Finite Group Databasebeta

← #30610453

Subgroups — #30610453

Order 15616.

1646 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C211yesmaximal, characteristic, complemented
2#21462495C211yesmaximal, characteristic, complemented
3#21461160C214yesmaximal, complemented
4#21461146C214yesmaximal, complemented
5#21461120C214yesmaximal, complemented
6C22×#14519739C211yesmaximal, characteristic
7#16840783—21no—
8#16840783C2212yescomplemented
9#16840782—21no—
10#16840782—21no—
11#16840779—21no—
12#16840779C2212yescomplemented
13#16840778C2212yescomplemented
14#16840778C2212yescomplemented
15#16840765—21no—
16#16840765C2212yescomplemented
17#16840732—21no—
18#16840732—21no—
19C4×#11758217—21no—
20C4×#11758217C2212yescomplemented
21#16840610C22116yescomplemented
22C23×D244C411yescharacteristic
23C23×C4×D61—21no—
24C2×#14519739—21no—
25C2×#14519739—21no—
26C2×#14519739—21no—
27C2×#14519739—21no—
28C2×#14519739—21no—
29C2×#14519739—21no—
30C2×#14519739C412yes—
31C2×#14519739C412yes—
32C2×#14519739C412yes—
33C2×#14519739C2212yes—
34C2×#14519739C2212yes—
35C2×#14519739C2212yes—
36C22×#11758198—21no—
37C22×C4×Dic61C2211yescharacteristic
38C22×C4⋊C4×C61C411yescharacteristic
39C2×#11758217—22no—
40C2×#11758217—22no—
41#14519844—22no—
42#14519844—22no—
43C4⋊#92420—22no—
44C4⋊#92420C2314yescomplemented
45C22⋊#92420—22no—
46C22⋊#92420—22no—
47C22⋊#92420—22no—
48C22⋊#92420—22no—
49#14519832—22no—
50#14519832—22no—
51C4×#92420—22no—
52C4×#92420C2314yescomplemented
53C24×D61—21no—
54C22×D244—21no—
55C22×D244—21no—
56C22×D244—21no—
57C22×D244—28no—
58C22×D244C2×C412yes—
59C22×D244C2×C412yes—
60C22×D244C2×C412yes—
61C23×Dic61D411yescharacteristic
62C23×Dic61D411yescharacteristic
63C22×C4×D61—22no—
64C22×C4×D61—22no—
65C22×C4×D61—22no—
66C22×C4×D61—22no—
67C22×C4×D61—22no—
68C22×C4×D61—22no—
69C22×C4×D61—48no—
70#14519739—22no—
71#14519739—22no—
72#14519739—22no—
73#14519739—22no—
74#14519739—22no—
75#14519739—22no—
76#14519739—22no—
77#14519739—22no—
78#14519739—22no—
79#14519739—22no—
80#14519739—22no—
81#14519739—22no—
82#14519739C2×C414yes—
83#14519739C2×C414yes—
84#14519739C2×C414yes—
85#14519739C2314yes—
86C2×#11758198—22no—
87C2×#11758198—22no—
88C2×#11758198—22no—
89C2×#11758198—22no—
90C2×#11758198—22no—
91C2×#11758198—22no—
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61C2×C411yescharacteristic
94C2×C4×Dic61C2×C411yescharacteristic
95C2×C4×Dic61D411yescharacteristic
96C2×C4×Dic61D411yescharacteristic
97C2×C4×Dic61D411yescharacteristic
98C2×C4×Dic61D411yescharacteristic
99C2×C4×Dic61D411yescharacteristic
100C2×C4×Dic61D411yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104C23×C4×C61—21no—
105C23×C4×C61C2×C411yescharacteristic
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61C2×C412yes—
110C2×C4⋊C4×C61C2×C412yes—
111C2×C4⋊C4×C61C2×C412yes—
112C24×C61C22⋊C411yescharacteristic
113C23×D61—28no—
114C23×D61—22no—
115C23×D61—22no—
116C23×D61—22no—
117C23×D61—44no—
118C23×D61—44no—
119C22×C4×C61—24no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—44no—
124C22×C4×C61C22⋊C411yescharacteristic
125C22×C4×C61C22⋊C411yescharacteristic
126C22×C4×C61C22⋊C411yescharacteristic
127C22×C4×C61C22×C411yescharacteristic
