Finite Group Databasebeta

← #14271962

Subgroups — #14271962

Order 1856.

262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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#41×D29C211yesmaximal, characteristic, complemented
2C2×#90809C211yesmaximal, characteristic, complemented
3C29×#137C211yesmaximal, characteristic, complemented
4#11745311C211yesmaximal, characteristic, complemented
5#11745304C211yesmaximal, characteristic, complemented
6#11745281C212yesmaximal, complemented
7#11745280C212yesmaximal, complemented
8#11745278C212yesmaximal, complemented
9#11745276C212yesmaximal, complemented
10#11745270C211yesmaximal, characteristic, complemented
11M16×D29C211yesmaximal, characteristic, complemented
12#41×C29C2211yescharacteristic
13C2×Q8×C29C2211yescharacteristic, complemented
14#90809—21no—
15#90809—21no—
16#90809C2212yes—
17#90809C2211yescharacteristic, complemented
18#90809C2212yescomplemented
19Q8×D29C2211yescharacteristic, complemented
20#90807—21no—
21#90807C2211yescharacteristic, complemented
22D4×D29—21no—
23D4×D29C2211yescharacteristic, complemented
24#90805—21no—
25#90805C2211yescharacteristic
26C2×D116—21no—
27C2×D116C2211yescharacteristic, complemented
28C2×C4×D29—21no—
29C2×C4×D29—21no—
30C2×C4×D29C2211yescharacteristic
31Q16×C29C2212yescomplemented
32SD16×C29C2212yescomplemented
33M16×C29C2211yescharacteristic, complemented
34#90785C2212yescomplemented
35#90784C2212yescomplemented
36#90784C2212yescomplemented
37#90782C2212yescomplemented
38#90777C2211yescharacteristic, complemented
39D232C2212yescomplemented
40#90773C2212yescomplemented
41#90772C2212yescomplemented
42C8×D29C2212yescomplemented
43C22×D29—21no—
44C22×D29—21no—
45C22×D29D411yescharacteristic
46Q8×C29—21no—
47Q8×C29C2311yescharacteristic
48Q8×C29C2312yes—
49D4×C29—21no—
50D4×C29C2311yescharacteristic
51C2×C4×C29—21no—
52C2×C4×C29—21no—
53C2×C4×C29C2311yescharacteristic
54C22⋊D29—21no—
55C22⋊D29—21no—
56C22⋊D29—21no—
57C2×Dic29—21no—
58C2×Dic29D411yescharacteristic
59D116—22no—
60D116—22no—
61D116—21no—
62D116—21no—
63D116C2312yes—
64D116C2311yescharacteristic
65C4×D29—21no—
66C4×D29—21no—
67C4×D29—21no—
68C4×D29—22no—
69C4×D29—22no—
70C4×D29D411yescharacteristic
71C4×D29D411yescharacteristic
72C4×D29C2311yescharacteristic
73C4×D29C2311yescharacteristic
74Dic58—21no—
75Dic58C2311yescharacteristic
76C8×C29C2312yes—
77#6597C2312yes—
78C22×C29—21no—
79C22×C29C2×D411yescharacteristic
80C2×D29—22no—
81C2×D29—21no—
82C2×D29—41no—
83C2×D29—42no—
84C2×D29—42no—
85C2×D29C2×D411yescharacteristic
86C2×D29C2×D411yescharacteristic
87C4×C29—21no—
88C4×C29—22no—
89C4×C29C2×D411yescharacteristic
90C4×C29C2411yescharacteristic
91Dic29—21no—
92Dic29C2×D411yescharacteristic
93Dic29C2×D411yescharacteristic
94#575—291nomaximal, Sylow
95C2×C29—21no—
96C2×C29—41no—
97C2×C29C22×D411yescharacteristic
98D29—21no—
99D29—21no—
100D29—42no—
101D29—41no—
102C2×#41—291no—
103C2×#41—291no—
104#137—291no—
105#137—292no—
106#137D2911yescharacteristic, complemented
