Finite Group Databasebeta

← #29567597

Subgroups — #29567597

Order 15616.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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#21446965C211yesmaximal, characteristic
2#21443751C211yesmaximal, characteristic
3C61×#1393C211yesmaximal, characteristic
4C2×#14519769C411yescharacteristic, complemented
5C2×#14519698—21no—
6#16839524—21no—
7#16839517C411yescharacteristic, complemented
8#16839488—21no—
9C2×#99×C61—21no—
10C61×#390C2211yescharacteristic
11C22×#92418—21no—
12#14519769—42no—
13C2×C4⋊Dic61—21no—
14C2×#11758196—41no—
15#14519698—42no—
16C22⋊#92418—41no—
17C22×D4×C61D411yescharacteristic
18C2×C4⋊C4×C61D411yescharacteristic
19C2×C22⋊C4×C61—41no—
20C2×C22⋊C4×C61—41no—
21C2×C42×C61C2×C411yescharacteristic
22#99×C61—22no—
23#99×C61—41no—
24C24×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—41no—
27C2×D4×C61—41no—
28C2×D4×C61SD1611yescharacteristic
29C2×D4×C61Q1611yescharacteristic
30C22×C4×C61—21no—
31C22×C4×C61—21no—
32C22×C4×C61—81no—
33C22×C4×C61C22⋊C411yescharacteristic
34C22×Dic61—41no—
35C4⋊C4×C61—41no—
36C22⋊C4×C61—42no—
37C22⋊C4×C61—82no—
38C22⋊C4×C61—81no—
39C42×C61—41no—
40C4⋊Dic61—22no—
41C4⋊Dic61—41no—
42#11758196—42no—
43#11758196—42no—
44C2×#92418—41no—
45C2×#92418—41no—
46C2×#92418—41no—
47C2×#92418—81no—
48C23×C61—21no—
49C23×C61—21no—
50C23×C61—41no—
51C23×C61—41no—
52C23×C61—81no—
53C23×C61—81no—
54C23×C61#9911yescharacteristic
55D4×C61—41no—
56D4×C61—41no—
57D4×C61—81no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61—81no—
65C2×C4×C61—82no—
66C2×C4×C61—161no—
67C2×C4×C61—161no—
68C2×C4×C61#10311yescharacteristic
69C2×C4×C61#10411yescharacteristic
70C2×Dic61—42no—
71C2×Dic61—81no—
72C2×Dic61—81no—
73#92418—81no—
74#92418—161no—
75#7428—611nomaximal, Sylow
76C22×C61—21no—
77C22×C61—21no—
78C22×C61—41no—
79C22×C61—41no—
80C22×C61—81no—
81C22×C61—81no—
82C22×C61—81no—
83C22×C61—81no—
84C22×C61—161no—
85C22×C61#32811yescharacteristic
86C22×C61AΣL(1,𝔽16)11yescharacteristic
87C22×C61#35411yescharacteristic
88C4×C61—21no—
89C4×C61—21no—
90C4×C61—81no—
91C4×C61—81no—
92C4×C61—162no—
93Dic61—82no—
94#2025—611no—
95#1393D6111yescharacteristic
96#1318—611no—
97C2×C61—21no—
98C2×C61—21no—
99C2×C61—81no—
100C2×C61—81no—
101C2×C61#135111yescharacteristic
102C2×C61#141211yescharacteristic
103C2×C61#141411yescharacteristic
104C2×#125—611no—
105C2×#102—1221no—
106C2×#99—21no—
107#390C2×D6111yescharacteristic
108#340—1221no—
109#336—611no—
110#324—1221no—
111C61#742811yescharacteristic, complemented, Sylow
112C22×D4C22⋊D6111yescharacteristic
113C22×C8—1221no—
114#125—2442no—
115C2×C4⋊C4—1221no—
116C2×C4⋊C4—2441no—
117C2×C4⋊C4D24411yescharacteristic
118C2×C22⋊C4—41no—
119C2×C22⋊C4—41no—
120C2×C42C4×D6111yescharacteristic
121#102—2442no—
122#99—22no—
123#99—41no—
124C22⋊C8—2441no—
125C24—21no—
126C2×D4—21no—
127C2×D4—41no—
128C2×D4—41no—
129C2×D4#1175820011yescharacteristic
130C2×D4#1175820211yescharacteristic
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—81no—
134C22×C4—2441no—
135C22×C4#1175819811yescharacteristic
136C2×C8—4881no—
137C2×C8—2441no—
138C2×C8—2441no—
139C2×C8—2441no—
140C4⋊C4—41no—
141C4⋊C4—1222no—
142C4⋊C4—2441no—
143C4⋊C4—2442no—
144C4⋊C4—2442no—
145C22⋊C4—42no—
146C22⋊C4—82no—
147C22⋊C4—81no—
148C42—41no—
149C23—21no—
150C23—21no—
151C23—41no—
152C23—41no—
153C23—81no—
154C23—81no—
155C23#1451969111yescharacteristic
156D4—41no—
157D4—41no—
158D4—81no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—81no—
166C2×C4—82no—
167C2×C4—161no—
168C2×C4—161no—
169C2×C4—4881no—
170C2×C4—4881no—
171C2×C4—2442no—
172C2×C4#1451970011yescharacteristic
173C2×C4#1451970511yescharacteristic
174C8—9761no—
175C8—4881no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—81no—
184C22—161no—
185C22#1683949811yescharacteristic
186C22#1683954811yescharacteristic
187C22#1683955611yescharacteristic
188C4—21no—
189C4—21no—
190C4—81no—
191C4—81no—
192C4—162no—
193C4—4882no—
194C2—21no—
195C2—21no—
196C2—81no—
197C2—81no—
198C2#2144383911yescharacteristic
199C2#2144398911yescharacteristic
200C2#2144399311yescharacteristic
subgroupG/H
centerC22#16839556
commutatorC2×C42×C61C2×C4
Frattini#390C2×D61
FittingC61×#1393C2
socleC22×C61#354
prime radicalC22×D4×C61D4
cosocleC61×#390C22
hypercenter#1393D61
hypocenterC61#7428
LCSG ▷ C2×C42×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1393

Complements

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

NH ≅ G/Ntype
4. C2×#14519769C4semidirect
7. #16839517C4semidirect
111. C61#7428semidirect

Maximal subgroups

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

subgroupindex
#214469652
#214437512
C61×#13932
#742861