Finite Group Databasebeta

← #16821443

Subgroups — #16821443

Order 3712.

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

normal subgroups only

This group has 216 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#14271603C212yesmaximal, complemented
2#14271421C211yesmaximal, characteristic, complemented
3#14270973C212yesmaximal, complemented
4#14270945C211yesmaximal, characteristic, complemented
5C29×#575C211yesmaximal, characteristic
6C2×#41×C29—21no—
7C29×#137—22no—
8C29×AGL(1,ℤ/8)—22no—
9C29×#135—21no—
10C29×#135C2212yes—
11C2×M16×C29C2211yescharacteristic
12#11745286—21no—
13C2×Dic116C2211yescharacteristic, complemented
14#11745177—22no—
15#11745175—22no—
16#11745165C2211yescharacteristic, complemented
17#11745164—21no—
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×Dic58—21no—
29Q16×C29—21no—
30Q16×C29D412yes—
31SD16×C29—22no—
32SD16×C29—22no—
33D8×C29—21no—
34D8×C29D412yes—
35M16×C29—22no—
36C2×C8×C29D411yescharacteristic
37C2×C8×C29C2311yescharacteristic
38C22⋊Dic29—41no—
39C4⋊Dic29—21no—
40#90779—41no—
41Dic116—22no—
42#90768—22no—
43C23×C29—41no—
44C23×C29D811yescharacteristic
45Q8×C29—22no—
46Q8×C29—41no—
47D4×C29—22no—
48D4×C29—41no—
49D4×C29—42no—
50D4×C29—42no—
51C2×C4×C29—21no—
52C2×C4×C29—21no—
53C2×C4×C29—42no—
54C2×C4×C29—41no—
55C2×C4×C29—42no—
56C2×C4×C29D811yescharacteristic
57C2×C4×C29C2×D411yescharacteristic
58C2×Dic29—41no—
59C2×Dic29—41no—
60Dic58—41no—
61Dic58—41no—
62C8×C29—21no—
63C8×C29C2×D412yes—
64#2191—291nomaximal, Sylow
65C22×C29—21no—
66C22×C29—41no—
67C22×C29—42no—
68C22×C29—82no—
69C22×C29C2×D811yescharacteristic
70C4×C29—21no—
71C4×C29—42no—
72C4×C29#12011yescharacteristic
73C4×C29AGL(1,ℤ/8)11yescharacteristic
74Dic29—81no—
75Dic29—81no—
76#575D2911yescharacteristic
77#510—292no—
78#470—291no—
79#360—292no—
80#349—291no—
81C2×C29—21no—
82C2×C29—41no—
83C2×C29—82no—
84C2×C29#44711yescharacteristic
85C2×#41—21no—
86#137—22no—
87AGL(1,ℤ/8)—22no—
88#135—21no—
89#135C2×D2912yes—
90C2×Q16—291no—
91C2×M16C2×D2911yescharacteristic
92C22⋊Q8—581no—
93Q32—582no—
94SD32—582no—
95M32—292no—
96#106—291no—
97#103—581no—
98C29#219111yescharacteristic, complemented, Sylow
99#41—22no—
100#41—22no—
101#41—41no—
102#41—41no—
103C2×Q8—21no—
104C2×Q8—581no—
105C2×D4—21no—
106C2×D4—41no—
107C22×C4—41no—
108C22×C4C22⋊D2911yescharacteristic
109Q16—21no—
110Q16—582no—
111Q16C22⋊D2912yes—
112SD16—22no—
113SD16—22no—
114D8—21no—
115D8C22⋊D2912yes—
116M16—22no—
117C2×C8C22⋊D2911yescharacteristic
118C2×C8C22×D2911yescharacteristic
119C4⋊C4—581no—
120C4⋊C4—1161no—
121C22⋊C4—1161no—
122C16—582no—
123C23—41no—
124C23#9078211yescharacteristic
125Q8—22no—
126Q8—41no—
127Q8—1161no—
128Q8—1161no—
129D4—22no—
130D4—41no—
131D4—42no—
132D4—42no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—42no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—1161no—
139C2×C4—1161no—
140C2×C4#9078211yescharacteristic
141C2×C4C2×C22⋊D2911yescharacteristic
142C8—21no—
143C8C2×C22⋊D2912yes—
144C22—21no—
145C22—41no—
146C22—42no—
147C22—82no—
148C22C2×#9078211yescharacteristic
149C4—21no—
150C4—42no—
151C4—2321no—
152C4—2321no—
153C4#1174529411yescharacteristic
154C4#1174531511yescharacteristic
155C2—21no—
156C2—41no—
157C2—82no—
158C2#1427129711yescharacteristic
subgroupG/H
centerC2#14271297
commutator, cosocleC2×C8×C29C23
FrattiniC2×C8C22×D29
Fitting, prime radicalC29×#575C2
socleC2×C29#447
hypercenter#575D29
hypocenterC29#2191
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. #14271603C2semidirect
2. #14271421C2semidirect
3. #14270973C2semidirect
4. #14270945C2semidirect
13. C2×Dic116C22semidirect
16. #11745165C22semidirect
18. #11745160C22semidirect
98. C29#2191semidirect

Maximal subgroups

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

subgroupindex
#142716032
#142714212
#142709732
#142709452
C29×#5752
#219129