Finite Group Databasebeta

← #16818497

Subgroups — #16818497

Order 3712.

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

normal subgroups only

This group has 254 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#14271744C211yesmaximal, characteristic
2#14271477C212yesmaximal, complemented
3#14271093C211yesmaximal, characteristic, complemented
4#14270898C212yesmaximal, complemented
5C29×#324C211yesmaximal, characteristic, complemented
6C2×#90805—21no—
7C2×C4⋊C4×C29C2211yescharacteristic
8#11745292—21no—
9#11745292C2212yes—
10C2×C4⋊Dic29C2211yescharacteristic
11C2×#90779—21no—
12#11745259—22no—
13#11745257—22no—
14C29×C22⋊C8C2212yes—
15#11745179—21no—
16#11745179C2211yescharacteristic
17#11745169—22no—
18#11745166—22no—
19C22×C4×C29D411yescharacteristic
20C22×C4×C29D411yescharacteristic
21C22×C4×C29C2311yescharacteristic
22C2×C22⋊D29—22no—
23C22×Dic29—21no—
24C22×Dic29—21no—
25#90805—42no—
26#90805—42no—
27C2×D116—21no—
28C2×D116—21no—
29C2×D116D412yes—
30C2×C4×D29—22no—
31C2×Dic58—21no—
32C2×C8×C29—22no—
33C4⋊C4×C29—22no—
34#90781—22no—
35#90781—22no—
36C4⋊Dic29—21no—
37C4⋊Dic29—22no—
38C4⋊Dic29D412yes—
39#90779—42no—
40C23×C29C2×D411yescharacteristic
41C22×D29—22no—
42C2×C4×C29—21no—
43C2×C4×C29—21no—
44C2×C4×C29—21no—
45C2×C4×C29—41no—
46C2×C4×C29—41no—
47C2×C4×C29D812yes—
48C2×C4×C29C2×D412yes—
49C22⋊D29—42no—
50C22⋊D29—42no—
51C2×Dic29—22no—
52C2×Dic29—22no—
53C2×Dic29—41no—
54C2×Dic29—41no—
55C2×Dic29—41no—
56C2×Dic29—41no—
57C2×Dic29—41no—
58D116—42no—
59D116—42no—
60D116—81no—
61C4×D29—44no—
62Dic58—42no—
63C8×C29—42no—
64#1610—291nomaximal, Sylow
65C22×C29—21no—
66C22×C29—21no—
67C22×C29#12011yescharacteristic
68C22×C29C2×D811yescharacteristic
69C22×C29AGL(1,ℤ/8)11yescharacteristic
70C2×D29—42no—
71C2×D29—42no—
72C2×D29—42no—
73C4×C29—22no—
74C4×C29—22no—
75C4×C29—41no—
76Dic29—42no—
77Dic29—42no—
78Dic29—81no—
79#537—291no—
80#480—292no—
81#398—291no—
82#327—292no—
83#324D2911yescharacteristic, complemented
84C2×C29—21no—
85C2×C29—21no—
86C2×C29#44711yescharacteristic
87C2×C29#45611yescharacteristic
88C2×C29#45811yescharacteristic
89D29—82no—
90C2×#41—581no—
91C22⋊Q8—582no—
92#121—292no—
93#121—582no—
94#121—581no—
95C2×C4⋊C4—291no—
96C2×C4⋊C4—581no—
97C2×C4⋊C4C2×D2911yescharacteristic
98#107—582no—
99#102—582no—
100C22⋊C8C2×D2912yes—
101#95—291no—
102#95—581no—
103C29#161011yescharacteristic, complemented, Sylow
104#41—1162no—
105#41—1162no—
106C2×Q8—581no—
107C2×D4—292no—
108C2×D4—581no—
109C2×D4—581no—
110C2×D4—582no—
111C22×C4—582no—
112C22×C4—581no—
113C22×C4—581no—
114C22×C4D11611yescharacteristic
115C22×C4D11611yescharacteristic
116C22×C4C22×D2911yescharacteristic
117C2×C8—22no—
118C4⋊C4—22no—
119C4⋊C4—292no—
120C4⋊C4—581no—
121C4⋊C4—582no—
122C4⋊C4—1162no—
123C22⋊C4—582no—
124C22⋊C4—582no—
125C23—582no—
126C23C2×D11611yescharacteristic
127Q8—1162no—
128D4—1162no—
129D4—1162no—
130D4—1162no—
131D4—1162no—
132D4—2321no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—582no—
139C2×C4—582no—
140C2×C4—1164no—
141C2×C4—1161no—
142C2×C4—1161no—
143C2×C4—1161no—
144C2×C4—1161no—
145C2×C4—1161no—
146C2×C4D23212yes—
147C2×C4D4×D2912yes—
148C8—42no—
149C22—21no—
150C22—21no—
151C22—1162no—
152C22—1162no—
153C22—1162no—
154C22#1174524411yescharacteristic
155C22C2×D23211yescharacteristic
156C22#1174527011yescharacteristic
157C4—22no—
158C4—22no—
159C4—41no—
160C4—1162no—
161C4—1162no—
162C4—2321no—
163C2—21no—
164C2—21no—
165C2—2322no—
166C2#1427129911yescharacteristic
167C2#1427134811yescharacteristic
168C2#1427135411yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#324C2
socleC22×C29#120
prime radical#14271744C2
hypercenter#324D29
hypocenterC29#1610
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
2. #14271477C2semidirect
3. #14271093C2semidirect
4. #14270898C2semidirect
5. C29×#324C2semidirect
83. #324D29semidirect
103. C29#1610semidirect

Maximal subgroups

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

subgroupindex
#142717442
#142714772
#142710932
#142708982
C29×#3242
#161029