Finite Group Databasebeta

← #16821438

Subgroups — #16821438

Order 3712.

226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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#14271598C212yesmaximal, complemented
2#14271416C211yesmaximal, characteristic, complemented
3#14270973C212yesmaximal, complemented
4#14270945C211yesmaximal, characteristic, complemented
5C29×#575C211yesmaximal, characteristic, complemented
6C2×#41×C29—21no—
7C29×#137—22no—
8C29×AGL(1,ℤ/8)—22no—
9C29×#135—21no—
10C29×#135C2212yes—
11C2×M16×C29C2211yescharacteristic
12#11745292—21no—
13C2×D232C2211yescharacteristic, complemented
14#11745176—22no—
15#11745174—22no—
16#11745169—21no—
17#11745165C2211yescharacteristic, complemented
18#11745160C2212yescomplemented
19#41×C29—22no—
20#41×C29—22no—
21#41×C29—41no—
22#41×C29—41no—
23C2×Q8×C29—21no—
24C2×D4×C29—21no—
25C2×D4×C29—41no—
26C22×C4×C29—41no—
27C22×C4×C29D411yescharacteristic
28C2×C22⋊D29—41no—
29C2×D116—21no—
30Q16×C29—21no—
31Q16×C29D412yescomplemented
32SD16×C29—22no—
33SD16×C29—22no—
34D8×C29—21no—
35D8×C29D412yescomplemented
36M16×C29—22no—
37C2×C8×C29D411yescharacteristic
38C2×C8×C29C2311yescharacteristic
39#90781—41no—
40C4⋊Dic29—21no—
41D232—22no—
42#90768—22no—
43C23×C29—41no—
44C23×C29D811yescharacteristic
45C22×D29—41no—
46Q8×C29—22no—
47Q8×C29—41no—
48D4×C29—22no—
49D4×C29—41no—
50D4×C29—42no—
51D4×C29—42no—
52C2×C4×C29—21no—
53C2×C4×C29—21no—
54C2×C4×C29—42no—
55C2×C4×C29—41no—
56C2×C4×C29—42no—
57C2×C4×C29D811yescharacteristic
58C2×C4×C29C2×D411yescharacteristic
59C22⋊D29—82no—
60C2×Dic29—41no—
61D116—41no—
62D116—41no—
63C8×C29—21no—
64C8×C29C2×D412yes—
65#2190—291nomaximal, Sylow
66C22×C29—21no—
67C22×C29—41no—
68C22×C29—42no—
69C22×C29—82no—
70C22×C29C2×D811yescharacteristic
71C2×D29—81no—
72C2×D29—81no—
73C2×D29—81no—
74C4×C29—21no—
75C4×C29—42no—
76C4×C29#12011yescharacteristic
77C4×C29AGL(1,ℤ/8)11yescharacteristic
78Dic29—81no—
79#575D2911yescharacteristic, complemented
80#509—292no—
81#469—291no—
82#360—292no—
83#349—291no—
84C2×C29—21no—
85C2×C29—41no—
86C2×C29—82no—
87C2×C29#44711yescharacteristic
88D29—161no—
89C2×#41—21no—
90#137—22no—
91AGL(1,ℤ/8)—22no—
92#135—21no—
93#135C2×D2912yes—
94C2×D8—291no—
95C2×M16C2×D2911yescharacteristic
96#121—581no—
97SD32—582no—
98D16—582no—
99M32—292no—
100#106—291no—
101#102—581no—
102C29#219011yescharacteristic, complemented, Sylow
103#41—22no—
104#41—22no—
105#41—41no—
106#41—41no—
107C2×Q8—21no—
108C2×D4—21no—
109C2×D4—41no—
110C2×D4—581no—
111C2×D4—1161no—
112C22×C4—41no—
113C22×C4C22⋊D2911yescharacteristic
114Q16—21no—
115Q16C22⋊D2912yescomplemented
116SD16—22no—
117SD16—22no—
118D8—21no—
119D8—582no—
120D8C22⋊D2912yescomplemented
121M16—22no—
122C2×C8C22⋊D2911yescharacteristic
123C2×C8C22×D2911yescharacteristic
124C4⋊C4—581no—
125C22⋊C4—1161no—
126C16—582no—
127C23—41no—
128C23—1161no—
129C23#9078211yescharacteristic
130Q8—22no—
131Q8—41no—
132D4—22no—
133D4—41no—
134D4—42no—
135D4—42no—
136D4—1161no—
137D4—1161no—
138D4—2322no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—42no—
144C2×C4—1161no—
145C2×C4#9078211yescharacteristic
146C2×C4C2×C22⋊D2911yescharacteristic
147C8—21no—
148C8C2×C22⋊D2912yes—
149C22—21no—
150C22—41no—
151C22—42no—
152C22—82no—
153C22—2321no—
154C22—2321no—
155C22—2321no—
156C22C2×#9078211yescharacteristic
157C4—21no—
158C4—42no—
159C4—2321no—
160C4#1174529411yescharacteristic
161C4#1174531511yescharacteristic
162C2—21no—
163C2—41no—
164C2—82no—
165C2—4641no—
166C2#1427129711yescharacteristic
subgroupG/H
centerC2#14271297
commutator, cosocleC2×C8×C29C23
FrattiniC2×C8C22×D29
FittingC29×#575C2
socleC2×C29#447
hypercenter#575D29
hypocenterC29#2190
LCSG ▷ C2×C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #14271598C2semidirect
2. #14271416C2semidirect
3. #14270973C2semidirect
4. #14270945C2semidirect
5. C29×#575C2semidirect
13. C2×D232C22semidirect
17. #11745165C22semidirect
18. #11745160C22semidirect
31. Q16×C29D4semidirect
35. D8×C29D4semidirect
79. #575D29semidirect
102. C29#2190semidirect
115. Q16C22⋊D29semidirect
120. D8C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
#142715982
#142714162
#142709732
#142709452
C29×#5752
#219029