Finite Group Databasebeta

← #29646079

Subgroups — #29646079

Order 15616.

1450 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×#14519759C211yesmaximal, characteristic
2#407×D61C212yesmaximal, complemented
3#21444164C218yesmaximal, complemented
4#21444148C212yesmaximal, complemented
5#21444146C211yesmaximal, characteristic, complemented
6C61×#1462C211yesmaximal, characteristic, complemented
7C23×C22⋊D61C411yescharacteristic
8C23×C4×D61C2211yescharacteristic
9C2×M16×D61—22no—
10C2×#14519759—22no—
11C2×#14519759—22no—
12C2×#14519759—22no—
13C2×#14519759—22no—
14C2×#14519759C414yes—
15C2×#14519759C2214yes—
16C22×C4⋊Dic61C411yescharacteristic
17C22×#11758196C2211yescharacteristic
18C22×C22⋊Dic61C411yescharacteristic
19C22×#11758198C411yescharacteristic
20#16839726C2212yes—
21#16839725—22no—
22#16839724—22no—
23#16839724C2214yescomplemented
24C22⋊C8×D61—22no—
25C22⋊C8×D61C2214yescomplemented
26#16839487C2218yescomplemented
27#16839486C2214yescomplemented
28C22×C22⋊C4×C61C2211yescharacteristic
29C61×#407C2212yes—
30C61×#323C2214yescomplemented
31C24×D61C2×C411yescharacteristic
32C22×C22⋊D61—22no—
33C22×C22⋊D61—21no—
34C22×C22⋊D61—21no—
35C22×C22⋊D61—44no—
36C22×C22⋊D61C2×C414yes—
37C23×Dic61C2×C411yescharacteristic
38C23×Dic61C2×C411yescharacteristic
39C23×Dic61C2×C411yescharacteristic
40C22×C4×D61—44no—
41C22×C4×D61C2×C412yes—
42C22×C4×D61D412yes—
43C22×C4×D61D412yes—
44C22×C4×D61D412yes—
45C22×C4×D61D412yes—
46C22×C4×D61C2312yes—
47C2×#11758194—22no—
48C2×#11758189—24no—
49M16×D61—48no—
50C2×C8×D61—24no—
51#14519759—24no—
52#14519759—24no—
53#14519759—24no—
54#14519759—24no—
55#14519759—24no—
56#14519759—24no—
57#14519759—24no—
58#14519759—24no—
59C2×C4⋊Dic61—22no—
60C2×C4⋊Dic61—21no—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61C2×C414yes—
63C2×#11758196—22no—
64C2×#11758196—22no—
65C2×#11758196C2×C412yes—
66C2×#11758196C2312yes—
67C2×C22⋊Dic61—22no—
68C2×C22⋊Dic61—21no—
69C2×C22⋊Dic61—21no—
70C2×C22⋊Dic61C2×C414yes—
71C2×#11758198—22no—
72C2×#11758198—21no—
73C2×#11758198—21no—
74C2×#11758198C2×C414yes—
75C22⋊#92418—22no—
76C22⋊#92418C2314yes—
77#14519689—24no—
78#14519689—24no—
79C25×C61C2×C411yescharacteristic
80C23×C4×C61C2×C411yescharacteristic
81C23×C4×C61C2311yescharacteristic
82C2×M16×C61—22no—
83C2×C22⋊C4×C61—22no—
84C2×C22⋊C4×C61—22no—
85C2×C22⋊C4×C61C2×C412yes—
86C2×C22⋊C4×C61C2312yes—
87C22⋊C8×C61—22no—
88C22⋊C8×C61C2314yes—
89C24×C61—21no—
90C24×C61—21no—
91C24×C61—42no—
92C24×C61—42no—
93C24×C61—42no—
94C24×C61C22×C411yescharacteristic
95C24×C61C22×C412yes—
96C23×D61—24no—
97C23×D61—42no—
98C23×D61—42no—
99C23×D61C22⋊C412yes—
100C23×D61C22⋊C411yescharacteristic
101C23×D61C22⋊C411yescharacteristic
102C23×D61C22×C412yes—
103C22×C4×C61—21no—
104C22×C4×C61—21no—
105C22×C4×C61—42no—
106C22×C4×C61—42no—
107C22×C4×C61C22×C412yes—
108C22×C4×C61C22×C411yescharacteristic
