Finite Group Databasebeta

← #26035033

Subgroups — #26035033

Order 11392.

1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.

normal subgroups only

This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 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#19152434C211yesmaximal, characteristic, complemented
2C2×#15668058C211yesmaximal, characteristic, complemented
3#19152410C218yesmaximal, complemented
4#19152403C218yesmaximal, complemented
5#19152398C216yesmaximal, complemented
6C2×#15668040C216yesmaximal, complemented
7#568×C89C211yesmaximal, characteristic, complemented
8#15668060—21no—
9#15668059C2214yescomplemented
10#15668058—24no—
11#15668058C2218yescomplemented
12#15668058C2214yescomplemented
13#15668057—23no—
14C2×#13083575—21no—
15C2×#13083574C2213yescomplemented
16C2×#13083574C2216yescomplemented
17#41×D89—24no—
18C22×D356C2213yescomplemented
19C2×D4×D89—23no—
20#15668045C2214yescomplemented
21#15668045C22112yescomplemented
22#15668040C22112yescomplemented
23#15668040C22124yescomplemented
24#15668040C22112yescomplemented
25#15668034C22124yescomplemented
26C2×#13083563C22112yescomplemented
27C2×D712C22112yescomplemented
28C2×#41×C89C2211yescharacteristic
29#131×C89C2218yescomplemented
30C2×M16×C89C2216yescomplemented
31C23×D89—23no—
32#13083575—24no—
33#13083575—28no—
34#13083574—26no—
35#13083574—26no—
36#13083574—26no—
37#13083574C23112yes—
38#13083574C2314yes—
39#13083574C23112yescomplemented
40#13083573—212no—
41C2×Dic178C2311yescharacteristic
42C2×Dic178C2316yescomplemented
43Q8×D89—24no—
44C2×D356—23no—
45C2×D356—26no—
46C2×D356C23112yes—
47C2×D356C2313yes—
48C2×D356C2316yescomplemented
49C2×C22⋊D89—23no—
50C2×C22⋊D89—26no—
51D4×D89—224no—
52D4×D89—212no—
53C2×C4×D89—23no—
54C2×C4×D89—26no—
55Dic356C2318yescomplemented
56#13083563C23124yescomplemented
57#13083563C2318yescomplemented
58D712C23124yescomplemented
59#41×C89D414yes—
60#41×C89C2314yes—
61C2×Q8×C89D411yescharacteristic
62C2×D4×C89D413yes—
63C22×C4×C89C2313yes—
64M16×C89C2314yes—
65M16×C89C23112yescomplemented
66C2×C8×C89C23112yescomplemented
67C23×C89C2×D413yes—
68C22×D89—23no—
69C22×D89—26no—
70C22×D89—212no—
71C22×D89—86no—
72Q8×C89C2×D414yes—
73D4×C89C2×D4112yes—
74C2×C4×C89C2×D413yes—
75C2×C4×C89C2×D416yes—
76C2×C4×C89C2416yes—
77C2×C4×C89C2411yescharacteristic
78C22⋊D89—212no—
79C22⋊D89—212no—
80C22⋊D89—24no—
81C2×Dic89—21no—
82C2×Dic89—26no—
83D356—212no—
84D356—26no—
85D356—23no—
86D356C2414yes—
87D356C2416yes—
88C4×D89—24no—
89C4×D89—212no—
90C4×D89—212no—
91Dic178—26no—
92Dic178—21no—
93Dic178C2414yes—
94Dic178C2412yes—
95C8×C89C2418yes—
96C22×C89—43no—
97C22×C89C22×D411yescharacteristic
98C22×C89C22×D416yes—
99C2×D89—24no—
100C2×D89—26no—
101C2×D89—46no—
102C2×D89—86no—
103C2×D89—812no—
104C4×C89C22×D411yescharacteristic
105C4×C89C22×D416yes—
106C4×C89C2511yescharacteristic
107Dic89—24no—
108Dic89—22no—
109C2×C89—21no—
110C2×C89—26no—
111C2×C89C23×D411yescharacteristic
112D89—46no—
113D89—44no—
114#3585—891nomaximal, Sylow
115C89#358511yescharacteristic, complemented, Sylow
116#585—891no—
117C2×H(5,𝔽2)—891no—
118#577—898no—
119#576—898no—
120#575—896no—
121C2×AGL(1,ℤ/8)—896no—
122#568D8911yescharacteristic, complemented
1232−1+4—894no—
1242−1+4—1781no—
125H(5,𝔽2)—894no—
126H(5,𝔽2)—898no—
127H(5,𝔽2)—1784no—
128H(5,𝔽2)—1783no—
129C2×#41—896no—
130C2×#41—893no—
131C2×#41—1784no—
132C2×#41—1781no—
133C2×#41C2×D8911yescharacteristic
134C22×D4—893no—
135C22×D4—1783no—
136#137—894no—
137#137—8912no—
138AGL(1,ℤ/8)—8912no—
139AGL(1,ℤ/8)—8924no—
140AGL(1,ℤ/8)—8912no—
141#135—8924no—
142C2×SD16—8912no—
143C2×D8—8912no—
144#131C2×D8918yescomplemented
145C2×M16C2×D8916yescomplemented
146C24—1783no—
147#41—8912no—
148#41—8912no—
149#41—894no—
150#41—1788no—
151#41—1784no—
152#41—17812no—
153#41—1786no—
154#41—1786no—
155#41—1786no—
156#41D35614yes—
157#41C22×D8914yes—
158C2×Q8—896no—
159C2×Q8—891no—
160C2×Q8—1784no—
161C2×Q8D35611yescharacteristic
162C2×D4—896no—
163C2×D4—8912no—
164C2×D4—893no—
165C2×D4—1783no—
166C2×D4—1786no—
167C2×D4—17824no—
168C2×D4—17812no—
169C2×D4—1783no—
170C2×D4—1786no—
171C2×D4D35613yes—
172C22×C4—1783no—
173C22×C4—1786no—
174C22×C4C22×D8913yes—
175Q16—898no—
176SD16—8924no—
177SD16—898no—
178D8—8924no—
179M16C22×D8914yes—
180M16C22×D89112yescomplemented
181C2×C8C22×D89112yescomplemented
182C23—1783no—
183C23—1786no—
184C23—17812no—
185C23—7126no—
186C23C2×D35613yes—
187Q8—894no—
188Q8—892no—
189Q8—1786no—
190Q8—1781no—
191Q8C2×D35614yes—
192D4—894no—
193D4—896no—
194D4—17812no—
195D4—1784no—
196D4—17812no—
197D4—1783no—
198D4—17812no—
199D4—1786no—
200D4C2×D356112yes—
201C2×C4—1781no—
202C2×C4—1786no—
203C2×C4—1784no—
204C2×C4—17812no—
205C2×C4—17812no—
206C2×C4C2×D35613yes—
207C2×C4C2×D35616yes—
208C2×C4C23×D8916yes—
209C2×C4C23×D8911yescharacteristic
210C8C23×D8918yes—
211C22—43no—
212C22—3566no—
213C22—1784no—
214C22—1786no—
215C22—71212no—
216C22—7126no—
217C22C22×D35611yescharacteristic
218C22C22×D35616yes—
219C4—1782no—
220C4—1784no—
221C4C22×D35611yescharacteristic
222C4C22×D35616yes—
223C4C24×D8911yescharacteristic
224C2—21no—
225C2—26no—
226C2—3566no—
227C2—3564no—
228C2C23×D35611yescharacteristic
subgroupG/H
centerC2C23×D356
commutator, cosocleC4×C89C25
FrattiniC4C24×D89
Fitting#568×C89C2
socleC2×C89C23×D4
hypercenter#568D89
hypocenterC89#3585
LCSG ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2 ◁ C2×#41 ◁ #568

