Finite Group Databasebeta

← #30594967

Subgroups — #30594967

Order 15616.

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

normal subgroups only

This group has 162 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#21460910C211yesmaximal, characteristic
2#21460754C211yesmaximal, characteristic
3#21447266C211yesmaximal, characteristic
4#16840748—21no—
5#16840658—21no—
6C2×#14519709C411yescharacteristic
7#16839764—21no—
8#16839728C2211yescharacteristic
9#16839530—21no—
10C61×#341C411yescharacteristic
11D61⋊M16—41no—
12#14519851—41no—
13#14519838—41no—
14#14519837—22no—
15C2×#11758222D411yescharacteristic
16C2×#11758194D411yescharacteristic
17C2×C4⋊Dic61—21no—
18#14519709—41no—
19#14519702—41no—
20#14519699—41no—
21#14519689—41no—
22C2×M16×C61—21no—
23C22×C8×C61C2×C411yescharacteristic
24C22×C4×C61C22⋊C411yescharacteristic
25C2×C22⋊D61—21no—
26C22×Dic61—41no—
27#11758222—41no—
28#11758222—41no—
29C2×D244SD1611yescharacteristic
30C2×C4×D61—21no—
31C2×Dic122D811yescharacteristic
32#11758217—42no—
33#11758213—81no—
34D61⋊C8—81no—
35M16×C61—41no—
36M16×C61—41no—
37C2×C8×C61—21no—
38C2×C8×C61—41no—
39C2×C8×C61—41no—
40C4⋊Dic61—41no—
41C4⋊Dic61—41no—
42#11758194—41no—
43C2×#92418—21no—
44#11758187—81no—
45C23×C61#10411yescharacteristic
46C22×D61—21no—
47C2×C4×C61—21no—
48C2×C4×C61—21no—
49C2×C4×C61#9911yescharacteristic
50C2×C4×C61#10211yescharacteristic
51C22⋊D61—81no—
52C2×Dic61—21no—
53C2×Dic61—81no—
54C2×Dic61—161no—
55D244—41no—
56C4×D61—41no—
57C4×D61—41no—
58Dic122—41no—
59#92420—82no—
60C8×C61—41no—
61C8×C61—81no—
62#92418—41no—
63#7411—611nomaximal, Sylow
64C22×C61—21no—
65C22×C61—41no—
66C22×C61#32711yescharacteristic
67C2×D61—41no—
68C2×D61—81no—
69C4×C61—21no—
70C4×C61#35211yescharacteristic
71C4×C61#35411yescharacteristic
72Dic61—41no—
73Dic61—161no—
74#2079—611no—
75#1392—611no—
76#1321—611no—
77C2×C61—21no—
78C2×C61—41no—
79C2×C61#134411yescharacteristic
80D61—81no—
81C2×#106—611no—
82#417—1221no—
83#413—1221no—
84#408—611no—
85#349—1221no—
86#343—1221no—
87#341#692311yescharacteristic
88C61#741111yescharacteristic, complemented, Sylow
89C2×#41—611no—
90C2×M16—21no—
91C2×M16—611no—
92C2×M16—2441no—
93C22×C8C2×#692311yescharacteristic
94C2×C4⋊C4—1221no—
95M32—2441no—
96#106—2441no—
97#103—2441no—
98#102—2441no—
99#101—2441no—
100#100—1222no—
101C22⋊C8—2441no—
102#41—2441no—
103#41—2441no—
104C2×Q8—611no—
105C2×D4—611no—
106C2×D4—1221no—
107C22×C4—1221no—
108C22×C4—2441no—
109C22×C4C22⋊#692311yescharacteristic
110M16—41no—
111M16—41no—
112M16—4881no—
113M16—2442no—
114M16—2441no—
115C2×C8—21no—
116C2×C8—41no—
117C2×C8—41no—
118C2×C8—1221no—
119C2×C8—4881no—
120C4⋊C4—2441no—
121C4⋊C4—2441no—
122C16—4881no—
123C23—1221no—
124C23#1451984211yescharacteristic
125Q8—2441no—
126D4—4881no—
127D4—2441no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—1221no—
131C2×C4—9761no—
132C2×C4—4881no—
133C2×C4—2441no—
134C2×C4—2441no—
135C2×C4#1451983611yescharacteristic
136C2×C4#1451983911yescharacteristic
137C8—41no—
138C8—81no—
139C8—4882no—
140C8—2441no—
141C22—21no—
142C22—41no—
143C22—4881no—
144C22—2441no—
145C22#1684061411yescharacteristic
146C4—21no—
147C4—9761no—
148C4—2441no—
149C4#1684066511yescharacteristic
150C4#1684066911yescharacteristic
151C2—21no—
152C2—41no—
153C2—4881no—
154C2#2146080011yescharacteristic
subgroupG/H
centerC2#21460800
commutatorC22×C8×C61C2×C4
FrattiniC22×C8C2×#6923
FittingC61×#341C4
socleC2×C61#1344
prime radicalC2×#11758222D4
cosocle#16839728C22
hypercenter#341#6923
hypocenterC61#7411
LCSG ▷ C22×C8×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #341

Complements

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

NH ≅ G/Ntype
88. C61#7411semidirect

Maximal subgroups

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

subgroupindex
#214609102
#214607542
#214472662
#741161