Finite Group Databasebeta

← #30595258

Subgroups — #30595258

Order 15616.

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

normal subgroups only

This group has 148 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#21460956C211yesmaximal, characteristic, complemented
2#21460828C211yesmaximal, characteristic, complemented
3#21444965C211yesmaximal, characteristic
4#16840685—21no—
5#16840673—21no—
6#16840478C411yescharacteristic
7#16840141C2211yescharacteristic
8#16840053—21no—
9#16839489—21no—
10C61×#333C411yescharacteristic
11#14519851—41no—
12#14519838—41no—
13C2×#11758202—41no—
14#14519777D411yescharacteristic
15#14519766—41no—
16#14519752—41no—
17C4×D244—21no—
18#14519735—41no—
19#14519709—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×C4×D61—41no—
28C2×Dic122—21no—
29#11758217—81no—
30C2×C8×C61—41no—
31C4⋊C4×C61—41no—
32C42×C61C22⋊C411yescharacteristic
33#11758202—81no—
34#11758202—81no—
35#11758198—42no—
36#11758198—41no—
37C4⋊Dic61—21no—
38C4⋊Dic61—41no—
39C4×Dic61—41no—
40C2×#92418—21no—
41#11758187—81no—
42C22×D61—41no—
43Q8×C61—81no—
44C2×C4×C61—21no—
45C2×C4×C61—41no—
46C2×C4×C61#9911yescharacteristic
47C2×Dic61—41no—
48C2×Dic61—41no—
49D244—41no—
50D244—41no—
51D244—161no—
52C4×D61—81no—
53C4×D61—81no—
54Dic122—81no—
55#92420—161no—
56C8×C61—81no—
57#92418—21no—
58#92418—21no—
59#7521—611nomaximal, Sylow
60C22×C61AΣL(1,𝔽16)11yescharacteristic
61C2×D61—81no—
62C2×D61—81no—
63C2×D61—81no—
64C4×C61—21no—
65C4×C61—21no—
66C4×C61—21no—
67C4×C61—81no—
68Dic61—81no—
69Dic61—81no—
70#1634—611no—
71#1411—611no—
72#1358—611no—
73C2×C61—21no—
74C2×C61#140211yescharacteristic
75D61—161no—
76#555—611no—
77#494—611no—
78#476—1221no—
79#364—1221no—
80#356—1221no—
81#333#692311yescharacteristic
82D4⋊C8—1221no—
83C61#752111yescharacteristic, complemented, Sylow
84C2×Q16—2441no—
85C4⋊Q8—611no—
86C4⋊Q8C2×#692311yescharacteristic
87#124—2441no—
88#121—2441no—
89C4×D4—1221no—
90#117—2441no—
91M32—2441no—
92#106—2441no—
93C4⋊C8—21no—
94#102—2441no—
95#101—2441no—
96C4×C8—611no—
97C2×Q8—21no—
98C2×Q8—1221no—
99C2×D4—1221no—
100C2×D4—2441no—
101C22×C4—2441no—
102Q16—4881no—
103Q16—4881no—
104M16—4881no—
105C2×C8—41no—
106C2×C8—1221no—
107C4⋊C4—41no—
108C4⋊C4—1221no—
109C4⋊C4—2441no—
110C22⋊C4—2442no—
111C22⋊C4—2441no—
112C42—2441no—
113C42C22⋊#692311yescharacteristic
114C16—4881no—
115C23—2441no—
116Q8—81no—
117Q8—4881no—
118D4—9761no—
119D4—2441no—
120D4—2441no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—4881no—
124C2×C4—4881no—
125C2×C4—2441no—
126C2×C4—2441no—
127C2×C4#1451983611yescharacteristic
128C8—81no—
129C8—1221no—
130C8—1221no—
131C8—9761no—
132C22—4881no—
133C22—4881no—
134C22—4881no—
135C22#1684066311yescharacteristic
136C4—21no—
137C4—21no—
138C4—21no—
139C4—81no—
140C4—4881no—
141C4—4881no—
142C2—21no—
143C2—9761no—
144C2#2146093911yescharacteristic
subgroupG/H
centerC2#21460939
commutatorC4⋊Q8×C61C2×C4
FrattiniC4⋊Q8C2×#6923
FittingC61×#333C4
socleC2×C61#1402
prime radical#16840478C4
cosocle#16840141C22
hypercenter#333#6923
hypocenterC61#7521
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
1. #21460956C2semidirect
2. #21460828C2semidirect
83. C61#7521semidirect

Maximal subgroups

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

subgroupindex
#214609562
#214608282
#214449652
#752161