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C22×C411yescharacteristic
130C22×Dic61—24no—
131C22×Dic61—42no—
132C22×Dic61C22⋊C411yescharacteristic
133C22×Dic61C22⋊C411yescharacteristic
134C22×Dic61C22⋊C411yescharacteristic
135C22×Dic61C22⋊C411yescharacteristic
136C22×Dic61C22⋊C411yescharacteristic
137C22×Dic61C22⋊C411yescharacteristic
138C22×Dic61C2×D411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140C22×Dic61C2×D411yescharacteristic
141C22×Dic61C2×D411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144C2×D244—28no—
145C2×D244—28no—
146C2×D244—28no—
147C2×D244—22no—
148C2×D244—22no—
149C2×D244—22no—
150C2×D244—24no—
151C2×D244—28no—
152C2×D244—28no—
153C2×D244M1618yescomplemented
154C2×D244C22×C414yes—
155C2×C4×D61—24no—
156C2×C4×D61—24no—
157C2×C4×D61—24no—
158C2×C4×D61—24no—
159C2×C4×D61—48no—
160C2×C4×D61—48no—
161C2×C4×D61—48no—
162C2×C4×D61—48no—
163C2×C4×D61—48no—
164C2×C4×D61—48no—
165#11758217—44no—
166#11758217—44no—
167C2×#92420—24no—
168C2×#92420—24no—
169C4⋊C4×C61—22no—
170C4⋊C4×C61—22no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61C22×C414yes—
173#11758198—24no—
174#11758198—24no—
175#11758198—24no—
176#11758198—24no—
177C4×Dic61C22⋊C411yescharacteristic
178C4×Dic61C22⋊C411yescharacteristic
179C4×Dic61C22⋊C411yescharacteristic
180C4×Dic61C22⋊C411yescharacteristic
181C4×Dic61C22⋊C411yescharacteristic
182C4×Dic61C22⋊C411yescharacteristic
183C4×Dic61C22×C411yescharacteristic
184C4×Dic61C22×C411yescharacteristic
185C4×Dic61C22×C411yescharacteristic
186C4×Dic61C2×D411yescharacteristic
187C4×Dic61C2×D411yescharacteristic
188C4×Dic61C2×D411yescharacteristic
189C4×Dic61C2×D411yescharacteristic
190C4×Dic61C2×D411yescharacteristic
191C4×Dic61C2×D411yescharacteristic
192C4×Dic61C2411yescharacteristic
193C23×C61—22no—
194C23×C61—22no—
195C23×C61—22no—
196C23×C61C2×C22⋊C411yescharacteristic
197C23×C61C2×C22⋊C411yescharacteristic
198C23×C61C2×C22⋊C411yescharacteristic
199C22×D61—28no—
200C22×D61—28no—
201C22×D61—24no—
202C22×D61—28no—
203C22×D61—44no—
204C22×D61—44no—
205C22×D61—432no—
206C22×D61—44no—
207C22×D61—44no—
208C22×D61—44no—
209C22×D61—44no—
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—24no—
216C2×C4×C61—44no—
217C2×C4×C61—44no—
218C2×C4×C61—44no—
219C2×C4×C61C2×C22⋊C411yescharacteristic
220C2×C4×C61C2×C22⋊C411yescharacteristic
221C2×C4×C61C2×C22⋊C411yescharacteristic
222C2×C4×C61C2×M1614yes—
223C2×C4×C61C23×C411yescharacteristic
224C2×Dic61—22no—
225C2×Dic61—22no—
226C2×Dic61—22no—
227C2×Dic61—22no—
228C2×Dic61—22no—
229C2×Dic61—22no—
230C2×Dic61—22no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61C2×C22⋊C411yescharacteristic
236C2×Dic61C2×C22⋊C411yescharacteristic
237C2×Dic61C2×C22⋊C411yescharacteristic
238C2×Dic61C2×C22⋊C411yescharacteristic
239C2×Dic61C2×C22⋊C411yescharacteristic
240C2×Dic61C2×C22⋊C411yescharacteristic
241C2×Dic61AGL(1,ℤ/8)14yes—
242C2×Dic61C22×D411yescharacteristic
243C2×Dic61C22×D411yescharacteristic
244D244—28no—
245D244—28no—
246D244—24no—
247D244—28no—
248D244C2×M1618yes—
249C4×D61—48no—
250C4×D61—48no—
251C4×D61—48no—
252C4×D61—48no—
253#92420—44no—
254#92420—44no—
255#17448—611nomaximal, Sylow
256C22×C61—28no—
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61#40712yes—
