Finite Group Databasebeta

← #29575745

Subgroups — #29575745

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#21454098C211yesmaximal, characteristic
2C2×#95×D61C211yesmaximal, characteristic, complemented
3#21445728C211yesmaximal, characteristic, complemented
4C2×#16839496C211yesmaximal, characteristic, complemented
5#21443699C211yesmaximal, characteristic, complemented
6#21443698C211yesmaximal, characteristic, complemented
7C2×C61×#327C211yesmaximal, characteristic, complemented
8C23×C4×D61—21no—
9C23×C4×D61C2211yescharacteristic
10C2×#14519748C412yescomplemented
11C2×#14519745—21no—
12C2×C22⋊#92418C2211yescharacteristic
13C2×#14519689—22no—
14#16839642—21no—
15#16839638—22no—
16#16839622C2211yescharacteristic
17#16839619C412yescomplemented
18C2×#14519684—21no—
19C2×#14519684C2211yescharacteristic
20#95×D61—22no—
21#95×D61—22no—
22#16839496—22no—
23C2×#121×C61C2211yescharacteristic
24C2×C22⋊C8×C61C2211yescharacteristic
25C2×#95×C61C2211yescharacteristic
26C61×#327—22no—
27C24×D61D411yescharacteristic
28C22×C22⋊D61—22no—
29C23×Dic61—21no—
30C23×Dic61D411yescharacteristic
31C22×C4×D61—28no—
32C22×C4×D61—24no—
33C22×C4×D61—21no—
34C22×C4×D61—21no—
35C22×C4×D61—21no—
36C22×C4×D61—21no—
37C22×C4×D61—44no—
38C22×C4×D61—44no—
39C22×C4×D61—42no—
40C22×C4×D61—42no—
41C22×C4×D61C2×C412yes—
42C22×C4×D61D412yes—
43C22×#92418—21no—
44#14519748—44no—
45#14519745—42no—
46#14519745—42no—
47C2×C4⋊Dic61C2×C412yescomplemented
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61—22no—
50C2×#11758198—22no—
51C22⋊#92418—21no—
52C22⋊#92418—21no—
53#14519689—44no—
54#14519684—24no—
55#14519684—21no—
56#14519684—21no—
57#14519684—22no—
58#14519684D412yescomplemented
59C22×D4×C61—21no—
60C22×D4×C61C2×C411yescharacteristic, complemented
61C23×C4×C61—21no—
62C23×C4×C61C2311yescharacteristic
63C22×C8×C61—21no—
64#121×C61—21no—
65#121×C61—21no—
66#121×C61—21no—
67#121×C61—21no—
68C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
69C2×C22⋊C4×C61—21no—
70C22⋊C8×C61—21no—
71C22⋊C8×C61—21no—
72#95×C61—21no—
73#95×C61D412yescomplemented
74C24×C61—21no—
75C24×C61C2×D411yescharacteristic
76C23×D61—21no—
77C23×D61—21no—
78C23×D61—21no—
79C23×D61—21no—
80C23×D61—24no—
81C23×D61—24no—
82C23×D61C22⋊C412yes—
83C23×D61D812yes—
84C23×D61SD1612yes—
85C2×D4×C61—21no—
86C2×D4×C61—21no—
87C2×D4×C61—42no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C22×C4×C61—24no—
95C22×C4×C61—22no—
96C22×C4×C61—21no—
97C22×C4×C61—42no—
98C22×C4×C61—42no—
99C22×C4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61C22×C411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61#4111yescharacteristic
106C22×C4×C61#4111yescharacteristic
107C2×C22⋊D61—44no—
108C2×C22⋊D61—44no—
109C2×C22⋊D61—44no—
110C22×Dic61—24no—
111C22×Dic61—22no—
112C22×Dic61—21no—
113C22×Dic61—21no—
114C22×Dic61—22no—
115C22×Dic61—42no—
116C22×Dic61—42no—
117C22×Dic61—41no—
118C22×Dic61—41no—
119C22×Dic61C22⋊C412yes—
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—21no—
140C4⋊C4×C61—21no—
141C22⋊C4×C61—41no—
142C22⋊C4×C61—41no—
143C22⋊Dic61—44no—
144C22⋊Dic61—41no—
145C22⋊Dic61—41no—
146#11758198—44no—
147C4⋊Dic61—42no—
148C2×#92418—42no—
149C2×#92418—41no—
150C23×C61—22no—
151C23×C61—22no—
152C23×C61—41no—
153C23×C61—42no—
154C23×C61—41no—
155C23×C61—41no—
156C23×C61—42no—
157C23×C61C2×C22⋊C411yescharacteristic
158C23×C61#12011yescharacteristic
159C23×C61#12311yescharacteristic
160C23×C61C2×D811yescharacteristic
161C23×C61C2×SD1611yescharacteristic
162C23×C61AGL(1,ℤ/8)11yescharacteristic
