Finite Group Databasebeta

← #30599219

Subgroups — #30599219

Order 15616.

786 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 112 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×#16839623C211yesmaximal, characteristic
4C2×C22⋊#92420—22no—
5C2×C22⋊#92420—22no—
6C2×C22⋊#92420C2214yes—
7C24×Dic61C2211yescharacteristic
8C22×C22⋊Dic61C411yescharacteristic
9#16839623—22no—
10#16839623—22no—
11C2×#14519684C412yes—
12C2×#14519684C2212yes—
13C22×C22⋊C4×C61C411yescharacteristic
14C22×#92420—24no—
15C22⋊#92420—28no—
16C22⋊#92420—44no—
17C22⋊#92420—44no—
18C23×Dic61—24no—
19C23×Dic61—42no—
20C23×Dic61—42no—
21C23×Dic61C2×C412yes—
22C23×Dic61C2×C411yescharacteristic
23C23×Dic61D412yes—
24C23×Dic61D412yes—
25C23×Dic61C2311yescharacteristic
26C2×C22⋊Dic61—21no—
27C2×C22⋊Dic61—21no—
28C2×C22⋊Dic61—42no—
29#14519684—24no—
30#14519684—24no—
31C25×C61C2×C411yescharacteristic
32C23×C4×C61C2×C412yes—
33C2×C22⋊C4×C61—21no—
34C2×C22⋊C4×C61—21no—
35C2×C22⋊C4×C61—42no—
36C24×C61—22no—
37C24×C61—22no—
38C24×C61—22no—
39C24×C61—24no—
40C24×C61—42no—
41C24×C61C22⋊C411yescharacteristic
42C24×C61C22⋊C411yescharacteristic
43C24×C61C22×C411yescharacteristic
44C22×C4×C61—22no—
45C22×C4×C61—24no—
46C22×C4×C61—42no—
47C22×C4×C61—42no—
48C22×Dic61—24no—
49C22×Dic61—24no—
50C22×Dic61—22no—
51C22×Dic61—24no—
52C22×Dic61—24no—
53C22×Dic61—22no—
54C22×Dic61—24no—
55C22×Dic61—41no—
56C22×Dic61—41no—
57C22×Dic61—42no—
58C22×Dic61—42no—
59C22×Dic61—41no—
60C22×Dic61—41no—
61C22×Dic61—416no—
62C22×Dic61—42no—
63C22×Dic61—42no—
64C22×Dic61C22⋊C412yes—
65C22×Dic61C2×D412yes—
66C22×Dic61#4114yes—
67C2×#92420—44no—
68C2×#92420—44no—
69C2×#92420—44no—
70C22⋊C4×C61—42no—
71C22⋊C4×C61—42no—
72C22⋊Dic61—42no—
73C22⋊Dic61—42no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61—22no—
77C23×C61—28no—
78C23×C61—21no—
79C23×C61—21no—
80C23×C61—22no—
81C23×C61—22no—
82C23×C61—21no—
83C23×C61—21no—
84C23×C61—22no—
85C23×C61—22no—
86C23×C61—48no—
87C23×C61—48no—
88C23×C61—44no—
89C23×C61—44no—
90C23×C61#9912yes—
91C23×C61#9912yes—
92C23×C61C2×C22⋊C411yescharacteristic
93C23×C61#11712yes—
94C23×C61#13114yes—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61—42no—
98C2×C4×C61—84no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—44no—
105C2×Dic61—48no—
106C2×Dic61—48no—
107C2×Dic61—44no—
108C2×Dic61—42no—
109C2×Dic61—42no—
110C2×Dic61—42no—
111C2×Dic61—84no—
112C2×Dic61#12314yes—
113#92420—84no—
114#8702—611nomaximal, Sylow
115C22×C61—22no—
116C22×C61—22no—
117C22×C61—24no—
118C22×C61—24no—
119C22×C61—22no—
120C22×C61—22no—
121C22×C61—24no—
122C22×C61—24no—
123C22×C61—416no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61—41no—
128C22×C61—42no—
129C22×C61—42no—
130C22×C61#38111yescharacteristic
131C22×C61#40812yes—
132C22×C61C2×#9911yescharacteristic
133C22×C61C2×#9911yescharacteristic
134C22×C61#41312yes—
135C22×C61#43314yes—
136C4×C61—82no—
137Dic61—24no—
138Dic61—42no—
139Dic61—82no—
140C2×#381—611no—
141#1779—612no—
142#1280—614no—
143C2×C61—24no—
144C2×C61—42no—
145C2×C61—42no—
