Finite Group Databasebeta

← #30599344

Subgroups — #30599344

Order 15616.

814 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461647C212yesmaximal
2#21460718C214yesmaximal, complemented
3#21448396C211yesmaximal, characteristic
4C2×#14519836—24no—
5#16840703C2214yes—
6C23×D244C2211yescharacteristic
7C2×C22⋊C4×D61C412yescomplemented
8#16839640—24no—
9#16839625C411yescharacteristic, complemented
10#16839617C2212yes—
11C61×#381C411yescharacteristic, complemented
12C2×C22⋊#6923—24no—
13C2×C22⋊#6923—28no—
14#14519836—48no—
15C24×D61C2×C411yescharacteristic
16C24×D61C2311yescharacteristic
17C22×D244—24no—
18C22×D244—44no—
19C22×D244D414yes—
20C22×C4×D61—22no—
21C2×C22⋊Dic61C2×C412yes—
22C2×#11758198—22no—
23C2×#11758198—24no—
24C22⋊C4×D61—44no—
25#14519684—22no—
26C23×C4×C61C2×C411yescharacteristic
27C2×C22⋊C4×C61C2×C412yes—
28#95×C61—22no—
29C24×C61C22×C411yescharacteristic
30C23×D61—22no—
31C23×D61—24no—
32C23×D61—42no—
33C23×D61—82no—
34C23×D61—82no—
35C23×D61C22⋊C412yes—
36C23×D61C2×D412yes—
37C23×D61#4114yes—
38C22×#6923—44no—
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61—42no—
42C22×C4×C61C22⋊C412yes—
43C22×Dic61—22no—
44C2×D244—28no—
45C2×D244—28no—
46C2×D244—44no—
47C2×D244—416no—
48C2×C4×D61—44no—
49C2×C4×D61—84no—
50C22⋊#6923—48no—
51C22⋊#6923—88no—
52C22⋊C4×C61—42no—
53C22⋊Dic61—42no—
54#11758198—44no—
55#11758198—84no—
56C23×C61—22no—
57C23×C61—42no—
58C23×C61C2×C22⋊C411yescharacteristic
59C23×C61#11712yes—
60C22×D61—22no—
61C22×D61—22no—
62C22×D61—28no—
63C22×D61—24no—
64C22×D61—44no—
65C22×D61—48no—
66C22×D61—44no—
67C22×D61—44no—
68C22×D61—84no—
69C22×D61—88no—
70C22×D61—88no—
71C22×D61#9914yes—
72C22×D61#12314yes—
73C2×#6923—84no—
74C2×#6923—88no—
75C2×C4×C61—22no—
76C2×C4×C61—24no—
77C2×C4×C61—44no—
78C2×C4×C61—44no—
79C2×C4×C61—42no—
80C2×Dic61—44no—
81C2×Dic61—42no—
82D244—416no—
83C4×D61—88no—
84#8746—611nomaximal, Sylow
85C22×C61—22no—
86C22×C61—22no—
87C22×C61—24no—
88C22×C61—44no—
89C22×C61#38111yescharacteristic
90C22×C61C2×#9912yes—
91C2×D61—24no—
92C2×D61—24no—
93C2×D61—28no—
94C2×D61—44no—
95C2×D61—44no—
96C2×D61—44no—
97C2×D61—84no—
98C2×D61—88no—
99C2×D61—88no—
100#6923—164no—
101C4×C61—42no—
102C4×C61—82no—
103Dic61—82no—
104#2308—611no—
105#1781—612no—
106#1304—614no—
107C2×C61—22no—
108C2×C61—42no—
109C2×C61#181911yescharacteristic
110C2×C61#182812yes—
111D61—44no—
112D61—44no—
113C23×D4—611no—
114C22×C22⋊C4—612no—
115C2×#99—1224no—
116#386—1224no—
117#381—611no—
118#381#692311yescharacteristic, complemented
119#379—612no—
120#379—614no—
121C61#874611yescharacteristic, complemented, Sylow
122C25—611no—
123C25—611no—
124C22×D4—614no—
125C22×D4—1224no—
126C22×D4—2444no—
127C23×C4—1222no—
128C23×C4C2×#692311yescharacteristic
129C2×C22⋊C4—612no—
130C2×C22⋊C4—1224no—
131C2×C22⋊C4—1228no—
132C2×C22⋊C4—1222no—
133C2×C22⋊C4—1224no—
134C2×C22⋊C4—2444no—
135C2×C22⋊C4C2×#692312yes—
136#99—2448no—
137#95—22no—
138#95—1222no—
139C24—612no—
140C24—612no—
141C24—614no—
142C24—1224no—
143C24—1222no—
144C24—4882no—
145C24—4882no—
146C24—2442no—
147C24C22×#692311yescharacteristic
148C2×D4—1228no—
149C2×D4—1228no—
150C2×D4—2444no—
151C2×D4—24416no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—42no—
155C22×C4—1222no—
156C22×C4—4884no—
157C22×C4—2444no—
158C22×C4—2444no—
159C22×C4C22⋊#692312yes—
160C22⋊C4—42no—
161C22⋊C4—4884no—
162C22⋊C4—4888no—
163C22⋊C4—2444no—
164C22⋊C4—2448no—
165C22⋊C4—2442no—
166C23—22no—
167C23—42no—
168C23—614no—
169C23—614no—
170C23—1228no—
171C23—1224no—
172C23—1222no—
173C23—1222no—
174C23—4884no—
175C23—4888no—
176C23—4888no—
177C23—2444no—
178C23—2448no—
179C23—2444no—
180C23—2444no—
181C23C2×C22⋊#692311yescharacteristic
182C23#1451985612yes—
183D4—24416no—
184C2×C4—22no—
185C2×C4—24no—
186C2×C4—44no—
187C2×C4—44no—
188C2×C4—42no—
189C2×C4—4888no—
190C2×C4—4888no—
191C2×C4—4884no—
192C2×C4—2444no—
193C2×C4—2442no—
194C22—22no—
195C22—22no—
196C22—24no—
197C22—44no—
198C22—1224no—
199C22—1224no—
200C22—1228no—
201C22—4884no—
202C22—4888no—
203C22—4888no—
204C22—2444no—
205C22—2444no—
206C22—2444no—
207C22#1684070511yescharacteristic
208C22D61⋊#9912yes—
209C4—42no—
210C4—82no—
211C4—9764no—
212C4—4882no—
213C2—22no—
214C2—42no—
215C2—2444no—
216C2—2444no—
217C2#2146171511yescharacteristic
218C2#2146173112yes—
subgroupG/H
centerC22#16840705
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC61×#381C4
socleC22×C61#381
prime radicalC23×D244C22
cosocleC24×D61C23
hypercenter#381#6923
hypocenterC61#8746
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #21460718C2semidirect
7. C2×C22⋊C4×D61C4semidirect
9. #16839625C4semidirect
11. C61×#381C4semidirect
118. #381#6923semidirect
121. C61#8746semidirect

Maximal subgroups

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

subgroupindex
#214616472
#214607182
#214483962
#874661