Finite Group Databasebeta

← #26041920

Subgroups — #26041920

Order 11584.

334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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×#15668450C211yesmaximal, characteristic, complemented
2C22×D724C211yesmaximal, characteristic, complemented
3#19153805C211yesmaximal, characteristic, complemented
4#19153801C212yesmaximal, complemented
5#19153791C211yesmaximal, characteristic, complemented
6#19153791C212yesmaximal, complemented
7#19153786C212yesmaximal, complemented
8#19153778C211yesmaximal, characteristic, complemented
9C4×C22⋊D181C211yesmaximal, characteristic, complemented
10C22⋊C4×D181C212yesmaximal, complemented
11C22⋊Q8×C181C211yesmaximal, characteristic, complemented
12C23×D181C2212yes—
13#15668450—24no—
14C2×D724—24no—
15C2×D724C2212yes—
16C2×D724C2211yescharacteristic
17C2×D724C2211yescharacteristic
18C2×D724C2212yescomplemented
19C2×D724C2212yescomplemented
20C2×C22⋊D181C2211yescharacteristic
21C2×C4×D181C2212yescomplemented
22C2×C4×D181C2211yescharacteristic, complemented
23C2×C4×D181C2212yescomplemented
24#15668428C2211yescharacteristic, complemented
25C22⋊Dic181C2211yescharacteristic
26#15668426C2212yescomplemented
27#15668426C2212yescomplemented
28#15668426C2211yescharacteristic, complemented
29#15668426C2212yescomplemented
30#15668426C2212yescomplemented
31C4×Dic181C2211yescharacteristic, complemented
32C2×Q8×C181C2211yescharacteristic, complemented
33C22×C4×C181C2211yescharacteristic
34C4⋊C4×C181C2211yescharacteristic, complemented
35C4⋊C4×C181C2212yescomplemented
36C22⋊C4×C181C2212yes—
37C22×D181—24no—
38C22×D181—24no—
39C22×D181—42no—
40C22×D181C2312yes—
41C22×D181C2311yescharacteristic
42C22×D181C2312yes—
43D724—24no—
44D724—24no—
45D724—22no—
46D724—42no—
47D724D414yescomplemented
48C22⋊D181—22no—
49C2×Dic181C2311yescharacteristic
50C2×Dic181C2311yescharacteristic
51C2×Dic181C2311yescharacteristic
52C4×D181—24no—
53C4×D181—22no—
54C4×D181—42no—
55C23×C181C2311yescharacteristic
56Q8×C181—22no—
57C2×C4×C181—22no—
58C2×C4×C181C2312yes—
59C2×C4×C181C2312yes—
60C2×C4×C181C2311yescharacteristic
61C2×C4×C181C2311yescharacteristic
62C22×C181—21no—
63C22×C181—21no—
64C22×C181#4112yescomplemented
65C22×C181C2411yescharacteristic
66C2×D181—22no—
67C2×D181—22no—
68C2×D181—21no—
69C2×D181—22no—
70C2×D181—21no—
71C2×D181—22no—
72C2×D181—21no—
73C2×D181—22no—
74C2×D181—48no—
75C2×D181C2×D414yes—
76C4×C181—21no—
77C4×C181—22no—
78C4×C181—22no—
79C4×C181C2×D412yes—
80Dic181—21no—
81Dic181—21no—
82Dic181—21no—
83C2×C181—22no—
84C2×C181C22×D411yescharacteristic
85C2×C181C2×#4111yescharacteristic
86C2×C181H(5,𝔽2)11yescharacteristic
87D181—24no—
88D181—41no—
89D181—42no—
90C181#54611yescharacteristic, complemented, Sylow
91#546—1811nomaximal, Sylow
92C2×#41—1811no—
93C22×D4—1811no—
94#124—1811no—
95#123—1812no—
96C22⋊Q8D18111yescharacteristic, complemented
97#121—1811no—
