Finite Group Databasebeta

← #29575747

Subgroups — #29575747

Order 15616.

1348 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454102C211yesmaximal, characteristic
2C2×#95×D61C211yesmaximal, characteristic, complemented
3#21445728C211yesmaximal, characteristic, complemented
4C2×#16839497C211yesmaximal, characteristic, complemented
5C2×#16839495C211yesmaximal, characteristic, complemented
6#21443697C211yesmaximal, characteristic, complemented
7C61×#1294C211yesmaximal, characteristic, complemented
8C23×C4×D61—21no—
9C23×C4×D61C2211yescharacteristic
10C2×#14519752C412yescomplemented
11C2×#14519751C2211yescharacteristic
12C2×#14519747—21no—
13C2×C22⋊#92418C2211yescharacteristic
14C2×#14519689—22no—
15#16839640—22no—
16#16839639—21no—
17#16839619C412yescomplemented
18C2×#14519684—21no—
19C2×#14519684C2211yescharacteristic
20#95×D61—22no—
21#95×D61—22no—
22#16839497—22no—
23#16839495—22no—
24C2×C22⋊C8×C61C2211yescharacteristic
25C61×#380C2211yescharacteristic
26C2×#95×C61C2211yescharacteristic
27C24×D61D411yescharacteristic
28C22×D244—22no—
29C22×D244C2×C411yescharacteristic, complemented
30C22×C22⋊D61—21no—
31C23×Dic61—21no—
32C23×Dic61D411yescharacteristic
33C22×C4×D61—28no—
34C22×C4×D61—24no—
35C22×C4×D61—21no—
36C22×C4×D61—21no—
37C22×C4×D61—21no—
38C22×C4×D61—21no—
39C22×C4×D61—44no—
40C22×C4×D61—44no—
41C22×C4×D61—42no—
42C22×C4×D61—42no—
43C22×C4×D61C2×C412yes—
44C22×C4×D61D412yes—
45C22×#92418—21no—
46#14519752—44no—
47#14519751—21no—
48#14519751—21no—
49#14519751—21no—
50#14519751—21no—
51#14519747—42no—
52#14519747—42no—
53C2×C4⋊Dic61C2×C411yescharacteristic, complemented
54C2×#11758198—22no—
55C2×#11758198—21no—
56C2×#11758198—22no—
57C22⋊#92418—21no—
58C22⋊#92418—21no—
59#14519689—44no—
60#14519684—24no—
61#14519684—21no—
62#14519684—22no—
63#14519684D412yescomplemented
64C23×C4×C61—21no—
65C23×C4×C61C2311yescharacteristic
66C22×C8×C61—21no—
67C2×C4⋊C4×C61C2×C412yescomplemented
68C2×C22⋊C4×C61—21no—
69C22⋊C8×C61—21no—
70C22⋊C8×C61—21no—
71#95×C61—21no—
72#95×C61—21no—
73#95×C61D412yescomplemented
74C24×C61C2×D411yescharacteristic
75C23×D61—21no—
76C23×D61—21no—
77C23×D61—21no—
78C23×D61—21no—
79C23×D61—24no—
80C23×D61—24no—
81C23×D61—21no—
82C23×D61C22⋊C412yes—
83C23×D61D812yes—
84C23×D61SD1612yes—
85C22×C4×C61—24no—
86C22×C4×C61—22no—
87C22×C4×C61—22no—
88C22×C4×C61—42no—
89C22×C4×C61—42no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61C22×C411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61#4111yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C2×C22⋊D61—41no—
99C2×C22⋊D61—41no—
100C2×C22⋊D61—41no—
101C2×C22⋊D61—41no—
102C2×C22⋊D61—41no—
103C2×C22⋊D61—41no—
104C22×Dic61—24no—
105C22×Dic61—22no—
106C22×Dic61—21no—
107C22×Dic61—21no—
108C22×Dic61—21no—
109C22×Dic61—42no—
110C22×Dic61—42no—
111C22×Dic61—41no—
112C22×Dic61—41no—
113C22×Dic61C22⋊C412yes—
114C2×D244—21no—
115C2×D244—21no—
116C2×D244—42no—
117C2×D244—44no—
118C2×D244—44no—
119C2×D244—44no—
120C2×C4×D61—216no—
121C2×C4×D61—24no—
