Finite Group Databasebeta

← #30599353

Subgroups — #30599353

Order 15616.

754 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 80 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#21448394C211yesmaximal, characteristic
4C2×#14519837—22no—
5C2×#14519837—22no—
6#16840732C2214yes—
7C23×C22⋊D61C2211yescharacteristic
8C22×C22⋊Dic61C411yescharacteristic
9#16839641—22no—
10#16839639—22no—
11#16839623C2212yes—
12#16839617C412yes—
13C22×C22⋊C4×C61C411yescharacteristic
14C2×#11758217—24no—
15#14519837—44no—
16#14519837—44no—
17C22⋊#92420—28no—
18C24×D61C2×C411yescharacteristic
19C22×C22⋊D61—24no—
20C22×C22⋊D61—42no—
21C22×C22⋊D61—42no—
22C22×C22⋊D61D412yes—
23C22×C22⋊D61D412yes—
24C23×Dic61—21no—
25C23×Dic61C2311yescharacteristic
26C2×C22⋊Dic61—21no—
27C2×C22⋊Dic61—42no—
28C2×C22⋊Dic61C2×C412yes—
29C2×#11758198—24no—
30#14519684—24no—
31C25×C61C2×C411yescharacteristic
32C23×C4×C61—21no—
33C2×C22⋊C4×C61—21no—
34C2×C22⋊C4×C61—42no—
35C2×C22⋊C4×C61C2×C412yes—
36C24×C61—22no—
37C24×C61—22no—
38C24×C61—22no—
39C24×C61—82no—
40C24×C61C22⋊C411yescharacteristic
41C24×C61C22⋊C411yescharacteristic
42C24×C61C22×C411yescharacteristic
43C23×D61—22no—
44C23×D61—41no—
45C23×D61—41no—
46C23×D61—82no—
47C23×D61C22⋊C412yes—
48C22×C4×C61—22no—
49C22×C4×C61—42no—
50C22×C4×C61—82no—
51C2×C22⋊D61—24no—
52C2×C22⋊D61—24no—
53C2×C22⋊D61—24no—
54C2×C22⋊D61—24no—
55C2×C22⋊D61—42no—
56C2×C22⋊D61—42no—
57C2×C22⋊D61—416no—
58C22×Dic61—22no—
59C22×Dic61—41no—
60C22×Dic61—41no—
61C22×Dic61—42no—
62C22×Dic61—82no—
63C22×Dic61C2×D412yes—
64C22×Dic61#4114yes—
65#11758217—44no—
66#11758217—44no—
67C2×#92420—44no—
68C22⋊C4×C61—42no—
69C22⋊C4×C61—42no—
70C22⋊Dic61—42no—
71C22⋊Dic61—42no—
72#11758198—84no—
73C23×C61—28no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—21no—
78C23×C61—21no—
79C23×C61—21no—
80C23×C61—42no—
81C23×C61—42no—
82C23×C61—42no—
83C23×C61—84no—
84C23×C61—84no—
85C23×C61—84no—
86C23×C61#9912yes—
87C23×C61#9912yes—
88C23×C61C2×C22⋊C411yescharacteristic
89C23×C61#11712yes—
90C22×D61—22no—
91C22×D61—22no—
92C22×D61—22no—
93C22×D61—44no—
94C22×D61—44no—
95C22×D61—84no—
96C22×D61—84no—
97C22×D61—84no—
98C2×C4×C61—44no—
99C2×C4×C61—42no—
100C2×C4×C61—84no—
101C22⋊D61—48no—
102C22⋊D61—48no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—44no—
106C2×Dic61—44no—
107C2×Dic61—42no—
108C2×Dic61—84no—
109C2×Dic61#12314yes—
110#92420—84no—
111#8751—611nomaximal, Sylow
112C22×C61—22no—
113C22×C61—22no—
114C22×C61—22no—
115C22×C61—22no—
116C22×C61—24no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61—42no—
120C22×C61—42no—
121C22×C61—42no—
122C22×C61—42no—
123C22×C61—42no—
124C22×C61—42no—
125C22×C61—88no—
126C22×C61#38111yescharacteristic
127C22×C61C2×#9911yescharacteristic
128C22×C61C2×#9911yescharacteristic
129C2×D61—42no—
130C2×D61—44no—
131C2×D61—88no—
132C2×D61—82no—
133C2×D61—82no—
134C4×C61—82no—
135Dic61—24no—
136Dic61—82no—
137#2308—611no—
138#1783—612no—
139#1306—614no—
140C2×C61—21no—
