Finite Group Databasebeta

← #30595007

Subgroups — #30595007

Order 15616.

226 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 36 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#21460913C211yesmaximal, characteristic
2#21460748C211yesmaximal, characteristic
3#21446962C211yesmaximal, characteristic
4C2×#14519836—21no—
5#16840607—21no—
6C2×#14519697—21no—
7#16839664C2211yescharacteristic
8#16839524—21no—
9#16839517C411yescharacteristic, complemented
10C2×#125×C61C411yescharacteristic, complemented
11C2×C22⋊#6923—41no—
12#14519836—22no—
13#14519836—41no—
14C22⋊#92420—41no—
15C22×D244D411yescharacteristic
16C22×#92418—21no—
17C2×C4⋊Dic61D411yescharacteristic
18C2×#11758198—41no—
19#14519697—42no—
20#125×C61—42no—
21C2×C4⋊C4×C61—21no—
22C2×C4⋊C4×C61—41no—
23C2×C42×C61C2×C411yescharacteristic
24C23×D61—21no—
25C22×#6923—81no—
26C22×C4×C61—21no—
27C22×C4×C61—41no—
28C22×C4×C61C22⋊C411yescharacteristic
29C22×Dic61—21no—
30C2×D244—21no—
31C2×D244—41no—
32C2×D244—41no—
33C2×D244SD1611yescharacteristic
34C2×D244Q1611yescharacteristic
35C22⋊#6923—42no—
36C22⋊#6923—81no—
37C2×#92420—81no—
38C4⋊C4×C61—22no—
39C4⋊C4×C61—41no—
40C4⋊C4×C61—42no—
41C4⋊C4×C61—42no—
42C42×C61—41no—
43#11758198—82no—
44C4⋊Dic61—41no—
45C2×#92418—41no—
46C2×#92418—41no—
47C2×#92418—41no—
48C23×C61#9911yescharacteristic
49C22×D61—21no—
50C22×D61—21no—
51C22×D61—41no—
52C22×D61—41no—
53C22×D61—81no—
54C22×D61—81no—
55C2×#6923—82no—
56C2×#6923—161no—
57C2×#6923—161no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61—42no—
64C2×C4×C61—81no—
65C2×C4×C61—81no—
66C2×C4×C61#10311yescharacteristic
67C2×C4×C61#10411yescharacteristic
68C2×Dic61—41no—
69C2×Dic61—81no—
70D244—41no—
71D244—41no—
72D244—81no—
73#92420—161no—
74#92418—81no—
75#7428—611nomaximal, Sylow
76C22×C61—21no—
77C22×C61—21no—
78C22×C61#32811yescharacteristic
79C22×C61AΣL(1,𝔽16)11yescharacteristic
80C22×C61#35411yescharacteristic
81C2×D61—41no—
82C2×D61—41no—
83C2×D61—81no—
84C2×D61—81no—
85C2×D61—81no—
86C2×D61—81no—
87C2×D61—161no—
88#6923—162no—
89C4×C61—21no—
90C4×C61—21no—
91C4×C61—81no—
92C4×C61—82no—
93Dic61—81no—
94#2025—611no—
95#1393—611no—
96#1318—611no—
97C2×C61—21no—
98C2×C61—21no—
99C2×C61#135111yescharacteristic
100C2×C61#141211yescharacteristic
101C2×C61#141411yescharacteristic
102D61—81no—
103D61—81no—
104C2×#125#692311yescharacteristic, complemented
105C2×#102—1221no—
106C2×#99—1221no—
107#390—611no—
108#340—1221no—
109#336—611no—
110#324—1221no—
111C61#742811yescharacteristic, complemented, Sylow
112C22×D4—611no—
113C22×C8—1221no—
114#125—42no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—611no—
118C2×C22⋊C4—2441no—
119C2×C22⋊C4—2441no—
120C2×C42C2×#692311yescharacteristic
121#102—2442no—
122#99—1222no—
123#99—2441no—
124C22⋊C8—2441no—
125C24—1221no—
126C2×D4—611no—
127C2×D4—611no—
128C2×D4—1221no—
129C2×D4—2441no—
130C2×D4—2441no—
131C22×C4—21no—
132C22×C4—41no—
133C22×C4—1221no—
134C22×C4—4881no—
135C22×C4C22⋊#692311yescharacteristic
136C2×C8—4881no—
137C2×C8—2441no—
138C2×C8—2441no—
139C2×C8—2441no—
140C4⋊C4—22no—
141C4⋊C4—41no—
142C4⋊C4—42no—
143C4⋊C4—42no—
144C4⋊C4—2441no—
145C22⋊C4—4882no—
146C22⋊C4—4881no—
147C22⋊C4—2442no—
148C42—41no—
149C23—1221no—
150C23—1221no—
151C23—4881no—
152C23—4881no—
153C23—2441no—
154C23—2441no—
155C23#1451983511yescharacteristic
156D4—4881no—
157D4—2441no—
158D4—2441no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4—9761no—
168C2×C4—9761no—
169C2×C4—4882no—
170C2×C4—4881no—
171C2×C4—2441no—
172C2×C4#1451984011yescharacteristic
173C2×C4#1451984211yescharacteristic
174C8—9761no—
175C8—4881no—
176C22—21no—
177C22—21no—
178C22—9761no—
179C22—4881no—
180C22—4881no—
181C22—4881no—
182C22—4881no—
183C22—2441no—
184C22—2441no—
185C22#1684061611yescharacteristic
186C22#1684066211yescharacteristic
187C22#1684066811yescharacteristic
188C4—21no—
189C4—21no—
190C4—81no—
191C4—82no—
192C4—9762no—
193C4—4881no—
194C2—21no—
195C2—21no—
196C2—4881no—
197C2—4881no—
198C2#2146081411yescharacteristic
199C2#2146095911yescharacteristic
200C2#2146096411yescharacteristic
subgroupG/H
centerC22#16840668
commutatorC2×C42×C61C2×C4
FrattiniC2×C42C2×#6923
FittingC2×#125×C61C4
socleC22×C61#354
prime radicalC22×D244D4
cosocle#16839664C22
hypercenterC2×#125#6923
hypocenterC61#7428
LCSG ▷ C2×C42×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
9. #16839517C4semidirect
10. C2×#125×C61C4semidirect
104. C2×#125#6923semidirect
111. C61#7428semidirect

Maximal subgroups

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

subgroupindex
#214609132
#214607482
#214469622
#742861