Finite Group Databasebeta

← #30594888

Subgroups — #30594888

Order 15616.

170 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 38 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#21460753C211yesmaximal, characteristic
2#21460741C211yesmaximal, characteristic
3#21446041C211yesmaximal, characteristic
4#16840658—21no—
5C22⋊#11758187—21no—
6#16840529C411yescharacteristic
7#16839811—21no—
8#16839729C2211yescharacteristic
9#16839526—21no—
10C61×#413C411yescharacteristic
11#14519851—41no—
12C2×#11758187—41no—
13#14519784—42no—
14C2×#11758194—21no—
15C2×#11758194—41no—
16C2×#11758194D411yescharacteristic
17C22×#92418D411yescharacteristic
18#14519713—42no—
19C22⋊#92418—41no—
20C2×#41×C61C2×C411yescharacteristic
21C2×M16×C61—21no—
22#101×C61—21no—
23#100×C61C812yes—
24#41×C61—41no—
25#41×C61—41no—
26C2×Q8×C61M1611yescharacteristic
27C2×D4×C61—21no—
28C2×D4×C61C2×C811yescharacteristic
29C22×C4×C61—21no—
30C22×C4×C61C22⋊C411yescharacteristic
31M16×C61—22no—
32M16×C61—41no—
33C2×C8×C61—41no—
34#11758194—22no—
35#11758194—42no—
36#11758194—41no—
37#11758194—41no—
38C2×#92418—21no—
39C2×#92418—21no—
40C2×#92418—41no—
41C2×#92418—41no—
42C2×#92418—42no—
43#11758187—81no—
44#11758187—81no—
45C23×C61—21no—
46C23×C61#10111yescharacteristic
47Q8×C61—41no—
48D4×C61—41no—
49D4×C61—42no—
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61C22⋊C811yescharacteristic
56C2×C4×C61#9911yescharacteristic
57C8×C61—42no—
58#92418—41no—
59#92418—42no—
60#92418—41no—
61#7377—611nomaximal, Sylow
62C22×C61—21no—
63C22×C61—41no—
64C22×C61—41no—
65C22×C61—81no—
66C22×C61#32411yescharacteristic
67C4×C61—21no—
68C4×C61—41no—
69C4×C61AΣL(1,𝔽16)11yescharacteristic
70C4×C61#35211yescharacteristic
71#1858—611no—
72#1321—611no—
73#1315—611no—
74C2×C61—21no—
75C2×C61—41no—
76C2×C61—81no—
77C2×C61#132611yescharacteristic
78#568—611no—
79#430—1221no—
80#413#692311yescharacteristic
81#408—611no—
82#349—1221no—
83C22⋊C16—1221no—
84#341—1221no—
85C61#737711yescharacteristic, complemented, Sylow
86C2×#41C2×#692311yescharacteristic
87#131—2442no—
88C2×M16—21no—
89C2×M16—611no—
90C2×M16—1221no—
91C2×M16—2441no—
92C22×C8—611no—
93M32—2441no—
94C2×C16—2441no—
95#108—2442no—
96#101—21no—
97#100#9242012yes—
98C22⋊C8—2441no—
99#41—41no—
100#41—41no—
101C2×Q8#1175821711yescharacteristic
102C2×D4—21no—
103C2×D4C2×#9242011yescharacteristic
104C22×C4—21no—
105C22×C4C22⋊#692311yescharacteristic
106M16—22no—
107M16—41no—
108M16—1222no—
109M16—2442no—
110M16—2441no—
111M16—2441no—
112C2×C8—41no—
113C2×C8—1221no—
114C2×C8—1221no—
115C2×C8—2441no—
116C2×C8—2441no—
117C2×C8—2442no—
118C16—4881no—
119C16—4881no—
120C23—21no—
121C23#1451983811yescharacteristic
122Q8—41no—
123D4—41no—
124D4—42no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4C22⋊#9242011yescharacteristic
131C2×C4#1451983611yescharacteristic
132C8—42no—
133C8—2441no—
134C8—2442no—
135C8—2441no—
136C22—21no—
137C22—41no—
138C22—41no—
139C22—81no—
140C22#1684060711yescharacteristic
141C4—21no—
142C4—41no—
143C4#1684066311yescharacteristic
144C4#1684066511yescharacteristic
145C2—21no—
146C2—41no—
147C2—81no—
148C2#2146076311yescharacteristic
subgroupG/H
centerC4#16840663
commutatorC2×D4×C61C2×C8
FrattiniC2×#41C2×#6923
FittingC61×#413C4
socleC2×C61#1326
prime radicalC2×#41×C61C2×C4
cosocle#16839729C22
hypercenter#413#6923
hypocenterC61#7377
LCSG ▷ C2×D4×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
85. C61#7377semidirect

Maximal subgroups

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

subgroupindex
#214607532
#214607412
#214460412
#737761