Finite Group Databasebeta

← #30604090

Subgroups — #30604090

Order 15616.

510 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461071C212yesmaximal
2#21460746C212yesmaximal
3#21460745C212yesmaximal
4#21448404C211yesmaximal, characteristic
5#16840783—22no—
6#16840608—22no—
7#16840605C2214yes—
8C23×Dic122C411yescharacteristic
9C2×#14519733C411yescharacteristic
10C2×#14519733C2211yescharacteristic
11#16839666—22no—
12#16839666—22no—
13#16839625C2211yescharacteristic
14#16839623C411yescharacteristic
15#16839623C2211yescharacteristic
16C61×#381C411yescharacteristic
17C4⋊#92420—42no—
18C22⋊#92420—24no—
19#14519832—42no—
20C22×Dic122—22no—
21C22×Dic122—21no—
22C22×Dic122—21no—
23C22×Dic122—22no—
24C22×Dic122—41no—
25C22×Dic122—41no—
26C22×Dic122—42no—
27C23×Dic61C2×C411yescharacteristic
28C23×Dic61C2×C411yescharacteristic
29#14519733—41no—
30#14519733—41no—
31#14519733—42no—
32C2×#11758196—21no—
33C2×#11758196D412yes—
34C2×C22⋊Dic61C2×C411yescharacteristic
35C2×C22⋊Dic61C2311yescharacteristic
36C2×C4×Dic61—21no—
37C2×C4×Dic61D412yes—
38#14519684—22no—
39#14519684—22no—
40#14519684—22no—
41C23×C4×C61C2×C411yescharacteristic
42C2×C22⋊C4×C61C2×C411yescharacteristic
43C2×C22⋊C4×C61C2×C411yescharacteristic
44#95×C61—22no—
45C24×C61C22×C411yescharacteristic
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61—41no—
50C22×C4×C61—41no—
51C22×C4×C61C22⋊C412yes—
52C22×C4×C61M1612yes—
53C22×Dic61—21no—
54C22×Dic61—21no—
55C22×Dic61—21no—
56C22×Dic61—21no—
57C22×Dic61—22no—
58C22×Dic61—21no—
59C22×Dic61—21no—
60C22×Dic61—21no—
61C22×Dic61—41no—
62C22×Dic61—41no—
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61M1612yes—
66C22×Dic61C2×D412yes—
67C2×Dic122—24no—
68C2×Dic122—24no—
69C2×Dic122—44no—
70C2×Dic122—44no—
71C2×Dic122—44no—
72C2×Dic122—44no—
73C2×Dic122—42no—
74C2×Dic122—42no—
75C2×Dic122—41no—
76C2×Dic122—41no—
77C2×Dic122—42no—
78C2×#92420—44no—
79C22⋊C4×C61—41no—
80C22⋊C4×C61—41no—
81C22⋊Dic61—41no—
82C22⋊Dic61—41no—
83#11758196—42no—
84#11758196—42no—
85C4×Dic61—22no—
86C4×Dic61—22no—
87C4×Dic61—42no—
88C23×C61—21no—
89C23×C61—21no—
90C23×C61—42no—
91C23×C61C2×C22⋊C411yescharacteristic
92C23×C61C2×M1611yescharacteristic
93C23×C61C2×M1611yescharacteristic
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—42no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—42no—
100C2×C4×C61—42no—
101C2×C4×C61—42no—
102C2×C4×C61—41no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—42no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—42no—
117C2×Dic61—42no—
118C2×Dic61—42no—
119C2×Dic61—41no—
120C2×Dic61#9911yescharacteristic
121C2×Dic61#9911yescharacteristic
122C2×Dic61#10012yes—
123Dic122—44no—
124Dic122—44no—
125Dic122—48no—
126#92420—84no—
127#11504—611nomaximal, Sylow
128C22×C61—22no—
129C22×C61—21no—
130C22×C61—21no—
131C22×C61—41no—
132C22×C61—41no—
133C22×C61—42no—
134C22×C61—42no—
135C22×C61#40711yescharacteristic
136C22×C61C2×#9911yescharacteristic
137C22×C61C2×#10011yescharacteristic
138C4×C61—42no—
139C4×C61—42no—
140C4×C61—81no—
141Dic61—21no—
142Dic61—21no—
143Dic61—22no—
144Dic61—42no—
145Dic61—42no—
146Dic61—81no—
147#2310—611no—
148#1464—612no—
