Finite Group Databasebeta

← #30595633

Subgroups — #30595633

Order 15616.

630 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 94 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#21461711C212yesmaximal, complemented
2#21460639C212yesmaximal, complemented
3#21460636C212yesmaximal, complemented
4#21448308C211yesmaximal, characteristic
5C2×#14519834—22no—
6#16840628—22no—
7#16840628C2214yes—
8C22×#11758226C411yescharacteristic
9C2×#14519735C411yescharacteristic
10C2×C42×D61C2211yescharacteristic
11#16839669C2211yescharacteristic
12#16839664C411yescharacteristic
13#16839663C2211yescharacteristic
14#16839640—22no—
15#16839609—22no—
16C61×#391C411yescharacteristic
17C22×#92420—24no—
18#14519834—44no—
19C2×#11758226—22no—
20C2×#11758226—22no—
21C2×#11758226—42no—
22C2×#11758226—42no—
23C22×D244—21no—
24C22×D244C2×C411yescharacteristic
25C22×C4×D61—21no—
26C22×C4×D61C2×C411yescharacteristic
27C22×C4×D61D412yes—
28#14519735—42no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×#11758198—21no—
31C2×#11758198—22no—
32C2×#11758198—22no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61D412yes—
35C2×C4×Dic61C2311yescharacteristic
36C42×D61—42no—
37#14519684—22no—
38C22×Q8×C61C2×C411yescharacteristic
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C42×C61C2×C411yescharacteristic
41#95×C61—22no—
42C23×D61—21no—
43C23×D61C22⋊C411yescharacteristic
44C2×Q8×C61—21no—
45C2×Q8×C61—41no—
46C2×Q8×C61—41no—
47C2×Q8×C61M1612yes—
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61C22⋊C412yes—
51C22×C4×C61C22×C411yescharacteristic
52C22×Dic61—21no—
53C22×Dic61C22⋊C411yescharacteristic
54C22×Dic61C2×D412yes—
55#11758226—48no—
56#11758226—48no—
57C2×D244—24no—
58C2×D244—21no—
59C2×D244—41no—
60C2×D244—41no—
61C2×D244—42no—
62C2×D244—42no—
63C2×D244M1612yes—
64C2×C4×D61—22no—
65C2×C4×D61—21no—
66C2×C4×D61—21no—
67C2×C4×D61—22no—
68C2×C4×D61—24no—
69C2×C4×D61—24no—
70C2×C4×D61—24no—
71C2×C4×D61—42no—
72C2×C4×D61—42no—
73C2×C4×D61—42no—
74C2×#92420—44no—
75C2×#92420—44no—
76C2×#92420—44no—
77C4⋊C4×C61—41no—
78C42×C61—41no—
79#11758198—44no—
80#11758198—42no—
81#11758198—44no—
82C4⋊Dic61—41no—
83C4×Dic61—42no—
84C4×Dic61—41no—
85C4×Dic61—42no—
86C23×C61C2×C22⋊C411yescharacteristic
87C22×D61—21no—
88C22×D61—21no—
89C22×D61—22no—
90C22×D61—22no—
91C22×D61—22no—
92C22×D61—41no—
93C22×D61—41no—
94C22×D61—42no—
95C22×D61—42no—
96C22×D61#9912yes—
97Q8×C61—42no—
98Q8×C61—42no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61—22no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—42no—
109C2×C4×C61C2×M1611yescharacteristic
110C2×C4×C61C2×M1611yescharacteristic
111C2×Dic61—21no—
112C2×Dic61—22no—
113C2×Dic61—21no—
114C2×Dic61—22no—
115C2×Dic61—41no—
116C2×Dic61—42no—
117C2×Dic61#10012yes—
118C2×Dic61#13514yes—
119D244—42no—
120D244—42no—
121D244—48no—
122C4×D61—24no—
123C4×D61—24no—
124C4×D61—48no—
125C4×D61—48no—
126#92420—84no—
127#7645—611nomaximal, Sylow
128C22×C61#40711yescharacteristic
129C22×C61C2×#9911yescharacteristic
130C22×C61C2×#10011yescharacteristic
131C22×C61#41612yes—
132C22×C61#42112yes—
133C2×D61—22no—
134C2×D61—24no—
135C2×D61—41no—
136C2×D61—41no—
137C2×D61—42no—
138C2×D61—42no—
139C2×D61—44no—
140C2×D61—81no—
141C2×D61—81no—
142C2×D61—82no—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—42no—
146C4×C61—42no—
147C4×C61—81no—
148Dic61—22no—
149Dic61—24no—
150Dic61—81no—
151#2297—611no—