109C22×C4×C61C2×D412yes—
110C22×C4×C61C2×D412yes—
111C22×C4×C61C2411yescharacteristic
112C2×C22⋊D61—24no—
113C2×C22⋊D61—24no—
114C2×C22⋊D61—48no—
115C2×C22⋊D61—44no—
116C2×C22⋊D61—44no—
117C2×C22⋊D61—48no—
118C22×Dic61—21no—
119C22×Dic61—21no—
120C22×Dic61—21no—
121C22×Dic61—21no—
122C22×Dic61—42no—
123C22×Dic61—42no—
124C22×Dic61—42no—
125C22×Dic61C22⋊C412yes—
126C22×Dic61C22⋊C411yescharacteristic
127C22×Dic61C22⋊C411yescharacteristic
128C22×Dic61C22×C412yes—
129C22×Dic61C22×C412yes—
130C22×Dic61C22×C412yes—
131C2×C4×D61—28no—
132C2×C4×D61—44no—
133C2×C4×D61—44no—
134C2×C4×D61—44no—
135C2×C4×D61—44no—
136C2×C4×D61—44no—
137C2×C4×D61C22⋊C412yes—
138C2×C4×D61C22⋊C412yes—
139C2×C4×D61C22⋊C412yes—
140C2×C4×D61C22⋊C412yes—
141C2×C4×D61C2×D412yes—
142C2×C4×D61C2×D412yes—
143C2×C4×D61C2×D412yes—
144C2×C4×D61C2×D412yes—
145M16×C61—44no—
146C2×C8×C61—24no—
147C22⋊C4×C61—24no—
148C22⋊C4×C61—24no—
149C22⋊Dic61—24no—
150C22⋊Dic61—24no—
151#11758198—24no—
152#11758198—24no—
153C4⋊Dic61—24no—
154C4⋊Dic61—24no—
155#11758196—24no—
156#11758196—24no—
157#11758194—44no—
158C2×#92418—24no—
159#11758189—48no—
160C8×D61—48no—
161C23×C61—22no—
162C23×C61—22no—
163C23×C61—22no—
164C23×C61—22no—
165C23×C61—24no—
166C23×C61—42no—
167C23×C61—42no—
168C23×C61—42no—
169C23×C61—42no—
170C23×C61—42no—
171C23×C61—42no—
172C23×C61—42no—
173C23×C61—42no—
174C23×C61—88no—
175C23×C61C2×C22⋊C411yescharacteristic
176C23×C61C2×C22⋊C411yescharacteristic
177C23×C61C23×C411yescharacteristic
178C22×D61—24no—
179C22×D61—22no—
180C22×D61—24no—
181C22×D61—24no—
182C22×D61—24no—
183C22×D61—41no—
184C22×D61—42no—
185C22×D61—41no—
186C22×D61—41no—
187C22×D61—41no—
188C22×D61—42no—
189C22×D61—416no—
190C22×D61#9914yes—
191C22×D61C2×C22⋊C412yes—
192C22×D61C2×C22⋊C412yes—
193C2×C4×C61—24no—
194C2×C4×C61—22no—
195C2×C4×C61—41no—
196C2×C4×C61—42no—
197C2×C4×C61—41no—
198C2×C4×C61—42no—
199C2×C4×C61—42no—
200C2×C4×C61—42no—
201C2×C4×C61C2×C22⋊C412yes—
202C2×C4×C61C22×D412yes—
203C22⋊D61—48no—
204C22⋊D61—48no—
205C2×Dic61—24no—
206C2×Dic61—22no—
207C2×Dic61—22no—
208C2×Dic61—24no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—42no—
212C2×Dic61—42no—
213C2×Dic61—42no—
214C2×Dic61—42no—
215C2×Dic61—42no—
216C2×Dic61—42no—
217C2×Dic61C2×C22⋊C412yes—
218C2×Dic61C2×C22⋊C412yes—
219C4×D61—24no—
220C4×D61—24no—
221C4×D61—24no—
222C4×D61—24no—
223C4×D61—42no—
224C4×D61—42no—
225C4×D61—42no—
226C4×D61—42no—
227C8×C61—44no—
228#92418—44no—
229#17392—611nomaximal, Sylow
230C22×C61—28no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—42no—
238C22×C61—42no—
239C22×C61—42no—
240C22×C61—84no—
241C22×C61—84no—
242C22×C61—84no—
243C22×C61C2×#9912yes—
244C22×C61#41312yes—
245C22×C61C22×C22⋊C411yescharacteristic
246C22×C61#56812yes—
247C2×D61—22no—
248C2×D61—22no—
249C2×D61—22no—
250C2×D61—22no—
251C2×D61—22no—
252C2×D61—44no—
253C2×D61—48no—
254C2×D61—48no—
