Finite Group Databasebeta

← #30597239

Subgroups — #30597239

Order 15616.

994 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 148 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#21462263C212yesmaximal
2#21460718C214yesmaximal
3#21448199C211yesmaximal, characteristic
4C2×#14519856—22no—
5#16840705—22no—
6#16840704—22no—
7#16840704C414yescomplemented
8#16840703C2214yes—
9C4×C22⋊#6923—22no—
10C4×C22⋊#6923C414yescomplemented
11C23×C4×D61C2211yescharacteristic
12C2×#14519733C412yescomplemented
13#16839625C411yescharacteristic, complemented
14#16839621—22no—
15#16839617C2212yes—
16#16839609—22no—
17C61×#381C411yescharacteristic, complemented
18#14519856—48no—
19C2×C4⋊#6923—24no—
20C2×C22⋊#6923—24no—
21C2×C22⋊#6923—24no—
22C2×C22⋊#6923C2×C418yes—
23C2×C4×#6923—24no—
24(C2×#6923)⋊C4—24no—
25(C2×#6923)⋊C4—24no—
26C24×D61C2311yescharacteristic
27C23×Dic61C2×C411yescharacteristic
28C22×C4×D61—44no—
29C22×C4×D61C2×C412yes—
30C22×C4×D61C2×C412yes—
31C22×C4×D61D412yes—
32C22×C4×D61D412yes—
33C22×C4×D61D412yes—
34C22×C4×D61Q812yes—
35#14519733—44no—
36C2×#11758196—22no—
37C2×C22⋊Dic61C2×C412yes—
38C2×#11758198—24no—
39C2×C4×Dic61—22no—
40#14519684—22no—
41C23×C4×C61C2×C411yescharacteristic
42C2×C22⋊C4×C61C2×C412yes—
43#95×C61—22no—
44C24×C61C22×C411yescharacteristic
45C23×D61—44no—
46C23×D61—42no—
47C23×D61C22×C412yes—
48C23×D61C2×D411yescharacteristic
49C23×D61C2×D412yes—
50C23×D61C2×Q811yescharacteristic
51C22×#6923—28no—
52C22×C4×C61—22no—
53C22×C4×C61—42no—
54C22×C4×C61C4211yescharacteristic
55C22×C4×C61C4211yescharacteristic
56C22×C4×C61C22⋊C412yes—
57C22×C4×C61C4⋊C412yes—
58C22×Dic61—24no—
59C22×Dic61—22no—
60C22×Dic61C4212yes—
61C22×Dic61C22⋊C411yescharacteristic
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C4⋊C412yes—
64C2×C4×D61—28no—
65C2×C4×D61—44no—
66C2×C4×D61—44no—
67C2×C4×D61—44no—
68C2×C4×D61—44no—
69C2×C4×D61—44no—
70C2×C4×D61C22⋊C412yes—
71C2×C4×D61C22⋊C412yes—
72C2×C4×D61C22⋊C412yes—
73C2×C4×D61C22⋊C412yes—
74C2×C4×D61C4⋊C412yes—
75C2×C4×D61C4⋊C412yes—
76C2×C4×D61C4⋊C412yes—
77C2×C4×D61C4⋊C412yes—
78C22⋊#6923—48no—
79C22⋊#6923—48no—
80C22⋊#6923—48no—
81C4⋊#6923—48no—
82C4×#6923—48no—
83C22⋊C4×C61—42no—
84C22⋊Dic61—42no—
85#11758198—48no—
86#11758196—44no—
87C4×Dic61—44no—
88C23×C61—22no—
89C23×C61—42no—
90C23×C61C2×C4211yescharacteristic
91C23×C61C2×C22⋊C411yescharacteristic
92C23×C61C2×C4⋊C411yescharacteristic
93C22×D61—24no—
94C22×D61—24no—
95C22×D61—24no—
96C22×D61—24no—
97C22×D61—42no—
98C22×D61—41no—
99C22×D61—41no—
100C22×D61—42no—
101C22×D61—42no—
102C22×D61—42no—
103C22×D61—416no—
104C22×D61C2×C22⋊C412yes—
105C22×D61C2×C4⋊C412yes—
106C2×#6923—48no—
107C2×#6923—48no—
108C2×#6923—48no—
109C2×C4×C61—24no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—42no—
113C2×C4×C61—44no—
114C2×C4×C61—42no—
115C2×C4×C61#9512yes—
116C2×C4×C61#9512yes—
117C2×Dic61—22no—
118C2×Dic61—24no—
119C2×Dic61—24no—
120C2×Dic61—44no—
121C2×Dic61—42no—
122C2×Dic61#9512yes—
123C2×Dic61#9512yes—
124C2×Dic61#9914yes—
125C4×D61—24no—
126C4×D61—24no—
127C4×D61—24no—
128C4×D61—24no—
129C4×D61—42no—
130C4×D61—42no—
131C4×D61—42no—
132C4×D61—42no—
133#8102—611nomaximal, Sylow
134C22×C61—22no—
135C22×C61—21no—
136C22×C61—21no—
137C22×C61—22no—
138C22×C61—22no—
139C22×C61—44no—
140C22×C61C2×#9511yescharacteristic
141C22×C61C2×#9912yes—
142C2×D61—22no—
143C2×D61—22no—
144C2×D61—22no—
145C2×D61—22no—
146C2×D61—22no—
147C2×D61—44no—
148C2×D61—48no—
149C2×D61—48no—
150C2×D61—44no—
151C2×D61#41014yes—
152#6923—88no—
153C4×C61—22no—
154C4×C61—22no—
155C4×C61—82no—
156Dic61—22no—
157Dic61—82no—
158Dic61#34214yes—
159#2280—611no—
