Finite Group Databasebeta

← #29573543

Subgroups — #29573543

Order 15616.

398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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#21448422C211yesmaximal, characteristic
2#21445899C211yesmaximal, characteristic
3#21443728C214yesmaximal
4C61×#1821C211yesmaximal, characteristic
5#16839726C2212yes—
6#16839648—22no—
7#16839648—22no—
8#16839625C2212yes—
9#16839622C412yes—
10C4×C22⋊Dic61C412yes—
11#16839531—22no—
12C22×C4⋊C4×C61C2211yescharacteristic
13C61×#407C2212yes—
14C61×#343—22no—
15C2×#11758194—22no—
16C2×C4⋊Dic61—22no—
17C2×C22⋊Dic61C2×C414yes—
18C2×C4×Dic61—22no—
19C22⋊#92418—24no—
20#14519684—22no—
21#14519684—22no—
22#14519684—22no—
23#14519684—22no—
24C23×C4×C61C2×C411yescharacteristic
25C23×C4×C61C2×C411yescharacteristic
26C23×C4×C61C2311yescharacteristic
27C2×M16×C61—22no—
28C2×C4⋊C4×C61—24no—
29C2×C4⋊C4×C61D412yes—
30C2×C4⋊C4×C61D412yes—
31C22⋊C8×C61—24no—
32C24×C61C22×C411yescharacteristic
33C22×C4×C61—22no—
34C22×C4×C61—22no—
35C22×C4×C61—42no—
36C22×C4×C61—81no—
37C22×C4×C61—81no—
38C22×C4×C61C22⋊C412yes—
39C22×C4×C61C22⋊C412yes—
40C22×C4×C61C2×D411yescharacteristic
41C22×C4×C61C2×D411yescharacteristic
42C22×C4×C61#4114yes—
43C22×Dic61—24no—
44M16×C61—44no—
45C2×C8×C61—42no—
46C4⋊C4×C61—24no—
47C4⋊C4×C61—24no—
48C22⋊Dic61—44no—
49C4⋊Dic61—82no—
50C4×Dic61—82no—
51#11758194—44no—
52C2×#92418—42no—
53C23×C61—22no—
54C23×C61—41no—
55C23×C61—41no—
56C23×C61C2×C22⋊C411yescharacteristic
57C23×C61#11712yes—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61—44no—
63C2×C4×C61—42no—
64C2×C4×C61—42no—
65C2×C4×C61—82no—
66C2×C4×C61—82no—
67C2×C4×C61#12312yes—
68C2×C4×C61#12312yes—
69C2×Dic61—44no—
70C2×Dic61—44no—
71C2×Dic61—44no—
72C8×C61—82no—
73#92418—82no—
74#8755—611nomaximal, Sylow
75C22×C61—21no—
76C22×C61—21no—
77C22×C61—22no—
78C22×C61—22no—
79C22×C61—22no—
80C22×C61—44no—
81C22×C61#38111yescharacteristic
82C22×C61#41012yes—
83C4×C61—22no—
84C4×C61—22no—
85C4×C61—42no—
86C4×C61—42no—
87Dic61—84no—
88#2313—611no—
89#1821—611no—
90#1821D6111yescharacteristic
91#1306—614no—
92C2×C61—22no—
93C2×C61—42no—
94C2×C61#182011yescharacteristic
95C2×C61#182911yescharacteristic
96C2×C61#183011yescharacteristic
97C22×C4⋊C4C2×D6111yescharacteristic
98#407—612no—
99#407C2×D6112yes—
100#387—1222no—
101#387—1222no—
102#381—612no—
103#380—612no—
104C4×C22⋊C4—612no—
105#343—22no—
106#343—1222no—
107C61#875511yescharacteristic, complemented, Sylow
108C23×C4C4×D6111yescharacteristic
109C23×C4C4×D6111yescharacteristic
110C23×C4C22×D6111yescharacteristic
111C2×M16—22no—
112C2×M16—1222no—
113C2×C4⋊C4—24no—
114C2×C4⋊C4—1222no—
115C2×C4⋊C4D24412yes—
116C2×C4⋊C4C22⋊D6112yes—
117C2×C22⋊C4—614no—
118C2×C42—1222no—
119C22⋊C8—24no—
120C22⋊C8—1224no—
121#95—1222no—
122#95—1222no—
123#95—1222no—
124#95—1222no—
125C24C2×C4×D6111yescharacteristic
126C22×C4—22no—
127C22×C4—22no—
128C22×C4—42no—
129C22×C4—81no—
130C22×C4—81no—
131C22×C4—1224no—
132C22×C4#1175819812yes—
133C22×C4#1175819812yes—
134C22×C4C2×D24411yescharacteristic
135C22×C4#1175822414yes—
136C22×C4C2×C22⋊D6111yescharacteristic
137M16—44no—
138M16—2444no—
139C2×C8—42no—
140C2×C8—2442no—
141C4⋊C4—24no—
142C4⋊C4—24no—
143C4⋊C4—4882no—
144C22⋊C4—2444no—
145C42—4882no—
146C23—22no—
147C23—41no—
148C23—41no—
149C23C2×#1175819811yescharacteristic
150C23#1451973312yes—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—44no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—82no—
159C2×C4—82no—
160C2×C4—2444no—
161C2×C4—2444no—
162C2×C4—2444no—
163C2×C4#1451975812yes—
164C2×C4#1451976112yes—
165C8—82no—
166C8—4882no—
167C22—21no—
168C22—21no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—44no—
173C22#1683962311yescharacteristic
174C22#1683973512yes—
175C4—22no—
176C4—22no—
177C4—42no—
178C4—42no—
179C4—4884no—
180C2—22no—
181C2—42no—
182C2#2144589411yescharacteristic
183C2#2144592811yescharacteristic
184C2#2144593111yescharacteristic
subgroupG/H
centerC22#16839623
commutator, prime radicalC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1821C2
socleC22×C61#381
cosocleC23×C4×C61C23
hypercenter#1821D61
hypocenterC61#8755
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
107. C61#8755semidirect

Maximal subgroups

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

subgroupindex
#214484222
#214458992
#214437282
C61×#18212
#875561