Finite Group Databasebeta

← #30599224

Subgroups — #30599224

Order 15616.

830 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 116 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#21461641C212yesmaximal
2#21460657C214yesmaximal, complemented
3C2×#16839620C211yesmaximal, characteristic
4C2×C22⋊#92420—22no—
5C2×C22⋊#92420—22no—
6C2×C22⋊#92420C2214yes—
7C24×Dic61C2211yescharacteristic
8C22×#11758196C412yes—
9C22×C22⋊Dic61C411yescharacteristic
10#16839620—22no—
11#16839620—22no—
12C2×#14519684C2212yes—
13C22×C22⋊C4×C61C411yescharacteristic
14C22×#92420—24no—
15C22⋊#92420—28no—
16C22⋊#92420—44no—
17C22⋊#92420—44no—
18C23×Dic61—24no—
19C23×Dic61—44no—
20C23×Dic61C2×C411yescharacteristic
21C23×Dic61C2×C412yes—
22C23×Dic61D412yes—
23C23×Dic61D412yes—
24C23×Dic61C2311yescharacteristic
25C2×#11758196—22no—
26C2×#11758196—22no—
27C2×#11758196—44no—
28C2×C22⋊Dic61—21no—
29C2×C22⋊Dic61—21no—
30C2×C22⋊Dic61—42no—
31#14519684—24no—
32C25×C61C2×C411yescharacteristic
33C23×C4×C61C2×C412yes—
34C2×C22⋊C4×C61—21no—
35C2×C22⋊C4×C61—21no—
36C2×C22⋊C4×C61—42no—
37C24×C61—22no—
38C24×C61—22no—
39C24×C61—22no—
40C24×C61—24no—
41C24×C61—42no—
42C24×C61C22⋊C411yescharacteristic
43C24×C61C22⋊C411yescharacteristic
44C24×C61C22×C411yescharacteristic
45C22×C4×C61—22no—
46C22×C4×C61—24no—
47C22×C4×C61—42no—
48C22×C4×C61—42no—
49C22×Dic61—22no—
50C22×Dic61—24no—
51C22×Dic61—24no—
52C22×Dic61—24no—
53C22×Dic61—24no—
54C22×Dic61—24no—
55C22×Dic61—22no—
56C22×Dic61—24no—
57C22×Dic61—42no—
58C22×Dic61—42no—
59C22×Dic61—42no—
60C22×Dic61—416no—
61C22×Dic61—42no—
62C22×Dic61—42no—
63C22×Dic61C22⋊C412yes—
64C22×Dic61C2×D412yes—
65C22×Dic61#4114yes—
66C2×#92420—44no—
67C2×#92420—44no—
68C2×#92420—44no—
69C22⋊C4×C61—42no—
70C22⋊C4×C61—42no—
71C22⋊Dic61—42no—
72C22⋊Dic61—42no—
73#11758196—44no—
74#11758196—44no—
75C23×C61—22no—
76C23×C61—21no—
77C23×C61—21no—
78C23×C61—28no—
79C23×C61—21no—
80C23×C61—21no—
81C23×C61—22no—
82C23×C61—22no—
83C23×C61—22no—
84C23×C61—22no—
85C23×C61—21no—
86C23×C61—21no—
87C23×C61—48no—
88C23×C61—48no—
89C23×C61—44no—
90C23×C61—44no—
91C23×C61#10012yes—
92C23×C61#10112yes—
93C23×C61C2×C22⋊C411yescharacteristic
94C23×C61#11712yes—
95C23×C61#13114yes—
96C2×C4×C61—42no—
97C2×C4×C61—42no—
98C2×C4×C61—42no—
99C2×C4×C61—84no—
100C2×Dic61—28no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—44no—
106C2×Dic61—48no—
107C2×Dic61—48no—
108C2×Dic61—42no—
109C2×Dic61—42no—
110C2×Dic61—42no—
111C2×Dic61—84no—
112C2×Dic61#9914yes—
113C2×Dic61#12314yes—
114#92420—84no—
115#8704—611nomaximal, Sylow
116C22×C61—22no—
117C22×C61—22no—
118C22×C61—24no—
119C22×C61—24no—
120C22×C61—22no—
121C22×C61—22no—
122C22×C61—24no—
123C22×C61—24no—
124C22×C61—416no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61—41no—
128C22×C61—41no—
129C22×C61—42no—
130C22×C61—42no—
131C22×C61#38111yescharacteristic
132C22×C61#40812yes—
133C22×C61C2×#9912yes—
134C22×C61C2×#10011yescharacteristic
135C22×C61C2×#10111yescharacteristic
136C22×C61#43314yes—
137C4×C61—82no—
138Dic61—24no—
139Dic61—24no—
140Dic61—82no—
141C2×#380—611no—
142#1779—612no—
143#1280—614no—
144C2×C61—24no—
145C2×C61—42no—
146C2×C61—42no—
147C2×C61#147112yes—
148C2×C61#147212yes—
