Finite Group Databasebeta

← #16821488

Subgroups — #16821488

Order 3712.

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

normal subgroups only

This group has 246 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#14271352C212yesmaximal, complemented
2#14271330C211yesmaximal, characteristic
3#14270956C211yesmaximal, characteristic, complemented
4#14270953C212yesmaximal, complemented
5C29×#559C211yesmaximal, characteristic, complemented
6#11745359C2211yescharacteristic
7C29×#127C2211yescharacteristic
8C29×#124—22no—
9C29×#123—21no—
10C29×#123C2212yes—
11C4×Q8×C29—21no—
12C4×D4×C29—22no—
13#11745294—21no—
14#11745291—22no—
15#11745182C2212yes—
16#11745181C2211yescharacteristic
17#11745154—22no—
18#11745153—21no—
19C2×Q8×C29—21no—
20C2×D4×C29—22no—
21C2×D4×C29D411yescharacteristic
22C2×D4×C29C2311yescharacteristic
23C22×C4×C29—21no—
24C22×C4×C29D412yes—
25C2×C22⋊D29—22no—
26#90807—41no—
27D4×D29—41no—
28#90805—21no—
29C4⋊C4×C29—21no—
30C4⋊C4×C29—22no—
31C22⋊C4×C29—22no—
32C22⋊C4×C29—21no—
33C22⋊C4×C29—22no—
34C22⋊C4×C29D412yes—
35C42×C29—22no—
36C42×C29D411yescharacteristic
37C22⋊Dic29—22no—
38#90783—41no—
39#90782—41no—
40#90781—42no—
41#90779—42no—
42#90777—21no—
43C23×C29—21no—
44C23×C29C2×D412yes—
45C22×D29—22no—
46Q8×C29—42no—
47D4×C29—41no—
48D4×C29—41no—
49D4×C29—44no—
50C2×C4×C29—21no—
51C2×C4×C29—22no—
52C2×C4×C29—22no—
53C2×C4×C29—42no—
54C2×C4×C29—81no—
55C2×C4×C29C2×D411yescharacteristic
56C22⋊D29—42no—
57C22⋊D29—41no—
58C2×Dic29—22no—
59C2×Dic29—42no—
60D116—21no—
61C4×D29—41no—
62Dic58—21no—
63#6597—41no—
64#2198—291nomaximal, Sylow
65C22×C29—22no—
66C22×C29—42no—
67C22×C29—42no—
68C22×C29—41no—
69C22×C29#12011yescharacteristic
70C2×D29—41no—
71C2×D29—82no—
72C4×C29—22no—
73C4×C29—21no—
74C4×C29—42no—
75C4×C29—42no—
76Dic29—41no—
77Dic29—82no—
78#559D2911yescharacteristic, complemented
79#458—292no—
80#453—291no—
81#353—291no—
82#352—292no—
83C2×C29—21no—
84C2×C29—42no—
85C2×C29—81no—
86C2×C29B(4,𝔽2)11yescharacteristic
87D29—81no—
88H(5,𝔽2)—291no—
89AGL(1,ℤ/8)—581no—
90#127C2×D2911yescharacteristic
91#124—22no—
92#123—21no—
93#123—582no—
94#123C2×D2912yes—
95C4×Q8—21no—
96C4×D4—22no—
97#104—581no—
98#100—291no—
99#99—292no—
100#99—582no—
101C29#219811yescharacteristic, complemented, Sylow
102#41—581no—
103#41—1161no—
104C2×Q8—21no—
105C2×D4—22no—
106C2×D4—582no—
107C2×D4—1161no—
108C2×D4C22⋊D2911yescharacteristic
109C2×D4C22×D2911yescharacteristic
110C22×C4—21no—
111C22×C4C22⋊D2912yes—
112SD16—1161no—
113D8—1161no—
114M16—581no—
115C4⋊C4—21no—
116C4⋊C4—22no—
117C4⋊C4—1162no—
118C22⋊C4—22no—
119C22⋊C4—21no—
120C22⋊C4—22no—
121C22⋊C4—582no—
122C22⋊C4—1162no—
123C22⋊C4C22⋊D2912yes—
124C42—22no—
125C42C22⋊D2911yescharacteristic
126C23—21no—
127C23—582no—
128C23C2×C22⋊D2912yes—
129Q8—42no—
130Q8—581no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—581no—
135D4—1162no—
136D4—1161no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—81no—
142C2×C4—582no—
143C2×C4—1161no—
144C2×C4—1162no—
145C2×C4C2×C22⋊D2911yescharacteristic
146C8—1161no—
147C22—22no—
148C22—42no—
149C22—42no—
150C22—41no—
151C22—1161no—
152C22—2322no—
153C22#1174531511yescharacteristic
154C4—22no—
155C4—21no—
156C4—42no—
157C4—42no—
158C4—1161no—
159C4—2322no—
160C2—21no—
161C2—42no—
162C2—81no—
163C2—2321no—
164C2#1427135011yescharacteristic
subgroupG/H
centerC2#14271350
commutator, cosocleC2×D4×C29C23
FrattiniC2×D4C22×D29
FittingC29×#559C2
socleC2×C29B(4,𝔽2)
prime radical#14271330C2
hypercenter#559D29
hypocenterC29#2198
LCSG ▷ C2×D4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #14271352C2semidirect
3. #14270956C2semidirect
4. #14270953C2semidirect
5. C29×#559C2semidirect
78. #559D29semidirect
101. C29#2198semidirect

Maximal subgroups

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

subgroupindex
#142713522
#142713302
#142709562
#142709532
C29×#5592
#219829