122C2×C4×D61—24no—
123C2×C4×D61—22no—
124C2×C4×D61—22no—
125C2×C4×D61—22no—
126C2×C4×D61—22no—
127C2×C4×D61—42no—
128C2×C4×D61—42no—
129C2×C4×D61—44no—
130C2×C4×D61—44no—
131C2×C4×D61—44no—
132C2×C4×D61—44no—
133C2×C4×D61—48no—
134C2×C4×D61—416no—
135C2×C4×D61—416no—
136C2×C4×D61—48no—
137C2×C8×C61—42no—
138C2×C8×C61—41no—
139C4⋊C4×C61—42no—
140C22⋊C4×C61—41no—
141C22⋊C4×C61—41no—
142#11758198—44no—
143#11758198—44no—
144#11758198—41no—
145#11758198—41no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C2×#92418—42no—
149C2×#92418—41no—
150C23×C61—22no—
151C23×C61—22no—
152C23×C61C2×C22⋊C411yescharacteristic
153C23×C61#12011yescharacteristic
154C23×C61#12311yescharacteristic
155C23×C61C2×D811yescharacteristic
156C23×C61C2×SD1611yescharacteristic
157C23×C61AGL(1,ℤ/8)11yescharacteristic
158C23×C61#13711yescharacteristic
159C22×D61—24no—
160C22×D61—24no—
161C22×D61—28no—
162C22×D61—24no—
163C22×D61—24no—
164C22×D61—28no—
165C22×D61—22no—
166C22×D61—22no—
167C22×D61—22no—
168C22×D61—22no—
169C22×D61—22no—
170C22×D61—22no—
171C22×D61—22no—
172C22×D61—22no—
173C22×D61—28no—
174C22×D61—28no—
175C22×D61—41no—
176C22×D61—42no—
177C22×D61—41no—
178C22×D61—41no—
179C22×D61—42no—
180C22×D61#9914yes—
181C22×D61#10214yes—
182C22×D61#10414yes—
183C2×C4×C61—22no—
184C2×C4×C61—22no—
185C2×C4×C61—24no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—42no—
191C2×C4×C61—44no—
192C2×C4×C61—44no—
193C2×C4×C61—42no—
194C2×C4×C61—42no—
195C2×C4×C61—42no—
196C2×C4×C61—42no—
197C2×C4×C61C4×D411yescharacteristic
198C2×C4×C61C4×D411yescharacteristic
199C2×C4×C61#12111yescharacteristic
200C2×C4×C61#12111yescharacteristic
201C22⋊D61—81no—
202C22⋊D61—81no—
203C22⋊D61—81no—
204C22⋊D61—81no—
205C2×Dic61—24no—
206C2×Dic61—22no—
207C2×Dic61—22no—
208C2×Dic61—22no—
209C2×Dic61—42no—
210C2×Dic61—44no—
211C2×Dic61—44no—
212C2×Dic61—42no—
213C2×Dic61—42no—
214C2×Dic61—42no—
215C2×Dic61—41no—
216C2×Dic61—41no—
217C2×Dic61—41no—
218D244—81no—
219D244—81no—
220D244—88no—
221C4×D61—44no—
222C4×D61—44no—
223C4×D61—44no—
224C4×D61—44no—
225C4×D61—432no—
226C8×C61—81no—
227#92418—81no—
228#9147—611nomaximal, Sylow
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—22no—
234C22×C61—22no—
235C22×C61—22no—
236C22×C61—22no—
237C22×C61#38611yescharacteristic
238C22×C61C2×#9912yes—
239C22×C61C2×#10211yescharacteristic
240C22×C61#41711yescharacteristic
241C22×C61C2×#10412yes—
242C22×C61#44711yescharacteristic
243C22×C61#44811yescharacteristic
244C22×C61#48011yescharacteristic
245C22×C61#48111yescharacteristic
246C2×D61—28no—
247C2×D61—28no—
248C2×D61—28no—
249C2×D61—28no—
250C2×D61—24no—
251C2×D61—24no—
252C2×D61—24no—
253C2×D61—24no—
254C2×D61—24no—
255C2×D61—24no—
256C2×D61—81no—
257C2×D61—81no—
258C2×D61—81no—
259C2×D61—82no—
260C2×D61—82no—
261C2×D61#32718yescomplemented
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—44no—
267C4×C61—82no—
268Dic61—44no—
269Dic61—42no—
270Dic61—81no—
271#2847—611no—
272C22×#95—611no—
273#1779—611no—
274C2×#327—611no—
275C2×#327—611no—
