Finite Group Databasebeta

← #34176119

Subgroups — #34176119

Order 20224.

126 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 25 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#23762726C211yesmaximal, characteristic
2#23761573C211yesmaximal, characteristic
3C79×#1356C211yesmaximal, characteristic
4C79⋊#564C411yescharacteristic
5#19098969—21no—
6#19098362—21no—
7#19098305C411yescharacteristic
8#19098304—21no—
9#491×C79C2211yescharacteristic
10#347×C79—21no—
11#14579153—21no—
12#14579152—41no—
13#14579151—41no—
14#14579151—41no—
15#14579094—41no—
16#14579092—41no—
17#14579080—41no—
18#14579072—21no—
19C4⋊Q8×C79D411yescharacteristic
20#125×C79C2×C411yescharacteristic
21M32×C79—41no—
22#103×C79—41no—
23#97×C79D411yescharacteristic
24#11929608—81no—
25C2×C79⋊C8—41no—
26C4⋊Dic79—21no—
27C4⋊Dic79—21no—
28C4⋊Dic79—41no—
29Dic79⋊C4—41no—
30Dic79⋊C4—41no—
31Dic79⋊C4—41no—
32Dic79⋊C4—41no—
33C4×Dic79—41no—
34C2×Q8×C79—21no—
35C2×C8×C79—21no—
36C4⋊C4×C79—21no—
37C4⋊C4×C79—41no—
38C4⋊C4×C79—41no—
39C42×C79C22⋊C411yescharacteristic
40C16×C79—42no—
41Q8×C79—81no—
42C2×C4×C79—21no—
43C2×C4×C79—41no—
44C2×C4×C79—41no—
45C2×C4×C79#9911yescharacteristic
46C2×Dic79—41no—
47C2×Dic79—41no—
48C8×C79—41no—
49C79⋊C8—42no—
50C79⋊C8—161no—
51C22×C79AΣL(1,𝔽16)11yescharacteristic
52C4×C79—21no—
53C4×C79—41no—
54C4×C79—81no—
55C4×C79—81no—
56Dic79—81no—
57Dic79—81no—
58#7526—791nomaximal, Sylow
59C2×C79—21no—
60C2×C79#140411yescharacteristic
61#1663—791no—
62#1413—791no—
63#1356D7911yescharacteristic
64C79#752611yescharacteristic, complemented, Sylow
65#564—791no—
66#501—1581no—
67#491C2×D7911yescharacteristic
68#356—1581no—
69#347—21no—
70#330—791no—
71#330—1581no—
72C4⋊Q8D31611yescharacteristic
73#125—3161no—
74#125—3161no—
75#125—3161no—
76#125—1581no—
77#125C4×D7911yescharacteristic
78M32—41no—
79#107—3161no—
80#106—3161no—
81#103—41no—
82#101—3161no—
83#97—1581no—
84#97C22⋊D7911yescharacteristic
85C2×Q8—21no—
86M16—6321no—
87C2×C8—21no—
88C2×C8—3161no—
89C4⋊C4—21no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C4⋊C4—3161no—
93C4⋊C4—3161no—
94C4⋊C4—3161no—
95C4⋊C4—3161no—
96C4⋊C4—3161no—
97C4⋊C4—1581no—
98C4⋊C4—1581no—
99C42—3161no—
100C42(C2×D79)⋊C411yescharacteristic
101C16—42no—
102Q8—81no—
103C2×C4—21no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—3161no—
107C2×C4—3161no—
108C2×C4#1457907511yescharacteristic
109C8—41no—
110C8—3162no—
111C8—12641no—
112C22#1909835111yescharacteristic
113C4—21no—
114C4—41no—
115C4—81no—
116C4—81no—
117C4—6321no—
118C4—6321no—
119C2—21no—
120C2#2376155211yescharacteristic
subgroupG/H
centerC2#23761552
commutator#125×C79C2×C4
Frattini#491C2×D79
FittingC79×#1356C2
socleC2×C79#1404
prime radicalC22×C79AΣL(1,𝔽16)
cosocle#491×C79C22
hypercenter#1356D79
hypocenterC79#7526
LCSG ▷ #125×C79 ▷ C42×C79 ▷ C2×C4×C79 ▷ C22×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #491 ◁ #1356

Complements

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

NH ≅ G/Ntype
64. C79#7526semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237627262
#237615732
C79×#13562
#752679