Finite Group Databasebeta

← #30607249

Subgroups — #30607249

Order 15616.

670 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461650C212yesmaximal
2#21460914C212yesmaximal, complemented
3#21460913C212yesmaximal, complemented
4#21448308C211yesmaximal, characteristic
5C2×#14519836—22no—
6C2×#14519836C2214yes—
7#16840705—22no—
8C22×#11758226C2211yescharacteristic
9C2×#14519735C411yescharacteristic, complemented
10C2×C42×D61C411yescharacteristic, complemented
11#16839669C411yescharacteristic, complemented
12#16839664C2211yescharacteristic
13#16839663C2211yescharacteristic
14#16839640—22no—
15#16839609—22no—
16C61×#391C411yescharacteristic, complemented
17C2×C22⋊#6923—24no—
18#14519836—28no—
19#14519836—44no—
20(C2×#6923)⋊C4—44no—
21C2×#11758226—24no—
22C2×#11758226—42no—
23C2×#11758226—42no—
24C22×D244D412yes—
25C22×D244C2311yescharacteristic
26C22×C4×D61—21no—
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D412yes—
29#14519735—42no—
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758198—21no—
32C2×#11758198—22no—
33C2×#11758198—22no—
34C2×C4×Dic61—21no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61C2×C411yescharacteristic
37C42×D61—42no—
38#14519684—22no—
39C22×Q8×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C42×C61C2×C411yescharacteristic
42#95×C61—22no—
43C23×D61C22⋊C411yescharacteristic
44C23×D61C2×D412yes—
45C22×#6923—44no—
46C2×Q8×C61—22no—
47C2×Q8×C61—41no—
48C2×Q8×C61—41no—
49C22×C4×C61—21no—
50C22×C4×C61—21no—
51C22×C4×C61C22⋊C412yes—
52C22×C4×C61C22×C411yescharacteristic
53C22×Dic61—21no—
54C22×Dic61—21no—
55C22×Dic61C22⋊C411yescharacteristic
56#11758226—416no—
57C2×D244—24no—
58C2×D244—24no—
59C2×D244—42no—
60C2×D244—41no—
61C2×D244—41no—
62C2×D244#4114yes—
63C2×C4×D61—22no—
64C2×C4×D61—22no—
65C2×C4×D61—22no—
66C2×C4×D61—24no—
67C2×C4×D61—24no—
68C2×C4×D61—42no—
69C2×C4×D61—42no—
70C2×C4×D61—42no—
71C2×C4×D61—42no—
72C22⋊#6923—44no—
73C22⋊#6923—44no—
74C4⋊C4×C61—41no—
75C42×C61—41no—
76#11758198—44no—
77#11758198—44no—
78#11758198—42no—
79C4⋊Dic61—41no—
80C4×Dic61—42no—
81C4×Dic61—42no—
82C4×Dic61—41no—
83C23×C61C2×C22⋊C411yescharacteristic
84C22×D61—21no—
85C22×D61—21no—
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—41no—
89C22×D61—41no—
90C22×D61—42no—
91C22×D61—42no—
92C22×D61#9912yes—
93C22×D61#12314yes—
94C2×#6923—84no—
95C2×#6923—84no—
96C2×#6923—84no—
97Q8×C61—44no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—42no—
107C2×C4×C61—41no—
108C2×C4×C61#11712yes—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—22no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—42no—
115C2×Dic61—41no—
116C2×Dic61#9912yes—
117D244—44no—
118D244—48no—
119C4×D61—28no—
120C4×D61—48no—
121C4×D61—48no—
122#12857—611nomaximal, Sylow
123C22×C61—21no—
124C22×C61—21no—
125C22×C61#38111yescharacteristic
126C22×C61C2×#9911yescharacteristic
127C22×C61C2×#9911yescharacteristic
128C2×D61—22no—
129C2×D61—24no—
130C2×D61—42no—
131C2×D61—42no—
132C2×D61—42no—
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—42no—
136C2×D61—44no—
137C2×D61—82no—
138#6923—164no—
139C4×C61—22no—
140C4×C61—42no—
141C4×C61—42no—
142C4×C61—81no—
143Dic61—22no—
144Dic61—42no—
145Dic61—81no—
146#2297—611no—
147#1782—612no—
148#1393—612no—
149#1393—612no—
150C2×C61—21no—
