Finite Group Databasebeta

← #29573462

Subgroups — #29573462

Order 15616.

404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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#21448317C211yesmaximal, characteristic
2#21444133C211yesmaximal, characteristic
3#21443651C212yesmaximal, complemented
4#21443647C212yesmaximal, complemented
5C61×#1458C211yesmaximal, characteristic
6#16839815C2212yes—
7#16839655—21no—
8#16839655—21no—
9#16839648—21no—
10#16839648—21no—
11C4×C4⋊Dic61C411yescharacteristic
12C4×C4⋊Dic61C411yescharacteristic
13C4×C22⋊Dic61C411yescharacteristic
14C4×C22⋊Dic61C411yescharacteristic
15#16839608C2211yescharacteristic
16C42×Dic61C2211yescharacteristic
17#16839488—21no—
18#16839486—21no—
19C2×#117×C61C2211yescharacteristic
20C61×#431C2212yes—
21C61×#324—21no—
22C61×#323—21no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—21no—
25C2×C22⋊Dic61—21no—
26C2×C22⋊Dic61—21no—
27C2×C4×Dic61—21no—
28C2×C4×Dic61—21no—
29C2×C4×Dic61C2×C411yescharacteristic
30C2×C4×Dic61C2×C411yescharacteristic
31C2×C4×Dic61C2×C411yescharacteristic
32C2×C4×Dic61C2×C411yescharacteristic
33C4⋊#92418—22no—
34C22⋊#92418—22no—
35C4×#92418—22no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42C23×C4×C61C2×C411yescharacteristic
43#117×C61—22no—
44#117×C61—22no—
45C2×C4⋊C4×C61D411yescharacteristic
46C2×C4⋊C4×C61D411yescharacteristic
47C2×C22⋊C4×C61D411yescharacteristic
48C2×C22⋊C4×C61D411yescharacteristic
49C2×C42×C61C2×C411yescharacteristic
50C2×C42×C61C2311yescharacteristic
51C4⋊C8×C61—22no—
52C22⋊C8×C61—22no—
53C4×C8×C61—22no—
54C24×C61C22⋊C411yescharacteristic
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C2×C8×C61—42no—
70C4⋊C4×C61—22no—
71C4⋊C4×C61—22no—
72C22⋊C4×C61—22no—
73C22⋊C4×C61—22no—
74C42×C61—21no—
75C42×C61—21no—
76C42×C61#4112yes—
77C42×C61#4112yes—
78C22⋊Dic61—42no—
79C22⋊Dic61—42no—
80C4⋊Dic61—42no—
81C4⋊Dic61—42no—
82C4×Dic61—22no—
83C4×Dic61—22no—
84C4×Dic61—22no—
85C4×Dic61—22no—
86C4×Dic61—42no—
87C4×Dic61—42no—
88C2×#92418—42no—
89C23×C61—21no—
90C23×C61—21no—
91C23×C61—21no—
92C23×C61—41no—
93C23×C61—41no—
94C23×C61C2×C22⋊C411yescharacteristic
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—42no—
103C2×C4×C61—42no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61#11711yescharacteristic
107C2×C4×C61#11711yescharacteristic
108C2×C4×C61#12312yes—
109C2×C4×C61#12312yes—
110C2×C4×C61#13112yes—
111C2×C4×C61#13112yes—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C8×C61—82no—
125#92418—82no—
126#8732—611nomaximal, Sylow
127C22×C61—21no—
128C22×C61—21no—
129C22×C61—41no—
130C22×C61—41no—
131C22×C61—41no—
132C22×C61—81no—
133C22×C61—81no—
134C22×C61#38111yescharacteristic
135C22×C61#40811yescharacteristic
136C22×C61#40811yescharacteristic
137C4×C61—22no—
138C4×C61—22no—
139C4×C61—41no—
140C4×C61—41no—
141C4×C61—41no—
142C4×C61#43312yes—
143C4×C61#43312yes—
144Dic61—42no—
145Dic61—42no—
146Dic61—81no—
147Dic61—81no—
148#2298—611no—
149#1458—611no—
150#1458D6111yescharacteristic
151#1276—612no—
152#1274—612no—
153C2×C61—21no—
154C2×C61—21no—
155C2×C61—81no—
156C2×C61#181811yescharacteristic
157C2×C61#182711yescharacteristic
