Finite Group Databasebeta

← #16835785

Subgroups — #16835785

Order 3712.

250 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 54 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#14272149C212yesmaximal, complemented
2#14272074C212yesmaximal, complemented
3#14272072C212yesmaximal, complemented
4#14271713C211yesmaximal, characteristic
5C2×#90805C411yescharacteristic
6C2×#90805C2211yescharacteristic
7D29⋊M16—22no—
8C2×C42×C29C411yescharacteristic
9#11745292—22no—
10#11745237C411yescharacteristic
11#11745237C2211yescharacteristic
12#11745236C411yescharacteristic
13C4×D116—22no—
14#11745231C2211yescharacteristic
15#11745229—22no—
16#11745221C2214yes—
17C22×C4×C29—21no—
18C22×C4×C29C2×C411yescharacteristic
19C2×C22⋊D29—21no—
20C2×C22⋊D29D412yes—
21#90805—41no—
22#90805—41no—
23#90805—41no—
24#90805—41no—
25C2×D116—22no—
26C2×D116C2×C411yescharacteristic
27C2×D116C2×C411yescharacteristic
28C2×C4×D29—21no—
29C2×C4×D29D412yes—
30C2×Dic58C2×C411yescharacteristic
31C2×Dic58C2311yescharacteristic
32#90800—24no—
33#90796—42no—
34D29⋊C8—42no—
35C42×C29—21no—
36C42×C29C2×C411yescharacteristic
37C42×C29C2×C411yescharacteristic
38#90781—22no—
39#90781—22no—
40C4⋊Dic29—22no—
41C23×C29C22⋊C411yescharacteristic
42C22×D29—21no—
43C22×D29C22⋊C412yes—
44C2×C4×C29—21no—
45C2×C4×C29—21no—
46C2×C4×C29—21no—
47C2×C4×C29—21no—
48C2×C4×C29—42no—
49C2×C4×C29C22⋊C411yescharacteristic
50C2×C4×C29C22×C411yescharacteristic
51C22⋊D29—42no—
52C22⋊D29—42no—
53C2×Dic29—21no—
54C2×Dic29C2×D412yes—
55D116—41no—
56D116—41no—
57D116—44no—
58C4×D29—22no—
59C4×D29—22no—
60C4×D29—41no—
61C4×D29—41no—
62Dic58—41no—
63Dic58—41no—
64#6599—44no—
65#2132—291nomaximal, Sylow
66C22×C29—21no—
67C22×C29—41no—
68C22×C29C2×C22⋊C411yescharacteristic
69C2×D29—22no—
70C2×D29—42no—
71C2×D29—42no—
72C2×D29—41no—
73C4×C29—22no—
74C4×C29—21no—
75C4×C29—41no—
76C4×C29#9911yescharacteristic
77C4×C29#9911yescharacteristic
78Dic29—22no—
79Dic29—41no—
80#532—291no—
81#413—292no—
82#356—292no—
83#355—292no—
84C2×C29—21no—
85C2×C29—41no—
86C2×C29C2×#9911yescharacteristic
87D29—42no—
88D29—81no—
89C2×#41—291no—
90C2×#41—291no—
91C2×M16—582no—
92C4⋊Q8—291no—
93#127—291no—
94#124—291no—
95#124—291no—
96#121—582no—
97C4×D4—582no—
98C2×C42#118111yescharacteristic
99#101—294no—
100#100—582no—
101C29#213211yescharacteristic, complemented, Sylow
102#41—1161no—
103#41—1161no—
104#41—1161no—
105#41—1161no—
106C2×Q8—291no—
107C2×Q8—291no—
108C2×D4—292no—
109C2×D4—291no—
110C2×D4—291no—
111C2×D4—582no—
112C2×D4—581no—
113C22×C4—21no—
114C22×C4—292no—
115C22×C4—581no—
116C22×C4C2×#118111yescharacteristic
117M16—584no—
118M16—1162no—
119C2×C8—1162no—
120C4⋊C4—582no—
121C22⋊C4—582no—
122C22⋊C4—582no—
123C42—21no—
124C42C2×#118111yescharacteristic
125C42C2×#118111yescharacteristic
126C23—292no—
127C23—581no—
128C23C22⋊#118111yescharacteristic
129Q8—1161no—
130Q8—1161no—
131D4—1161no—
132D4—1161no—
133D4—1164no—
134D4—1162no—
135D4—1162no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—42no—
141C2×C4—292no—
142C2×C4—582no—
143C2×C4—582no—
144C2×C4—581no—
145C2×C4—1161no—
146C2×C4—1161no—
147C2×C4C22⋊#118111yescharacteristic
148C2×C4C22×#118111yescharacteristic
149C8—1164no—
150C22—21no—
151C22—41no—
152C22—582no—
153C22—1162no—
154C22—1162no—
155C22—1161no—
156C22C2×C22⋊#118111yescharacteristic
157C4—22no—
158C4—21no—
159C4—41no—
160C4—582no—
161C4—1161no—
162C4#1174521511yescharacteristic
163C4#1174521511yescharacteristic
164C2—21no—
165C2—41no—
166C2—1162no—
167C2—2321no—
168C2C2×#1174521511yescharacteristic
subgroupG/H
centerC4#11745215
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC2×C42×C29C4
socleC2×C29C2×#99
prime radical#14271713C2
cosocleC2×Dic58C23
hypercenterC2×C42#1181
hypocenterC29#2132
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #14272149C2semidirect
2. #14272074C2semidirect
3. #14272072C2semidirect
101. C29#2132semidirect

Maximal subgroups

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

subgroupindex
#142721492
#142720742
#142720722
#142717132
#213229