Finite Group Databasebeta

← #23765479

Subgroups — #23765479

Order 10112.

150 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 45 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#19099003C211yesmaximal, characteristic
2#19098941C211yesmaximal, characteristic, complemented
3#19098680C211yesmaximal, characteristic
4#19098383C211yesmaximal, characteristic, complemented
5#19098380C211yesmaximal, characteristic, complemented
6#19098379C211yesmaximal, characteristic, complemented
7#510×C79C211yesmaximal, characteristic
8C2×Dic316C2211yescharacteristic
9C2×#11929614—21no—
10#14579168—21no—
11#14579159—21no—
12#14579107—21no—
13#14579105—21no—
14#14579101C2211yescharacteristic
15#14579097C2211yescharacteristic
16#14579088—21no—
17C8×Dic79C2211yescharacteristic
18#135×C79C2211yescharacteristic
19C2×Q16×C79C2211yescharacteristic
20Q32×C79—21no—
21SD32×C79—21no—
22M32×C79C2211yescharacteristic
23C2×Dic158—21no—
24Dic316—21no—
25Dic316—21no—
26#11929614—41no—
27#11929614—41no—
28#11929608—21no—
29#11929608—41no—
30C2×C79⋊C8—41no—
31C2×C79⋊C8D411yescharacteristic
32Dic79⋊C4—42no—
33C4×Dic79D411yescharacteristic
34C79⋊C16—21no—
35#41×C79—21no—
36C2×Q8×C79—21no—
37Q16×C79—21no—
38Q16×C79—21no—
39Q16×C79D411yescharacteristic
40SD16×C79—21no—
41D8×C79D411yescharacteristic
42C2×C8×C79C2311yescharacteristic
43C16×C79—21no—
44Q8×C79—21no—
45Q8×C79—41no—
46Q8×C79—41no—
47D4×C79—21no—
48D4×C79—41no—
49C2×C4×C79—41no—
50C2×C4×C79—41no—
51C2×C4×C79C2×D411yescharacteristic
52C2×Dic79—21no—
53C2×Dic79—41no—
54Dic158—41no—
55Dic158—41no—
56C8×C79C2×D411yescharacteristic
57C8×C79#4111yescharacteristic
58C79⋊C8—41no—
59C79⋊C8D811yescharacteristic
60C79⋊C8D811yescharacteristic
61C22×C79—41no—
62C22×C79AGL(1,ℤ/8)11yescharacteristic
63C4×C79—41no—
64C4×C79—81no—
65C4×C79#12111yescharacteristic
66C4×C79C2×D811yescharacteristic
67Dic79—22no—
68Dic79—81no—
69C2×C79—21no—
70C2×C79—81no—
71C2×C79#45911yescharacteristic
72#2214—791nomaximal, Sylow
73C79#221411yescharacteristic, complemented, Sylow
74#510—791no—
75#510D7911yescharacteristic
76#494—791no—
77#443—791no—
78#364—791no—
79#362—791no—
80#362—791no—
81#135C2×D7911yescharacteristic
82C2×Q16—791no—
83C2×Q16—1581no—
84C2×Q16C2×D7911yescharacteristic
85#131—1581no—
86C4⋊Q8—1581no—
87Q32—21no—
88Q32—1581no—
89SD32—21no—
90SD32—1581no—
91M32—791no—
92M32C2×D7911yescharacteristic
93#108—791no—
94#104—1581no—
95C4×C8—791no—
96#41—21no—
97C2×Q8—21no—
98C2×Q8—1581no—
99Q16—21no—
100Q16—21no—
101Q16—3161no—
102Q16—3161no—
103Q16—1581no—
104Q16—1581no—
105Q16C22⋊D7911yescharacteristic
106SD16—21no—
107D8C22⋊D7911yescharacteristic
108M16—3161no—
109M16—1581no—
110C2×C8—3161no—
111C2×C8—791no—
112C2×C8C22×D7911yescharacteristic
113C4⋊C4—3162no—
114C42—791no—
115C16—21no—
116C16—1581no—
117Q8—21no—
118Q8—41no—
119Q8—41no—
120Q8—3161no—
121Q8—3161no—
122D4—21no—
123D4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—3161no—
127C2×C4—1581no—
128C2×C4D4×D7911yescharacteristic
129C8—3161no—
130C8—791no—
131C8—791no—
132C8C2×C22⋊D7911yescharacteristic
133C8#1192962311yescharacteristic
134C22—41no—
135C22#1457918511yescharacteristic
136C4—41no—
137C4—81no—
138C4—6321no—
139C4—1582no—
140C4#1457913311yescharacteristic
141C4D8×D7911yescharacteristic
142C2—21no—
143C2—81no—
144C2#1909875611yescharacteristic
subgroupG/H
centerC2#19098756
commutator, cosocleC2×C8×C79C23
FrattiniC2×C8C22×D79
Fitting#510×C79C2
socleC2×C79#459
prime radical#135×C79C22
hypercenter#510D79
hypocenterC79#2214
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. #19098941C2semidirect
4. #19098383C2semidirect
5. #19098380C2semidirect
6. #19098379C2semidirect
73. C79#2214semidirect