98#121—1812no—
99#120—1812no—
100C4×D4—1811no—
101C4×D4—1811no—
102C2×C22⋊C4—1812no—
103C24—1812no—
104#41—3624no—
105C2×Q8C2×D18111yescharacteristic, complemented
106C2×D4—3624no—
107C2×D4—1811no—
108C2×D4—1812no—
109C2×D4—1812no—
110C2×D4—1811no—
111C2×D4—1811no—
112C2×D4—1812no—
113C22×C4—1812no—
114C22×C4—1811no—
115C22×C4—1812no—
116C22×C4C2×D18111yescharacteristic
117C4⋊C4—1811no—
118C4⋊C4C2×D18111yescharacteristic, complemented
119C4⋊C4C2×D18112yescomplemented
120C22⋊C4—1811no—
121C22⋊C4—1812no—
122C22⋊C4—1812no—
123C22⋊C4—1812no—
124C22⋊C4—1811no—
125C22⋊C4—1812no—
126C22⋊C4C2×D18112yes—
127C42—1811no—
128C23—3624no—
129C23—3624no—
130C23—1812no—
131C23—1811no—
132C23—1812no—
133C23—7242no—
134C23C22×D18111yescharacteristic
135Q8—22no—
136D4—3624no—
137D4—3624no—
138D4—3622no—
139D4—3622no—
140D4—1814no—
141D4—7242no—
142C2×C4—22no—
143C2×C4—3624no—
144C2×C4—3622no—
145C2×C4—1811no—
146C2×C4—1811no—
147C2×C4—1811no—
148C2×C4—7242no—
149C2×C4C22×D18112yes—
150C2×C4C22×D18112yes—
151C2×C4C22×D18111yescharacteristic
152C2×C4C22×D18111yescharacteristic
153C22—21no—
154C22—21no—
155C22—3622no—
156C22—3622no—
157C22—3621no—
158C22—3622no—
159C22—3621no—
160C22—3622no—
161C22—3621no—
162C22—3622no—
163C22—1814no—
164C22—7248no—
165C22#1566845012yescomplemented
166C22C23×D18111yescharacteristic
167C4—21no—
168C4—22no—
169C4—22no—
170C4—3621no—
171C4—3621no—
172C4—3621no—
173C4D4×D18112yes—
174C2—22no—
175C2—3624no—
176C2—7242no—
177C2—7241no—
178C2C2×D4×D18111yescharacteristic
179C2C2×#1566845011yescharacteristic
180C2#1915386211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D181
commutator, socle, cosocleC22×C181C24
FittingC22⋊Q8×C181C2
hypercenterC22⋊Q8D181
hypocenterC181#546
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#15668450C2semidirect
2. C22×D724C2semidirect
3. #19153805C2semidirect
4. #19153801C2semidirect
5. #19153791C2semidirect
6. #19153791C2semidirect
7. #19153786C2semidirect
8. #19153778C2semidirect
9. C4×C22⋊D181C2semidirect
10. C22⋊C4×D181C2semidirect
11. C22⋊Q8×C181C2semidirect
18. C2×D724C22semidirect
19. C2×D724C22semidirect
21. C2×C4×D181C22semidirect
22. C2×C4×D181C22semidirect
23. C2×C4×D181C22semidirect
24. #15668428C22semidirect
26. #15668426C22semidirect
27. #15668426C22semidirect
28. #15668426C22semidirect
29. #15668426C22semidirect
30. #15668426C22semidirect
31. C4×Dic181C22semidirect
32. C2×Q8×C181C22semidirect
34. C4⋊C4×C181C22semidirect
35. C4⋊C4×C181C22semidirect
47. D724D4semidirect
64. C22×C181#41semidirect
90. C181#546semidirect
96. C22⋊Q8D181semidirect
105. C2×Q8C2×D181semidirect
118. C4⋊C4C2×D181semidirect
119. C4⋊C4C2×D181semidirect
165. C22#15668450semidirect

Maximal subgroups

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

subgroupindex
C2×#156684502
C22×D7242
#191538052
#191538012
#191537912
#191537862
#191537782
C4×C22⋊D1812
C22⋊C4×D1812
C22⋊Q8×C1812
#546181