Finite Group Databasebeta

← #29689040

Subgroups — #29689040

Order 15616.

1842 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519752C211yesmaximal, characteristic
2C2×C22⋊C8×D61C211yesmaximal, characteristic, complemented
3#21448201C211yesmaximal, characteristic, complemented
4#21446246C214yesmaximal, complemented
5#21446140C214yesmaximal, complemented
6#21445909C211yesmaximal, characteristic, complemented
7#21445751C211yesmaximal, characteristic, complemented
8#21445749C211yesmaximal, characteristic, complemented
9C61×#1824C211yesmaximal, characteristic, complemented
10C23×D244—21no—
11C23×D244C2211yescharacteristic
12C23×C4×D61C2211yescharacteristic
13C22×C8×D61C2212yescomplemented
14C2×#14519752—21no—
15C2×#14519752—21no—
16C2×#14519752—24no—
17C2×#14519752C418yescomplemented
18C2×#14519752C2212yes—
19C2×#14519752C2212yes—
20C2×#14519735C2212yescomplemented
21C22×#11758198—21no—
22C2×#14519699C2214yescomplemented
23C2×#14519697C2214yescomplemented
24C2×C22⋊#92418C2211yescharacteristic
25C2×#14519689C2212yescomplemented
26C22⋊C8×D61—24no—
27#16839624—21no—
28#16839622C2211yescharacteristic
29#16839619C2212yescomplemented
30#16839617—21no—
31C22⋊C4×Dic61—21no—
32#16839609—21no—
33#16839524C2214yescomplemented
34C22×C4⋊C4×C61C2211yescharacteristic
35C2×C22⋊C8×C61C2211yescharacteristic
36C61×#380C2211yescharacteristic
37C61×#340C2214yescomplemented
38C24×D61—21no—
39C24×D61D411yescharacteristic
40C22×D244—28no—
41C22×D244—22no—
42C22×D244—22no—
43C22×D244—21no—
44C22×D244—22no—
45C22×D244—44no—
46C22×D244—48no—
47C22×D244C2×C414yes—
48C22×D244C2312yes—
49C23×Dic61D411yescharacteristic
50C22×C4×D61—44no—
51C22×C4×D61C2×C414yes—
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D414yes—
55C22×C4×D61C2311yescharacteristic
56C22×C4×D61C2311yescharacteristic
57C22×#92418C2312yes—
58C2×C8×D61—24no—
59C2×C8×D61—44no—
60#14519752—28no—
61#14519752—28no—
62#14519752—24no—
63#14519752—24no—
64#14519752C2×C418yes—
65#14519752C2×C418yes—
66#14519735—44no—
67C2×C4⋊Dic61C2312yes—
68C2×C22⋊Dic61—21no—
69C2×#11758198—28no—
70C2×#11758198—22no—
71C2×#11758198—22no—
72C2×#11758198—22no—
73C2×#11758198—22no—
74C2×C4×Dic61—22no—
75#14519699—44no—
76#14519697—44no—
77C22⋊#92418—22no—
78#14519689—24no—
79#14519684—21no—
80#14519684—22no—
81C23×C4×C61—21no—
82C23×C4×C61C2311yescharacteristic
83C22×C8×C61C2312yes—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61—22no—
86C2×C4⋊C4×C61C2×C414yes—
87C2×C4⋊C4×C61C2312yes—
88C2×C4⋊C4×C61C2312yes—
89C2×C22⋊C4×C61—21no—
90C22⋊C8×C61—22no—
91#95×C61—21no—
92C24×C61C2×D411yescharacteristic
93C23×D61—22no—
94C23×D61—22no—
95C23×D61—24no—
96C23×D61—24no—
97C23×D61—22no—
98C23×D61—42no—
99C23×D61—44no—
100C23×D61—44no—
101C23×D61—42no—
102C23×D61—42no—
103C23×D61C22⋊C414yes—
104C23×D61C2×D411yescharacteristic
105C23×D61C2×D411yescharacteristic
106C22×C4×C61—24no—
107C22×C4×C61—24no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—44no—
111C22×C4×C61C22×C412yes—
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D412yes—
