Finite Group Databasebeta

← #23765626

Subgroups — #23765626

Order 10112.

140 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 51 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#19098967C211yesmaximal, characteristic
2#19098941C211yesmaximal, characteristic
3#19098368C211yesmaximal, characteristic
4#19098367C211yesmaximal, characteristic
5#19098366C211yesmaximal, characteristic
6C16×Dic79C211yesmaximal, characteristic
7#358×C79C211yesmaximal, characteristic
8C2×Dic316C2211yescharacteristic
9C2×#11929614—21no—
10#14579160—21no—
11#14579159—21no—
12C2×C79⋊C16C2211yescharacteristic
13#14579095C2211yescharacteristic
14#14579094—21no—
15C8×Dic79C2211yescharacteristic
16C2×Q16×C79C2211yescharacteristic
17C2×C16×C79C2211yescharacteristic
18#107×C79C2211yescharacteristic
19C2×Dic158—21no—
20C2×Dic158—41no—
21Dic316—21no—
22Dic316—21no—
23#11929614—42no—
24C2×C79⋊C8D411yescharacteristic
25C4⋊Dic79—21no—
26Dic79⋊C4—41no—
27Dic79⋊C4—41no—
28Dic79⋊C4—41no—
29C4×Dic79D411yescharacteristic
30C79⋊C16—21no—
31C2×Q8×C79—21no—
32Q16×C79—21no—
33Q16×C79—21no—
34C2×C8×C79C2311yescharacteristic
35C4⋊C4×C79—21no—
36C16×C79—21no—
37Q8×C79—41no—
38Q8×C79—41no—
39C2×C4×C79—41no—
40C2×C4×C79—41no—
41C2×C4×C79C2×D411yescharacteristic
42C2×Dic79—41no—
43C2×Dic79—41no—
44C2×Dic79D811yescharacteristic
45C2×Dic79D811yescharacteristic
46Dic158—41no—
47Dic158—41no—
48Dic158—82no—
49C8×C79#4111yescharacteristic
50C8×C79#4111yescharacteristic
51C79⋊C8SD1612yes—
52C22×C79C2×D811yescharacteristic
53C4×C79—81no—
54C4×C79—81no—
55C4×C79#12411yescharacteristic
56C4×C79C2×SD1611yescharacteristic
57Dic79—81no—
58Dic79—81no—
59Dic79SD3212yes—
60Dic79Q3212yes—
61C2×C79#48611yescharacteristic
62C2×C79C2×SD3211yescharacteristic
63C2×C79C2×Q3211yescharacteristic
64#2241—791nomaximal, Sylow
65C79#224111yescharacteristic, complemented, Sylow
66#500—791no—
67#494—791no—
68#358—791no—
69#358—791no—
70#358—791no—
71#358D7911yescharacteristic
72C4×C16—791no—
73C2×Q16—791no—
74C2×Q16—1581no—
75C2×Q16C2×D7911yescharacteristic
76C4⋊Q8—1581no—
77C4⋊Q8—1581no—
78C2×C16—791no—
79C2×C16C2×D7911yescharacteristic
80#107—791no—
81#107—1581no—
82#107C2×D7911yescharacteristic
83C4×C8—791no—
84C2×Q8—21no—
85C2×Q8—3161no—
86C2×Q8—1581no—
87Q16—21no—
88Q16—21no—
89Q16—3162no—
90Q16—1581no—
91Q16—1581no—
92C2×C8—791no—
93C2×C8C22×D7911yescharacteristic
94C4⋊C4—21no—
95C4⋊C4—3161no—
96C4⋊C4—3161no—
97C4⋊C4—3161no—
98C4⋊C4—1581no—
99C42—791no—
100C16—21no—
101C16—1581no—
102Q8—41no—
103Q8—41no—
104Q8—3161no—
105Q8—3161no—
106Q8—6322no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—3161no—
110C2×C4—3161no—
111C2×C4—791no—
112C2×C4—791no—
113C2×C4D4×D7911yescharacteristic
114C8—792no—
115C8#1192962311yescharacteristic
116C8#1192962411yescharacteristic
117C22D8×D7911yescharacteristic
118C4—81no—
119C4—81no—
120C4—792no—
121C4—792no—
122C4—6321no—
123C4—6321no—
124C4#1457914711yescharacteristic
125C4SD16×D7911yescharacteristic
126C2#1909890811yescharacteristic
127C2SD32×D7911yescharacteristic
128C2Q32×D7911yescharacteristic
subgroupG/H
centerC22D8×D79
commutator, cosocleC2×C8×C79C23
FrattiniC2×C8C22×D79
Fitting#358×C79C2
socle, prime radicalC22×C79C2×D8
hypercenter#358D79
hypocenterC79#2241
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
65. C79#2241semidirect