Finite Group Databasebeta

← #11899699

Subgroups — #11899699

Order 1152.

1080 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596237C211yesmaximal, characteristic, complemented
2#10596228C211yesmaximal, characteristic, complemented
3C2×C32×SD32C211yesmaximal, characteristic, complemented
4#10592878C211yesmaximal, characteristic, complemented
5#10592846C211yesmaximal, characteristic, complemented
6#10592615C212yesmaximal, complemented
7#10592614C212yesmaximal, complemented
8#10592613C212yesmaximal, complemented
9C3⋊D3×SD32C212yesmaximal, complemented
10#10592603C211yesmaximal, characteristic, complemented
11#10592600C211yesmaximal, characteristic, complemented
12#82024—34nomaximal
13#64364—21no—
14#64361—21no—
15C2×C32×Q16C2211yescharacteristic, complemented
16C2×C32×D8C2211yescharacteristic
17#64151—21no—
18#64141—21no—
19#64128C2212yescomplemented
20#64127—22no—
21Q16×C3⋊D3C2212yescomplemented
22#64121C2212yes—
23#64120—22no—
24D8×C3⋊D3C2212yes—
25#64113C2211yescharacteristic
26#64113C2211yescharacteristic, complemented
27#64110C2211yescharacteristic
28C32×SD32C2212yescomplemented
29C32×SD32C2212yescomplemented
30C2×C32×C16C2211yescharacteristic, complemented
31#63656C2212yescomplemented
32#63655C2212yescomplemented
33#63654C2212yescomplemented
34#63653C2212yescomplemented
35#63639C2211yescharacteristic, complemented
36#63628C2211yescharacteristic, complemented
37#63627C2211yescharacteristic, complemented
38#63627C2211yescharacteristic, complemented
39#63626C2211yescharacteristic, complemented
40#63625C2212yescomplemented
41C16×C3⋊D3C2212yescomplemented
42#5766—34no—
43#5757—34no—
44C2×C3×SD32D314yescomplemented
45#5179—34no—
46#5147—34no—
47#4916—38no—
48#4915—38no—
49#4914—38no—
50D3×SD32—38no—
51#4904—34no—
52#4901—34no—
53C2×C32×Q8—21no—
54C2×C32×D4—21no—
55C2×#638—42no—
56#3832—22no—
57#3832—41no—
58Q8×C3⋊D3—22no—
59Q8×C3⋊D3—41no—
60#3830—22no—
61#3830—41no—
62D4×C3⋊D3—22no—
63D4×C3⋊D3—41no—
64#3828—21no—
65#3828—21no—
66#3828—42no—
67#3828D411yescharacteristic
68C32×Q16—21no—
69C32×Q16C2312yes—
70C32×D8—21no—
71C32×D8C2312yes—
72C2×C32×C8C2311yescharacteristic
73#3756—22no—
74#3755—22no—
75#3754—22no—
76#3753—22no—
77#3748D411yescharacteristic
78#3746C2311yescharacteristic
79#3746C2311yescharacteristic
80#3745C2311yescharacteristic
81#3745C2311yescharacteristic
82#3744—21no—
83#3744—21no—
84#3743D412yes—
85C8×C3⋊D3C2312yes—
86C32×C16C2311yescharacteristic
87C32×C16C2311yescharacteristic
88C3⋊(C3⋊C16)C2312yes—
89#3416—91noSylow
90#1007—64no—
91#1004—64no—
92C2×C3×Q16C2×D314yescomplemented
93C2×C3×D8C2×D314yes—
94#942—64no—
95#932—64no—
96#919—38no—
97#918—68no—
98D3×Q16—38no—
99#912—38no—
100#911—68no—
101D3×D8—38no—
102#904—34no—
103#904—34no—
104#901—34no—
105C3×SD32C2×D318yescomplemented
106C3×SD32C2×D318yescomplemented
107C2×C3×C16C2×D314yescomplemented
108#829—38no—
109#828—38no—
110#827—38no—
111#826—38no—
112#812—34no—
113Dic24—34no—
114#800—34no—
115#800—34no—
116D48—34no—
117#798—38no—
118D3×C16—38no—
119C23×C32—41no—
120C22×C3⋊D3—42no—