264C22×C61#41812yes—
265C22×C61#42112yes—
266C22×C61C22×C22⋊C411yescharacteristic
267C2×D61—28no—
268C2×D61—416no—
269C2×D61—416no—
270C2×D61—416no—
271C2×D61—44no—
272C2×D61—44no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—44no—
276C4×C61#40712yes—
277C4×C61C22×M1612yes—
278Dic61—21no—
279Dic61—21no—
280Dic61—21no—
281Dic61—21no—
282Dic61—21no—
283Dic61—21no—
284Dic61#41812yes—
285Dic61C2×AGL(1,ℤ/8)12yes—
286C22×C4×D4—611no—
287#2920—611no—
288#2920—611no—
289#1490—614no—
290#1486—614no—
291#1478—614no—
292C2×C61—22no—
293C2×C61—22no—
294C2×C61—22no—
295C2×C61C2×#40711yescharacteristic
296C2×C61C2×#41811yescharacteristic
297C2×C61C2×#42111yescharacteristic
298D61—48no—
299C23×D4—611no—
300C24×C4—1221no—
301C2×C4×D4—612no—
302C2×C4×D4—612no—
303C2×C4×D4—612no—
304C2×C4×D4—612no—
305C2×C4×D4—612no—
306C2×C4×D4—612no—
307C2×C4×D4—1221no—
308C2×C4×D4—1221no—
309C2×C4×D4—1221no—
310C2×C4×D4—1221no—
311C2×C4×D4—1221no—
312C2×C4×D4—1221no—
313C22×C4⋊C4#692311yescharacteristic
314C22×C22⋊C4—1221no—
315C22×C42—611no—
316#432—612no—
317#432—1221no—
318#432—1221no—
319#432—1221no—
320#431—612no—
321#431—612no—
322#431—612no—
323#431—1221no—
324#423—612no—
325#423—1221no—
326#407—1221no—
327#407—1221no—
328C4×M16—612no—
329C4×M16—1221no—
330D4⋊C8—6116no—
331C61#1744811yescharacteristic, complemented, Sylow
332C25—1221no—
333C22×D4—612no—
334C22×D4—612no—
335C22×D4—612no—
336C22×D4—1228no—
337C22×D4—1221no—
338C22×D4—1221no—
339C22×D4—1221no—
340C23×C4—21no—
341C23×C4—611no—
342C23×C4—611no—
343C23×C4—1222no—
344C23×C4—1222no—
345C23×C4—1222no—
346C23×C4—1222no—
347C23×C4—1222no—
348C23×C4—1222no—
349C23×C4—2448no—
350C23×C4C2×#692311yescharacteristic
351C2×M16—1222no—
352C2×M16—1222no—
353C4×D4—614no—
354C4×D4—614no—
355C4×D4—614no—
356C4×D4—614no—
357C4×D4—1222no—
358C4×D4—1222no—
359C4×D4—1222no—
360C4×D4—1222no—
361C4×D4—1222no—
362C4×D4—1222no—
363C4×D4—1222no—
364C4×D4—1222no—
365C4×D4—1222no—
366C4×D4—1222no—
367C4×D4—1222no—
368C4×D4—1222no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4C2×#692312yes—
373C2×C4⋊C4C2×#692312yes—
374C2×C4⋊C4C2×#692312yes—
375C2×C22⋊C4—1222no—
376C2×C22⋊C4—1222no—
377C2×C22⋊C4—1222no—
378C2×C22⋊C4—1222no—
379C2×C22⋊C4—1222no—
380C2×C22⋊C4—1222no—
381C2×C42—611no—
382C2×C42—611no—
383C2×C42—611no—
384C2×C42—611no—
385C2×C42—611no—
386C2×C42—611no—
387C2×C42—611no—
388C2×C42—611no—
389C2×C42—611no—
390C2×C42—611no—
391C2×C42—611no—
392C2×C42—611no—
393C4⋊C8—614no—
394C4⋊C8—1222no—
395C4⋊C8—1222no—
396C4⋊C8—1222no—
397C22⋊C8—1222no—
398C22⋊C8—1222no—
399C22⋊C8—1222no—
400C22⋊C8—1222no—
401#97—1222no—
402#97—1222no—
403C4×C8—614no—
404C4×C8—1222no—
405C24—1228no—
406C24—1222no—
407C24—1222no—
408C24—1222no—
409C24—2444no—
410C24—2444no—
411C24C22⋊#692311yescharacteristic
412C2×D4—618no—
413C2×D4—614no—
414C2×D4—1228no—
415C2×D4—1228no—
416C2×D4—1228no—
417C2×D4—1228no—
418C2×D4—1228no—
419C2×D4—1222no—
420C2×D4—1222no—
421C2×D4—1222no—
422C2×D4—1224no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—44no—
428C22×C4—611no—
429C22×C4—611no—
430C22×C4—611no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—1224no—
441C22×C4—1224no—
442C22×C4—1224no—
443C22×C4—1224no—
444C22×C4—1224no—
