Finite Group Databasebeta

← #29838155

Subgroups — #29838155

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×#16840191C211yesmaximal, characteristic, complemented
2#508×D61C211yesmaximal, characteristic, complemented
3#21448139C211yesmaximal, characteristic, complemented
4#21448136C211yesmaximal, characteristic, complemented
5#21448135C212yesmaximal, complemented
6#21448132C211yesmaximal, characteristic, complemented
7#21448130C212yesmaximal, complemented
8#21448127C212yesmaximal, complemented
9#21448125C212yesmaximal, complemented
10M64×D61C211yesmaximal, characteristic, complemented
11C61×#2263C211yesmaximal, characteristic, complemented
12C2×#14519796—21no—
13#135×D61—21no—
14#16840195C2211yescharacteristic, complemented
15#16840194C2211yescharacteristic
16#16840193—21no—
17#16840192—21no—
18#16840191—21no—
19#16840191—21no—
20#16840191C2212yes—
21#16840191C2211yescharacteristic, complemented
22#16840191C2212yescomplemented
23C2×Dic488C2211yescharacteristic, complemented
24Q32×D61C2211yescharacteristic, complemented
25C2×#14519721—21no—
26SD32×D61—21no—
27D16×D61C2211yescharacteristic, complemented
28C2×C16×D61C2211yescharacteristic
29Dic976C2212yescomplemented
30#16839602C2212yescomplemented
31#16839601C2212yescomplemented
32#16839600C2212yescomplemented
33#16839600C2212yescomplemented
34#16839597C2212yescomplemented
35#16839596C2211yescharacteristic, complemented
36#16839595C2212yescomplemented
37C32×D61C2212yescomplemented
38C61×#508C2211yescharacteristic
39C2×D16×C61C2211yescharacteristic, complemented
40C61×SD64C2212yescomplemented
41C61×D32C2212yescomplemented
42C61×M64C2211yescharacteristic, complemented
43C2×#11758224—41no—
44#41×D61—41no—
45#14519800—21no—
46#14519799—21no—
47#14519798—41no—
48#14519797—41no—
49#14519796—21no—
50#14519796—22no—
51#14519796—22no—
52#14519796—41no—
53#14519796—41no—
54C2×Dic244—21no—
55Q16×D61—21no—
56C2×#11758200—41no—
57SD16×D61—41no—
58D8×D61—21no—
59C2×C8×D61D411yescharacteristic
60Dic488—21no—
61Dic488C2311yescharacteristic
62Dic488C2312yes—
63#14519723—21no—
64#14519722—21no—
65#14519721—21no—
66#14519721—22no—
67#14519721—22no—
68#14519720—21no—
69D976C2311yescharacteristic
70#14519718—21no—
71C2×#11758185D411yescharacteristic
72C16×D61D411yescharacteristic
73C16×D61D411yescharacteristic
74C16×D61C2311yescharacteristic
75C16×D61C2311yescharacteristic
76#14519683C2312yes—
77#135×C61—21no—
78C2×D8×C61—21no—
79Q32×C61C2311yescharacteristic
80SD32×C61—21no—
81D16×C61—21no—
82D16×C61C2311yescharacteristic
83D16×C61C2312yes—
84C2×C16×C61C2311yescharacteristic
85C32×C61C2312yes—
86#41×C61—41no—
87C2×D4×C61—41no—
88C2×C22⋊D61—81no—
89C22×Dic61—81no—
90#11758226—41no—
91Q8×D61—41no—
92#11758224—41no—
93#11758224—42no—
94#11758224—42no—
95#11758224—81no—
96#11758224—81no—
97#11758224—81no—
98D4×D61—41no—
99D4×D61—81no—
100#11758222—41no—
101#11758222—81no—
102C2×C4×D61—81no—
103C2×C4×D61D811yescharacteristic
104C2×Dic122—41no—
105Q16×C61—21no—
106SD16×C61—41no—
107D8×C61—22no—
108D8×C61—21no—
109D8×C61—41no—
110C2×C8×C61C2×D411yescharacteristic
111#11758202—41no—
112#11758201—41no—
113#11758200—41no—
114#11758200—42no—
115#11758200—42no—
116#11758199—41no—
117C2×#92418D811yescharacteristic
118Dic244—22no—
119Dic244—21no—
120Dic244—41no—
121D488—21no—
122#11758190—41no—
123C8×D61D811yescharacteristic
124C8×D61D811yescharacteristic
125C8×D61C2×D411yescharacteristic
126C8×D61C2×D411yescharacteristic
127C16×C61C2×D411yescharacteristic
128C16×C61C2411yescharacteristic
129#11758185C2×D411yescharacteristic
130#11758185C2×D411yescharacteristic
131C23×C61—81no—
132C22×D61—81no—
133C22×D61D1611yescharacteristic
134Q8×C61—41no—
135D4×C61—41no—
136D4×C61—42no—
137D4×C61—81no—
138D4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61C2×D811yescharacteristic
141C22⋊D61—81no—
142C22⋊D61—81no—
143C22⋊D61—82no—
144C22⋊D61—82no—
145C22⋊D61—81no—
146C2×Dic61—81no—
147C2×Dic61—81no—
148C2×Dic61—82no—
149C2×Dic61—82no—
150C2×Dic61D1611yescharacteristic
