Finite Group Databasebeta

← #16818780

Subgroups — #16818780

Order 3712.

262 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 45 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#14271550C212yesmaximal, complemented
3#14270903C211yesmaximal, characteristic, complemented
4#14270902C212yesmaximal, complemented
5C29×#496C211yesmaximal, characteristic, complemented
6C2×SD16×C29—21no—
7C2×D8×C29—21no—
8C29×#127C2211yescharacteristic, complemented
9C29×#124C2211yescharacteristic
10#11745309—21no—
11#11745299—21no—
12C2×#90783—22no—
13C2×#90782—22no—
14#11745247—22no—
15#11745244—22no—
16#11745237C2212yes—
17C29×#97C2211yescharacteristic, complemented
18#11745151C2212yescomplemented
19C23×D29—21no—
20C2×Q8×C29D411yescharacteristic
21C2×D4×C29—22no—
22C2×D4×C29—21no—
23C2×D4×C29D411yescharacteristic
24C2×C22⋊D29—22no—
25C2×D116—21no—
26C2×D116D412yes—
27C2×Dic58D412yes—
28SD16×C29—42no—
29D8×C29—42no—
30C2×C8×C29—21no—
31C22⋊C4×C29—22no—
32C42×C29C2311yescharacteristic
33C22⋊Dic29—21no—
34#90783—44no—
35#90782—44no—
36#90781—22no—
37#90781—22no—
38#90781—22no—
39C4×Dic29—21no—
40C2×#6597—22no—
41C23×C29—21no—
42C23×C29—41no—
43C22×D29—22no—
44C22×D29—82no—
45C22×D29—81no—
46Q8×C29—41no—
47D4×C29—41no—
48D4×C29—42no—
49D4×C29—42no—
50D4×C29—41no—
51D4×C29—41no—
52C2×C4×C29—21no—
53C2×C4×C29C2×D412yes—
54C2×C4×C29C2×D411yescharacteristic
55C22⋊D29—82no—
56C2×Dic29—22no—
57D116—42no—
58D116—81no—
59Dic58—42no—
60C8×C29—22no—
61#6597—24no—
62#1655—291nomaximal, Sylow
63C22×C29—42no—
64C22×C29—41no—
65C22×C29—82no—
66C22×C29—81no—
67C22×C29#12011yescharacteristic
68C2×D29—42no—
69C2×D29—42no—
70C2×D29—42no—
71C2×D29—84no—
72C4×C29—22no—
73C4×C29—21no—
74C4×C29—41no—
75Dic29—42no—
76H(3,𝔽4)—291no—
77#496—292no—
78#496D2911yescharacteristic, complemented
79#329—291no—
80#329—292no—
81C2×C29—81no—
82C2×C29—161no—
83C2×C29#45312yes—
84C2×C29#45311yescharacteristic
85D29—82no—
86C2×SD16—21no—
87C2×SD16—582no—
88C2×D8—21no—
89C2×D8—582no—
90#127C2×D2911yescharacteristic, complemented
91#124—292no—
92#124—582no—
93#124—581no—
94#124C2×D2911yescharacteristic
95#120—582no—
96#120—581no—
97#97—292no—
98#97C2×D2911yescharacteristic, complemented
99C29#165511yescharacteristic, complemented, Sylow
100C24—581no—
101C2×Q8—292no—
102C2×Q8C22⋊D2911yescharacteristic
103C2×D4—22no—
104C2×D4—21no—
105C2×D4—292no—
106C2×D4—581no—
107C2×D4—582no—
108C2×D4C22⋊D2911yescharacteristic
109SD16—42no—
110SD16—1164no—
111D8—42no—
112D8—1164no—
113C2×C8—21no—
114C2×C8—582no—
115C22⋊C4—22no—
116C22⋊C4—582no—
117C22⋊C4—581no—
118C22⋊C4—582no—
119C22⋊C4—582no—
120C42—581no—
121C42C22×D2911yescharacteristic
122C23—21no—
123C23—41no—
124C23—582no—
125C23—2322no—
126C23—2321no—
127Q8—41no—
128Q8—1162no—
129D4—41no—
130D4—41no—
131D4—42no—
132D4—41no—
133D4—42no—
134D4—1162no—
135D4—2321no—
136D4—2322no—
137C2×C4—21no—
138C2×C4—582no—
139C2×C4D4×D2912yes—
140C2×C4C2×C22⋊D2911yescharacteristic
141C8—22no—
142C8—584no—
143C22—42no—
144C22—41no—
145C22—82no—
146C22—81no—
147C22—1162no—
148C22—1162no—
149C22—1162no—
150C22—2324no—
151C22#1174529911yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—1162no—
156C2—81no—
157C2—161no—
158C2—2322no—
159C2#1427132912yes—
160C2#1427133011yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#496C2
socleC22×C29#120
hypercenter#496D29
hypocenterC29#1655
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #14271905C2semidirect
2. #14271550C2semidirect
3. #14270903C2semidirect
4. #14270902C2semidirect
5. C29×#496C2semidirect
8. C29×#127C22semidirect
17. C29×#97C22semidirect
18. #11745151C22semidirect
78. #496D29semidirect
90. #127C2×D29semidirect
98. #97C2×D29semidirect
99. C29#1655semidirect

Maximal subgroups

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

subgroupindex
#142719052
#142715502
#142709032
#142709022
C29×#4962
#165529