Finite Group Databasebeta

← #29571464

Subgroups — #29571464

Order 15616.

908 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840296C211yesmaximal, characteristic
2C2×#16839500C212yesmaximal, complemented
3C2×#16839497C212yesmaximal
4#21444046C211yesmaximal, characteristic, complemented
5C61×#1817C211yesmaximal, characteristic, complemented
6#16840296—24no—
7#16840296—24no—
8C2×#14519771—21no—
9C2×#14519769C411yescharacteristic, complemented
10C2×#14519765C411yescharacteristic, complemented
11C2×#14519760—21no—
12C2×#14519756C2211yescharacteristic
13C2×#14519751C2211yescharacteristic
14C2×C4×Dic122C411yescharacteristic, complemented
15C2×C4×D244C411yescharacteristic, complemented
16C2×C4×C22⋊D61—21no—
17C2×#14519734—21no—
18C2×#14519684—21no—
19C2×#14519684—21no—
20C2×#14519684C2212yes—
21#16839500—24no—
22#16839497—24no—
23C22×C42×C61C2211yescharacteristic
24C2×C22⋊C8×C61C2212yes—
25C61×#336—21no—
26C61×#336—21no—
27C22×Dic122C2×C411yescharacteristic
28C22×D244C2×C411yescharacteristic
29C22×C22⋊D61—21no—
30C23×Dic61—22no—
31C22×C4×D61—21no—
32#14519771—28no—
33#14519769—22no—
34#14519769—22no—
35#14519765—22no—
36#14519765—22no—
37#14519760—28no—
38#14519756—22no—
39#14519756D414yes—
40#14519751—22no—
41#14519751D414yes—
42C4×Dic122—22no—
43C4×Dic122—22no—
44C4×D244—22no—
45C4×D244—22no—
46C4×C22⋊D61—28no—
47#14519734—28no—
48C2×C4⋊Dic61C2×C411yescharacteristic
49C2×C4⋊Dic61C2×C411yescharacteristic
50C2×#11758196—21no—
51C2×#11758196—21no—
52C2×#11758196—21no—
53C2×#11758196—21no—
54C2×C22⋊Dic61—21no—
55C2×#11758198—21no—
56C2×#11758198—21no—
57C2×#11758198—21no—
58C2×#11758198—21no—
59C2×C4×Dic61—21no—
60#14519684—24no—
61#14519684—22no—
62#14519684—22no—
63#14519684—42no—
64C23×C4×C61D411yescharacteristic
65C23×C4×C61D411yescharacteristic
66C23×C4×C61C2311yescharacteristic
67C22×C8×C61—22no—
68C2×C42×C61—22no—
69C2×C42×C61—22no—
70C2×C42×C61C2×C411yescharacteristic
71C2×C42×C61C2×C411yescharacteristic
72C2×C42×C61D411yescharacteristic
73C2×C42×C61D411yescharacteristic
74C22⋊C8×C61—22no—
75C22⋊C8×C61—22no—
76C24×C61C2×D411yescharacteristic
77C23×D61—21no—
78C22×C4×C61—22no—
79C22×C4×C61—22no—
80C22×C4×C61—22no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—22no—
84C22×C4×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61C22⋊C411yescharacteristic
88C22×C4×C61C22⋊C411yescharacteristic
89C22×C4×C61C22⋊C411yescharacteristic
90C22×C4×C61C22⋊C411yescharacteristic
91C22×C4×C61C22×C411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D412yes—
94C22×C4×C61C2×D412yes—
95C2×C22⋊D61—24no—
96C2×C22⋊D61—42no—
97C2×C22⋊D61—41no—
98C2×C22⋊D61—41no—
99C22×Dic61—21no—
100C22×Dic61—21no—
101C22×Dic61—21no—
102C22×Dic61—24no—
103C22×Dic61—42no—
104C22×Dic61—42no—
105C22×Dic61—42no—
106C22×Dic61—42no—
107C22×Dic61—42no—
108C22×Dic61—42no—
109C2×D244—21no—
110C2×D244—41no—
111C2×D244—41no—
112C2×D244C22⋊C412yes—
113C2×C4×D61—24no—
114C2×C4×D61—42no—
115C2×C4×D61—42no—
116C2×Dic122—21no—
117C2×Dic122—41no—
118C2×Dic122—41no—
119C2×Dic122C22⋊C412yes—
120C2×C8×C61—42no—
121C2×C8×C61—42no—
122C2×C8×C61—42no—
123C42×C61—21no—
124C42×C61—21no—
125C42×C61—21no—
126C42×C61—21no—
127C42×C61—22no—
128C42×C61—22no—
129C22⋊Dic61—24no—
130#11758198—24no—
131#11758198—24no—
132#11758198—24no—
133#11758198—24no—
134C4⋊Dic61—21no—
135C4⋊Dic61—21no—
136C4⋊Dic61C22⋊C412yes—
137C4⋊Dic61C22⋊C412yes—
138#11758196—24no—
139#11758196—24no—
140#11758196—24no—
141#11758196—24no—
142C4×Dic61—24no—