121C32×Q8—22no—
122C32×Q8—41no—
123C32×D4—22no—
124C32×D4—41no—
125C2×C32×C4—41no—
126C2×C32×C4C2×D411yescharacteristic
127#638—41no—
128#638—41no—
129#638—42no—
130#638—42no—
131#638D812yes—
132C2×C3⋊Dic3—42no—
133C4⋊(C3⋊D3)—21no—
134C4⋊(C3⋊D3)—21no—
135C4⋊(C3⋊D3)—42no—
136C4⋊(C3⋊D3)D811yescharacteristic
137C4×C3⋊D3—42no—
138C4×C3⋊D3—41no—
139C4×C3⋊D3—41no—
140C4×C3⋊D3—42no—
141C4×C3⋊D3C2×D412yes—
142#634—21no—
143#634—21no—
144#634—42no—
145#634D811yescharacteristic
146C32×C8C2×D411yescharacteristic
147C32×C8C2411yescharacteristic
148C3⋊(C3⋊C8)C2×D412yes—
149#578—91no—
150#576—91no—
151#510—91no—
152#510—92no—
153#509—91no—
154#509—92no—
155#508—92no—
156#508—91no—
157C2×SD32—92no—
158C2×SD32C3⋊D311yescharacteristic, complemented
159#504—91no—
160C2×C3×Q8—24no—
161C2×C3×D4—24no—
162C2×#67—128no—
163#239—68no—
164#239—124no—
165D3×Q8—68no—
166D3×Q8—124no—
167#237—68no—
168#237—124no—
169D3×D4—68no—
170D3×D4—124no—
171#235—34no—
172#235—64no—
173#235—64no—
174#235—128no—
175C3×Q16—24no—
176C3×Q16C22×D318yes—
177C3×D8—24no—
178C3×D8C22×D318yes—
179C2×C3×C8C22×D314yes—
180#216—68no—
181#215—68no—
182#214—68no—
183#213—68no—
184#208—34no—
185Dic12—34no—
186Dic12—34no—
187D24—34no—
188D24—34no—
189#204—64no—
190#204—64no—
191ΓL(1,𝔽25)—38no—
192D3×C8—38no—
193C3×C16C22×D314yes—
194C3×C16C22×D314yes—
195C3⋊C16—38no—
196C22×C32—42no—
197C22×C32—161no—
198C22×C32C2×D811yescharacteristic
199C2×C3⋊D3—41no—
200C2×C3⋊D3—41no—
201C2×C3⋊D3—162no—
202C2×C3⋊D3C2×D812yes—
203C32×C4—42no—
204C32×C4C2×D811yescharacteristic
205C32×C4C22×D411yescharacteristic
206C3⋊Dic3—41no—
207C3⋊Dic3—41no—
208C3⋊Dic3C2×D812yes—
2092−1+4—181no—
210H(5,𝔽2)—181no—
211#137—182no—
212#137—181no—
213AGL(1,ℤ/8)—182no—
214AGL(1,ℤ/8)—181no—
215#135—92no—
216#135—92no—
217#135—91no—
218#135—91no—
219C2×Q16—92no—
220C2×Q16C2×C3⋊D311yescharacteristic, complemented
221C2×D8—92no—
222C2×D8C2×C3⋊D311yescharacteristic
223#131—91no—
224Q32—92no—
225Q32—91no—
226SD32—92no—
227SD32—92no—
228SD32—91no—
229SD32—91no—
230SD32C2×C3⋊D312yescomplemented
231SD32C2×C3⋊D312yescomplemented
232D16—92no—
233D16—91no—
234M32—91no—
235M32—92no—
236C2×C16—92no—
237C2×C16C2×C3⋊D311yescharacteristic, complemented
238C23×C3—44no—
239C22×D3—128no—
240C3×Q8—28no—
241C3×Q8—44no—
242C3×D4—28no—
243C3×D4—44no—
244C2×C3×C4—44no—
245C2×C3×C4D3×D414yes—
246#67—38no—
247#67—128no—
248#67—128no—
249#67—124no—
250#67—124no—
251C2×Dic3—128no—
252D12—34no—
253D12—64no—
254D12—64no—
255D12—128no—
256C4×D3—38no—
257C4×D3—128no—
258C4×D3—128no—
259C4×D3—124no—
260C4×D3—124no—
261Dic6—34no—
262Dic6—64no—
263Dic6—64no—
264Dic6—128no—
265C3×C8D3×D414yes—
266C3×C8C23×D314yes—
267C3⋊C8—38no—
268C2×C32—21no—
269C2×C32—82no—
270C2×C32C22×D811yescharacteristic
271C3⋊D3—22no—
272C3⋊D3—81no—
273C3⋊D3—81no—
274#41—91no—
275#41—182no—
276#41—182no—
277#41—181no—
278#41—181no—
279#41—362no—
280#41—361no—
281#41—361no—
282C2×Q8—21no—
283C2×Q8—182no—
284C2×Q8—361no—
285C2×D4—21no—
286C2×D4—182no—
287C2×D4—361no—
288C2×D4—362no—
289Q16—21no—
290Q16—91no—
291Q16—91no—
