Finite Group Databasebeta

← #11866176

Subgroups — #11866176

Order 1152.

1578 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2#10596301C211yesmaximal, characteristic, complemented
3#10596269C211yesmaximal, characteristic, complemented
4C22×#3753C211yesmaximal, characteristic, complemented
5#10592932C211yesmaximal, characteristic, complemented
6#10592864C214yesmaximal, complemented
7#10592849C214yesmaximal, complemented
8#10592830C211yesmaximal, characteristic, complemented
9#10592818C211yesmaximal, characteristic, complemented
10#83934—34nomaximal
11C2×C32×#41C2211yescharacteristic
12C22×C32×D4C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C32×AGL(1,ℤ/8)—24no—
15C2×C32×SD16C2212yescomplemented
16C2×C32×D8C2212yescomplemented
17C2×C32×M16C2211yescharacteristic
18C2×#3757—22no—
19#64156C2212yescomplemented
20#64149C2212yescomplemented
21#64146—22no—
22D4×C3⋊Dic3—22no—
23D4×C3⋊Dic3C2214yescomplemented
24C2×#3753—24no—
25C2×#3753C2214yes—
26#64139—22no—
27#64135C2211yescharacteristic
28#64135C2211yescharacteristic
29C22×C3⋊(C3⋊C8)C2211yescharacteristic
30#63662C2212yescomplemented
31#63659C2212yescomplemented
32#63648C2214yescomplemented
33#63641C2214yescomplemented
34C2×C3×AGL(1,ℤ/8)D314yescomplemented
35#5830—34no—
36#5798—34no—
37C22×#213—34no—
38#5233—34no—
39#5165—316no—
40#5150—316no—
41#5131—34no—
42#5119—34no—
43C24×C32—21no—
44C23×C3⋊D3—21no—
45C32×#41—22no—
46C32×#41—22no—
47C2×C32×Q8C2311yescharacteristic
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—22no—
51C2×C32×D4D414yescomplemented
52C2×C32×D4C2311yescharacteristic
53C2×C32×D4C2312yes—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C2×#638—24no—
57C22×C3⋊Dic3—24no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)C2312yes—
62C32×SD16—24no—
63C32×D8—24no—
64C32×M16—22no—
65C2×C32×C8C2312yes—
66#3757—21no—
67#3757—24no—
68#3757D412yes—
69#3753—28no—
70#3752—24no—
71C4⋊(C3⋊Dic3)D412yes—
72C4⋊(C3⋊Dic3)C2312yes—
73C4×C3⋊Dic3—21no—
74C4×C3⋊Dic3C2312yes—
75C2×C3⋊(C3⋊C8)—22no—
76C2×C3⋊(C3⋊C8)C2312yes—
77#3041—91noSylow
78C2×C3×#41C2×D314yes—
79C22×C3×D4C2×D314yes—
80C22×D12—34no—
81C3×AGL(1,ℤ/8)—216no—
82C2×C3×SD16C2×D318yescomplemented
83C2×C3×D8C2×D318yescomplemented
84C2×C3×M16C2×D314yes—
85C2×#217—68no—
86#947—38no—
87#940—38no—
88#937—68no—
89D4×Dic3—316no—
90D4×Dic3—68no—
91C2×#213—316no—
92C2×#213—616no—
93#930—68no—
94#926—34no—
95#926—34no—
96C22×C3⋊C8—34no—
97#835—38no—
98#832—38no—
99#821—316no—
100Dic3⋊C8—316no—
101C23×C32—22no—
102C23×C32—24no—
103C23×C32—21no—
104C23×C32—82no—
105C23×C32C2×D411yescharacteristic
106C22×C3⋊D3—22no—
107C22×C3⋊D3—42no—
108C22×C3⋊D3—82no—
109C32×Q8—21no—
110C32×Q8—21no—
111C32×D4—24no—
112C32×D4—21no—
113C32×D4—22no—
114C32×D4—21no—
115C32×D4—42no—
116C32×D4C2×D414yes—
117C2×C32×C4—21no—
118C2×C32×C4—42no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D412yes—
