Finite Group Databasebeta

← #30597233

Subgroups — #30597233

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×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C22×C4×D61D412yes—
35C22×C4×D61Q811yescharacteristic
36C22×C4×D61Q811yescharacteristic
37#14519733—44no—
38C2×#11758196—22no—
39C2×C22⋊Dic61C2×C412yes—
40C2×#11758198—24no—
41C2×C4×Dic61—22no—
42#14519684—22no—
43C23×C4×C61C2×C411yescharacteristic
44C2×C22⋊C4×C61C2×C412yes—
45#95×C61—22no—
46C24×C61C22×C411yescharacteristic
47C23×D61—44no—
48C23×D61—42no—
49C23×D61C22×C412yes—
50C23×D61C2×D411yescharacteristic
51C23×D61C2×D412yes—
52C23×D61C2×Q811yescharacteristic
53C22×#6923—28no—
54C22×C4×C61—22no—
55C22×C4×C61—42no—
56C22×C4×C61C4212yes—
57C22×C4×C61C22⋊C412yes—
58C22×C4×C61C4⋊C411yescharacteristic
59C22×C4×C61C4⋊C411yescharacteristic
60C22×Dic61—24no—
61C22×Dic61—22no—
62C22×Dic61C4211yescharacteristic
63C22×Dic61C4211yescharacteristic
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C4⋊C411yescharacteristic
67C22×Dic61C4⋊C411yescharacteristic
68C2×C4×D61—28no—
69C2×C4×D61—44no—
70C2×C4×D61—44no—
71C2×C4×D61—42no—
72C2×C4×D61—42no—
73C2×C4×D61—42no—
74C2×C4×D61—42no—
75C2×C4×D61—44no—
76C2×C4×D61C22⋊C412yes—
77C2×C4×D61C22⋊C412yes—
78C2×C4×D61C22⋊C412yes—
79C2×C4×D61C22⋊C412yes—
80C2×C4×D61C4⋊C412yes—
81C2×C4×D61C4⋊C412yes—
82C2×C4×D61C4⋊C412yes—
83C2×C4×D61C4⋊C412yes—
84C22⋊#6923—48no—
85C22⋊#6923—48no—
86C22⋊#6923—48no—
87C4⋊#6923—48no—
88C4×#6923—48no—
89C22⋊C4×C61—42no—
90C22⋊Dic61—42no—
91#11758198—48no—
92#11758196—44no—
93C4×Dic61—44no—
94C23×C61—22no—
95C23×C61—42no—
96C23×C61C2×C4211yescharacteristic
97C23×C61C2×C22⋊C411yescharacteristic
98C23×C61C2×C4⋊C411yescharacteristic
99C22×D61—24no—
100C22×D61—24no—
101C22×D61—24no—
102C22×D61—24no—
103C22×D61—42no—
104C22×D61—41no—
105C22×D61—41no—
106C22×D61—42no—
107C22×D61—42no—
108C22×D61—42no—
109C22×D61—416no—
110C22×D61C2×C22⋊C412yes—
111C22×D61C2×C4⋊C412yes—
112C2×#6923—48no—
113C2×#6923—48no—
114C2×#6923—48no—
115C2×C4×C61—24no—
116C2×C4×C61—42no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—44no—
120C2×C4×C61—42no—
121C2×C4×C61#9512yes—
122C2×C4×C61#9512yes—
123C2×Dic61—22no—
124C2×Dic61—22no—
125C2×Dic61—22no—
126C2×Dic61—22no—
127C2×Dic61—22no—
128C2×Dic61—44no—
129C2×Dic61—42no—
130C2×Dic61#9511yescharacteristic
131C2×Dic61#9511yescharacteristic
132C2×Dic61#9511yescharacteristic
133C2×Dic61#9511yescharacteristic
134C2×Dic61#9914yes—
135C4×D61—24no—
136C4×D61—24no—
137C4×D61—24no—
138C4×D61—24no—
139C4×D61—42no—
140C4×D61—42no—
141C4×D61—42no—
142C4×D61—42no—
143#8100—611nomaximal, Sylow
144C22×C61—22no—
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—22no—
148C22×C61—22no—
149C22×C61—44no—
150C22×C61C2×#9511yescharacteristic
151C22×C61C2×#9912yes—
152C2×D61—22no—
153C2×D61—22no—
154C2×D61—22no—
155C2×D61—22no—
156C2×D61—22no—
157C2×D61—44no—
158C2×D61—48no—
159C2×D61—48no—
160C2×D61—44no—
161C2×D61#41014yes—
162#6923—88no—
163C4×C61—22no—
164C4×C61—22no—
165C4×C61—82no—
166Dic61—21no—
167Dic61—21no—
168Dic61—82no—
169Dic61#34212yes—
170Dic61#34212yes—
171#2280—611no—
172#2280—612no—
173#1304—614no—
174C2×C61—22no—
175C2×C61—41no—
176C2×C61—41no—
177C2×C61C2×#34211yescharacteristic
178C2×C61#174012yes—
179D61—24no—
180D61—42no—
181C24×C4—611no—
182C2×#117—612no—
183C2×#117—1222no—