143C23×C61—21no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61C2×C22⋊C411yescharacteristic
148C23×C61#12012yes—
149C23×C61#13512yes—
150C23×C61AGL(1,ℤ/8)11yescharacteristic
151C23×C61#13711yescharacteristic
152C22×D61—22no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61—41no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—42no—
175C2×C4×C61—42no—
176C2×C4×C61—44no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×C4×C61#10412yes—
180C2×C4×C61C2×C22⋊C411yescharacteristic
181C2×C4×C61C2×C22⋊C411yescharacteristic
182C2×C4×C61#12012yes—
183C22⋊D61—44no—
184C22⋊D61—44no—
185C2×Dic61—22no—
186C2×Dic61—22no—
187C2×Dic61—22no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—44no—
195C2×Dic61—44no—
196C2×Dic61—44no—
197C2×Dic61—82no—
198C2×Dic61—82no—
199C2×Dic61—82no—
200C2×Dic61—82no—
201D244—42no—
202D244—42no—
203C4×D61—48no—
204Dic122—42no—
205Dic122—42no—
206C8×C61—82no—
207#8330—611nomaximal, Sylow
208C22×C61—22no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—22no—
214C22×C61—22no—
215C22×C61—22no—
216C22×C61#37911yescharacteristic
217C22×C61#41011yescharacteristic
218C22×C61#41011yescharacteristic
219C22×C61#41611yescharacteristic
220C22×C61#41711yescharacteristic
221C22×C61C2×#10411yescharacteristic
222C22×C61#42111yescharacteristic
223C22×C61#44912yes—
224C22×C61#45212yes—
225C2×D61—42no—
226C2×D61—42no—
227C2×D61—42no—
228C2×D61—81no—
229C2×D61—81no—
230C2×D61—81no—
231C2×D61—81no—
232C4×C61—22no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—22no—
236C4×C61—41no—
237C4×C61—41no—
238C4×C61—41no—
239Dic61—42no—
240Dic61—42no—
241Dic61—42no—
242Dic61—84no—
243C2×#529—611no—
244#1817D6111yescharacteristic, complemented
245C2×#328—612no—
246C2×#327—612no—
247#1434—611no—
248C2×C61—22no—
249C2×C61—22no—
250C2×C61#150011yescharacteristic
251C2×C61#150911yescharacteristic
252C2×C61#151211yescharacteristic
253C2×C61#152111yescharacteristic
254C2×C61#178211yescharacteristic
255C2×C61#178811yescharacteristic
256C2×C61#178911yescharacteristic
257D61—82no—
258#529—1224no—
259#529—1224no—
260C2×#126—1221no—
261C2×#125—611no—
262C2×#124—611no—
263C2×#123—1221no—
264C2×C22⋊Q8—611no—
265C2×#121—611no—
266C2×C4×Q8—611no—
267C2×C4×D4—611no—
268C2×C4×D4—1221no—
269C2×#117—1221no—
270C22×C42C2×D6111yescharacteristic
271C2×C22⋊C8C2×D6112yes—
272C2×#95—612no—
273C2×#95—1221no—
274C2×#95—1221no—
275#336—21no—
276#336—21no—
277#328—1224no—
278#327—1224no—
279C61#833011yescharacteristic, complemented, Sylow
280C22×Q8—611no—
281C22×D4—611no—
282C22×D4—1221no—
283C23×C4—1221no—
284C23×C4—1222no—
285C23×C4D24411yescharacteristic
286C23×C4D24411yescharacteristic
287C23×C4C22×D6111yescharacteristic
288C22×C8—22no—
289#126—1228no—
290#125—1222no—
291#125—1222no—
292#124—1222no—
293#124—1222no—
294#123—1228no—
295C22⋊Q8—614no—
296C22⋊Q8—1222no—
297#121—614no—
298#121—1222no—
299C4×Q8—1222no—
300C4×Q8—1222no—
301C4×D4—1222no—
302C4×D4—1222no—
303C4×D4—1228no—
304#117—1228no—
305C2×C4⋊C4—611no—
306C2×C4⋊C4—611no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4—1221no—
309C2×C4⋊C4—1221no—
310C2×C4⋊C4—1221no—
311C2×C22⋊C4—1221no—
312C2×C22⋊C4—1221no—
313C2×C22⋊C4—1221no—
314C2×C22⋊C4—1221no—
315C2×C22⋊C4—1221no—
316C2×C42—22no—
317C2×C42—22no—
318C2×C42—1221no—
319C2×C42C4×D6111yescharacteristic
320C2×C42C4×D6111yescharacteristic
321C2×C42C22⋊D6111yescharacteristic
322C2×C42C22⋊D6111yescharacteristic
323C22⋊C8—22no—
324C22⋊C8—22no—
325#95—1224no—
326#95—1222no—
327#95—1222no—
328#95—2442no—
329C24—1221no—
330C24C2×D24411yescharacteristic