114C22×C4×C61C2411yescharacteristic
115C22×Dic61—22no—
116C22×Dic61—42no—
117C22×Dic61C22⋊C414yes—
118C22×Dic61C2×D411yescharacteristic
119C22×Dic61C2×D411yescharacteristic
120C2×D244—24no—
121C2×D244—24no—
122C2×D244—28no—
123C2×D244—28no—
124C2×D244—24no—
125C2×D244—22no—
126C2×D244—48no—
127C2×D244—44no—
128C2×D244—48no—
129C2×D244—48no—
130C2×D244—432no—
131C2×D244—48no—
132C2×D244C22×C414yes—
133C2×C4×D61—24no—
134C2×C4×D61—24no—
135C2×C4×D61—48no—
136C2×C4×D61—48no—
137C2×C4×D61—42no—
138C2×C4×D61—42no—
139C2×C4×D61C22⋊C414yes—
140C2×C4×D61C22⋊C414yes—
141C2×C4×D61C22×C412yes—
142C2×C4×D61C22×C412yes—
143C2×C4×D61C2×D412yes—
144C2×C4×D61C2×D412yes—
145C2×C8×C61—22no—
146C2×C8×C61—24no—
147C4⋊C4×C61—24no—
148C4⋊C4×C61—22no—
149C4⋊C4×C61—24no—
150C4⋊C4×C61C22×C414yes—
151C22⋊C4×C61—42no—
152C22⋊Dic61—42no—
153#11758198—28no—
154#11758198—28no—
155#11758198—44no—
156#11758198—44no—
157C4⋊Dic61—24no—
158C4×Dic61—44no—
159C2×#92418—22no—
160C2×#92418—24no—
161C8×D61—48no—
162C23×C61—22no—
163C23×C61—22no—
164C23×C61C2×C22⋊C412yes—
165C23×C61#13512yes—
166C23×C61#13512yes—
167C23×C61C22×D411yescharacteristic
168C22×D61—22no—
169C22×D61—21no—
170C22×D61—21no—
171C22×D61—22no—
172C22×D61—21no—
173C22×D61—21no—
174C22×D61—22no—
175C22×D61—28no—
176C22×D61—28no—
177C22×D61—24no—
178C22×D61—44no—
179C22×D61—48no—
180C22×D61—48no—
181C22×D61—48no—
182C22×D61—48no—
183C22×D61—44no—
184C22×D61—42no—
185C22×D61—42no—
186C22×D61—44no—
187C22×D61—48no—
188C22×D61—88no—
189C22×D61—88no—
190C22×D61C2×C22⋊C412yes—
191C22×D61C2×C22⋊C412yes—
192C22×D61AGL(1,ℤ/8)14yes—
193C2×C4×C61—22no—
194C2×C4×C61—24no—
195C2×C4×C61—24no—
196C2×C4×C61—24no—
197C2×C4×C61—48no—
198C2×C4×C61—44no—
199C2×C4×C61—42no—
200C2×C4×C61—42no—
201C2×C4×C61—42no—
202C2×C4×C61C2×C22⋊C412yes—
203C2×C4×C61C23×C411yescharacteristic
204C2×C4×C61C22×D411yescharacteristic
205C2×C4×C61H(5,𝔽2)14yes—
206C2×Dic61—22no—
207C2×Dic61—22no—
208C2×Dic61—44no—
209C2×Dic61—42no—
210C2×Dic61—42no—
211C2×Dic61—42no—
212C2×Dic61C2×C22⋊C412yes—
213C2×Dic61C2×C22⋊C412yes—
214D244—24no—
215D244—24no—
216D244—48no—
217D244—416no—
218D244—416no—
219D244—44no—
220C4×D61—24no—
221C4×D61—24no—
222C4×D61—24no—
223C4×D61—24no—
224C4×D61—44no—
225C4×D61—44no—
226C8×C61—42no—
227#92418—42no—
228#21761—611nomaximal, Sylow
229C22×C61—22no—
230C22×C61—22no—
231C22×C61—24no—
232C22×C61—24no—
233C22×C61#41614yes—
234C22×C61C22×C22⋊C411yescharacteristic
235C22×C61#53412yes—
236C22×C61C2×#13511yescharacteristic
237C22×C61C2×#13511yescharacteristic
238C22×C61C2×AGL(1,ℤ/8)12yes—
239C2×D61—22no—
240C2×D61—22no—
241C2×D61—24no—
242C2×D61—24no—
243C2×D61—22no—
244C2×D61—22no—
245C2×D61—22no—
246C2×D61—416no—
247C2×D61—42no—
248C2×D61—42no—
249C2×D61—44no—
250C2×D61—44no—
251C2×D61—44no—
252C2×D61—816no—
253C2×D61—84no—
254C2×D61—84no—
255C2×D61#41814yes—
256C4×C61—22no—
257C4×C61—44no—
258C4×C61—82no—
259C4×C61#51812yes—
260C4×C61#53412yes—
261Dic61—22no—
262Dic61—22no—
263Dic61—82no—
264C22×#121—611no—
265C22×C22⋊C8—611no—
266#2280—611no—
267#1893—614no—
268#1875—614no—