445C22×C4—2448no—
446C22×C4—2448no—
447C22×C4—2448no—
448C22×C4—2448no—
449C22×C4—2448no—
450C22×C4—2448no—
451C22×C4—2442no—
452C22×C4C22⋊#692311yescharacteristic
453C22×C4C22⋊#692311yescharacteristic
454C22×C4C22⋊#692311yescharacteristic
455C22×C4C22×#692311yescharacteristic
456C22×C4C22×#692311yescharacteristic
457C22×C4C22×#692311yescharacteristic
458M16—2444no—
459M16—2444no—
460C2×C8—1224no—
461C2×C8—1224no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4C22×#692314yes—
466C22⋊C4—1224no—
467C22⋊C4—1224no—
468C22⋊C4—1224no—
469C22⋊C4—1224no—
470C42—611no—
471C42—611no—
472C42—611no—
473C42—611no—
474C42—611no—
475C42—611no—
476C42—611no—
477C42—611no—
478C42—611no—
479C42—611no—
480C42—611no—
481C42—611no—
482C42—611no—
483C42—611no—
484C42—611no—
485C42—611no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—1228no—
490C23—1228no—
491C23—1228no—
492C23—1224no—
493C23—2444no—
494C23—2444no—
495C23—24432no—
496C23—2444no—
497C23—2444no—
498C23—2444no—
499C23—2444no—
500C23C2×C22⋊#692311yescharacteristic
501C23C2×C22⋊#692311yescharacteristic
502C23C2×C22⋊#692311yescharacteristic
503D4—618no—
504D4—1228no—
505D4—1228no—
506D4—1228no—
507D4—1224no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—44no—
515C2×C4—44no—
516C2×C4—44no—
517C2×C4—614no—
518C2×C4—611no—
519C2×C4—611no—
520C2×C4—611no—
521C2×C4—611no—
522C2×C4—611no—
523C2×C4—611no—
524C2×C4—611no—
525C2×C4—611no—
526C2×C4—1222no—
527C2×C4—1222no—
528C2×C4—1222no—
529C2×C4—1222no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—2448no—
534C2×C4—2448no—
535C2×C4—2448no—
536C2×C4—2448no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4C2×C22⋊#692311yescharacteristic
542C2×C4C2×C22⋊#692311yescharacteristic
543C2×C4C2×C22⋊#692311yescharacteristic
544C2×C4D61⋊M1614yes—
545C2×C4C23×#692311yescharacteristic
546C8—2444no—
547C8—2444no—
548C22—28no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—1228no—
556C22—24416no—
557C22—24416no—
558C22—24416no—
559C22—2444no—
560C22—2444no—
561C22#1684073412yes—
562C22#1684075412yes—
563C22#1684076112yes—
564C22C22×C22⋊#692311yescharacteristic
565C4—21no—
566C4—21no—
567C4—44no—
568C4—612no—
569C4—612no—
570C4—1221no—
571C4—1221no—
572C4—1221no—
573C4—1221no—
574C4—1221no—
575C4—1221no—
576C4#1684073412yes—
577C4C2×D61⋊M1612yes—
578C2—22no—
579C2—22no—
580C2—22no—
581C2—2448no—
582C2C2×#1684073411yescharacteristic
583C2C2×#1684075411yescharacteristic
584C2C2×#1684076111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC23×D244C4
cosocleC4×Dic61C24
hypercenterC22×C4⋊C4#6923
hypocenterC61#17448
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #21462495C2semidirect
2. #21462495C2semidirect
3. #21461160C2semidirect
4. #21461146C2semidirect
5. #21461120C2semidirect
8. #16840783C22semidirect
12. #16840779C22semidirect
13. #16840778C22semidirect
14. #16840778C22semidirect
16. #16840765C22semidirect
20. C4×#11758217C22semidirect
21. #16840610C22semidirect
44. C4⋊#92420C23semidirect
52. C4×#92420C23semidirect
153. C2×D244M16semidirect
331. C61#17448semidirect

Maximal subgroups

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

subgroupindex
#214624952
#214611602
#214611462
#214611202
C22×#145197392
#1744861