Finite Group Databasebeta

← #29570047

Subgroups — #29570047

Order 15616.

1014 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C8×D61C211yesmaximal, characteristic
2#21448201C211yesmaximal, characteristic
3C2×#16839624C211yesmaximal, characteristic
4#21443699C211yesmaximal, characteristic, complemented
5#21443698C211yesmaximal, characteristic, complemented
6#21443697C211yesmaximal, characteristic, complemented
7C61×#1294C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C22×C8×D61—21no—
10C2×#14519735C412yescomplemented
11C22×#11758198—21no—
12C2×C22⋊#92418C2211yescharacteristic
13C2×#14519689—21no—
14C22⋊C8×D61—22no—
15C22⋊C8×D61C414yescomplemented
16#16839624—22no—
17#16839624—21no—
18#16839624C414yescomplemented
19#16839622C2211yescharacteristic
20#16839619C412yescomplemented
21#16839617—21no—
22C22⋊C4×Dic61—21no—
23#16839609—21no—
24C2×#14519684—21no—
25C2×#14519684C2211yescharacteristic
26C2×C22⋊C8×C61C2211yescharacteristic
27C61×#380C2211yescharacteristic
28C2×#95×C61C2211yescharacteristic
29C24×D61D411yescharacteristic
30C23×Dic61—21no—
31C23×Dic61D411yescharacteristic
32C22×C4×D61—44no—
33C22×C4×D61C2×C411yescharacteristic
34C22×C4×D61C2×C412yes—
35C22×C4×D61C2×C411yescharacteristic
36C22×C4×D61C2×C412yes—
37C22×C4×D61D411yescharacteristic
38C22×C4×D61D412yes—
39C22×C4×D61D411yescharacteristic
40C22×C4×D61Q812yes—
41C22×#92418—21no—
42C2×C8×D61—24no—
43C2×C8×D61—44no—
44#14519735—44no—
45C2×C4⋊Dic61C2×C412yes—
46C2×C22⋊Dic61—21no—
47C2×#11758198—24no—
48C2×#11758198—22no—
49C2×#11758198—22no—
50C2×#11758198—44no—
51C2×C4×Dic61—22no—
52C22⋊#92418—21no—
53C22⋊#92418C2×C412yes—
54#14519689—24no—
55#14519684—21no—
56#14519684—21no—
57#14519684—24no—
58#14519684—22no—
59#14519684C2×C412yes—
60C23×C4×C61—21no—
61C23×C4×C61C2311yescharacteristic
62C22×C8×C61—21no—
63C2×C4⋊C4×C61C2×C412yes—
64C2×C22⋊C4×C61—21no—
65C22⋊C8×C61—21no—
66C22⋊C8×C61C2×C412yes—
67#95×C61—21no—
68#95×C61—21no—
69#95×C61C2×C412yes—
70C24×C61C2×D411yescharacteristic
71C23×D61—21no—
72C23×D61—21no—
73C23×D61—21no—
74C23×D61—21no—
75C23×D61—24no—
76C23×D61—42no—
77C23×D61C22⋊C411yescharacteristic
78C23×D61C22⋊C412yes—
79C23×D61C22⋊C411yescharacteristic
80C23×D61C4⋊C412yes—
81C22×C4×C61—22no—
82C22×C4×C61—22no—
83C22×C4×C61—42no—
84C22×C4×C61—42no—
85C22×C4×C61—42no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61C22×C411yescharacteristic
89C22×C4×C61C22×C411yescharacteristic
90C22×C4×C61C22×C411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×Q811yescharacteristic
94C22×Dic61—22no—
95C22×Dic61—22no—
96C22×Dic61—42no—
97C22×Dic61—42no—
98C22×Dic61—42no—
99C22×Dic61—41no—
100C22×Dic61—41no—
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C22⋊C412yes—
104C22×Dic61C4⋊C412yes—
105C2×C4×D61—24no—
106C2×C4×D61—24no—
107C2×C4×D61—44no—
