Finite Group Databasebeta

← #10595464

Subgroups — #10595464

Order 576.

547 conjugacy classes of subgroups.

The subgroup lattice has 395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#1009C211yesmaximal, characteristic, complemented
2#64297C211yesmaximal, characteristic, complemented
3#64159C211yesmaximal, characteristic, complemented
4C3×#951C211yesmaximal, characteristic, complemented
5#63949C212yesmaximal, complemented
6#63943C212yesmaximal, complemented
7#63934C212yesmaximal, complemented
8D3×#214C212yesmaximal, complemented
9#63830C211yesmaximal, characteristic, complemented
10C2×#3715C211yesmaximal, characteristic, complemented
11#63815C211yesmaximal, characteristic, complemented
12#5836—31nomaximal
13#5778—31nomaximal
14C32×#41C2211yescharacteristic
15#3828C2211yescharacteristic, complemented
16C3×#239C2212yes—
17C3×D3×D4—22no—
18C3×D3×D4C2212yes—
19C3×#235—21no—
20C3×#235C2211yescharacteristic
21C2×C3×D12—21no—
22C2×C3×D12C2211yescharacteristic
23C2×C3×Dic6C2211yescharacteristic, complemented
24#3804—22no—
25#3799C2212yescomplemented
26#3797—21no—
27#3796—21no—
28D3×Dic6C2212yescomplemented
29#3756C2211yescharacteristic, complemented
30#3755C2211yescharacteristic, complemented
31#3754C2211yescharacteristic, complemented
32#3753C2211yescharacteristic, complemented
33C2×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
34C3×#216C2212yescomplemented
35C3×#214C2212yescomplemented
36C3×#208C2211yescharacteristic, complemented
37#3716C2212yescomplemented
38#3715C2212yescomplemented
39#3715C2212yescomplemented
40#3714C2212yescomplemented
41#3711C2212yescomplemented
42D3×C3⋊C8C2212yescomplemented
43C3×H(5,𝔽2)—31no—
44#1010—31no—
45#1009D311yescharacteristic, complemented
46#1007—31no—
47C3×#137—31no—
48#951—32no—
49#951D311yescharacteristic, complemented
50#950—31no—
51#950—31no—
52#950—32no—
53#950—61no—
54#948—31no—
55C2×#215—31no—
56C2×#214—31no—
57C2×#214—32no—
58#932—32no—
59#932—31no—
60#919—32no—
61#918—32no—
62#914—32no—
63D3×SD16—32no—
64#908—31no—
65#907—31no—
66C22×C3×D3—21no—
67C22×C3×D3—22no—
68C32×Q8C2311yescharacteristic
69C32×D4—21no—
70C32×D4C2311yescharacteristic
71C2×C32×C4—21no—
72C2×C32×C4C2311yescharacteristic
73#638—21no—
74C4⋊(C3⋊D3)C2311yescharacteristic
75C4×C3⋊D3—21no—
76#634C2311yescharacteristic
77C3×#67—22no—
78C3×#67D412yes—
79C2×C3×Dic3—21no—
80C3×D12—22no—
81C3×D12—21no—
82C3×D12D411yescharacteristic
83C3×D12C2312yes—
84C3×C4×D3—22no—
85C3×C4×D3C2312yes—
86C3×Dic6—21no—
87C3×Dic6D411yescharacteristic
88C3×Dic6C2312yes—
89#627—22no—
90#626—22no—
91#624—22no—
92D3×Dic3—22no—
93C3⋊(C3⋊C8)C2311yescharacteristic
94C3⋊(C3⋊C8)C2311yescharacteristic
95C3×C3⋊C8C2312yes—
96#577—91noSylow
97C3×#41—21no—
98C3×#41—31no—
99C3×#41—32no—
100C3×#41—61no—
101C3×#41C2×D311yescharacteristic
102C3×#41C2×D311yescharacteristic
103C2×C3×Q8—31no—
104C2×C3×D4—32no—
105C2×C3×D4—31no—
106C2×C3×D4—61no—
107C2×C3×D4—62no—
108#239—32no—
109#239—61no—
110#239C2×D312yes—
111D3×Q8—32no—
112D3×Q8—61no—
113D3×Q8—61no—
114#237—61no—
115#237—62no—
116D3×D4—22no—
117D3×D4C2×D312yes—
