Finite Group Databasebeta

← #11886847

Subgroups — #11886847

Order 1152.

1380 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 217 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596233C214yesmaximal, complemented
2C32×#492C211yesmaximal, characteristic, complemented
3#10592876C214yesmaximal, complemented
4#10592794C212yesmaximal, complemented
5#10592776C212yesmaximal, complemented
6#10592399C212yesmaximal, complemented
7#81774—34nomaximal
8#64364C2212yes—
9#64361C2212yescomplemented
10C2×C32×SD16C2214yescomplemented
11C32×C4⋊Q8C2211yescharacteristic, complemented
12C32×#127C2211yescharacteristic
13#64151C2214yescomplemented
14#64141C2214yes—
15#64125—24no—
16#64124—24no—
17#64123—24no—
18SD16×C3⋊D3—24no—
19#64113C2212yes—
20#64110C2214yescomplemented
21C32×C4×C8C2211yescharacteristic, complemented
22#63663C2212yescomplemented
23#63660C2212yescomplemented
24#63646C2212yescomplemented
25#63632C2214yescomplemented
26#5762—316no—
27C3×#492D314yescomplemented
28#5177—316no—
29#5095—38no—
30#5077—38no—
31#4700—38no—
32C2×C32×Q8C2312yes—
33C2×C32×D4—41no—
34C2×C32×D4C2312yes—
35C2×#638—42no—
36#3832—24no—
37Q8×C3⋊D3—24no—
38#3830—24no—
39D4×C3⋊D3—24no—
40#3828—42no—
41#3828C2314yes—
42C32×SD16—24no—
43C32×SD16—24no—
44C2×C32×C8C2312yes—
45C32×C4⋊C4—41no—
46C32×C42C2311yescharacteristic
47#3756—24no—
48#3755—24no—
49#3754—24no—
50#3753—24no—
51#3748C2314yes—
52#3746D412yescomplemented
53#3745D412yescomplemented
54#3744D414yescomplemented
55#3743—24no—
56C8×C3⋊D3—24no—
57#3291—91noSylow
58#1007—38no—
59#1004—38no—
60C2×C3×SD16C2×D3116yescomplemented
61C3×C4⋊Q8C2×D314yescomplemented
62C3×#127C2×D314yes—
63#942—316no—
64#932—316no—
65#916—616no—
66#915—616no—
67#914—616no—
68D3×SD16—616no—
69#904—38no—
70#901—316no—
71C3×C4×C8C2×D314yescomplemented
72#836—38no—
73#833—38no—
74#819—38no—
75#805—316no—
76C23×C32—22no—
77C22×C3⋊D3—42no—
78C32×Q8—24no—
79C32×D4—24no—
80C32×D4—82no—
81C2×C32×C4—21no—
82C2×C32×C4—22no—
83C2×C32×C4C2411yescharacteristic
84#638—24no—
85#638—44no—
86C2×C3⋊Dic3—42no—
87C4⋊(C3⋊D3)—42no—
88C4⋊(C3⋊D3)C2×D414yes—
89C4×C3⋊D3—24no—
90C4×C3⋊D3—44no—
91#634—42no—
92#634C2×D414yes—
93C32×C8C2×D412yes—
94C32×C8C2×D412yes—
95C3⋊(C3⋊C8)—24no—
96#577—94no—
97#492C3⋊D311yescharacteristic, complemented
98#471—94no—
99#456—92no—
100#453—92no—
101#443—92no—
102C2×C3×Q8C22×D318yes—
103C2×C3×D4—44no—
104C2×C3×D4C22×D318yes—
105C2×#67—128no—
106#239—616no—
107D3×Q8—616no—
108#237—616no—
109D3×D4—616no—
110#235—316no—
111#235—128no—
112C3×SD16—216no—
113C3×SD16—216no—
114C2×C3×C8C22×D318yes—
115C3×C4⋊C4—44no—
116C3×C42C22×D314yes—
117#216—616no—
118#215—616no—
119#214—616no—
120#213—616no—
121#208—316no—
122Dic12—38no—
123D24—38no—
124#204—316no—
125ΓL(1,𝔽25)—616no—
126D3×C8—616no—
127C22×C32—42no—
128C22×C32—82no—
129C22×C32H(5,𝔽2)11yescharacteristic
130C2×C3⋊D3—24no—
131C2×C3⋊D3—162no—
132C32×C4—22no—
133C32×C4—42no—
134C32×C4C22×D412yes—
135C3⋊Dic3—24no—
1362−1+4—92no—
137H(5,𝔽2)—92no—
138#137—94no—
139#137—184no—
140AGL(1,ℤ/8)—94no—
141AGL(1,ℤ/8)—184no—
142#135—92no—
