Finite Group Databasebeta

← #16818536

Subgroups — #16818536

Order 3712.

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

normal subgroups only

This group has 202 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#14271499C212yesmaximal
3#14271102C211yesmaximal, characteristic
4#14270901C212yesmaximal
5C29×#324C211yesmaximal, characteristic
6C2×C4⋊C4×C29C2211yescharacteristic
7#11745288—21no—
8C2×C4⋊Dic29C2211yescharacteristic
9#11745286—21no—
10#11745286C2212yes—
11#11745252—22no—
12#11745250—22no—
13C29×C22⋊C8C2212yes—
14#11745179—21no—
15#11745179—21no—
16#11745179C2211yescharacteristic
17#11745166—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—
36C4×Dic29—22no—
37C23×C29C2×D411yescharacteristic
38C2×C4×C29—21no—
39C2×C4×C29—21no—
40C2×C4×C29—21no—
41C2×C4×C29—41no—
42C2×C4×C29—41no—
43C2×C4×C29Q1612yes—
44C2×C4×C29C2×D412yes—
45C2×Dic29—22no—
46C2×Dic29—22no—
47C2×Dic29—41no—
48C2×Dic29—41no—
49C2×Dic29—42no—
50C2×Dic29—41no—
51C2×Dic29—41no—
52Dic58—42no—
53Dic58—81no—
54C8×C29—42no—
55#1617—291nomaximal, Sylow
56C22×C29—21no—
57C22×C29—21no—
58C22×C29#12011yescharacteristic
59C22×C29C2×Q1611yescharacteristic
60C22×C29#13711yescharacteristic
61C4×C29—22no—
62C4×C29—22no—
63C4×C29—41no—
64Dic29—42no—
65Dic29—42no—
66Dic29—81no—
67Dic29—81no—
68#544—291no—
69#484—292no—
70#400—291no—
71#328—292no—
72#324D2911yescharacteristic
73C2×C29—21no—
74C2×C29—21no—
75C2×C29#45111yescharacteristic
76C2×C29#45411yescharacteristic
77C2×C29#45811yescharacteristic
78C4⋊Q8—582no—
79#125—582no—
80C22⋊Q8—292no—
81C22⋊Q8—581no—
82#117—581no—
83C2×C4⋊C4—291no—
84C2×C4⋊C4C2×D2911yescharacteristic
85#107—582no—
86#103—582no—
87C22⋊C8C2×D2912yes—
88#95—291no—
89#95—581no—
90#95—581no—
91C29#161711yescharacteristic, complemented, Sylow
92C2×Q8—292no—
93C2×Q8—581no—
94C22×C4—581no—
95C22×C4—581no—
96C22×C4D11611yescharacteristic
97C22×C4D11611yescharacteristic
98C22×C4C22×D2911yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—292no—
102C4⋊C4—581no—
103C4⋊C4—581no—
104C4⋊C4—581no—
105C4⋊C4—582no—
106C4⋊C4—582no—
107C4⋊C4—582no—
108C22⋊C4—582no—
109C42—582no—
110C23C2×D11611yescharacteristic
111Q8—1162no—
112Q8—2321no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—582no—
119C2×C4—582no—
120C2×C4—1161no—
121C2×C4—1161no—
122C2×C4—1162no—
123C2×C4—1161no—
124C2×C4—1161no—
125C2×C4Dic11612yes—
126C2×C4D4×D2912yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#1174524411yescharacteristic
131C22C2×Dic11611yescharacteristic
132C22#1174527111yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—1162no—
137C4—1162no—
138C4—2321no—
139C4—2321no—
140C2—21no—
141C2—21no—
142C2#1427132111yescharacteristic
143C2#1427133811yescharacteristic
144C2#1427135411yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#324C2
socleC22×C29#120
prime radicalC23×C29C2×D4
hypercenter#324D29
hypocenterC29#1617
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
91. C29#1617semidirect

Maximal subgroups

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

subgroupindex
#142717942
#142714992
#142711022
#142709012
C29×#3242
#161729