Finite Group Databasebeta

← #30598783

Subgroups — #30598783

Order 15616.

1198 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 108 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#21461067C214yesmaximal, complemented
3C22×#14519761C211yesmaximal, characteristic
4C2×#14519837—24no—
5#16840732C2214yes—
6#16840607—28no—
7C23×C22⋊D61C2211yescharacteristic
8C24×Dic61C411yescharacteristic
9C2×#14519761—28no—
10C2×#14519761—24no—
11C22×C4⋊Dic61C2212yes—
12C22×#11758198C412yes—
13C22×C22⋊C4×C61C411yescharacteristic
14C2×#11758217—24no—
15#14519837—48no—
16C22⋊#92420—28no—
17C24×D61C2×C411yescharacteristic
18C22×C22⋊D61—24no—
19C22×C22⋊D61—44no—
20C22×C22⋊D61D414yes—
21C23×Dic61—22no—
22C23×Dic61—24no—
23C23×Dic61—44no—
24C23×Dic61C2×C412yes—
25C23×Dic61C2311yescharacteristic
26#14519761—232no—
27C2×C4⋊Dic61—24no—
28C2×C4⋊Dic61—24no—
29C2×C4⋊Dic61D418yes—
30C2×#11758198—24no—
31C2×#11758198—24no—
32C2×#11758198—24no—
33C25×C61C2×C411yescharacteristic
34C23×C4×C61C2×C412yes—
35C2×C22⋊C4×C61—22no—
36C2×C22⋊C4×C61—24no—
37C24×C61—24no—
38C24×C61—22no—
39C24×C61—44no—
40C24×C61C22⋊C412yes—
41C24×C61C22×C411yescharacteristic
42C23×D61—22no—
43C23×D61—42no—
44C23×D61—44no—
45C23×D61C22⋊C412yes—
46C22×C4×C61—22no—
47C22×C4×C61—22no—
48C22×C4×C61—44no—
49C22×C4×C61C22⋊C414yes—
50C2×C22⋊D61—28no—
51C2×C22⋊D61—28no—
52C2×C22⋊D61—44no—
53C2×C22⋊D61—416no—
54C22×Dic61—28no—
55C22×Dic61—22no—
56C22×Dic61—22no—
57C22×Dic61—42no—
58C22×Dic61—416no—
59C22×Dic61—44no—
60C22×Dic61—44no—
61C22×Dic61—44no—
62C22×Dic61C22⋊C414yes—
63C22×Dic61C2×D412yes—
64C22×Dic61C2×D414yes—
65#11758217—48no—
66C2×#92420—44no—
67C22⋊C4×C61—28no—
68#11758198—216no—
69C4⋊Dic61—216no—
70C23×C61—22no—
71C23×C61—24no—
72C23×C61—28no—
73C23×C61—22no—
74C23×C61—22no—
75C23×C61—416no—
76C23×C61—44no—
77C23×C61—44no—
78C23×C61—44no—
79C23×C61#9914yes—
80C23×C61C2×C22⋊C411yescharacteristic
81C23×C61C2×C22⋊C412yes—
82C22×D61—22no—
83C22×D61—24no—
84C22×D61—44no—
85C22×D61—44no—
86C22×D61—44no—
87C22×D61—44no—
88C22×D61—88no—
89C2×C4×C61—24no—
90C2×C4×C61—28no—
91C2×C4×C61—44no—
92C2×C4×C61—44no—
93C22⋊D61—416no—
94C2×Dic61—24no—
95C2×Dic61—24no—
96C2×Dic61—44no—
97C2×Dic61—44no—
98C2×Dic61—416no—
99C2×Dic61—44no—
100C2×Dic61—44no—
101C2×Dic61#12014yes—
102#92420—84no—
103#8548—611nomaximal, Sylow
104C22×C61—28no—
105C22×C61—22no—
106C22×C61—22no—
107C22×C61—22no—
108C22×C61—24no—
109C22×C61—44no—
110C22×C61—44no—
111C22×C61—416no—
112C22×C61—44no—
113C22×C61#37911yescharacteristic
114C22×C61C2×#9912yes—
115C22×C61#41314yes—
116C2×D61—42no—
117C2×D61—44no—
118C2×D61—88no—
119C2×D61—84no—
120C4×C61—44no—
121Dic61—24no—
122Dic61—44no—
123C22×#123—611no—
124#1783—612no—
125#1463—614no—
126C2×C61—22no—
127C2×C61—24no—
