Finite Group Databasebeta

← #29838158

Subgroups — #29838158

Order 15616.

466 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840195C211yesmaximal, characteristic, complemented
2#508×D61C211yesmaximal, characteristic, complemented
3#21448138C212yesmaximal, complemented
4#21448137C211yesmaximal, characteristic, complemented
5#21448134C211yesmaximal, characteristic, complemented
6#21448133C212yesmaximal, complemented
7#21448131C211yesmaximal, characteristic, complemented
8#21448129C212yesmaximal, complemented
9#21448127C212yesmaximal, complemented
10M64×D61C211yesmaximal, characteristic, complemented
11C61×#2264C211yesmaximal, characteristic, complemented
12C2×#14519800—21no—
13#135×D61—21no—
14#16840195—21no—
15#16840195—21no—
16#16840195C2212yes—
17#16840195C2212yescomplemented
18#16840195C2211yescharacteristic, complemented
19#16840194C2211yescharacteristic
20#16840193—21no—
21#16840192—21no—
22#16840191C2211yescharacteristic, complemented
23Q32×D61C2211yescharacteristic, complemented
24C2×#14519720—21no—
25SD32×D61—21no—
26C2×D976C2211yescharacteristic, complemented
27D16×D61C2211yescharacteristic, complemented
28C2×C16×D61C2211yescharacteristic
29#16839602C2212yescomplemented
30#16839601C2212yescomplemented
31#16839599C2212yescomplemented
32#16839599C2212yescomplemented
33D1952C2212yescomplemented
34#16839597C2212yescomplemented
35#16839596C2211yescharacteristic, complemented
36#16839595C2212yescomplemented
37C32×D61C2212yescomplemented
38C61×#508C2211yescharacteristic
39C2×Q32×C61C2211yescharacteristic, complemented
40C61×Q64C2212yescomplemented
41C61×SD64C2212yescomplemented
42C61×M64C2211yescharacteristic, complemented
43C2×#11758226—41no—
44#41×D61—41no—
45#14519800—21no—
46#14519800—22no—
47#14519800—22no—
48#14519800—41no—
49#14519800—41no—
50#14519799—21no—
51#14519798—41no—
52#14519797—41no—
53#14519796—21no—
54Q16×D61—21no—
55C2×#11758201—41no—
56SD16×D61—41no—
57C2×D488—21no—
58D8×D61—21no—
59C2×C8×D61D411yescharacteristic
60Dic488C2311yescharacteristic
61#14519723—21no—
62#14519722—21no—
63#14519721—21no—
64#14519720—21no—
65#14519720—22no—
66#14519720—22no—
67D976—21no—
68D976C2311yescharacteristic
69D976C2312yes—
70#14519718—21no—
71C2×#11758185D411yescharacteristic
72C16×D61D411yescharacteristic
73C16×D61D411yescharacteristic
74C16×D61C2311yescharacteristic
75C16×D61C2311yescharacteristic
76#14519683C2312yes—
77#135×C61—21no—
78C2×Q16×C61—21no—
79Q32×C61—21no—
80Q32×C61C2312yes—
81Q32×C61C2311yescharacteristic
82SD32×C61—21no—
83D16×C61C2311yescharacteristic
84C2×C16×C61C2311yescharacteristic
85C32×C61C2312yes—
86#41×C61—41no—
87C2×Q8×C61—41no—
88#11758226—41no—
89#11758226—42no—
90#11758226—42no—
91#11758226—81no—
92#11758226—81no—
93Q8×D61—41no—
94#11758224—41no—
95#11758224—81no—
96D4×D61—41no—
97D4×D61—81no—
98#11758222—41no—
99#11758222—81no—
100C2×D244—41no—
101C2×D244—81no—
102C2×C4×D61—81no—
103C2×C4×D61—81no—
104C2×C4×D61D811yescharacteristic
105Q16×C61—21no—
106Q16×C61—22no—
107Q16×C61—41no—
108SD16×C61—41no—
109D8×C61—21no—
110C2×C8×C61C2×D411yescharacteristic
111#11758202—41no—
112#11758201—41no—
113#11758201—42no—
114#11758201—42no—
115#11758200—41no—
116#11758199—41no—
117C2×#92418D811yescharacteristic
118Dic244—21no—
119D488—21no—
120D488—22no—
121D488—41no—
122#11758190—41no—
123C8×D61D811yescharacteristic
124C8×D61D811yescharacteristic
125C8×D61C2×D411yescharacteristic
126C8×D61C2×D411yescharacteristic
127C16×C61C2×D411yescharacteristic
128C16×C61C2411yescharacteristic
129#11758185C2×D411yescharacteristic
130#11758185C2×D411yescharacteristic
131C22×D61—81no—
132C22×D61—81no—
133C22×D61D1611yescharacteristic
134Q8×C61—42no—
135Q8×C61—41no—
136Q8×C61—81no—
137D4×C61—41no—
138D4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61—81no—
141C2×C4×C61C2×D811yescharacteristic
142C22⋊D61—81no—
143C22⋊D61—81no—
144C22⋊D61—81no—
145C2×Dic61—81no—
146C2×Dic61D1611yescharacteristic
147D244—41no—
148D244—42no—
149D244—82no—
150D244—82no—
151D244—81no—
152D244—81no—
153C4×D61—81no—
154C4×D61—81no—
155C4×D61—81no—
156C4×D61—82no—
157C4×D61—82no—
158C4×D61D1611yescharacteristic
159C4×D61D1611yescharacteristic
160C4×D61C2×D811yescharacteristic
161C4×D61C2×D811yescharacteristic
162Dic122—41no—