Complements

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

NH ≅ G/Ntype
1. #19152434C2semidirect
2. C2×#15668058C2semidirect
3. #19152410C2semidirect
4. #19152403C2semidirect
5. #19152398C2semidirect
6. C2×#15668040C2semidirect
7. #568×C89C2semidirect
9. #15668059C22semidirect
11. #15668058C22semidirect
12. #15668058C22semidirect
15. C2×#13083574C22semidirect
16. C2×#13083574C22semidirect
18. C22×D356C22semidirect
20. #15668045C22semidirect
21. #15668045C22semidirect
22. #15668040C22semidirect
23. #15668040C22semidirect
24. #15668040C22semidirect
25. #15668034C22semidirect
26. C2×#13083563C22semidirect
27. C2×D712C22semidirect
29. #131×C89C22semidirect
30. C2×M16×C89C22semidirect
39. #13083574C23semidirect
42. C2×Dic178C23semidirect
48. C2×D356C23semidirect
55. Dic356C23semidirect
56. #13083563C23semidirect
57. #13083563C23semidirect
58. D712C23semidirect
65. M16×C89C23semidirect
66. C2×C8×C89C23semidirect
115. C89#3585semidirect
122. #568D89semidirect
144. #131C2×D89semidirect
145. C2×M16C2×D89semidirect
180. M16C22×D89semidirect
181. C2×C8C22×D89semidirect

Maximal subgroups

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

subgroupindex
#191524342
C2×#156680582
#191524102
#191524032
#191523982
C2×#156680402
#568×C892
#358589