Finite Group Databasebeta

← #30594813

Subgroups — #30594813

Order 15616.

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

normal subgroups only

This group has 452 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#21460751C212yesmaximal, complemented
2#21445739C211yesmaximal, characteristic
3#16840658—22no—
4C23×D244C411yescharacteristic
5C2×#14519693—22no—
6#16839726C2211yescharacteristic
7C61×#407C411yescharacteristic
8#14519851—42no—
9C24×D61—21no—
10C22×D244—21no—
11C22×D244—44no—
12C22×D244—41no—
13C22×D244—41no—
14C22×D244C812yes—
15C2×#11758194D412yes—
16#14519693—44no—
17C22⋊#92418—41no—
18C23×C4×C61C2×C411yescharacteristic
19C2×M16×C61—21no—
20C22⋊C8×C61—41no—
21C24×C61M1611yescharacteristic
22C23×D61—22no—
23C23×D61—44no—
24C23×D61—42no—
25C23×D61—84no—
26C22×C4×C61—21no—
27C22×C4×C61—21no—
28C22×C4×C61—42no—
29C22×C4×C61C22⋊C411yescharacteristic
30C22×C4×C61C2×C811yescharacteristic
31C2×D244—24no—
32C2×D244—42no—
33C2×D244—42no—
34C2×D244—48no—
35C2×D244—44no—
36C2×D244—41no—
37C2×D244—41no—
38C2×D244—44no—
39C2×D244—44no—
40M16×C61—42no—
41C2×C8×C61—41no—
42#11758194—42no—
43C2×#92418—22no—
44#11758187—82no—
45C23×C61—21no—
46C23×C61—41no—
47C23×C61—42no—
48C23×C61C22⋊C811yescharacteristic
49C22×D61—24no—
50C22×D61—42no—
51C22×D61—48no—
52C22×D61—42no—
53C22×D61—84no—
54C22×D61—84no—
55C22×D61—88no—
56C22×D61—88no—
57C22×D61—84no—
58C2×C4×C61—22no—
59C2×C4×C61—21no—
60C2×C4×C61—42no—
61C2×C4×C61—42no—
62C2×C4×C61—41no—
63C2×C4×C61#9911yescharacteristic
64C2×C4×C61#10011yescharacteristic
65D244—44no—
66D244—44no—
67D244—44no—
68D244—44no—
69C8×C61—81no—
70#92418—42no—
71#7342—611nomaximal, Sylow
72C22×C61—22no—
73C22×C61—21no—
74C22×C61—41no—
75C22×C61—41no—
76C22×C61—42no—
77C22×C61—42no—
78C22×C61—41no—
79C22×C61#32311yescharacteristic
80C2×D61—44no—
81C2×D61—84no—
82C2×D61—84no—
83C2×D61—816no—
84C2×D61—84no—
85C4×C61—21no—
86C4×C61—41no—
87C4×C61AΣL(1,𝔽16)12yes—
88#1783—611no—
89#1320—612no—
90C2×C61—21no—
91C2×C61—42no—
92C2×C61—41no—
93C2×C61#131611yescharacteristic
94D61—84no—
95C23×D4—611no—
96C2×#100—1222no—
97#407—611no—
98#407#692311yescharacteristic
99#349—1222no—
100C61#734211yescharacteristic, complemented, Sylow
101C25—1221no—
102C22×D4—612no—
103C22×D4—1221no—
104C22×D4—2441no—
105C22×D4—2441no—
106C22×D4—2444no—
107C23×C4C2×#692311yescharacteristic
108C2×M16—21no—
109C2×M16—612no—
110M32—2442no—
111#100—2444no—
112C22⋊C8—41no—
113C22⋊C8—2441no—
114C24—1222no—
115C24—4884no—
116C24—2442no—
117C24—2444no—
118C24#1175821311yescharacteristic
119C2×D4—1224no—
120C2×D4—2442no—
121C2×D4—2442no—
122C2×D4—2448no—
123C2×D4—2444no—
124C2×D4—2444no—
125C2×D4—2444no—
126C2×D4—2441no—
127C2×D4—2441no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—42no—
131C22×C4D61⋊C811yescharacteristic
132C22×C4C22⋊#692311yescharacteristic
133M16—42no—
134M16—2442no—
135C2×C8—41no—
136C2×C8—1222no—
137C16—4882no—
138C23—21no—
139C23—41no—
140C23—42no—
141C23—1224no—
142C23—4884no—
143C23—4884no—
144C23—4884no—
145C23—4888no—
146C23—4888no—
147C23—2442no—
148C23—2448no—
149C23—2442no—
150C23#1451983411yescharacteristic
151D4—2444no—
152D4—2444no—
153D4—2444no—
154D4—2444no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—41no—
160C2×C4#1451983611yescharacteristic
161C2×C4#1451983711yescharacteristic
162C8—81no—
163C8—2442no—
164C22—22no—
165C22—21no—
166C22—41no—
167C22—41no—
168C22—42no—
169C22—42no—
170C22—41no—
171C22—4884no—
172C22—4884no—
173C22—48816no—
174C22—4884no—
175C22—2444no—
176C22#1684060611yescharacteristic
177C4—21no—
178C4—41no—
179C4#1684066312yes—
180C2—21no—
181C2—42no—
182C2—41no—
183C2—4884no—
184C2#2146074411yescharacteristic
subgroupG/H
centerC2#21460744
commutatorC22×C4×C61C2×C8
FrattiniC23×C4C2×#6923
FittingC61×#407C4
socleC2×C61#1316
prime radicalC23×D244C4
cosocle#16839726C22
hypercenter#407#6923
hypocenterC61#7342
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #21460751C2semidirect
100. C61#7342semidirect

Maximal subgroups

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

subgroupindex
#214607512
#214457392
#734261