184#381—611no—
185#381—1222no—
186#381#692311yescharacteristic, complemented
187#380—614no—
188#380—1222no—
189#380—1222no—
190#379—614no—
191#379—612no—
192C4×C22⋊C4—614no—
193C4×C22⋊C4—1222no—
194C4×C22⋊C4—1222no—
195C61#810011yescharacteristic, complemented, Sylow
196C25—611no—
197C23×C4—611no—
198C23×C4—612no—
199C23×C4—612no—
200C23×C4—612no—
201C23×C4—611no—
202C23×C4—611no—
203C23×C4—611no—
204C23×C4—611no—
205C23×C4—612no—
206C23×C4—2444no—
207C23×C4C2×#692311yescharacteristic
208#117—2448no—
209#117—2444no—
210C2×C4⋊C4—1222no—
211C2×C4⋊C4—1224no—
212C2×C22⋊C4—618no—
213C2×C22⋊C4—612no—
214C2×C22⋊C4—1224no—
215C2×C22⋊C4—1224no—
216C2×C22⋊C4—1224no—
217C2×C22⋊C4C2×#692312yes—
218C2×C42—1222no—
219C2×C42—1224no—
220#95—22no—
221#95—1224no—
222#95—1224no—
223#95—1222no—
224C24—612no—
225C24—611no—
226C24—612no—
227C24—611no—
228C24—2442no—
229C24—2444no—
230C24C22×#692311yescharacteristic
231C22×C4—22no—
232C22×C4—42no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—612no—
240C22×C4—612no—
241C22×C4—612no—
242C22×C4—612no—
243C22×C4—612no—
244C22×C4—612no—
245C22×C4—612no—
246C22×C4—612no—
247C22×C4—1228no—
248C22×C4—1224no—
249C22×C4—1228no—
250C22×C4—1222no—
251C22×C4—2444no—
252C22×C4—2444no—
253C22×C4—2444no—
254C22×C4—2442no—
255C22×C4—2442no—
256C22×C4—2442no—
257C22×C4—2442no—
258C22×C4C4×#692312yes—
259C22×C4C4⋊#692311yescharacteristic
260C22×C4C4⋊#692311yescharacteristic
261C22×C4C22⋊#692312yes—
262C4⋊C4—2444no—
263C4⋊C4—2448no—
264C22⋊C4—42no—
265C22⋊C4—2448no—
266C22⋊C4—2448no—
267C22⋊C4—2448no—
268C22⋊C4—2442no—
269C22⋊C4—2448no—
270C42—2444no—
271C42—2448no—
272C23—22no—
273C23—42no—
274C23—612no—
275C23—612no—
276C23—1224no—
277C23—1224no—
278C23—1224no—
279C23—1224no—
280C23—2442no—
281C23—2441no—
282C23—2441no—
283C23—2442no—
284C23—2442no—
285C23—2442no—
286C23—24416no—
287C23C2×C4×#692311yescharacteristic
288C23C2×C22⋊#692311yescharacteristic
289C23C2×C4⋊#692311yescharacteristic
290C2×C4—24no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—44no—
295C2×C4—42no—
296C2×C4—614no—
297C2×C4—611no—
298C2×C4—611no—
299C2×C4—611no—
300C2×C4—611no—
301C2×C4—1224no—
302C2×C4—1224no—
303C2×C4—1224no—
304C2×C4—1224no—
305C2×C4—1222no—
306C2×C4—1222no—
307C2×C4—1222no—
308C2×C4—1222no—
309C2×C4—1222no—
310C2×C4—2442no—
311C2×C4—2442no—
312C2×C4—2442no—
313C2×C4—2442no—
314C2×C4—2444no—
315C2×C4—2448no—
316C2×C4—2448no—
317C2×C4—2448no—
318C2×C4—2442no—
319C2×C4(C2×#6923)⋊C412yes—
320C2×C4(C2×#6923)⋊C412yes—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—22no—
325C22—22no—
326C22—44no—
327C22—614no—
328C22—1222no—
329C22—1222no—
330C22—1222no—
331C22—1222no—
332C22—1222no—
333C22—2448no—
334C22—2444no—
335C22—2448no—
336C22—2444no—
337C22C2×(C2×#6923)⋊C411yescharacteristic
338C22D61⋊#9912yes—
339C4—22no—
340C4—22no—
341C4—82no—
342C4—612no—
343C4—612no—
344C4—1221no—
345C4—1221no—
346C4—4882no—
347C4—4888no—
348C2—22no—
349C2—41no—
350C2—41no—
351C2—1224no—
352C2—2442no—
353C2#2146151611yescharacteristic
354C2#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#8100
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
186. #381#6923semidirect
195. C61#8100semidirect

Maximal subgroups

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

subgroupindex
#214622632
#214607182
#214481992
#810061