Finite Group Databasebeta

← #11899664

Subgroups — #11899664

Order 1152.

555 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 555 conjugacy classes of subgroups — too many to draw. Only its 136 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#10589871C212yesmaximal, complemented
2C9×#508C211yesmaximal, characteristic, complemented
3#10588873C212yesmaximal, complemented
4#10588599C212yesmaximal, complemented
5#10588594C214yesmaximal, complemented
6D9×D16C212yesmaximal, complemented
7C2×D144C211yesmaximal, characteristic, complemented
8#10588581C211yesmaximal, characteristic, complemented
9#82031—31nomaximal
10#63715—22no—
11C9×#135C2212yescomplemented
12#63512—22no—
13#63481C2214yescomplemented
14#63476—24no—
15D8×D9C2214yescomplemented
16C2×D72C2212yescomplemented
17#63464C2211yescharacteristic
18C9×Q32C2211yescharacteristic, complemented
19C9×SD32C2212yescomplemented
20C9×D16C2211yescharacteristic, complemented
21C2×C9×C16C2211yescharacteristic, complemented
22#63387C2214yescomplemented
23#63385C2214yescomplemented
24#63371C2211yescharacteristic, complemented
25D144C2212yescomplemented
26D144C2212yescomplemented
27#63357C2212yescomplemented
28C16×D9C2212yescomplemented
29#5769—32no—
30C3×#508D311yescharacteristic
31#5193—32no—
32#4919—32no—
33#4914—34no—
34D3×D16—32no—
35C2×D48—31no—
36#4901—31no—
37C9×#41—22no—
38#3701—24no—
39D4×D9—24no—
40D4×D9—44no—
41#3697—42no—
42#3697D411yescharacteristic
43C2×D36—22no—
44C2×D36—42no—
45C9×Q16C2312yes—
46C9×SD16—22no—
47C9×D8C2312yes—
48C2×C8×C9C2311yescharacteristic
49#3675—24no—
50#3673—24no—
51#3667D411yescharacteristic
52D72—22no—
53D72C2314yes—
54#3663D412yes—
55C8×D9C2312yes—
56C9×C16C2311yescharacteristic
57C9×C16C2311yescharacteristic
58C9⋊C16C2312yes—
59#3415—91noSylow
60#1009—62no—
61C3×#135C2×D312yes—
62#949—62no—
63#919—34no—
64#914—64no—
65D3×D8—34no—
66C2×D24—32no—
67#901—31no—
68C3×Q32C2×D311yescharacteristic
69C3×SD32C2×D312yes—
70C3×D16C2×D311yescharacteristic
71C2×C3×C16C2×D311yescharacteristic
72#828—34no—
73#826—34no—
74#812—31no—
75D48—32no—
76D48—32no—
77#798—32no—
78D3×C16—32no—
79C22×D9—42no—
80C22×D9—44no—
81Q8×C9—22no—
82D4×C9—22no—
83D4×C9—42no—
84C2×C4×C9—42no—
85C2×C4×C9C2×D411yescharacteristic
86#611—44no—
87#611D812yes—
88D36—24no—
89D36—44no—
90D36—42no—
91D36D811yescharacteristic
92C4×D9—44no—
93C4×D9C2×D412yes—
94Dic18D811yescharacteristic
95C8×C9C2×D411yescharacteristic
96C8×C9C2411yescharacteristic
97C9⋊C8C2×D412yes—
98#576—92no—
99#509—92no—
100#509—94no—
101#508—92no—
102#508D911yescharacteristic, complemented
103C2×D16—92no—
104C2×D16—91no—
105#504—91no—
106C3×#41—22no—
107#239—64no—
108D3×D4—64no—
109D3×D4—124no—
110#235—31no—
111#235—122no—
112C2×D12—62no—
113C2×D12—122no—
114C3×Q16C22×D312yes—
115C3×SD16—22no—
116C3×D8C22×D312yes—
117C2×C3×C8C22×D311yescharacteristic
118#215—64no—
119#213—64no—
120#208—31no—
121D24—34no—
122D24—62no—
123ΓL(1,𝔽25)—32no—
124D3×C8—32no—
125C3×C16C22×D311yescharacteristic
126C3×C16C22×D311yescharacteristic
127C3⋊C16—32no—
128C22×C9—42no—
129C22×C9C2×D811yescharacteristic
130C2×D9—44no—
131C2×D9—164no—
132C2×D9—162no—
133C2×D9C2×D812yes—
