Finite Group Databasebeta

← #16818468

Subgroups — #16818468

Order 3712.

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

normal subgroups only

This group has 238 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
2#14271321C212yesmaximal
3#14271083C211yesmaximal, characteristic
4#14270901C212yesmaximal
5C29×#324C211yesmaximal, characteristic
6C22×Dic58C2211yescharacteristic
7C2×C4⋊C4×C29C2211yescharacteristic
8#11745288—21no—
9#11745286—21no—
10#11745286C2212yes—
11C2×#90779—21no—
12C2×Dic116—22no—
13#11745252—22no—
14#11745250—22no—
15C29×C22⋊C8C2212yes—
16#11745179—21no—
17#11745179C2211yescharacteristic
18#11745164—22no—
19C22×C4×C29D411yescharacteristic
20C22×C4×C29D411yescharacteristic
21C22×C4×C29C2311yescharacteristic
22C22×Dic29—21no—
23C22×Dic29—21no—
24C2×Dic58—22no—
25C2×Dic58—21no—
26C2×Dic58—42no—
27C2×Dic58D412yes—
28C2×C8×C29—22no—
29C4⋊C4×C29—22no—
30C22⋊Dic29—22no—
31C4⋊Dic29—21no—
32C4⋊Dic29—21no—
33C4⋊Dic29—21no—
34C4⋊Dic29D412yes—
35#90779—22no—
36#90779—22no—
37#90779—42no—
38C4×Dic29—22no—
39Dic116—44no—
40C23×C29C2×D411yescharacteristic
41C2×C4×C29—21no—
42C2×C4×C29—21no—
43C2×C4×C29—21no—
44C2×C4×C29—41no—
45C2×C4×C29—41no—
46C2×C4×C29Q1612yescomplemented
47C2×C4×C29C2×D412yes—
48C2×Dic29—22no—
49C2×Dic29—22no—
50C2×Dic29—22no—
51C2×Dic29—22no—
52C2×Dic29—41no—
53C2×Dic29—41no—
54C2×Dic29—41no—
55C2×Dic29—41no—
56Dic58—24no—
57Dic58—42no—
58Dic58—42no—
59Dic58—81no—
60C8×C29—42no—
61#1605—291nomaximal, Sylow
62C22×C29—21no—
63C22×C29—21no—
64C22×C29#12011yescharacteristic
65C22×C29C2×Q1611yescharacteristic
66C22×C29#13711yescharacteristic
67C4×C29—22no—
68C4×C29—22no—
69C4×C29—41no—
70Dic29—42no—
71Dic29—42no—
72Dic29—42no—
73Dic29—42no—
74#544—291no—
75#451—292no—
76#395—291no—
77#328—292no—
78#324D2911yescharacteristic
79C2×C29—21no—
80C2×C29—21no—
81C2×C29#45111yescharacteristic
82C2×C29#45611yescharacteristic
83C2×C29B(4,𝔽2)11yescharacteristic
84C22×Q8—291no—
85C2×Q16—582no—
86C4⋊Q8—582no—
87#125—582no—
88C22⋊Q8—292no—
89C22⋊Q8—581no—
90#117—581no—
91C2×C4⋊C4—581no—
92C2×C4⋊C4C2×D2911yescharacteristic
93#103—582no—
94C22⋊C8C2×D2912yes—
95#95—291no—
96#95—581no—
97C29#160511yescharacteristic, complemented, Sylow
98C2×Q8—292no—
99C2×Q8—581no—
100C2×Q8—582no—
101C2×Q8—1162no—
102C22×C4—581no—
103C22×C4—581no—
104C22×C4D11611yescharacteristic
105C22×C4D11611yescharacteristic
106C22×C4C22×D2911yescharacteristic
107Q16—1164no—
108C2×C8—22no—
109C4⋊C4—22no—
110C4⋊C4—292no—
111C4⋊C4—581no—
112C4⋊C4—581no—
113C4⋊C4—581no—
114C4⋊C4—582no—
115C4⋊C4—582no—
116C4⋊C4—1162no—
117C22⋊C4—582no—
118C42—582no—
119C23C2×D11611yescharacteristic
120Q8—584no—
121Q8—1162no—
122Q8—1162no—
123Q8—2321no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—582no—
130C2×C4—582no—
131C2×C4—582no—
132C2×C4—582no—
133C2×C4—1161no—
134C2×C4—1161no—
135C2×C4—1161no—
136C2×C4—1161no—
137C2×C4Dic11612yescomplemented
138C2×C4D4×D2912yes—
139C8—42no—
140C22—21no—
141C22—21no—
142C22#1174524411yescharacteristic
143C22C2×Dic11611yescharacteristic
144C22#1174527111yescharacteristic
145C4—22no—
146C4—22no—
147C4—41no—
148C4—1162no—
149C4—1162no—
150C4—1162no—
151C4—1162no—
152C2—21no—
153C2—21no—
154C2#1427132111yescharacteristic
155C2#1427134811yescharacteristic
156C2#1427135111yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#324C2
socleC22×C29#120
prime radicalC23×C29C2×D4
hypercenter#324D29
hypocenterC29#1605
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
46. C2×C4×C29Q16semidirect
97. C29#1605semidirect
137. C2×C4Dic116semidirect

Maximal subgroups

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

subgroupindex
#142717942
#142713212
#142710832
#142709012
C29×#3242
#160529