Finite Group Databasebeta

← #29570015

Subgroups — #29570015

Order 15616.

1026 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839724C211yesmaximal, characteristic
2#21448201C211yesmaximal, characteristic
3C2×#16839621C211yesmaximal, characteristic
4#21443699C211yesmaximal, characteristic, complemented
5#21443698C211yesmaximal, characteristic, complemented
6#21443697C211yesmaximal, characteristic, complemented
7C61×#1294C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C22×#11758189—21no—
10C2×#14519735C412yescomplemented
11C22×#11758196—21no—
12C22×#11758198—21no—
13#16839724—22no—
14#16839724C414yescomplemented
15C2×C22⋊#92418C2211yescharacteristic
16C2×#14519689—21no—
17#16839624—21no—
18#16839622C2211yescharacteristic
19#16839621—22no—
20#16839621C414yescomplemented
21#16839619C412yescomplemented
22#16839617—21no—
23C22⋊C4×Dic61—21no—
24#16839609—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×D61D411yescharacteristic
39C22×C4×D61D412yes—
40C22×C4×D61Q812yes—
41C2×#11758189—24no—
42C2×#11758189—44no—
43C22×#92418—21no—
44#14519735—44no—
45C2×C4⋊Dic61C2×C412yes—
46C2×#11758196—24no—
47C2×#11758196—44no—
48C2×C22⋊Dic61—21no—
49C2×#11758198—24no—
50C2×#11758198—22no—
51C2×#11758198—22no—
52C2×#11758198—42no—
53C2×#11758198—42no—
54C2×C4×Dic61—22no—
55C22⋊#92418—21no—
56C22⋊#92418C2×C412yes—
57#14519689—24no—
58#14519684—21no—
59#14519684—21no—
60#14519684—22no—
61#14519684C2×C412yes—
62C23×C4×C61—21no—
63C23×C4×C61C2311yescharacteristic
64C22×C8×C61—21no—
65C2×C4⋊C4×C61C2×C412yes—
66C2×C22⋊C4×C61—21no—
67C22⋊C8×C61—21no—
68C22⋊C8×C61C2×C412yes—
69#95×C61—21no—
70#95×C61—21no—
71#95×C61C2×C412yes—
72C24×C61C2×D411yescharacteristic
73C23×D61—21no—
74C23×D61—21no—
75C23×D61—21no—
76C23×D61—21no—
77C23×D61—42no—
78C23×D61—42no—
79C23×D61C22⋊C411yescharacteristic
80C23×D61C22⋊C411yescharacteristic
81C23×D61C22⋊C412yes—
82C23×D61C4⋊C412yes—
83C22×C4×C61—22no—
84C22×C4×C61—22no—
85C22×C4×C61—42no—
86C22×C4×C61—42no—
87C22×C4×C61—42no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61C22×C411yescharacteristic
91C22×C4×C61C22×C411yescharacteristic
92C22×C4×C61C22×C411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×Q811yescharacteristic
96C22×Dic61—24no—
97C22×Dic61—22no—
98C22×Dic61—22no—
99C22×Dic61—42no—
100C22×Dic61—42no—
101C22×Dic61—41no—
102C22×Dic61—41no—
103C22×Dic61C22⋊C411yescharacteristic
104C22×Dic61C22⋊C412yes—
105C22×Dic61C22⋊C411yescharacteristic
106C22×Dic61C4⋊C412yes—
107C2×C4×D61—24no—
108C2×C4×D61—24no—
109C2×C4×D61—44no—
110C2×C4×D61—44no—
111C2×C4×D61—44no—
112C2×C4×D61—44no—
113C2×C4×D61—42no—
114C2×C4×D61—42no—
115C2×C4×D61C4212yes—
116C2×C4×D61C4212yes—
117C2×C4×D61C22⋊C412yes—
118C2×C4×D61C22⋊C412yes—
119C2×C4×D61C4⋊C412yes—
120C2×C4×D61C4⋊C412yes—
121C2×C4×D61C4⋊C412yes—
122C2×C4×D61C4⋊C412yes—
123C2×C8×C61—22no—
124C2×C8×C61—42no—
125C4⋊C4×C61—42no—
126C22⋊C4×C61—41no—
127C22⋊C4×C61—41no—
128C22⋊Dic61—41no—
129C22⋊Dic61—41no—
130#11758198—44no—
131#11758198—48no—
132#11758198—44no—
133C4⋊Dic61—42no—
134#11758196—48no—
135C4×Dic61—44no—
136C2×#92418—22no—
137C2×#92418—42no—
138#11758189—48no—
139C23×C61—22no—
140C23×C61—22no—
141C23×C61C2×C22⋊C411yescharacteristic
142C23×C61C2×C22⋊C411yescharacteristic
143C23×C61C2×C4⋊C411yescharacteristic
144C23×C61AGL(1,ℤ/8)11yescharacteristic
145C23×C61AGL(1,ℤ/8)11yescharacteristic
146C23×C61#13711yescharacteristic
147C23×C61#13711yescharacteristic
148C22×D61—22no—
149C22×D61—22no—
150C22×D61—21no—
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—22no—
155C22×D61—22no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—42no—