118#235—21no—
119#235—31no—
120#235—31no—
121#235—32no—
122#235—61no—
123#235—62no—
124#235C2×D311yescharacteristic
125C2×D12—21no—
126C2×D12C2×D311yescharacteristic
127C2×Dic6—32no—
128C2×Dic6C2×D311yescharacteristic, complemented
129C3×Q16—32no—
130C3×SD16—32no—
131C3×M16—31no—
132#216—31no—
133#216—31no—
134#216—61no—
135#216C2×D312yescomplemented
136#215—31no—
137#215—31no—
138#215—32no—
139#215—32no—
140#215—61no—
141#214—31no—
142#214—31no—
143#214—32no—
144#214—32no—
145#214—32no—
146#214—61no—
147#214C2×D312yescomplemented
148#213—31no—
149#213—31no—
150#213—32no—
151#213—61no—
152#208—32no—
153#208C2×D311yescharacteristic, complemented
154C2×C3⋊C8—31no—
155C2×C3⋊C8—31no—
156C2×C3⋊C8—32no—
157C2×C3⋊C8—61no—
158D24—32no—
159#204—32no—
160ΓL(1,𝔽25)—32no—
161D3×C8—32no—
162C22×C32—21no—
163C22×C32C2×D411yescharacteristic
164C2×C3⋊D3—21no—
165C2×C3×D3—22no—
166C2×C3×D3—82no—
167C2×C3×D3—81no—
168C2×C3×D3C2×D412yes—
169C32×C4—21no—
170C32×C4C2×D411yescharacteristic
171C32×C4C2411yescharacteristic
172C3⋊Dic3—21no—
173C3×Dic3—22no—
174C3×Dic3C2×D412yes—
1752−1+4—91no—
176H(5,𝔽2)—31no—
177#137—31no—
178#137—92no—
179AGL(1,ℤ/8)—91no—
180AGL(1,ℤ/8)—92no—
181#135—92no—
182#135—91no—
183C2×SD16—92no—
184C2×SD16—91no—
185#131—91no—
186C23×C3—62no—
187C23×C3—61no—
188C22×D3—21no—
189C22×D3—22no—
190C3×Q8—21no—
191C3×Q8—31no—
192C3×Q8—32no—
193C3×Q8—61no—
194C3×Q8C22×D311yescharacteristic
195C3×Q8C22×D311yescharacteristic
196C3×D4—21no—
197C3×D4—21no—
198C3×D4—21no—
199C3×D4—32no—
200C3×D4—31no—
201C3×D4—32no—
202C3×D4—41no—
203C3×D4—62no—
204C3×D4—62no—
205C3×D4—61no—
206C3×D4C22×D311yescharacteristic
207C3×D4C22×D311yescharacteristic
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—32no—
212C2×C3×C4—41no—
213C2×C3×C4—62no—
214C2×C3×C4—61no—
215C2×C3×C4C22×D311yescharacteristic
216C2×C3×C4C22×D311yescharacteristic
217#67—22no—
218#67—62no—
219#67—61no—
220#67—61no—
221#67—121no—
222#67#6712yes—
223C2×Dic3—21no—
224C2×Dic3—62no—
225D12—22no—
226D12—21no—
227D12—31no—
228D12—31no—
229D12—61no—
230D12—62no—
231D12#6711yescharacteristic
232D12C22×D312yes—
233C4×D3—22no—
234C4×D3—62no—
235C4×D3—62no—
236C4×D3—61no—
237C4×D3—61no—
238C4×D3—62no—
239C4×D3—121no—
240C4×D3C22×D312yes—
241Dic6—21no—
242Dic6—31no—
243Dic6—31no—
244Dic6—61no—
245Dic6—62no—
246Dic6—62no—
247Dic6#6711yescharacteristic
248Dic6C22×D312yes—
249C3×C8—32no—
250C3⋊C8—31no—
251C3⋊C8—31no—
252C3⋊C8—31no—
253C3⋊C8—31no—
254C3⋊C8—61no—
255C3⋊C8—61no—
256C3⋊C8C22×D312yes—
257C2×C32—21no—
258C2×C32—41no—
259C2×C32C22×D411yescharacteristic
260C3⋊D3—41no—
261C3×D3—22no—
262C3×D3—42no—
263#41—31no—
264#41—32no—
265#41—61no—
266#41—92no—
267#41—91no—
268#41—182no—
269#41—181no—
270#41D3211yescharacteristic
271C2×Q8—31no—
272C2×Q8—92no—
273C2×Q8—181no—
274C2×D4—32no—
275C2×D4—31no—
276C2×D4—61no—
277C2×D4—62no—
278Q16—32no—
279Q16—91no—
280SD16—32no—
281SD16—92no—
282SD16—92no—
283SD16—92no—
284SD16—91no—
285SD16—91no—
286D8—92no—
287D8—91no—
288M16—31no—
289M16—92no—
290C2×C8—92no—
291C2×C8—91no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—32no—