108C2×C4×D61—44no—
109C2×C4×D61—44no—
110C2×C4×D61—44no—
111C2×C4×D61—42no—
112C2×C4×D61—42no—
113C2×C4×D61C4212yes—
114C2×C4×D61C4212yes—
115C2×C4×D61C22⋊C412yes—
116C2×C4×D61C22⋊C412yes—
117C2×C4×D61C4⋊C412yes—
118C2×C4×D61C4⋊C412yes—
119C2×C4×D61C4⋊C412yes—
120C2×C4×D61C4⋊C412yes—
121C2×C8×C61—22no—
122C2×C8×C61—42no—
123C4⋊C4×C61—42no—
124C22⋊C4×C61—41no—
125C22⋊C4×C61—41no—
126C22⋊Dic61—41no—
127C22⋊Dic61—41no—
128#11758198—44no—
129#11758198—48no—
130#11758198—44no—
131C4⋊Dic61—42no—
132C4×Dic61—44no—
133C2×#92418—22no—
134C2×#92418—42no—
135C8×D61—48no—
136C23×C61—22no—
137C23×C61—22no—
138C23×C61C2×C22⋊C411yescharacteristic
139C23×C61C2×C22⋊C411yescharacteristic
140C23×C61C2×C4⋊C411yescharacteristic
141C23×C61#13511yescharacteristic
142C23×C61#13511yescharacteristic
143C23×C61#13511yescharacteristic
144C23×C61#13511yescharacteristic
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—22no—
148C22×D61—22no—
149C22×D61—22no—
150C22×D61—22no—
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—22no—
154C22×D61—22no—
155C22×D61—22no—
156C22×D61—24no—
157C22×D61—24no—
158C22×D61—42no—
159C22×D61—42no—
160C22×D61—44no—
161C22×D61—44no—
162C22×D61—44no—
163C22×D61—44no—
164C22×D61#9512yes—
165C22×D61#9512yes—
166C22×D61#9914yes—
167C2×C4×C61—22no—
168C2×C4×C61—22no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—42no—
174C2×C4×C61—42no—
175C2×C4×C61—42no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×C4×C61—82no—
180C2×C4×C61—82no—
181C2×C4×C61C2×C4211yescharacteristic
182C2×C4×C61C2×C22⋊C411yescharacteristic
183C2×C4×C61C2×C4⋊C411yescharacteristic
184C2×C4×C61C2×C4⋊C411yescharacteristic
185C2×Dic61—22no—
186C2×Dic61—22no—
187C2×Dic61—42no—
188C2×Dic61—42no—
189C2×Dic61—42no—
190C2×Dic61—42no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193C2×Dic61—42no—
194C2×Dic61—42no—
195C2×Dic61—82no—
196C2×Dic61—82no—
197C2×Dic61#9512yes—
198C2×Dic61#9512yes—
199C4×D61—24no—
200C4×D61—24no—
201C4×D61—24no—
202C4×D61—24no—
203C4×D61—42no—
204C4×D61—42no—
205C4×D61—42no—
206C4×D61—42no—
207C8×C61—42no—
208#92418—42no—
209#8024—611nomaximal, Sylow
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—22no—
215C22×C61—22no—
216C22×C61—22no—
217C22×C61—22no—
218C22×C61C2×#9511yescharacteristic
219C22×C61C2×#9912yes—
220C22×C61#41611yescharacteristic
221C22×C61#41611yescharacteristic
222C22×C61#41611yescharacteristic
223C22×C61#41611yescharacteristic
224C22×C61#42112yes—
225C22×C61#42711yescharacteristic
226C22×C61#42711yescharacteristic
227C2×D61—22no—
228C2×D61—22no—
229C2×D61—24no—
230C2×D61—24no—
231C2×D61—22no—
232C2×D61—22no—
233C2×D61—22no—
234C2×D61—44no—
235C2×D61—44no—
236C2×D61—44no—
237C2×D61—44no—
238C2×D61—42no—
239C2×D61—42no—
240C2×D61#34214yes—
241C4×C61—21no—
242C4×C61—21no—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—82no—
