Finite Group Databasebeta

← #34091878

Subgroups — #34091878

Order 19904.

142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 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#23755755C211yesmaximal, characteristic
2#23755741C211yesmaximal, characteristic, complemented
3#23755738C211yesmaximal, characteristic, complemented
4#23755708C211yesmaximal, characteristic, complemented
5#23755636C211yesmaximal, characteristic, complemented
6#23755626C211yesmaximal, characteristic, complemented
7#104×C311C211yesmaximal, characteristic, complemented
8#19097315—21no—
9#19097315C2211yescharacteristic
10#19097314—22no—
11#19097314—21no—
12C2×Dic622—21no—
13C2×Dic622C2211yescharacteristic
14C2×Dic622C2211yescharacteristic
15Q8×D311—21no—
16Dic1244—21no—
17#19097305—21no—
18#19097304—21no—
19#19097303—21no—
20#19097299C2211yescharacteristic
21C4⋊Dic311—22no—
22#41×C311C2211yescharacteristic
23M16×C311C2211yescharacteristic
24C42×C311C2211yescharacteristic
25Dic622—22no—
26Dic622—21no—
27Dic622—21no—
28Dic622—21no—
29Dic622—21no—
30Dic622D411yescharacteristic
31D1244D411yescharacteristic
32C22⋊D311—22no—
33C22⋊D311—21no—
34C2×Dic311—22no—
35C2×Dic311—21no—
36C2×Dic311D412yes—
37C4×D311—22no—
38C4×D311—21no—
39C311⋊C8—21no—
40Q8×C311D411yescharacteristic
41D4×C311—21no—
42D4×C311D411yescharacteristic
43C2×C4×C311—21no—
44C2×C4×C311—21no—
45C2×C4×C311C2311yescharacteristic
46C8×C311—21no—
47C22×C311—21no—
48C22×C311C2×D411yescharacteristic
49C2×D311—21no—
50C4×C311—22no—
51C4×C311—21no—
52C4×C311C2×D411yescharacteristic
53C4×C311C2×D411yescharacteristic
54Dic311—21no—
55Dic311—22no—
56Dic311—41no—
57C2×C311—21no—
58C2×C311—41no—
59C2×C311#12011yescharacteristic
60D311—41no—
61C311#45611yescharacteristic, complemented, Sylow
62#456—3111nomaximal, Sylow
632−1+4—3111no—
64#137—3111no—
65#137—3111no—
66C4⋊Q8—3111no—
67#104—3111no—
68#104D31111yescharacteristic, complemented
69#101—3111no—
70#41—3111no—
71#41—6221no—
72#41—6222no—
73#41—6221no—
74#41C2×D31111yescharacteristic
75C2×Q8—3111no—
76C2×Q8—3111no—
77C2×Q8—6221no—
78C2×Q8—6221no—
79Q16—6221no—
80Q16—6221no—
81SD16—6221no—
82SD16—6221no—
83M16—3111no—
84M16C2×D31111yescharacteristic
85C4⋊C4—6222no—
86C42C2×D31111yescharacteristic
87Q8—3111no—
88Q8—6222no—
89Q8—6221no—
90Q8—6221no—
91Q8—6221no—
92Q8—6221no—
93Q8D124411yescharacteristic
94D4—21no—
95D4—3111no—
96D4—6222no—
97D4—6221no—
98D4D124411yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—3112no—
102C2×C4—6222no—
103C2×C4—6222no—
104C2×C4—6221no—
105C2×C4—6221no—
106C2×C4C22×D31111yescharacteristic
107C8—21no—
108C8—6221no—
109C22—21no—
110C22—6221no—
111C22D4×D31111yescharacteristic
112C4—22no—
113C4—21no—
114C4—6222no—
115C4—6221no—
116C4—12441no—
117C4D4×D31111yescharacteristic
118C4C2×D124411yescharacteristic
119C2—21no—
120C2—41no—
121C2—12441no—
122C2#2375567811yescharacteristic
subgroupG/H
centerC2#23755678
commutator, cosocleC2×C4×C311C23
FrattiniC2×C4C22×D311
Fitting#104×C311C2
socleC2×C311#120
prime radical#23755755C2
hypercenter#104D311
hypocenterC311#456
LCSG ▷ C2×C4×C311 ▷ C2×C311 ▷ C311
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #23755741C2semidirect
3. #23755738C2semidirect
4. #23755708C2semidirect
5. #23755636C2semidirect
6. #23755626C2semidirect
7. #104×C311C2semidirect
61. C311#456semidirect
68. #104D311semidirect

Maximal subgroups

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

subgroupindex
#237557552
#237557412
#237557382
#237557082
#237556362
#237556262
#104×C3112
#456311