Finite Group Databasebeta

← #16820649

Subgroups — #16820649

Order 3712.

282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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, complemented
2#14271169C212yesmaximal
3#14271064C211yesmaximal, characteristic
4#14270924C212yesmaximal, complemented
5C29×#343C211yesmaximal, characteristic, complemented
6C22×D116C2211yescharacteristic
7C2×M16×C29C2212yes—
8C2×C4⋊C4×C29C2211yescharacteristic
9C2×#90781—22no—
10#11745288C2212yes—
11#11745286—22no—
12C2×C4×Dic29C2211yescharacteristic
13#11745252—22no—
14#11745250—22no—
15#11745169—22no—
16#11745169—22no—
17C23×D29—21no—
18C22×C4×C29D412yes—
19C22×C4×C29C2311yescharacteristic
20C22×Dic29—21no—
21C2×D116—22no—
22C2×D116—22no—
23C2×D116—21no—
24C2×D116Q812yescomplemented
25C2×Dic58—22no—
26M16×C29—22no—
27M16×C29—22no—
28C2×C8×C29—22no—
29C4⋊C4×C29—22no—
30C22⋊Dic29—22no—
31#90781—44no—
32C4⋊Dic29—22no—
33C4⋊Dic29D412yes—
34C4⋊Dic29D412yes—
35#90779—24no—
36C4×Dic29—22no—
37C4×Dic29—22no—
38C23×C29C2×D411yescharacteristic
39C22×D29—22no—
40C22×D29—42no—
41C22×D29—42no—
42C22×D29—41no—
43C22×D29—41no—
44C2×C4×C29—22no—
45C2×C4×C29—42no—
46C2×C4×C29C2×D412yes—
47C2×C4×C29C2×Q811yescharacteristic
48C2×C4×C29#4112yes—
49C2×C4×C29#4111yescharacteristic
50C2×Dic29—22no—
51C2×Dic29—22no—
52C2×Dic29—22no—
53C2×Dic29—41no—
54C2×Dic29—41no—
55D116—24no—
56D116—42no—
57Dic58—82no—
58C8×C29—42no—
59#2027—291nomaximal, Sylow
60C22×C29—21no—
61C22×C29—21no—
62C22×C29#12011yescharacteristic
63C22×C29C22⋊Q811yescharacteristic
64C22×C29#12411yescharacteristic
65C2×D29—44no—
66C2×D29—42no—
67C2×D29—82no—
68C2×D29—81no—
69C2×D29—81no—
70C4×C29—42no—
71C4×C29C22⋊Q812yes—
72C4×C29#12412yes—
73Dic29—42no—
74Dic29—42no—
75Dic29—42no—
76#544—291no—
77#418—292no—
78#390—291no—
79#343D2911yescharacteristic, complemented
80#339—292no—
81C2×C29—21no—
82C2×C29—21no—
83C2×C29#39311yescharacteristic
84C2×C29#45311yescharacteristic
85C2×C29#45411yescharacteristic
86D29—82no—
87C22×D4—291no—
88C2×M16C2×D2912yes—
89C4⋊Q8—582no—
90#125—582no—
91C22⋊Q8—582no—
92#117—292no—
93C2×C4⋊C4C2×D2911yescharacteristic
94C2×C22⋊C4—582no—
95C2×C42—291no—
96#102—582no—
97#102—582no—
98C29#202711yescharacteristic, complemented, Sylow
99C24—581no—
100C2×Q8—582no—
101C2×D4—292no—
102C2×D4—582no—
103C2×D4—582no—
104C2×D4—581no—
105C22×C4—581no—
106C22×C4D11612yes—
107C22×C4C22×D2911yescharacteristic
108M16—22no—
109M16—22no—
110C2×C8—22no—
111C4⋊C4—22no—
112C4⋊C4—292no—
113C4⋊C4—292no—
114C4⋊C4—582no—
115C4⋊C4—584no—
116C22⋊C4—582no—
117C22⋊C4—1164no—
118C42—582no—
119C42—582no—
120C23—582no—
121C23—1162no—
122C23—1162no—
123C23—1161no—
124C23—1161no—
125C23C2×D11611yescharacteristic
126Q8—2322no—
127D4—584no—
128D4—1162no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—582no—
132C2×C4—582no—
133C2×C4—582no—
134C2×C4—1161no—
135C2×C4—1161no—
136C2×C4#9080512yes—
137C2×C4D4×D2912yes—
138C2×C4#9080711yescharacteristic
139C2×C4Q8×D2911yescharacteristic
140C8—42no—
141C22—21no—
142C22—21no—
143C22—1164no—
144C22—1162no—
145C22—2322no—
146C22—2321no—
147C22—2321no—
148C22#1174523711yescharacteristic
149C22#1174524411yescharacteristic
150C22#1174525911yescharacteristic
151C4—42no—
152C4—1162no—
153C4—1162no—
154C4—1162no—
155C4#1174524712yes—
156C4#1174525812yes—
157C2—21no—
158C2—21no—
159C2—2322no—
160C2#1427107611yescharacteristic
161C2#1427133311yescharacteristic
162C2#1427133811yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#343C2
socleC22×C29#120
prime radicalC22×D116C22
hypercenter#343D29
hypocenterC29#2027
LCSG ▷ C22×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. #14271794C2semidirect
4. #14270924C2semidirect
5. C29×#343C2semidirect
24. C2×D116Q8semidirect
79. #343D29semidirect
98. C29#2027semidirect

Maximal subgroups

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

subgroupindex
#142717942
#142711692
#142710642
#142709242
C29×#3432
#202729