Finite Group Databasebeta

← #30605293

Subgroups — #30605293

Order 15616.

432 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 66 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#21461720C211yesmaximal, characteristic, complemented
2#21461052C211yesmaximal, characteristic, complemented
3#21460817C212yesmaximal, complemented
4#21460802C212yesmaximal, complemented
5#21451387C211yesmaximal, characteristic
6#16840778—21no—
7#16840734—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840606—21no—
12C2×C4×D244C411yescharacteristic
13C2×#14519734C2211yescharacteristic
14#16839702C2211yescharacteristic
15#16839699C411yescharacteristic
16#16839680C2211yescharacteristic
17#16839672C411yescharacteristic
18#16839654—21no—
19#16839640—21no—
20#16839640—21no—
21#16839636—21no—
22C61×#383C411yescharacteristic
23C2×#11758217—22no—
24C4⋊#92420—41no—
25#14519834—41no—
26#14519834—41no—
27C22⋊#92420—22no—
28C4×#92420—41no—
29C22×D244—21no—
30C22×D244C2×C411yescharacteristic
31C22×C4×D61—21no—
32C22×C4×D61D411yescharacteristic
33C4×D244—41no—
34C4×D244—41no—
35#14519734—41no—
36#14519734—41no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196D411yescharacteristic
40C2×#11758196C2311yescharacteristic
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198C2×C411yescharacteristic
47C2×#11758198D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519684—21no—
50#14519684—21no—
51C2×C42×C61C2×C411yescharacteristic
52#95×C61—21no—
53#95×C61—21no—
54#95×C61C2×C411yescharacteristic
55#95×C61C2×C411yescharacteristic
56C23×D61—21no—
57C23×D61C22⋊C411yescharacteristic
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—21no—
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C2×D244—41no—
68C2×D244—42no—
69C2×D244—42no—
70C2×D244—42no—
71C2×D244—81no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—22no—
75C2×C4×D61—41no—
76C2×C4×D61—42no—
77C2×C4×D61—81no—
78C2×C4×D61—81no—
79#11758217—42no—
80#11758217—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C42×C61—21no—
84C42×C61—21no—
85#11758198—41no—
86#11758198—41no—
87#11758198—42no—
88#11758198—41no—
89#11758198—41no—
90#11758198—42no—
91#11758198—81no—
92#11758198—81no—
93C4⋊Dic61—41no—
94C4⋊Dic61—81no—
95#11758196—41no—
96#11758196—41no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C23×C61C2×C22⋊C411yescharacteristic
100C22×D61—22no—
101C22×D61—21no—
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—41no—
105C22×D61—41no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61—41no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61—41no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61#9911yescharacteristic
125C2×C4×C61#9911yescharacteristic
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61#13512yes—
136D244—42no—
137D244—42no—
138D244—84no—
139C4×D61—42no—
140C4×D61—42no—
141C4×D61—84no—
142#92420—82no—
143#92420—82no—
144#11847—611nomaximal, Sylow
145C22×C61—21no—
146C22×C61—21no—
147C22×C61C2×#9911yescharacteristic
148C22×C61#41611yescharacteristic
149C22×C61#42111yescharacteristic
150C2×D61—42no—
151C2×D61—42no—
152C2×D61—42no—
153C2×D61—42no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—81no—
158C2×D61—81no—
159C2×D61—81no—
160C2×D61—81no—
161C2×D61—81no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61—81no—
167C4×C61—81no—
168Dic61—22no—
169Dic61—41no—
170Dic61—41no—
171Dic61—81no—
172#2598—611no—
173#1822—611no—
174#1458—611no—
175#1353—612no—
176#1345—612no—
177C2×C61—21no—