151D244—41no—
152D244—81no—
153C4×D61—81no—
154C4×D61—81no—
155C4×D61—81no—
156C4×D61D1611yescharacteristic
157C4×D61D1611yescharacteristic
158C4×D61C2×D811yescharacteristic
159C4×D61C2×D811yescharacteristic
160Dic122—41no—
161Dic122—42no—
162Dic122—81no—
163Dic122—81no—
164C8×C61C2×D811yescharacteristic
165C8×C61C22×D411yescharacteristic
166#92418C2×D811yescharacteristic
167#92418C2×D811yescharacteristic
168#33981—611nomaximal, Sylow
169C22×C61—82no—
170C22×C61—81no—
171C22×C61—162no—
172C22×C61C2×D1611yescharacteristic
173C2×D61—41no—
174C2×D61—81no—
175C2×D61—162no—
176C2×D61C2×D1611yescharacteristic
177C2×D61C2×D1611yescharacteristic
178C4×C61—81no—
179C4×C61C2×D1611yescharacteristic
180C4×C61C22×D811yescharacteristic
181Dic61—81no—
182Dic61—82no—
183Dic61C2×D1611yescharacteristic
184Dic61C2×D1611yescharacteristic
185C2×#508—611no—
186C2×#508—611no—
187#2264—611no—
188#2264—612no—
189#2264—611no—
190#2263—611no—
191#2263—612no—
192#2263D6111yescharacteristic, complemented
193#2262—612no—
194#2262—612no—
195C2×M64—611no—
196C2×C61—21no—
197C2×C61—161no—
198C2×C61—162no—
199C2×C61C22×D1611yescharacteristic
200D61—21no—
201D61—21no—
202D61—161no—
203C2×#135—1221no—
204C2×#135—1221no—
205#508—611no—
206#508—612no—
207#508—611no—
208#508—612no—
209#508—611no—
210#508—1221no—
211#508—1221no—
212#508—1221no—
213#508—1221no—
214#508C2×D6111yescharacteristic
215C2×Q32—611no—
216C2×Q32—611no—
217C2×SD32—1221no—
218C2×SD32—1221no—
219C2×D16—611no—
220C2×D16C2×D6111yescharacteristic, complemented
221C22×C16—611no—
222Q64—612no—
223Q64—612no—
224SD64—612no—
225SD64—612no—
226SD64—612no—
227SD64C2×D6112yescomplemented
228D32—612no—
229D32C2×D6112yescomplemented
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—1222no—
239#135—1222no—
240#135—1221no—
241#135—1221no—
242#135—1221no—
243#135—2441no—
244#135—2441no—
245#135—2441no—
246#135—2441no—
247C2×Q16—1221no—
248C2×Q16—1221no—
249C2×SD16—2441no—
250C2×SD16—2441no—
251C2×D8—21no—
252C2×D8—1221no—
253C22×C8—611no—
254Q32—611no—
255Q32—612no—
256Q32—1221no—
257Q32—1221no—
258Q32C22×D6111yescharacteristic
259SD32—21no—
260SD32—1222no—
261SD32—1222no—
262SD32—1221no—
263SD32—1221no—
264SD32—1221no—
265D16—21no—
266D16—611no—
267D16—1221no—
268D16C22×D6112yes—
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—2442no—
284#41—2442no—
285#41—2441no—
286#41—2441no—
287#41—2441no—
288C2×Q8—2441no—
289C2×Q8—2441no—
290C2×D4—41no—
291C2×D4—4881no—
292C2×D4—4881no—
293C2×D4—2441no—
294C22×C4—611no—
295C22×C4—4881no—
296C22×C4—4881no—
297Q16—21no—
298Q16—1222no—
299Q16—1221no—
300Q16—2441no—
301Q16—2441no—
302SD16—41no—
303SD16—2442no—
304SD16—2442no—
305SD16—2441no—
306SD16—2441no—
307SD16—2441no—
308D8—22no—
309D8—21no—
310D8—41no—
311D8—1221no—
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—81no—
324C23—611no—
325C23—4881no—
326Q8—41no—
327Q8—4881no—
328Q8—4881no—
329Q8—2441no—
330Q8—2442no—
331D4—42no—
332D4—41no—
333D4—81no—
334D4—81no—
335D4—4881no—
336D4—4881no—
337D4—4881no—
338D4—4882no—
339D4—4882no—
340D4—4881no—
341D4—2441no—
342C2×C4—81no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—4881no—
349C2×C4—4881no—
350C2×C4—4881no—
351C2×C4—4882no—
352C2×C4—4882no—
353C2×C4—4881no—
354C2×C4—4881no—
355C2×C4D8×D6111yescharacteristic
356C8—611no—
357C8—611no—
358C8D8×D6111yescharacteristic
359C8C2×D4×D6111yescharacteristic
360C22—81no—
361C22—82no—
362C22—162no—
363C22—611no—
364C22—611no—
365C22—9762no—
366C22—4881no—
367C22—2441no—
368C22D16×D6111yescharacteristic
369C4—81no—
370C4—611no—
371C4—611no—
372C4—4881no—
373C4—4882no—
374C4D16×D6111yescharacteristic
375C4C2×D8×D6111yescharacteristic
376C2—21no—
377C2—162no—
378C2—161no—
379C2—1221no—
380C2—1221no—
381C2—9761no—
382C2C2×D16×D6111yescharacteristic
subgroupG/H
centerC2C2×D16×D61
commutator, cosocleC16×C61C24
FrattiniC16C23×D61
FittingC61×#2263C2
socleC2×C61C22×D16
hypercenter#2263D61
hypocenterC61#33981
LCSG ▷ C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2263

