Finite Group Databasebeta

← #16818434

Subgroups — #16818434

Order 3712.

266 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 53 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#14271794C211yesmaximal, characteristic, complemented
2#14271316C212yesmaximal
3#14271080C211yesmaximal, characteristic
4#14270901C212yesmaximal, complemented
5C29×#324C211yesmaximal, characteristic, complemented
6C22×D116C2211yescharacteristic
7C2×C4⋊C4×C29C2211yescharacteristic
8C2×#90781—21no—
9C2×#90781—21no—
10#11745288—21no—
11#11745286—21no—
12#11745286C2212yes—
13C2×#90773—22no—
14#11745252—22no—
15#11745250—22no—
16C29×C22⋊C8C2212yes—
17#11745179C2211yescharacteristic
18#11745169—22no—
19C23×D29—21no—
20C22×C4×C29D411yescharacteristic
21C22×C4×C29D411yescharacteristic
22C22×C4×C29C2311yescharacteristic
23C22×Dic29—21no—
24C2×D116—22no—
25C2×D116—42no—
26C2×Dic58—21no—
27C2×Dic58D412yes—
28C2×C8×C29—22no—
29C4⋊C4×C29—22no—
30C22⋊Dic29—22no—
31#90781—42no—
32#90781—42no—
33C4⋊Dic29—21no—
34C4⋊Dic29—21no—
35C4⋊Dic29—21no—
36C4⋊Dic29D412yes—
37#90779—22no—
38#90779—22no—
39C4×Dic29—22no—
40#90773—44no—
41C23×C29C2×D411yescharacteristic
42C22×D29—22no—
43C22×D29—41no—
44C22×D29—41no—
45C22×D29—41no—
46C22×D29—41no—
47C22×D29—41no—
48C22×D29—41no—
49C2×C4×C29—21no—
50C2×C4×C29—21no—
51C2×C4×C29—21no—
52C2×C4×C29—41no—
53C2×C4×C29—41no—
54C2×C4×C29SD1612yescomplemented
55C2×C4×C29C2×D412yes—
56C2×Dic29—22no—
57C2×Dic29—22no—
58C2×Dic29—41no—
59C2×Dic29—41no—
60C2×Dic29—41no—
61D116—24no—
62D116—42no—
63Dic58—42no—
64Dic58—81no—
65C8×C29—42no—
66#1599—291nomaximal, Sylow
67C22×C29—21no—
68C22×C29—21no—
69C22×C29#12011yescharacteristic
70C22×C29C2×SD1611yescharacteristic
71C22×C29#13711yescharacteristic
72C2×D29—42no—
73C2×D29—42no—
74C2×D29—42no—
75C2×D29—81no—
76C2×D29—81no—
77C2×D29—81no—
78C2×D29—81no—
79C4×C29—22no—
80C4×C29—22no—
81C4×C29—41no—
82Dic29—42no—
83Dic29—42no—
84Dic29—81no—
85#544—291no—
86#450—292no—
87#394—291no—
88#328—292no—
89#324D2911yescharacteristic, complemented
90C2×C29—21no—
91C2×C29—21no—
92C2×C29#44811yescharacteristic
93C2×C29#45411yescharacteristic
94C2×C29B(4,𝔽2)11yescharacteristic
95D29—82no—
96C22×D4—291no—
97C2×SD16—582no—
98C4⋊Q8—582no—
99#125—582no—
100C22⋊Q8—292no—
101C22⋊Q8—581no—
102#117—581no—
103C2×C4⋊C4C2×D2911yescharacteristic
104C2×C22⋊C4—581no—
105C2×C22⋊C4—581no—
106#102—582no—
107C22⋊C8C2×D2912yes—
108#95—291no—
109C29#159911yescharacteristic, complemented, Sylow
110C24—581no—
111C2×Q8—292no—
112C2×Q8—581no—
113C2×D4—582no—
114C2×D4—1162no—
115C22×C4—581no—
116C22×C4D11611yescharacteristic
117C22×C4D11611yescharacteristic
118C22×C4C22×D2911yescharacteristic
119SD16—1164no—
120C2×C8—22no—
121C4⋊C4—22no—
122C4⋊C4—292no—
123C4⋊C4—581no—
124C4⋊C4—581no—
125C4⋊C4—581no—
126C4⋊C4—582no—
127C4⋊C4—582no—
128C22⋊C4—582no—
129C22⋊C4—1162no—
130C22⋊C4—1162no—
131C42—582no—
132C23—582no—
133C23—1161no—
134C23—1161no—
135C23—1161no—
136C23—1161no—
137C23—1161no—
138C23—1161no—
139C23C2×D11611yescharacteristic
140Q8—1162no—
141Q8—2321no—
142D4—584no—
143D4—1162no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—582no—
150C2×C4—582no—
151C2×C4—1161no—
152C2×C4—1161no—
153C2×C4—1161no—
154C2×C4#9077312yescomplemented
155C2×C4D4×D2912yes—
156C8—42no—
157C22—21no—
158C22—21no—
159C22—1162no—
160C22—1162no—
161C22—1162no—
162C22—2321no—
163C22—2321no—
164C22—2321no—
165C22—2321no—
166C22#1174524411yescharacteristic
167C22C2×#9077311yescharacteristic
168C22#1174527111yescharacteristic
169C4—22no—
170C4—22no—
171C4—41no—
172C4—1162no—
173C4—1162no—
174C4—2321no—
175C2—21no—
176C2—21no—
177C2—2322no—
178C2#1427130411yescharacteristic
179C2#1427133811yescharacteristic
180C2#1427135111yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#324C2
socleC22×C29#120
prime radicalC22×D116C22
hypercenter#324D29
hypocenterC29#1599
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
1. #14271794C2semidirect
4. #14270901C2semidirect
5. C29×#324C2semidirect
54. C2×C4×C29SD16semidirect
89. #324D29semidirect
109. C29#1599semidirect
154. C2×C4#90773semidirect

Maximal subgroups

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

subgroupindex
#142717942
#142713162
#142710802
#142709012
C29×#3242
#159929