276#1294—611no—
277#1294D6111yescharacteristic, complemented
278C2×C61—21no—
279C2×C61—21no—
280C2×C61—21no—
281C2×C61—21no—
282C2×C61C2×#32712yes—
283C2×C61#150412yes—
284C2×C61#187411yescharacteristic
285C2×C61#189611yescharacteristic
286C2×C61#189811yescharacteristic
287D61—28no—
288D61—161no—
289C24×C4—611no—
290C24×C4—1221no—
291C2×#121—611no—
292C2×#121—612no—
293C2×#120—1221no—
294C2×C22⋊C8—611no—
295C2×C22⋊C8—1222no—
296C2×C22⋊C8C2×D6111yescharacteristic
297#386—1222no—
298#386—1221no—
299#380—612no—
300#380C2×D6111yescharacteristic
301C2×#95—611no—
302C2×#95—1222no—
303C2×#95—1221no—
304C2×#95—1222no—
305C2×#95C2×D6111yescharacteristic
306#327—1222no—
307#327—1222no—
308C61#914711yescharacteristic, complemented, Sylow
309C25—611no—
310C22×D4—611no—
311C22×D4—1222no—
312C22×D4—1221no—
313C23×C4—21no—
314C23×C4—611no—
315C23×C4—612no—
316C23×C4—612no—
317C23×C4—1228no—
318C23×C4—1224no—
319C23×C4—1221no—
320C23×C4—1221no—
321C23×C4—1221no—
322C23×C4—1221no—
323C23×C4—1221no—
324C23×C4—2444no—
325C23×C4—2442no—
326C23×C4—2444no—
327C23×C4—2442no—
328C23×C4C22×D6111yescharacteristic
329C22×C8—21no—
330C22×C8—1221no—
331#121—1221no—
332#121—1221no—
333#121—1221no—
334#121—1221no—
335#121—2444no—
336#120—2442no—
337#120—2442no—
338C2×C4⋊C4—611no—
339C2×C4⋊C4C4×D6112yescomplemented
340C2×C22⋊C4—21no—
341C2×C22⋊C4—1222no—
342C2×C22⋊C4—1222no—
343C2×C22⋊C4—1221no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8—1221no—
347C22⋊C8—1221no—
348C22⋊C8—2444no—
349#95—21no—
350#95—21no—
351#95—612no—
352#95—1222no—
353#95—1224no—
354#95—1221no—
355#95D24412yescomplemented
356C24—612no—
357C24—612no—
358C24—612no—
359C24—1224no—
360C24—1224no—
361C24—1221no—
362C24—1221no—
363C24—1221no—
364C24—1221no—
365C24—1221no—
366C24D4×D6111yescharacteristic
367C2×D4—1221no—
368C2×D4—1221no—
369C2×D4—2442no—
370C2×D4—2444no—
371C2×D4—2444no—
372C2×D4—2444no—
373C2×D4—2441no—
374C2×D4—2441no—
375C2×D4—2441no—
376C2×D4—2441no—
377C2×D4—2441no—
378C2×D4—2441no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—612no—
387C22×C4—1224no—
388C22×C4—1224no—
389C22×C4—12216no—
390C22×C4—1224no—
391C22×C4—1222no—
392C22×C4—1221no—
393C22×C4—1221no—
394C22×C4—1222no—
395C22×C4—1222no—
396C22×C4—1222no—
397C22×C4—1222no—
398C22×C4—1221no—
399C22×C4—2442no—
400C22×C4—2442no—
401C22×C4—2444no—
402C22×C4—2444no—
403C22×C4—2444no—
404C22×C4—2444no—
405C22×C4—24416no—
406C22×C4—2448no—
407C22×C4—24416no—
408C22×C4—2448no—
409C22×C4—2442no—
410C22×C4—2442no—
411C22×C4—2441no—
412C22×C4—2441no—
413C22×C4C2×C4×D6111yescharacteristic
414C22×C4C2×D24411yescharacteristic
415C22×C4#1175822211yescharacteristic
416C22×C4D4×D6111yescharacteristic
417C22×C4D4×D6111yescharacteristic
418C22×C4#1175822611yescharacteristic
419C2×C8—42no—
420C2×C8—41no—
421C2×C8—2442no—
422C2×C8—2441no—
423C4⋊C4—42no—
424C4⋊C4—1221no—
425C4⋊C4—1221no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—2444no—
429C22⋊C4—2444no—
430C22⋊C4—2441no—
431C22⋊C4—2441no—
432C23—22no—