Complements

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

NH ≅ G/Ntype
1. C2×#16840191C2semidirect
2. #508×D61C2semidirect
3. #21448139C2semidirect
4. #21448136C2semidirect
5. #21448135C2semidirect
6. #21448132C2semidirect
7. #21448130C2semidirect
8. #21448127C2semidirect
9. #21448125C2semidirect
10. M64×D61C2semidirect
11. C61×#2263C2semidirect
14. #16840195C22semidirect
21. #16840191C22semidirect
22. #16840191C22semidirect
23. C2×Dic488C22semidirect
24. Q32×D61C22semidirect
27. D16×D61C22semidirect
29. Dic976C22semidirect
30. #16839602C22semidirect
31. #16839601C22semidirect
32. #16839600C22semidirect
33. #16839600C22semidirect
34. #16839597C22semidirect
35. #16839596C22semidirect
36. #16839595C22semidirect
37. C32×D61C22semidirect
39. C2×D16×C61C22semidirect
40. C61×SD64C22semidirect
41. C61×D32C22semidirect
42. C61×M64C22semidirect
192. #2263D61semidirect
220. C2×D16C2×D61semidirect
227. SD64C2×D61semidirect
229. D32C2×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×#168401912
#508×D612
#214481392
#214481362
#214481352
#214481322
#214481302
#214481272
#214481252
M64×D612
C61×#22632
#3398161