152#1817—612no—
153#1272—612no—
154#1270—612no—
155C2×C61#146211yescharacteristic
156C2×C61#148812yes—
157C2×C61#151612yes—
158C2×C61#153611yescharacteristic
159C2×C61#154311yescharacteristic
160D61—42no—
161D61—82no—
162C22×#41—611no—
163C2×#117—611no—
164C22×C42—611no—
165C2×C22⋊C8—1222no—
166#391—611no—
167#391#692311yescharacteristic
168#390—611no—
169#390—611no—
170#386—1222no—
171C4×C22⋊C4—1222no—
172#336—614no—
173#336—1222no—
174C61#764511yescharacteristic, complemented, Sylow
175C2×#41—1222no—
176C2×#41—1222no—
177C2×#41—2442no—
178C2×#41—2442no—
179C22×Q8C2×#692311yescharacteristic
180C22×D4—611no—
181C22×D4—1221no—
182C23×C4—611no—
183C23×C4—612no—
184C23×C4—1221no—
185C22×C8—1224no—
186#117—2442no—
187C2×C4⋊C4—611no—
188C2×C4⋊C4C2×#692311yescharacteristic
189C2×C22⋊C4—1222no—
190C2×C22⋊C4—1221no—
191C2×C22⋊C4—1222no—
192C2×C42—612no—
193C2×C42—611no—
194C2×C42—1221no—
195C2×C42—2442no—
196C2×C42C2×#692311yescharacteristic
197C22⋊C8—2444no—
198#95—22no—
199#95—1222no—
200C24—611no—
201C24—1221no—
202#41—2448no—
203#41—2448no—
204C2×Q8—21no—
205C2×Q8—41no—
206C2×Q8—41no—
207C2×Q8#1175821312yes—
208C2×D4—612no—
209C2×D4—1224no—
210C2×D4—1221no—
211C2×D4—2441no—
212C2×D4—2441no—
213C2×D4—2442no—
214C2×D4—2442no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—612no—
218C22×C4—611no—
219C22×C4—1222no—
220C22×C4—1224no—
221C22×C4—1222no—
222C22×C4—1224no—
223C22×C4—1224no—
224C22×C4—1221no—
225C22×C4—1221no—
226C22×C4—1221no—
227C22×C4—2442no—
228C22×C4—2442no—
229C22×C4—2442no—
230C22×C4C22⋊#692312yes—
231C22×C4C22×#692311yescharacteristic
232C2×C8—2444no—
233C2×C8—2444no—
234C2×C8—2444no—
235C4⋊C4—41no—
236C4⋊C4—2441no—
237C22⋊C4—2444no—
238C22⋊C4—2444no—
239C22⋊C4—2442no—
240C42—41no—
241C42—2441no—
242C42—2442no—
243C42—2442no—
244C23—612no—
245C23—1221no—
246C23—1221no—
247C23—1222no—
248C23—1222no—
249C23—1222no—
250C23—2441no—
251C23—2441no—
252C23—2442no—
253C23—2442no—
254C23C2×C22⋊#692311yescharacteristic
255Q8—42no—
256Q8—42no—
257D4—2442no—
258D4—2442no—
259D4—2448no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—612no—
271C2×C4—614no—
272C2×C4—1224no—
273C2×C4—1224no—
274C2×C4—1221no—
275C2×C4—1222no—
276C2×C4—1221no—
277C2×C4—1222no—
278C2×C4—2448no—
279C2×C4—2448no—
280C2×C4—2441no—
281C2×C4—2442no—
282C2×C4D61⋊M1611yescharacteristic
283C2×C4C2×#1175821311yescharacteristic
284C8—4884no—
285C22—1222no—
286C22—1224no—
287C22—4881no—
288C22—4881no—
289C22—4882no—
290C22—2442no—
291C22—2444no—
292C22—2441no—
293C22—2441no—
294C22—2442no—
295C22#1684073311yescharacteristic
296C22D61⋊#9911yescharacteristic
297C22D61⋊#10011yescharacteristic
298C22#1684075212yes—
299C22#1684076112yes—
300C4—21no—
301C4—21no—
302C4—42no—
303C4—42no—
304C4—81no—
305C4—1222no—
306C4—1224no—
307C4—4881no—
308C2—4882no—
309C2—2442no—
310C2#2146106511yescharacteristic
311C2#2146115312yes—
312C2#2146124612yes—
313C2#2146130911yescharacteristic
314C2#2146132311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC23×C61C2×C22⋊C4
prime radicalC22×#11758226C4
cosocleC2×C4×Dic61C23
hypercenter#391#6923
hypocenterC61#7645
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
1. #21461711C2semidirect
2. #21460639C2semidirect
3. #21460636C2semidirect
174. C61#7645semidirect

Maximal subgroups

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

subgroupindex
#214617112
#214606392
#214606362
#214483082
#764561