Finite Group Databasebeta

← #30607258

Subgroups — #30607258

Order 15616.

638 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461654C212yesmaximal
2#21460917C212yesmaximal, complemented
3#21460916C212yesmaximal, complemented
4#391×D61C211yesmaximal, characteristic
5C2×#14519838—22no—
6C2×#14519838C2214yes—
7#16840734—22no—
8C22×Q8×D61C2211yescharacteristic
9C2×C4⋊C4×D61C411yescharacteristic
10C2×C42×D61C411yescharacteristic
11#16839669C411yescharacteristic
12#16839668C2211yescharacteristic
13#16839667C2211yescharacteristic
14#16839666—22no—
15#95×D61—22no—
16C61×#391C411yescharacteristic
17C2×#11758217—24no—
18#14519838—28no—
19#14519838—44no—
20#14519834—42no—
21#14519834—42no—
22C22×Dic122D412yes—
23C22×Dic122C2311yescharacteristic
24C2×Q8×D61—24no—
25C2×Q8×D61—42no—
26C2×Q8×D61—41no—
27C2×Q8×D61—41no—
28C22×C4×D61—21no—
29C22×C4×D61—21no—
30C22×C4×D61C2×C411yescharacteristic
31C22×C4×D61D412yes—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×#11758196—21no—
34C4⋊C4×D61—41no—
35C4⋊C4×D61—41no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61C2×C411yescharacteristic
38C42×D61—42no—
39#14519684—22no—
40#14519684—22no—
41#14519684—22no—
42C22×Q8×C61C2×C411yescharacteristic
43C2×C4⋊C4×C61C2×C411yescharacteristic
44C2×C42×C61C2×C411yescharacteristic
45#95×C61—22no—
46C23×D61C22⋊C411yescharacteristic
47C2×Q8×C61—22no—
48C2×Q8×C61—41no—
49C2×Q8×C61—41no—
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61C22⋊C412yes—
53C22×C4×C61C22×C411yescharacteristic
54C22×Dic61—21no—
55C22×Dic61—21no—
56C22×Dic61C22⋊C411yescharacteristic
57C22×Dic61C2×D412yes—
58Q8×D61—48no—
59Q8×D61—48no—
60C2×C4×D61—21no—
61C2×C4×D61—21no—
62C2×C4×D61—22no—
63C2×C4×D61—22no—
64C2×C4×D61—24no—
65C2×C4×D61—22no—
66C2×C4×D61—22no—
67C2×C4×D61—24no—
68C2×C4×D61—42no—
69C2×C4×D61—42no—
70C2×C4×D61—42no—
71C2×C4×D61—44no—
72C2×C4×D61—41no—
73C2×C4×D61—41no—
74C2×Dic122—24no—
75C2×Dic122—24no—
76C2×Dic122—42no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122#4114yes—
80#11758217—44no—
81#11758217—44no—
82C2×#92420—44no—
83C4⋊C4×C61—41no—
84C42×C61—41no—
85C4⋊Dic61—41no—
86#11758196—42no—
87C4×Dic61—42no—
88C4×Dic61—41no—
89C23×C61C2×C22⋊C411yescharacteristic
90C22×D61—21no—
91C22×D61—21no—
92C22×D61—22no—
93C22×D61—22no—
94C22×D61#9911yescharacteristic
95C22×D61#9911yescharacteristic
96Q8×C61—44no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—42no—
106C2×C4×C61—41no—
107C2×C4×C61#11712yes—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—42no—
116C2×Dic61—41no—
117C2×Dic61#9912yes—
118C2×Dic61#12314yes—
119C4×D61—24no—
120C4×D61—24no—
121C4×D61—44no—
122C4×D61—44no—
123C4×D61—48no—
124C4×D61—82no—
125C4×D61—82no—
126Dic122—44no—
127Dic122—48no—
128#92420—84no—
129#12860—611nomaximal, Sylow
130C22×C61—21no—
131C22×C61—21no—
132C22×C61#38111yescharacteristic
133C22×C61C2×#9911yescharacteristic
134C22×C61C2×#9911yescharacteristic
135C2×D61—24no—
136C2×D61—24no—
137C2×D61—21no—
138C2×D61—21no—
139C2×D61—21no—
140C2×D61—21no—
141C2×D61#35512yes—
142C2×D61#35612yes—
143C4×C61—22no—
144C4×C61—42no—
145C4×C61—42no—
146C4×C61—81no—
147Dic61—24no—
148Dic61—22no—
149Dic61—42no—
150Dic61—81no—
151C2×#391—611no—
152#1784—612no—
153#1394—612no—
154#1394—612no—
155C2×C61—21no—
156C2×C61—21no—