246C4×C61—82no—
247Dic61—22no—
248Dic61—22no—
249Dic61—82no—
250Dic61—82no—
251C22×C22⋊C8—611no—
252#2280—611no—
253C2×#381—611no—
254#1294—611no—
255#1294—611no—
256#1294—611no—
257#1294D6111yescharacteristic, complemented
258C2×C61—21no—
259C2×C61—21no—
260C2×C61—21no—
261C2×C61—21no—
262C2×C61#151612yes—
263C2×C61#151612yes—
264C2×C61#173311yescharacteristic
265C2×C61#173511yescharacteristic
266C2×C61C2×#34211yescharacteristic
267D61—24no—
268D61—42no—
269C24×C4—611no—
270C23×C8—1221no—
271C2×#117—612no—
272C22×C22⋊C4—1221no—
273C2×C22⋊C8—611no—
274C2×C22⋊C8—614no—
275C2×C22⋊C8—1222no—
276C2×C22⋊C8—1221no—
277C2×C22⋊C8C2×D6111yescharacteristic
278#381—614no—
279#381—1222no—
280#381—1221no—
281#380—611no—
282#380—612no—
283#380C2×D6111yescharacteristic
284#379—1221no—
285C4×C22⋊C4—1221no—
286C4×C22⋊C4—1221no—
287C2×#95—611no—
288C2×#95—1221no—
289C2×#95C2×D6111yescharacteristic
290C61#802411yescharacteristic, complemented, Sylow
291C25—611no—
292C23×C4—21no—
293C23×C4—611no—
294C23×C4—611no—
295C23×C4—611no—
296C23×C4—611no—
297C23×C4—612no—
298C23×C4—612no—
299C23×C4—611no—
300C23×C4—612no—
301C23×C4—612no—
302C23×C4—1221no—
303C23×C4—2444no—
304C23×C4C22×D6111yescharacteristic
305C22×C8—21no—
306C22×C8—1224no—
307C22×C8—1221no—
308C22×C8—2444no—
309#117—2444no—
310C2×C4⋊C4—612no—
311C2×C4⋊C4C4×D6112yes—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—1224no—
314C2×C22⋊C4—1222no—
315C2×C22⋊C4—1222no—
316C2×C22⋊C4—1221no—
317C2×C22⋊C4—2444no—
318C2×C42—1222no—
319C22⋊C8—21no—
320C22⋊C8—612no—
321C22⋊C8—1224no—
322C22⋊C8—1221no—
323C22⋊C8C4×D6112yes—
324#95—21no—
325#95—21no—
326#95—612no—
327#95—1224no—
328#95—1222no—
329#95—1221no—
330#95—1221no—
331#95C4×D6112yes—
332C24—611no—
333C24—611no—
334C24—612no—
335C24—612no—
336C24—1224no—
337C24—1221no—
338C24—1221no—
339C24—1221no—
340C24—1221no—
341C24—2442no—
342C24D4×D6111yescharacteristic
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—611no—
351C22×C4—611no—
352C22×C4—612no—
353C22×C4—612no—
354C22×C4—612no—
355C22×C4—612no—
356C22×C4—612no—
357C22×C4—612no—
358C22×C4—612no—
359C22×C4—612no—
360C22×C4—612no—
361C22×C4—612no—
362C22×C4—1224no—
363C22×C4—1224no—
364C22×C4—1222no—
365C22×C4—1222no—
366C22×C4—2442no—
367C22×C4—2442no—
368C22×C4—2444no—
369C22×C4—2444no—
370C22×C4—2444no—
371C22×C4—2444no—
372C22×C4—2442no—
373C22×C4—2442no—
374C22×C4—2442no—
375C22×C4—2441no—
376C22×C4—2441no—
377C22×C4C2×C4×D6111yescharacteristic
378C22×C4C2×C4×D6111yescharacteristic
379C22×C4C2×C4×D6111yescharacteristic
380C22×C4D4×D6111yescharacteristic
381C22×C4D4×D6111yescharacteristic
382C22×C4Q8×D6111yescharacteristic
383C2×C8—22no—
384C2×C8—42no—
385C2×C8—1222no—
386C2×C8—2448no—
387C2×C8—2442no—
388C4⋊C4—42no—