134C4×C9—42no—
135C4×C9C2×D811yescharacteristic
136C4×C9C22×D411yescharacteristic
137Dic9C2×D812yes—
138H(5,𝔽2)—182no—
139AGL(1,ℤ/8)—184no—
140AGL(1,ℤ/8)—182no—
141#135—94no—
142#135C2×D912yescomplemented
143C2×D8—94no—
144C2×D8—92no—
145#131—91no—
146Q32C2×D911yescharacteristic, complemented
147SD32—94no—
148SD32C2×D912yescomplemented
149D16—94no—
150D16—92no—
151D16—92no—
152D16C2×D911yescharacteristic, complemented
153M32—91no—
154M32—92no—
155C2×C16—92no—
156C2×C16C2×D911yescharacteristic, complemented
157C22×D3—124no—
158C22×D3—122no—
159C3×Q8—22no—
160C3×D4—22no—
161C3×D4—42no—
162C2×C3×C4—42no—
163C2×C3×C4D3×D411yescharacteristic
164#67—32no—
165#67—124no—
166D12—31no—
167D12—64no—
168D12—124no—
169D12—122no—
170C4×D3—32no—
171C4×D3—124no—
172Dic6—31no—
173C3×C8D3×D411yescharacteristic
174C3×C8C23×D311yescharacteristic
175C3⋊C8—32no—
176C2×C9—21no—
177C2×C9—82no—
178C2×C9C22×D811yescharacteristic
179D9—22no—
180D9—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×D912yes—
190SD16—22no—
191SD16—184no—
192D8—94no—
193D8—184no—
194D8—182no—
195D8C22×D912yes—
196M16—91no—
197M16—92no—
198C2×C8—92no—
199C2×C8C22×D911yescharacteristic
200C16—92no—
201C16C22×D911yescharacteristic
202C16C22×D911yescharacteristic
203C22×C3—42no—
204C22×C3D3×D811yescharacteristic
205C2×D3—32no—
206C2×D3—124no—
207C2×D3—484no—
208C2×D3—482no—
209C3×C4—42no—
210C3×C4D3×D811yescharacteristic
211C3×C4C2×D3×D411yescharacteristic
212Dic3—32no—
213C9#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×D911yescharacteristic
230C8—92no—
231C8D4×D911yescharacteristic
232C8C23×D911yescharacteristic
233C2×C3—21no—
234C2×C3—82no—
235C2×C3C2×D3×D811yescharacteristic
236D3—62no—
237D3—244no—
238C22—42no—
239C22—92no—
240C22—364no—
241C22—1442no—
242C22—1444no—
243C22D8×D911yescharacteristic
244C4—42no—
245C4—92no—
246C4D8×D911yescharacteristic
247C4C2×D4×D911yescharacteristic
248C3#8203111yescharacteristic
249C2—21no—
250C2—82no—
251C2—182no—
252C2—724no—
253C2C2×D8×D911yescharacteristic
subgroupG/H
centerC2C2×D8×D9
commutator, cosocleC8×C9C24
FrattiniC3×C8C23×D3
FittingC9×#508C2
socleC2×C3C2×D3×D8
hypercenter#508D9
hypocenterC9#3415
LCSG ▷ C8×C9 ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #10589871C2semidirect
2. C9×#508C2semidirect
3. #10588873C2semidirect
4. #10588599C2semidirect
5. #10588594C2semidirect
6. D9×D16C2semidirect
7. C2×D144C2semidirect
8. #10588581C2semidirect
11. C9×#135C22semidirect
13. #63481C22semidirect
15. D8×D9C22semidirect
16. C2×D72C22semidirect
18. C9×Q32C22semidirect
19. C9×SD32C22semidirect
20. C9×D16C22semidirect
21. C2×C9×C16C22semidirect
22. #63387C22semidirect
23. #63385C22semidirect
24. #63371C22semidirect
25. D144C22semidirect
26. D144C22semidirect
27. #63357C22semidirect
28. C16×D9C22semidirect
102. #508D9semidirect
142. #135C2×D9semidirect
146. Q32C2×D9semidirect
148. SD32C2×D9semidirect
152. D16C2×D9semidirect
156. C2×C16C2×D9semidirect
213. C9#3415semidirect

Maximal subgroups

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

subgroupindex
#105898712
C9×#5082
#105888732
#105885992
#105885942
D9×D162
C2×D1442
#105885812
#820313