292Q16—182no—
293Q16C22×C3⋊D312yes—
294SD16—182no—
295SD16—182no—
296SD16—181no—
297SD16—181no—
298D8—21no—
299D8—91no—
300D8—91no—
301D8—182no—
302D8C22×C3⋊D312yes—
303M16—91no—
304M16—92no—
305C2×C8—92no—
306C2×C8C22×C3⋊D311yescharacteristic
307C16—92no—
308C16C22×C3⋊D311yescharacteristic
309C16C22×C3⋊D311yescharacteristic
310C22×C3—48no—
311C22×C3—164no—
312C22×C3D3×D814yes—
313C2×D3—38no—
314C2×D3—124no—
315C2×D3—124no—
316C2×D3—488no—
317C3×C4—48no—
318C3×C4D3×D814yes—
319C3×C4C2×D3×D414yes—
320Dic3—38no—
321Dic3—124no—
322Dic3—124no—
323C32#341611yescharacteristic, complemented, Sylow
324C23—41no—
325C23—362no—
326Q8—22no—
327Q8—41no—
328Q8—91no—
329Q8—181no—
330Q8—181no—
331Q8—362no—
332D4—22no—
333D4—41no—
334D4—92no—
335D4—91no—
336D4—181no—
337D4—181no—
338D4—362no—
339D4—362no—
340D4—362no—
341D4—361no—
342D4—361no—
343C2×C4—41no—
344C2×C4—92no—
345C2×C4—362no—
346C2×C4—362no—
347C2×C4—362no—
348C2×C4—361no—
349C2×C4—361no—
350C2×C4D4×C3⋊D311yescharacteristic
351C8—92no—
352C8D4×C3⋊D311yescharacteristic
353C8C23×C3⋊D311yescharacteristic
354C2×C3—24no—
355C2×C3—88no—
356C2×C3C2×D3×D814yes—
357D3—68no—
358D3—244no—
359D3—244no—
360C22—42no—
361C22—92no—
362C22—161no—
363C22—361no—
364C22—361no—
365C22—1442no—
366C22D8×C3⋊D311yescharacteristic
367C4—42no—
368C4—92no—
369C4—361no—
370C4—361no—
371C4D8×C3⋊D311yescharacteristic
372C4C2×D4×C3⋊D311yescharacteristic
373C3#8202414yescomplemented
374C2—21no—
375C2—82no—
376C2—182no—
377C2—721no—
378C2—721no—
379C2C2×D8×C3⋊D311yescharacteristic
subgroupG/H
centerC2C2×D8×C3⋊D3
commutator, cosocleC32×C8C24
FrattiniC8C23×C3⋊D3
FittingC2×C32×SD32C2
socleC2×C32C22×D8
hypercenterC2×SD32C3⋊D3
hypocenterC32#3416
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #10596237C2semidirect
2. #10596228C2semidirect
3. C2×C32×SD32C2semidirect
4. #10592878C2semidirect
5. #10592846C2semidirect
6. #10592615C2semidirect
7. #10592614C2semidirect
8. #10592613C2semidirect
9. C3⋊D3×SD32C2semidirect
10. #10592603C2semidirect
11. #10592600C2semidirect
15. C2×C32×Q16C22semidirect
19. #64128C22semidirect
21. Q16×C3⋊D3C22semidirect
26. #64113C22semidirect
28. C32×SD32C22semidirect
29. C32×SD32C22semidirect
30. C2×C32×C16C22semidirect
31. #63656C22semidirect
32. #63655C22semidirect
33. #63654C22semidirect
34. #63653C22semidirect
35. #63639C22semidirect
36. #63628C22semidirect
37. #63627C22semidirect
38. #63627C22semidirect
39. #63626C22semidirect
40. #63625C22semidirect
41. C16×C3⋊D3C22semidirect
44. C2×C3×SD32D3semidirect
92. C2×C3×Q16C2×D3semidirect
105. C3×SD32C2×D3semidirect
106. C3×SD32C2×D3semidirect
107. C2×C3×C16C2×D3semidirect
158. C2×SD32C3⋊D3semidirect
220. C2×Q16C2×C3⋊D3semidirect
230. SD32C2×C3⋊D3semidirect
231. SD32C2×C3⋊D3semidirect
237. C2×C16C2×C3⋊D3semidirect
323. C32#3416semidirect
373. C3#82024semidirect

Maximal subgroups

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

subgroupindex
#105962372
#105962282
C2×C32×SD322
#105928782
#105928462
#105926152
#105926142
#105926132
C3⋊D3×SD322
#105926032
#105926002
#820243