Finite Group Databasebeta

← #16821508

Subgroups — #16821508

Order 3712.

248 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 41 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#14271905C211yesmaximal, characteristic, complemented
2#14271336C212yesmaximal, complemented
3#14270960C211yesmaximal, characteristic, complemented
4#14270959C212yesmaximal, complemented
5C29×#454C211yesmaximal, characteristic, complemented
6C29×2−1+4C2211yescharacteristic, complemented
7C29×AGL(1,ℤ/8)—21no—
8C29×#124C2211yescharacteristic
9#11745311—22no—
10#11745309C2212yes—
11#11745299—21no—
12#11745247—22no—
13#11745244—22no—
14#11745237—21no—
15C29×#104—21no—
16C29×#101C2211yescharacteristic, complemented
17#11745185—22no—
18#11745184C2212yescomplemented
19C23×D29—21no—
20#41×C29—22no—
21#41×C29—21no—
22#41×C29—41no—
23C2×Q8×C29—41no—
24C2×Q8×C29C2311yescharacteristic
25C2×D4×C29D411yescharacteristic
26C2×C22⋊D29—22no—
27C2×D116—21no—
28C2×D116D412yes—
29C2×Dic58—21no—
30SD16×C29—41no—
31D8×C29—41no—
32M16×C29—21no—
33C22⋊C4×C29—22no—
34C42×C29D411yescharacteristic
35C22⋊Dic29—21no—
36#90784—42no—
37#90782—42no—
38#90781—22no—
39#90781—22no—
40#90781—22no—
41C4×Dic29D412yes—
42#90777—22no—
43C23×C29—21no—
44C22×D29—22no—
45C22×D29—82no—
46C22×D29—81no—
47Q8×C29—22no—
48Q8×C29—21no—
49Q8×C29—41no—
50D4×C29—22no—
51D4×C29—21no—
52D4×C29—41no—
53D4×C29—41no—
54C2×C4×C29—21no—
55C2×C4×C29—42no—
56C2×C4×C29—41no—
57C2×C4×C29C2×D412yes—
58C2×C4×C29C2×D411yescharacteristic
59C22⋊D29—82no—
60C2×Dic29—22no—
61D116—42no—
62D116—81no—
63Dic58—81no—
64C8×C29—41no—
65#6597—42no—
66#2202—291nomaximal, Sylow
67C22×C29—42no—
68C22×C29—41no—
69C22×C29—41no—
70C22×C29#12011yescharacteristic
71C2×D29—42no—
72C2×D29—42no—
73C2×D29—42no—
74C2×D29—84no—
75C4×C29—22no—
76C4×C29—21no—
77C4×C29—41no—
78C4×C29—41no—
79Dic29—42no—
80H(3,𝔽4)—291no—
81#454—292no—
82#454D2911yescharacteristic, complemented
83#355—291no—
84#355—292no—
85C2×C29—21no—
86C2×C29—81no—
87C2×C29—81no—
88C2×C29B(4,𝔽2)11yescharacteristic
89D29—82no—
902−1+4C2×D2911yescharacteristic, complemented
91AGL(1,ℤ/8)—21no—
92AGL(1,ℤ/8)—582no—
93#124—292no—
94#124—582no—
95#124—581no—
96#124C2×D2911yescharacteristic
97#120—582no—
98#120—581no—
99#104—21no—
100#104—582no—
101#101—292no—
102#101C2×D2911yescharacteristic, complemented
103C29#220211yescharacteristic, complemented, Sylow
104C24—581no—
105#41—22no—
106#41—21no—
107#41—41no—
108C2×Q8—41no—
109C2×Q8—581no—
110C2×Q8C22×D2911yescharacteristic
111C2×D4—292no—
112C2×D4—581no—
113C2×D4—582no—
114C2×D4C22⋊D2911yescharacteristic
115SD16—41no—
116SD16—1162no—
117D8—41no—
118D8—1162no—
119M16—21no—
120M16—582no—
121C22⋊C4—22no—
122C22⋊C4—582no—
123C22⋊C4—581no—
124C22⋊C4—582no—
125C22⋊C4—582no—
126C42—292no—
127C42C22⋊D2911yescharacteristic
128C23—21no—
129C23—582no—
130C23—2322no—
131C23—2321no—
132Q8—21no—
133Q8—22no—
134Q8—41no—
135Q8—2321no—
136D4—21no—
137D4—22no—
138D4—41no—
139D4—41no—
140D4—1162no—
141D4—2321no—
142D4—2322no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—42no—
146C2×C4—582no—
147C2×C4D4×D2912yes—
148C2×C4C2×C22⋊D2911yescharacteristic
149C8—41no—
150C8—1162no—
151C22—42no—
152C22—41no—
153C22—41no—
154C22—1162no—
155C22—1162no—
156C22—1162no—
157C22—2324no—
158C22#1174529911yescharacteristic
159C4—21no—
160C4—22no—
161C4—41no—
162C4—41no—
163C4—1162no—
164C2—21no—
165C2—81no—
166C2—81no—
167C2—2322no—
168C2#1427134911yescharacteristic
subgroupG/H
centerC2#14271349
commutator, cosocleC2×Q8×C29C23
FrattiniC2×Q8C22×D29
FittingC29×#454C2
socleC2×C29B(4,𝔽2)
hypercenter#454D29
hypocenterC29#2202
LCSG ▷ C2×Q8×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #14271905C2semidirect
2. #14271336C2semidirect
3. #14270960C2semidirect
4. #14270959C2semidirect
5. C29×#454C2semidirect
6. C29×2−1+4C22semidirect
16. C29×#101C22semidirect
18. #11745184C22semidirect
82. #454D29semidirect
90. 2−1+4C2×D29semidirect
102. #101C2×D29semidirect
103. C29#2202semidirect

Maximal subgroups

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

subgroupindex
#142719052
#142713362
#142709602
#142709592
C29×#4542
#220229