Finite Group Databasebeta

← #16818502

Subgroups — #16818502

Order 3712.

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

normal subgroups only

This group has 210 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#14271494C212yesmaximal
3#14271093C211yesmaximal, characteristic
4#14270901C212yesmaximal
5C29×#324C211yesmaximal, characteristic
6C2×C4⋊C4×C29C2211yescharacteristic
7#11745288—21no—
8C2×C4⋊Dic29C2211yescharacteristic
9#11745286—21no—
10#11745286C2212yes—
11C2×#90779—21no—
12#11745252—22no—
13#11745250—22no—
14C29×C22⋊C8C2212yes—
15#11745179—21no—
16#11745179C2211yescharacteristic
17#11745165—22no—
18#11745164—22no—
19C22×C4×C29D411yescharacteristic
20C22×C4×C29D411yescharacteristic
21C22×C4×C29C2311yescharacteristic
22C22×Dic29—21no—
23C22×Dic29—21no—
24C2×Dic58—21no—
25C2×Dic58D412yes—
26C2×C8×C29—22no—
27C4⋊C4×C29—22no—
28C22⋊Dic29—22no—
29C4⋊Dic29—21no—
30C4⋊Dic29—21no—
31C4⋊Dic29—21no—
32C4⋊Dic29—22no—
33C4⋊Dic29D412yes—
34#90779—22no—
35#90779—22no—
36#90779—42no—
37C4×Dic29—22no—
38C23×C29C2×D411yescharacteristic
39C2×C4×C29—21no—
40C2×C4×C29—21no—
41C2×C4×C29—21no—
42C2×C4×C29—41no—
43C2×C4×C29—41no—
44C2×C4×C29SD1612yes—
45C2×C4×C29C2×D412yes—
46C2×Dic29—22no—
47C2×Dic29—22no—
48C2×Dic29—22no—
49C2×Dic29—41no—
50C2×Dic29—41no—
51C2×Dic29—41no—
52C2×Dic29—41no—
53C2×Dic29—41no—
54Dic58—42no—
55Dic58—81no—
56C8×C29—42no—
57#1611—291nomaximal, Sylow
58C22×C29—21no—
59C22×C29—21no—
60C22×C29#12011yescharacteristic
61C22×C29C2×SD1611yescharacteristic
62C22×C29#13711yescharacteristic
63C4×C29—22no—
64C4×C29—22no—
65C4×C29—41no—
66Dic29—42no—
67Dic29—42no—
68Dic29—42no—
69Dic29—81no—
70#544—291no—
71#483—292no—
72#398—291no—
73#328—292no—
74#324D2911yescharacteristic
75C2×C29—21no—
76C2×C29—21no—
77C2×C29#44811yescharacteristic
78C2×C29#45611yescharacteristic
79C2×C29#45811yescharacteristic
80C4⋊Q8—582no—
81#125—582no—
82C22⋊Q8—292no—
83C22⋊Q8—581no—
84#117—581no—
85C2×C4⋊C4—291no—
86C2×C4⋊C4—581no—
87C2×C4⋊C4C2×D2911yescharacteristic
88#106—582no—
89#103—582no—
90C22⋊C8C2×D2912yes—
91#95—291no—
92#95—581no—
93C29#161111yescharacteristic, complemented, Sylow
94C2×Q8—292no—
95C2×Q8—581no—
96C22×C4—581no—
97C22×C4—581no—
98C22×C4D11611yescharacteristic
99C22×C4D11611yescharacteristic
100C22×C4C22×D2911yescharacteristic
101C2×C8—22no—
102C4⋊C4—22no—
103C4⋊C4—292no—
104C4⋊C4—581no—
105C4⋊C4—581no—
106C4⋊C4—581no—
107C4⋊C4—582no—
108C4⋊C4—582no—
109C4⋊C4—582no—
110C4⋊C4—1162no—
111C22⋊C4—582no—
112C42—582no—
113C23C2×D11611yescharacteristic
114Q8—1162no—
115Q8—2321no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—582no—
122C2×C4—582no—
123C2×C4—582no—
124C2×C4—1161no—
125C2×C4—1161no—
126C2×C4—1161no—
127C2×C4—1161no—
128C2×C4—1161no—
129C2×C4#9077312yes—
130C2×C4D4×D2912yes—
131C8—42no—
132C22—21no—
133C22—21no—
134C22#1174524411yescharacteristic
135C22C2×#9077311yescharacteristic
136C22#1174527111yescharacteristic
137C4—22no—
138C4—22no—
139C4—41no—
140C4—1162no—
141C4—1162no—
142C4—1162no—
143C4—2321no—
144C2—21no—
145C2—21no—
146C2#1427130411yescharacteristic
147C2#1427134811yescharacteristic
148C2#1427135411yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#324C2
socleC22×C29#120
prime radicalC23×C29C2×D4
hypercenter#324D29
hypocenterC29#1611
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
93. C29#1611semidirect

Maximal subgroups

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

subgroupindex
#142717942
#142714942
#142710932
#142709012
C29×#3242
#161129