Finite Group Databasebeta

← #29835439

Subgroups — #29835439

Order 15616.

918 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840200C211yesmaximal, characteristic, complemented
2C2×#16840198C211yesmaximal, characteristic, complemented
3C2×#16840197C211yesmaximal, characteristic, complemented
4#21456243C211yesmaximal, characteristic, complemented
5C2×#16840137C211yesmaximal, characteristic, complemented
6#21448084C212yesmaximal, complemented
7#21448082C212yesmaximal, complemented
8#21448073C212yesmaximal, complemented
9#21448067C212yesmaximal, complemented
10M32×Dic61C211yesmaximal, characteristic, complemented
11C2×C61×#509C211yesmaximal, characteristic, complemented
12C2×#14519799C2211yescharacteristic
13C2×#14519797—21no—
14C22×D488C2211yescharacteristic
15C22×#11758199—21no—
16#16840308—21no—
17C2×#14519773—21no—
18#16840200—24no—
19#16840198—24no—
20#16840197—24no—
21C2×#14519722C2212yescomplemented
22C2×#14519721C2212yescomplemented
23C2×#14519720C2212yescomplemented
24C2×D976C2212yescomplemented
25C2×#14519718C2212yescomplemented
26C2×#14519718C2212yescomplemented
27C2×#14519717C2211yescharacteristic
28#16840147C2211yescharacteristic, complemented
29#16840145C2211yescharacteristic, complemented
30#16840143—21no—
31#16840140C2211yescharacteristic, complemented
32#16840137—21no—
33#16840137—21no—
34#16840137C2212yes—
35#16840137C2212yes—
36#16840137C2211yescharacteristic, complemented
37#16840133—21no—
38C2×C8×Dic61C2211yescharacteristic
39#16839537C2212yescomplemented
40C16×Dic61C2212yescomplemented
41C2×#135×C61C2211yescharacteristic
42C22×D8×C61C2211yescharacteristic
43C61×#509—24no—
44C2×SD32×C61C2212yescomplemented
45C2×D16×C61C2212yescomplemented
46C2×M32×C61C2211yescharacteristic
47C2×#11758222—21no—
48C22×D244—21no—
49C22×C22⋊D61—42no—
50#14519799—22no—
51#14519799—22no—
52#14519797—44no—
53C2×Dic244C2311yescharacteristic
54C2×#11758202—21no—
55C2×#11758190—21no—
56C2×#11758200—21no—
57C2×#11758201—21no—
58C2×D488—22no—
59C2×D488—22no—
60C2×D488—21no—
61C2×D488C2312yes—
62C2×D488C2311yescharacteristic
63C2×#11758199—22no—
64C2×#11758199—22no—
65C2×#11758199—21no—
66C2×#11758199—44no—
67C22×#92418D411yescharacteristic
68#14519775—21no—
69#14519773—22no—
70#14519773—22no—
71#14519773—21no—
72#14519773—42no—
73#14519766—21no—
74#14519764—21no—
75#14519749—42no—
76C4×C22⋊D61—42no—
77C2×C4×Dic61D411yescharacteristic
78#14519722—24no—
79#14519721—24no—
80#14519720—24no—
81D976—24no—
82#14519718—24no—
83#14519718—24no—
84#14519717D414yescomplemented
85C2×#11758185C2312yes—
86C8×Dic61D411yescharacteristic
87C8×Dic61D411yescharacteristic
88C8×Dic61C2311yescharacteristic
89C8×Dic61C2311yescharacteristic
90C2×#41×C61—21no—
91C22×D4×C61—21no—
92#135×C61—22no—
93#135×C61—22no—
94C2×Q16×C61C2311yescharacteristic
95C2×SD16×C61—21no—
96C2×D8×C61—22no—
97C2×D8×C61—22no—
98C2×D8×C61—21no—
