Finite Group Databasebeta

← #30595028

Subgroups — #30595028

Order 15616.

174 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 32 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#21460908C211yesmaximal, characteristic
2#21460742C211yesmaximal, characteristic
3#21447373C211yesmaximal, characteristic
4#16840741—21no—
5C22⋊#11758187—21no—
6#16839811C411yescharacteristic, complemented
7#16839789—21no—
8#16839780—21no—
9#16839730C2211yescharacteristic
10C61×H(3,ℤ/4)C411yescharacteristic, complemented
11#14519856—41no—
12C2×#11758187—41no—
13#14519836—41no—
14#14519835—22no—
15C2×#11758222D411yescharacteristic
16C2×#11758194—21no—
17C22×#92418D411yescharacteristic
18#14519713—41no—
19C4⋊#92418—42no—
20#14519705—42no—
21#14519689—41no—
22C2×M16×C61C2×C411yescharacteristic
23#117×C61—21no—
24C22×C4×C61C22⋊C411yescharacteristic
25C2×C22⋊D61—21no—
26#11758222—41no—
27#11758222—41no—
28C2×D244SD1611yescharacteristic
29C2×C4×D61—21no—
30C2×Dic122Q1611yescharacteristic
31C22⋊#6923—42no—
32C4⋊#6923—81no—
33C4×#6923—81no—
34M16×C61—41no—
35C2×C8×C61—21no—
36C4⋊C4×C61—41no—
37C22⋊C4×C61—41no—
38C42×C61—22no—
39#11758194—41no—
40#11758194—41no—
41C2×#92418—21no—
42C2×#92418—41no—
43C2×#92418—41no—
44#11758187—81no—
45C23×C61#10411yescharacteristic
46C22×D61—21no—
47C2×#6923—82no—
48C2×C4×C61—21no—
49C2×C4×C61—21no—
50C2×C4×C61—42no—
51C2×C4×C61#9911yescharacteristic
52C2×C4×C61#10311yescharacteristic
53C22⋊D61—81no—
54C2×Dic61—21no—
55D244—41no—
56C4×D61—41no—
57C4×D61—41no—
58Dic122—41no—
59C8×C61—41no—
60#92418—41no—
61#92418—81no—
62#7438—611nomaximal, Sylow
63C22×C61—21no—
64C22×C61—41no—
65C22×C61#32811yescharacteristic
66C2×D61—41no—
67C2×D61—81no—
68#6923—162no—
69C4×C61—21no—
70C4×C61—82no—
71C4×C61#35211yescharacteristic
72C4×C61#35311yescharacteristic
73Dic61—41no—
74#2098—611no—
75#1391—611no—
76#1315—611no—
77C2×C61—21no—
78C2×C61—41no—
79C2×C61#135211yescharacteristic
80D61—81no—
81#430—611no—
82#424—1221no—
83#421—1221no—
84#410—1221no—
85#408—611no—
86C22⋊C16—1221no—
87H(3,ℤ/4)#692311yescharacteristic, complemented
88C61#743811yescharacteristic, complemented, Sylow
89C2×#41—611no—
90C2×M16—1221no—
91C2×M16C2×#692311yescharacteristic
92C22×C8—611no—
93#117—21no—
94#117—2441no—
95C2×C16—2441no—
96#108—2441no—
97C4⋊C8—2442no—
98#104—2442no—
99#99—1222no—
100#99—2441no—
101C22⋊C8—2441no—
102#41—2441no—
103#41—2441no—
104C2×Q8—611no—
105C2×D4—611no—
106C2×D4—1221no—
107C22×C4—1221no—
108C22×C4C22⋊#692311yescharacteristic
109M16—41no—
110M16—2441no—
111M16—2441no—
112C2×C8—21no—
113C2×C8—1221no—
114C2×C8—2441no—
115C2×C8—2441no—
116C4⋊C4—41no—
117C4⋊C4—4881no—
118C22⋊C4—41no—
119C22⋊C4—2442no—
120C42—22no—
121C42—4881no—
122C16—4881no—
123C23—1221no—
124C23#1451984111yescharacteristic
125Q8—2441no—
126D4—4881no—
127D4—2441no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—42no—
131C2×C4—1221no—
132C2×C4—4882no—
133C2×C4—2441no—
134C2×C4—2441no—
135C2×C4#1451983611yescharacteristic
136C2×C4#1451984011yescharacteristic
137C8—41no—
138C8—4881no—
139C8—2441no—
140C22—21no—
141C22—41no—
142C22—4881no—
143C22—2441no—
144C22#1684061511yescharacteristic
145C4—21no—
146C4—82no—
147C4—9762no—
148C4—2441no—
149C4#1684066511yescharacteristic
150C4#1684066711yescharacteristic
151C2—21no—
152C2—41no—
153C2—4881no—
154C2#2146081511yescharacteristic
subgroupG/H
centerC4#16840667
commutatorC2×M16×C61C2×C4
FrattiniC2×M16C2×#6923
FittingC61×H(3,ℤ/4)C4
socleC2×C61#1352
prime radicalC2×#11758222D4
cosocle#16839730C22
hypercenterH(3,ℤ/4)#6923
hypocenterC61#7438
LCSG ▷ C2×M16×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
6. #16839811C4semidirect
10. C61×H(3,ℤ/4)C4semidirect
87. H(3,ℤ/4)#6923semidirect
88. C61#7438semidirect

Maximal subgroups

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

subgroupindex
#214609082
#214607422
#214473732
#743861