Finite Group Databasebeta

← #29569999

Subgroups — #29569999

Order 15616.

1122 conjugacy classes of subgroups.

The subgroup lattice has 528 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×#16839609C211yesmaximal, 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—
12C22×C4×Dic61—21no—
13C2×C22⋊#92418C2211yescharacteristic
14C2×#14519689—21no—
15C22⋊C8×D61—22no—
16C22⋊C8×D61C414yescomplemented
17#16839624—21no—
18#16839622C2211yescharacteristic
19#16839619C412yescomplemented
20#16839617—21no—
21C22⋊C4×Dic61—21no—
22#16839609—21no—
23#16839609—22no—
24#16839609C414yescomplemented
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×C412yes—
36C22×C4×D61C2×C411yescharacteristic
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—28no—
48C2×#11758198—24no—
49C2×#11758198—22no—
50C2×#11758198—22no—
51C2×C4×Dic61—24no—
52C2×C4×Dic61—22no—
53C2×C4×Dic61—44no—
54C22⋊#92418—21no—
55C22⋊#92418C2×C412yes—
56#14519689—24no—
57#14519684—21no—
58#14519684—21no—
59#14519684—22no—
60#14519684C2×C412yes—
61C23×C4×C61—21no—
62C23×C4×C61C2311yescharacteristic
63C22×C8×C61—21no—
64C2×C4⋊C4×C61C2×C412yes—
65C2×C22⋊C4×C61—21no—
66C22⋊C8×C61—21no—
67C22⋊C8×C61C2×C412yes—
68#95×C61—21no—
69#95×C61—21no—
70#95×C61C2×C412yes—
71C24×C61C2×D411yescharacteristic
72C23×D61—21no—
73C23×D61—21no—
74C23×D61—21no—
75C23×D61—21no—
76C23×D61—24no—
77C23×D61—42no—
78C23×D61C22⋊C411yescharacteristic
79C23×D61C22⋊C412yes—
80C23×D61C22⋊C411yescharacteristic
81C23×D61C4⋊C412yes—
82C22×C4×C61—24no—
83C22×C4×C61—22no—
84C22×C4×C61—22no—
85C22×C4×C61—42no—
86C22×C4×C61—42no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61C22×C411yescharacteristic
90C22×C4×C61C22×C411yescharacteristic
91C22×C4×C61C22×C411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×Q811yescharacteristic
95C22×Dic61—24no—
96C22×Dic61—24no—
97C22×Dic61—22no—
98C22×Dic61—22no—
99C22×Dic61—42no—
100C22×Dic61—41no—
101C22×Dic61—41no—
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C22⋊C412yes—
104C22×Dic61C22⋊C411yescharacteristic
105C22×Dic61C4⋊C412yes—
106C2×C4×D61—24no—
107C2×C4×D61—24no—
108C2×C4×D61—44no—
109C2×C4×D61—44no—
110C2×C4×D61—44no—
111C2×C4×D61—44no—
112C2×C4×D61—42no—
113C2×C4×D61—42no—
114C2×C4×D61C4212yes—
115C2×C4×D61C4212yes—
116C2×C4×D61C22⋊C412yes—
117C2×C4×D61C22⋊C412yes—
118C2×C4×D61C4⋊C412yes—
119C2×C4×D61C4⋊C412yes—
120C2×C4×D61C4⋊C412yes—
121C2×C4×D61C4⋊C412yes—
122C2×C8×C61—22no—
123C2×C8×C61—42no—
124C4⋊C4×C61—42no—
125C22⋊C4×C61—41no—
126C22⋊C4×C61—41no—
127C22⋊Dic61—41no—
128C22⋊Dic61—41no—
129#11758198—216no—
130#11758198—44no—
131#11758198—44no—
132C4⋊Dic61—42no—
133C4×Dic61—48no—
134C4×Dic61—44no—
135C2×#92418—22no—
136C2×#92418—42no—
137C8×D61—48no—
138C23×C61—22no—
139C23×C61—22no—
140C23×C61C2×C22⋊C411yescharacteristic
141C23×C61C2×C22⋊C411yescharacteristic
142C23×C61C2×C4⋊C411yescharacteristic
143C23×C61#13511yescharacteristic
144C23×C61#13511yescharacteristic
145C23×C61#13511yescharacteristic
146C23×C61#13511yescharacteristic
147C22×D61—22no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—22no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61—22no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—24no—
159C22×D61—24no—
160C22×D61—42no—
161C22×D61—42no—
162C22×D61—44no—
163C22×D61—44no—
164C22×D61—44no—
165C22×D61—44no—
166C22×D61#9512yes—
167C22×D61#9512yes—
168C22×D61#10414yes—
169C2×C4×C61—22no—
170C2×C4×C61—22no—
