Finite Group Databasebeta

← #23765256

Subgroups — #23765256

Order 10112.

150 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 59 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×#14579107C211yesmaximal, characteristic
2Q16×Dic79C211yesmaximal, characteristic
3#19098657C211yesmaximal, characteristic
4#19098388C211yesmaximal, characteristic
5#19098368C211yesmaximal, characteristic
6C16×Dic79C211yesmaximal, characteristic
7#358×C79C211yesmaximal, characteristic
8C2×Dic316C2211yescharacteristic
9Q8×Dic79—21no—
10#14579126—21no—
11#14579107C414yescomplemented
12C2×C79⋊C16C2211yescharacteristic
13#14579095C2211yescharacteristic
14#14579085—21no—
15#14579084—21no—
16C8×Dic79C2211yescharacteristic
17C2×Q16×C79C2211yescharacteristic
18C2×C16×C79C2211yescharacteristic
19#107×C79C2211yescharacteristic
20C2×Dic158—21no—
21Dic316—21no—
22Dic316C2×C412yes—
23C2×C79⋊C8D411yescharacteristic
24C4⋊Dic79—21no—
25C4⋊Dic79—41no—
26Dic79⋊C4—41no—
27C4×Dic79—41no—
28C4×Dic79—41no—
29C4×Dic79D411yescharacteristic
30C79⋊C16C2×C412yes—
31C2×Q8×C79—21no—
32Q16×C79—21no—
33Q16×C79C2×C412yes—
34C2×C8×C79C2311yescharacteristic
35C4⋊C4×C79—21no—
36C16×C79—21no—
37Q8×C79—22no—
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—22no—
47Dic158—41no—
48C8×C79C22×C411yescharacteristic
49C8×C79#4111yescharacteristic
50C79⋊C8—21no—
51C22×C79C2×D811yescharacteristic
52C4×C79—42no—
53C4×C79—81no—
54C4×C79C4×D411yescharacteristic
55C4×C79#13511yescharacteristic
56Dic79—21no—
57Dic79—42no—
58Dic79—81no—
59Dic79Q3212yescomplemented
60C2×C79C4×D811yescharacteristic
61C2×C79C2×Q3211yescharacteristic
62C2×C79#50811yescharacteristic
63C4×Q32—791nomaximal, Sylow
64C79C4×Q3211yescharacteristic, complemented, Sylow
65C2×Q32—791no—
66C4×Q16—791no—
67C4×Q16—791no—
68#366—791no—
69#358—791no—
70#358D7911yescharacteristic
71C4×C16—791no—
72C2×Q16—791no—
73C2×Q16C2×D7911yescharacteristic
74C4×Q8—1581no—
75C4×Q8—1581no—
76Q32—794no—
77C2×C16—791no—
78C2×C16C2×D7911yescharacteristic
79#107—791no—
80#107C2×D7911yescharacteristic
81#103—1581no—
82#103—1581no—
83C4×C8—791no—
84C2×Q8—21no—
85C2×Q8—1581no—
86Q16—21no—
87Q16—792no—
88Q16—1581no—
89Q16C4×D7912yes—
90C2×C8—791no—
91C2×C8C22×D7911yescharacteristic
92C4⋊C4—21no—
93C4⋊C4—3161no—
94C4⋊C4—3161no—
95C4⋊C4—1581no—
96C42—3161no—
97C42—3161no—
98C42—791no—
99C16—21no—
100C16—792no—
101Q8—22no—
102Q8—41no—
103Q8—3161no—
104Q8—1582no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—3161no—
108C2×C4—3161no—
109C2×C4—791no—
110C2×C4—791no—
111C2×C4D4×D7911yescharacteristic
112C8—1581no—
113C8C2×C4×D7911yescharacteristic
114C8#1192962311yescharacteristic
115C22D8×D7911yescharacteristic
116C4—42no—
117C4—81no—
118C4—3162no—
119C4—792no—
120C4—6321no—
121C4—1581no—
122C4(C22⋊D79)⋊C411yescharacteristic
123C4#1457918211yescharacteristic
124C2#1909864311yescharacteristic
125C2Q32×D7911yescharacteristic
126C2#1909899411yescharacteristic
subgroupG/H
centerC22D8×D79
commutatorC8×C79C22×C4
FrattiniC2×C8C22×D79
Fitting#358×C79C2
socle, prime radicalC22×C79C2×D8
cosocleC2×C8×C79C23
hypercenter#358D79
hypocenterC79C4×Q32
LCSG ▷ 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
11. #14579107C4semidirect
59. Dic79Q32semidirect
64. C79C4×Q32semidirect