158C2×C61#182711yescharacteristic
159C2×#117C2×D6111yescharacteristic
160#431—612no—
161#431C2×D6112yes—
162#388—1221no—
163#388—1221no—
164#387—1221no—
165#387—1221no—
166C4×C4⋊C4—611no—
167C4×C4⋊C4—611no—
168C4×C22⋊C4—611no—
169C4×C22⋊C4—611no—
170#376—611no—
171C43—611no—
172#324—21no—
173#324—1221no—
174#323—21no—
175#323—1221no—
176C61#873211yescharacteristic, complemented, Sylow
177C23×C4C4×D6111yescharacteristic
178#117—22no—
179#117—22no—
180C2×C4⋊C4—1221no—
181C2×C4⋊C4—1221no—
182C2×C4⋊C4D24411yescharacteristic
183C2×C4⋊C4C22⋊D6111yescharacteristic
184C2×C22⋊C4—1221no—
185C2×C22⋊C4—1221no—
186C2×C22⋊C4D24411yescharacteristic
187C2×C22⋊C4C22⋊D6111yescharacteristic
188C2×C42—611no—
189C2×C42—611no—
190C2×C42—611no—
191C2×C42—611no—
192C2×C42—1221no—
193C2×C42—1221no—
194C2×C42C4×D6111yescharacteristic
195C2×C42C22×D6111yescharacteristic
196C4⋊C8—22no—
197C4⋊C8—1222no—
198C22⋊C8—22no—
199C22⋊C8—1222no—
200C4×C8—22no—
201C4×C8—1222no—
202#95—1221no—
203#95—1221no—
204#95—1221no—
205#95—1221no—
206#95—1221no—
207#95—1221no—
208C24#1175819811yescharacteristic
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—1221no—
214C22×C4—1221no—
215C22×C4—1221no—
216C22×C4—1221no—
217C22×C4#1175819811yescharacteristic
218C22×C4#1175819811yescharacteristic
219C22×C4#1175819811yescharacteristic
220C22×C4C2×C4×D6111yescharacteristic
221C22×C4C2×D24411yescharacteristic
222C22×C4C2×C22⋊D6111yescharacteristic
223C2×C8—42no—
224C2×C8—2442no—
225C4⋊C4—22no—
226C4⋊C4—22no—
227C4⋊C4—2442no—
228C4⋊C4—2442no—
229C22⋊C4—22no—
230C22⋊C4—22no—
231C22⋊C4—2442no—
232C22⋊C4—2442no—
233C42—21no—
234C42—21no—
235C42—1222no—
236C42—1222no—
237C42—1222no—
238C42—1222no—
239C42—2442no—
240C42—2442no—
241C42#1175822412yes—
242C42#1175822412yes—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—41no—
247C23—41no—
248C23C2×#1175819811yescharacteristic
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—1222no—
261C2×C4—1222no—
262C2×C4—2441no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4—2441no—
272C2×C4#1451973311yescharacteristic
273C2×C4#1451973311yescharacteristic
274C2×C4#1451975812yes—
275C2×C4#1451976112yes—
276C2×C4#1451978312yes—
277C2×C4#1451978512yes—
278C8—82no—
279C8—4882no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—81no—
286C22—81no—
287C22#1683962311yescharacteristic
288C22#1683972811yescharacteristic
289C22#1683973011yescharacteristic
290C4—22no—
291C4—22no—
292C4—41no—
293C4—41no—
294C4—41no—
295C4—4881no—
296C4—4881no—
297C4—2442no—
298C4—2442no—
299C4#1683982012yes—
300C4#1683982012yes—
301C2—21no—
302C2—21no—
303C2—81no—
304C2#2144588811yescharacteristic
305C2#2144592011yescharacteristic
306C2#2144592411yescharacteristic
subgroupG/H
centerC2×C4#14519733
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1458C2
socleC22×C61#381
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1458D61
hypocenterC61#8732
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #21443651C2semidirect
4. #21443647C2semidirect
176. C61#8732semidirect

Maximal subgroups

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

subgroupindex
#214483172
#214441332
#214436512
#214436472
C61×#14582
#873261