149C2×C61#181811yescharacteristic
150C2×C61#181911yescharacteristic
151C2×C61#182111yescharacteristic
152C24×C4—611no—
153C22×C4⋊C4—612no—
154C22×C22⋊C4—611no—
155C22×C22⋊C4#692311yescharacteristic
156C2×C22⋊C8—614no—
157C2×C22⋊C8—1222no—
158C2×C22⋊C8—1222no—
159#380—1222no—
160#380—1222no—
161C2×#95—612no—
162C61#870411yescharacteristic, complemented, Sylow
163C25C2×#692311yescharacteristic
164C23×C4—611no—
165C23×C4—611no—
166C23×C4—612no—
167C23×C4—612no—
168C23×C4—612no—
169C23×C4—1224no—
170C23×C4—2444no—
171C23×C4C2×#692312yes—
172C22×C8—1224no—
173C2×C4⋊C4—1222no—
174C2×C4⋊C4—1222no—
175C2×C4⋊C4—2444no—
176C2×C22⋊C4—21no—
177C2×C22⋊C4—21no—
178C2×C22⋊C4—42no—
179C2×C22⋊C4—1221no—
180C2×C22⋊C4—1221no—
181C2×C22⋊C4—2442no—
182C22⋊C8—1228no—
183C22⋊C8—2444no—
184C22⋊C8—2444no—
185#95—1224no—
186C24—22no—
187C24—22no—
188C24—22no—
189C24—24no—
190C24—42no—
191C24C22⋊#692311yescharacteristic
192C24C22⋊#692311yescharacteristic
193C24C22×#692311yescharacteristic
194C22×C4—22no—
195C22×C4—24no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—612no—
199C22×C4—612no—
200C22×C4—614no—
201C22×C4—1224no—
202C22×C4—1224no—
203C22×C4—1224no—
204C22×C4—1224no—
205C22×C4—1224no—
206C22×C4—1222no—
207C22×C4—1224no—
208C22×C4—1222no—
209C22×C4—2442no—
210C22×C4—2442no—
211C22×C4—2442no—
212C22×C4—24416no—
213C22×C4—2442no—
214C22×C4—2442no—
215C2×C8—2444no—
216C2×C8—2444no—
217C2×C8—2444no—
218C4⋊C4—2444no—
219C4⋊C4—2444no—
220C22⋊C4—42no—
221C22⋊C4—42no—
222C22⋊C4—2442no—
223C22⋊C4—2442no—
224C23—22no—
225C23—21no—
226C23—21no—
227C23—28no—
228C23—21no—
229C23—21no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—21no—
235C23—21no—
236C23—48no—
237C23—48no—
238C23—44no—
239C23—44no—
240C23#1451983712yes—
241C23#1451983812yes—
242C23C2×C22⋊#692311yescharacteristic
243C23#1451985612yes—
244C23#1451986414yes—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—84no—
249C2×C4—614no—
250C2×C4—614no—
251C2×C4—1228no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1222no—
255C2×C4—1222no—
256C2×C4—4884no—
257C2×C4—2444no—
258C2×C4—2448no—
259C2×C4—2448no—
260C2×C4—2442no—
261C2×C4—2442no—
262C2×C4—2442no—
263C8—4884no—
264C22—24no—
265C22—24no—
266C22—22no—
267C22—22no—
268C22—24no—
269C22—24no—
270C22—22no—
271C22—22no—
272C22—416no—
273C22—42no—
274C22—42no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22#1684070511yescharacteristic
280C22#1684073512yes—
281C22D61⋊#9912yes—
282C22C2×#1451983711yescharacteristic
283C22C2×#1451983811yescharacteristic
284C22#1684078614yes—
285C4—82no—
286C4—1224no—
287C4—1224no—
288C4—4882no—
289C2—24no—
290C2—42no—
291C2—42no—
292C2#2146109512yes—
293C2#2146109812yes—
294C2#2146171211yescharacteristic
295C2#2146171511yescharacteristic
296C2#2146171811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C22⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC25×C61C2×C4
cosocleC23×Dic61C23
hypercenterC22×C22⋊C4#6923
hypocenterC61#8704
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #21460657C2semidirect
162. C61#8704semidirect

Maximal subgroups

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

subgroupindex
#214616412
#214606572
C2×#168396202
#870461