Finite Group Databasebeta

← #16835000

Subgroups — #16835000

Order 3712.

344 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 70 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#14272181C211yesmaximal, characteristic, complemented
2#14272168C211yesmaximal, characteristic, complemented
3#14272021C214yesmaximal, complemented
4#127×D29C211yesmaximal, characteristic
5C2×D4×D29—21no—
6C2×D4×D29—21no—
7C2×D4×D29C412yes—
8C2×#90796—21no—
9C29×#127C411yescharacteristic
10#11745302—21no—
11#11745302—21no—
12#11745302C2212yes—
13#11745236C411yescharacteristic
14C42×D29C2211yescharacteristic
15#11745220—21no—
16#11745220C2212yescomplemented
17#11745220C2212yescomplemented
18#11745219—21no—
19C4×#6599—21no—
20C23×D29—22no—
21C2×D4×C29—21no—
22C2×D4×C29—21no—
23C2×D4×C29C2×C412yes—
24C2×C22⋊D29—22no—
25C2×C22⋊D29—22no—
26C2×C22⋊D29—22no—
27D4×D29—44no—
28D4×D29—44no—
29D4×D29—42no—
30D4×D29—42no—
31C2×D116—21no—
32C2×D116—21no—
33C2×D116C2×C412yes—
34C2×C4×D29C2×C411yescharacteristic
35C2×C4×D29D411yescharacteristic
36C2×C4×D29D411yescharacteristic
37C2×#6599—22no—
38C2×#6599—22no—
39#90796—42no—
40C42×C29C2×C411yescharacteristic
41C4×Dic29D411yescharacteristic
42C4×Dic29D411yescharacteristic
43C4×Dic29C2311yescharacteristic
44C23×C29—22no—
45C22×D29—22no—
46C22×D29—44no—
47C22×D29—44no—
48C22×D29—44no—
49C22×D29C22⋊C411yescharacteristic
50D4×C29—42no—
51D4×C29—42no—
52D4×C29—42no—
53C2×C4×C29C22⋊C411yescharacteristic
54C2×C4×C29C22⋊C411yescharacteristic
55C2×C4×C29C22×C411yescharacteristic
56C22⋊D29—44no—
57C22⋊D29—42no—
58C22⋊D29—42no—
59C22⋊D29—44no—
60C2×Dic29C22⋊C411yescharacteristic
61C2×Dic29C2×D411yescharacteristic
62C2×Dic29C2×D411yescharacteristic
63D116—42no—
64D116—42no—
65D116—42no—
66C4×D29—22no—
67C4×D29—22no—
68C4×D29D812yes—
69C4×D29SD1612yes—
70#6599—42no—
71#6599—42no—
72#1545—291nomaximal, Sylow
73C22×C29—42no—
74C22×C29—42no—
75C22×C29—42no—
76C22×C29C2×C22⋊C411yescharacteristic
77C2×D29—21no—
78C2×D29—21no—
79C2×D29—42no—
80C2×D29—42no—
81C2×D29—42no—
82C2×D29—88no—
83C2×D29#10212yes—
84C4×C29—21no—
85C4×C29—21no—
86C4×C29#10212yes—
87Dic29#10012yes—
88Dic29C2×D811yescharacteristic
89Dic29C2×SD1611yescharacteristic
90Dic29AGL(1,ℤ/8)12yes—
91C2×#127—291no—
92#431—291no—
93#423—291no—
94#331—294no—
95C2×C29—82no—
96C2×C29C2×#10011yescharacteristic
97C2×C29C2×#10211yescharacteristic
98C2×C29#41811yescharacteristic
99D29—22no—
100D29—82no—
101C22×D4—292no—
102C22×D4—581no—
103C22×D4—581no—
104C2×M16—581no—
105#127—292no—
106#127—291no—
107#127—581no—
108#127—581no—
109#127#118111yescharacteristic
110C2×C42—291no—
111C4⋊C8—292no—
112C4⋊C8—292no—
113C4⋊C8—581no—
114C22⋊C8—581no—
115C4×C8—581no—
116C29#154511yescharacteristic, complemented, Sylow
117C24—582no—
118C2×D4—21no—
119C2×D4—21no—
120C2×D4—292no—
121C2×D4—582no—
122C2×D4—582no—
123C2×D4—582no—
124C2×D4—581no—
125C2×D4—581no—
126C2×D4—1162no—
127C2×D4—1162no—
128C2×D4—1164no—
129C2×D4—1164no—
130C2×D4C2×#118112yes—
131C22×C4—291no—
132C22×C4—291no—
133C22×C4—291no—
134M16—1162no—
135C2×C8—582no—
136C2×C8—582no—
137C42—291no—
138C42—291no—
139C42—291no—
140C42C2×#118111yescharacteristic
141C23—22no—
142C23—291no—
143C23—582no—
144C23—1164no—
145C23—1164no—
146C23—1164no—
147D4—42no—
148D4—42no—
149D4—42no—
150D4—1162no—
151D4—1162no—
152D4—1162no—
153D4—1162no—
154D4—1164no—
155D4—1164no—
156D4—1162no—
157C2×C4—291no—
158C2×C4—291no—
159C2×C4—291no—
160C2×C4—292no—
161C2×C4—292no—
162C2×C4—582no—
163C2×C4—582no—
164C2×C4C22⋊#118111yescharacteristic
165C2×C4C22⋊#118111yescharacteristic
166C2×C4C22×#118111yescharacteristic
167C8—1162no—
168C8—1162no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—292no—
173C22—581no—
174C22—581no—
175C22—1162no—
176C22—1162no—
177C22—1162no—
178C22—2328no—
179C22C2×C22⋊#118111yescharacteristic
180C4—21no—
181C4—21no—
182C4—292no—
183C4—291no—
184C4—291no—
185C4—292no—
186C4#1174522312yes—
187C2—82no—
188C2—582no—
189C2—2322no—
190C2D29⋊#10011yescharacteristic
191C2C2×#1174522311yescharacteristic
192C2#1427215511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#127C4
socleC22×C29C2×C22⋊C4
prime radical#127×D29C2
cosocleC4×Dic29C23
hypercenter#127#1181
hypocenterC29#1545
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #14272181C2semidirect
2. #14272168C2semidirect
3. #14272021C2semidirect
16. #11745220C22semidirect
17. #11745220C22semidirect
116. C29#1545semidirect

Maximal subgroups

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

subgroupindex
#142721812
#142721682
#142720212
#127×D292
#154529