149#1317—612no—
150#1317—612no—
151C2×C61—21no—
152C2×C61—21no—
153C2×C61—41no—
154C2×C61—41no—
155C2×C61#146211yescharacteristic
156C2×C61#212312yes—
157C23×Q8—611no—
158C2×#117—611no—
159C2×#117—611no—
160#432—1222no—
161#391—1222no—
162#391—1222no—
163#381—611no—
164#381—611no—
165#381—611no—
166#381#692311yescharacteristic
167#324—1222no—
168#323—614no—
169C61#1150411yescharacteristic, complemented, Sylow
170C22×Q8—1222no—
171C22×Q8—1221no—
172C22×Q8—1221no—
173C22×Q8—1222no—
174C22×Q8—2441no—
175C22×Q8—2441no—
176C22×Q8—2442no—
177C23×C4—611no—
178C23×C4—611no—
179C23×C4C2×#692311yescharacteristic
180#117—2441no—
181#117—2441no—
182#117—2442no—
183C2×C4⋊C4—612no—
184C2×C4⋊C4—1221no—
185C2×C22⋊C4—611no—
186C2×C22⋊C4—611no—
187C2×C22⋊C4C2×#692311yescharacteristic
188C2×C22⋊C4C2×#692311yescharacteristic
189C2×C42—612no—
190C2×C42—1221no—
191C4⋊C8—2442no—
192C22⋊C8—1224no—
193#97—2442no—
194#95—22no—
195#95—1222no—
196#95—1222no—
197#95—1222no—
198C24C22×#692311yescharacteristic
199C2×Q8—1224no—
200C2×Q8—1224no—
201C2×Q8—2441no—
202C2×Q8—2441no—
203C2×Q8—2442no—
204C2×Q8—2444no—
205C2×Q8—2444no—
206C2×Q8—2442no—
207C2×Q8—2442no—
208C2×Q8—2444no—
209C2×Q8—2444no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—611no—
216C22×C4—611no—
217C22×C4—612no—
218C22×C4—612no—
219C22×C4—1221no—
220C22×C4—1221no—
221C22×C4—1222no—
222C22×C4—1221no—
223C22×C4—1221no—
224C22×C4—1221no—
225C22×C4—1221no—
226C22×C4—1221no—
227C22×C4—2441no—
228C22×C4—2441no—
229C22×C4#1175821312yes—
230C22×C4C22⋊#692312yes—
231C2×C8—2444no—
232C4⋊C4—2442no—
233C4⋊C4—2442no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C22⋊C4—2441no—
237C22⋊C4—2441no—
238C42—1222no—
239C42—1222no—
240C42—2442no—
241C23—21no—
242C23—21no—
243C23—42no—
244C23C2×C22⋊#692311yescharacteristic
245C23D61⋊M1611yescharacteristic
246C23C2×#1175821311yescharacteristic
247Q8—2444no—
248Q8—2444no—
249Q8—2448no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—611no—
260C2×C4—611no—
261C2×C4—612no—
262C2×C4—1222no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1222no—
271C2×C4—1222no—
272C2×C4—2442no—
273C2×C4—2441no—
274C2×C4—2442no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2442no—
278C2×C4—2442no—
279C8—4884no—
280C22—22no—
281C22—21no—
282C22—21no—
283C22—41no—
284C22—41no—
285C22—42no—
286C22—42no—
287C22#1684073311yescharacteristic
288C22D61⋊#9911yescharacteristic
289C22D61⋊#10011yescharacteristic
290C4—42no—
291C4—42no—
292C4—81no—
293C4—1221no—
294C4—1221no—
295C4—1222no—
296C4—4881no—
297C4—2442no—
298C4—2442no—
299C2—21no—
300C2—21no—
301C2—41no—
302C2—41no—
303C2#2146106511yescharacteristic
304C2#2146208212yes—
subgroupG/H
centerC22D61⋊#99
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC61×#381C4
socleC22×C61C2×#99
cosocleC2×C22⋊Dic61C23
hypercenter#381#6923
hypocenterC61#11504
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #381

Complements

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

NH ≅ G/Ntype
169. C61#11504semidirect

Maximal subgroups

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

subgroupindex
#214610712
#214607462
#214607452
#214484042
#1150461