Finite Group Databasebeta

← #30595254

Subgroups — #30595254

Order 15616.

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

normal subgroups only

This group has 162 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, complemented
2#21460830C211yesmaximal, characteristic, complemented
3#21444903C211yesmaximal, characteristic
4#16840685—21no—
5#16840667—21no—
6#16840478C411yescharacteristic, complemented
7#16840136C2211yescharacteristic
8#16839958—21no—
9#16839489—21no—
10C61×#333C411yescharacteristic, complemented
11#14519851—41no—
12#14519836—41no—
13C2×#11758201—41no—
14C2×D488—41no—
15#14519774D411yescharacteristic
16#14519766—41no—
17#14519752—41no—
18C4×D244—21no—
19#14519735—41no—
20#14519699—41no—
21C4×#92418D411yescharacteristic
22C4⋊Q8×C61C2×C411yescharacteristic
23C4⋊C8×C61—21no—
24C2×Q8×C61—21no—
25C2×D244—21no—
26C2×D244—21no—
27C2×D244—41no—
28C2×D244—41no—
29C2×C4×D61—41no—
30C22⋊#6923—81no—
31C2×C8×C61—41no—
32C4⋊C4×C61—41no—
33C42×C61C22⋊C411yescharacteristic
34#11758201—81no—
35#11758201—81no—
36#11758198—42no—
37#11758198—41no—
38C4⋊Dic61—21no—
39C4×Dic61—41no—
40C2×#92418—21no—
41D488—82no—
42#11758187—81no—
43C22×D61—41no—
44C22×D61—41no—
45C2×#6923—161no—
46Q8×C61—81no—
47C2×C4×C61—21no—
48C2×C4×C61—41no—
49C2×C4×C61#9911yescharacteristic
50C2×Dic61—41no—
51D244—41no—
52D244—41no—
53D244—81no—
54D244—81no—
55D244—81no—
56D244—161no—
57C4×D61—81no—
58C4×D61—81no—
59C8×C61—81no—
60#92418—21no—
61#92418—21no—
62#7519—611nomaximal, Sylow
63C22×C61AΣL(1,𝔽16)11yescharacteristic
64C2×D61—81no—
65C2×D61—81no—
66C2×D61—81no—
67C2×D61—81no—
68C2×D61—161no—
69#6923—321no—
70C4×C61—21no—
71C4×C61—21no—
72C4×C61—21no—
73C4×C61—81no—
74Dic61—81no—
75#1624—611no—
76#1409—611no—
77#1359—611no—
78C2×C61—21no—
79C2×C61#140211yescharacteristic
80D61—161no—
81D61—161no—
82#555—611no—
83#492—611no—
84#459—1221no—
85#364—1221no—
86#353—1221no—
87#333#692311yescharacteristic, complemented
88D4⋊C8—1221no—
89C61#751911yescharacteristic, complemented, Sylow
90C2×SD16—2441no—
91C2×D8—2441no—
92C4⋊Q8C2×#692311yescharacteristic
93#127—611no—
94#124—2441no—
95#121—2441no—
96C4×D4—1221no—
97#117—2441no—
98M32—2441no—
99C4⋊C8—21no—
100#102—2441no—
101#99—2441no—
102C4×C8—611no—
103C2×Q8—21no—
104C2×D4—1221no—
105C2×D4—1221no—
106C2×D4—2441no—
107C2×D4—2441no—
108C22×C4—2441no—
109SD16—4881no—
110SD16—4881no—
111D8—4882no—
112C2×C8—41no—
113C2×C8—1221no—
114C4⋊C4—41no—
115C4⋊C4—1221no—
116C22⋊C4—4881no—
117C22⋊C4—2442no—
118C22⋊C4—2441no—
119C42—2441no—
120C42C22⋊#692311yescharacteristic
121C16—4881no—
122C23—2441no—
123C23—2441no—
124Q8—81no—
125D4—9761no—
126D4—4881no—
127D4—4881no—
128D4—4881no—
129D4—2441no—
130D4—2441no—
131C2×C4—21no—
132C2×C4—41no—
133C2×C4—9761no—
134C2×C4—4881no—
135C2×C4—4881no—
136C2×C4—2441no—
137C2×C4#1451983611yescharacteristic
138C8—81no—
139C8—1221no—
140C8—1221no—
141C22—9761no—
142C22—4881no—
143C22—4881no—
144C22—4881no—
145C22—4881no—
146C22#1684066311yescharacteristic
147C4—21no—
148C4—21no—
149C4—21no—
150C4—81no—
151C4—19521no—
152C4—4881no—
153C2—21no—
154C2—9761no—
155C2—9761no—
156C2#2146093911yescharacteristic
subgroupG/H
centerC2#21460939
commutatorC4⋊Q8×C61C2×C4
FrattiniC4⋊Q8C2×#6923
FittingC61×#333C4
socleC2×C61#1402
prime radical#21444903C2
cosocle#16840136C22
hypercenter#333#6923
hypocenterC61#7519
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. #21460952C2semidirect
2. #21460830C2semidirect
6. #16840478C4semidirect
10. C61×#333C4semidirect
87. #333#6923semidirect
89. C61#7519semidirect

Maximal subgroups

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

subgroupindex
#214609522
#214608302
#214449032
#751961