255C2×D61—44no—
256C2×D61C2×#9914yes—
257C4×C61—22no—
258C4×C61—22no—
259C4×C61—42no—
260Dic61—22no—
261Dic61—22no—
262Dic61—42no—
263Dic61—42no—
264C22×#123—611no—
265C2×#407—612no—
266#1468—618no—
267#1463—612no—
268#1462—611no—
269#1462D6111yescharacteristic, complemented
270C2×C61—22no—
271C2×C61—22no—
272C2×C61—22no—
273C2×C61—82no—
274C2×C61#287911yescharacteristic
275C2×C61C22×#9911yescharacteristic
276C2×C61C2×#41311yescharacteristic
277D61—24no—
278D61—42no—
279C23×D4—611no—
280C24×C4—611no—
281C22×M16—1222no—
282C2×#123—614no—
283C2×#123—614no—
284C2×#123—1222no—
285C2×#123—1222no—
286C2×#123—1222no—
287C2×#123—1222no—
288C22×C4⋊C4—611no—
289C22×C4⋊C4—611no—
290C22×C22⋊C4—611no—
291C22×C22⋊C4—611no—
292C22×C22⋊C4C2×D6111yescharacteristic
293#407—612no—
294#407—614no—
295#407—1222no—
296#407—1222no—
297#407C2×D6112yes—
298C2×C22⋊C8—614no—
299C2×C22⋊C8—1222no—
300#324—618no—
301#323—614no—
302#323C2×D6114yescomplemented
303C61#1739211yescharacteristic, complemented, Sylow
304C25—611no—
305C25C4×D6111yescharacteristic
306C22×D4—614no—
307C22×D4—1221no—
308C22×D4—1222no—
309C22×D4—1221no—
310C22×D4—2444no—
311C23×C4—611no—
312C23×C4—612no—
313C23×C4—612no—
314C23×C4—612no—
315C23×C4—612no—
316C23×C4—612no—
317C23×C4—612no—
318C23×C4—611no—
319C23×C4—611no—
320C23×C4—2444no—
321C23×C4C4×D6111yescharacteristic
322C23×C4C22×D6111yescharacteristic
323C2×M16—22no—
324C2×M16—1224no—
325C2×M16—1222no—
326C2×M16—2448no—
327C22×C8—1224no—
328#123—1224no—
329#123—1224no—
330#123—1224no—
331#123—1224no—
332#123—1224no—
333#123—1224no—
334#123—1224no—
335#123—1224no—
336C2×C4⋊C4—612no—
337C2×C4⋊C4—614no—
338C2×C4⋊C4—612no—
339C2×C4⋊C4—1222no—
340C2×C4⋊C4—1221no—
341C2×C4⋊C4—1221no—
342C2×C4⋊C4—1222no—
343C2×C4⋊C4—1222no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—614no—
347C2×C22⋊C4—614no—
348C2×C22⋊C4—1221no—
349C2×C22⋊C4—1222no—
350C2×C22⋊C4—1221no—
351C2×C22⋊C4—1222no—
352C2×C22⋊C4—1221no—
353C2×C22⋊C4—1221no—
354C2×C22⋊C4C4×D6112yes—
355C2×C22⋊C4C22×D6112yes—
356C22⋊C8—22no—
357C22⋊C8—614no—
358C22⋊C8—1224no—
359C22⋊C8—1224no—
360C22⋊C8—1222no—
361C22⋊C8C22×D6114yes—
362C24—21no—
363C24—21no—
364C24—42no—
365C24—42no—
366C24—42no—
367C24—611no—
368C24—612no—
369C24—612no—
370C24—611no—
371C24—1224no—
372C24—2442no—
373C24—2442no—
374C24C2×C4×D6111yescharacteristic
375C24C2×C4×D6112yes—
376C2×D4—1224no—
377C2×D4—1224no—
378C2×D4—2444no—
379C2×D4—2448no—
380C2×D4—2444no—
381C2×D4—2448no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—612no—
387C22×C4—612no—
388C22×C4—611no—
389C22×C4—611no—
390C22×C4—612no—
391C22×C4—612no—
392C22×C4—612no—
393C22×C4—612no—
394C22×C4—612no—
395C22×C4—612no—
396C22×C4—612no—
397C22×C4—612no—
398C22×C4—612no—
399C22×C4—612no—
400C22×C4—1228no—
401C22×C4—1221no—
402C22×C4—1221no—
403C22×C4—1221no—
404C22×C4—1221no—
405C22×C4—2444no—
406C22×C4—2444no—
