Finite Group Databasebeta

← #16821504

Subgroups — #16821504

Order 3712.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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#14271913C211yesmaximal, characteristic, complemented
2#14271353C212yesmaximal
3#14270958C211yesmaximal, characteristic, complemented
4#14270954C212yesmaximal, complemented
5C29×#455C211yesmaximal, characteristic
6C29×H(5,𝔽2)C2211yescharacteristic
7C29×#137—21no—
8C29×#124C2211yescharacteristic
9#11745306—21no—
10#11745297—22no—
11#11745297C2212yes—
12#11745241—22no—
13#11745240—22no—
14#11745232—21no—
15C29×#104—21no—
16C29×#100C2211yescharacteristic
17#11745182—22no—
18#11745182C2212yes—
19#41×C29—21no—
20#41×C29—41no—
21C2×Q8×C29D411yescharacteristic
22C2×D4×C29—22no—
23C2×D4×C29—41no—
24C2×D4×C29C2311yescharacteristic
25C22×Dic29D412yes—
26C2×Dic58—21no—
27Q16×C29—41no—
28SD16×C29—41no—
29M16×C29—21no—
30C22⋊C4×C29—22no—
31C42×C29D411yescharacteristic
32C22⋊Dic29—22no—
33C22⋊Dic29—22no—
34C22⋊Dic29—42no—
35C22⋊Dic29D412yes—
36C4⋊Dic29—21no—
37C4⋊Dic29—21no—
38#90779—22no—
39#90779—22no—
40#90779—22no—
41#90779—42no—
42C4×Dic29—21no—
43C23×C29—22no—
44C23×C29C2×D412yes—
45Q8×C29—21no—
46Q8×C29—41no—
47D4×C29—21no—
48D4×C29—41no—
49D4×C29—42no—
50D4×C29—41no—
51C2×C4×C29—22no—
52C2×C4×C29—21no—
53C2×C4×C29—21no—
54C2×C4×C29—41no—
55C2×C4×C29C2×D411yescharacteristic
56C2×Dic29—22no—
57C2×Dic29—22no—
58C2×Dic29—42no—
59C2×Dic29—42no—
60Dic58—81no—
61C8×C29—41no—
62#2201—291nomaximal, Sylow
63C22×C29—22no—
64C22×C29—42no—
65C22×C29—41no—
66C22×C29—82no—
67C22×C29#12011yescharacteristic
68C4×C29—21no—
69C4×C29—41no—
70C4×C29—41no—
71C4×C29—41no—
72Dic29—42no—
73Dic29—42no—
74Dic29—82no—
75#563—291no—
76#458—292no—
77#455D2911yescharacteristic
78#354—291no—
79#352—292no—
80C2×C29—21no—
81C2×C29—42no—
82C2×C29—81no—
83C2×C29B(4,𝔽2)11yescharacteristic
84H(5,𝔽2)C2×D2911yescharacteristic
85#137—21no—
86C4⋊Q8—581no—
87#126—582no—
88#125—581no—
89#124C2×D2911yescharacteristic
90#123—292no—
91#123—582no—
92C22⋊Q8—582no—
93#104—21no—
94#100C2×D2911yescharacteristic
95#99—292no—
96#99—582no—
97C29#220111yescharacteristic, complemented, Sylow
98#41—21no—
99#41—41no—
100C2×Q8—581no—
101C2×Q8C22⋊D2911yescharacteristic
102C2×D4—22no—
103C2×D4—41no—
104C2×D4C22×D2911yescharacteristic
105C22×C4—292no—
106Q16—41no—
107SD16—41no—
108M16—21no—
109C4⋊C4—581no—
110C4⋊C4—582no—
111C4⋊C4—582no—
112C4⋊C4—581no—
113C4⋊C4—582no—
114C4⋊C4—1162no—
115C22⋊C4—22no—
116C22⋊C4—292no—
117C22⋊C4—582no—
118C22⋊C4—582no—
119C22⋊C4—1162no—
120C42—581no—
121C42C22⋊D2911yescharacteristic
122C23—22no—
123C23D4×D2912yes—
124Q8—21no—
125Q8—41no—
126Q8—2321no—
127D4—21no—
128D4—41no—
129D4—42no—
130D4—41no—
131C2×C4—22no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—582no—
136C2×C4—582no—
137C2×C4—1162no—
138C2×C4—1162no—
139C2×C4C2×C22⋊D2911yescharacteristic
140C8—41no—
141C22—22no—
142C22—42no—
143C22—41no—
144C22—82no—
145C22#1174529911yescharacteristic
146C4—21no—
147C4—41no—
148C4—41no—
149C4—41no—
150C4—1162no—
151C4—1162no—
152C4—2322no—
153C2—21no—
154C2—42no—
155C2—81no—
156C2#1427134911yescharacteristic
subgroupG/H
centerC2#14271349
commutator, cosocleC2×D4×C29C23
FrattiniC2×D4C22×D29
FittingC29×#455C2
socleC2×C29B(4,𝔽2)
prime radicalC29×H(5,𝔽2)C22
hypercenter#455D29
hypocenterC29#2201
LCSG ▷ C2×D4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #14271913C2semidirect
3. #14270958C2semidirect
4. #14270954C2semidirect
97. C29#2201semidirect

Maximal subgroups

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

subgroupindex
#142719132
#142713532
#142709582
#142709542
C29×#4552
#220129