Finite Group Databasebeta

← #29589385

Subgroups — #29589385

Order 15616.

510 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 77 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#21448404C211yesmaximal, characteristic
2#21444150C212yesmaximal
3#21443749C211yesmaximal, characteristic
4#21443748C212yesmaximal
5C61×#1317C211yesmaximal, characteristic
6C23×Dic122C411yescharacteristic
7C2×#14519733C411yescharacteristic
8C2×#14519733C2211yescharacteristic
9#16839816—22no—
10#16839666—22no—
11#16839666—22no—
12#16839625C411yescharacteristic
13#16839623C411yescharacteristic
14#16839623C2211yescharacteristic
15#16839487—22no—
16#16839486C2212yes—
17C61×#381C2211yescharacteristic
18C61×#323C2212yes—
19C22×Dic122—22no—
20C22×Dic122—21no—
21C22×Dic122—21no—
22C22×Dic122—22no—
23C22×Dic122—41no—
24C22×Dic122—41no—
25C22×Dic122—42no—
26C23×Dic61C2×C411yescharacteristic
27C23×Dic61C2×C411yescharacteristic
28#14519733—41no—
29#14519733—41no—
30#14519733—42no—
31C2×#11758196—21no—
32C2×#11758196D412yes—
33C2×C22⋊Dic61C2×C411yescharacteristic
34C2×C22⋊Dic61C2×C411yescharacteristic
35C2×C4×Dic61—21no—
36C2×C4×Dic61D412yes—
37#14519706—42no—
38C22⋊#92418—22no—
39#14519687—42no—
40#14519684—22no—
41#14519684—22no—
42#14519684—22no—
43C23×C4×C61C2×C411yescharacteristic
44C2×C22⋊C4×C61C2×C411yescharacteristic
45C2×C22⋊C4×C61C2311yescharacteristic
46C22⋊C8×C61—22no—
47#95×C61—22no—
48C24×C61C22×C411yescharacteristic
49C22×C4×C61—21no—
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61—41no—
53C22×C4×C61—41no—
54C22×C4×C61M1612yes—
55C22×C4×C61C2×D412yes—
56C22×Dic61—21no—
57C22×Dic61—21no—
58C22×Dic61—21no—
59C22×Dic61—21no—
60C22×Dic61—22no—
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61—41no—
65C22×Dic61—41no—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C22⋊C412yes—
69C22×Dic61M1612yes—
70C2×Dic122—24no—
71C2×Dic122—24no—
72C2×Dic122—44no—
73C2×Dic122—44no—
74C2×Dic122—44no—
75C2×Dic122—44no—
76C2×Dic122—42no—
77C2×Dic122—42no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122—42no—
81C2×C8×C61—42no—
82C22⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C22⋊Dic61—41no—
85C22⋊Dic61—41no—
86#11758196—42no—
87#11758196—42no—
88C4×Dic61—22no—
89C4×Dic61—22no—
90C4×Dic61—42no—
91C2×#92418—42no—
92C23×C61—21no—
93C23×C61—21no—
94C23×C61—42no—
95C23×C61C2×C22⋊C411yescharacteristic
96C23×C61C2×M1611yescharacteristic
97C23×C61C2×M1611yescharacteristic
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—42no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—42no—
104C2×C4×C61—42no—
105C2×C4×C61—42no—
106C2×C4×C61—41no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—22no—
116C2×Dic61—22no—
117C2×Dic61—42no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—42no—
121C2×Dic61—42no—
122C2×Dic61—42no—
123C2×Dic61—41no—
124C2×Dic61#9911yescharacteristic
125C2×Dic61#9911yescharacteristic
126C2×Dic61#10012yes—
127Dic122—44no—
128Dic122—44no—
129Dic122—48no—
130C8×C61—82no—
131#92418—82no—
132#11504—611nomaximal, Sylow
133C22×C61—22no—
134C22×C61—21no—
135C22×C61—21no—
136C22×C61—41no—
137C22×C61—41no—
138C22×C61—42no—
139C22×C61—42no—
140C22×C61#40711yescharacteristic
141C22×C61C2×#9911yescharacteristic
142C22×C61C2×#10011yescharacteristic
143C4×C61—42no—
144C4×C61—42no—
145C4×C61—81no—
146Dic61—21no—
