Finite Group Databasebeta

← #30604076

Subgroups — #30604076

Order 15616.

706 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 78 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#21461065C212yesmaximal
2#21460746C212yesmaximal, complemented
3#21460745C212yesmaximal, complemented
4#381×D61C211yesmaximal, characteristic
5#16840733—22no—
6#16840606—22no—
7#16840605C2214yes—
8C23×C4×D61C411yescharacteristic
9C2×C22⋊C4×D61C411yescharacteristic
10C2×C22⋊C4×D61C2211yescharacteristic
11#16839625C2211yescharacteristic
12#16839624—22no—
13#16839623C411yescharacteristic
14#16839623C2211yescharacteristic
15#95×D61—22no—
16C61×#381C411yescharacteristic
17C2×#11758213—42no—
18#14519834—42no—
19C22⋊#92420—24no—
20C24×D61C2×C411yescharacteristic
21C23×Dic61C2×C411yescharacteristic
22C22×C4×D61—21no—
23C22×C4×D61—21no—
24C22×C4×D61—22no—
25C22×C4×D61—22no—
26C22×C4×D61—21no—
27C22×C4×D61—42no—
28C22×C4×D61—42no—
29C22×C4×D61D412yes—
30C2×C22⋊Dic61C2×C411yescharacteristic
31C2×C22⋊Dic61C2311yescharacteristic
32C2×#11758198—21no—
33C2×#11758198D412yes—
34C22⋊C4×D61—42no—
35C22⋊C4×D61—42no—
36#14519684—22no—
37#14519684—22no—
38#14519684—22no—
39C23×C4×C61C2×C411yescharacteristic
40C2×C22⋊C4×C61C2×C411yescharacteristic
41C2×C22⋊C4×C61C2×C411yescharacteristic
42#95×C61—22no—
43C24×C61C22×C411yescharacteristic
44C23×D61—21no—
45C23×D61—21no—
46C23×D61—22no—
47C23×D61—22no—
48C23×D61—44no—
49C23×D61C22⋊C411yescharacteristic
50C23×D61C22⋊C411yescharacteristic
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—41no—
55C22×C4×C61—41no—
56C22×C4×C61C22⋊C412yes—
57C22×C4×C61M1612yescomplemented
58C22×Dic61—21no—
59C22×Dic61—21no—
60C22×Dic61—21no—
61C22×Dic61—41no—
62C22×Dic61—41no—
63C22×Dic61M1612yescomplemented
64C22×Dic61C2×D412yes—
65C2×C4×D61—24no—
66C2×C4×D61—24no—
67C2×C4×D61—22no—
68C2×C4×D61—22no—
69C2×C4×D61—48no—
70C2×C4×D61—42no—
71C2×C4×D61—42no—
72C2×C4×D61—48no—
73C2×C4×D61—42no—
74C2×C4×D61—42no—
75C2×C4×D61—44no—
76C2×C4×D61—44no—
77C2×C4×D61—42no—
78C2×#92420—44no—
79#11758213—84no—
80C22⋊C4×C61—41no—
81C22⋊C4×C61—41no—
82C22⋊Dic61—41no—
83C22⋊Dic61—41no—
84#11758198—42no—
85#11758198—42no—
86C23×C61—21no—
87C23×C61—21no—
88C23×C61—42no—
89C23×C61C2×C22⋊C411yescharacteristic
90C23×C61C2×M1611yescharacteristic
91C23×C61C2×M1611yescharacteristic
92C22×D61—21no—
93C22×D61—21no—
94C22×D61—24no—
95C22×D61—24no—
96C22×D61—24no—
97C22×D61—21no—
98C22×D61—21no—
99C22×D61—48no—
100C22×D61—44no—
101C22×D61—44no—
102C22×D61—44no—
103C22×D61—44no—
104C22×D61—42no—
105C22×D61#9912yes—
106C22×D61#10012yes—
107C2×C4×C61—22no—
108C2×C4×C61—22no—
109C2×C4×C61—42no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—42no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61—41no—
116C2×Dic61—22no—
117C2×Dic61—22no—
118C2×Dic61—42no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—42no—
122C2×Dic61—42no—
123C2×Dic61—42no—
124C2×Dic61—41no—
125C4×D61—48no—
126C4×D61—48no—
127C4×D61—44no—
128C4×D61—82no—
129C4×D61—84no—
130#92420—84no—
131#11500—611nomaximal, Sylow
132C22×C61—22no—
133C22×C61—21no—
134C22×C61—21no—
135C22×C61—41no—
136C22×C61—41no—
137C22×C61—42no—
138C22×C61—42no—
139C22×C61#40711yescharacteristic
140C22×C61C2×#9911yescharacteristic
141C22×C61C2×#10011yescharacteristic
142C2×D61—24no—
143C2×D61—24no—
144C2×D61—22no—
145C2×D61—22no—
146C2×D61—22no—
147C2×D61—48no—
148C2×D61—48no—
149C2×D61—42no—
150C2×D61—42no—
151C2×D61—42no—
152C2×D61#35214yes—
153C4×C61—42no—
154C4×C61—42no—
155C4×C61—81no—
156Dic61—42no—
157Dic61—42no—
158Dic61—81no—
159C2×#381—611no—
160#1462—612no—
