Finite Group Databasebeta

← #11899662

Subgroups — #11899662

Order 1152.

1110 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 1110 conjugacy classes of subgroups — too many to draw. Only its 205 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#10596228C212yesmaximal, complemented
2C2×C32×D16C211yesmaximal, characteristic, complemented
3#10592846C212yesmaximal, complemented
4#10592611C212yesmaximal, complemented
5#10592610C214yesmaximal, complemented
6C3⋊D3×D16C212yesmaximal, complemented
7#10592603C211yesmaximal, characteristic, complemented
8#10592600C211yesmaximal, characteristic, complemented
9#82019—34nomaximal
10#64361—22no—
11C2×C32×D8C2212yescomplemented
12#64141—22no—
13#64121C2214yescomplemented
14#64120—24no—
15D8×C3⋊D3C2214yescomplemented
16#64113C2212yescomplemented
17#64110C2211yescharacteristic
18C32×D16C2212yescomplemented
19C32×D16C2212yescomplemented
20C2×C32×C16C2211yescharacteristic, complemented
21#63654C2214yescomplemented
22#63653C2214yescomplemented
23#63639C2211yescharacteristic, complemented
24#63628C2211yescharacteristic, complemented
25#63627C2212yescomplemented
26#63626C2211yescharacteristic, complemented
27#63625C2212yescomplemented
28C16×C3⋊D3C2212yescomplemented
29#5757—38no—
30C2×C3×D16D314yescomplemented
31#5147—38no—
32#4912—38no—
33#4911—316no—
34D3×D16—38no—
35#4904—34no—
36#4901—34no—
37C2×C32×D4—22no—
38C2×#638—44no—
39#3830—24no—
40#3830—42no—
41D4×C3⋊D3—24no—
42D4×C3⋊D3—42no—
43#3828—22no—
44#3828D411yescharacteristic
45C32×D8—22no—
46C32×D8C2314yes—
47C2×C32×C8C2311yescharacteristic
48#3754—24no—
49#3753—24no—
50#3748D411yescharacteristic
51#3746C2312yes—
52#3745C2312yes—
53#3744—22no—
54#3743D412yes—
55C8×C3⋊D3C2312yes—
56C32×C16C2311yescharacteristic
57C32×C16C2311yescharacteristic
58C3⋊(C3⋊C16)C2312yes—
59#3415—91noSylow
60#1004—68no—
61C2×C3×D8C2×D318yescomplemented
62#932—68no—
63#912—316no—
64#911—616no—
65D3×D8—316no—
66#904—38no—
67#901—34no—
68C3×D16C2×D318yescomplemented
69C3×D16C2×D318yescomplemented
70C2×C3×C16C2×D314yescomplemented
71#827—316no—
72#826—316no—
73#812—34no—
74Dic24—34no—
75#800—38no—
76D48—34no—
77#798—38no—
78D3×C16—38no—
79C23×C32—42no—
80C22×C3⋊D3—44no—
81C32×D4—24no—
82C32×D4—42no—
83C2×C32×C4C2×D411yescharacteristic
84#638—42no—
85#638—44no—
86#638—44no—
87#638D812yes—
88C2×C3⋊Dic3—44no—
89C4⋊(C3⋊D3)—22no—
90C4⋊(C3⋊D3)D811yescharacteristic
91C4×C3⋊D3—42no—
92C4×C3⋊D3C2×D412yes—
93#634—22no—
94#634D811yescharacteristic
95C32×C8C2×D411yescharacteristic
96C32×C8C2411yescharacteristic
97C3⋊(C3⋊C8)C2×D412yes—
98#576—92no—
99#509—92no—
100#509—94no—
101#508—92no—
102#508—91no—
103C2×D16—92no—
104C2×D16C3⋊D311yescharacteristic, complemented
105#504—91no—
106C2×C3×D4—28no—
107C2×#67—1216no—
108#237—616no—
109#237—128no—
110D3×D4—616no—
111D3×D4—128no—
112#235—34no—
113#235—68no—
114C3×D8—28no—
115C3×D8C22×D3116yes—
116C2×C3×C8C22×D314yes—
117#214—616no—
118#213—616no—
119#208—34no—
120Dic12—38no—
121D24—38no—
122#204—68no—
123ΓL(1,𝔽25)—38no—
124D3×C8—38no—
125C3×C16C22×D314yes—
126C3×C16C22×D314yes—
127C3⋊C16—38no—
128C22×C32—44no—
129C22×C32—162no—
130C22×C32C2×D811yescharacteristic
131C2×C3⋊D3—42no—
132C2×C3⋊D3—164no—
133C2×C3⋊D3C2×D812yes—
134C32×C4C2×D811yescharacteristic
135C32×C4C22×D411yescharacteristic
136C3⋊Dic3—42no—
137C3⋊Dic3C2×D812yes—
138H(5,𝔽2)—182no—
139AGL(1,ℤ/8)—184no—