171C2×C4×C61—24no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—42no—
177C2×C4×C61—44no—
178C2×C4×C61—44no—
179C2×C4×C61—42no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61C2×C4211yescharacteristic
184C2×C4×C61C2×C22⋊C411yescharacteristic
185C2×C4×C61C2×C4⋊C411yescharacteristic
186C2×C4×C61C2×C4⋊C411yescharacteristic
187C2×Dic61—22no—
188C2×Dic61—24no—
189C2×Dic61—24no—
190C2×Dic61—24no—
191C2×Dic61—42no—
192C2×Dic61—44no—
193C2×Dic61—44no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61—42no—
198C2×Dic61#9512yes—
199C2×Dic61#9512yes—
200C2×Dic61#9914yes—
201C4×D61—24no—
202C4×D61—24no—
203C4×D61—24no—
204C4×D61—24no—
205C4×D61—42no—
206C4×D61—42no—
207C4×D61—42no—
208C4×D61—42no—
209C8×C61—42no—
210#92418—42no—
211#8012—611nomaximal, Sylow
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—22no—
217C22×C61—22no—
218C22×C61—22no—
219C22×C61—22no—
220C22×C61C2×#9511yescharacteristic
221C22×C61C2×#9912yes—
222C22×C61#41611yescharacteristic
223C22×C61#41611yescharacteristic
224C22×C61#41611yescharacteristic
225C22×C61#41611yescharacteristic
226C22×C61C2×#10412yes—
227C22×C61#42711yescharacteristic
228C22×C61#42711yescharacteristic
229C2×D61—22no—
230C2×D61—22no—
231C2×D61—24no—
232C2×D61—24no—
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#33914yes—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—21no—
246C4×C61—21no—
247C4×C61—44no—
248C4×C61—82no—
249Dic61—22no—
250Dic61—44no—
251Dic61—82no—
252Dic61#34214yes—
253C22×C22⋊C8—611no—
254#2280—611no—
255C2×C4×C22⋊C4—611no—
256#1294—611no—
257#1294—611no—
258#1294—611no—
259#1294D6111yescharacteristic, complemented
260C2×C61—21no—
261C2×C61—21no—
262C2×C61—21no—
263C2×C61—21no—
264C2×C61#150112yes—
265C2×C61#150112yes—
266C2×C61C2×#33911yescharacteristic
267C2×C61#173511yescharacteristic
268C2×C61C2×#34211yescharacteristic
269D61—24no—
270D61—42no—
271C24×C4—611no—
272C23×C8—1221no—
273C2×#117—612no—
274C22×C22⋊C4—1221no—
275C22×C42—1221no—
276C2×C22⋊C8—611no—
277C2×C22⋊C8—614no—
278C2×C22⋊C8—1222no—
279C2×C22⋊C8—1221no—
280C2×C22⋊C8C2×D6111yescharacteristic
281#381—1221no—
282#380—611no—
283#380—612no—
284#380C2×D6111yescharacteristic
285#379—1221no—
286C4×C22⋊C4—614no—
287C4×C22⋊C4—1222no—
288C4×C22⋊C4—1221no—
289C4×C22⋊C4—1221no—
290C2×#95—611no—
291C2×#95C2×D6111yescharacteristic
292C61#801211yescharacteristic, complemented, Sylow
293C25—611no—
294C23×C4—21no—
295C23×C4—611no—
296C23×C4—611no—
297C23×C4—611no—
298C23×C4—612no—
299C23×C4—611no—
300C23×C4—612no—
301C23×C4—612no—
302C23×C4—611no—
303C23×C4—612no—
304C23×C4—1221no—
305C23×C4—2444no—
306C23×C4C22×D6111yescharacteristic
307C22×C8—21no—
308C22×C8—1224no—
309C22×C8—1221no—
310C22×C8—2444no—
311#117—2444no—
312C2×C4⋊C4—612no—
313C2×C4⋊C4C4×D6112yes—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—1224no—
316C2×C22⋊C4—1228no—
317C2×C22⋊C4—1222no—
318C2×C22⋊C4—1222no—
319C2×C22⋊C4—1221no—
320C2×C42—1222no—
321C2×C42—1224no—
322C2×C42—2444no—
323C22⋊C8—21no—
324C22⋊C8—612no—
325C22⋊C8—1224no—
326C22⋊C8—1221no—
327C22⋊C8C4×D6112yes—
328#95—21no—
329#95—21no—
330#95—612no—
331#95—1222no—
332#95—1221no—
333#95—1221no—
334#95C4×D6112yes—
335C24—611no—
336C24—611no—
337C24—612no—
338C24—612no—
339C24—1224no—
340C24—1221no—
341C24—1221no—
342C24—1221no—
343C24—1221no—
344C24—2442no—
345C24D4×D6111yescharacteristic
346C22×C4—24no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—611no—
354C22×C4—612no—