178C2×C61—21no—
179C2×C61#151611yescharacteristic
180C2×C61#212011yescharacteristic
181C2×C61#213411yescharacteristic
182D61—81no—
183D61—82no—
184C2×C4×D4—611no—
185C2×#117—611no—
186#431—1221no—
187#407—1221no—
188#400—611no—
189#399—611no—
190#394—611no—
191#392—611no—
192#388—1221no—
193#386—1221no—
194#386—1221no—
195#385—1221no—
196#383#692311yescharacteristic
197#343—612no—
198#343—1221no—
199#324—612no—
200#323—1221no—
201C61#1184711yescharacteristic, complemented, Sylow
202C22×D4—611no—
203C22×D4—1221no—
204C23×C4—611no—
205C23×C4—1221no—
206C2×M16—1222no—
207C4×D4—2441no—
208C4×D4—2441no—
209#117—2441no—
210#117—2441no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1221no—
215C2×C22⋊C4—611no—
216C2×C22⋊C4—611no—
217C2×C22⋊C4—1221no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4—1221no—
222C2×C42—611no—
223C2×C42C2×#692311yescharacteristic
224C4⋊C8—2441no—
225C22⋊C8—1222no—
226C22⋊C8—2441no—
227C22⋊C8—2441no—
228C4×C8—2441no—
229#95—21no—
230#95—21no—
231#95—1221no—
232#95—1221no—
233#95C2×#692311yescharacteristic
234#95C2×#692311yescharacteristic
235C24—611no—
236C24—1221no—
237C2×D4—4881no—
238C2×D4—2441no—
239C2×D4—2442no—
240C2×D4—2442no—
241C2×D4—2442no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—1222no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—4881no—
252C22×C4—4881no—
253C22×C4—2441no—
254C22×C4—2442no—
255C22×C4C22⋊#692311yescharacteristic
256C22×C4C22⋊#692311yescharacteristic
257C22×C4C22×#692311yescharacteristic
258M16—2442no—
259M16—2442no—
260C2×C8—2442no—
261C2×C8—2442no—
262C4⋊C4—4881no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2441no—
266C22⋊C4—4881no—
267C22⋊C4—4881no—
268C22⋊C4—2441no—
269C22⋊C4—2441no—
270C22⋊C4—2442no—
271C22⋊C4—2442no—
272C22⋊C4—2441no—
273C22⋊C4—2441no—
274C42—21no—
275C42—21no—
276C42—1221no—
277C42—1221no—
278C23—1222no—
279C23—1221no—
280C23—1221no—
281C23—1221no—
282C23—2441no—
283C23—2441no—
284C23—2441no—
285C23—2441no—
286C23—2441no—
287C23—2441no—
288C23—2441no—
289C23—2441no—
290C23C2×C22⋊#692311yescharacteristic
291D4—4884no—
292D4—2442no—
293D4—2442no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—612no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—4884no—
312C2×C4—2442no—
313C2×C4—2442no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4#1451983611yescharacteristic
320C2×C4#1451983611yescharacteristic
321C8—4882no—
322C8—4882no—
323C22—21no—
324C22—21no—
325C22—4881no—
326C22—4881no—
327C22—4881no—
328C22—4881no—
329C22—4881no—
330C22—2442no—
331C22—2442no—
332C22—2442no—
333C22—2442no—
334C22—2441no—
335C22—2441no—
336C22—2441no—
337C22C2×#1451983611yescharacteristic
338C22#1684075211yescharacteristic
339C22#1684075911yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—81no—
345C4—81no—
346C4—1222no—
347C4—4881no—
348C4—2441no—
349C4—2441no—
350C2—21no—
351C2—21no—
352C2—4882no—
353C2—4881no—
354C2#2146124711yescharacteristic
355C2#2146207211yescharacteristic
356C2#2146212011yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#383C4
socleC22×C61C2×#99
prime radical#16839672C4
cosocleC2×#11758196C23
hypercenter#383#6923
hypocenterC61#11847
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
1. #21461720C2semidirect
2. #21461052C2semidirect
3. #21460817C2semidirect
4. #21460802C2semidirect
201. C61#11847semidirect

Maximal subgroups

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

subgroupindex
#214617202
#214610522
#214608172
#214608022
#214513872
#1184761