140AGL(1,ℤ/8)—182no—
141#135—94no—
142#135—92no—
143C2×D8—94no—
144C2×D8C2×C3⋊D312yescomplemented
145#131—91no—
146Q32—91no—
147SD32—94no—
148SD32—92no—
149D16—94no—
150D16—91no—
151D16C2×C3⋊D312yescomplemented
152D16C2×C3⋊D312yescomplemented
153M32—91no—
154M32—92no—
155C2×C16—92no—
156C2×C16C2×C3⋊D311yescharacteristic, complemented
157C23×C3—48no—
158C22×D3—1216no—
159C3×D4—216no—
160C3×D4—48no—
161C2×C3×C4D3×D414yes—
162#67—38no—
163#67—1216no—
164#67—1216no—
165#67—128no—
166C2×Dic3—1216no—
167D12—34no—
168D12—68no—
169C4×D3—38no—
170C4×D3—128no—
171Dic6—34no—
172Dic6—68no—
173C3×C8D3×D414yes—
174C3×C8C23×D314yes—
175C3⋊C8—38no—
176C2×C32—21no—
177C2×C32—84no—
178C2×C32C22×D811yescharacteristic
179C3⋊D3—22no—
180C3⋊D3—82no—
181#41—91no—
182#41—184no—
183#41—182no—
184#41—362no—
185C2×D4—22no—
186C2×D4—184no—
187C2×D4—362no—
188C2×D4—364no—
189Q16—92no—
190SD16—184no—
191SD16—182no—
192D8—22no—
193D8—92no—
194D8—184no—
195D8C22×C3⋊D314yes—
196M16—91no—
197M16—92no—
198C2×C8—92no—
199C2×C8C22×C3⋊D311yescharacteristic
200C16—92no—
201C16C22×C3⋊D311yescharacteristic
202C16C22×C3⋊D311yescharacteristic
203C22×C3—416no—
204C22×C3—168no—
205C22×C3D3×D814yes—
206C2×D3—38no—
207C2×D3—128no—
208C2×D3—4816no—
209C3×C4D3×D814yes—
210C3×C4C2×D3×D414yes—
211Dic3—38no—
212Dic3—128no—
213C32#341511yescharacteristic, complemented, Sylow
214C23—42no—
215C23—364no—
216Q8—91no—
217Q8—182no—
218D4—24no—
219D4—42no—
220D4—92no—
221D4—91no—
222D4—182no—
223D4—364no—
224D4—364no—
225D4—362no—
226C2×C4—92no—
227C2×C4—364no—
228C2×C4—362no—
229C2×C4D4×C3⋊D311yescharacteristic
230C8—92no—
231C8D4×C3⋊D311yescharacteristic
232C8C23×C3⋊D311yescharacteristic
233C2×C3—24no—
234C2×C3—816no—
235C2×C3C2×D3×D814yes—
236D3—68no—
237D3—248no—
238C22—44no—
239C22—92no—
240C22—162no—
241C22—362no—
242C22—1444no—
243C22D8×C3⋊D311yescharacteristic
244C4—92no—
245C4—362no—
246C4D8×C3⋊D311yescharacteristic
247C4C2×D4×C3⋊D311yescharacteristic
248C3#8201914yescomplemented
249C2—21no—
250C2—84no—
251C2—182no—
252C2—722no—
253C2C2×D8×C3⋊D311yescharacteristic
subgroupG/H
centerC2C2×D8×C3⋊D3
commutator, cosocleC32×C8C24
FrattiniC8C23×C3⋊D3
FittingC2×C32×D16C2
socleC2×C32C22×D8
hypercenterC2×D16C3⋊D3
hypocenterC32#3415
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #10596228C2semidirect
2. C2×C32×D16C2semidirect
3. #10592846C2semidirect
4. #10592611C2semidirect
5. #10592610C2semidirect
6. C3⋊D3×D16C2semidirect
7. #10592603C2semidirect
8. #10592600C2semidirect
11. C2×C32×D8C22semidirect
13. #64121C22semidirect
15. D8×C3⋊D3C22semidirect
16. #64113C22semidirect
18. C32×D16C22semidirect
19. C32×D16C22semidirect
20. C2×C32×C16C22semidirect
21. #63654C22semidirect
22. #63653C22semidirect
23. #63639C22semidirect
24. #63628C22semidirect
25. #63627C22semidirect
26. #63626C22semidirect
27. #63625C22semidirect
28. C16×C3⋊D3C22semidirect
30. C2×C3×D16D3semidirect
61. C2×C3×D8C2×D3semidirect
68. C3×D16C2×D3semidirect
69. C3×D16C2×D3semidirect
70. C2×C3×C16C2×D3semidirect
104. C2×D16C3⋊D3semidirect
144. C2×D8C2×C3⋊D3semidirect
151. D16C2×C3⋊D3semidirect
152. D16C2×C3⋊D3semidirect
156. C2×C16C2×C3⋊D3semidirect
213. C32#3415semidirect
248. C3#82019semidirect

Maximal subgroups

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

subgroupindex
#105962282
C2×C32×D162
#105928462
#105926112
#105926102
C3⋊D3×D162
#105926032
#105926002
#820193