Finite Group Databasebeta

← #30595255

Subgroups — #30595255

Order 15616.

156 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 22 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#21460952C211yesmaximal, characteristic
2#21460830C211yesmaximal, characteristic
3#21444897C211yesmaximal, characteristic
4#16840685—21no—
5#16840667—21no—
6#16840136C2211yescharacteristic
7#16839962—21no—
8#16839511C411yescharacteristic, complemented
9Q8⋊#92418—21no—
10Q82×C61C411yescharacteristic, complemented
11#14519851—41no—
12#14519836—41no—
13C2×#11758201—41no—
14C2×#11758201—41no—
15#14519774D411yescharacteristic
16C4⋊#92418—21no—
17#14519697—41no—
18C4×#92418D411yescharacteristic
19C4⋊Q8×C61—41no—
20C4⋊Q8×C61—41no—
21C4⋊Q8×C61C2×C411yescharacteristic
22C4×Q8×C61—21no—
23C4×Q8×C61—41no—
24C2×Q8×C61—21no—
25C2×Q8×C61—21no—
26C2×Q8×C61—41no—
27C2×D244—21no—
28C2×D244—41no—
29C22⋊#6923—81no—
30C4⋊C4×C61—21no—
31C4⋊C4×C61—41no—
32C4⋊C4×C61—42no—
33C4⋊C4×C61—41no—
34C42×C61—41no—
35C42×C61—41no—
36C42×C61C22⋊C411yescharacteristic
37#11758201—81no—
38#11758201—81no—
39#11758201—82no—
40C2×#92418—21no—
41C2×#92418—41no—
42#11758187—81no—
43C22×D61—41no—
44C2×#6923—161no—
45Q8×C61—22no—
46Q8×C61—41no—
47Q8×C61—81no—
48Q8×C61—161no—
49C2×C4×C61—21no—
50C2×C4×C61—41no—
51C2×C4×C61—41no—
52C2×C4×C61—41no—
53C2×C4×C61#9911yescharacteristic
54D244—81no—
55D244—81no—
56D244—81no—
57#92418—21no—
58#92418—21no—
59#92418—81no—
60#7520—611nomaximal, Sylow
61C22×C61AΣL(1,𝔽16)11yescharacteristic
62C2×D61—81no—
63C2×D61—161no—
64#6923—321no—
65C4×C61—21no—
66C4×C61—21no—
67C4×C61—21no—
68C4×C61—42no—
69C4×C61—81no—
70C4×C61—81no—
71#1623—611no—
72#1409—611no—
73#1359—611no—
74C2×C61—21no—
75C2×C61#140211yescharacteristic
76D61—161no—
77Q82#692311yescharacteristic, complemented
78#492—611no—
79#460—1221no—
80#364—1221no—
81#353—1221no—
82#333—611no—
83Q8⋊C8—1221no—
84C61#752011yescharacteristic, complemented, Sylow
85C2×SD16—2441no—
86C2×SD16—2441no—
87C4⋊Q8—41no—
88C4⋊Q8—41no—
89C4⋊Q8C2×#692311yescharacteristic
90#127—611no—
91C4×Q8—21no—
92C4×Q8—41no—
93M32—2441no—
94C4⋊C8—1221no—
95#102—2441no—
96#99—2441no—
97C4×C8—611no—
98C2×Q8—21no—
99C2×Q8—21no—
100C2×Q8—41no—
101C2×D4—1221no—
102C2×D4—2441no—
103SD16—4881no—
104SD16—4881no—
105SD16—4882no—
106C2×C8—1221no—
107C2×C8—2441no—
108C4⋊C4—21no—
109C4⋊C4—41no—
110C4⋊C4—42no—
111C4⋊C4—41no—
112C22⋊C4—4881no—
113C42—41no—
114C42—41no—
115C42C22⋊#692311yescharacteristic
116C16—4881no—
117C23—2441no—
118Q8—22no—
119Q8—41no—
120Q8—81no—
121Q8—161no—
122D4—4881no—
123D4—4881no—
124D4—4881no—
125C2×C4—21no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—9761no—
130C2×C4#1451983511yescharacteristic
131C8—1221no—
132C8—1221no—
133C8—4881no—
134C22—9761no—
135C22—4881no—
136C22#1684066211yescharacteristic
137C4—21no—
138C4—21no—
139C4—21no—
140C4—42no—
141C4—81no—
142C4—81no—
143C4—19521no—
144C2—21no—
145C2—9761no—
146C2#2146093811yescharacteristic
subgroupG/H
centerC2#21460938
commutatorC4⋊Q8×C61C2×C4
FrattiniC4⋊Q8C2×#6923
FittingQ82×C61C4
socleC2×C61#1402
prime radical#14519774D4
cosocle#16840136C22
hypercenterQ82#6923
hypocenterC61#7520
LCSG ▷ C4⋊Q8×C61 ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4⋊Q8 ◁ Q82

Complements

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

NH ≅ G/Ntype
8. #16839511C4semidirect
10. Q82×C61C4semidirect
77. Q82#6923semidirect
84. C61#7520semidirect

Maximal subgroups

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

subgroupindex
#214609522
#214608302
#214448972
#752061