107AGL(1,ℤ/8)—291no—
108AGL(1,ℤ/8)—292no—
109AGL(1,ℤ/8)—291no—
110#135—292no—
111#135—292no—
112C2×M16—291no—
113C29#57511yescharacteristic, complemented, Sylow
114#41—291no—
115#41—292no—
116#41—292no—
117#41—291no—
118#41—291no—
119#41—581no—
120#41—581no—
121#41—581no—
122#41—581no—
123#41C2×D2911yescharacteristic
124C2×Q8—291no—
125C2×Q8C2×D2911yescharacteristic, complemented
126C2×D4—291no—
127C2×D4—291no—
128C2×D4—581no—
129C2×D4—581no—
130C22×C4—291no—
131C22×C4—581no—
132C22×C4—581no—
133Q16—292no—
134Q16C2×D2912yescomplemented
135SD16—292no—
136SD16—292no—
137SD16—292no—
138SD16C2×D2912yescomplemented
139D8—292no—
140D8—292no—
141M16—291no—
142M16—292no—
143M16C2×D2911yescharacteristic, complemented
144C2×C8—292no—
145C23—291no—
146C23—581no—
147C23—581no—
148Q8—21no—
149Q8—291no—
150Q8—581no—
151Q8C22×D2911yescharacteristic
152Q8C22×D2912yes—
153D4—21no—
154D4—292no—
155D4—291no—
156D4—581no—
157D4—582no—
158D4—582no—
159D4—581no—
160D4—581no—
161D4—581no—
162D4—581no—
163D4C22×D2911yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—291no—
167C2×C4—291no—
168C2×C4—291no—
169C2×C4—291no—
170C2×C4—291no—
171C2×C4—581no—
172C2×C4—582no—
173C2×C4—582no—
174C2×C4—581no—
175C2×C4—581no—
176C2×C4—581no—
177C2×C4C22×D2911yescharacteristic
178C8—292no—
179C8C22×D2912yes—
180C22—21no—
181C22—291no—
182C22—291no—
183C22—582no—
184C22—581no—
185C22—1161no—
186C22—1162no—
187C22—1162no—
188C22D4×D2911yescharacteristic
189C4—21no—
190C4—22no—
191C4—291no—
192C4—291no—
193C4—581no—
194C4D4×D2911yescharacteristic
195C4C23×D2911yescharacteristic
196C2—21no—
197C2—41no—
198C2—581no—
199C2—581no—
200C2—1162no—
201C2—1161no—
202C2C2×D4×D2911yescharacteristic
subgroupG/H
centerC2C2×D4×D29
commutator, cosocleC4×C29C24
FrattiniC4C23×D29
FittingC29×#137C2
socleC2×C29C22×D4
hypercenter#137D29
hypocenterC29#575
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. #41×D29C2semidirect
2. C2×#90809C2semidirect
3. C29×#137C2semidirect
4. #11745311C2semidirect
5. #11745304C2semidirect
6. #11745281C2semidirect
7. #11745280C2semidirect
8. #11745278C2semidirect
9. #11745276C2semidirect
10. #11745270C2semidirect
11. M16×D29C2semidirect
13. C2×Q8×C29C22semidirect
17. #90809C22semidirect
18. #90809C22semidirect
19. Q8×D29C22semidirect
21. #90807C22semidirect
23. D4×D29C22semidirect
27. C2×D116C22semidirect
31. Q16×C29C22semidirect
32. SD16×C29C22semidirect
33. M16×C29C22semidirect
34. #90785C22semidirect
35. #90784C22semidirect
36. #90784C22semidirect
37. #90782C22semidirect
38. #90777C22semidirect
39. D232C22semidirect
40. #90773C22semidirect
41. #90772C22semidirect
42. C8×D29C22semidirect
106. #137D29semidirect
113. C29#575semidirect
125. C2×Q8C2×D29semidirect
134. Q16C2×D29semidirect
138. SD16C2×D29semidirect
143. M16C2×D29semidirect

Maximal subgroups

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

subgroupindex
#41×D292
C2×#908092
C29×#1372
#117453112
#117453042
#117452812
#117452802
#117452782
#117452762
#117452702
M16×D292
#57529