141C2×C61—21no—
142C2×C61—42no—
143C2×C61—42no—
144C2×C61—42no—
145C2×C61#181911yescharacteristic
146C2×C61#182912yes—
147D61—82no—
148C23×D4—611no—
149C22×C22⋊C4—611no—
150C22×C22⋊C4#692311yescharacteristic
151C2×#100—1222no—
152C2×#100—1222no—
153#407—614no—
154#386—1222no—
155#386—1222no—
156#381—612no—
157#379—612no—
158C61#875111yescharacteristic, complemented, Sylow
159C25—611no—
160C25C2×#692311yescharacteristic
161C22×D4—612no—
162C22×D4—612no—
163C22×D4—1224no—
164C22×D4—2442no—
165C22×D4—2442no—
166C23×C4—21no—
167C23×C4—611no—
168C23×C4—1221no—
169C2×M16—1224no—
170C2×C22⋊C4—21no—
171C2×C22⋊C4—42no—
172C2×C22⋊C4—612no—
173C2×C22⋊C4—1224no—
174C2×C22⋊C4—1221no—
175C2×C22⋊C4—2442no—
176C2×C22⋊C4C2×#692312yes—
177#100—2444no—
178#100—2444no—
179C22⋊C8—1228no—
180#95—1224no—
181C24—22no—
182C24—22no—
183C24—22no—
184C24—82no—
185C24—612no—
186C24—1222no—
187C24—4882no—
188C24—2441no—
189C24—2441no—
190C24C22⋊#692311yescharacteristic
191C24C22⋊#692311yescharacteristic
192C24C22×#692311yescharacteristic
193C2×D4—1224no—
194C2×D4—1224no—
195C2×D4—1224no—
196C2×D4—1224no—
197C2×D4—2442no—
198C2×D4—2442no—
199C2×D4—24416no—
200C22×C4—22no—
201C22×C4—42no—
202C22×C4—82no—
203C22×C4—612no—
204C22×C4—614no—
205C22×C4—1222no—
206C22×C4—4882no—
207C22×C4—2441no—
208C22×C4—2441no—
209C22×C4—2442no—
210M16—2444no—
211M16—2444no—
212C2×C8—2444no—
213C22⋊C4—42no—
214C22⋊C4—42no—
215C22⋊C4—4884no—
216C22⋊C4—2442no—
217C22⋊C4—2442no—
218C23—28no—
219C23—21no—
220C23—21no—
221C23—21no—
222C23—21no—
223C23—21no—
224C23—21no—
225C23—42no—
226C23—42no—
227C23—42no—
228C23—84no—
229C23—84no—
230C23—84no—
231C23—1222no—
232C23—1222no—
233C23—1222no—
234C23—4884no—
235C23—4884no—
236C23—4884no—
237C23—2444no—
238C23—2444no—
239C23#1451983512yes—
240C23#1451983612yes—
241C23C2×C22⋊#692311yescharacteristic
242C23#1451985612yes—
243D4—2448no—
244D4—2448no—
245C2×C4—44no—
246C2×C4—42no—
247C2×C4—84no—
248C2×C4—614no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—4884no—
252C2×C4—2444no—
253C2×C4—2444no—
254C2×C4—2442no—
255C8—4884no—
256C22—22no—
257C22—22no—
258C22—22no—
259C22—22no—
260C22—24no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—88no—
270C22—4882no—
271C22—4882no—
272C22—4888no—
273C22—2442no—
274C22—2444no—
275C22#1684070511yescharacteristic
276C22C2×#1451983511yescharacteristic
277C22C2×#1451983611yescharacteristic
278C4—82no—
279C4—1224no—
280C4—4882no—
281C2—21no—
282C2—21no—
283C2—42no—
284C2—42no—
285C2—42no—
286C2—4882no—
287C2#2146171411yescharacteristic
288C2#2146173212yes—
subgroupG/H
centerC22#16840705
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61#381
prime radicalC23×C22⋊D61C22
cosocleC23×Dic61C23
hypercenterC22×C22⋊C4#6923
hypocenterC61#8751
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. #21460722C2semidirect
158. C61#8751semidirect

Maximal subgroups

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

subgroupindex
#214616512
#214607222
#214483942
#875161