99C2×D8×C61C2312yes—
100C2×D8×C61C2311yescharacteristic
101C22×C8×C61C2311yescharacteristic
102SD32×C61—24no—
103D16×C61—24no—
104M32×C61D414yescomplemented
105C2×C16×C61C2312yes—
106C24×C61—41no—
107C23×D61—41no—
108#41×C61—42no—
109#41×C61—42no—
110C2×Q8×C61—21no—
111C2×D4×C61—22no—
112C2×D4×C61—21no—
113C2×D4×C61—41no—
114C2×D4×C61—42no—
115C2×D4×C61—42no—
116C2×D4×C61—41no—
117C22×C4×C61—41no—
118C22×C4×C61C2×D411yescharacteristic
119C2×C22⋊D61—41no—
120C2×C22⋊D61—44no—
121C2×C22⋊D61—44no—
122C2×C22⋊D61—42no—
123C2×C22⋊D61—88no—
124C22×Dic61D812yes—
125#11758222—42no—
126#11758222—42no—
127C2×D244—22no—
128C2×D244—21no—
129C2×D244—42no—
130C2×D244—42no—
131C2×D244—41no—
132C2×C4×D61—41no—
133C2×Dic122—21no—
134Q16×C61—21no—
135Q16×C61—21no—
136SD16×C61—42no—
137D8×C61—21no—
138D8×C61—22no—
139D8×C61—22no—
140D8×C61—21no—
141D8×C61—42no—
142C2×C8×C61C2×D411yescharacteristic
143C2×C8×C61C2×D412yes—
144C2×C8×C61C2×D412yes—
145C2×C8×C61C2411yescharacteristic
146C22⋊Dic61—42no—
147#11758202—42no—
148#11758201—42no—
149#11758200—42no—
150#11758199—44no—
151#11758199—44no—
152#11758199—42no—
153#11758198—42no—
154#11758196—42no—
155C4×Dic61D812yes—
156C4×Dic61C2×D411yescharacteristic
157C4×Dic61C2×D411yescharacteristic
158C2×#92418D814yes—
159C2×#92418C2×D411yescharacteristic
160C2×#92418C2×D411yescharacteristic
161Dic244—21no—
162Dic244—21no—
163D488—21no—
164D488—22no—
165D488—21no—
166D488—22no—
167D488—42no—
168#11758190—42no—
169C16×C61C2×D414yescomplemented
170#11758185C2×D414yescomplemented
171C23×C61—41no—
172C23×C61—42no—
173C23×C61—84no—
174C23×C61—82no—
175C23×C61C2×D811yescharacteristic
176C22×D61—41no—
177C22×D61—42no—
178C22×D61—84no—
179C22×D61—82no—
180Q8×C61—41no—
181Q8×C61—41no—
182D4×C61—42no—
183D4×C61—41no—
184D4×C61—42no—
185D4×C61—41no—
186D4×C61—82no—
187D4×C61—82no—
188C2×C4×C61—41no—
189C2×C4×C61—82no—
190C2×C4×C61#12712yes—
191C2×C4×C61C2×D812yes—
192C2×C4×C61C2×D811yescharacteristic
193C2×C4×C61C22×D411yescharacteristic
194C22⋊D61—88no—
195C22⋊D61—82no—
196C22⋊D61—84no—
197C22⋊D61—88no—
198C2×Dic61—24no—
199C2×Dic61—41no—
200C2×Dic61C2×D812yes—
201C2×Dic61C2×D812yes—
202D244—41no—
203D244—42no—
204D244—42no—
205D244—41no—
206D244—82no—
207C4×D61—82no—
208Dic122—41no—
209Dic122—41no—
210C8×C61#12712yes—
211C8×C61C22×D411yescharacteristic
212C8×C61C22×D411yescharacteristic
213#92418C2×D812yes—
214#92418C2×D812yes—
215#33717—611nomaximal, Sylow
216C22×C61—22no—
217C22×C61—81no—
218C22×C61—82no—
219C22×C61—84no—
220C22×C61—82no—
221C22×C61—164no—
222C22×C61#49312yes—
223C22×C61C22×D811yescharacteristic
224C2×D61—81no—
225C2×D61—82no—
226C2×D61—84no—
227C2×D61—82no—
228C2×D61—164no—
229C4×C61—81no—
230C4×C61#49312yes—
231C4×C61C2×#12711yescharacteristic
232C4×C61C22×D811yescharacteristic
233Dic61—22no—
234Dic61—81no—
235Dic61#50914yescomplemented
236C2×#509—611no—
237C2×#509—611no—