121C2×C32×C4#4112yes—
122C2×C32×C4C2411yescharacteristic
123#638—84no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—84no—
126C2×C3⋊Dic3C2×D414yes—
127C4⋊(C3⋊D3)—22no—
128C4⋊(C3⋊D3)—22no—
129C4⋊(C3⋊D3)—42no—
130C32×C8—22no—
131C3⋊(C3⋊C8)—22no—
132C2×AGL(1,ℤ/8)C3⋊D311yescharacteristic, complemented
133C22×D8—91no—
134#535—91no—
135#518—91no—
136#463—94no—
137#459—94no—
138#424—91no—
139#418—91no—
140#416—91no—
141C24×C3—24no—
142C23×D3—64no—
143C3×#41—28no—
144C3×#41—28no—
145C2×C3×Q8C22×D314yes—
146C2×C3×D4—24no—
147C2×C3×D4—24no—
148C2×C3×D4—28no—
149C2×C3×D4#67116yescomplemented
150C2×C3×D4C22×D314yes—
151C2×C3×D4C22×D318yes—
152C22×C3×C4—24no—
153C22×C3×C4C22×D314yes—
154C2×#67—616no—
155C22×Dic3—616no—
156C2×D12—38no—
157C2×D12—68no—
158C2×D12—68no—
159C2×D12—64no—
160C3×SD16—216no—
161C3×D8—216no—
162C3×M16—28no—
163C2×C3×C8C22×D318yes—
164#217—38no—
165#217—616no—
166#217—64no—
167#213—632no—
168(C2×D3)⋊C4—616no—
169C4⋊Dic3—38no—
170C4⋊Dic3—38no—
171C4×Dic3—38no—
172C4×Dic3—64no—
173C2×C3⋊C8—38no—
174C2×C3⋊C8—68no—
175C22×C32—22no—
176C22×C32—24no—
177C22×C32—44no—
178C22×C32—41no—
179C22×C32—42no—
180C22×C32—84no—
181C22×C32#12112yes—
182C22×C32C22×D411yescharacteristic
183C2×C3⋊D3—42no—
184C2×C3⋊D3—44no—
185C2×C3⋊D3—84no—
186C32×C4—41no—
187C32×C4#12112yes—
188C32×C4C22×D411yescharacteristic
189C32×C4C2×#4111yescharacteristic
190C3⋊Dic3—24no—
191C3⋊Dic3—42no—
192C2×#41C2×C3⋊D311yescharacteristic
193C22×D4—91no—
194C22×D4C2×C3⋊D311yescharacteristic
195AGL(1,ℤ/8)—24no—
196C2×SD16C2×C3⋊D312yescomplemented
197C2×D8—94no—
198C2×D8—184no—
199C2×D8C2×C3⋊D312yescomplemented
200C2×M16C2×C3⋊D311yescharacteristic
201C22×C8—91no—
202#127—92no—
203#124—92no—
204#121—182no—
205#120—182no—
206C4×D4—94no—
207C4×D4—182no—
208#117—91no—
209#117—91no—
210C2×C22⋊C4—182no—
211C4⋊C8—94no—
212#103—92no—
213#102—92no—
214#102—94no—
215C23×C3—28no—
216C23×C3—216no—
217C23×C3—24no—
218C23×C3—88no—
219C23×C3D3×D414yes—
220C22×D3—68no—
221C22×D3—128no—
222C22×D3—248no—
223C3×Q8—24no—
224C3×Q8—24no—
225C3×D4—216no—
226C3×D4—28no—
227C3×D4—24no—
228C3×D4—24no—
229C3×D4—48no—
230C3×D4C2×#67116yes—
231C2×C3×C4—24no—
232C2×C3×C4—48no—
233C2×C3×C4D3×D414yes—
234C2×C3×C4#23718yes—
235C2×C3×C4C2×#6718yes—
236C2×C3×C4C23×D314yes—
237#67—2416no—
238C2×Dic3—316no—
239C2×Dic3—68no—
240C2×Dic3—2416no—
241D12—68no—
242D12—68no—
243D12—128no—
244C3×C8—28no—
245C3⋊C8—68no—
246C2×C32—22no—
247C2×C32—44no—
248C2×C32—81no—
249C2×C32C2×#12111yescharacteristic
250C2×C32#57612yes—
251C3⋊D3—82no—
252C24—21no—
253C24—181no—
254#41—22no—
255#41—22no—
256C2×Q8C22×C3⋊D311yescharacteristic
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—22no—
260C2×D4—92no—
261C2×D4—184no—
262C2×D4—181no—
263C2×D4—182no—
264C2×D4—182no—
265C2×D4#63814yescomplemented
266C2×D4C22×C3⋊D311yescharacteristic
267C2×D4C22×C3⋊D312yes—