355C22×C4—611no—
356C22×C4—612no—
357C22×C4—612no—
358C22×C4—612no—
359C22×C4—612no—
360C22×C4—612no—
361C22×C4—612no—
362C22×C4—612no—
363C22×C4—612no—
364C22×C4—612no—
365C22×C4—1224no—
366C22×C4—1224no—
367C22×C4—1224no—
368C22×C4—1224no—
369C22×C4—1222no—
370C22×C4—1222no—
371C22×C4—2442no—
372C22×C4—2442no—
373C22×C4—2444no—
374C22×C4—2444no—
375C22×C4—2444no—
376C22×C4—2444no—
377C22×C4—2442no—
378C22×C4—2441no—
379C22×C4—2441no—
380C22×C4C2×C4×D6111yescharacteristic
381C22×C4C2×C4×D6111yescharacteristic
382C22×C4C2×C4×D6111yescharacteristic
383C22×C4D4×D6111yescharacteristic
384C22×C4D4×D6111yescharacteristic
385C22×C4Q8×D6111yescharacteristic
386C2×C8—22no—
387C2×C8—42no—
388C2×C8—1222no—
389C2×C8—2448no—
390C2×C8—2442no—
391C4⋊C4—42no—
392C4⋊C4—2442no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—12216no—
396C22⋊C4—2444no—
397C22⋊C4—2444no—
398C22⋊C4—2441no—
399C22⋊C4—2441no—
400C42—2444no—
401C42—2448no—
402C23—22no—
403C23—22no—
404C23—614no—
405C23—612no—
406C23—612no—
407C23—1224no—
408C23—1224no—
409C23—1222no—
410C23—1221no—
411C23—1221no—
412C23—1222no—
413C23—1222no—
414C23—1221no—
415C23—1222no—
416C23—1221no—
417C23—1222no—
418C23—1222no—
419C23—1222no—
420C23—2442no—
421C23—2442no—
422C23—2444no—
423C23—2444no—
424C23—2444no—
425C23—2444no—
426C23C22⋊C4×D6111yescharacteristic
427C23C22⋊C4×D6111yescharacteristic
428C23C4⋊C4×D6111yescharacteristic
429C23#1451979611yescharacteristic
430C23#1451979811yescharacteristic
431C23#1451979811yescharacteristic
432C23#1451980011yescharacteristic
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—44no—
442C2×C4—44no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—614no—
448C2×C4—612no—
449C2×C4—612no—
450C2×C4—1224no—
451C2×C4—1224no—
452C2×C4—1224no—
453C2×C4—1224no—
454C2×C4—1224no—
455C2×C4—1224no—
456C2×C4—1222no—
457C2×C4—1224no—
458C2×C4—2442no—
459C2×C4—2442no—
460C2×C4—2442no—
461C2×C4—2442no—
462C2×C4—2442no—
463C2×C4—2442no—
464C2×C4—2442no—
465C2×C4—2442no—
466C2×C4—2444no—
467C2×C4—2444no—
468C2×C4—2442no—
469C2×C4C42×D6111yescharacteristic
470C2×C4C22⋊C4×D6111yescharacteristic
471C2×C4C4⋊C4×D6111yescharacteristic
472C2×C4C4⋊C4×D6111yescharacteristic
473C8—42no—
474C8—2442no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—614no—
484C22—1222no—
485C22—1222no—
486C22—1224no—
487C22—1224no—
488C22—1222no—
489C22—1222no—
490C22—1222no—
491C22—2444no—
492C22—2444no—
493C22—2444no—
494C22—2444no—
495C22—2442no—
496C22—2442no—
497C22#95×D6111yescharacteristic
498C22#99×D6112yes—
499C22#1683975511yescharacteristic
500C22#1683975511yescharacteristic
501C22#1683975711yescharacteristic
502C22#1683975711yescharacteristic
503C22#104×D6112yes—
504C22#1683979711yescharacteristic
505C22#1683979911yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—44no—
511C4—82no—
512C4—614no—
513C4—1222no—
514C4—4882no—
515C4—2444no—
516C2—21no—
517C2—21no—
518C2—21no—
519C2—21no—
520C2—1224no—
521C2—2442no—
522C2#2144430712yes—
523C2#2144430912yes—
524C2#339×D6111yescharacteristic
525C2#2144553411yescharacteristic
526C2#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#8012
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
16. C22⋊C8×D61C4semidirect
19. #16839619C4semidirect
24. #16839609C4semidirect
259. #1294D61semidirect
292. C61#8012semidirect

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×#168396092
#214436992
#214436982
#214436972
C61×#12942
#801261