Finite Group Databasebeta

← #16818499

Subgroups — #16818499

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#14271493C212yesmaximal
3#14270899C212yesmaximal
4#14270889C211yesmaximal, characteristic
5C29×#398C211yesmaximal, characteristic
6C2×C4⋊C4×C29—21no—
7C2×C4⋊C4×C29C2211yescharacteristic
8C2×C4⋊C4×C29C2211yescharacteristic
9#11745288—21no—
10#11745286—21no—
11#11745286C2212yes—
12#11745252—22no—
13#11745250—22no—
14C29×#95—21no—
15C29×#95C2211yescharacteristic
16C22⋊#6597C2212yes—
17#11745158—22no—
18#11745156—22no—
19C22×C4×C29—21no—
20C22×C4×C29—21no—
21C22×C4×C29D411yescharacteristic
22C22×C4×C29D411yescharacteristic
23C22×C4×C29C2311yescharacteristic
24C2×Dic58—21no—
25C2×Dic58D412yes—
26C4⋊C4×C29—22no—
27C4⋊C4×C29—22no—
28C4⋊C4×C29—42no—
29C22⋊Dic29—22no—
30C4⋊Dic29—21no—
31C4⋊Dic29—21no—
32C4⋊Dic29—21no—
33C4⋊Dic29D412yes—
34#90779—22no—
35#90779—22no—
36C4×Dic29—22no—
37C2×#6597—22no—
38C23×C29C2×D411yescharacteristic
39C2×C4×C29—21no—
40C2×C4×C29—21no—
41C2×C4×C29—22no—
42C2×C4×C29—21no—
43C2×C4×C29—41no—
44C2×C4×C29—41no—
45C2×C4×C29—41no—
46C2×C4×C29—41no—
47C2×C4×C29—41no—
48C2×C4×C29—41no—
49C2×C4×C29—41no—
50C2×C4×C29SD1612yes—
51C2×C4×C29C2×D412yes—
52C2×Dic29—22no—
53C2×Dic29—22no—
54Dic58—42no—
55Dic58—81no—
56#6597—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—42no—
66C4×C29—41no—
67C4×C29—81no—
68Dic29—42no—
69Dic29—42no—
70#544—291no—
71#483—292no—
72#398D2911yescharacteristic
73#328—292no—
74#324—291no—
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—21no—
86C2×C4⋊C4C2×D2911yescharacteristic
87C2×C4⋊C4C2×D2911yescharacteristic
88#106—582no—
89#103—582no—
90C22⋊C8—292no—
91#95—21no—
92#95C2×D2911yescharacteristic
93C29#161111yescharacteristic, complemented, Sylow
94C2×Q8—292no—
95C2×Q8—581no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4C22⋊D2911yescharacteristic
99C22×C4C22⋊D2911yescharacteristic
100C22×C4C22×D2911yescharacteristic
101C2×C8—582no—
102C4⋊C4—22no—
103C4⋊C4—22no—
104C4⋊C4—42no—
105C4⋊C4—292no—
106C4⋊C4—581no—
107C4⋊C4—581no—
108C4⋊C4—581no—
109C4⋊C4—582no—
110C4⋊C4—582no—
111C22⋊C4—582no—
112C42—582no—
113C23C2×C22⋊D2911yescharacteristic
114Q8—1162no—
115Q8—2321no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—21no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—582no—
128C2×C4—582no—
129C2×C4#9078312yes—
130C2×C4D4×D2912yes—
131C8—1162no—
132C22—21no—
133C22—21no—
134C22C2×#9078311yescharacteristic
135C22#1174529911yescharacteristic
136C22#1174531311yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—41no—
141C4—81no—
142C4—1162no—
143C4—1162no—
144C2—21no—
145C2—21no—
146C2#1427130111yescharacteristic
147C2#1427134511yescharacteristic
148C2#1427135211yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#398C2
socleC22×C29#120
prime radicalC23×C29C2×D4
hypercenter#398D29
hypocenterC29#1611
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

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
#142714932
#142708992
#142708892
C29×#3982
#161129