163Dic122—81no—
164C8×C61C2×D811yescharacteristic
165C8×C61C22×D411yescharacteristic
166#92418C2×D811yescharacteristic
167#92418C2×D811yescharacteristic
168#33981—611nomaximal, Sylow
169C22×C61—81no—
170C22×C61C2×D1611yescharacteristic
171C2×D61—41no—
172C2×D61—82no—
173C2×D61—81no—
174C2×D61—162no—
175C2×D61—162no—
176C2×D61C2×D1611yescharacteristic
177C2×D61C2×D1611yescharacteristic
178C4×C61—81no—
179C4×C61—82no—
180C4×C61C2×D1611yescharacteristic
181C4×C61C22×D811yescharacteristic
182Dic61—81no—
183Dic61C2×D1611yescharacteristic
184Dic61C2×D1611yescharacteristic
185C2×#508—611no—
186C2×#508—611no—
187#2264—611no—
188#2264—612no—
189#2264D6111yescharacteristic, complemented
190#2263—611no—
191#2263—612no—
192#2263—611no—
193#2262—612no—
194#2262—612no—
195C2×M64—611no—
196C2×C61—21no—
197C2×C61—161no—
198C2×C61C22×D1611yescharacteristic
199D61—21no—
200D61—21no—
201D61—162no—
202D61—161no—
203C2×#135—1221no—
204C2×#135—1221no—
205#508—612no—
206#508—611no—
207#508—612no—
208#508—611no—
209#508—611no—
210#508—1221no—
211#508—1221no—
212#508—1221no—
213#508—1221no—
214#508C2×D6111yescharacteristic
215C2×Q32—611no—
216C2×Q32C2×D6111yescharacteristic, complemented
217C2×SD32—1221no—
218C2×SD32—1221no—
219C2×D16—611no—
220C2×D16—611no—
221C22×C16—611no—
222Q64—612no—
223Q64C2×D6112yescomplemented
224SD64—612no—
225SD64—612no—
226SD64—612no—
227SD64C2×D6112yescomplemented
228D32—612no—
229D32—612no—
230M64—611no—
231M64—612no—
232M64C2×D6111yescharacteristic, complemented
233C2×C32—612no—
234C61#3398111yescharacteristic, complemented, Sylow
235C2×#41—2441no—
236C2×#41—2441no—
237#135—21no—
238#135—1221no—
239#135—1222no—
240#135—1221no—
241#135—1222no—
242#135—1221no—
243#135—2441no—
244#135—2441no—
245#135—2441no—
246#135—2441no—
247C2×Q16—21no—
248C2×Q16—1221no—
249C2×SD16—2441no—
250C2×SD16—2441no—
251C2×D8—1221no—
252C2×D8—1221no—
253C22×C8—611no—
254Q32—21no—
255Q32—611no—
256Q32—1221no—
257Q32C22×D6111yescharacteristic
258Q32C22×D6112yes—
259SD32—21no—
260SD32—1221no—
261SD32—1222no—
262SD32—1221no—
263SD32—1222no—
264SD32—1221no—
265D16—612no—
266D16—611no—
267D16—1221no—
268D16—1221no—
269D16C22×D6111yescharacteristic
270C2×C16—611no—
271C2×C16—611no—
272C2×C16—611no—
273C2×C16—611no—
274C2×C16—611no—
275C2×C16C22×D6111yescharacteristic
276C32—612no—
277C32C22×D6112yes—
278#41—41no—
279#41—4881no—
280#41—4881no—
281#41—4881no—
282#41—4881no—
283#41—2441no—
284#41—2442no—
285#41—2441no—
286#41—2442no—
287#41—2441no—
288C2×Q8—41no—
289C2×Q8—2441no—
290C2×D4—4881no—
291C2×D4—4881no—
292C2×D4—2441no—
293C2×D4—2441no—
294C22×C4—611no—
295C22×C4—4881no—
296C22×C4—4881no—
297Q16—21no—
298Q16—22no—
299Q16—41no—
300Q16—1221no—
301Q16—2441no—
302SD16—41no—
303SD16—2441no—
304SD16—2442no—
305SD16—2441no—
306SD16—2442no—
307SD16—2441no—
308D8—21no—
309D8—1221no—
310D8—1222no—
311D8—2441no—
312D8—2441no—
313C2×C8—611no—
314C2×C8—611no—
315C2×C8—611no—
316C2×C8—611no—
317C2×C8—611no—
318C2×C8D4×D6111yescharacteristic
319C16—611no—
320C16—611no—
321C16D4×D6111yescharacteristic
322C16C23×D6111yescharacteristic
323C23—611no—
324C23—4881no—
325C23—4881no—
326Q8—41no—
327Q8—42no—
328Q8—81no—
329Q8—4881no—
330Q8—2441no—
331D4—41no—
332D4—81no—
333D4—4881no—
334D4—4882no—
335D4—4882no—
336D4—4881no—
337D4—4881no—
338D4—4881no—
339D4—4881no—
340D4—2441no—
341D4—2442no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—4881no—
350C2×C4—4882no—
351C2×C4—4882no—
352C2×C4—4881no—
353C2×C4—4881no—
354C2×C4—4881no—
355C2×C4D8×D6111yescharacteristic
356C8—611no—
357C8—611no—
358C8D8×D6111yescharacteristic
359C8C2×D4×D6111yescharacteristic
360C22—81no—
361C22—611no—
362C22—611no—
363C22—9762no—
364C22—9762no—
365C22—4882no—
366C22—4881no—
367C22—2441no—
368C22D16×D6111yescharacteristic
369C4—81no—
370C4—82no—
371C4—611no—
372C4—611no—
373C4—4881no—
374C4D16×D6111yescharacteristic
375C4C2×D8×D6111yescharacteristic
376C2—21no—
377C2—161no—
378C2—1221no—
379C2—1221no—
380C2—9762no—
381C2—9761no—
382C2C2×D16×D6111yescharacteristic
subgroupG/H
centerC2C2×D16×D61
commutator, cosocleC16×C61C24
FrattiniC16C23×D61
FittingC61×#2264C2
socleC2×C61C22×D16
hypercenter#2264D61
hypocenterC61#33981
LCSG ▷ C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2264