160#2280—612no—
161#1304—614no—
162C2×C61—22no—
163C2×C61—41no—
164C2×C61—41no—
165C2×C61C2×#34211yescharacteristic
166C2×C61#174012yes—
167D61—24no—
168D61—42no—
169C24×C4—611no—
170C2×#117—612no—
171C2×#117—1222no—
172#381—611no—
173#381—1222no—
174#381#692311yescharacteristic, complemented
175#380—614no—
176#380—1222no—
177#380—1222no—
178#379—614no—
179#379—612no—
180C4×C22⋊C4—614no—
181C4×C22⋊C4—1222no—
182C4×C22⋊C4—1222no—
183C61#810211yescharacteristic, complemented, Sylow
184C25—611no—
185C23×C4—611no—
186C23×C4—612no—
187C23×C4—612no—
188C23×C4—612no—
189C23×C4—612no—
190C23×C4—612no—
191C23×C4—612no—
192C23×C4—2444no—
193C23×C4C2×#692311yescharacteristic
194#117—2444no—
195#117—2448no—
196C2×C4⋊C4—1222no—
197C2×C4⋊C4—1224no—
198C2×C22⋊C4—618no—
199C2×C22⋊C4—612no—
200C2×C22⋊C4—1224no—
201C2×C22⋊C4—1224no—
202C2×C22⋊C4—1224no—
203C2×C22⋊C4C2×#692312yes—
204C2×C42—1222no—
205C2×C42—1224no—
206#95—22no—
207#95—1224no—
208#95—1224no—
209#95—1222no—
210C24—612no—
211C24—611no—
212C24—612no—
213C24—611no—
214C24—2442no—
215C24—2444no—
216C24C22×#692311yescharacteristic
217C22×C4—22no—
218C22×C4—42no—
219C22×C4—611no—
220C22×C4—612no—
221C22×C4—611no—
222C22×C4—612no—
223C22×C4—612no—
224C22×C4—612no—
225C22×C4—612no—
226C22×C4—612no—
227C22×C4—612no—
228C22×C4—612no—
229C22×C4—612no—
230C22×C4—612no—
231C22×C4—1228no—
232C22×C4—1224no—
233C22×C4—1228no—
234C22×C4—1222no—
235C22×C4—2444no—
236C22×C4—2444no—
237C22×C4—2444no—
238C22×C4—2444no—
239C22×C4—2444no—
240C22×C4C4×#692311yescharacteristic
241C22×C4C4×#692311yescharacteristic
242C22×C4C4⋊#692312yes—
243C22×C4C22⋊#692312yes—
244C4⋊C4—2444no—
245C4⋊C4—2448no—
246C22⋊C4—42no—
247C22⋊C4—2448no—
248C22⋊C4—2448no—
249C22⋊C4—2448no—
250C22⋊C4—2442no—
251C22⋊C4—2448no—
252C42—2444no—
253C42—2448no—
254C23—22no—
255C23—42no—
256C23—612no—
257C23—612no—
258C23—1224no—
259C23—1224no—
260C23—1224no—
261C23—1224no—
262C23—2442no—
263C23—2441no—
264C23—2441no—
265C23—2442no—
266C23—2442no—
267C23—2442no—
268C23—24416no—
269C23C2×C4×#692311yescharacteristic
270C23C2×C22⋊#692311yescharacteristic
271C23C2×C4⋊#692311yescharacteristic
272C2×C4—24no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—44no—
277C2×C4—42no—
278C2×C4—614no—
279C2×C4—612no—
280C2×C4—612no—
281C2×C4—1224no—
282C2×C4—1224no—
283C2×C4—1224no—
284C2×C4—1224no—
285C2×C4—1224no—
286C2×C4—1224no—
287C2×C4—1222no—
288C2×C4—2442no—
289C2×C4—2442no—
290C2×C4—2442no—
291C2×C4—2442no—
292C2×C4—2444no—
293C2×C4—2448no—
294C2×C4—2448no—
295C2×C4—2448no—
296C2×C4—2442no—
297C2×C4(C2×#6923)⋊C412yes—
298C2×C4(C2×#6923)⋊C412yes—
299C22—22no—
300C22—21no—
301C22—21no—
302C22—22no—
303C22—22no—
304C22—44no—
305C22—614no—
306C22—1222no—
307C22—1222no—
308C22—1222no—
309C22—1222no—
310C22—1222no—
311C22—2448no—
312C22—2444no—
313C22—2448no—
314C22—2444no—
315C22C2×(C2×#6923)⋊C411yescharacteristic
316C22D61⋊#9912yes—
317C4—22no—
318C4—22no—
319C4—82no—
320C4—614no—
321C4—1222no—
322C4—4882no—
323C4—4888no—
324C2—22no—
325C2—41no—
326C2—41no—
327C2—1224no—
328C2—2442no—
329C2#2146151611yescharacteristic
330C2#2146151712yes—
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC61×#381C4
socleC22×C61C2×#95
prime radical, cosocleC24×D61C23
hypercenter#381#6923
hypocenterC61#8102
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
7. #16840704C4semidirect
10. C4×C22⋊#6923C4semidirect
12. C2×#14519733C4semidirect
13. #16839625C4semidirect
17. C61×#381C4semidirect
174. #381#6923semidirect
183. C61#8102semidirect

Maximal subgroups

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

subgroupindex
#214622632
#214607182
#214481992
#810261