238C2×#509—611no—
239C2×#509D6111yescharacteristic, complemented
240#3147—611no—
241C2×#493—611no—
242#2250—612no—
243#2250—612no—
244#2248—612no—
245#2246—612no—
246C4×M32—611no—
247C2×C61—22no—
248C2×C61—161no—
249C2×C61—162no—
250C2×C61C2×#49311yescharacteristic
251C2×C61C2×#50912yes—
252D61—161no—
253D61—162no—
254C2×#135—611no—
255C2×#135—1221no—
256C2×#135C2×D6111yescharacteristic
257C22×D8—611no—
258C22×D8—1221no—
259C22×D8C2×D6111yescharacteristic
260#532—1221no—
261C2×#127—1221no—
262#509—24no—
263#509—1224no—
264#509—1224no—
265#509—1224no—
266C2×SD32—612no—
267C2×SD32—612no—
268C2×SD32—612no—
269C2×SD32C2×D6112yescomplemented
270C2×D16—612no—
271C2×D16—612no—
272C2×D16—612no—
273C2×D16C2×D6112yescomplemented
274C2×M32—611no—
275C2×M32C2×D6111yescharacteristic
276#495—611no—
277#495—611no—
278#495—1221no—
279#494—611no—
280#493—612no—
281#493—612no—
282#493—611no—
283#493—1221no—
284#493—1221no—
285#492—1221no—
286C2×C4×C8—611no—
287#346—612no—
288C4×C16—612no—
289C61#3371711yescharacteristic, complemented, Sylow
290C2×#41—21no—
291C2×#41—1221no—
292C22×D4—21no—
293C22×D4—1221no—
294C22×D4—2442no—
295#135—22no—
296#135—22no—
297#135—1222no—
298#135—1222no—
299#135—2444no—
300C2×Q16—611no—
301C2×Q16—1221no—
302C2×Q16C22×D6111yescharacteristic
303C2×SD16—21no—
304C2×SD16—1221no—
305C2×SD16—1221no—
306C2×SD16—1221no—
307C2×D8—22no—
308C2×D8—21no—
309C2×D8—22no—
310C2×D8—612no—
311C2×D8—611no—
312C2×D8—1222no—
313C2×D8—1222no—
314C2×D8—1221no—
315C2×D8—1222no—
316C2×D8—1221no—
317C2×D8—1222no—
318C2×D8—2444no—
319C2×D8C22×D6112yes—
320C2×D8C22×D6111yescharacteristic
321C22×C8—611no—
322C22×C8C22×D6111yescharacteristic
323C4⋊Q8—1221no—
324#127—1222no—
325#127—1222no—
326#127—1221no—
327#127—2442no—
328#124—1221no—
329#124—1221no—
330#121—2442no—
331C4×D4—2442no—
332C2×C42—611no—
333SD32—24no—
334SD32—1224no—
335SD32—1224no—
336SD32—1224no—
337D16—24no—
338D16—1224no—
339D16—1224no—
340D16—1224no—
341M32—614no—
342M32C22⋊D6114yescomplemented
343C2×C16—612no—
344C2×C16C22×D6112yes—
345C4×C8—611no—
346C4×C8—611no—
347C4×C8—611no—
348C4×C8—611no—
349C24—41no—
350C24—2441no—
351#41—42no—
352#41—42no—
353#41—2442no—
354#41—2442no—
355C2×Q8—21no—
356C2×Q8—1221no—
357C2×D4—21no—
358C2×D4—22no—
359C2×D4—41no—
360C2×D4—42no—
361C2×D4—42no—
362C2×D4—41no—
363C2×D4—1221no—
364C2×D4—1222no—
365C2×D4—4888no—
366C2×D4—2442no—
367C2×D4—2444no—
368C2×D4—2444no—
369C2×D4—2441no—
370C2×D4—2442no—
371C2×D4—2441no—
372C2×D4—2442no—
373C22×C4—41no—
374C22×C4—612no—
375C22×C4—2441no—
376C22×C4D4×D6111yescharacteristic
377Q16—21no—
378Q16—21no—
379Q16—1221no—
380Q16—1221no—
381Q16—2442no—
382SD16—42no—
383SD16—2442no—
384SD16—2442no—
385SD16—2442no—
386D8—21no—
387D8—22no—
388D8—21no—
389D8—22no—
390D8—42no—
391D8—1221no—
392D8—1222no—
393D8—1221no—
394D8—1222no—
395D8—2444no—
396D8—2444no—
397D8—2442no—
398D8—2442no—
