Finite Group Databasebeta

← #16818460

Subgroups — #16818460

Order 3712.

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

normal subgroups only

This group has 282 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#14271744C211yesmaximal, characteristic
2#14271302C212yesmaximal, complemented
3#14270896C212yesmaximal, complemented
4#14270889C211yesmaximal, characteristic, complemented
5C29×#395C211yesmaximal, characteristic, complemented
6C22×Q8×C29C2211yescharacteristic
7C2×#90805—21no—
8C2×C4⋊C4×C29—21no—
9C2×C4⋊C4×C29C2211yescharacteristic
10C2×#90784—22no—
11#11745292—21no—
12#11745292C2212yes—
13#11745259—22no—
14#11745257—22no—
15C29×#95—21no—
16C29×#95C2211yescharacteristic
17#11745183—22no—
18C22⋊#6597C2212yes—
19C2×Q8×C29—22no—
20C2×Q8×C29—42no—
21C22×C4×C29—21no—
22C22×C4×C29—21no—
23C22×C4×C29D411yescharacteristic
24C22×C4×C29D411yescharacteristic
25C22×C4×C29C2311yescharacteristic
26C2×C22⋊D29—22no—
27#90805—42no—
28#90805—42no—
29C2×D116—21no—
30C2×D116—21no—
31C2×D116D412yes—
32C2×C4×D29—22no—
33C2×Dic58—21no—
34C4⋊C4×C29—22no—
35C4⋊C4×C29—42no—
36#90784—44no—
37#90781—22no—
38#90781—22no—
39C4⋊Dic29—21no—
40C4⋊Dic29D412yes—
41C2×#6597—22no—
42C23×C29C2×D411yescharacteristic
43C22×D29—22no—
44Q8×C29—24no—
45Q8×C29—42no—
46C2×C4×C29—21no—
47C2×C4×C29—21no—
48C2×C4×C29—22no—
49C2×C4×C29—22no—
50C2×C4×C29—21no—
51C2×C4×C29—41no—
52C2×C4×C29—41no—
53C2×C4×C29—41no—
54C2×C4×C29—41no—
55C2×C4×C29—41no—
56C2×C4×C29—41no—
57C2×C4×C29SD1612yescomplemented
58C2×C4×C29C2×D412yes—
59C22⋊D29—42no—
60C22⋊D29—42no—
61C2×Dic29—22no—
62D116—42no—
63D116—42no—
64D116—81no—
65C4×D29—44no—
66Dic58—42no—
67#6597—42no—
68#1604—291nomaximal, Sylow
69C22×C29—21no—
70C22×C29—21no—
71C22×C29#12011yescharacteristic
72C22×C29C2×SD1611yescharacteristic
73C22×C29AGL(1,ℤ/8)11yescharacteristic
74C2×D29—42no—
75C2×D29—42no—
76C2×D29—42no—
77C4×C29—22no—
78C4×C29—22no—
79C4×C29—42no—
80C4×C29—41no—
81C4×C29—42no—
82Dic29—42no—
83#537—291no—
84#448—292no—
85#395D2911yescharacteristic, complemented
86#327—292no—
87#324—291no—
88C2×C29—21no—
89C2×C29—21no—
90C2×C29#45011yescharacteristic
91C2×C29#45611yescharacteristic
92C2×C29B(4,𝔽2)11yescharacteristic
93D29—82no—
94C2×#41—581no—
95C22×Q8C2×D2911yescharacteristic
96C2×SD16—582no—
97C22⋊Q8—582no—
98#121—292no—
99#121—582no—
100#121—581no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4C2×D2911yescharacteristic
103#103—582no—
104C22⋊C8—292no—
105#95—21no—
106#95C2×D2911yescharacteristic
107C29#160411yescharacteristic, complemented, Sylow
108#41—1162no—
109#41—1162no—
110C2×Q8—22no—
111C2×Q8—42no—
112C2×Q8—581no—
113C2×D4—292no—
114C2×D4—581no—
115C2×D4—581no—
116C2×D4—582no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—582no—
120C22×C4C22⋊D2911yescharacteristic
121C22×C4C22⋊D2911yescharacteristic
122C22×C4C22×D2911yescharacteristic
123SD16—1164no—
124C2×C8—582no—
125C4⋊C4—22no—
126C4⋊C4—42no—
127C4⋊C4—292no—
128C4⋊C4—581no—
129C22⋊C4—582no—
130C22⋊C4—582no—
131C23—582no—
132C23C2×C22⋊D2911yescharacteristic
133Q8—24no—
134Q8—42no—
135Q8—1162no—
136D4—1162no—
137D4—1162no—
138D4—1162no—
139D4—1162no—
140D4—2321no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—582no—
153C2×C4—1164no—
154C2×C4#9078412yescomplemented
155C2×C4D4×D2912yes—
156C8—1162no—
157C22—21no—
158C22—21no—
159C22—1162no—
160C22—1162no—
161C22—1162no—
162C22#1174529911yescharacteristic
163C22C2×#9078411yescharacteristic
164C22#1174531111yescharacteristic
165C4—22no—
166C4—22no—
167C4—42no—
168C4—42no—
169C4—41no—
170C4—1162no—
171C2—21no—
172C2—21no—
173C2—2322no—
174C2#1427131311yescharacteristic
175C2#1427134511yescharacteristic
176C2#1427134911yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#395C2
socleC22×C29#120
prime radical#14271744C2
hypercenter#395D29
hypocenterC29#1604
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
2. #14271302C2semidirect
3. #14270896C2semidirect
4. #14270889C2semidirect
5. C29×#395C2semidirect
57. C2×C4×C29SD16semidirect
85. #395D29semidirect
107. C29#1604semidirect
154. C2×C4#90784semidirect

Maximal subgroups

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

subgroupindex
#142717442
#142713022
#142708962
#142708892
C29×#3952
#160429