Finite Group Databasebeta

← #30599354

Subgroups — #30599354

Order 15616.

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

normal subgroups only

This group has 754 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#21461651C212yesmaximal
2#21460722C214yesmaximal, complemented
3#21448395C211yesmaximal, characteristic
4C2×#14519837—24no—
5#16840732C2214yes—
6C23×C22⋊D61C2211yescharacteristic
7C2×C22⋊C4×D61C412yes—
8#16839638—24no—
9#16839623C2212yes—
10#16839618C411yescharacteristic
11C61×#379C411yescharacteristic
12C2×#11758217—24no—
13#14519837—48no—
14C22⋊#92420—28no—
15C24×D61C2×C411yescharacteristic
16C22×C22⋊D61—24no—
17C22×C22⋊D61—44no—
18C22×C22⋊D61D414yes—
19C23×Dic61C2311yescharacteristic
20C22×C4×D61—22no—
21C2×C22⋊Dic61—22no—
22C2×C22⋊Dic61C2×C412yes—
23C2×#11758198—22no—
24C22⋊C4×D61—44no—
25#14519684—24no—
26C25×C61C2×C411yescharacteristic
27C2×C22⋊C4×C61—22no—
28C2×C22⋊C4×C61C2×C412yes—
29C24×C61—22no—
30C24×C61—42no—
31C24×C61—82no—
32C24×C61C22⋊C412yes—
33C24×C61C22×C411yescharacteristic
34C23×D61—22no—
35C23×D61—24no—
36C23×D61—82no—
37C23×D61C22⋊C412yes—
38C22×C4×C61—22no—
39C2×C22⋊D61—28no—
40C2×C22⋊D61—28no—
41C2×C22⋊D61—44no—
42C2×C22⋊D61—416no—
43C22×Dic61—22no—
44C22×Dic61—42no—
45C22×Dic61C2×D412yes—
46C22×Dic61#4114yes—
47C2×C4×D61—44no—
48C2×C4×D61—84no—
49#11758217—48no—
50C2×#92420—44no—
51C22⋊C4×C61—42no—
52C22⋊C4×C61—82no—
53C22⋊Dic61—42no—
54C22⋊Dic61—82no—
55#11758198—44no—
56C23×C61—22no—
57C23×C61—22no—
58C23×C61—24no—
59C23×C61—42no—
60C23×C61—44no—
61C23×C61—42no—
62C23×C61—42no—
63C23×C61—84no—
64C23×C61—88no—
65C23×C61C2×C22⋊C411yescharacteristic
66C23×C61#11712yes—
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—28no—
70C22×D61—44no—
71C22×D61—84no—
72C22×D61—88no—
73C22×D61#9914yes—
74C2×C4×C61—44no—
75C2×C4×C61—42no—
76C22⋊D61—416no—
77C2×Dic61—24no—
78C2×Dic61—44no—
79C2×Dic61—44no—
80C2×Dic61—42no—
81C2×Dic61#12314yes—
82C4×D61—88no—
83#92420—84no—
84#8751—611nomaximal, Sylow
85C22×C61—22no—
86C22×C61—22no—
87C22×C61—24no—
88C22×C61—44no—
89C22×C61—42no—
90C22×C61—42no—
91C22×C61—42no—
92C22×C61—84no—
93C22×C61—88no—
94C22×C61#38111yescharacteristic
95C22×C61C2×#9912yes—
96C2×D61—24no—
97C2×D61—44no—
98C2×D61—44no—
99C2×D61—44no—
100C2×D61—88no—
101C4×C61—82no—
102Dic61—24no—
103Dic61—82no—
104#2308—611no—
105#1783—612no—
106#1306—614no—
107C2×C61—22no—
108C2×C61—42no—
109C2×C61—82no—
110C2×C61#181911yescharacteristic
111C2×C61#182912yes—
112D61—44no—
113C23×D4—611no—
114C22×C22⋊C4—612no—
115C2×#100—1224no—
116#407—614no—
117#386—1224no—
118#381—612no—
119#379—611no—
120#379#692311yescharacteristic
121C61#875111yescharacteristic, complemented, Sylow
122C25—611no—
123C25C2×#692311yescharacteristic
124C22×D4—614no—
125C22×D4—1224no—
126C22×D4—2444no—
127C23×C4—611no—
128C23×C4—1222no—
129C2×M16—1224no—
130C2×C22⋊C4—22no—
131C2×C22⋊C4—612no—
132C2×C22⋊C4—1222no—
133C2×C22⋊C4—1222no—
134C2×C22⋊C4—2444no—
135C2×C22⋊C4C2×#692312yes—
136#100—2448no—
137C22⋊C8—1228no—
138#95—1224no—
139C24—22no—
140C24—42no—
141C24—82no—
142C24—612no—
143C24—1224no—
144C24—1222no—
145C24—4882no—
146C24C22⋊#692312yes—
147C24C22×#692311yescharacteristic
148C2×D4—1228no—
149C2×D4—1228no—
150C2×D4—2444no—
151C2×D4—24416no—
152C22×C4—22no—
153C22×C4—612no—
154C22×C4—614no—
155C22×C4—1222no—
156C22×C4—4884no—
157C22×C4—2444no—
158C22×C4—2442no—
159M16—2448no—
160C2×C8—2444no—
161C22⋊C4—42no—
162C22⋊C4—82no—
163C22⋊C4—4882no—
164C22⋊C4—2444no—
165C22⋊C4—2442no—
166C23—22no—
167C23—22no—
168C23—24no—
169C23—42no—
170C23—44no—
171C23—42no—
172C23—42no—
173C23—84no—
174C23—88no—
175C23—614no—
176C23—1228no—
177C23—1222no—
178C23—1222no—
179C23—4884no—
180C23—4888no—
181C23—2444no—
182C23C2×C22⋊#692311yescharacteristic
183C23#1451985612yes—
184D4—24416no—
185C2×C4—44no—
186C2×C4—42no—
187C2×C4—614no—
188C2×C4—1224no—
189C2×C4—4888no—
190C2×C4—2444no—
191C2×C4—2444no—
192C2×C4—2442no—
193C8—4884no—
194C22—22no—
195C22—22no—
196C22—24no—
197C22—44no—
198C22—42no—
199C22—42no—
200C22—42no—
201C22—84no—
202C22—88no—
203C22—1224no—
204C22—4888no—
205C22—2444no—
206C22—2444no—
207C22—2444no—
208C22#1684070511yescharacteristic
209C22D61⋊#9912yes—
210C4—82no—
211C4—1224no—
212C4—4882no—
213C2—22no—
214C2—42no—
215C2—82no—
216C2—2444no—
217C2#2146171511yescharacteristic
218C2#2146173212yes—
subgroupG/H
centerC22#16840705
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC61×#379C4
socleC22×C61#381
prime radicalC23×C22⋊D61C22
cosocleC23×Dic61C23
hypercenter#379#6923
hypocenterC61#8751
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
2. #21460722C2semidirect
121. C61#8751semidirect

Maximal subgroups

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

subgroupindex
#214616512
#214607222
#214483952
#875161