399C2×C8—611no—
400C2×C8—611no—
401C2×C8—614no—
402C2×C8D4×D6112yes—
403C2×C8D4×D6111yescharacteristic
404C2×C8C2×C22⋊D6112yes—
405C2×C8C23×D6111yescharacteristic
406C4⋊C4—2442no—
407C22⋊C4—2442no—
408C22⋊C4—2442no—
409C42—611no—
410C42—611no—
411C42—612no—
412C16—614no—
413C16C2×C22⋊D6114yescomplemented
414C23—41no—
415C23—42no—
416C23—84no—
417C23—82no—
418C23—4884no—
419C23—4882no—
420C23—2441no—
421C23—2442no—
422C23D8×D6111yescharacteristic
423Q8—41no—
424Q8—41no—
425Q8—2441no—
426Q8—2441no—
427D4—42no—
428D4—41no—
429D4—42no—
430D4—41no—
431D4—82no—
432D4—82no—
433D4—4888no—
434D4—4884no—
435D4—4888no—
436D4—4882no—
437D4—4882no—
438D4—2442no—
439D4—2441no—
440D4—2442no—
441D4—2441no—
442C2×C4—41no—
443C2×C4—82no—
444C2×C4—612no—
445C2×C4—612no—
446C2×C4—1224no—
447C2×C4—4882no—
448C2×C4—2441no—
449C2×C4#1451977312yes—
450C2×C4D8×D6112yes—
451C2×C4D8×D6111yescharacteristic
452C2×C4C2×D4×D6111yescharacteristic
453C8—612no—
454C8—612no—
455C8#1451977312yes—
456C8C2×D4×D6111yescharacteristic
457C8C22×C22⋊D6111yescharacteristic
458C22—22no—
459C22—81no—
460C22—82no—
461C22—84no—
462C22—82no—
463C22—164no—
464C22—9764no—
465C22—4881no—
466C22—4882no—
467C22—4884no—
468C22—4882no—
469C22#1684013712yes—
470C22C2×D8×D6111yescharacteristic
471C4—81no—
472C4—614no—
473C4—1222no—
474C4—4881no—
475C4#1684013712yes—
476C4C2×#1451977311yescharacteristic
477C4C2×D8×D6111yescharacteristic
478C2—22no—
479C2—162no—
480C2—161no—
481C2—9762no—
482C2—9761no—
483C2C2×#1684013711yescharacteristic
484C2#509×D6112yes—
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#509C2
socleC22×C61C22×D8
hypercenterC2×#509D61
hypocenterC61#33717
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. C2×#16840200C2semidirect
2. C2×#16840198C2semidirect
3. C2×#16840197C2semidirect
4. #21456243C2semidirect
5. C2×#16840137C2semidirect
6. #21448084C2semidirect
7. #21448082C2semidirect
8. #21448073C2semidirect
9. #21448067C2semidirect
10. M32×Dic61C2semidirect
11. C2×C61×#509C2semidirect
21. C2×#14519722C22semidirect
22. C2×#14519721C22semidirect
23. C2×#14519720C22semidirect
24. C2×D976C22semidirect
25. C2×#14519718C22semidirect
26. C2×#14519718C22semidirect
28. #16840147C22semidirect
29. #16840145C22semidirect
31. #16840140C22semidirect
36. #16840137C22semidirect
39. #16839537C22semidirect
40. C16×Dic61C22semidirect
44. C2×SD32×C61C22semidirect
45. C2×D16×C61C22semidirect
84. #14519717D4semidirect
104. M32×C61D4semidirect
169. C16×C61C2×D4semidirect
170. #11758185C2×D4semidirect
235. Dic61#509semidirect
239. C2×#509D61semidirect
269. C2×SD32C2×D61semidirect
273. C2×D16C2×D61semidirect
289. C61#33717semidirect
342. M32C22⋊D61semidirect
413. C16C2×C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402002
C2×#168401982
C2×#168401972
#214562432
C2×#168401372
#214480842
#214480822
#214480732
#214480672
M32×Dic612
C2×C61×#5092
#3371761