407C22×C4—2444no—
408C22×C4—2444no—
409C22×C4—2444no—
410C22×C4—2442no—
411C22×C4—2442no—
412C22×C4—2442no—
413C22×C4C2×C4×D6112yes—
414C22×C4C2×C4×D6111yescharacteristic
415C22×C4D4×D6112yes—
416C22×C4D4×D6112yes—
417C22×C4C23×D6111yescharacteristic
418M16—44no—
419M16—2448no—
420M16—2444no—
421C2×C8—24no—
422C2×C8—1224no—
423C2×C8—2448no—
424C4⋊C4—1224no—
425C4⋊C4—1224no—
426C4⋊C4—1224no—
427C4⋊C4—1224no—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—1224no—
431C22⋊C4—1224no—
432C22⋊C4—1224no—
433C22⋊C4—1224no—
434C23—22no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—24no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—88no—
448C23—612no—
449C23—614no—
450C23—612no—
451C23—1224no—
452C23—1224no—
453C23—1222no—
454C23—1224no—
455C23—1224no—
456C23—2441no—
457C23—2442no—
458C23—2441no—
459C23—2442no—
460C23—2441no—
461C23—2441no—
462C23—24416no—
463C23C22⋊C4×D6111yescharacteristic
464C23C22⋊C4×D6111yescharacteristic
465C23C22×C4×D6111yescharacteristic
466D4—2448no—
467D4—2448no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—612no—
477C2×C4—612no—
478C2×C4—1224no—
479C2×C4—1224no—
480C2×C4—1224no—
481C2×C4—1224no—
482C2×C4—1224no—
483C2×C4—1222no—
484C2×C4—1222no—
485C2×C4—1224no—
486C2×C4—2442no—
487C2×C4—2442no—
488C2×C4—2442no—
489C2×C4—2442no—
490C2×C4—2442no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2442no—
494C2×C4—2442no—
495C2×C4—2442no—
496C2×C4—2442no—
497C2×C4—2442no—
498C2×C4C22⋊C4×D6112yes—
499C2×C4C2×D4×D6112yes—
500C8—44no—
501C8—2444no—
502C22—28no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—84no—
513C22—84no—
514C22—84no—
515C22—614no—
516C22—1222no—
517C22—1222no—
518C22—1222no—
519C22—1222no—
520C22—1222no—
521C22—2444no—
522C22—2448no—
523C22—2448no—
524C22—2444no—
525C22#99×D6112yes—
526C22#1683974312yes—
527C22C2×C22⋊C4×D6111yescharacteristic
528C22#1684052812yes—
529C4—22no—
530C4—22no—
531C4—42no—
532C4—1222no—
533C4—1222no—
534C4—2442no—
535C4—2442no—
536C2—22no—
537C2—22no—
538C2—22no—
539C2—82no—
540C2—1224no—
541C2—2442no—
542C2#2145426211yescharacteristic
543C2C2×#99×D6111yescharacteristic
544C2C2×#1683974311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1462C2
socleC22×C61C22×C22⋊C4
prime radicalC23×C22⋊D61C4
cosocleC22×C4×C61C24
hypercenter#1462D61
hypocenterC61#17392
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
2. #407×D61C2semidirect
3. #21444164C2semidirect
4. #21444148C2semidirect
5. #21444146C2semidirect
6. C61×#1462C2semidirect
23. #16839724C22semidirect
25. C22⋊C8×D61C22semidirect
26. #16839487C22semidirect
27. #16839486C22semidirect
30. C61×#323C22semidirect
269. #1462D61semidirect
302. #323C2×D61semidirect
303. C61#17392semidirect

Maximal subgroups

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

subgroupindex
C22×#145197592
#407×D612
#214441642
#214441482
#214441462
C61×#14622
#1739261