146C2×C61#146812yes—
147C2×C61#146812yes—
148C2×C61#181811yescharacteristic
149C2×C61#181911yescharacteristic
150C2×C61#182211yescharacteristic
151C24×C4—611no—
152C22×C22⋊C4—611no—
153C22×C22⋊C4#692311yescharacteristic
154C2×C22⋊C8—614no—
155C2×C22⋊C8—1222no—
156C2×C22⋊C8—1222no—
157#381—1222no—
158#381—1222no—
159C2×#95—612no—
160C2×#95—612no—
161C61#870211yescharacteristic, complemented, Sylow
162C25C2×#692311yescharacteristic
163C23×C4—611no—
164C23×C4—612no—
165C23×C4—612no—
166C23×C4—611no—
167C23×C4—612no—
168C23×C4—1224no—
169C23×C4—2442no—
170C23×C4—2442no—
171C23×C4C2×#692312yes—
172C22×C8—1224no—
173C2×C22⋊C4—21no—
174C2×C22⋊C4—21no—
175C2×C22⋊C4—42no—
176C2×C22⋊C4—1221no—
177C2×C22⋊C4—1221no—
178C2×C22⋊C4—2442no—
179C22⋊C8—1228no—
180C22⋊C8—2444no—
181C22⋊C8—2444no—
182#95—1224no—
183#95—1224no—
184C24—22no—
185C24—22no—
186C24—22no—
187C24—24no—
188C24—42no—
189C24C22⋊#692311yescharacteristic
190C24C22⋊#692311yescharacteristic
191C24C22×#692311yescharacteristic
192C22×C4—22no—
193C22×C4—24no—
194C22×C4—42no—
195C22×C4—42no—
196C22×C4—612no—
197C22×C4—614no—
198C22×C4—612no—
199C22×C4—1224no—
200C22×C4—1224no—
201C22×C4—1224no—
202C22×C4—1224no—
203C22×C4—1222no—
204C22×C4—1224no—
205C22×C4—1222no—
206C22×C4—2441no—
207C22×C4—2442no—
208C22×C4—2441no—
209C22×C4—2442no—
210C22×C4—2441no—
211C22×C4—2441no—
212C22×C4—2442no—
213C22×C4—2442no—
214C22×C4—24416no—
215C2×C8—2444no—
216C2×C8—2444no—
217C2×C8—2444no—
218C22⋊C4—42no—
219C22⋊C4—42no—
220C22⋊C4—2442no—
221C22⋊C4—2442no—
222C23—21no—
223C23—21no—
224C23—22no—
225C23—28no—
226C23—21no—
227C23—21no—
228C23—22no—
229C23—22no—
230C23—21no—
231C23—21no—
232C23—22no—
233C23—22no—
234C23—48no—
235C23—48no—
236C23—44no—
237C23—44no—
238C23#1451983512yes—
239C23#1451983612yes—
240C23C2×C22⋊#692311yescharacteristic
241C23#1451985612yes—
242C23#1451986414yes—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—84no—
247C2×C4—614no—
248C2×C4—1222no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—4884no—
254C2×C4—2444no—
255C2×C4—2448no—
256C2×C4—2448no—
257C2×C4—2442no—
258C2×C4—2442no—
259C2×C4—2442no—
260C2×C4—2444no—
261C8—4884no—
262C22—24no—
263C22—24no—
264C22—22no—
265C22—22no—
266C22—24no—
267C22—24no—
268C22—22no—
269C22—22no—
270C22—416no—
271C22—42no—
272C22—42no—
273C22—41no—
274C22—41no—
275C22—41no—
276C22—41no—
277C22#1684070511yescharacteristic
278C22#1684073512yes—
279C22C2×#1451983511yescharacteristic
280C22C2×#1451983611yescharacteristic
281C22#1684074912yes—
282C22#1684078614yes—
283C4—82no—
284C4—1224no—
285C4—4882no—
286C4—2442no—
287C2—24no—
288C2—42no—
289C2—42no—
290C2#2146108412yes—
291C2#2146108612yes—
292C2#2146171211yescharacteristic
293C2#2146171411yescharacteristic
294C2#2146172111yescharacteristic
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#8702
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
161. C61#8702semidirect

Maximal subgroups

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

subgroupindex
#214616412
#214606572
C2×#168396232
#870261