163C23×C61#13711yescharacteristic
164C22×D61—24no—
165C22×D61—24no—
166C22×D61—28no—
167C22×D61—24no—
168C22×D61—24no—
169C22×D61—28no—
170C22×D61—22no—
171C22×D61—22no—
172C22×D61—22no—
173C22×D61—22no—
174C22×D61—22no—
175C22×D61—22no—
176C22×D61—22no—
177C22×D61—22no—
178C22×D61—28no—
179C22×D61—28no—
180C22×D61#9914yes—
181C22×D61#10214yes—
182C22×D61#10414yes—
183D4×C61—81no—
184D4×C61—81no—
185D4×C61—81no—
186D4×C61—81no—
187D4×C61—81no—
188D4×C61—81no—
189C2×C4×C61—22no—
190C2×C4×C61—22no—
191C2×C4×C61—24no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—42no—
197C2×C4×C61—44no—
198C2×C4×C61—44no—
199C2×C4×C61—42no—
200C2×C4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—41no—
203C2×C4×C61C4×D411yescharacteristic
204C2×C4×C61C4×D411yescharacteristic
205C2×C4×C61#12111yescharacteristic
206C2×C4×C61#12111yescharacteristic
207C22⋊D61—88no—
208C2×Dic61—24no—
209C2×Dic61—22no—
210C2×Dic61—22no—
211C2×Dic61—22no—
212C2×Dic61—42no—
213C2×Dic61—44no—
214C2×Dic61—44no—
215C2×Dic61—42no—
216C2×Dic61—42no—
217C2×Dic61—42no—
218C2×Dic61—42no—
219C2×Dic61—42no—
220C2×Dic61—42no—
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—81no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61—82no—
241C22×C61—82no—
242C22×C61#38611yescharacteristic
243C22×C61C2×#9912yes—
244C22×C61C2×#10211yescharacteristic
245C22×C61#41711yescharacteristic
246C22×C61C2×#10412yes—
247C22×C61#44711yescharacteristic
248C22×C61#44811yescharacteristic
249C22×C61#48011yescharacteristic
250C22×C61#48111yescharacteristic
251C2×D61—28no—
252C2×D61—28no—
253C2×D61—28no—
254C2×D61—28no—
255C2×D61—24no—
256C2×D61—24no—
257C2×D61—24no—
258C2×D61—24no—
259C2×D61—24no—
260C2×D61—24no—
261C2×D61#32718yescomplemented
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—44no—
267C4×C61—81no—
268Dic61—44no—
269Dic61—42no—
270Dic61—82no—
271#2847—611no—
272C22×#95—611no—
273#1779—611no—
274C2×#327—611no—
275C2×#327D6111yescharacteristic, complemented
276#1294—611no—
277#1294—611no—
278C2×C61—21no—
279C2×C61—21no—
280C2×C61—21no—
281C2×C61—21no—
282C2×C61—161no—
283C2×C61C2×#32712yes—
284C2×C61#150412yes—
285C2×C61#187411yescharacteristic
286C2×C61#189611yescharacteristic
287C2×C61#189811yescharacteristic
288D61—28no—
289C24×C4—611no—
290C24×C4—1221no—
291C2×#121—612no—
292C2×#121C2×D6111yescharacteristic
293C2×#120—1221no—
294C2×C22⋊C8—611no—
295C2×C22⋊C8—1222no—
296C2×C22⋊C8C2×D6111yescharacteristic
297#386—1222no—
298#386—1221no—
299#380—611no—
300#380—612no—
301C2×#95—611no—
302C2×#95—1222no—
303C2×#95—1221no—
304C2×#95—1222no—
305C2×#95C2×D6111yescharacteristic
306#327—22no—
307#327—1222no—
308C61#914711yescharacteristic, complemented, Sylow
309C25—611no—
310C22×D4—21no—
311C22×D4—1222no—
312C22×D4C4×D6111yescharacteristic, complemented
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—21no—
332#121—21no—
333#121—21no—
334#121—21no—
335#121—2444no—
336#120—2442no—
337#120—2442no—
338C2×C4⋊C4—612no—
339C2×C4⋊C4C4×D6111yescharacteristic, complemented
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—612no—
351#95—1222no—
352#95—1224no—
353#95—1221no—
354#95—1221no—
355#95C22⋊D6112yescomplemented
356C24—21no—
357C24—612no—
358C24—612no—
359C24—612no—
360C24—1224no—
361C24—1224no—
362C24—1221no—
363C24—1221no—
364C24—1221no—
365C24—1221no—
366C24D4×D6111yescharacteristic
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—42no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—2444no—
377C2×D4—2444no—
