteristic
586C2#2144627611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1294D61
hypocenterC61#9114
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
1. C2×#16839812C2semidirect
5. #21444043C2semidirect
6. #21443697C2semidirect
7. C61×#1294C2semidirect
16. #16839663C4semidirect
17. #16839663C4semidirect
18. #16839661C4semidirect
19. #16839661C4semidirect
288. #1294D61semidirect
324. C61#9114semidirect

Maximal subgroups

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

subgroupindex
C2×#168398122
#214541512
C2×#168394972
C2×#168394952
#214440432
#214436972
C61×#12942
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