Finite Group Databasebeta

← #16835784

Subgroups — #16835784

Order 3712.

250 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 52 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#14272150C212yesmaximal, complemented
2#14272074C212yesmaximal, complemented
3#14272071C212yesmaximal, complemented
4#14271711C211yesmaximal, characteristic
5C2×#90807C411yescharacteristic
6C2×#90807C2211yescharacteristic
7C2×#90800—22no—
8C29×#127C411yescharacteristic
9#11745300—22no—
10#11745298C411yescharacteristic
11#11745298C2211yescharacteristic
12D4×Dic29—22no—
13C42×D29C411yescharacteristic
14#11745231C2211yescharacteristic
15#11745229—22no—
16#11745221C2214yes—
17C2×D4×C29—22no—
18C2×D4×C29C2×C411yescharacteristic
19C2×D4×C29C2×C411yescharacteristic
20C2×C22⋊D29—21no—
21C2×C22⋊D29D412yes—
22C22×Dic29—21no—
23C22×Dic29D412yes—
24#90807—41no—
25#90807—41no—
26#90807—41no—
27#90807—41no—
28C2×C4×D29—21no—
29C2×C4×D29C2×C411yescharacteristic
30C2×Dic58C2×C411yescharacteristic
31C2×Dic58C2311yescharacteristic
32#90800—24no—
33#90800—42no—
34C2×#6599—42no—
35C42×C29C2×C411yescharacteristic
36C22⋊Dic29—22no—
37C22⋊Dic29—22no—
38C4⋊Dic29—22no—
39C4×Dic29—21no—
40C4×Dic29C2×C411yescharacteristic
41C23×C29—21no—
42C23×C29C22⋊C412yes—
43C22×D29C22⋊C411yescharacteristic
44D4×C29—41no—
45D4×C29—41no—
46D4×C29—44no—
47C2×C4×C29—21no—
48C2×C4×C29C22×C411yescharacteristic
49C22⋊D29—42no—
50C22⋊D29—42no—
51C2×Dic29—22no—
52C2×Dic29—22no—
53C2×Dic29—21no—
54C2×Dic29—21no—
55C2×Dic29—41no—
56C2×Dic29—41no—
57C2×Dic29C22⋊C411yescharacteristic
58C2×Dic29C2×D412yes—
59C4×D29—21no—
60C4×D29—21no—
61C4×D29—42no—
62Dic58—41no—
63Dic58—41no—
64#6599—44no—
65#2132—291nomaximal, Sylow
66C22×C29—22no—
67C22×C29—42no—
68C22×C29—42no—
69C22×C29—41no—
70C22×C29C2×C22⋊C411yescharacteristic
71C2×D29—21no—
72C2×D29—41no—
73C4×C29—22no—
74C4×C29—21no—
75Dic29—22no—
76Dic29—41no—
77Dic29—41no—
78Dic29#9911yescharacteristic
79Dic29#9911yescharacteristic
80#532—291no—
81#413—292no—
82#356—292no—
83#355—292no—
84C2×C29—21no—
85C2×C29—42no—
86C2×C29—81no—
87C2×C29C2×#9911yescharacteristic
88D29—41no—
89C2×#41—291no—
90C2×#41—291no—
91C2×M16—582no—
92C4⋊Q8—291no—
93#127#118111yescharacteristic
94#124—291no—
95#124—291no—
96#121—582no—
97C4×D4—582no—
98C2×C42—291no—
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—22no—
109C2×D4—292no—
110C2×D4—581no—
111C2×D4C2×#118111yescharacteristic
112C2×D4C2×#118111yescharacteristic
113C22×C4—292no—
114C22×C4—291no—
115C22×C4—581no—
116C22×C4—581no—
117M16—584no—
118M16—1162no—
119C2×C8—1162no—
120C4⋊C4—582no—
121C22⋊C4—582no—
122C22⋊C4—582no—
123C42—291no—
124C42—581no—
125C42C2×#118111yescharacteristic
126C23—21no—
127C23—291no—
128C23C22⋊#118112yes—
129Q8—1161no—
130Q8—1161no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—1162no—
135D4—1162no—
136C2×C4—21no—
137C2×C4—291no—
138C2×C4—292no—
139C2×C4—581no—
140C2×C4—581no—
141C2×C4—582no—
142C2×C4—582no—
143C2×C4—581no—
144C2×C4—581no—
145C2×C4—1162no—
146C2×C4—1161no—
147C2×C4—1161no—
148C2×C4C22×#118111yescharacteristic
149C8—1164no—
150C22—22no—
151C22—42no—
152C22—42no—
153C22—41no—
154C22—581no—
155C22—1161no—
156C22C2×C22⋊#118111yescharacteristic
157C4—22no—
158C4—21no—
159C4—291no—
160C4—291no—
161C4—582no—
162C4—1161no—
163C4—1161no—
164C2—21no—
165C2—42no—
166C2—81no—
167C2—1161no—
168C2D29⋊#9911yescharacteristic
subgroupG/H
centerC2D29⋊#99
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#127C4
socleC2×C29C2×#99
prime radical#14271711C2
cosocleC2×Dic58C23
hypercenter#127#1181
hypocenterC29#2132
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #14272150C2semidirect
2. #14272074C2semidirect
3. #14272071C2semidirect
101. C29#2132semidirect

Maximal subgroups

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

subgroupindex
#142721502
#142720742
#142720712
#142717112
#213229