Complements

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

NH ≅ G/Ntype
1. C2×#16840195C2semidirect
2. #508×D61C2semidirect
3. #21448138C2semidirect
4. #21448137C2semidirect
5. #21448134C2semidirect
6. #21448133C2semidirect
7. #21448131C2semidirect
8. #21448129C2semidirect
9. #21448127C2semidirect
10. M64×D61C2semidirect
11. C61×#2264C2semidirect
17. #16840195C22semidirect
18. #16840195C22semidirect
22. #16840191C22semidirect
23. Q32×D61C22semidirect
26. C2×D976C22semidirect
27. D16×D61C22semidirect
29. #16839602C22semidirect
30. #16839601C22semidirect
31. #16839599C22semidirect
32. #16839599C22semidirect
33. D1952C22semidirect
34. #16839597C22semidirect
35. #16839596C22semidirect
36. #16839595C22semidirect
37. C32×D61C22semidirect
39. C2×Q32×C61C22semidirect
40. C61×Q64C22semidirect
41. C61×SD64C22semidirect
42. C61×M64C22semidirect
189. #2264D61semidirect
216. C2×Q32C2×D61semidirect
223. Q64C2×D61semidirect
227. SD64C2×D61semidirect
232. M64C2×D61semidirect
234. C61#33981semidirect

Maximal subgroups

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

subgroupindex
C2×#168401952
#508×D612
#214481382
#214481372
#214481342
#214481332
#214481312
#214481292
#214481272
M64×D612
C61×#22642
#3398161