161#1317—612no—
162#1317—612no—
163C2×C61—21no—
164C2×C61—21no—
165C2×C61—41no—
166C2×C61—41no—
167C2×C61#146211yescharacteristic
168C2×C61C2×#35212yes—
169D61—24no—
170D61—42no—
171C24×C4—611no—
172C22×C22⋊C4—611no—
173C22×C22⋊C4—611no—
174#407—1222no—
175#381—611no—
176#381—611no—
177#381—611no—
178#381—1222no—
179#381#692311yescharacteristic
180C2×#95—1222no—
181#323—614no—
182#323—1222no—
183C61#1150011yescharacteristic, complemented, Sylow
184C25—611no—
185C23×C4—611no—
186C23×C4—612no—
187C23×C4—1222no—
188C23×C4—1221no—
189C23×C4—1221no—
190C23×C4—1221no—
191C23×C4—1222no—
192C23×C4—2442no—
193C23×C4—2442no—
194C23×C4C2×#692311yescharacteristic
195C2×M16—2442no—
196C2×C22⋊C4—611no—
197C2×C22⋊C4—612no—
198C2×C22⋊C4—611no—
199C2×C22⋊C4—1221no—
200C2×C22⋊C4—2442no—
201C2×C22⋊C4—2442no—
202C2×C22⋊C4C2×#692311yescharacteristic
203C2×C22⋊C4C2×#692311yescharacteristic
204C22⋊C8—1224no—
205C22⋊C8—2442no—
206#95—22no—
207#95—1222no—
208#95—1222no—
209#95—1222no—
210C24—611no—
211C24—611no—
212C24—1222no—
213C24—1222no—
214C24—1221no—
215C24—1221no—
216C24—2444no—
217C24C22×#692311yescharacteristic
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—612no—
224C22×C4—612no—
225C22×C4—1222no—
226C22×C4—1222no—
227C22×C4—1224no—
228C22×C4—1224no—
229C22×C4—1221no—
230C22×C4—1221no—
231C22×C4—1221no—
232C22×C4—2442no—
233C22×C4—2444no—
234C22×C4—2444no—
235C22×C4—2442no—
236C22×C4—2442no—
237C22×C4—2448no—
238C22×C4—2442no—
239C22×C4—2442no—
240C22×C4—2448no—
241C22×C4—2441no—
242C22×C4—2441no—
243C22×C4#1175821312yescomplemented
244C22×C4C22⋊#692312yes—
245M16—4884no—
246C2×C8—2444no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—2442no—
250C22⋊C4—2442no—
251C22⋊C4—2441no—
252C22⋊C4—2441no—
253C23—21no—
254C23—21no—
255C23—42no—
256C23—612no—
257C23—612no—
258C23—1224no—
259C23—1224no—
260C23—1224no—
261C23—1221no—
262C23—1221no—
263C23—1221no—
264C23—1221no—
265C23—2442no—
266C23—2444no—
267C23—2444no—
268C23—2444no—
269C23—2448no—
270C23—2444no—
271C23C2×C22⋊#692311yescharacteristic
272C23D61⋊M1611yescharacteristic
273C23C2×#1175821311yescharacteristic
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—1222no—
284C2×C4—1222no—
285C2×C4—4882no—
286C2×C4—4884no—
287C2×C4—2444no—
288C2×C4—2448no—
289C2×C4—2448no—
290C2×C4—2442no—
291C2×C4—2441no—
292C2×C4—2442no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2442no—
296C2×C4—2442no—
297C8—4884no—
298C22—22no—
299C22—21no—
300C22—21no—
301C22—41no—
302C22—41no—
303C22—42no—
304C22—42no—
305C22—614no—
306C22—1224no—
307C22—1224no—
308C22—1222no—
309C22—1222no—
310C22—1222no—
311C22—2442no—
312C22—2442no—
313C22—2448no—
314C22—2448no—
315C22—2442no—
316C22#1684073311yescharacteristic
317C22D61⋊#9911yescharacteristic
318C22D61⋊#10011yescharacteristic
319C4—42no—
320C4—42no—
321C4—81no—
322C4—4881no—
323C4—2442no—
324C4—2442no—
325C2—21no—
326C2—21no—
327C2—41no—
328C2—41no—
329C2—1224no—
330C2—2442no—
331C2#2146106511yescharacteristic
332C2D61⋊#35212yes—
subgroupG/H
centerC22D61⋊#99
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC61×#381C4
socleC22×C61C2×#99
prime radicalC24×D61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenter#381#6923
hypocenterC61#11500
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
2. #21460746C2semidirect
3. #21460745C2semidirect
57. C22×C4×C61M16semidirect
63. C22×Dic61M16semidirect
183. C61#11500semidirect
243. C22×C4#11758213semidirect

Maximal subgroups

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

subgroupindex
#214610652
#214607462
#214607452
#381×D612
#1150061