Finite Group Databasebeta

← #14271969

Subgroups — #14271969

Order 1856.

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

normal subgroups only

This group has 258 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#11745362C211yesmaximal, characteristic, complemented
2#11745359C211yesmaximal, characteristic, complemented
3C2×SD16×C29C211yesmaximal, characteristic, complemented
4#11745304C211yesmaximal, characteristic, complemented
5#11745294C211yesmaximal, characteristic, complemented
6#11745278C212yesmaximal, complemented
7#11745277C212yesmaximal, complemented
8#11745276C212yesmaximal, complemented
9SD16×D29C212yesmaximal, complemented
10#11745266C211yesmaximal, characteristic, complemented
11#11745263C211yesmaximal, characteristic, complemented
12C2×Q8×C29C2211yescharacteristic, complemented
13C2×D4×C29C2211yescharacteristic
14C2×C22⋊D29—22no—
15#90809—21no—
16#90809C2212yescomplemented
17Q8×D29—21no—
18Q8×D29C2212yescomplemented
19#90807—21no—
20#90807C2212yes—
21D4×D29—21no—
22D4×D29C2212yes—
23#90805—22no—
24#90805C2211yescharacteristic
25#90805C2211yescharacteristic
26#90805C2211yescharacteristic, complemented
27SD16×C29C2212yescomplemented
28SD16×C29C2212yescomplemented
29C2×C8×C29C2211yescharacteristic, complemented
30#90785C2212yescomplemented
31#90784C2212yescomplemented
32#90783C2212yescomplemented
33#90782C2212yescomplemented
34#90777C2211yescharacteristic, complemented
35Dic116C2211yescharacteristic, complemented
36D232C2211yescharacteristic, complemented
37#90773C2211yescharacteristic, complemented
38#90773C2211yescharacteristic, complemented
39#90772C2212yescomplemented
40C8×D29C2212yescomplemented
41C23×C29—21no—
42C22×D29—22no—
43Q8×C29—21no—
44Q8×C29C2312yes—
45D4×C29—21no—
46D4×C29C2312yes—
47C2×C4×C29—21no—
48C2×C4×C29C2311yescharacteristic
49C22⋊D29—21no—
50C22⋊D29—21no—
51C22⋊D29—22no—
52C22⋊D29—22no—
53C22⋊D29D412yes—
54C2×Dic29—22no—
55D116—22no—
56D116D411yescharacteristic
57D116C2311yescharacteristic
58D116C2311yescharacteristic
59C4×D29—22no—
60C4×D29—21no—
61C4×D29—21no—
62C4×D29—22no—
63C4×D29C2312yes—
64Dic58—22no—
65Dic58D411yescharacteristic
66Dic58C2311yescharacteristic
67Dic58C2311yescharacteristic
68C8×C29C2311yescharacteristic
69C8×C29C2311yescharacteristic
70#6597C2312yes—
71C22×C29—22no—
72C22×C29—81no—
73C22×C29C2×D411yescharacteristic
74C2×D29—21no—
75C2×D29—21no—
76C2×D29—82no—
77C2×D29C2×D412yes—
78C4×C29—22no—
79C4×C29C2×D411yescharacteristic
80C4×C29C2411yescharacteristic
81Dic29—21no—
82Dic29—21no—
83Dic29C2×D412yes—
84#577—291nomaximal, Sylow
85C2×C29—21no—
86C2×C29—42no—
87C2×C29C22×D411yescharacteristic
88D29—22no—
89D29—41no—
90D29—41no—
912−1+4—291no—
92H(5,𝔽2)—291no—
93#137—291no—
94#137—292no—
95AGL(1,ℤ/8)—291no—
96AGL(1,ℤ/8)—292no—
97#135—292no—
98#135—291no—
99C2×SD16—292no—
100C2×SD16D2911yescharacteristic, complemented
101#131—291no—
102C29#57711yescharacteristic, complemented, Sylow
103#41—291no—
104#41—292no—
105#41—292no—
106#41—291no—
107#41—291no—
108#41—582no—
109#41—581no—
110#41—581no—
111C2×Q8—292no—
112C2×Q8—581no—
113C2×Q8C2×D2911yescharacteristic, complemented
114C2×D4—292no—
115C2×D4—581no—
116C2×D4—582no—
117C2×D4C2×D2911yescharacteristic
118Q16—292no—
119Q16—291no—
120SD16—292no—
121SD16—292no—
122SD16—291no—
123SD16—291no—
124SD16C2×D2912yescomplemented
125SD16C2×D2912yescomplemented
126D8—292no—
127D8—291no—
128M16—291no—
129M16—292no—
130C2×C8—292no—
131C2×C8C2×D2911yescharacteristic, complemented
132C23—21no—
133C23—582no—
134Q8—21no—
135Q8—291no—
136Q8—291no—
137Q8—291no—
138Q8—582no—
139Q8C22×D2912yes—
140D4—21no—
141D4—292no—
142D4—291no—
143D4—291no—
144D4—291no—
145D4—582no—
146D4—582no—
147D4—582no—
148D4—581no—
149D4—581no—
150D4C22×D2912yes—
151C2×C4—21no—
152C2×C4—292no—
153C2×C4—582no—
154C2×C4—582no—
155C2×C4—582no—
156C2×C4—581no—
157C2×C4—581no—
158C2×C4C22×D2911yescharacteristic
159C8—292no—
160C8C22×D2911yescharacteristic
161C8C22×D2911yescharacteristic
162C22—22no—
163C22—81no—
164C22—292no—
165C22—581no—
166C22—581no—
167C22—2322no—
168C22D4×D2911yescharacteristic
169C4—22no—
170C4—292no—
171C4—581no—
172C4—581no—
173C4D4×D2911yescharacteristic
174C4C23×D2911yescharacteristic
175C2—21no—
176C2—42no—
177C2—582no—
178C2—1161no—
179C2—1161no—
180C2C2×D4×D2911yescharacteristic
subgroupG/H
centerC2C2×D4×D29
commutator, cosocleC4×C29C24
FrattiniC4C23×D29
FittingC2×SD16×C29C2
socleC2×C29C22×D4
hypercenterC2×SD16D29
hypocenterC29#577
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #11745362C2semidirect
2. #11745359C2semidirect
3. C2×SD16×C29C2semidirect
4. #11745304C2semidirect
5. #11745294C2semidirect
6. #11745278C2semidirect
7. #11745277C2semidirect
8. #11745276C2semidirect
9. SD16×D29C2semidirect
10. #11745266C2semidirect
11. #11745263C2semidirect
12. C2×Q8×C29C22semidirect
16. #90809C22semidirect
18. Q8×D29C22semidirect
26. #90805C22semidirect
27. SD16×C29C22semidirect
28. SD16×C29C22semidirect
29. C2×C8×C29C22semidirect
30. #90785C22semidirect
31. #90784C22semidirect
32. #90783C22semidirect
33. #90782C22semidirect
34. #90777C22semidirect
35. Dic116C22semidirect
36. D232C22semidirect
37. #90773C22semidirect
38. #90773C22semidirect
39. #90772C22semidirect
40. C8×D29C22semidirect
100. C2×SD16D29semidirect
102. C29#577semidirect
113. C2×Q8C2×D29semidirect
124. SD16C2×D29semidirect
125. SD16C2×D29semidirect
131. C2×C8C2×D29semidirect

Maximal subgroups

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

subgroupindex
#117453622
#117453592
C2×SD16×C292
#117453042
#117452942
#117452782
#117452772
#117452762
SD16×D292
#117452662
#117452632
#57729