Finite Group Databasebeta

← #23762407

Subgroups — #23762407

Order 10112.

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

normal subgroups only

This group has 210 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#19099194C211yesmaximal, characteristic
2#19098893C212yesmaximal
3#19098299C212yesmaximal
4#19098289C211yesmaximal, characteristic
5#398×C79C211yesmaximal, characteristic
6#14579160—22no—
7#14579152—22no—
8#14579140—21no—
9#14579140C2212yes—
10#14579120—21no—
11#14579092—22no—
12#14579084—22no—
13C22⋊(C79⋊C8)C2212yes—
14C2×C4⋊C4×C79—21no—
15C2×C4⋊C4×C79C2211yescharacteristic
16C2×C4⋊C4×C79C2211yescharacteristic
17#95×C79—21no—
18#95×C79C2211yescharacteristic
19C2×Dic158—21no—
20C2×Dic158D412yes—
21C2×C79⋊C8—22no—
22C4⋊Dic79—21no—
23C4⋊Dic79—21no—
24C4⋊Dic79—21no—
25C4⋊Dic79D412yes—
26Dic79⋊C4—22no—
27Dic79⋊C4—22no—
28C22⋊Dic79—22no—
29C4×Dic79—22no—
30C22×C4×C79—21no—
31C22×C4×C79—21no—
32C22×C4×C79D411yescharacteristic
33C22×C4×C79D411yescharacteristic
34C22×C4×C79C2311yescharacteristic
35C4⋊C4×C79—22no—
36C4⋊C4×C79—22no—
37C4⋊C4×C79—42no—
38C23×C79C2×D411yescharacteristic
39C2×C4×C79—21no—
40C2×C4×C79—21no—
41C2×C4×C79—22no—
42C2×C4×C79—21no—
43C2×C4×C79—41no—
44C2×C4×C79—41no—
45C2×C4×C79—41no—
46C2×C4×C79—41no—
47C2×C4×C79—41no—
48C2×C4×C79—41no—
49C2×C4×C79—41no—
50C2×C4×C79SD1612yes—
51C2×C4×C79C2×D412yes—
52C2×Dic79—22no—
53C2×Dic79—22no—
54Dic158—42no—
55Dic158—81no—
56C79⋊C8—42no—
57C22×C79—21no—
58C22×C79—21no—
59C22×C79#12011yescharacteristic
60C22×C79C2×SD1611yescharacteristic
61C22×C79#13711yescharacteristic
62C4×C79—22no—
63C4×C79—22no—
64C4×C79—42no—
65C4×C79—41no—
66C4×C79—81no—
67Dic79—42no—
68Dic79—42no—
69C2×C79—21no—
70C2×C79—21no—
71C2×C79#44811yescharacteristic
72C2×C79#45611yescharacteristic
73C2×C79#45811yescharacteristic
74#1611—791nomaximal, Sylow
75C79#161111yescharacteristic, complemented, Sylow
76#544—791no—
77#483—792no—
78#398D7911yescharacteristic
79#328—792no—
80#324—791no—
81C4⋊Q8—1582no—
82#125—1582no—
83C22⋊Q8—792no—
84C22⋊Q8—1581no—
85#117—1581no—
86C2×C4⋊C4—21no—
87C2×C4⋊C4C2×D7911yescharacteristic
88C2×C4⋊C4C2×D7911yescharacteristic
89#106—1582no—
90#103—1582no—
91C22⋊C8—792no—
92#95—21no—
93#95C2×D7911yescharacteristic
94C2×Q8—792no—
95C2×Q8—1581no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4C22⋊D7911yescharacteristic
99C22×C4C22⋊D7911yescharacteristic
100C22×C4C22×D7911yescharacteristic
101C2×C8—1582no—
102C4⋊C4—22no—
103C4⋊C4—22no—
104C4⋊C4—42no—
105C4⋊C4—792no—
106C4⋊C4—1582no—
107C4⋊C4—1581no—
108C4⋊C4—1581no—
109C4⋊C4—1581no—
110C4⋊C4—1582no—
111C22⋊C4—1582no—
112C42—1582no—
113C23C2×C22⋊D7911yescharacteristic
114Q8—3162no—
115Q8—6321no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—21no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—1582no—
128C2×C4—1582no—
129C2×C4#1192961212yes—
130C2×C4D4×D7912yes—
131C8—3162no—
132C22—21no—
133C22—21no—
134C22#1457912911yescharacteristic
135C22C2×#1192961211yescharacteristic
136C22#1457919111yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—41no—
141C4—81no—
142C4—3162no—
143C4—3162no—
144C2—21no—
145C2—21no—
146C2#1909870111yescharacteristic
147C2#1909874511yescharacteristic
148C2#1909875211yescharacteristic
subgroupG/H
centerC22#14579129
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
Fitting#398×C79C2
socleC22×C79#120
prime radicalC23×C79C2×D4
hypercenter#398D79
hypocenterC79#1611
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
75. C79#1611semidirect