Finite Group Databasebeta

← #29577985

Subgroups — #29577985

Order 15616.

522 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 103 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#21454860C211yesmaximal, characteristic
2#21450136C211yesmaximal, characteristic
3#21445897C212yesmaximal, complemented
4#21443726C212yesmaximal, complemented
5C61×#1465C211yesmaximal, characteristic
6C22×C4⋊Dic61C2211yescharacteristic
7#16839840—24no—
8#16839815—21no—
9#16839726—21no—
10#16839726C2212yes—
11#16839701—21no—
12#16839698—21no—
13#16839660—21no—
14#16839642C412yes—
15#16839634C412yes—
16#16839622—21no—
17#16839622C2211yescharacteristic
18#16839530—24no—
19C2×C4×D4×C61C2211yescharacteristic
20C61×#407C2212yes—
21C61×#324—21no—
22C61×#323—21no—
23C23×Dic61C2×C412yes—
24C2×#11758194—22no—
25C2×#11758194D414yes—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—22no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—22no—
31C2×#11758196—22no—
32C2×C22⋊Dic61—22no—
33C2×C22⋊Dic61C2×C412yes—
34C4⋊#92418—22no—
35C22⋊#92418—22no—
36C22⋊#92418—22no—
37C22⋊#92418—22no—
38C4×#92418—22no—
39#14519684—22no—
40#14519684—22no—
41#14519684—21no—
42C22×D4×C61C2×C411yescharacteristic
43C23×C4×C61D411yescharacteristic
44C23×C4×C61C2311yescharacteristic
45C2×M16×C61—22no—
46C4×D4×C61—22no—
47C4×D4×C61—22no—
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C22⋊C4×C61C2×C411yescharacteristic
50C2×C22⋊C4×C61D411yescharacteristic
51C2×C42×C61D411yescharacteristic
52C22⋊C8×C61—22no—
53C22⋊C8×C61—22no—
54C24×C61C22⋊C411yescharacteristic
55C24×C61C22×C411yescharacteristic
56C2×D4×C61—22no—
57C2×D4×C61—22no—
58C2×D4×C61—41no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—42no—
62C22×C4×C61—42no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C2×D412yes—
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61#4112yes—
70C22×Dic61—22no—
71C22×Dic61—22no—
72C22×Dic61—24no—
73C22×Dic61—82no—
74M16×C61—44no—
75C2×C8×C61—42no—
76C4⋊C4×C61—22no—
77C22⋊C4×C61—22no—
78C22⋊C4×C61—22no—
79C42×C61—21no—
80C42×C61—21no—
81C22⋊Dic61—42no—
82C22⋊Dic61—82no—
83C4⋊Dic61—42no—
84C4⋊Dic61—41no—
85C4⋊Dic61—42no—
86C4⋊Dic61—41no—
87#11758196—82no—
88#11758194—44no—
89#11758194—82no—
90C2×#92418—24no—
91C23×C61—21no—
92C23×C61—21no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—41no—
97C23×C61—41no—
98C23×C61—41no—
99C23×C61—41no—
100C23×C61C2×C22⋊C411yescharacteristic
101C23×C61C4×D412yes—
102D4×C61—44no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—24no—
106C2×C4×C61—22no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—41no—
110C2×C4×C61—42no—
111C2×C4×C61—42no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—81no—
115C2×C4×C61#10112yes—
116C2×C4×C61#12011yescharacteristic
117C2×C4×C61#12112yes—
118C2×C4×C61#12311yescharacteristic
119C2×Dic61—42no—
120C2×Dic61—42no—
121C2×Dic61—42no—
122C2×Dic61—42no—
123C2×Dic61—42no—
124C2×Dic61—42no—
125C2×Dic61—84no—
126C8×C61—82no—
127#92418—44no—
128#9510—611nomaximal, Sylow
129C22×C61—21no—
130C22×C61—21no—
131C22×C61—22no—
132C22×C61—22no—
133C22×C61—22no—
134C22×C61—42no—
135C22×C61—42no—
136C22×C61—42no—
137C22×C61—41no—
138C22×C61—41no—
139C22×C61—41no—
140C22×C61—81no—
141C22×C61#38611yescharacteristic
142C22×C61C2×#10111yescharacteristic
143C22×C61#41311yescharacteristic
144C4×C61—22no—
145C4×C61—21no—
146C4×C61—22no—
147C4×C61—41no—
148C4×C61—41no—
149C4×C61#45812yes—
150Dic61—82no—
151Dic61—82no—
152#2975—611no—
