Finite Group Databasebeta

← #23762583

Subgroups — #23762583

Order 10112.

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

normal subgroups only

This group has 212 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#19099299C211yesmaximal, characteristic
2#19098845C211yesmaximal, characteristic, complemented
3#19098770C211yesmaximal, characteristic, complemented
4#19098307C211yesmaximal, characteristic
5#19098295C211yesmaximal, characteristic, complemented
6#19098295C211yesmaximal, characteristic, complemented
7#486×C79C211yesmaximal, characteristic
8C2×#11929614—21no—
9#14579148—21no—
10#14579148—21no—
11#14579142—22no—
12C4×Dic158C2211yescharacteristic
13C4×Dic158C2211yescharacteristic
14D4×Dic79—21no—
15D4×Dic79—21no—
16#14579092—21no—
17C4⋊(C79⋊C8)C2211yescharacteristic
18C4⋊(C79⋊C8)C2211yescharacteristic
19#14579085—21no—
20#14579084—21no—
21C4⋊Q8×C79C2211yescharacteristic
22#127×C79C2211yescharacteristic
23#102×C79—22no—
24C4×C8×C79C2211yescharacteristic
25C2×Dic158D411yescharacteristic
26C2×Dic158D411yescharacteristic
27C22×Dic79—22no—
28#11929614—42no—
29C2×C79⋊C8—21no—
30C2×C79⋊C8—21no—
31C4⋊Dic79D411yescharacteristic
32C4⋊Dic79D411yescharacteristic
33Dic79⋊C4—21no—
34Dic79⋊C4—21no—
35C22⋊Dic79—22no—
36C22⋊Dic79—22no—
37C22⋊Dic79—22no—
38C4×Dic79—21no—
39C4×Dic79—21no—
40C2×Q8×C79—21no—
41C2×D4×C79—21no—
42C2×D4×C79—21no—
43C2×D4×C79D412yes—
44C2×C8×C79—21no—
45C4⋊C4×C79—21no—
46C4⋊C4×C79—21no—
47C42×C79C2311yescharacteristic
48C23×C79—22no—
49Q8×C79—41no—
50Q8×C79—41no—
51D4×C79—42no—
52D4×C79—41no—
53D4×C79—41no—
54D4×C79—41no—
55D4×C79—41no—
56C2×C4×C79—41no—
57C2×C4×C79C2×D411yescharacteristic
58C2×C4×C79C2×D411yescharacteristic
59C2×C4×C79C2×D411yescharacteristic
60C2×Dic79—21no—
61C2×Dic79—21no—
62C2×Dic79—21no—
63C2×Dic79—21no—
64C2×Dic79—82no—
65Dic158—21no—
66Dic158—21no—
67Dic158—21no—
68Dic158—21no—
69C8×C79—41no—
70C79⋊C8—41no—
71C79⋊C8—41no—
72C22×C79—42no—
73C22×C79—42no—
74C22×C79—42no—
75C22×C79#12011yescharacteristic
76C4×C79—21no—
77C4×C79—81no—
78C4×C79#13511yescharacteristic
79C4×C79#13511yescharacteristic
80C4×C79AGL(1,ℤ/8)11yescharacteristic
81C4×C79#13711yescharacteristic
82Dic79—41no—
83Dic79—41no—
84Dic79—41no—
85Dic79—41no—
86C2×C79—82no—
87C2×C79#44911yescharacteristic
88C2×C79#45211yescharacteristic
89C2×C79#45511yescharacteristic
90#1640—791nomaximal, Sylow
91C79#164011yescharacteristic, complemented, Sylow
92#559—791no—
93#486D7911yescharacteristic
94#475—791no—
95#462—791no—
96#331—791no—
97Q8⋊C8—791no—
98Q8⋊C8—791no—
99C2×Q16—1581no—
100C4⋊Q8C2×D7911yescharacteristic
101#127C2×D7911yescharacteristic
102#124—1581no—
103#124—1581no—
104#123—1582no—
105C4×Q8—791no—
106C4×Q8—791no—
107C4×D4—1581no—
108C4×D4—1581no—
109#106—1581no—
110C4⋊C8—791no—
111C4⋊C8—791no—
112#103—1581no—
113#103—1581no—
114#102—22no—
115C4×C8C2×D7911yescharacteristic
116C2×Q8—21no—
117C2×Q8—791no—
118C2×Q8—791no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4C22⋊D7912yes—
122C22×C4—1582no—
123Q16—3162no—
124C2×C8—21no—
125C2×C8—1581no—
126C2×C8—1581no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—791no—
130C4⋊C4—791no—
131C4⋊C4—1581no—
132C4⋊C4—1581no—
133C22⋊C4—1582no—
134C22⋊C4—1582no—
135C22⋊C4—1582no—
136C42—1581no—
137C42—1581no—
138C42C22×D7911yescharacteristic
139C23—22no—
140Q8—41no—
141Q8—41no—
142Q8—1581no—
143Q8—1581no—
144Q8—1581no—
145Q8—1581no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—41no—
152C2×C4—6322no—
153C2×C4—1581no—
154C2×C4—1581no—
155C2×C4—1581no—
156C2×C4—1581no—
157C2×C4D4×D7911yescharacteristic
158C2×C4D4×D7911yescharacteristic
159C2×C4C2×C22⋊D7911yescharacteristic
160C8—41no—
161C8—3161no—
162C8—3161no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#1457912911yescharacteristic
167C4—21no—
168C4—81no—
169C4—3161no—
170C4—3161no—
171C4—3161no—
172C4—3161no—
173C4#1457918011yescharacteristic
174C4#1457918211yescharacteristic
175C4#1457918511yescharacteristic
176C4#1457919011yescharacteristic
177C2—82no—
178C2#1909870511yescharacteristic
179C2#1909872211yescharacteristic
180C2#1909874011yescharacteristic
subgroupG/H
centerC22#14579129
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#486×C79C2
socleC22×C79#120
prime radical#127×C79C22
hypercenter#486D79
hypocenterC79#1640
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #19098845C2semidirect
3. #19098770C2semidirect
5. #19098295C2semidirect
6. #19098295C2semidirect
91. C79#1640semidirect