Finite Group Databasebeta

← #23762281

Subgroups — #23762281

Order 10112.

166 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 61 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#19098687C211yesmaximal, characteristic, complemented
2C4×#11929612C211yesmaximal, characteristic
3#19098641C211yesmaximal, characteristic
4#19098315C211yesmaximal, characteristic, complemented
5#19098295C211yesmaximal, characteristic, complemented
6#19098284C211yesmaximal, characteristic, complemented
7D4⋊C8×C79C211yesmaximal, characteristic
8C2×#11929612C411yescharacteristic
9C2×#11929608—21no—
10C4×Dic158C2211yescharacteristic
11#14579092C411yescharacteristic
12C4⋊(C79⋊C8)C2211yescharacteristic
13Dic79⋊C8—21no—
14#14579084C411yescharacteristic
15#14579082C411yescharacteristic
16C22⋊(C79⋊C8)—21no—
17C4×C79⋊C8C2211yescharacteristic
18C4×C79⋊C8C2211yescharacteristic
19C8×Dic79—21no—
20C4×D4×C79C2211yescharacteristic
21C4⋊C8×C79C2211yescharacteristic
22C4×C8×C79C2211yescharacteristic
23C2×Dic158C2×C411yescharacteristic
24#11929612—22no—
25#11929608—42no—
26C2×C79⋊C8—21no—
27C2×C79⋊C8C2×C411yescharacteristic
28C2×C79⋊C8C2×C411yescharacteristic
29C2×C79⋊C8D411yescharacteristic
30C2×C79⋊C8D411yescharacteristic
31C4⋊Dic79C2×C411yescharacteristic
32Dic79⋊C4—21no—
33C4×Dic79—21no—
34C2×D4×C79C2×C411yescharacteristic
35C22×C4×C79—21no—
36C2×C8×C79—21no—
37C2×C8×C79—21no—
38C4⋊C4×C79C2×C411yescharacteristic
39C22⋊C4×C79—21no—
40C42×C79C2311yescharacteristic
41C23×C79—21no—
42D4×C79—21no—
43D4×C79—21no—
44C2×C4×C79—21no—
45C2×C4×C79—41no—
46C2×C4×C79—41no—
47C2×C4×C79C22×C411yescharacteristic
48C2×C4×C79C2×D411yescharacteristic
49C2×C4×C79#4111yescharacteristic
50C2×Dic79—21no—
51C2×Dic79—21no—
52Dic158—21no—
53Dic158M1612yescomplemented
54C8×C79—22no—
55C8×C79—41no—
56C79⋊C8—21no—
57C79⋊C8—21no—
58C79⋊C8—21no—
59C79⋊C8—21no—
60C79⋊C8—41no—
61C22×C79—41no—
62C22×C79—41no—
63C22×C79—41no—
64C22×C79C4×D411yescharacteristic
65C4×C79—21no—
66C4×C79—41no—
67C4×C79C2×M1611yescharacteristic
68C4×C79#13111yescharacteristic
69C4×C79AGL(1,ℤ/8)11yescharacteristic
70C4×C79#13711yescharacteristic
71Dic79—22no—
72Dic79—41no—
73C2×C79—81no—
74C2×C79#43511yescharacteristic
75C2×C79#44011yescharacteristic
76C2×C79#44311yescharacteristic
77#1588—791nomaximal, Sylow
78C79#158811yescharacteristic, complemented, Sylow
79C8×Q8—791no—
80C4×SD16—791no—
81#436—791no—
82#335—791no—
83Q8⋊C8—791no—
84D4⋊C8D7911yescharacteristic
85#322—791no—
86C2×SD16—791no—
87C2×M16—1581no—
88C4×Q8—791no—
89C4×D4C2×D7911yescharacteristic
90#106—791no—
91C4⋊C8—791no—
92C4⋊C8—1581no—
93C4⋊C8C2×D7911yescharacteristic
94#103—791no—
95#102—791no—
96C22⋊C8—1581no—
97C4×C8—791no—
98C4×C8—791no—
99C4×C8—1581no—
100C4×C8C2×D7911yescharacteristic
101C2×Q8—791no—
102C2×D4C4×D7911yescharacteristic
103C22×C4—21no—
104SD16—1582no—
105M16—3162no—
106C2×C8—21no—
107C2×C8—21no—
108C2×C8—791no—
109C2×C8—791no—
110C2×C8—791no—
111C2×C8—791no—
112C2×C8—1581no—
113C4⋊C4—791no—
114C4⋊C4—1581no—
115C4⋊C4C4×D7911yescharacteristic
116C22⋊C4—21no—
117C42—1581no—
118C42C22×D7911yescharacteristic
119C23—21no—
120Q8—792no—
121Q8—1581no—
122D4—21no—
123D4—21no—
124C2×C4—21no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—1581no—
128C2×C4—1581no—
129C2×C4C2×C4×D7911yescharacteristic
130C2×C4D4×D7911yescharacteristic
131C2×C4#1192962311yescharacteristic
132C8—22no—
133C8—41no—
134C8—3161no—
135C8—1581no—
136C8—1581no—
137C8—1581no—
138C8—1581no—
139C22—41no—
140C22—41no—
141C22—41no—
142C22(C22⋊D79)⋊C411yescharacteristic
143C4—21no—
144C4—41no—
145C4—3161no—
146C4—1582no—
147C4M16×D7911yescharacteristic
148C4#1457916711yescharacteristic
149C4#1457918511yescharacteristic
150C4#1457919011yescharacteristic
151C2—81no—
152C2#1909863711yescharacteristic
153C2#1909866011yescharacteristic
154C2#1909867711yescharacteristic
subgroupG/H
centerC2×C4D4×D79
commutatorC2×C4×C79C22×C4
FrattiniC42C22×D79
FittingD4⋊C8×C79C2
socleC22×C79C4×D4
prime radicalC2×D4×C79C2×C4
cosocleC42×C79C23
hypercenterD4⋊C8D79
hypocenterC79#1588
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #19098687C2semidirect
4. #19098315C2semidirect
5. #19098295C2semidirect
6. #19098284C2semidirect
53. Dic158M16semidirect
78. C79#1588semidirect