143#135—184no—
144C2×SD16—184no—
145C2×SD16C2×C3⋊D314yescomplemented
146#131—94no—
147C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
148#127C2×C3⋊D311yescharacteristic
149#108—92no—
150#104—94no—
151#101—92no—
152#100—92no—
153C4×C8C2×C3⋊D311yescharacteristic, complemented
154C23×C3—28no—
155C22×D3—128no—
156C3×Q8—216no—
157C3×D4—216no—
158C3×D4—88no—
159C2×C3×C4—24no—
160C2×C3×C4—28no—
161C2×C3×C4C23×D314yes—
162#67—616no—
163#67—1216no—
164C2×Dic3—128no—
165D12—316no—
166D12—128no—
167C4×D3—616no—
168C4×D3—1216no—
169Dic6—316no—
170Dic6—128no—
171C3×C8D3×D418yes—
172C3×C8D3×D418yes—
173C3⋊C8—616no—
174C2×C32—21no—
175C2×C32—82no—
176C2×C32D4211yescharacteristic
177C3⋊D3—44no—
178#41—94no—
179#41—184no—
180#41—184no—
181#41—362no—
182C2×Q8—184no—
183C2×Q8C22×C3⋊D312yes—
184C2×D4—41no—
185C2×D4—184no—
186C2×D4—362no—
187C2×D4C22×C3⋊D312yes—
188Q16—92no—
189Q16—184no—
190SD16—24no—
191SD16—24no—
192SD16—94no—
193SD16—184no—
194SD16—184no—
195D8—92no—
196D8—184no—
197M16—94no—
198M16—184no—
199C2×C8—184no—
200C2×C8C22×C3⋊D312yes—
201C4⋊C4—41no—
202C42C22×C3⋊D311yescharacteristic
203C22×C3—48no—
204C22×C3—88no—
205C22×C3#100414yes—
206C2×D3—616no—
207C2×D3—488no—
208C3×C4—28no—
209C3×C4—48no—
210C3×C4C2×D3×D418yes—
211Dic3—616no—
212C32#329111yescharacteristic, complemented, Sylow
213C23—22no—
214C23—362no—
215Q8—24no—
216Q8—94no—
217Q8—362no—
218D4—24no—
219D4—82no—
220D4—94no—
221D4—184no—
222D4—362no—
223D4—364no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—184no—
227C2×C4—364no—
228C2×C4—362no—
229C2×C4C23×C3⋊D311yescharacteristic
230C8—184no—
231C8D4×C3⋊D312yes—
232C8D4×C3⋊D312yes—
233C2×C3—24no—
234C2×C3—88no—
235C2×C3#571714yes—
236D3—1216no—
237C22—42no—
238C22—82no—
239C22—184no—
240C22—1442no—
241C22#6436111yescharacteristic
242C4—22no—
243C4—42no—
244C4—184no—
245C4C2×D4×C3⋊D312yes—
246C3#8177414yescomplemented
247C2—21no—
248C2—82no—
249C2—364no—
250C2#1059618811yescharacteristic
subgroupG/H
centerC2#10596188
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#492C2
socleC2×C32D42
hypercenter#492C3⋊D3
hypocenterC32#3291
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #10596233C2semidirect
2. C32×#492C2semidirect
3. #10592876C2semidirect
4. #10592794C2semidirect
5. #10592776C2semidirect
6. #10592399C2semidirect
9. #64361C22semidirect
10. C2×C32×SD16C22semidirect
11. C32×C4⋊Q8C22semidirect
13. #64151C22semidirect
20. #64110C22semidirect
21. C32×C4×C8C22semidirect
22. #63663C22semidirect
23. #63660C22semidirect
24. #63646C22semidirect
25. #63632C22semidirect
27. C3×#492D3semidirect
52. #3746D4semidirect
53. #3745D4semidirect
54. #3744D4semidirect
60. C2×C3×SD16C2×D3semidirect
61. C3×C4⋊Q8C2×D3semidirect
71. C3×C4×C8C2×D3semidirect
97. #492C3⋊D3semidirect
145. C2×SD16C2×C3⋊D3semidirect
147. C4⋊Q8C2×C3⋊D3semidirect
153. C4×C8C2×C3⋊D3semidirect
212. C32#3291semidirect
246. C3#81774semidirect

Maximal subgroups

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

subgroupindex
#105962332
C32×#4922
#105928762
#105927942
#105927762
#105923992
#817743