161C22×D61—42no—
162C22×D61—42no—
163C22×D61—42no—
164C22×D61—44no—
165C22×D61—44no—
166C22×D61—44no—
167C22×D61—44no—
168C22×D61#9512yes—
169C22×D61#9512yes—
170C2×C4×C61—22no—
171C2×C4×C61—22no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×C4×C61—42no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61—82no—
183C2×C4×C61—82no—
184C2×C4×C61C2×C4211yescharacteristic
185C2×C4×C61C2×C22⋊C411yescharacteristic
186C2×C4×C61C2×C4⋊C411yescharacteristic
187C2×C4×C61C2×C4⋊C411yescharacteristic
188C2×Dic61—22no—
189C2×Dic61—24no—
190C2×Dic61—24no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193C2×Dic61—42no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61—82no—
198C2×Dic61—82no—
199C2×Dic61#9512yes—
200C2×Dic61#9512yes—
201C2×Dic61#9914yes—
202C4×D61—24no—
203C4×D61—24no—
204C4×D61—24no—
205C4×D61—24no—
206C4×D61—42no—
207C4×D61—42no—
208C4×D61—42no—
209C4×D61—42no—
210C8×C61—42no—
211#92418—42no—
212#8016—611nomaximal, Sylow
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—21no—
217C22×C61—22no—
218C22×C61—22no—
219C22×C61—22no—
220C22×C61—22no—
221C22×C61C2×#9511yescharacteristic
222C22×C61C2×#9912yes—
223C22×C61#41711yescharacteristic
224C22×C61#41711yescharacteristic
225C22×C61#41811yescharacteristic
226C22×C61#41911yescharacteristic
227C22×C61#42112yes—
228C22×C61#42811yescharacteristic
229C22×C61#42811yescharacteristic
230C2×D61—22no—
231C2×D61—22no—
232C2×D61—22no—
233C2×D61—22no—
234C2×D61—22no—
235C2×D61—22no—
236C2×D61—44no—
237C2×D61—44no—
238C2×D61—44no—
239C2×D61—44no—
240C2×D61—42no—
241C2×D61—42no—
242C2×D61—42no—
243C2×D61—42no—
244C4×C61—21no—
245C4×C61—21no—
246C4×C61—21no—
247C4×C61—21no—
248C4×C61—82no—
249C4×C61—82no—
250Dic61—22no—
251Dic61—82no—
252Dic61—82no—
253Dic61#34214yes—
254C2×#407—611no—
255#2280—611no—
256C2×#380—611no—
257#1294—611no—
258#1294—611no—
259#1294—611no—
260#1294D6111yescharacteristic, complemented
261C2×C61—21no—
262C2×C61—21no—
263C2×C61—21no—
264C2×C61—21no—
265C2×C61#151312yes—
266C2×C61#151312yes—
267C2×C61#173311yescharacteristic
268C2×C61#173611yescharacteristic
269C2×C61C2×#34211yescharacteristic
270D61—42no—
271D61—42no—
272C24×C4—611no—
273C22×M16—1221no—
274C2×#117—612no—
275C22×C4⋊C4—1221no—
276C22×C22⋊C4—1221no—
277#407—614no—
278#407—1222no—
279C2×C22⋊C8—611no—
280C2×C22⋊C8—1221no—
281C2×C22⋊C8C2×D6111yescharacteristic
282#381—1221no—
283#380—614no—
284#380—611no—
285#380—612no—
286#380—1222no—
287#380C2×D6111yescharacteristic
288#379—1221no—
289C4×C22⋊C4—1221no—
290C4×C22⋊C4—1221no—
291C2×#95—611no—
292C2×#95C2×D6111yescharacteristic
293C61#801611yescharacteristic, complemented, Sylow
294C25—611no—
295C23×C4—21no—
296C23×C4—611no—
297C23×C4—611no—
298C23×C4—611no—
299C23×C4—612no—
300C23×C4—611no—
301C23×C4—612no—
302C23×C4—612no—
303C23×C4—611no—
304C23×C4—612no—
305C23×C4—1221no—
306C23×C4—2444no—
307C23×C4C22×D6111yescharacteristic
308C2×M16—1224no—
309C2×M16—2444no—
310C22×C8—21no—
311C22×C8—1221no—
312#117—2444no—
313C2×C4⋊C4—612no—
314C2×C4⋊C4—1224no—
315C2×C4⋊C4—2444no—
316C2×C4⋊C4C4×D6112yes—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—1224no—
319C2×C22⋊C4—1222no—
320C2×C22⋊C4—1222no—
321C2×C22⋊C4—1221no—
322C2×C22⋊C4—2442no—
323C2×C22⋊C4—2442no—
324C2×C42—1222no—
325C22⋊C8—21no—
326C22⋊C8—612no—
327C22⋊C8—1224no—
328C22⋊C8—1221no—
329C22⋊C8C4×D6112yes—
330#95—21no—
331#95—21no—
332#95—612no—
333#95—1222no—
334#95—1221no—
335#95—1221no—
336#95C4×D6112yes—
337C24—611no—
338C24—611no—
339C24—612no—
340C24—612no—
341C24—1221no—
342C24—1221no—
343C24—1221no—
344C24—1221no—