433C23—22no—
434C23—614no—
435C23—614no—
436C23—614no—
437C23—1228no—
438C23—1228no—
439C23—1224no—
440C23—1224no—
441C23—1224no—
442C23—1228no—
443C23—1224no—
444C23—1228no—
445C23—1222no—
446C23—1222no—
447C23—1222no—
448C23—1222no—
449C23—1222no—
450C23—1222no—
451C23—1222no—
452C23—1222no—
453C23—2442no—
454C23—2441no—
455C23—2441no—
456C23—2442no—
457C23—2441no—
458C23C22⋊C4×D6111yescharacteristic
459C23#1451974711yescharacteristic
460C23#1451976211yescharacteristic
461C23D8×D6111yescharacteristic
462C23SD16×D6111yescharacteristic
463C23#1451980411yescharacteristic
464C23#1451980911yescharacteristic
465D4—4881no—
466D4—4881no—
467D4—4888no—
468D4—4881no—
469D4—4881no—
470D4—4881no—
471D4—4881no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—1224no—
487C2×C4—1222no—
488C2×C4—1222no—
489C2×C4—1222no—
490C2×C4—2444no—
491C2×C4—2444no—
492C2×C4—2444no—
493C2×C4—2444no—
494C2×C4—24432no—
495C2×C4—2441no—
496C2×C4—2441no—
497C2×C4—2441no—
498C2×C4—2442no—
499C2×C4—2444no—
500C2×C4—2444no—
501C2×C4—2442no—
502C2×C4—2442no—
503C2×C4—2442no—
504C2×C4#1451973911yescharacteristic
505C2×C4C4×D24411yescharacteristic
506C2×C4#1451975011yescharacteristic
507C2×C4#1451975211yescharacteristic
508C8—81no—
509C8—4881no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—22no—
518C22—618no—
519C22—1228no—
520C22—1228no—
521C22—1228no—
522C22—1228no—
523C22—1224no—
524C22—1224no—
525C22—1224no—
526C22—1224no—
527C22—1224no—
528C22—1224no—
529C22—4881no—
530C22—4881no—
531C22—4882no—
532C22—4882no—
533C22—4881no—
534C22#1683964011yescharacteristic
535C22#99×D6112yes—
536C22#102×D6111yescharacteristic
537C22#1683976211yescharacteristic
538C22#104×D6112yes—
539C22#1683989711yescharacteristic
540C22#1683990211yescharacteristic
541C22#1684007711yescharacteristic
542C22#1684008211yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—44no—
548C4—82no—
549C4—4881no—
550C4—2444no—
551C4—2442no—
552C2—21no—
553C2—21no—
554C2—21no—
555C2—21no—
556C2—1228no—
557C2—9761no—
558C2#327×D6112yes—
559C2#2144432212yes—
560C2#2144613511yescharacteristic
561C2#2144626111yescharacteristic
562C2#2144627111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC23×C61C2×C22⋊C4
prime radical#21454102C2
cosocleC23×C4×C61C23
hypercenter#1294D61
hypocenterC61#9147
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
2. C2×#95×D61C2semidirect
3. #21445728C2semidirect
4. C2×#16839497C2semidirect
5. C2×#16839495C2semidirect
6. #21443697C2semidirect
7. C61×#1294C2semidirect
10. C2×#14519752C4semidirect
17. #16839619C4semidirect
29. C22×D244C2×C4semidirect
53. C2×C4⋊Dic61C2×C4semidirect
63. #14519684D4semidirect
67. C2×C4⋊C4×C61C2×C4semidirect
73. #95×C61D4semidirect
261. C2×D61#327semidirect
277. #1294D61semidirect
308. C61#9147semidirect
339. C2×C4⋊C4C4×D61semidirect
355. #95D244semidirect

Maximal subgroups

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

subgroupindex
#214541022
C2×#95×D612
#214457282
C2×#168394972
C2×#168394952
#214436972
C61×#12942
#914761