Finite Group Databasebeta

← #26030718

Subgroups — #26030718

Order 11392.

572 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C2×#15668045C212yesmaximal, complemented
2C2×#15668040C212yesmaximal, complemented
3#19152148C211yesmaximal, characteristic, complemented
4C2×#15668000C211yesmaximal, characteristic, complemented
5#19151992C212yesmaximal, complemented
6#19151987C212yesmaximal, complemented
7#19151982C214yesmaximal, complemented
8C4×M16×C89C211yesmaximal, characteristic, complemented
9C2×#13083574C2212yes—
10C22×Dic178C2211yescharacteristic
11C22×D356C2211yescharacteristic
12#15668045—28no—
13#15668040—28no—
14C2×Dic356C2214yescomplemented
15C2×#13083563C2214yes—
16C2×#13083563C2214yescomplemented
17C2×D712C2214yes—
18#15668012C2211yescharacteristic, complemented
19#15668009C2211yescharacteristic, complemented
20#15668000—22no—
21#15668000C2212yes—
22#15668000C2212yes—
23#15668000C2212yescomplemented
24#15667986—22no—
25C4×D356—22no—
26C2×#13083551—22no—
27C2×M16×C89C2212yes—
28C2×C42×C89C2211yescharacteristic
29#97×C89C2212yescomplemented
30C4×C8×C89C2212yescomplemented
31C23×D89—21no—
32#13083574—24no—
33#13083574—24no—
34C2×Dic178—24no—
35C2×Dic178—21no—
36C2×Dic178C2312yes—
37C2×Dic178C2312yes—
38C2×D356—24no—
39C2×D356—22no—
40C2×D356—21no—
41C2×D356C2312yes—
42C2×D356C2312yes—
43C2×C22⋊D89—22no—
44C22×Dic89—21no—
45C2×C4×D89—22no—
46Dic356—28no—
47#13083563—28no—
48#13083563—28no—
49D712—28no—
50C4⋊Dic89—22no—
51#13083551—24no—
52#13083551—24no—
53#13083551—24no—
54C22×C4×C89D412yes—
55C22×C4×C89C2311yescharacteristic
56M16×C89D418yescomplemented
57C2×C8×C89C2314yes—
58C42×C89D412yes—
59C42×C89C2311yescharacteristic
60C42×C89C2311yescharacteristic
61C23×C89C2×D411yescharacteristic
62C22×D89—22no—
63C22×D89—22no—
64C22×D89—44no—
65C22×D89—42no—
66C2×C4×C89—42no—
67C2×C4×C89C2×D412yes—
68C2×C4×C89C2×D412yes—
69C2×C4×C89C2×D411yescharacteristic
70C2×C4×C89C2×D414yes—
71C2×C4×C89C2411yescharacteristic
72C22⋊D89—44no—
73C2×Dic89—22no—
74C2×Dic89—22no—
75C2×Dic89—42no—
76D356—22no—
77D356—24no—
78D356—22no—
79D356—44no—
80D356—42no—
81C4×D89—44no—
82Dic178—22no—
83Dic178—24no—
84Dic178—22no—
85Dic178—42no—
86C8×C89C2×D418yes—
87C22×C89—22no—
88C22×C89#12712yes—
89C22×C89C22×D411yescharacteristic
90C2×D89—42no—
91C2×D89—42no—
92C2×D89—44no—
93C2×D89—44no—
94C2×D89—84no—
95C4×C89—22no—
96C4×C89—22no—
97C4×C89#12712yes—
98C4×C89C22×D412yes—
99Dic89—42no—
100Dic89—42no—
101C2×C89—22no—
102C2×C89C2×#12711yescharacteristic
103C2×C89#57512yes—
104D89—82no—
105D89—82no—
106#3153—891nomaximal, Sylow
107C89#315311yescharacteristic, complemented, Sylow
108C2×#137—892no—
109C2×AGL(1,ℤ/8)—892no—
110#532—891no—
111C2×#124—891no—
112#497—892no—
113#496—892no—
114#495—894no—
115C4×M16D8911yescharacteristic, complemented