296C22×C3—41no—
297C22×C3—62no—
298C22×C3—241no—
299C22×C3—242no—
300C22×C3D3×D411yescharacteristic
301C22×C3C2×#6711yescharacteristic
302C2×D3—22no—
303C2×D3—61no—
304C2×D3—61no—
305C2×D3—82no—
306C2×D3—81no—
307C2×D3—121no—
308C2×D3C2×#6712yes—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—32no—
314C3×C4—41no—
315C3×C4—62no—
316C3×C4D3×D411yescharacteristic
317C3×C4C2×#6711yescharacteristic
318C3×C4C23×D311yescharacteristic
319C3×C4C23×D311yescharacteristic
320Dic3—22no—
321Dic3—61no—
322Dic3—61no—
323Dic3—121no—
324Dic3C2×#6712yes—
325C32#57711yescharacteristic, complemented, Sylow
326C23—62no—
327C23—61no—
328Q8—31no—
329Q8—32no—
330Q8—61no—
331Q8—91no—
332Q8—182no—
333Q8C2×D3211yescharacteristic
334D4—21no—
335D4—32no—
336D4—32no—
337D4—31no—
338D4—62no—
339D4—62no—
340D4—61no—
341D4—91no—
342D4—182no—
343D4—181no—
344D4C2×D3211yescharacteristic
345C2×C4—21no—
346C2×C4—32no—
347C2×C4—62no—
348C2×C4—61no—
349C2×C4—182no—
350C2×C4—182no—
351C2×C4—181no—
352C2×C4C2×D3211yescharacteristic
353C8—32no—
354C8—91no—
355C8—91no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—41no—
360C2×C3—41no—
361C2×C3—41no—
362C2×C3—62no—
363C2×C3—81no—
364C2×C3—122no—
365C2×C3C2×D3×D411yescharacteristic
366C2×C3C22×#6711yescharacteristic
367D3—22no—
368D3—42no—
369D3—121no—
370D3—121no—
371D3—241no—
372C22—21no—
373C22—32no—
374C22—62no—
375C22—181no—
376C22—241no—
377C22—242no—
378C22D3×#6711yescharacteristic
379C4—21no—
380C4—32no—
381C4—62no—
382C4—181no—
383C4D3×#6711yescharacteristic
384C4C22×D3211yescharacteristic
385C3—21no—
386C3#577811yescharacteristic, complemented
387C3#583611yescharacteristic, complemented
388C2—21no—
389C2—41no—
390C2—62no—
391C2—122no—
392C2—361no—
393C2C2×D3×#6711yescharacteristic
subgroupG/H
centerC2C2×D3×#67
commutator, cosocleC32×C4C24
FrattiniC4C22×D32
FittingC32×#41C22
socleC2×C32C22×D4
hypercenter#41D32
hypocenterC32#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C3×#1009C2semidirect
2. #64297C2semidirect
3. #64159C2semidirect
4. C3×#951C2semidirect
5. #63949C2semidirect
6. #63943C2semidirect
7. #63934C2semidirect
8. D3×#214C2semidirect
9. #63830C2semidirect
10. C2×#3715C2semidirect
11. #63815C2semidirect
15. #3828C22semidirect
23. C2×C3×Dic6C22semidirect
25. #3799C22semidirect
28. D3×Dic6C22semidirect
29. #3756C22semidirect
30. #3755C22semidirect
31. #3754C22semidirect
32. #3753C22semidirect
33. C2×C3⋊(C3⋊C8)C22semidirect
34. C3×#216C22semidirect
35. C3×#214C22semidirect
36. C3×#208C22semidirect
37. #3716C22semidirect
38. #3715C22semidirect
39. #3715C22semidirect
40. #3714C22semidirect
41. #3711C22semidirect
42. D3×C3⋊C8C22semidirect
45. #1009D3semidirect
49. #951D3semidirect
128. C2×Dic6C2×D3semidirect
135. #216C2×D3semidirect
147. #214C2×D3semidirect
153. #208C2×D3semidirect
325. C32#577semidirect
386. C3#5778semidirect
387. C3#5836semidirect

Maximal subgroups

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

subgroupindex
C3×#10092
#642972
#641592
C3×#9512
#639492
#639432
#639342
D3×#2142
#638302
C2×#37152
#638152
#58363
#57783