Finite Group Databasebeta

← #11899665

Subgroups — #11899665

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#10596240C212yesmaximal, complemented
2C32×#508C211yesmaximal, characteristic, complemented
3#10592892C212yesmaximal, complemented
4#10592618C212yesmaximal, complemented
5#10592613C214yesmaximal, complemented
6C3⋊D3×D16C212yesmaximal, complemented
7C2×#63626C211yesmaximal, characteristic, complemented
8#10592600C211yesmaximal, characteristic, complemented
9#82031—34nomaximal
10#64366—22no—
11C32×#135C2212yescomplemented
12#64158—22no—
13#64128C2214yescomplemented
14#64123—24no—
15D8×C3⋊D3C2214yescomplemented
16C2×#3745C2212yescomplemented
17#64110C2211yescharacteristic
18C32×Q32C2211yescharacteristic, complemented
19C32×SD32C2212yescomplemented
20C32×D16C2211yescharacteristic, complemented
21C2×C32×C16C2211yescharacteristic, complemented
22#63655C2214yescomplemented
23#63653C2214yescomplemented
24#63639C2211yescharacteristic, complemented
25#63626C2212yescomplemented
26#63626C2212yescomplemented
27#63625C2212yescomplemented
28C16×C3⋊D3C2212yescomplemented
29#5769—38no—
30C3×#508D314yescomplemented
31#5193—38no—
32#4919—38no—
33#4914—316no—
34D3×D16—38no—
35C2×D48—34no—
36#4901—34no—
37C32×#41—22no—
38#3832—24no—
39D4×C3⋊D3—24no—
40D4×C3⋊D3—44no—
41#3828—42no—
42#3828D411yescharacteristic
43C2×C4⋊(C3⋊D3)—22no—
44C2×C4⋊(C3⋊D3)—42no—
45C32×Q16C2312yes—
46C32×SD16—22no—
47C32×D8C2312yes—
48C2×C32×C8C2311yescharacteristic
49#3755—24no—
50#3753—24no—
51#3748D411yescharacteristic
52#3745—22no—
53#3745C2314yes—
54#3743D412yes—
55C8×C3⋊D3C2312yes—
56C32×C16C2311yescharacteristic
57C32×C16C2311yescharacteristic
58C3⋊(C3⋊C16)C2312yes—
59#3415—91noSylow
60#1009—68no—
61C3×#135C2×D318yescomplemented
62#949—68no—
63#919—316no—
64#914—616no—
65D3×D8—316no—
66C2×D24—38no—
67#901—34no—
68C3×Q32C2×D314yescomplemented
69C3×SD32C2×D318yescomplemented
70C3×D16C2×D314yescomplemented
71C2×C3×C16C2×D314yescomplemented
72#828—316no—
73#826—316no—
74#812—34no—
75D48—38no—
76D48—38no—
77#798—38no—
78D3×C16—38no—
79C22×C3⋊D3—42no—
80C22×C3⋊D3—44no—
81C32×Q8—22no—
82C32×D4—22no—
83C32×D4—42no—
84C2×C32×C4—42no—
85C2×C32×C4C2×D411yescharacteristic
86#638—44no—
87#638D812yes—
88C4⋊(C3⋊D3)—24no—
89C4⋊(C3⋊D3)—44no—
90C4⋊(C3⋊D3)—42no—
91C4⋊(C3⋊D3)D811yescharacteristic
92C4×C3⋊D3—44no—
93C4×C3⋊D3C2×D412yes—
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#508C3⋊D311yescharacteristic, complemented
103C2×D16—92no—
104C2×D16—91no—
105#504—91no—
106C3×#41—28no—
107#239—616no—
108D3×D4—616no—
109D3×D4—1216no—
110#235—34no—
111#235—128no—
112C2×D12—68no—
113C2×D12—128no—
114C3×Q16C22×D318yes—
115C3×SD16—28no—
116C3×D8C22×D318yes—
117C2×C3×C8C22×D314yes—
118#215—616no—
119#213—616no—
120#208—34no—
121D24—316no—
122D24—68no—
123ΓL(1,𝔽25)—38no—
124D3×C8—38no—
125C3×C16C22×D314yes—
126C3×C16C22×D314yes—
127C3⋊C16—38no—
128C22×C32—42no—
129C22×C32C2×D811yescharacteristic
130C2×C3⋊D3—44no—
131C2×C3⋊D3—164no—
132C2×C3⋊D3—162no—
133C2×C3⋊D3C2×D812yes—
134C32×C4—42no—
135C32×C4C2×D811yescharacteristic
136C32×C4C22×D411yescharacteristic
137C3⋊Dic3C2×D812yes—
138H(5,𝔽2)—182no—
139AGL(1,ℤ/8)—184no—
140AGL(1,ℤ/8)—182no—
141#135—94no—
142#135C2×C3⋊D312yescomplemented
143C2×D8—94no—
144C2×D8—92no—
145#131—91no—
146Q32C2×C3⋊D311yescharacteristic, complemented