147Dic61—21no—
148Dic61—22no—
149Dic61—42no—
150Dic61—42no—
151Dic61—81no—
152#2310—611no—
153#1464—612no—
154#1317—611no—
155#1317—612no—
156#1317D6111yescharacteristic
157C2×C61—21no—
158C2×C61—21no—
159C2×C61—41no—
160C2×C61—41no—
161C2×C61#146211yescharacteristic
162C2×C61#212312yes—
163C23×Q8—611no—
164C2×#117—611no—
165C2×#117—611no—
166#432—1222no—
167#391—1222no—
168#391—1222no—
169#381—611no—
170#381—611no—
171#381—611no—
172#381C2×D6111yescharacteristic
173#324—1222no—
174#323—612no—
175#323C2×D6112yes—
176C61#1150411yescharacteristic, complemented, Sylow
177C22×Q8—1222no—
178C22×Q8—1221no—
179C22×Q8—1221no—
180C22×Q8—1222no—
181C22×Q8—2441no—
182C22×Q8—2441no—
183C22×Q8—2442no—
184C23×C4—611no—
185C23×C4—611no—
186C23×C4C4×D6111yescharacteristic
187#117—2441no—
188#117—2441no—
189#117—2442no—
190C2×C4⋊C4—612no—
191C2×C4⋊C4—1221no—
192C2×C22⋊C4—611no—
193C2×C22⋊C4—611no—
194C2×C22⋊C4C4×D6111yescharacteristic
195C2×C22⋊C4C22×D6111yescharacteristic
196C2×C42—612no—
197C2×C42—1221no—
198C4⋊C8—2442no—
199C22⋊C8—22no—
200C22⋊C8—1222no—
201#97—2442no—
202#95—22no—
203#95—1222no—
204#95—1222no—
205#95—1222no—
206C24C2×C4×D6111yescharacteristic
207C2×Q8—1224no—
208C2×Q8—1224no—
209C2×Q8—2441no—
210C2×Q8—2441no—
211C2×Q8—2442no—
212C2×Q8—2444no—
213C2×Q8—2444no—
214C2×Q8—2442no—
215C2×Q8—2442no—
216C2×Q8—2444no—
217C2×Q8—2444no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—612no—
226C22×C4—612no—
227C22×C4—1221no—
228C22×C4—1221no—
229C22×C4—1222no—
230C22×C4—1221no—
231C22×C4—1221no—
232C22×C4—1221no—
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4—2441no—
236C22×C4—2441no—
237C22×C4#1175818912yes—
238C22×C4D4×D6112yes—
239C2×C8—42no—
240C2×C8—2442no—
241C4⋊C4—2442no—
242C4⋊C4—2442no—
243C22⋊C4—41no—
244C22⋊C4—41no—
245C22⋊C4—2441no—
246C22⋊C4—2441no—
247C42—1222no—
248C42—1222no—
249C42—2442no—
250C23—21no—
251C23—21no—
252C23—42no—
253C23C22⋊C4×D6111yescharacteristic
254C23M16×D6111yescharacteristic
255C23C2×#1175818911yescharacteristic
256Q8—2444no—
257Q8—2444no—
258Q8—2448no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—611no—
269C2×C4—611no—
270C2×C4—612no—
271C2×C4—1222no—
272C2×C4—1222no—
273C2×C4—1222no—
274C2×C4—1222no—
275C2×C4—1221no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1222no—
280C2×C4—1222no—
281C2×C4—2442no—
282C2×C4—2441no—
283C2×C4—2442no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2442no—
287C2×C4—2442no—
288C8—82no—
289C8—4882no—
290C22—22no—
291C22—21no—
292C22—21no—
293C22—41no—
294C22—41no—
295C22—42no—
296C22—42no—
297C22#1683972411yescharacteristic
298C22#99×D6111yescharacteristic
299C22#100×D6111yescharacteristic
300C4—42no—
301C4—42no—
302C4—81no—
303C4—1221no—
304C4—1221no—
305C4—1222no—
306C4—4881no—
307C4—2442no—
308C4—2442no—
309C2—21no—
310C2—21no—
311C2—41no—
312C2—41no—
313C2#2144414411yescharacteristic
314C2#2144747112yes—
subgroupG/H
centerC22#99×D61
commutator, prime radicalC24×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1317C2
socleC22×C61C2×#99
cosocleC2×C22⋊C4×C61C23
hypercenter#1317D61
hypocenterC61#11504
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
176. C61#11504semidirect

Maximal subgroups

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

subgroupindex
#214484042
#214441502
#214437492
#214437482
C61×#13172
#1150461