Finite Group Databasebeta

← #30595256

Subgroups — #30595256

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#21444898C211yesmaximal, characteristic
4#16840685—21no—
5#16840667—21no—
6#16840492C411yescharacteristic, complemented
7#16840136C2211yescharacteristic
8#16839963—21no—
9#16839492—21no—
10C61×#333C411yescharacteristic, complemented
11#14519851—41no—
12#14519836—41no—
13C2×#11758190—41no—
14C2×#11758201—41no—
15#14519776—41no—
16#14519775—41no—
17#14519774D411yescharacteristic
18C4×Dic122—21no—
19#14519742—41no—
20#14519699—41no—
21C4×#92418D411yescharacteristic
22C4⋊Q8×C61C2×C411yescharacteristic
23C4⋊C8×C61—21no—
24C2×Q8×C61—21no—
25C2×D244—21no—
26C2×D244—41no—
27C2×Dic122—21no—
28C2×Dic122—41no—
29C22⋊#6923—81no—
30C2×C8×C61—41no—
31C4⋊C4×C61—41no—
32C42×C61C22⋊C411yescharacteristic
33#11758201—81no—
34#11758201—81no—
35C4⋊Dic61—21no—
36#11758196—42no—
37#11758196—41no—
38C4×Dic61—41no—
39C4×Dic61—41no—
40C2×#92418—21no—
41#11758190—82no—
42#11758187—81no—
43C22×D61—41no—
44C2×#6923—161no—
45Q8×C61—81no—
46C2×C4×C61—21no—
47C2×C4×C61—41no—
48C2×C4×C61#9911yescharacteristic
49C2×Dic61—41no—
50C2×Dic61—41no—
51D244—81no—
52D244—81no—
53D244—81no—
54Dic122—22no—
55Dic122—41no—
56Dic122—161no—
57C8×C61—81no—
58#92418—21no—
59#92418—21no—
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—81no—
69Dic61—42no—
70Dic61—81no—
71#1623—611no—
72#1409—611no—
73#1359—611no—
74C2×C61—21no—
75C2×C61#140211yescharacteristic
76D61—161no—
77Q82—611no—
78#492—611no—
79#460—1221no—
80#364—1221no—
81#353—1221no—
82#333#692311yescharacteristic, complemented
83Q8⋊C8—1221no—
84C61#752011yescharacteristic, complemented, Sylow
85C2×SD16—2441no—
86C2×SD16—2441no—
87C4⋊Q8—2441no—
88C4⋊Q8—2441no—
89C4⋊Q8C2×#692311yescharacteristic
90#127—611no—
91C4×Q8—1221no—
92C4×Q8—2441no—
93M32—2441no—
94C4⋊C8—21no—
95#102—2441no—
96#99—2441no—
97C4×C8—611no—
98C2×Q8—21no—
99C2×Q8—1221no—
100C2×Q8—2441no—
101C2×D4—1221no—
102C2×D4—2441no—
103SD16—4882no—
104SD16—4881no—
105SD16—4881no—
106C2×C8—41no—
107C2×C8—1221no—
108C4⋊C4—41no—
109C4⋊C4—1221no—
110C4⋊C4—2442no—
111C4⋊C4—2441no—
112C22⋊C4—4881no—
113C42—2441no—
114C42—2441no—
115C42C22⋊#692311yescharacteristic
116C16—4881no—
117C23—2441no—
118Q8—81no—
119Q8—1222no—
120Q8—9761no—
121Q8—2441no—
122D4—4881no—
123D4—4881no—
124D4—4881no—
125C2×C4—21no—
126C2×C4—41no—
127C2×C4—9761no—
128C2×C4—2441no—
129C2×C4—2441no—
130C2×C4#1451983611yescharacteristic
131C8—81no—
132C8—1221no—
133C8—1221no—
134C22—9761no—
135C22—4881no—
136C22#1684066311yescharacteristic
137C4—21no—
138C4—21no—
139C4—21no—
140C4—81no—
141C4—19521no—
142C4—4881no—
143C4—2442no—
144C2—21no—
145C2—9761no—
146C2#2146093911yescharacteristic
subgroupG/H
centerC2#21460939
commutatorC4⋊Q8×C61C2×C4
FrattiniC4⋊Q8C2×#6923
FittingC61×#333C4
socleC2×C61#1402
prime radical#14519774D4
cosocle#16840136C22
hypercenter#333#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 ◁ #333

Complements

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

NH ≅ G/Ntype
6. #16840492C4semidirect
10. C61×#333C4semidirect
82. #333#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
#214448982
#752061