147SD32—94no—
148SD32C2×C3⋊D312yescomplemented
149D16—94no—
150D16—92no—
151D16—92no—
152D16C2×C3⋊D311yescharacteristic, complemented
153M32—91no—
154M32—92no—
155C2×C16—92no—
156C2×C16C2×C3⋊D311yescharacteristic, complemented
157C22×D3—1216no—
158C22×D3—128no—
159C3×Q8—28no—
160C3×D4—28no—
161C3×D4—48no—
162C2×C3×C4—48no—
163C2×C3×C4D3×D414yes—
164#67—38no—
165#67—1216no—
166D12—34no—
167D12—616no—
168D12—1216no—
169D12—128no—
170C4×D3—38no—
171C4×D3—1216no—
172Dic6—34no—
173C3×C8D3×D414yes—
174C3×C8C23×D314yes—
175C3⋊C8—38no—
176C2×C32—21no—
177C2×C32—82no—
178C2×C32C22×D811yescharacteristic
179C3⋊D3—22no—
180C3⋊D3—84no—
181#41—22no—
182#41—91no—
183#41—184no—
184#41—362no—
185C2×D4—184no—
186C2×D4—182no—
187C2×D4—362no—
188C2×D4—364no—
189Q16C22×C3⋊D312yes—
190SD16—22no—
191SD16—184no—
192D8—94no—
193D8—184no—
194D8—182no—
195D8C22×C3⋊D312yes—
196M16—91no—
197M16—92no—
198C2×C8—92no—
199C2×C8C22×C3⋊D311yescharacteristic
200C16—92no—
201C16C22×C3⋊D311yescharacteristic
202C16C22×C3⋊D311yescharacteristic
203C22×C3—48no—
204C22×C3D3×D814yes—
205C2×D3—38no—
206C2×D3—1216no—
207C2×D3—4816no—
208C2×D3—488no—
209C3×C4—48no—
210C3×C4D3×D814yes—
211C3×C4C2×D3×D414yes—
212Dic3—38no—
213C32#341511yescharacteristic, complemented, Sylow
214C23—364no—
215C23—362no—
216Q8—22no—
217Q8—91no—
218D4—22no—
219D4—42no—
220D4—92no—
221D4—91no—
222D4—184no—
223D4—364no—
224D4—364no—
225D4—362no—
226C2×C4—42no—
227C2×C4—92no—
228C2×C4—364no—
229C2×C4D4×C3⋊D311yescharacteristic
230C8—92no—
231C8D4×C3⋊D311yescharacteristic
232C8C23×C3⋊D311yescharacteristic
233C2×C3—24no—
234C2×C3—88no—
235C2×C3C2×D3×D814yes—
236D3—68no—
237D3—2416no—
238C22—42no—
239C22—92no—
240C22—364no—
241C22—1442no—
242C22—1444no—
243C22D8×C3⋊D311yescharacteristic
244C4—42no—
245C4—92no—
246C4D8×C3⋊D311yescharacteristic
247C4C2×D4×C3⋊D311yescharacteristic
248C3#8203114yescomplemented
249C2—21no—
250C2—82no—
251C2—182no—
252C2—724no—
253C2C2×D8×C3⋊D311yescharacteristic
subgroupG/H
centerC2C2×D8×C3⋊D3
commutator, cosocleC32×C8C24
FrattiniC8C23×C3⋊D3
FittingC32×#508C2
socleC2×C32C22×D8
hypercenter#508C3⋊D3
hypocenterC32#3415
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #10596240C2semidirect
2. C32×#508C2semidirect
3. #10592892C2semidirect
4. #10592618C2semidirect
5. #10592613C2semidirect
6. C3⋊D3×D16C2semidirect
7. C2×#63626C2semidirect
8. #10592600C2semidirect
11. C32×#135C22semidirect
13. #64128C22semidirect
15. D8×C3⋊D3C22semidirect
16. C2×#3745C22semidirect
18. C32×Q32C22semidirect
19. C32×SD32C22semidirect
20. C32×D16C22semidirect
21. C2×C32×C16C22semidirect
22. #63655C22semidirect
23. #63653C22semidirect
24. #63639C22semidirect
25. #63626C22semidirect
26. #63626C22semidirect
27. #63625C22semidirect
28. C16×C3⋊D3C22semidirect
30. C3×#508D3semidirect
61. C3×#135C2×D3semidirect
68. C3×Q32C2×D3semidirect
69. C3×SD32C2×D3semidirect
70. C3×D16C2×D3semidirect
71. C2×C3×C16C2×D3semidirect
102. #508C3⋊D3semidirect
142. #135C2×C3⋊D3semidirect
146. Q32C2×C3⋊D3semidirect
148. SD32C2×C3⋊D3semidirect
152. D16C2×C3⋊D3semidirect
156. C2×C16C2×C3⋊D3semidirect
213. C32#3415semidirect
248. C3#82031semidirect

Maximal subgroups

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

subgroupindex
#105962402
C32×#5082
#105928922
#105926182
#105926132
C3⋊D3×D162
C2×#636262
#105926002
#820313