116C2×#41—892no—
117C22×Q8—891no—
118C22×D4—891no—
119#137—1788no—
120AGL(1,ℤ/8)—1788no—
121C2×Q16—894no—
122C2×SD16—894no—
123C2×SD16—894no—
124C2×D8—894no—
125C2×M16C2×D8912yes—
126C4⋊Q8—891no—
127#127—891no—
128#124—892no—
129#124—892no—
130#124—892no—
131#124—1782no—
132#121—1782no—
133C4×D4—1782no—
134C2×C22⋊C4—1782no—
135C2×C42C2×D8911yescharacteristic
136#97C2×D8912yescomplemented
137C4×C8C2×D8912yescomplemented
138C24—1781no—
139#41—1784no—
140#41—1784no—
141C2×Q8—892no—
142C2×Q8—892no—
143C2×Q8—1784no—
144C2×Q8—1781no—
145C2×D4—892no—
146C2×D4—892no—
147C2×D4—1782no—
148C2×D4—1782no—
149C2×D4—1781no—
150C2×D4—1784no—
151C22×C4—1781no—
152C22×C4—1782no—
153C22×C4D35612yes—
154C22×C4C22×D8911yescharacteristic
155Q16—1788no—
156SD16—1788no—
157SD16—1788no—
158D8—1788no—
159M16D35618yescomplemented
160C2×C8C22×D8914yes—
161C4⋊C4—1782no—
162C22⋊C4—1784no—
163C22⋊C4—1784no—
164C22⋊C4—1784no—
165C42D35612yes—
166C42C22×D8911yescharacteristic
167C42C22×D8911yescharacteristic
168C23—3564no—
169C23—3562no—
170C23—1782no—
171C23—1782no—
172C23C2×D35611yescharacteristic
173Q8—3562no—
174Q8—1782no—
175Q8—1784no—
176Q8—1782no—
177D4—3564no—
178D4—3564no—
179D4—3562no—
180D4—1782no—
181D4—1784no—
182D4—1782no—
183C2×C4—42no—
184C2×C4—3562no—
185C2×C4—3564no—
186C2×C4—1782no—
187C2×C4—1782no—
188C2×C4C2×D35612yes—
189C2×C4C2×D35612yes—
190C2×C4C2×D35611yescharacteristic
191C2×C4C2×D35614yes—
192C2×C4C23×D8911yescharacteristic
193C8C2×D35618yes—
194C22—22no—
195C22—3562no—
196C22—3562no—
197C22—3564no—
198C22—3564no—
199C22—7124no—
200C22#1566800912yes—
201C22C22×D35611yescharacteristic
202C4—22no—
203C4—22no—
204C4—3562no—
205C4—3562no—
206C4#1566800912yes—
207C4C22×D35612yes—
208C2—22no—
209C2—7122no—
210C2—7122no—
211C2C2×#1566800911yescharacteristic
212C2#1915239812yes—
subgroupG/H
centerC22C22×D356
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC4×M16×C89C2
socleC22×C89C22×D4
hypercenterC4×M16D89
hypocenterC89#3153
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#15668045C2semidirect
2. C2×#15668040C2semidirect
3. #19152148C2semidirect
4. C2×#15668000C2semidirect
5. #19151992C2semidirect
6. #19151987C2semidirect
7. #19151982C2semidirect
8. C4×M16×C89C2semidirect
14. C2×Dic356C22semidirect
16. C2×#13083563C22semidirect
18. #15668012C22semidirect
19. #15668009C22semidirect
23. #15668000C22semidirect
29. #97×C89C22semidirect
30. C4×C8×C89C22semidirect
56. M16×C89D4semidirect
107. C89#3153semidirect
115. C4×M16D89semidirect
136. #97C2×D89semidirect
137. C4×C8C2×D89semidirect
159. M16D356semidirect

Maximal subgroups

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

subgroupindex
C2×#156680452
C2×#156680402
#191521482
C2×#156680002
#191519922
#191519872
#191519822
C4×M16×C892
#315389