157C2×C61#181911yescharacteristic
158C2×C61C2×#35511yescharacteristic
159C2×C61C2×#35611yescharacteristic
160D61—22no—
161D61—22no—
162C23×Q8—611no—
163C22×C4⋊C4—611no—
164C22×C42—611no—
165C2×#101—614no—
166C2×#101—1222no—
167#407—1222no—
168#391—611no—
169#391—611no—
170#391—611no—
171#391—1222no—
172#391#692311yescharacteristic
173C2×#95—1222no—
174C61#1286011yescharacteristic, complemented, Sylow
175C22×Q8—612no—
176C22×Q8—611no—
177C22×Q8—1224no—
178C22×Q8—2441no—
179C22×Q8—2441no—
180C22×Q8—2442no—
181C22×Q8C2×#692311yescharacteristic
182C23×C4—611no—
183C23×C4—612no—
184C23×C4—1221no—
185C23×C4—1221no—
186C2×M16—1224no—
187C2×C4⋊C4—611no—
188C2×C4⋊C4—1221no—
189C2×C4⋊C4—2441no—
190C2×C4⋊C4—2441no—
191C2×C4⋊C4C2×#692311yescharacteristic
192C2×C42—611no—
193C2×C42—1221no—
194C2×C42—2442no—
195C2×C42C2×#692311yescharacteristic
196#101—1228no—
197#101—2444no—
198C22⋊C8—2442no—
199C22⋊C8—2442no—
200#95—22no—
201#95—1222no—
202#95—1222no—
203#95—1222no—
204C24—611no—
205C2×Q8—22no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8—614no—
209C2×Q8—1224no—
210C2×Q8—1224no—
211C2×Q8—2441no—
212C2×Q8—2441no—
213C2×Q8—2442no—
214C2×Q8—2448no—
215C2×Q8—2448no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—612no—
219C22×C4—611no—
220C22×C4—1222no—
221C22×C4—1224no—
222C22×C4—1221no—
223C22×C4—1221no—
224C22×C4—1222no—
225C22×C4—1222no—
226C22×C4—1224no—
227C22×C4—1222no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4—2442no—
231C22×C4—2441no—
232C22×C4—2441no—
233C22×C4—2444no—
234C22×C4—2442no—
235C22×C4—2442no—
236C22×C4C22⋊#692312yes—
237C22×C4C22×#692311yescharacteristic
238M16—2444no—
239M16—2444no—
240C2×C8—2444no—
241C4⋊C4—41no—
242C4⋊C4—2441no—
243C4⋊C4—2442no—
244C42—41no—
245C42—2441no—
246C42—2442no—
247C23—611no—
248C23—611no—
249C23—1222no—
250C23—1222no—
251C23—1221no—
252C23—1221no—
253C23C2×C22⋊#692311yescharacteristic
254Q8—44no—
255Q8—2444no—
256Q8—2448no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—614no—
268C2×C4—612no—
269C2×C4—1224no—
270C2×C4—1224no—
271C2×C4—1221no—
272C2×C4—1222no—
273C2×C4—1221no—
274C2×C4—1222no—
275C2×C4—1222no—
276C2×C4—4882no—
277C2×C4—4882no—
278C2×C4—2444no—
279C2×C4—2444no—
280C2×C4—2448no—
281C2×C4—2442no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4#1451985612yes—
286C8—4884no—
287C22—21no—
288C22—21no—
289C22—612no—
290C22—612no—
291C22—1224no—
292C22—1224no—
293C22—1221no—
294C22—1221no—
295C22—1221no—
296C22—1221no—
297C22#1684070511yescharacteristic
298C22D61⋊#9911yescharacteristic
299C22D61⋊#9911yescharacteristic
300C4—22no—
301C4—42no—
302C4—42no—
303C4—81no—
304C4—1224no—
305C4—1222no—
306C4—4881no—
307C4—2442no—
308C2—21no—
309C2—21no—
310C2—1222no—
311C2—1222no—
312C2#2146171511yescharacteristic
313C2D61⋊#35511yescharacteristic
314C2D61⋊#35611yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC22×Dic122C23
hypercenter#391#6923
hypocenterC61#12860
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #391

Complements

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

NH ≅ G/Ntype
2. #21460917C2semidirect
3. #21460916C2semidirect
174. C61#12860semidirect

Maximal subgroups

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

subgroupindex
#214616542
#214609172
#214609162
#391×D612
#1286061