Finite Group Databasebeta

← #23761950

Subgroups — #23761950

Order 10112.

208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 69 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#19099120C211yesmaximal, characteristic
2#19098620C211yesmaximal, characteristic
3#19098299C214yesmaximal
4#383×C79C211yesmaximal, characteristic
5#14579161C411yescharacteristic, complemented
6#14579161C411yescharacteristic, complemented
7#14579153—21no—
8#14579140—21no—
9#14579140C2212yes—
10C4×Dic158—21no—
11C4×Dic158C412yescomplemented
12#14579120—21no—
13C4⋊(C79⋊C8)—21no—
14C22⋊(C79⋊C8)C2212yes—
15#14579072—21no—
16C2×C42×C79C2211yescharacteristic
17#95×C79—21no—
18#95×C79—21no—
19#95×C79C2212yes—
20C2×Dic158—21no—
21C2×Dic158C2×C412yes—
22C2×C79⋊C8—22no—
23C4⋊Dic79—21no—
24C4⋊Dic79—21no—
25C4⋊Dic79—21no—
26C4⋊Dic79C2×C412yes—
27Dic79⋊C4—22no—
28Dic79⋊C4—22no—
29C22⋊Dic79—22no—
30C4×Dic79—22no—
31C22×C4×C79—22no—
32C22×C4×C79D411yescharacteristic
33C22×C4×C79D411yescharacteristic
34C22×C4×C79C2311yescharacteristic
35C42×C79C2×C411yescharacteristic
36C42×C79C2×C411yescharacteristic
37C42×C79D411yescharacteristic
38C42×C79D411yescharacteristic
39C23×C79C2×D411yescharacteristic
40C2×C4×C79—22no—
41C2×C4×C79—41no—
42C2×C4×C79—41no—
43C2×C4×C79—42no—
44C2×C4×C79—42no—
45C2×C4×C79—42no—
46C2×C4×C79C22⋊C411yescharacteristic
47C2×C4×C79C22⋊C411yescharacteristic
48C2×C4×C79C22⋊C411yescharacteristic
49C2×C4×C79C22⋊C411yescharacteristic
50C2×C4×C79C22×C411yescharacteristic
51C2×C4×C79C2×D411yescharacteristic
52C2×Dic79—22no—
53C2×Dic79—22no—
54Dic158—42no—
55Dic158—42no—
56C79⋊C8—42no—
57C22×C79—21no—
58C22×C79—21no—
59C22×C79C2×C22⋊C411yescharacteristic
60C22×C79#13712yes—
61C4×C79—21no—
62C4×C79—21no—
63C4×C79—21no—
64C4×C79—21no—
65C4×C79—21no—
66C4×C79—21no—
67C4×C79—82no—
68Dic79—42no—
69Dic79—42no—
70C2×C79—22no—
71C2×C79#41011yescharacteristic
72C2×C79#41911yescharacteristic
73C2×C79#42111yescharacteristic
74#1515—791nomaximal, Sylow
75C79#151511yescharacteristic, complemented, Sylow
76#533—791no—
77#432—791no—
78#383D7911yescharacteristic
79#328—794no—
80C4⋊Q8—791no—
81C4⋊Q8—791no—
82#125—1581no—
83C22⋊Q8—792no—
84C22⋊Q8—1581no—
85C4×Q8—792no—
86C4×Q8—1581no—
87#117—1581no—
88C2×C42C2×D7911yescharacteristic
89C4⋊C8—1581no—
90C22⋊C8—792no—
91#97—1581no—
92#95—21no—
93#95—21no—
94#95C2×D7912yes—
95C2×Q8—792no—
96C2×Q8—1581no—
97C22×C4—22no—
98C22×C4C22⋊D7911yescharacteristic
99C22×C4C22⋊D7911yescharacteristic
100C22×C4C22×D7911yescharacteristic
101C2×C8—1582no—
102C4⋊C4—792no—
103C4⋊C4—1582no—
104C4⋊C4—1581no—
105C4⋊C4—1581no—
106C4⋊C4—1581no—
107C4⋊C4—1582no—
108C22⋊C4—1582no—
109C42—1582no—
110C42C4×D7911yescharacteristic
111C42C4×D7911yescharacteristic
112C42D31611yescharacteristic
113C42D31611yescharacteristic
114C23C2×C22⋊D7911yescharacteristic
115Q8—3162no—
116Q8—3162no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—42no—
122C2×C4—42no—
123C2×C4—1582no—
124C2×C4—1582no—
125C2×C4(C2×D79)⋊C411yescharacteristic
126C2×C4(C2×D79)⋊C411yescharacteristic
127C2×C4(C2×D79)⋊C411yescharacteristic
128C2×C4(C2×D79)⋊C411yescharacteristic
129C2×C4C2×C4×D7911yescharacteristic
130C2×C4C2×D31611yescharacteristic
131C8—3162no—
132C22—21no—
133C22—21no—
134C22C2×(C2×D79)⋊C411yescharacteristic
135C22#1457919112yes—
136C4—21no—
137C4—21no—
138C4—21no—
139C4—21no—
140C4—21no—
141C4—21no—
142C4—82no—
143C4—3162no—
144C4—3162no—
145C2—22no—
146C2#1909853611yescharacteristic
147C2#1909857111yescharacteristic
148C2#1909858111yescharacteristic
subgroupG/H
centerC22C2×(C2×D79)⋊C4
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#383×C79C2
socleC22×C79C2×C22⋊C4
prime radicalC23×C79C2×D4
cosocleC22×C4×C79C23
hypercenter#383D79
hypocenterC79#1515
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
5. #14579161C4semidirect
6. #14579161C4semidirect
11. C4×Dic158C4semidirect
75. C79#1515semidirect