151C2×C61—21no—
152C2×C61#181911yescharacteristic
153C2×C61#212611yescharacteristic
154C2×C61#212611yescharacteristic
155D61—44no—
156D61—42no—
157C22×#41—611no—
158C2×#117—611no—
159C22×C42—611no—
160C2×#99—614no—
161C2×#99—1222no—
162#391—611no—
163#391#692311yescharacteristic, complemented
164#390—611no—
165#390—611no—
166#386—1222no—
167#381—1222no—
168C4×C22⋊C4—1222no—
169C61#1285711yescharacteristic, complemented, Sylow
170C2×#41—1224no—
171C2×#41—2442no—
172C2×#41—2442no—
173C22×Q8C2×#692311yescharacteristic
174C22×D4—612no—
175C22×D4—611no—
176C23×C4—611no—
177C23×C4—612no—
178C23×C4—1221no—
179#117—2442no—
180C2×C4⋊C4—611no—
181C2×C4⋊C4C2×#692311yescharacteristic
182C2×C22⋊C4—1221no—
183C2×C22⋊C4—1222no—
184C2×C22⋊C4—1222no—
185C2×C22⋊C4—1224no—
186C2×C42—611no—
187C2×C42—1221no—
188C2×C42—1221no—
189C2×C42—2442no—
190C2×C42C2×#692311yescharacteristic
191#99—1228no—
192#99—2444no—
193#95—22no—
194#95—1222no—
195#95—2444no—
196C24—612no—
197C24—611no—
198#41—24416no—
199C2×Q8—22no—
200C2×Q8—41no—
201C2×Q8—41no—
202C2×D4—614no—
203C2×D4—1224no—
204C2×D4—1224no—
205C2×D4—2441no—
206C2×D4—2441no—
207C2×D4—2442no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—611no—
211C22×C4—1222no—
212C22×C4—1224no—
213C22×C4—1222no—
214C22×C4—1224no—
215C22×C4—1222no—
216C22×C4—1221no—
217C22×C4—1221no—
218C22×C4—2442no—
219C22×C4—2442no—
220C22×C4—2442no—
221C22×C4—2442no—
222C22×C4—2444no—
223C22×C4C22⋊#692312yes—
224C22×C4C22×#692311yescharacteristic
225C4⋊C4—41no—
226C4⋊C4—2441no—
227C22⋊C4—2444no—
228C22⋊C4—2444no—
229C22⋊C4—2442no—
230C22⋊C4—2444no—
231C22⋊C4—2444no—
232C42—41no—
233C42—2441no—
234C42—2442no—
235C42—2442no—
236C23—614no—
237C23—612no—
238C23—1222no—
239C23—1221no—
240C23—1221no—
241C23—1222no—
242C23—2442no—
243C23—2442no—
244C23—2441no—
245C23—2441no—
246C23C2×C22⋊#692311yescharacteristic
247Q8—44no—
248D4—2444no—
249D4—2448no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—612no—
261C2×C4—1228no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—1222no—
265C2×C4—4884no—
266C2×C4—4884no—
267C2×C4—4884no—
268C2×C4—2448no—
269C2×C4—2448no—
270C2×C4—2442no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4#1451985612yes—
275C22—21no—
276C22—21no—
277C22—1222no—
278C22—1224no—
279C22—4882no—
280C22—2442no—
281C22—2444no—
282C22—2442no—
283C22—2442no—
284C22—2441no—
285C22—2442no—
286C22—2441no—
287C22#1684070511yescharacteristic
288C22D61⋊#9911yescharacteristic
289C22D61⋊#9911yescharacteristic
290C4—22no—
291C4—42no—
292C4—42no—
293C4—81no—
294C4—1222no—
295C4—9764no—
296C4—4881no—
297C4—2442no—
298C2—21no—
299C2—21no—
300C2—2444no—
301C2—2442no—
302C2#2146171511yescharacteristic
303C2#2146209111yescharacteristic
304C2#2146209311yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC22×C61C2×#99
prime radicalC22×#11758226C22
cosocleC22×D244C23
hypercenter#391#6923
hypocenterC61#12857
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. #21460914C2semidirect
3. #21460913C2semidirect
9. C2×#14519735C4semidirect
10. C2×C42×D61C4semidirect
11. #16839669C4semidirect
16. C61×#391C4semidirect
163. #391#6923semidirect
169. C61#12857semidirect

Maximal subgroups

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

subgroupindex
#214616502
#214609142
#214609132
#214483082
#1285761