Finite Group Databasebeta

← #16821143

Subgroups — #16821143

Order 3712.

266 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 65 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#14271727C211yesmaximal, characteristic
2#14271137C211yesmaximal, characteristic, complemented
3#14270951C214yesmaximal, complemented
4C29×#413C211yesmaximal, characteristic, complemented
5C2×#41×C29C2211yescharacteristic
6C22×D116C411yescharacteristic, complemented
7C2×M16×C29—21no—
8#11745309—21no—
9#11745302—21no—
10#11745299C412yescomplemented
11#11745299C2212yes—
12#11745292—21no—
13#11745292—21no—
14#11745288—21no—
15#11745288C411yescharacteristic, complemented
16C29×#101—21no—
17C29×#100C2212yes—
18#11745182—21no—
19#11745182C2212yes—
20C23×D29C2×C412yes—
21#41×C29—41no—
22#41×C29—41no—
23C2×Q8×C29D411yescharacteristic
24C2×D4×C29C2×C411yescharacteristic
25C2×D4×C29D411yescharacteristic
26C2×D4×C29C2311yescharacteristic
27C22×C4×C29C2×C411yescharacteristic
28C22×C4×C29D411yescharacteristic
29C22×C4×C29D411yescharacteristic
30C2×C22⋊D29—22no—
31C2×C22⋊D29—22no—
32C2×D116—21no—
33C2×D116—21no—
34C2×D116—41no—
35C2×D116—41no—
36M16×C29—22no—
37M16×C29—41no—
38C2×C8×C29—41no—
39C22⋊Dic29—22no—
40C22⋊Dic29C2×C412yes—
41#90781—22no—
42#90781—22no—
43C4⋊Dic29—21no—
44C4⋊Dic29—41no—
45C4×Dic29—21no—
46C4×Dic29—41no—
47C23×C29C22⋊C411yescharacteristic
48C23×C29C22×C411yescharacteristic
49C23×C29C2×D411yescharacteristic
50C22×D29—22no—
51C22×D29—42no—
52C22×D29—82no—
53Q8×C29—41no—
54D4×C29—41no—
55D4×C29—41no—
56D4×C29—41no—
57C2×C4×C29—21no—
58C2×C4×C29—21no—
59C2×C4×C29—21no—
60C2×C4×C29—21no—
61C2×C4×C29—21no—
62C2×C4×C29—21no—
63C2×C4×C29C22⋊C411yescharacteristic
64C2×C4×C29C22⋊C411yescharacteristic
65C2×C4×C29C22⋊C411yescharacteristic
66C2×C4×C29C2×D411yescharacteristic
67C22⋊D29—82no—
68C22⋊D29—82no—
69C2×Dic29—22no—
70C2×Dic29—42no—
71D116—42no—
72D116—41no—
73D116—41no—
74C8×C29—42no—
75#2122—291nomaximal, Sylow
76C22×C29—21no—
77C22×C29—21no—
78C22×C29—21no—
79C22×C29—41no—
80C22×C29—41no—
81C22×C29—41no—
82C22×C29C2×C22⋊C411yescharacteristic
83C2×D29—42no—
84C2×D29—42no—
85C2×D29—42no—
86C2×D29—84no—
87C4×C29—21no—
88C4×C29—21no—
89C4×C29—21no—
90C4×C29#9911yescharacteristic
91C4×C29#9911yescharacteristic
92Dic29—42no—
93Dic29—82no—
94#535—291no—
95#413D2911yescharacteristic, complemented
96#410—291no—
97AΣL(1,𝔽16)—294no—
98C2×C29—21no—
99C2×C29—41no—
100C2×C29—41no—
101C2×C29—41no—
102C2×C29C2×#9911yescharacteristic
103D29—82no—
104C2×#41C2×D2911yescharacteristic
105C22×D4—291no—
106C2×M16—21no—
107#127—581no—
108#124—581no—
109#121—581no—
110#121—581no—
111#120—292no—
112#120—292no—
113#117—291no—
114#117—581no—
115#101—21no—
116#100C2×D2912yes—
117#99—292no—
118#99—581no—
119C29#212211yescharacteristic, complemented, Sylow
120C24—292no—
121#41—41no—
122#41—41no—
123C2×Q8C22⋊D2911yescharacteristic
124C2×D4—582no—
125C2×D4—582no—
126C2×D4—581no—
127C2×D4—581no—
128C2×D4—1161no—
129C2×D4—1161no—
130C2×D4C4×D2911yescharacteristic
131C2×D4D11611yescharacteristic
132C2×D4C22×D2911yescharacteristic
133C22×C4C4×D2911yescharacteristic
134C22×C4D11611yescharacteristic
135C22×C4C22⋊D2911yescharacteristic
136M16—22no—
137M16—41no—
138C2×C8—41no—
139C4⋊C4—581no—
140C4⋊C4—1161no—
141C22⋊C4—292no—
142C22⋊C4—582no—
143C22⋊C4—582no—
144C22⋊C4—582no—
145C42—581no—
146C42—1161no—
147C23—582no—
148C23—1162no—
149C23—2322no—
150C23#9078111yescharacteristic
151C23C2×C4×D2911yescharacteristic
152C23C2×D11611yescharacteristic
153Q8—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—1162no—
158D4—1161no—
159D4—1161no—
160D4—2322no—
161D4—2322no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—582no—
169C2×C4—1162no—
170C2×C4#9078111yescharacteristic
171C2×C4#9078111yescharacteristic
172C2×C4#9078111yescharacteristic
173C2×C4C2×C22⋊D2911yescharacteristic
174C8—42no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—1162no—
182C22—1162no—
183C22—1162no—
184C22—2324no—
185C22C2×#9078111yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—1162no—
190C4—2322no—
191C4#1174515411yescharacteristic
192C4#1174515411yescharacteristic
193C2—21no—
194C2—41no—
195C2—41no—
196C2—41no—
197C2—2322no—
198C2C2×#1174515411yescharacteristic
subgroupG/H
centerC2C2×#11745154
commutatorC23×C29C22×C4
FrattiniC2×D4C22×D29
FittingC29×#413C2
socleC2×C29C2×#99
prime radical#14271727C2
cosocleC2×D4×C29C23
hypercenter#413D29
hypocenterC29#2122
LCSG ▷ C23×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #14271137C2semidirect
3. #14270951C2semidirect
4. C29×#413C2semidirect
6. C22×D116C4semidirect
10. #11745299C4semidirect
15. #11745288C4semidirect
95. #413D29semidirect
119. C29#2122semidirect

Maximal subgroups

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

subgroupindex
#142717272
#142711372
#142709512
C29×#4132
#212229