389C4⋊C4—2442no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—2444no—
393C22⋊C4—2448no—
394C22⋊C4—2444no—
395C22⋊C4—2441no—
396C22⋊C4—2441no—
397C42—2444no—
398C23—22no—
399C23—22no—
400C23—614no—
401C23—612no—
402C23—612no—
403C23—1224no—
404C23—1224no—
405C23—1221no—
406C23—1221no—
407C23—1222no—
408C23—1222no—
409C23—1222no—
410C23—1221no—
411C23—1222no—
412C23—1221no—
413C23—1222no—
414C23—1222no—
415C23—1222no—
416C23—2442no—
417C23—2442no—
418C23—2444no—
419C23—2444no—
420C23—2444no—
421C23—2444no—
422C23C22⋊C4×D6111yescharacteristic
423C23C22⋊C4×D6111yescharacteristic
424C23C4⋊C4×D6111yescharacteristic
425C23#1451979611yescharacteristic
426C23#1451979811yescharacteristic
427C23#1451979811yescharacteristic
428C23#1451980011yescharacteristic
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4—612no—
444C2×C4—612no—
445C2×C4—1224no—
446C2×C4—1224no—
447C2×C4—1224no—
448C2×C4—1224no—
449C2×C4—1222no—
450C2×C4—1222no—
451C2×C4—4882no—
452C2×C4—4882no—
453C2×C4—2442no—
454C2×C4—2442no—
455C2×C4—2442no—
456C2×C4—2442no—
457C2×C4—2442no—
458C2×C4—2442no—
459C2×C4—2442no—
460C2×C4—2442no—
461C2×C4—2442no—
462C2×C4—2442no—
463C2×C4—2442no—
464C2×C4—2442no—
465C2×C4C42×D6111yescharacteristic
466C2×C4C22⋊C4×D6111yescharacteristic
467C2×C4C4⋊C4×D6111yescharacteristic
468C2×C4C4⋊C4×D6111yescharacteristic
469C8—42no—
470C8—2442no—
471C22—22no—
472C22—22no—
473C22—22no—
474C22—22no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—614no—
480C22—1224no—
481C22—1224no—
482C22—1222no—
483C22—1222no—
484C22—1222no—
485C22—1222no—
486C22—1222no—
487C22—2444no—
488C22—2444no—
489C22—2444no—
490C22—2444no—
491C22—2442no—
492C22—2442no—
493C22#95×D6111yescharacteristic
494C22#99×D6112yes—
495C22#1683975511yescharacteristic
496C22#1683975511yescharacteristic
497C22#1683975711yescharacteristic
498C22#1683975711yescharacteristic
499C22#1683977712yes—
500C22#1683979711yescharacteristic
501C22#1683979911yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—82no—
507C4—82no—
508C4—1222no—
509C4—1222no—
510C4—4882no—
511C4—4882no—
512C2—21no—
513C2—21no—
514C2—21no—
515C2—21no—
516C2—1224no—
517C2—2442no—
518C2#2144437212yes—
519C2#2144437412yes—
520C2#2144552711yescharacteristic
521C2#2144553411yescharacteristic
522C2#342×D6111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61D4
cosocleC23×C4×C61C23
hypercenter#1294D61
hypocenterC61#8024
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
4. #21443699C2semidirect
5. #21443698C2semidirect
6. #21443697C2semidirect
7. C61×#1294C2semidirect
10. C2×#14519735C4semidirect
15. C22⋊C8×D61C4semidirect
18. #16839624C4semidirect
20. #16839619C4semidirect
257. #1294D61semidirect
290. C61#8024semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C8×D612
#214482012
C2×#168396242
#214436992
#214436982
#214436972
C61×#12942
#802461