345C24—2442no—
346C24—2442no—
347C24D4×D6111yescharacteristic
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—611no—
356C22×C4—612no—
357C22×C4—611no—
358C22×C4—612no—
359C22×C4—612no—
360C22×C4—612no—
361C22×C4—612no—
362C22×C4—612no—
363C22×C4—612no—
364C22×C4—612no—
365C22×C4—612no—
366C22×C4—612no—
367C22×C4—1224no—
368C22×C4—1224no—
369C22×C4—1224no—
370C22×C4—1222no—
371C22×C4—1222no—
372C22×C4—2442no—
373C22×C4—2442no—
374C22×C4—2444no—
375C22×C4—2444no—
376C22×C4—2444no—
377C22×C4—2444no—
378C22×C4—2442no—
379C22×C4—2442no—
380C22×C4—2441no—
381C22×C4—2441no—
382C22×C4C2×C4×D6111yescharacteristic
383C22×C4C2×C4×D6111yescharacteristic
384C22×C4C2×C4×D6111yescharacteristic
385C22×C4D4×D6111yescharacteristic
386C22×C4D4×D6111yescharacteristic
387C22×C4Q8×D6111yescharacteristic
388M16—2448no—
389C2×C8—22no—
390C2×C8—42no—
391C2×C8—1222no—
392C2×C8—2442no—
393C4⋊C4—42no—
394C4⋊C4—2442no—
395C4⋊C4—2448no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—2448no—
399C22⋊C4—2444no—
400C22⋊C4—2444no—
401C22⋊C4—2441no—
402C22⋊C4—2441no—
403C42—2444no—
404C23—22no—
405C23—22no—
406C23—612no—
407C23—612no—
408C23—1222no—
409C23—1222no—
410C23—1221no—
411C23—1221no—
412C23—1221no—
413C23—1221no—
414C23—1222no—
415C23—1222no—
416C23—1222no—
417C23—1222no—
418C23—1222no—
419C23—1222no—
420C23—2442no—
421C23—2442no—
422C23—2442no—
423C23—2442no—
424C23—2444no—
425C23—2444no—
426C23—2444no—
427C23—2444no—
428C23C22⋊C4×D6111yescharacteristic
429C23C22⋊C4×D6111yescharacteristic
430C23C4⋊C4×D6111yescharacteristic
431C23#1451980111yescharacteristic
432C23#1451980411yescharacteristic
433C23#1451980611yescharacteristic
434C23#1451980911yescharacteristic
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4—614no—
450C2×C4—612no—
451C2×C4—612no—
452C2×C4—1224no—
453C2×C4—1224no—
454C2×C4—1224no—
455C2×C4—1224no—
456C2×C4—1224no—
457C2×C4—1224no—
458C2×C4—1222no—
459C2×C4—4882no—
460C2×C4—4882no—
461C2×C4—2442no—
462C2×C4—2442no—
463C2×C4—2442no—
464C2×C4—2442no—
465C2×C4—2442no—
466C2×C4—2442no—
467C2×C4—2442no—
468C2×C4—2442no—
469C2×C4—2442no—
470C2×C4—2442no—
471C2×C4C42×D6111yescharacteristic
472C2×C4C22⋊C4×D6111yescharacteristic
473C2×C4C4⋊C4×D6111yescharacteristic
474C2×C4C4⋊C4×D6111yescharacteristic
475C8—42no—
476C8—2442no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—1222no—
486C22—1222no—
487C22—1222no—
488C22—1222no—
489C22—1222no—
490C22—1222no—
491C22—2444no—
492C22—2444no—
493C22—2444no—
494C22—2444no—
495C22—2442no—
496C22—2442no—
497C22—2442no—
498C22—2442no—
499C22#95×D6111yescharacteristic
500C22#99×D6112yes—
501C22#1683976011yescharacteristic
502C22#1683976211yescharacteristic
503C22#1683976511yescharacteristic
504C22#1683976911yescharacteristic
505C22#1683977712yes—
506C22#1683980111yescharacteristic
507C22#1683980311yescharacteristic
508C4—21no—
509C4—21no—
510C4—21no—
511C4—21no—
512C4—82no—
513C4—82no—
514C4—614no—
515C4—1222no—
516C4—4882no—
517C4—4882no—
518C2—21no—
519C2—21no—
520C2—21no—
521C2—21no—
522C2—2442no—
523C2—2442no—
524C2#2144435912yes—
525C2#2144436112yes—
526C2#2144552711yescharacteristic
527C2#2144553711yescharacteristic
528C2#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#8016
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
14. #16839724C4semidirect
20. #16839621C4semidirect
21. #16839619C4semidirect
260. #1294D61semidirect
293. C61#8016semidirect

Maximal subgroups

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

subgroupindex
C2×#168397242
#214482012
C2×#168396212
#214436992
#214436982
#214436972
C61×#12942
#801661