Finite Group Databasebeta

← #11886846

Subgroups — #11886846

Order 1152.

690 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 142 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#10589864C214yesmaximal, complemented
2C9×#492C211yesmaximal, characteristic, complemented
3#10588857C214yesmaximal, complemented
4#10588775C212yesmaximal, complemented
5#10588757C212yesmaximal, complemented
6#10588380C212yesmaximal, complemented
7#81774—31nomaximal
8#63713C2212yes—
9#63710C2212yescomplemented
10C2×C9×SD16C2214yescomplemented
11C9×C4⋊Q8C2211yescharacteristic, complemented
12C9×#127C2211yescharacteristic
13#63505C2214yescomplemented
14#63495C2214yes—
15#63478—24no—
16#63477—24no—
17#63476—24no—
18SD16×D9—24no—
19#63467C2212yes—
20#63464C2214yescomplemented
21C4×C8×C9C2211yescharacteristic, complemented
22#63394C2212yescomplemented
23#63391C2212yescomplemented
24#63372C2212yescomplemented
25#63364C2214yescomplemented
26#5762—34no—
27C3×#492D311yescharacteristic
28#5177—34no—
29#5095—32no—
30#5077—32no—
31#4700—32no—
32C2×Q8×C9C2312yes—
33C2×D4×C9—41no—
34C2×D4×C9C2312yes—
35C2×#611—42no—
36#3701—24no—
37Q8×D9—24no—
38#3699—24no—
39D4×D9—24no—
40#3697—42no—
41#3697C2314yes—
42C9×SD16—24no—
43C9×SD16—24no—
44C2×C8×C9C2312yes—
45C9×C4⋊C4—41no—
46C42×C9C2311yescharacteristic
47#3675—24no—
48#3674—24no—
49#3673—24no—
50#3672—24no—
51#3667C2314yes—
52D72D412yescomplemented
53#3664D414yescomplemented
54#3663—24no—
55C8×D9—24no—
56Dic36D412yescomplemented
57#3291—91noSylow
58#1007—32no—
59#1004—32no—
60C2×C3×SD16C2×D314yes—
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×#127C2×D311yescharacteristic
63#942—34no—
64#932—34no—
65#916—64no—
66#915—64no—
67#914—64no—
68D3×SD16—64no—
69#904—32no—
70#901—34no—
71C3×C4×C8C2×D311yescharacteristic
72#836—32no—
73#833—32no—
74#819—32no—
75#805—34no—
76C23×C9—22no—
77C22×D9—42no—
78Q8×C9—24no—
79D4×C9—24no—
80D4×C9—82no—
81C2×C4×C9—21no—
82C2×C4×C9—22no—
83C2×C4×C9C2411yescharacteristic
84#611—24no—
85#611—44no—
86C2×Dic9—42no—
87D36—42no—
88D36C2×D414yes—
89C4×D9—24no—
90C4×D9—44no—
91Dic18—42no—
92Dic18C2×D414yes—
93C8×C9C2×D412yes—
94C8×C9C2×D412yes—
95C9⋊C8—24no—
96#577—94no—
97#492D911yescharacteristic, complemented
98#471—94no—
99#456—92no—
100#453—92no—
101#443—92no—
102C2×C3×Q8C22×D312yes—
103C2×C3×D4—41no—
104C2×C3×D4C22×D312yes—
105C2×#67—122no—
106#239—64no—
107D3×Q8—64no—
108#237—64no—
109D3×D4—64no—
110#235—34no—
111#235—122no—
112C3×SD16—24no—
113C3×SD16—24no—
114C2×C3×C8C22×D312yes—
115C3×C4⋊C4—41no—
116C3×C42C22×D311yescharacteristic
117#216—64no—
118#215—64no—
119#214—64no—
120#213—64no—
121#208—34no—
122Dic12—32no—
123D24—32no—
124#204—34no—
125ΓL(1,𝔽25)—64no—
126D3×C8—64no—
127C22×C9—42no—
128C22×C9—82no—
129C22×C9H(5,𝔽2)11yescharacteristic
130C2×D9—24no—
131C2×D9—162no—
132C4×C9—22no—
133C4×C9—42no—
134C4×C9C22×D412yes—
135Dic9—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×D914yescomplemented
146#131—94no—
147C4⋊Q8C2×D911yescharacteristic, complemented
148#127C2×D911yescharacteristic
149#108—92no—
150#104—94no—
151#101—92no—
152#100—92no—
153C4×C8C2×D911yescharacteristic, complemented
154C23×C3—22no—
155C22×D3—122no—
156C3×Q8—24no—
157C3×D4—24no—
158C3×D4—82no—
159C2×C3×C4—21no—
160C2×C3×C4—22no—
161C2×C3×C4C23×D311yescharacteristic
162#67—64no—
163#67—124no—
164C2×Dic3—122no—
165D12—34no—
166D12—122no—
167C4×D3—64no—
168C4×D3—124no—
169Dic6—34no—
170Dic6—122no—
171C3×C8D3×D412yes—
172C3×C8D3×D412yes—
173C3⋊C8—64no—
174C2×C9—21no—
175C2×C9—82no—
176C2×C9D4211yescharacteristic
177D9—44no—
178#41—94no—
179#41—184no—
180#41—184no—
181#41—362no—
182C2×Q8—184no—
183C2×Q8C22×D912yes—
184C2×D4—41no—
185C2×D4—184no—
186C2×D4—362no—
187C2×D4C22×D912yes—
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×D912yes—
201C4⋊C4—41no—
202C42C22×D911yescharacteristic
203C22×C3—42no—
204C22×C3—82no—
205C22×C3#100411yescharacteristic
206C2×D3—64no—
207C2×D3—482no—
208C3×C4—22no—
209C3×C4—42no—
210C3×C4C2×D3×D412yes—
211Dic3—64no—
212C9#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×D911yescharacteristic
230C8—184no—
231C8D4×D912yes—
232C8D4×D912yes—
233C2×C3—21no—
234C2×C3—82no—
235C2×C3#571711yescharacteristic
236D3—124no—
237C22—42no—
238C22—82no—
239C22—184no—
240C22—1442no—
241C22#6371011yescharacteristic
242C4—22no—
243C4—42no—
244C4—184no—
245C4C2×D4×D912yes—
246C3#8177411yescharacteristic
247C2—21no—
248C2—82no—
249C2—364no—
250C2#1058981911yescharacteristic
subgroupG/H
centerC2#10589819
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#492C2
socleC2×C3#5717
hypercenter#492D9
hypocenterC9#3291
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C2×C4 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #10589864C2semidirect
2. C9×#492C2semidirect
3. #10588857C2semidirect
4. #10588775C2semidirect
5. #10588757C2semidirect
6. #10588380C2semidirect
9. #63710C22semidirect
10. C2×C9×SD16C22semidirect
11. C9×C4⋊Q8C22semidirect
13. #63505C22semidirect
20. #63464C22semidirect
21. C4×C8×C9C22semidirect
22. #63394C22semidirect
23. #63391C22semidirect
24. #63372C22semidirect
25. #63364C22semidirect
52. D72D4semidirect
53. #3664D4semidirect
56. Dic36D4semidirect
97. #492D9semidirect
145. C2×SD16C2×D9semidirect
147. C4⋊Q8C2×D9semidirect
153. C4×C8C2×D9semidirect
212. C9#3291semidirect

Maximal subgroups

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

subgroupindex
#105898642
C9×#4922
#105888572
#105887752
#105887572
#105883802
#817743