269#1824—611no—
270#1824D6111yescharacteristic, complemented
271#1786—611no—
272#1786—611no—
273C2×C61—24no—
274C2×C61#230811yescharacteristic
275C2×C61C2×#41611yescharacteristic
276C2×C61C2×#41811yescharacteristic
277C2×C61#318812yes—
278C2×C61#318812yes—
279D61—24no—
280D61—42no—
281D61—84no—
282C23×D4—611no—
283C23×D4—1221no—
284C24×C4—611no—
285C23×C8—612no—
286C2×#121—618no—
287C2×#121—612no—
288C2×#121—612no—
289C2×#121—1221no—
290C2×#121—1221no—
291C2×#121—1224no—
292C2×#117—612no—
293C22×C4⋊C4C2×D6111yescharacteristic
294C22×C22⋊C4—1221no—
295C2×#102—614no—
296C2×#102—614no—
297C2×C22⋊C8—611no—
298C2×C22⋊C8—612no—
299C2×C22⋊C8—1224no—
300C2×C22⋊C8C2×D6111yescharacteristic
301#381—1221no—
302#380—611no—
303#380—612no—
304#380C2×D6111yescharacteristic
305#379—1221no—
306C4×C22⋊C4—1221no—
307C4×C22⋊C4—1221no—
308#340—614no—
309#340C2×D6114yescomplemented
310C61#2176111yescharacteristic, complemented, Sylow
311C25—611no—
312C25—1221no—
313C22×D4—614no—
314C22×D4—612no—
315C22×D4—1222no—
316C22×D4—1222no—
317C22×D4—1228no—
318C22×D4—1222no—
319C22×D4—1221no—
320C22×D4—2444no—
321C22×D4—2448no—
322C23×C4—21no—
323C23×C4—611no—
324C23×C4—611no—
325C23×C4—611no—
326C23×C4—614no—
327C23×C4—611no—
328C23×C4—611no—
329C23×C4—614no—
330C23×C4—2444no—
331C23×C4C22×D6111yescharacteristic
332C22×C8—612no—
333C22×C8—1224no—
334C22×C8—2444no—
335C22×C8C22×D6112yes—
336#121—618no—
337#121—618no—
338#121—1224no—
339#121—1224no—
340#121—1228no—
341#121—1228no—
342#117—2444no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—612no—
346C2×C4⋊C4C4×D6114yes—
347C2×C4⋊C4C22×D6112yes—
348C2×C4⋊C4C22×D6112yes—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—1222no—
351C2×C22⋊C4—1222no—
352C2×C22⋊C4—1228no—
353C2×C22⋊C4—1222no—
354C2×C22⋊C4—1222no—
355C2×C22⋊C4—1221no—
356C2×C42—1222no—
357#102—2444no—
358#102—2444no—
359C22⋊C8—22no—
360C22⋊C8—1224no—
361C22⋊C8—1222no—
362#95—21no—
363#95—1222no—
364#95—1221no—
365C24—611no—
366C24—611no—
367C24—614no—
368C24—1224no—
369C24—1222no—
370C24—1222no—
371C24—1222no—
372C24—1224no—
373C24—2442no—
374C24—2444no—
375C24—2444no—
376C24—2442no—
377C24—2442no—
378C24D4×D6111yescharacteristic
379C2×D4—614no—
380C2×D4—1228no—
381C2×D4—1228no—
382C2×D4—1222no—
383C2×D4—1224no—
384C2×D4—1224no—
385C2×D4—1224no—
386C2×D4—2448no—
387C2×D4—2444no—
388C2×D4—2448no—
389C2×D4—2448no—
390C2×D4—24432no—
391C2×D4—2448no—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—24no—
395C22×C4—22no—
396C22×C4—44no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—614no—
400C22×C4—612no—
401C22×C4—612no—
402C22×C4—612no—
403C22×C4—612no—
404C22×C4—614no—
405C22×C4—614no—
406C22×C4—1224no—
407C22×C4—1224no—
408C22×C4—1222no—
409C22×C4—2448no—
410C22×C4—2448no—
411C22×C4—2442no—
412C22×C4—2442no—
413C22×C4—2442no—
414C22×C4C2×C4×D6112yes—
415C22×C4D4×D6112yes—
416C22×C4D4×D6111yescharacteristic
417C22×C4C23×D6111yescharacteristic
418C2×C8—22no—
419C2×C8—24no—
420C2×C8—1222no—
421C2×C8—1224no—
422C2×C8—2448no—
423C4⋊C4—22no—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—1224no—