331C2×Q8—612no—
332C2×Q8—1221no—
333C2×Q8—2441no—
334C2×Q8—2441no—
335C2×D4—612no—
336C2×D4—1224no—
337C2×D4—1221no—
338C2×D4—2441no—
339C2×D4—2441no—
340C2×D4—2441no—
341C2×D4—2442no—
342C2×D4—2441no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—1224no—
353C22×C4—1221no—
354C22×C4—1221no—
355C22×C4—1221no—
356C22×C4—1224no—
357C22×C4—2442no—
358C22×C4—2442no—
359C22×C4—2442no—
360C22×C4—2442no—
361C22×C4—2442no—
362C22×C4—2442no—
363C22×C4—2442no—
364C22×C4—2442no—
365C22×C4#1175819811yescharacteristic
366C22×C4#1175819811yescharacteristic
367C22×C4#1175819811yescharacteristic
368C22×C4#1175819811yescharacteristic
369C22×C4C2×C4×D6111yescharacteristic
370C22×C4D4×D6112yes—
371C22×C4D4×D6112yes—
372C22×C4C2×C22⋊D6111yescharacteristic
373C2×C8—42no—
374C2×C8—42no—
375C2×C8—42no—
376C4⋊C4—612no—
377C4⋊C4—612no—
378C4⋊C4—1224no—
379C4⋊C4—1224no—
380C4⋊C4—1224no—
381C4⋊C4—1221no—
382C4⋊C4—1221no—
383C4⋊C4—1224no—
384C22⋊C4—1224no—
385C22⋊C4—1224no—
386C22⋊C4—1224no—
387C22⋊C4—1224no—
388C22⋊C4—1224no—
389C42—21no—
390C42—21no—
391C42—21no—
392C42—21no—
393C42—22no—
394C42—22no—
395C42—1224no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—1222no—
401C23—2441no—
402C23—2441no—
403C23—2441no—
404C23—2441no—
405C23—2441no—
406C23—2441no—
407C23C2×#1175819811yescharacteristic
408C23#1451974712yes—
409C23#1451979912yes—
410C23#1451980511yescharacteristic
411C23#1451981011yescharacteristic
412Q8—2442no—
413Q8—2442no—
414D4—2442no—
415D4—2442no—
416D4—2444no—
417D4—2444no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—44no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—1222no—
439C2×C4—1222no—
440C2×C4—1222no—
441C2×C4—4882no—
442C2×C4—4882no—
443C2×C4—4882no—
444C2×C4—4882no—
445C2×C4—2448no—
446C2×C4—2444no—
447C2×C4—2444no—
448C2×C4—2444no—
449C2×C4—2441no—
450C2×C4—2441no—
451C2×C4—2441no—
452C2×C4—2441no—
453C2×C4—2441no—
454C2×C4—2441no—
455C2×C4#1451970312yes—
456C2×C4C22⋊C4×D6111yescharacteristic
457C2×C4C22⋊C4×D6111yescharacteristic
458C2×C4#1451974512yes—
459C8—82no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—21no—
467C22—21no—
468C22—4881no—
469C22—4881no—
470C22—4881no—
471C22—4881no—
472C22—2442no—
473C22—2442no—
474C22—2442no—
475C22#1683961711yescharacteristic
476C22#1683973511yescharacteristic
477C22#1683973511yescharacteristic
478C22#1683975911yescharacteristic
479C22#1683976411yescharacteristic
480C22C2×#1451970311yescharacteristic
481C22#1683977811yescharacteristic
482C22#1683990912yes—
483C22#1683992612yes—
484C4—22no—
485C4—21no—
486C4—21no—
487C4—22no—
488C4—41no—
489C4—41no—
490C4—41no—
491C4—4884no—
492C4—2442no—
493C4—2442no—
494C4—2442no—
495C2—22no—
496C2—22no—
497C2—4882no—
498C2#2144430611yescharacteristic
499C2#2144434511yescharacteristic
500C2#2144435811yescharacteristic
501C2#2144439711yescharacteristic
502C2#2144573611yescharacteristic
503C2#2144576011yescharacteristic
504C2#2144576211yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1817C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1817D61
hypocenterC61#8330
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. C2×#16839500C2semidirect
4. #21444046C2semidirect
5. C61×#1817C2semidirect
9. C2×#14519769C4semidirect
10. C2×#14519765C4semidirect
14. C2×C4×Dic122C4semidirect
15. C2×C4×D244C4semidirect
244. #1817D61semidirect
279. C61#8330semidirect

Maximal subgroups

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

subgroupindex
C2×#168402962
C2×#168395002
C2×#168394972
#214440462
C61×#18172
#833061