128C2×C61—44no—
129C2×C61#178111yescharacteristic
130C2×C61#178512yes—
131D61—82no—
132C23×D4—611no—
133C24×C4—611no—
134C2×#123—1228no—
135C2×#123—1224no—
136C22×C4⋊C4—612no—
137C22×C22⋊C4—612no—
138C22×C22⋊C4#692311yescharacteristic
139C2×#100—1224no—
140#407—614no—
141#324—1228no—
142C61#854811yescharacteristic, complemented, Sylow
143C25—611no—
144C25C2×#692311yescharacteristic
145C22×D4—614no—
146C22×D4—1224no—
147C22×D4—2444no—
148C23×C4—611no—
149C23×C4—612no—
150C23×C4—1224no—
151C23×C4—1222no—
152C23×C4—2444no—
153C23×C4C2×#692312yes—
154C2×M16—1224no—
155#123—12232no—
156C2×C4⋊C4—618no—
157C2×C4⋊C4—1224no—
158C2×C4⋊C4—1224no—
159C2×C22⋊C4—22no—
160C2×C22⋊C4—24no—
161C2×C22⋊C4—1224no—
162C2×C22⋊C4—1224no—
163C2×C22⋊C4—1224no—
164#100—2448no—
165C22⋊C8—1228no—
166C24—24no—
167C24—22no—
168C24—44no—
169C24—612no—
170C24—1222no—
171C24—2442no—
172C24—2444no—
173C24C22⋊#692312yes—
174C24C22×#692311yescharacteristic
175C2×D4—1228no—
176C2×D4—1228no—
177C2×D4—2444no—
178C2×D4—24416no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—44no—
182C22×C4—612no—
183C22×C4—614no—
184C22×C4—614no—
185C22×C4—1228no—
186C22×C4—1222no—
187C22×C4—1222no—
188C22×C4—2442no—
189C22×C4—24416no—
190C22×C4—2444no—
191C22×C4—2444no—
192C22×C4—2444no—
193C22×C4C22⋊#692314yes—
194M16—2448no—
195C2×C8—2444no—
196C4⋊C4—12216no—
197C22⋊C4—28no—
198C22⋊C4—12216no—
199C23—22no—
200C23—24no—
201C23—28no—
202C23—22no—
203C23—22no—
204C23—44no—
205C23—416no—
206C23—44no—
207C23—44no—
208C23—1224no—
209C23—1222no—
210C23—4888no—
211C23—2444no—
212C23—2444no—
213C23—2444no—
214C23—2444no—
215C23#1451983614yes—
216C23C2×C22⋊#692311yescharacteristic
217C23C2×C22⋊#692312yes—
218D4—24416no—
219C2×C4—28no—
220C2×C4—24no—
221C2×C4—44no—
222C2×C4—44no—
223C2×C4—614no—
224C2×C4—1224no—
225C2×C4—1224no—
226C2×C4—2444no—
227C2×C4—2444no—
228C2×C4—24416no—
229C2×C4—2444no—
230C2×C4—2444no—
231C8—4884no—
232C22—28no—
233C22—22no—
234C22—22no—
235C22—22no—
236C22—24no—
237C22—44no—
238C22—44no—
239C22—416no—
240C22—44no—
241C22—4884no—
242C22—4888no—
243C22—2442no—
244C22—2444no—
245C22#1684070311yescharacteristic
246C22C2×#1451983612yes—
247C22#1684074914yes—
248C4—44no—
249C4—1224no—
250C4—2444no—
251C2—22no—
252C2—24no—
253C2—44no—
254C2—4882no—
255C2#2146164711yescharacteristic
256C2#2146165612yes—
subgroupG/H
centerC22#16840703
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61#379
prime radicalC23×C22⋊D61C22
cosocleC23×Dic61C23
hypercenterC22×C22⋊C4#6923
hypocenterC61#8548
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #21461067C2semidirect
142. C61#8548semidirect

Maximal subgroups

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

subgroupindex
#214616512
#214610672
C22×#145197612
#854861