268C22×C4—21no—
269C22×C4—184no—
270C22×C4C22×C3⋊D311yescharacteristic
271SD16—24no—
272D8—24no—
273D8—188no—
274M16—22no—
275C2×C8—92no—
276C2×C8—182no—
277C2×C8C22×C3⋊D312yes—
278C4⋊C4—92no—
279C4⋊C4—92no—
280C22⋊C4—92no—
281C22⋊C4—184no—
282C22⋊C4—184no—
283C22⋊C4—181no—
284C42—92no—
285C42—181no—
286C22×C3—28no—
287C22×C3—216no—
288C22×C3—416no—
289C22×C3—48no—
290C22×C3—44no—
291C22×C3—816no—
292C22×C3#93918yes—
293C22×C3C2×D3×D414yes—
294C2×D3—1216no—
295C2×D3—128no—
296C2×D3—2416no—
297C3×C4—44no—
298C3×C4#93918yes—
299C3×C4C2×#23714yes—
300C3×C4C22×#6714yes—
301Dic3—616no—
302Dic3—128no—
303C32#304111yescharacteristic, complemented, Sylow
304C23—22no—
305C23—24no—
306C23—21no—
307C23—82no—
308C23—182no—
309C23—362no—
310C23—722no—
311C23D4×C3⋊D311yescharacteristic
312Q8—21no—
313Q8—21no—
314D4—22no—
315D4—21no—
316D4—21no—
317D4—24no—
318D4—42no—
319D4—182no—
320D4—182no—
321D4—362no—
322D4—724no—
323D4C2×#63814yes—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—94no—
327C2×C4—182no—
328C2×C4—724no—
329C2×C4D4×C3⋊D311yescharacteristic
330C2×C4#383012yes—
331C2×C4C2×#63812yes—
332C2×C4C23×C3⋊D311yescharacteristic
333C8—22no—
334C8—182no—
335C2×C3—28no—
336C2×C3—416no—
337C2×C3—84no—
338C2×C3#577418yes—
339C2×C3C2×#93914yes—
340D3—248no—
341C22—22no—
342C22—24no—
343C22—44no—
344C22—42no—
345C22—41no—
346C22—84no—
347C22—364no—
348C22—362no—
349C22—724no—
350C22#6414812yes—
351C22C2×D4×C3⋊D311yescharacteristic
352C4—41no—
353C4—184no—
354C4—362no—
355C4#6414812yes—
356C4C2×#383011yescharacteristic
357C4C22×#63811yescharacteristic
358C3#8393414yescomplemented
359C2—22no—
360C2—44no—
361C2—81no—
362C2—722no—
363C2#1059624512yes—
364C2C2×#6414811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×AGL(1,ℤ/8)C2
socleC22×C32C22×D4
hypercenterC2×AGL(1,ℤ/8)C3⋊D3
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C32×AGL(1,ℤ/8)C2semidirect
2. #10596301C2semidirect
3. #10596269C2semidirect
4. C22×#3753C2semidirect
5. #10592932C2semidirect
6. #10592864C2semidirect
7. #10592849C2semidirect
8. #10592830C2semidirect
9. #10592818C2semidirect
15. C2×C32×SD16C22semidirect
16. C2×C32×D8C22semidirect
19. #64156C22semidirect
20. #64149C22semidirect
23. D4×C3⋊Dic3C22semidirect
30. #63662C22semidirect
31. #63659C22semidirect
32. #63648C22semidirect
33. #63641C22semidirect
34. C2×C3×AGL(1,ℤ/8)D3semidirect
51. C2×C32×D4D4semidirect
82. C2×C3×SD16C2×D3semidirect
83. C2×C3×D8C2×D3semidirect
132. C2×AGL(1,ℤ/8)C3⋊D3semidirect
149. C2×C3×D4#67semidirect
196. C2×SD16C2×C3⋊D3semidirect
199. C2×D8C2×C3⋊D3semidirect
265. C2×D4#638semidirect
303. C32#3041semidirect
358. C3#83934semidirect

Maximal subgroups

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

subgroupindex
C2×C32×AGL(1,ℤ/8)2
#105963012
#105962692
C22×#37532
#105929322
#105928642
#105928492
#105928302
#105928182
#839343