Finite Group Databasebeta

← #23764344

Subgroups — #23764344

Order 10112.

260 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 97 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
2C4×C4⋊Dic79C211yesmaximal, characteristic
3#19098324C214yesmaximal
4C4×M16×C79C211yesmaximal, characteristic
5#14579161C411yescharacteristic, complemented
6#14579161C411yescharacteristic, complemented
7#14579153C412yescomplemented
8#14579140—21no—
9#14579140—21no—
10C4×Dic158—21no—
11C4×Dic158—21no—
12#14579120C2212yes—
13C2×C4⋊Dic79—21no—
14C2×C4×Dic79C2212yes—
15C79⋊#95—21no—
16C2×M16×C79C2212yes—
17C2×C42×C79C2211yescharacteristic
18#97×C79—21no—
19C4×C8×C79—21no—
20C2×Dic158—21no—
21C2×Dic158—21no—
22C22×Dic79—22no—
23C4⋊Dic79—24no—
24C4⋊Dic79—21no—
25C4⋊Dic79—21no—
26C4⋊Dic79C2×C412yes—
27C4⋊Dic79C2×C412yes—
28Dic79⋊C4—22no—
29Dic79⋊C4—22no—
30C22⋊Dic79—22no—
31C4×Dic79—22no—
32C4×Dic79—24no—
33C22×C4×C79D411yescharacteristic
34C22×C4×C79D411yescharacteristic
35C22×C4×C79C2311yescharacteristic
36M16×C79—22no—
37M16×C79Q814yescomplemented
38C2×C8×C79—22no—
39C42×C79C2×C411yescharacteristic
40C42×C79C2×C411yescharacteristic
41C42×C79D411yescharacteristic
42C42×C79D411yescharacteristic
43C23×C79C2×D411yescharacteristic
44C2×C4×C79—22no—
45C2×C4×C79—41no—
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×C4×C79C2×Q812yes—
53C2×C4×C79#4112yes—
54C2×Dic79—24no—
55C2×Dic79—22no—
56C2×Dic79—22no—
57C2×Dic79—42no—
58C2×Dic79—42no—
59Dic158—42no—
60Dic158—42no—
61C8×C79—24no—
62C22×C79—21no—
63C22×C79—21no—
64C22×C79C2×C22⋊C411yescharacteristic
65C22×C79#12411yescharacteristic
66C22×C79C4⋊Q811yescharacteristic
67C4×C79—21no—
68C4×C79—21no—
69C4×C79—21no—
70C4×C79#10412yes—
71C4×C79C4×Q812yes—
72C4×C79C22⋊Q812yes—
73Dic79—44no—
74Dic79—42no—
75Dic79—42no—
76C2×C79—21no—
77C2×C79—21no—
78C2×C79#39111yescharacteristic
79C2×C79C2×#10411yescharacteristic
80C2×C79#42111yescharacteristic
81#1986—791nomaximal, Sylow
82C79#198611yescharacteristic, complemented, Sylow
83#533—791no—
84C4×M16D7911yescharacteristic
85C4×C4⋊C4—791no—
86#339—794no—
87C2×M16C2×D7912yes—
88C4⋊Q8—791no—
89C4⋊Q8—791no—
90#125—792no—
91C22⋊Q8—1581no—
92C22⋊Q8—1581no—
93C4×Q8—1581no—
94C4×Q8—1581no—
95#117—792no—
96C2×C4⋊C4—1581no—
97C2×C42—792no—
98C2×C42C2×D7911yescharacteristic
99#97—21no—
100C4×C8—21no—
101#95—1581no—
102C2×Q8—1581no—
103C2×Q8—1581no—
104C22×C4—1582no—
105C22×C4D31611yescharacteristic
106C22×C4D31611yescharacteristic
107C22×C4C22×D7911yescharacteristic
108M16—22no—
109M16Dic15814yescomplemented
110C2×C8—22no—
111C4⋊C4—792no—
112C4⋊C4—792no—
113C4⋊C4—1584no—
114C4⋊C4—1582no—
115C4⋊C4—1582no—
116C4⋊C4—1581no—
117C4⋊C4—1581no—
118C22⋊C4—1582no—
119C42—1584no—
120C42—1582no—
121C42C4×D7911yescharacteristic
122C42C4×D7911yescharacteristic
123C42C22⋊D7911yescharacteristic
124C42C22⋊D7911yescharacteristic
125C23C2×D31611yescharacteristic
126Q8—3162no—
127Q8—3162no—
128C2×C4—22no—
129C2×C4—41no—
130C2×C4—3162no—
131C2×C4—3162no—
132C2×C4—1584no—
133C2×C4—1582no—
134C2×C4—1582no—
135C2×C4(C2×D79)⋊C411yescharacteristic
136C2×C4(C2×D79)⋊C411yescharacteristic
137C2×C4(C2×D79)⋊C411yescharacteristic
138C2×C4(C2×D79)⋊C411yescharacteristic
139C2×C4C2×C4×D7911yescharacteristic
140C2×C4C2×C22⋊D7911yescharacteristic
141C2×C4C2×Dic15812yes—
142C2×C4#1192962412yes—
143C8—24no—
144C22—21no—
145C22—21no—
146C22C2×(C2×D79)⋊C411yescharacteristic
147C22#1457914911yescharacteristic
148C22#1457916111yescharacteristic
149C4—21no—
150C4—21no—
151C4—21no—
152C4—3164no—
153C4—3162no—
154C4—3162no—
155C4#1457908712yes—
156C4C4×Dic15812yes—
157C4#1457914012yes—
158C2—21no—
159C2—21no—
160C2#1909846911yescharacteristic
161C2C2×#1457908711yescharacteristic
162C2#1909857911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D79
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
FittingC4×M16×C79C2
socleC22×C79C2×C22⋊C4
prime radicalC23×C79C2×D4
cosocleC22×C4×C79C23
hypercenterC4×M16D79
hypocenterC79#1986
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
5. #14579161C4semidirect
6. #14579161C4semidirect
7. #14579153C4semidirect
37. M16×C79Q8semidirect
82. C79#1986semidirect
109. M16Dic158semidirect