378C2×D4—2444no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—21no—
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—1222no—
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×C4#1175822211yescharacteristic
415C22×C4D4×D6111yescharacteristic
416C22×C4D4×D6111yescharacteristic
417C22×C4#1175822411yescharacteristic
418C22×C4C2×C22⋊D6111yescharacteristic
419C2×C8—42no—
420C2×C8—41no—
421C2×C8—2442no—
422C2×C8—2441no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—2442no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—2444no—
429C22⋊C4—2444no—
430C22⋊C4—2441no—
431C22⋊C4—2441no—
432C23—22no—
433C23—22no—
434C23—42no—
435C23—41no—
436C23—41no—
437C23—42no—
438C23—41no—
439C23—614no—
440C23—614no—
441C23—614no—
442C23—1228no—
443C23—1228no—
444C23—1224no—
445C23—1224no—
446C23—1224no—
447C23—1228no—
448C23—1224no—
449C23—1228no—
450C23—1222no—
451C23—1222no—
452C23—1222no—
453C23—1222no—
454C23—1222no—
455C23—1222no—
456C23—1222no—
457C23—1222no—
458C23C22⋊C4×D6111yescharacteristic
459C23#1451974511yescharacteristic
460C23#1451975911yescharacteristic
461C23D8×D6111yescharacteristic
462C23SD16×D6111yescharacteristic
463C23#1451980111yescharacteristic
464C23#1451980611yescharacteristic
465D4—81no—
466D4—81no—
467D4—81no—
468D4—81no—
469D4—81no—
470D4—81no—
471D4—4888no—
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—41no—
484C2×C4—41no—
485C2×C4—41no—
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—2442no—
496C2×C4—2442no—
497C2×C4—2442no—
498C2×C4—2442no—
499C2×C4—2444no—
500C2×C4—2444no—
501C2×C4—2442no—
502C2×C4—2442no—
503C2×C4—2442no—
504C2×C4#1451973711yescharacteristic
505C2×C4C4×C22⋊D6111yescharacteristic
506C2×C4#1451974811yescharacteristic
507C2×C4#1451975011yescharacteristic
508C8—81no—
509C8—4881no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—22no—
518C22—81no—
519C22—81no—
520C22—82no—
521C22—82no—
522C22—81no—
523C22—618no—
524C22—1228no—
525C22—1228no—
526C22—1228no—
527C22—1228no—
528C22—1224no—
529C22—1224no—
530C22—1224no—
531C22—1224no—
532C22—1224no—
533C22—1224no—
534C22#1683963811yescharacteristic
535C22#99×D6112yes—
536C22#102×D6111yescharacteristic
537C22#1683976011yescharacteristic
538C22#104×D6112yes—
539C22#1683989411yescharacteristic
540C22#1683989911yescharacteristic
541C22#1684007411yescharacteristic
542C22#1684007911yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—44no—
548C4—81no—
549C4—4882no—
550C4—2444no—
551C4—2442no—
552C2—21no—
553C2—21no—
554C2—21no—
555C2—21no—
556C2—161no—
557C2—1228no—
558C2#327×D6112yes—
559C2#2144432012yes—
560C2#2144613311yescharacteristic
561C2#2144625911yescharacteristic
562C2#2144626911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#327C2
socleC23×C61C2×C22⋊C4
prime radical#21454098C2
cosocleC23×C4×C61C23
hypercenterC2×#327D61
hypocenterC61#9147
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#95×D61C2semidirect
3. #21445728C2semidirect
4. C2×#16839496C2semidirect
5. #21443699C2semidirect
6. #21443698C2semidirect
7. C2×C61×#327C2semidirect
10. C2×#14519748C4semidirect
17. #16839619C4semidirect
47. C2×C4⋊Dic61C2×C4semidirect
58. #14519684D4semidirect
60. C22×D4×C61C2×C4semidirect
68. C2×C4⋊C4×C61C2×C4semidirect
73. #95×C61D4semidirect
261. C2×D61#327semidirect
275. C2×#327D61semidirect
308. C61#9147semidirect
312. C22×D4C4×D61semidirect
339. C2×C4⋊C4C4×D61semidirect
355. #95C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214540982
C2×#95×D612
#214457282
C2×#168394962
#214436992
#214436982
C2×C61×#3272
#914761