Finite Group Databasebeta

← #16821512

Subgroups — #16821512

Order 3712.

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

normal subgroups only

This group has 216 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#14271346C212yesmaximal, complemented
3#14270961C212yesmaximal, complemented
4#14270960C211yesmaximal, characteristic, complemented
5C29×#454C211yesmaximal, characteristic
6C29×2−1+4C2211yescharacteristic
7C29×AGL(1,ℤ/8)—21no—
8C29×#124C2211yescharacteristic
9#11745313—22no—
10#11745306C2212yes—
11#11745297—21no—
12#11745241—22no—
13#11745240—22no—
14#11745232—21no—
15C29×#104—21no—
16C29×#101C2211yescharacteristic
17#11745185—22no—
18#11745184C2212yes—
19#41×C29—22no—
20#41×C29—21no—
21#41×C29—41no—
22C2×Q8×C29—41no—
23C2×Q8×C29C2311yescharacteristic
24C2×D4×C29D411yescharacteristic
25C22×Dic29—21no—
26C2×Dic58D412yes—
27SD16×C29—41no—
28D8×C29—41no—
29M16×C29—21no—
30C22⋊C4×C29—22no—
31C42×C29D411yescharacteristic
32C22⋊Dic29—22no—
33C22⋊Dic29—21no—
34#90785—42no—
35#90783—42no—
36C4⋊Dic29—21no—
37C4⋊Dic29—21no—
38#90779—22no—
39#90779—22no—
40#90779—22no—
41C4×Dic29D412yes—
42#90777—22no—
43C23×C29—21no—
44Q8×C29—22no—
45Q8×C29—21no—
46Q8×C29—41no—
47D4×C29—22no—
48D4×C29—21no—
49D4×C29—41no—
50D4×C29—41no—
51C2×C4×C29—21no—
52C2×C4×C29—42no—
53C2×C4×C29—41no—
54C2×C4×C29C2×D412yes—
55C2×C4×C29C2×D411yescharacteristic
56C2×Dic29—22no—
57C2×Dic29—22no—
58C2×Dic29—81no—
59Dic58—42no—
60C8×C29—41no—
61#6597—42no—
62#2203—291nomaximal, Sylow
63C22×C29—42no—
64C22×C29—41no—
65C22×C29—41no—
66C22×C29#12011yescharacteristic
67C4×C29—22no—
68C4×C29—21no—
69C4×C29—41no—
70C4×C29—41no—
71Dic29—42no—
72Dic29—42no—
73#563—291no—
74#456—292no—
75#454D2911yescharacteristic
76#356—292no—
77#355—291no—
78C2×C29—21no—
79C2×C29—81no—
80C2×C29—81no—
81C2×C29B(4,𝔽2)11yescharacteristic
822−1+4C2×D2911yescharacteristic
83#137—582no—
84AGL(1,ℤ/8)—21no—
85C4⋊Q8—292no—
86#126—582no—
87#125—581no—
88#124C2×D2911yescharacteristic
89#123—581no—
90C22⋊Q8—582no—
91#104—21no—
92#104—582no—
93#101—292no—
94#101C2×D2911yescharacteristic
95C29#220311yescharacteristic, complemented, Sylow
96#41—22no—
97#41—21no—
98#41—41no—
99C2×Q8—41no—
100C2×Q8—292no—
101C2×Q8C22×D2911yescharacteristic
102C2×D4C22⋊D2911yescharacteristic
103C22×C4—581no—
104Q16—1162no—
105SD16—41no—
106SD16—1162no—
107D8—41no—
108M16—21no—
109M16—582no—
110C4⋊C4—581no—
111C4⋊C4—582no—
112C4⋊C4—581no—
113C4⋊C4—582no—
114C4⋊C4—582no—
115C22⋊C4—22no—
116C22⋊C4—582no—
117C22⋊C4—581no—
118C42—292no—
119C42C22⋊D2911yescharacteristic
120C23—21no—
121Q8—21no—
122Q8—22no—
123Q8—41no—
124Q8—1162no—
125D4—21no—
126D4—22no—
127D4—41no—
128D4—41no—
129C2×C4—21no—
130C2×C4—41no—
131C2×C4—42no—
132C2×C4—582no—
133C2×C4—582no—
134C2×C4—2321no—
135C2×C4D4×D2912yes—
136C2×C4C2×C22⋊D2911yescharacteristic
137C8—41no—
138C8—1162no—
139C22—42no—
140C22—41no—
141C22—41no—
142C22#1174529911yescharacteristic
143C4—21no—
144C4—22no—
145C4—41no—
146C4—41no—
147C4—1162no—
148C4—1162no—
149C2—21no—
150C2—81no—
151C2—81no—
152C2#1427134911yescharacteristic
subgroupG/H
centerC2#14271349
commutator, cosocleC2×Q8×C29C23
FrattiniC2×Q8C22×D29
Fitting, prime radicalC29×#454C2
socleC2×C29B(4,𝔽2)
hypercenter#454D29
hypocenterC29#2203
LCSG ▷ C2×Q8×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #14271913C2semidirect
2. #14271346C2semidirect
3. #14270961C2semidirect
4. #14270960C2semidirect
95. C29#2203semidirect

Maximal subgroups

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

subgroupindex
#142719132
#142713462
#142709612
#142709602
C29×#4542
#220329