Finite Group Databasebeta

← #16821183

Subgroups — #16821183

Order 3712.

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

normal subgroups only

This group has 262 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#14271147C211yesmaximal, characteristic, complemented
3#14270959C214yesmaximal, complemented
4C29×#413C211yesmaximal, characteristic, complemented
5C2×#41×C29C2211yescharacteristic
6C22×D116C411yescharacteristic
7C2×M16×C29—21no—
8#11745309C2212yes—
9#11745302C412yes—
10#11745299—21no—
11#11745299—21no—
12#11745292—21no—
13#11745292—21no—
14#11745288C411yescharacteristic
15C2×#90777—21no—
16C29×#101C2212yescomplemented
17C29×#100—21no—
18#11745184C2212yescomplemented
19#11745181—21no—
20C23×D29—21no—
21#41×C29—41no—
22#41×C29—41no—
23C2×Q8×C29C2311yescharacteristic
24C2×D4×C29C2×C411yescharacteristic
25C2×D4×C29D411yescharacteristic
26C2×D4×C29D411yescharacteristic
27C22×C4×C29C2×C411yescharacteristic
28C22×C4×C29D411yescharacteristic
29C22×C4×C29D411yescharacteristic
30C2×C22⋊D29—22no—
31C2×C22⋊D29—22no—
32C2×D116—21no—
33C2×D116—41no—
34C2×D116—41no—
35C2×D116C2×C412yes—
36M16×C29—22no—
37M16×C29—41no—
38C2×C8×C29—41no—
39C22⋊Dic29—21no—
40#90781—22no—
41#90781—22no—
42C4⋊Dic29—21no—
43C4×Dic29C2×C412yes—
44#90777—22no—
45#90777—41no—
46C2×#6597—41no—
47C23×C29C22⋊C411yescharacteristic
48C23×C29C22⋊C411yescharacteristic
49C23×C29C22⋊C411yescharacteristic
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×C29C2×D411yescharacteristic
66C2×C4×C29C2×D411yescharacteristic
67C22⋊D29—82no—
68C22⋊D29—82no—
69C2×Dic29—22no—
70D116—42no—
71D116—41no—
72D116—41no—
73C8×C29—42no—
74#6597—42no—
75#2134—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—
93#535—291no—
94#413—291no—
95#413D2911yescharacteristic, complemented
96#355—294no—
97C2×C29—21no—
98C2×C29—41no—
99C2×C29—41no—
100C2×C29—41no—
101C2×C29C2×#9911yescharacteristic
102D29—82no—
103C2×#41C2×D2911yescharacteristic
104C22×D4—291no—
105C2×M16—21no—
106C2×M16—581no—
107#127—292no—
108#124—292no—
109#121—581no—
110#121—581no—
111#120—581no—
112#120—581no—
113#117—291no—
114#101—292no—
115#101C2×D2912yescomplemented
116#100—21no—
117#100—581no—
118C29#213411yescharacteristic, complemented, Sylow
119C24—581no—
120#41—41no—
121#41—41no—
122C2×Q8C22×D2911yescharacteristic
123C2×D4—292no—
124C2×D4—582no—
125C2×D4—582no—
126C2×D4—581no—
127C2×D4—1161no—
128C2×D4—1161no—
129C2×D4C4×D2911yescharacteristic
130C2×D4D11611yescharacteristic
131C2×D4C22⋊D2911yescharacteristic
132C22×C4C4×D2911yescharacteristic
133C22×C4D11611yescharacteristic
134C22×C4C22⋊D2911yescharacteristic
135M16—22no—
136M16—41no—
137M16—582no—
138M16—1161no—
139C2×C8—41no—
140C2×C8—1161no—
141C4⋊C4—581no—
142C22⋊C4—581no—
143C22⋊C4—582no—
144C22⋊C4—582no—
145C42—292no—
146C23—582no—
147C23—1162no—
148C23—2322no—
149C23#9078111yescharacteristic
150C23#9078111yescharacteristic
151C23#9078111yescharacteristic
152Q8—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—1162no—
157D4—1161no—
158D4—1161no—
159D4—2322no—
160D4—2322no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—582no—
168C2×C4#9078111yescharacteristic
169C2×C4C2×C4×D2911yescharacteristic
170C2×C4C2×D11611yescharacteristic
171C2×C4C2×C22⋊D2911yescharacteristic
172C8—42no—
173C8—1162no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22—1162no—
181C22—1162no—
182C22—1162no—
183C22—2324no—
184C22C2×#9078111yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—1162no—
189C4#1174515411yescharacteristic
190C4#1174515411yescharacteristic
191C2—21no—
192C2—41no—
193C2—41no—
194C2—41no—
195C2—2322no—
196C2C2×#1174515411yescharacteristic
subgroupG/H
centerC2C2×#11745154
commutatorC2×C4×C29C22×C4
FrattiniC2×Q8C22×D29
FittingC29×#413C2
socleC2×C29C2×#99
prime radical#14271727C2
cosocleC2×Q8×C29C23
hypercenter#413D29
hypocenterC29#2134
LCSG ▷ C2×C4×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. #14271147C2semidirect
3. #14270959C2semidirect
4. C29×#413C2semidirect
16. C29×#101C22semidirect
18. #11745184C22semidirect
95. #413D29semidirect
115. #101C2×D29semidirect
118. C29#2134semidirect

Maximal subgroups

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

subgroupindex
#142717272
#142711472
#142709592
C29×#4132
#213429