Finite Group Databasebeta

← #23765609

Subgroups — #23765609

Order 10112.

132 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 49 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#19098804C211yesmaximal, characteristic
2#19098601C211yesmaximal, characteristic
3#19098391C211yesmaximal, characteristic, complemented
4#19098389C211yesmaximal, characteristic, complemented
5#19098368C211yesmaximal, characteristic, complemented
6#19098368C211yesmaximal, characteristic, complemented
7C22⋊C16×C79C211yesmaximal, characteristic
8C2×Dic316C2211yescharacteristic
9#14579140—21no—
10#14579120—21no—
11#14579095C2211yescharacteristic
12#14579095C2211yescharacteristic
13#14579095C2211yescharacteristic
14#14579093—21no—
15#14579086—21no—
16C22×C8×C79C2211yescharacteristic
17C2×C16×C79C2211yescharacteristic
18C2×C16×C79C2211yescharacteristic
19C2×Dic158—21no—
20Dic316—21no—
21Dic316—21no—
22C4⋊Dic79—21no—
23C4⋊Dic79—21no—
24C4⋊Dic79—21no—
25Dic79⋊C4—41no—
26C22⋊Dic79—41no—
27C22⋊Dic79—41no—
28C4×Dic79—41no—
29C22×C4×C79D411yescharacteristic
30C2×C8×C79—21no—
31C2×C8×C79—21no—
32C2×C8×C79D411yescharacteristic
33C2×C8×C79C2311yescharacteristic
34C16×C79—21no—
35C16×C79—21no—
36C23×C79D811yescharacteristic
37C2×C4×C79—21no—
38C2×C4×C79—21no—
39C2×C4×C79D811yescharacteristic
40C2×C4×C79C2×D411yescharacteristic
41C2×Dic79—41no—
42C2×Dic79—41no—
43C2×Dic79—41no—
44C2×Dic79—41no—
45Dic158—41no—
46Dic158—41no—
47C8×C79—21no—
48C8×C79#4111yescharacteristic
49C8×C79#4111yescharacteristic
50C22×C79—21no—
51C22×C79—21no—
52C22×C79—21no—
53C22×C79C2×D811yescharacteristic
54C4×C79—21no—
55C4×C79#12311yescharacteristic
56C4×C79#13711yescharacteristic
57Dic79—81no—
58Dic79—81no—
59Dic79—81no—
60Dic79—81no—
61C2×C79—41no—
62C2×C79#48011yescharacteristic
63C2×C79#50811yescharacteristic
64C2×C79#51011yescharacteristic
65#2237—791nomaximal, Sylow
66C79#223711yescharacteristic, complemented, Sylow
67#467—791no—
68#427—791no—
69#367—791no—
70#366—791no—
71#358—791no—
72#358—791no—
73C22⋊C16D7911yescharacteristic
74C2×Q16—791no—
75C22×C8C2×D7911yescharacteristic
76C22⋊Q8—1581no—
77#117—1581no—
78C2×C16C2×D7911yescharacteristic
79C2×C16C2×D7911yescharacteristic
80#107—791no—
81#107—791no—
82#107—791no—
83#106—1581no—
84#103—1581no—
85C2×Q8—1581no—
86C22×C4D31611yescharacteristic
87Q16—1581no—
88Q16—1581no—
89C2×C8—21no—
90C2×C8—21no—
91C2×C8D31611yescharacteristic
92C2×C8C22×D7911yescharacteristic
93C4⋊C4—3161no—
94C4⋊C4—1581no—
95C4⋊C4—1581no—
96C4⋊C4—1581no—
97C22⋊C4—3161no—
98C22⋊C4—3161no—
99C42—3161no—
100C16—21no—
101C16—21no—
102C23D63211yescharacteristic
103Q8—3161no—
104Q8—3161no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—3161no—
108C2×C4—3161no—
109C2×C4—3161no—
110C2×C4—3161no—
111C2×C4D63211yescharacteristic
112C2×C4C2×D31611yescharacteristic
113C8—21no—
114C8#1192962311yescharacteristic
115C8#1192962311yescharacteristic
116C22—21no—
117C22—21no—
118C22—21no—
119C22C2×D63211yescharacteristic
120C4—21no—
121C4—6321no—
122C4—6321no—
123C4—6321no—
124C4—6321no—
125C4#1457914511yescharacteristic
126C4#1457919411yescharacteristic
127C2—41no—
128C2#1909887711yescharacteristic
129C2#1909899511yescharacteristic
130C2#1909900611yescharacteristic
subgroupG/H
centerC22C2×D632
commutator, cosocleC2×C8×C79C23
FrattiniC2×C8C22×D79
FittingC22⋊C16×C79C2
socleC22×C79C2×D8
prime radicalC23×C79D8
hypercenterC22⋊C16D79
hypocenterC79#2237
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
3. #19098391C2semidirect
4. #19098389C2semidirect
5. #19098368C2semidirect
6. #19098368C2semidirect
66. C79#2237semidirect