Finite Group Databasebeta

← #23763500

Subgroups — #23763500

Order 10112.

306 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#14579120C211yesmaximal, characteristic
2#19098527C211yesmaximal, characteristic
3#19098323C214yesmaximal, complemented
4C4×C22⋊C4×C79C211yesmaximal, characteristic
5C2×#11929608C2212yes—
6#14579120—21no—
7#14579120—21no—
8#14579120C412yescomplemented
9#14579120C2212yes—
10C2×C4⋊Dic79C411yescharacteristic, complemented
11C2×C4⋊Dic79C411yescharacteristic, complemented
12C2×C22⋊Dic79—21no—
13C2×C4×Dic79—21no—
14C22⋊(C79⋊C8)—21no—
15C22⋊(C79⋊C8)—21no—
16C23×C4×C79C2211yescharacteristic
17C2×C22⋊C4×C79—21no—
18C2×C42×C79C2212yes—
19#95×C79—21no—
20C22×Dic79—21no—
21C22×Dic79—21no—
22#11929608—24no—
23C2×C79⋊C8—22no—
24C4⋊Dic79—21no—
25C4⋊Dic79—21no—
26C4⋊Dic79C2×C412yes—
27C4⋊Dic79C2×C412yes—
28C22⋊Dic79—22no—
29C22⋊Dic79—22no—
30C4×Dic79—22no—
31C4×Dic79—22no—
32C24×C79D411yescharacteristic
33C22×C4×C79—24no—
34C22×C4×C79—22no—
35C22×C4×C79C2×C411yescharacteristic
36C22×C4×C79C2×C411yescharacteristic
37C22×C4×C79D411yescharacteristic
38C22×C4×C79D411yescharacteristic
39C22×C4×C79D411yescharacteristic
40C22×C4×C79C2311yescharacteristic
41C22⋊C4×C79—24no—
42C42×C79—24no—
43C23×C79—22no—
44C23×C79—22no—
45C23×C79—41no—
46C23×C79C22⋊C411yescharacteristic
47C23×C79C22⋊C411yescharacteristic
48C23×C79C2×D411yescharacteristic
49C2×C4×C79—22no—
50C2×C4×C79—22no—
51C2×C4×C79—22no—
52C2×C4×C79—22no—
53C2×C4×C79—22no—
54C2×C4×C79—24no—
55C2×C4×C79—42no—
56C2×C4×C79—42no—
57C2×C4×C79C22⋊C411yescharacteristic
58C2×C4×C79C22⋊C411yescharacteristic
59C2×C4×C79C22×C411yescharacteristic
60C2×C4×C79C2×D411yescharacteristic
61C2×C4×C79#4114yes—
62C2×Dic79—22no—
63C2×Dic79—22no—
64C2×Dic79—42no—
65C2×Dic79—42no—
66C79⋊C8—42no—
67C22×C79—21no—
68C22×C79—21no—
69C22×C79—21no—
70C22×C79—21no—
71C22×C79—21no—
72C22×C79—21no—
73C22×C79—21no—
74C22×C79—44no—
75C22×C79#10412yes—
76C22×C79C2×C22⋊C411yescharacteristic
77C22×C79#12312yes—
78C4×C79—21no—
79C4×C79—21no—
80C4×C79—44no—
81C4×C79#11712yes—
82C4×C79#12312yes—
83Dic79—42no—
84Dic79—42no—
85C2×C79—22no—
86C2×C79—22no—
87C2×C79—41no—
88C2×C79#38111yescharacteristic
89C2×C79C2×#10411yescharacteristic
90C2×C79#42111yescharacteristic
91#1826—791nomaximal, Sylow
92C79#182611yescharacteristic, complemented, Sylow
93C2×#117—791no—
94#407—791no—
95C4×C22⋊C4D7911yescharacteristic
96#339—794no—
97C23×C4C2×D7911yescharacteristic
98C2×M16—792no—
99#117—792no—
100#117—792no—
101#117—1581no—
102#117—1581no—
103C2×C4⋊C4—791no—
104C2×C4⋊C4—791no—
105C2×C22⋊C4—21no—
106C2×C22⋊C4—1581no—
107C2×C42—1581no—
108C2×C42C2×D7912yes—
109C22⋊C8—1581no—
110C22⋊C8—1581no—
111#95—21no—
112C24C22⋊D7911yescharacteristic
113C22×C4—24no—
114C22×C4—22no—
115C22×C4—1581no—
116C22×C4—1581no—
117C22×C4C4×D7911yescharacteristic
118C22×C4C4×D7911yescharacteristic
119C22×C4D31611yescharacteristic
120C22×C4D31611yescharacteristic
121C22×C4C22⋊D7911yescharacteristic
122C22×C4C22×D7911yescharacteristic
123M16—1584no—
124C2×C8—1582no—
125C4⋊C4—792no—
126C4⋊C4—792no—
127C4⋊C4—1581no—
128C4⋊C4—1581no—
129C22⋊C4—24no—
130C22⋊C4—1582no—
131C22⋊C4—1582no—
132C42—24no—
133C42—1582no—
134C42—1582no—
135C23—22no—
136C23—22no—
137C23—41no—
138C23(C2×D79)⋊C411yescharacteristic
139C23(C2×D79)⋊C411yescharacteristic
140C23C2×C22⋊D7911yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—24no—
147C2×C4—42no—
148C2×C4—42no—
149C2×C4—3162no—
150C2×C4—3162no—
151C2×C4—1582no—
152C2×C4—1582no—
153C2×C4(C2×D79)⋊C411yescharacteristic
154C2×C4(C2×D79)⋊C411yescharacteristic
155C2×C4C2×C4×D7911yescharacteristic
156C2×C4C2×D31611yescharacteristic
157C2×C4#1192962314yes—
158C8—3162no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—44no—
167C22#1457908912yes—
168C22C2×(C2×D79)⋊C411yescharacteristic
169C22#1457914212yes—
170C4—21no—
171C4—21no—
172C4—44no—
173C4—3162no—
174C4—3162no—
175C4#1457911712yes—
176C4#1457914512yes—
177C2—22no—
178C2—22no—
179C2—41no—
180C2#1909842411yescharacteristic
181C2C2×#1457908911yescharacteristic
182C2#1909858111yescharacteristic
subgroupG/H
centerC2×C4C2×D316
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
FittingC4×C22⋊C4×C79C2
socleC22×C79C2×C22⋊C4
prime radicalC24×C79D4
cosocleC22×C4×C79C23
hypercenterC4×C22⋊C4D79
hypocenterC79#1826
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #19098323C2semidirect
8. #14579120C4semidirect
10. C2×C4⋊Dic79C4semidirect
11. C2×C4⋊Dic79C4semidirect
92. C79#1826semidirect