427C4⋊C4C2×C4×D6114yes—
428C22⋊C4—42no—
429C22⋊C4—1228no—
430C22⋊C4—1228no—
431C22⋊C4—2444no—
432C22⋊C4—2444no—
433C22⋊C4—2442no—
434C42—2444no—
435C23—22no—
436C23—22no—
437C23—612no—
438C23—614no—
439C23—612no—
440C23—1228no—
441C23—1221no—
442C23—1221no—
443C23—1222no—
444C23—1228no—
445C23—1221no—
446C23—1221no—
447C23—1222no—
448C23—1222no—
449C23—1224no—
450C23—4888no—
451C23—4888no—
452C23—2444no—
453C23—2448no—
454C23—2448no—
455C23—2448no—
456C23—2448no—
457C23—2448no—
458C23—2442no—
459C23—2442no—
460C23—2444no—
461C23—2444no—
462C23C22⋊C4×D6112yes—
463C23#1451979812yes—
464C23#1451980012yes—
465C23C2×D4×D6111yescharacteristic
466D4—1224no—
467D4—1224no—
468D4—2448no—
469D4—24416no—
470D4—24416no—
471D4—2444no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—48no—
477C2×C4—44no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—612no—
482C2×C4—612no—
483C2×C4—1222no—
484C2×C4—1222no—
485C2×C4—1224no—
486C2×C4—1224no—
487C2×C4—1224no—
488C2×C4—1224no—
489C2×C4—2444no—
490C2×C4—2444no—
491C2×C4—2444no—
492C2×C4—2442no—
493C2×C4—2442no—
494C2×C4—2442no—
495C2×C4C22⋊C4×D6112yes—
496C2×C4C22×C4×D6111yescharacteristic
497C2×C4C2×D4×D6111yescharacteristic
498C2×C4#1451982314yes—
499C8—42no—
500C8—2442no—
501C22—24no—
502C22—22no—
503C22—24no—
504C22—22no—
505C22—614no—
506C22—1224no—
507C22—1222no—
508C22—1224no—
509C22—1222no—
510C22—1222no—
511C22—1222no—
512C22—1222no—
513C22—48816no—
514C22—4884no—
515C22—4884no—
516C22—24416no—
517C22—2444no—
518C22—2444no—
519C22—2444no—
520C22—2442no—
521C22—2442no—
522C22#1683975714yes—
523C22C2×C22⋊C4×D6111yescharacteristic
524C22#1684032312yes—
525C22C2×#1451979811yescharacteristic
526C22C2×#1451980011yescharacteristic
527C22AGL(1,ℤ/8)×D6112yes—
528C4—22no—
529C4—44no—
530C4—82no—
531C4—1222no—
532C4—1222no—
533C4—4882no—
534C4#1684023612yes—
535C4#1684032312yes—
536C2—24no—
537C2—1224no—
538C2—4884no—
539C2—2442no—
540C2#2144839611yescharacteristic
541C2C2×#1683975711yescharacteristic
542C2#418×D6111yescharacteristic
543C2#2145658312yes—
544C2#2145658912yes—
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1824C2
socleC23×C61C22×D4
prime radicalC22×#14519752C2
cosocleC22×C4×C61C24
hypercenter#1824D61
hypocenterC61#21761
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C8×D61C2semidirect
3. #21448201C2semidirect
4. #21446246C2semidirect
5. #21446140C2semidirect
6. #21445909C2semidirect
7. #21445751C2semidirect
8. #21445749C2semidirect
9. C61×#1824C2semidirect
13. C22×C8×D61C22semidirect
17. C2×#14519752C4semidirect
20. C2×#14519735C22semidirect
22. C2×#14519699C22semidirect
23. C2×#14519697C22semidirect
25. C2×#14519689C22semidirect
29. #16839619C22semidirect
33. #16839524C22semidirect
37. C61×#340C22semidirect
270. #1824D61semidirect
309. #340C2×D61semidirect
310. C61#21761semidirect

Maximal subgroups

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

subgroupindex
C22×#145197522
C2×C22⋊C8×D612
#214482012
#214462462
#214461402
#214459092
#214457512
#214457492
C61×#18242
#2176161