153#2487—611no—
154#1821—612no—
155#1465D6111yescharacteristic
156#1305—612no—
157C2×C61—21no—
158C2×C61—21no—
159C2×C61—42no—
160C2×C61—81no—
161C2×C61#189011yescharacteristic
162C2×C61#190111yescharacteristic
163C2×C61#191411yescharacteristic
164C2×C4×D4C2×D6111yescharacteristic
165C22×C4⋊C4—611no—
166#436—1224no—
167#431—1221no—
168#407—612no—
169#407—1221no—
170#407C2×D6112yes—
171#400—1221no—
172#399—1221no—
173#389—1221no—
174#386—612no—
175#385—612no—
176#380—611no—
177#380—1221no—
178#343—1224no—
179#324—21no—
180#323—21no—
181C61#951011yescharacteristic, complemented, Sylow
182C22×D4C4×D6111yescharacteristic
183C23×C4—612no—
184C23×C4D24411yescharacteristic
185C23×C4C22×D6111yescharacteristic
186C2×M16—22no—
187C2×M16—614no—
188C2×M16—1222no—
189C4×D4—22no—
190C4×D4—22no—
191C2×C4⋊C4—1222no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1222no—
195C2×C4⋊C4—1222no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4C22⋊D6111yescharacteristic
198C2×C22⋊C4—612no—
199C2×C22⋊C4—1222no—
200C2×C22⋊C4C4×D6111yescharacteristic
201C2×C22⋊C4C22⋊D6111yescharacteristic
202C2×C42D24411yescharacteristic
203C4⋊C8—1222no—
204C22⋊C8—22no—
205C22⋊C8—22no—
206C22⋊C8—1222no—
207C22⋊C8—1222no—
208C22⋊C8—1222no—
209C4×C8—1222no—
210#95—1222no—
211#95—1222no—
212#95—1221no—
213C24#1175819811yescharacteristic
214C24C2×C4×D6111yescharacteristic
215C2×D4—22no—
216C2×D4—22no—
217C2×D4—41no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—1224no—
223C22×C4—1222no—
224C22×C4—1222no—
225C22×C4—4882no—
226C22×C4#1175819811yescharacteristic
227C22×C4#1175819811yescharacteristic
228C22×C4#1175819811yescharacteristic
229C22×C4C2×D24411yescharacteristic
230C22×C4D4×D6112yes—
231C22×C4#1175822412yes—
232C22×C4C2×C22⋊D6111yescharacteristic
233M16—44no—
234M16—4882no—
235M16—2444no—
236C2×C8—42no—
237C2×C8—1224no—
238C4⋊C4—22no—
239C4⋊C4—4882no—
240C4⋊C4—2442no—
241C4⋊C4—2441no—
242C4⋊C4—2442no—
243C4⋊C4—2441no—
244C22⋊C4—22no—
245C22⋊C4—22no—
246C22⋊C4—4882no—
247C22⋊C4—2442no—
248C42—21no—
249C42—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23—41no—
259C23C2×#1175819811yescharacteristic
260C23#1451973712yes—
261D4—44no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—24no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—81no—
274C2×C4—4884no—
275C2×C4—2442no—
276C2×C4—2442no—
277C2×C4—2442no—
278C2×C4—2442no—
279C2×C4—2442no—
280C2×C4—2442no—
281C2×C4#1451969512yes—
282C2×C4#1451974711yescharacteristic
283C2×C4#1451974912yes—
284C2×C4#1451976111yescharacteristic
285C8—82no—
286C8—2444no—
287C22—21no—
288C22—21no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—81no—
299C22#1683963911yescharacteristic
300C22C2×#1451969511yescharacteristic
301C22#1683974411yescharacteristic
302C4—22no—
303C4—21no—
304C4—22no—
305C4—41no—
306C4—41no—
307C4—4882no—
308C4—4882no—
309C4#1683995312yes—
310C2—21no—
311C2—21no—
312C2—42no—
313C2—81no—
314C2#2144623011yescharacteristic
315C2#2144628511yescharacteristic
316C2#2144636411yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1465C2
socleC22×C61#386
prime radicalC22×D4×C61C2×C4
cosocleC23×C4×C61C23
hypercenter#1465D61
hypocenterC61#9510
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #21445897C2semidirect
4. #21443726C2semidirect
181. C61#9510semidirect

Maximal subgroups

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

subgroupindex
#214548602
#214501362
#214458972
#214437262
C61×#14652
#951061