Finite Group Databasebeta

← #16821521

Subgroups — #16821521

Order 3712.

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

normal subgroups only

This group has 224 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#14271893C211yesmaximal, characteristic, complemented
2#14271346C212yesmaximal
3#14270962C211yesmaximal, characteristic, complemented
4#14270961C212yesmaximal, complemented
5C29×#456C211yesmaximal, characteristic
6C29×2−1+4C2211yescharacteristic
7C29×#137—21no—
8C29×C4⋊Q8C2211yescharacteristic
9#11745313—22no—
10#11745306—21no—
11#11745306C2212yes—
12#11745250—22no—
13#11745249—22no—
14C4×Dic58—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×C29D411yescharacteristic
24C2×Q8×C29C2311yescharacteristic
25C2×Dic58—21no—
26C2×Dic58—21no—
27C2×Dic58D412yes—
28Q16×C29—41no—
29SD16×C29—41no—
30M16×C29—21no—
31C4⋊C4×C29—22no—
32C42×C29D411yescharacteristic
33#90785—42no—
34#90783—42no—
35C4⋊Dic29—21no—
36#90779—22no—
37#90779—22no—
38#90779—22no—
39C4×Dic29—21no—
40C4×Dic29—22no—
41C4×Dic29D412yes—
42#90777—22no—
43Q8×C29—22no—
44Q8×C29—21no—
45Q8×C29—41no—
46Q8×C29—41no—
47D4×C29—22no—
48D4×C29—21no—
49D4×C29—41no—
50C2×C4×C29—21no—
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—
58Dic58—24no—
59Dic58—42no—
60Dic58—81no—
61C8×C29—41no—
62#6597—42no—
63#2205—291nomaximal, Sylow
64C22×C29—41no—
65C22×C29#12011yescharacteristic
66C4×C29—22no—
67C4×C29—22no—
68C4×C29—21no—
69C4×C29—41no—
70C4×C29—41no—
71Dic29—24no—
72Dic29—42no—
73Q82—291no—
74#456—292no—
75#456D2911yescharacteristic
76#356—291no—
77#356—292no—
78C2×C29—21no—
79C2×C29—81no—
80C2×C29B(4,𝔽2)11yescharacteristic
812−1+4C2×D2911yescharacteristic
82#137—21no—
83#137—582no—
84C4⋊Q8—292no—
85C4⋊Q8—582no—
86C4⋊Q8—581no—
87C4⋊Q8C2×D2911yescharacteristic
88C4×Q8—582no—
89C4×Q8—581no—
90#104—21no—
91#104—582no—
92#101—292no—
93#101C2×D2911yescharacteristic
94C29#220511yescharacteristic, complemented, Sylow
95#41—22no—
96#41—21no—
97#41—41no—
98C2×Q8—41no—
99C2×Q8—292no—
100C2×Q8—581no—
101C2×Q8—581no—
102C2×Q8C22⋊D2911yescharacteristic
103C2×Q8C22×D2911yescharacteristic
104Q16—41no—
105Q16—1162no—
106SD16—41no—
107SD16—1162no—
108M16—21no—
109M16—582no—
110C4⋊C4—22no—
111C4⋊C4—582no—
112C4⋊C4—581no—
113C4⋊C4—582no—
114C4⋊C4—582no—
115C42—292no—
116C42—582no—
117C42—581no—
118C42C22⋊D2911yescharacteristic
119Q8—21no—
120Q8—22no—
121Q8—41no—
122Q8—41no—
123Q8—584no—
124Q8—1162no—
125Q8—2321no—
126D4—21no—
127D4—22no—
128D4—41no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—42no—
133C2×C4—582no—
134C2×C4—582no—
135C2×C4D4×D2912yes—
136C2×C4C2×C22⋊D2911yescharacteristic
137C8—41no—
138C8—1162no—
139C22—41no—
140C22#1174529911yescharacteristic
141C4—22no—
142C4—21no—
143C4—22no—
144C4—41no—
145C4—41no—
146C4—584no—
147C4—1162no—
148C2—21no—
149C2—81no—
150C2#1427134911yescharacteristic
subgroupG/H
centerC2#14271349
commutator, cosocleC2×Q8×C29C23
FrattiniC2×Q8C22×D29
FittingC29×#456C2
socleC2×C29B(4,𝔽2)
prime radicalC29×2−1+4C22
hypercenter#456D29
hypocenterC29#2205
LCSG ▷ C2×Q8×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #14271893C2semidirect
3. #14270962C2semidirect
4. #14270961C2semidirect
94. C29#2205semidirect

Maximal subgroups

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

subgroupindex
#142718932
#142713462
#142709622
#142709612
C29×#4562
#220529